13th International Conference on Compressors and Their Systems: Conference Proceedings (Springer Proceedings in Energy) [1st ed. 2024] 3031426622, 9783031426629
132 22 46MB
English Pages 910 [877] Year 2024
Contents
Screw Compressors
Comparison of PV-Diagrams Between CFD and Experimental Results for Twin-Screw Compressors
1 Introduction
2 CFD Simulation
3 Experimental Validation
4 Results and Discussion
4.1 Simulation and Experimental Results at 30Hz
4.2 Examination of Pressure Near the Economizer Port
4.3 Simulation and Experimental Results at 60Hz and 95Hz
5 Conclusion
References
Model Validation of Twin Screw Compressor with Optimized Injection Port for Unit Efficiency
1 Introduction
1.1 Motivation
1.2 Vapor Compression Cycle with Economizer Port
2 Economizer Port Optimization
3 Modified Screw Compressor Testing
3.1 Experimental Setup
4 Results and Discussion
4.1 Compressor Results
4.2 Unit Results
5 Conclusions
References
Simplified Engineering Calculation Methods of the Temperature Distribution Along the Screw Compressor Rotors
1 Introduction
2 Calculation of Temperature Fields of Rotors and Their Thermal Deformations
2.1 Impact of the Compressor Design Parameters, As Well As the Operating Mode on the Thermal State of the Rotors
2.2 Calculation Results
3 Conclusions
References
CFD Analysis of Leakage Flow in Radial Tip Gap of Roots Blower
1 Introduction
2 Computational Fluid Dynamics
2.1 Conservation Laws of Fluids
3 Computational Analysis of Roots Blower
3.1 Computational Domain of Simplified Roots Blower
3.2 Simulation Set-Up
4 Results and Discussion
4.1 Validation
4.2 Tip Design Concept Study
4.3 Rotor Tip Design Study
5 Conclusion and Future Scope
References
Thermodynamic Properties of Oil Droplets Impacting on Chamber Wall in Oil-Injected Screw Compressors
1 Introduction
2 Computational Model
2.1 Model Parameters and Boundary Settings
2.2 Governing Equations
2.3 Grid Independence Verification
3 Oil Film Heat Transfer with Droplet Impacting on the Wall
3.1 The Influence of Oil Film Thickness
3.2 The Influence of Oil Drop Temperature
3.3 The Influence of Oil Droplet Velocity
3.4 The Influence of Oil Droplet Diameter
4 Conclusions
References
Experimental Investigation of the Distribution of Two-Phase Flow in Oil-Injected Twin-Screw Compressors
1 Introduction
2 Experimental Setup
2.1 Operation Point and Compressor
2.2 Reference Measurements
3 Modeling Hydraulic Losses
3.1 Acceleration Power Loss
3.2 Fluid Friction Power Loss
3.3 Momentum Power Loss
3.4 Squeezed Oil
4 Conclusion
References
Mesh Generation for Twin-Screw Compressors by Spline-Based Parameterization Using Preconditioned Anderson Acceleration
1 Introduction
2 Workflow of Our Analysis-Suitable Parameterization Method for Rotary Twin-Screw Compressors
3 Elliptic Grid Generation Using Preconditioned Anderson Acceleration
3.1 Elliptic Grid Generation (EGG) and Its Discretization
3.2 Discretization in Sobolev Space
3.3 Anderson Acceleration with Dynamic Preconditioning Strategy
4 Analysis-Suitable Parameterizations for Planar Slices
5 Conclusion and Future Work
References
Orthogonal Mesh Generation of Screw Compressors for Capturing Tip Leakage Flows
1 Introduction
1.1 GridPro's Topology Paradigm
1.2 Dynamic Boundary Conforming (DBC) Technology
2 Conformal Interface Approach
3 Existing Approach—Transverse Plane Grid Generation
3.1 Rounding the Housing Cusp
4 3D Smoothing of the Transverse Grid
4.1 3D Smoothing Results
5 Rotor Helix Normal Grid Generation Method
5.1 Methodology
5.2 Suitability of the Mesh for Different Solvers
References
Two Way Coupling of CFD Conjugate Heat Transfer Simulation with Solid Thermal Expansion in a Twin Screw Compressor
1 Introduction
1.1 Compressor Conjugate Heat Transfer and Thermal Expansion
1.2 Proposed Simulation Approach with Required Capabilities/Tools
1.3 Governing Equations and Physics Models
2 Twin Screw Compressor Test Case
2.1 Fluid Model
2.2 Solid Heat Transfer Model
2.3 Solid Thermal Expansion Model
3 Results and Discussion
4 Conclusion and Future Works
References
Investigating Alternative Rotor Materials to Increase Displacement and Efficiency of Screw Compressor While Considering Cost and Manufacturability
1 Introduction
1.1 Exploring Lightweight Materials and Innovative Manufacturing Techniques for Screw Compressor Rotors
1.2 Metal Additive Manufacturing and Alternative Materials for Different Screw Compressor Applications
2 Numerical Simulation
2.1 Modelling Methodologies
2.2 Rotor Grid Generation left parenthesis upper S upper C upper O upper R upper G Superscript upper T upper M Baseline right parenthesis(SCORGTM)
2.3 Structural Analysis Boundary Conditions
2.4 SCORPATH Modelling
3 Result and Discussion
4 Conclusion
5 Further Study
References
Investigation and Optimization of a Twin-Screw Compressor with Internal Cooling Channels
1 Introduction
2 Twin Screw Compressor Model
2.1 Geometry Model
2.2 Heat Transfer Model
3 Simulation Setup
3.1 Geometry Setup and Operating Conditions
3.2 Simulation Methods and Meshing
4 Results and Discussion
4.1 Model Verification
4.2 Rotor Discharge Temperature Slices
4.3 Rotor Surface Temperature Plots
4.4 Performance Parameters
4.5 Solid and Hollow Rotor Comparison
5 Conclusion
References
Design of Hobbing Cutter for Variable-Pitch Screw Rotor
1 Introduction
2 Constant-Pitch Hobbing Algorithm
2.1 Coordinate Systems and Coordinate Transformation
2.2 Meshing Equation
2.3 Three-Degree-of-Freedom Hobbing Method
3 Variable-Pitch Hobbing Algorithm
4 Example of Variable-Pitch Hob Design
5 Conclusions
References
Influence of Bearing and Seal Design on Performance of an Oil-Injected Screw Compressor for Refrigeration Applications
1 Introduction
2 Definition of Test Cases
3 Bearings and Seals Selection and Design
3.1 Bearing Design Constraints
3.2 Bearings and Seals Loss Modelling
3.3 Bearing Selection Methodology
4 Performance Analysis of Bearing-Seal Configurations
4.1 Cylindrical Roller Bearing
4.2 Hydrodynamic Bearing
4.3 Dual Oil Seal
4.4 Bearing Configuration Comparison
5 Conclusions
References
Theoretical Analysis of Hydrodynamic Water-Lubricated Plain Bearings for High-Speed Applications
1 Introduction
2 Layout and Operational Bearing Forces
3 Materials for Water-Lubricated Journal Bearings
4 Flow Characteristics and Gap Tolerance
5 Minimum Lubricant Film Thickness
5.1 Hydrodynamic Lubrication
5.2 Allowable Minimum Lubricant Film Thickness hlim
5.3 Ratio of Length and Diameter and Relative Eccentricity
6 Conclusion
References
A Novel Screw Compressor with a Shunt Enhanced Decompression and Pulsation Trap (SEDAPT)
1 Introduction
2 Process Analysis of Two Parallel Compression Schemes
2.1 Arrangement of Screw Compression in Parallel: UC Only Scheme—SECAPT
2.2 Arrangement of Screw Compression in Parallel: OC Only Scheme—SEDAPT [2, 3]
2.3 A One-Stage SEDAPT Example and Design Rules
3 Design Optimization of SEDAPT Scheme by Computational Model Analysis
3.1 Computational Model Simulation—Code Description
3.2 Computational Model Simulation Example—Optimization Procedure
3.3 Comparison of the Pros and Cons of Several Compression Schemes with SEDAPT
4 Conclusions and Recommendations for Future Work
4.1 Conclusions
4.2 Recommendations for Future Work
References
Scroll Compressors
Preliminary Design and Performance Evaluation of Micro Scroll Compressor Used in Refrigeration Systems
1 Introduction
2 Preliminary Design of Micro Scroll Compressor
2.1 Basic Parameters
2.2 Structure Design
3 Performance Analysis Model
3.1 Physical Model
3.2 Meshing
3.3 Calculation Method and Boundary Conditions
4 Results and Discussion
4.1 Analysis of Internal Flow of Compressor
4.2 Performance Analysis Under Variable Working Conditions
5 Conclusions
References
A Study to Improve Efficiency of a Variable Speed Scroll Compressor
1 Introduction
2 Optimization
2.1 Economizer
2.2 Speed Optimization
2.3 Discharge Port Delay
2.4 Involute Start Angle
3 Conclusion
References
Performance Anlaysis of Water-Cooled VRF System in Cooling Mode by Changing Scroll Compressor Geometry
1 First Section
2 Measurement Device
3 Mathematical Model
3.1 Water-Cooled VRF System
3.2 Scroll Compressor
3.3 Other Components
4 Results and Discussion
4.1 Validation of the Simulation
4.2 Analysis of VRF System Performance by Changing Geometry of Scroll Compressor
5 Conclusions
References
Experimental Testing of a Scroll Compressor with Two-Phase Refrigerant Flows
1 Introduction
2 Test Bench Description
3 Results Post-processing
3.1 Assumptions
3.2 Inlet Vapor Quality Calculation
3.3 Volumetric Efficiency
3.4 Isentropic Efficiency
4 Results and Discussions
4.1 Volumetric Efficiency
4.2 Isentropic Efficiency
5 Conclusion
References
Experimental Comparison into the Effect of Oversized Heat Exchangers on Seasonal Performance Improvements of a Two-Stage and a Variable Speed Compressor in an R410A Chiller
1 Introduction
2 Experimental Facility Description
3 Standard Used for Testing
4 Results and Discussion
4.1 Charge Optimization with Oversized Condenser
4.2 Seasonal Performance of a Variable Speed Compressor with Different Condensers
4.3 Seasonal Performance of a Two-Stage Compressor with Different Condensers
4.4 Effect of Charge Optimization and Condenser Sizing on the Two-Stage Compressor Seasonal Performance
4.5 Comparison of IPLV.SI for Different Compressor Modulation Strategies and Condenser Sizes
5 Conclusions
References
Experimental Investigation and Advanced Exergy Analysis of Different Factors That Can Affect Seasonal Performance in an R410A Chiller
1 Introduction
2 Experimental Facility Description
3 Standard Used for Testing
4 Advanced Exergy Analysis (AEA)
5 Results and Discussion
5.1 Effect of Improved Compressor Motor (Higher Isentropic Efficiency)
5.2 Effect of Upgrading the Condenser (Oversized Condenser)
5.3 Comparison of Two Compressor Modulation Strategies
6 Conclusions
References
CFD Simulation Motion Analysis of an Orbiting Scroll Bearing Hub
1 Introduction
2 Simulation Setup
2.1 Geometry Preparation
2.2 CFD Setup
3 Results
4 Conclusion
References
CFD Simulation of an Orbiting Scroll Bearing Hub
1 Introduction
2 Simulation Setup
2.1 Geometry Preparation
2.2 CFD Setup
3 Results
4 Conclusion
References
Hybrid Wrap-Based Shape Optimization of a Scroll Compressor with Deep Reinforcement Learning
1 Introduction
2 Methodology
2.1 Geometry of the Scroll Compressor
2.2 Analytic Model for Compression Process
2.3 Optimization with DRL
3 Results
3.1 Analytic Model Result
3.2 Shape Optimization Results
4 Conclusions
References
Integrated Optimization of High-Speed Motor Drive and Compressor System: A Case Study
1 Introduction
2 Modelling of the Integrated Optimization Framework
2.1 Semi-Empirical Compressor Model
2.2 Motor Model
2.3 Objective Function
3 Results and Discussion
3.1 Compressor Model
3.2 Motor Model
4 Case Study
5 Conclusions
References
Experimental Research of Pressure-Volume Diagrams in a Scroll Compressor at High Speed
1 Introduction
2 Theory of Experiment
2.1 Thermodynamic Model of Compression Chambers
2.2 Efficiency of Compression Chambers
3 Test Method and Equipment
3.1 Testing Compressor
3.2 Pressure Measurement
3.3 Volume Measurement
4 Results and Discussion
4.1 Experiment Condition
4.2 Data Analysis
5 Conclusions
References
Numerical and Experimental Study of 120 °C Heat Pump Using a Scroll Compressor
1 Introduction
2 System Simulation
3 Pilot Study
4 Performance Parameters
5 Hot Air Generation
6 Results and Discussion
6.1 Emission Study
7 Conclusion
References
Application of 1D Numerical Transient Compressor Model to Optimize Performance of Vapor Injection Heat Pump System
1 Introduction
2 Compressor Model
2.1 Geometry Generation
2.2 1D Dynamic Flow Model
2.3 Vapor Injection Port Geometry Optimization
3 Heat Pump System Model
3.1 System Layout: Heat Pump with Vapor Injection
3.2 1D Dynamic Flow Model
4 Compressor and Heat Pump System Optimization Loop
4.1 System Preliminary Performance Optimization
4.2 Compressor Design Optimization
4.3 System-Level Compressor Model
4.4 Heat Pump System Results
5 Conclusions
References
Reciprocating Compressors
Feasibility Study on Two Novel Lubricants for a Carbon Dioxide Reciprocating Compressor
1 Introduction
2 Experimental Setup
2.1 System Descriptions
2.2 Instrumentation
3 Data Collection and Processing
4 Results and Discussion
4.1 Consistency of Operating Conditions
4.2 System Performance Comparisons
5 Conclusions
References
Numerical Analysis of a Vapor-Injected Reciprocating Compressor for a Multi-evaporator Domestic Refrigerator/Freezer Application
1 Introduction
2 Vapor Injection in Reciprocating Compressor
3 Modeling Approach
4 Results and Discussion
4.1 Baseline Compressor
4.2 Vapor Injection Compressor Simulation Results
4.3 Parametric Study of Injection Opening Time
5 Conclusion and Future Work
Appendix
References
Numerical Analysis of the Dynamic Two-Phase Flow Behavior in the Ionic Compressor with a Novel H-shaped Piston
1 Introduction
2 Methodology
2.1 Physical Model
2.2 Numerical Model and Solution Method
3 Results and Discussions
4 Conclusion
References
Development of Reduced Order Model for Performance Prediction of Reciprocating Compressor
1 Introduction
2 Training Data
2.1 3D FSI Data
2.2 Input and Output Parameter
2.3 Reliability Verification of Training Data
3 Data Extending
3.1 ANN Method
3.2 Data Extending Method Using ANN Method
4 Reduced Order Model
4.1 Concept of Reduced Order Model
4.2 Development of Reduced Order Model
4.3 Response Surface Type
5 Results and Discussion
5.1 Results of ANN
5.2 Reliability Verification of Extended Data
5.3 Accuracy of Reduced Order Model
6 Conclusions
References
Numerical Investigation of the Effect of Cylinder Head Torque on Gas Leakage in Hermetic Compressors
1 Introduction
1.1 Objective
1.2 Literature Review
1.3 Hypothesis
1.4 Paper Organization
2 Methodology
2.1 Numerical Studies
2.2 Experimental Studies
3 Results and Discussion
4 Conclusions
References
Parametric Analysis in Crankshaft Design for the Reciprocating Compressors
1 Introduction
2 Material and Methods
2.1 Force and Bearing Model
2.2 Experimental Setup
2.3 Genetic Algorithm for Design Optimization
3 Results
3.1 Mechanical Loss Validations and Forces
3.2 Genetic Algorithm Optimized Design and Sensitivity Analysis
4 Discussion
5 Conclusion
References
Influence of 3D Printed Elastic Structures on the Pressure Pulsations in the Reciprocating Compressor Manifold
1 Introduction
2 3D Printed Elastic Structures
2.1 3D Printing Process Details
2.2 Determination of the Spring Stiffness Coefficient
3 Tests on a Compressor Station
3.1 Test Results
3.2 Determining the Fundamental Natural Frequency of a 3D Printed Spring
4 Conclusions
References
Experimental and Numerical Investigation of the Discharge Valve Limiter Geometric Features Change on Compressor Thermal Efficiency
1 Introduction
2 Experimental Setup and Procedure
3 Numerical Model
4 Experimental Result
5 Numerical Result
6 Conclusion
References
New Concept for Electrically Driven Air Compressors for Commercial Vehicles—General Layout and Indicator Measurements
1 Introduction
2 Compressor Layout
3 Experimental Methodology for Indicator Measurements
3.1 Instrumentation
3.2 Crank Angle Error Analysis
3.3 Indicated Work and Loss Analysis
4 Results and Discussion
4.1 Indicator Diagrams
4.2 Suction and Discharge Pressure Losses
4.3 Indicated Isentropic Efficiency
5 Conclusions
References
Novel Machines
Demonstration of Computationally Efficient Vapor Injection Optimization Method for Spool Compressor
1 Introduction
2 Mechanistic Chamber Model
2.1 Model Validation
3 Model Updates to Include Vapor Injection in Mechanistic Chamber Model
4 Optimization Model
5 Results and Discussion
6 Conclusion
References
Theory and Test of Expansion Power Recovery of Rotary Cylinder Compressor
1 Introduction
2 Test Method and Principle
2.1 Test Principle
2.2 Test Conditions
2.3 Theoretical Calculation of Expansion Angle
3 PV Test Analysis of Expansion Process
4 Compressor Optimization Design and Experimental Results
5 Conclusion
References
An Investigation of Internally Geared Screw Compressor Performance Using a Chamber Modelling Approach
1 Introduction
2 Thermodynamic of the Compression-Expansion Process
3 Thermodynamic Analysis of Internally Geared Screw Machine
4 Conclusion
References
Development of Numerical Grid and CFD Model for Analysis of Oil-Injected IGSM
1 Introduction
2 Grid Generation for Internally Geared Screw Rotors
2.1 Rotor Grid Generation Procedure
2.2 Profile Adaptability
2.3 Lead Variation
3 CFD Model of Oil Injected IGSC
4 Results and Discussion
4.1 Pressure Distribution
4.2 Rotor Torque Variation
4.3 Compressor Performance Analysis
4.4 Port Flow Dynamics
5 Conclusions
References
Experimental Study of Conical Rotary Compressor for High Pressure Ratio Applications
1 Introduction
2 Rotor Design
2.1 Rotor Geometry
2.2 Vi Calculation
2.3 Sealing Line Length
3 Experimental Results
3.1 Test Rig
3.2 Performance Comparison of CRC with Different Vi
3.3 Efficiency Comparison at Same Pressure Ratio
3.4 Efficiency Contour
4 Conclusions
References
Other Compressor Types
Numerical Simulation and Experimental Research of Multi-stage Roots Vacuum Pump
1 Introduction
2 Geometric Structure
3 Mesh Generation and Simulation Setup
4 Case Studies
5 Results
6 Conclusions
References
Numerical Analysis of Real Fluid Behavior Effects on a Sliding-Vane Compressor Comprehensive Model
1 Introduction
2 Comprehensive Model
2.1 Input Modules
2.2 Main Model
2.3 Fluid Models
3 Case Studies
3.1 Machine Geometry
3.2 Numerical Campaign
3.3 Experimental Validation
4 Results and Discussion
4.1 Numerical Results
5 Conclusions
References
Performance Improvements of Scroll and Sliding Vane Expanders Via a Double Intake Port Technology for ORC-Based Power Units
1 Introduction
2 Materials and Methods
3 Results
4 Conclusion
References
Measured Reed Valve Dynamics of Diaphragm Pumps with Laser Doppler Vibrometer
1 Introduction
2 Methodology
2.1 Laser Doppler Vibrometer Approach
2.2 Measurement Concept and Experimental Setup
2.3 Operating Conditions and Procedure
3 Results
4 Conclusion
References
CFD Studies on Ejectors Configured with Twisted Circular Profile Lobed Nozzle
1 Introduction
2 Geometric Modelling
3 Numerical Studies
3.1 Numerical Method
3.2 Grid Independence Test
3.3 Validation of CFD
3.4 Velocity Magnitude Contour
3.5 Velocity Vector Contour
3.6 Velocity Plot and Static Pressure Plot
4 Conclusions
References
Development and Performance Evaluation of a Micro Air Blower
1 Introduction
2 Blower Design
3 Experimental Setup
4 Numerical Methodology
5 Results and Discussion
5.1 Experimental Results
5.2 Numerical Simulation Results
6 Conclusions
References
Active Magnetic Bearings, Variable-Speed Centrifugal Air Compressors Suitable to Reduce Carbon Footprint, is it Really the Case?
1 Introduction
2 Life Cycle Inventory
2.1 High Speed Direct Drive Maglev Air-Compressor
2.2 Studied Compressors
2.3 Material Use
2.4 Use Stage
2.5 GHG Emission Reduction Over 5-Year Cycle Operation
2.6 Recycling and End of Life After 20-Year Operation
3 Conclusion and Discussion
References
Noise and Vibration
In-Line Sphere Arrays as Pressure Pulsation and Pipeline Vibration Dampers in Reciprocating Compressor Manifold
1 Introduction
2 Design of the Nozzles
3 Test Stand
4 Results
5 Conclusions
References
Acoustic and Energy Efficiency Analysis of Alternative Geometries of Plastic Suction Muffler
1 Introduction
2 Methodology
2.1 Design Parameters
2.2 Numerical Analysis of the Muffler
3 Results
3.1 CFD Results
3.2 Transmission Loss Analysis Results
3.3 Calorimeter and Semi-anechoic Test Results
4 Conclusion
References
Multi-physical Modeling of Noise and Vibration Due to Refrigerant Discharge in Hermetic Compressors
1 Introduction
2 Multi-physical Modeling
2.1 Thermomechanical Model
2.2 Discharge Pulsations and Consequent Noise and Vibration
2.3 Interior Gas Flow and Resulting Aerodynamic Noise and Vibration
3 Results and Discussion
3.1 Thermomechanical Simulation
3.2 Noise and Vibration Due to Discharge Pulsation
3.3 Aerodynamic Noise and Vibration
4 Conclusions and Future Work
References
Mitigation of Fluid-Induced Noise Generated by Discharge Flow in a Hermetic Rolling Piston Compressor
1 Introduction
2 Methodology
2.1 Overview
2.2 Simulation Model Description and Verification
3 Results Analysis
3.1 Valve Design Parameters
3.2 Muffler Design Parameters
4 Conclusion
5 Future Works
References
Prediction of Pressure Pulsation Damping Efficiency with the Use of Shaped Nozzles Based on Their Geometrical Parameters
1 Introduction
2 Sensitive Models
3 Carried Out Research
4 Conclusions
References
Hydrogen Compression
Effects of Oil Compressibility on the Thermal Performances of Diaphragm Compressors Used in the Hydrogen Refuelling Station with a Mathematical Method
1 Introduction
2 Methodology
2.1 The Working Process Analysis of a Diaphragm Compressor
2.2 Mathematical Model
3 Experimental Validation
4 Results and Discussion
4.1 Effects on the Diaphragm Deformation and Flow Rate
4.2 Effects on the Power Consumption
4.3 Effect on the Suction Pressure Range
5 Conclusion
References
Study of Effects of Hydraulic Parameters on the Motion of the Free Piston in Ionic Liquid Compressors in Hydrogen Refuelling Stations
1 Introduction
2 Basic Structure and Physical Model of the Ionic Liquid Compressor
3 Mathematical Modelling
4 Results and Discussions
4.1 The Effect of the Buffer Clearance on the Piston Dynamic Characteristics
4.2 The Effect of the Oil Charging Flow Rate on the Piston Dynamic Characteristics
4.3 The Effect of the Oil Overflow Pressure on the Piston Dynamic Characteristics
5 Conclusions
References
Analysis and Enhancement of Heat Transfer of the Gas Head Cover of Hydrogen Diaphragm Compressors
1 Introduction
2 Analysis of the Heat Transfer Related to the Gas Head Cover
2.1 Heat Transfer from Compressed Gas to the Surface of the Gas Cavity
2.2 Heat Transfer from the Outer Surface of the Gas Head Cover to the Environment
2.3 Heat Transfer Between the Gas and the Suction and Discharge Holes
3 Finite Element Analysis of the Temperature Field
3.1 Geometric Model of the Gas Head Cover
3.2 Mesh Generation
3.3 Thermal Loads
4 Experimental Validation
5 Results and Discussion
5.1 Simulation Results and Comparison with Experimental Values
5.2 Effect of Different Structures for Enhancing Heat Transfer
5.3 Effect of Different Materials for Enhancing Heat Transfer
6 Conclusions
References
Hydrogen Compressors: A Few Technical Challenges
1 Introduction: Hydrogen, a Way to «Decarbonization»
2 Hydrogen: A Compression Challenge
3 Special Cylinder Arrangement with Dry Seals for No Gas Contamination
4 Efficient Containment of Gas Leaks to the Compressor Frame and Atmosphere
5 Design and Manufacturing Critical Due to High Pressure Hydrogen Effects
6 Conclusions
References
Working Fluid and System
Analysis of R454B as a Low-GWP Refrigerant Alternative for R410A in a Vapor-Injected Rotary Compressor
1 Introduction
2 Experimental Setup
3 Results and Discussion
3.1 Discharge Temperature
3.2 Compressor Power
3.3 Isentropic Efficiency
3.4 Volumetric Efficiency
3.5 Heating and Cooling Capacities
3.6 cop
4 Conclusion
References
Compressor Performance for Varying Compositions of High-Glide Mixtures R1233zd(E)/R1234yf and R1336mzz(Z)/R1234yf
1 Introduction
2 Experimental Test Setup
3 Test Matrix and Data Quality
3.1 Test Matrix
3.2 Data Quality
3.3 Performance Measures
3.4 Measurement Uncertainty
4 Results
4.1 Performance Measures
4.2 Empirical Description
5 Discussion
6 Conclusions
References
Use of CFD and Geometry Optimization to Improve the Secondary Oil Separation of an Oil Flooded Rotary Vane Compressor
1 Introduction
2 Measurement Setup
2.1 Operating Point Simulated
3 Case Setup
3.1 CFX Steady State Setup
3.2 Rotating or Unsteady Simulation Setup
4 Results and Discussions
4.1 Baseline Model
4.2 Optimization
5 Conclusions
References
An Appraisal of the 1950 Festival Hall Heat Pump
1 Introduction
2 Purpose and Scope of the Proposal
3 Design Details
4 Equipment Details
5 Installation Details
6 Operating Details
7 Performance Details
8 Lessons to Learn for Modern Installations
9 Conclusions
References
Development of a Digital Twin of an Oil-Flooded Screw Compressor Using Measurement Data and Numerical Simulations
1 Introduction
2 Description of the Prototype
3 One-Dimensional Mathematical Model of the Compressor Circuit
4 Neural Network Modelling
4.1 Neural Network Topology Selection
4.2 Dryer Data Model
5 Comparison of Individual Approaches
6 Conclusion
References
Sizing of Scroll and Rolling Piston Compressor for Low-Pressure Refrigerants in Residential Air Conditioning and Heat Pump Systems
1 Introduction
2 Detailed Compressor Modeling
3 Results and Discussions
3.1 Scroll Compressor Sizing
3.2 Rolling Piston Compressor Sizing
3.3 Optimization Case Study
4 Conclusions
References
Numerical Simulation of Twin-Screw Expander and Its Effect on the Performance of ORC System
1 Introduction
2 Methodology
2.1 Numerical Simulation of the Twin-Screw Expander Working Process
2.2 Numerical Simulation of ORC System
3 Results and Discussion
4 Conclusions
References
Development of a Residential Scale, Economized, Compressor Load Stand to Measure Compressor Performance Using Low GWP, Flammable Refrigerants
1 Introduction
2 Load Stand
2.1 Load Stand Design
2.2 Instrumentation
3 Results and Discussion
3.1 Load Stand Validation
3.2 Preliminary Test Results
4 Conclusions and Future Work
References
Compressor Lubricants
Study of Lubricant Compatibility with a Low-GWP Refrigerant as an Alternative to R410A in a Compressor Test Loop
1 Introduction
2 Technical Review of Refrigerant-Lubricant Oil Compatibility
3 Test Loop for Refrigerant-Lubricant Oil Compatibility
3.1 Test Loop Design and Installation
3.2 Off-Design Analysis of the Test Loop for Developing Operation Manual
3.3 Oil Sampling Methods
4 Conclusion
References
Solubility and Viscosity of Variably Miscible Mixtures of Refrigerant and Lubricant
1 Introduction
2 Background
3 Data and Discussion
4 Conclusion
References
Compressor Designs, Lubricant Options and Refrigerant Selections: Putting the Puzzle Together
1 Introduction
2 Refrigerants
3 Lubricants
4 Refrigerant and Lubricant Interaction
5 Bearings
6 Compressor Testing
7 Conclusion
7.1 High Solubility
7.2 Decreased Refrigerant Stability
7.3 Miscibility
References
Characteristics and Lubricity of Refrigeration Oil for R290
1 Introduction
2 Experimental
2.1 Test Oil
2.2 Solubility and Viscosity of Oil/R290 Mixtures
2.3 Phase Separation Temperature
2.4 Stability with R290
2.5 Evaluation of Lubricity
3 Results of Test and Discussion
3.1 Mixture Properties of Oil and R290
3.2 Lubricity and Lubricating Films
4 Conclusion
References
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Springer Proceedings in Energy
Matthew Read Sham Rane Ivona Ivkovic-Kihic Ahmed Kovacevic Editors
13th International Conference on Compressors and Their Systems Conference Proceedings
Springer Proceedings in Energy Series Editors Muhammad H. Rashid, Department of Electrical and Computer Engineering, Florida Polytechnic University, Lakeland, FL, USA Mohan Lal Kolhe, Faculty of Engineering and Science, University of Agder, Kristiansand, Norway
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Matthew Read · Sham Rane · Ivona Ivkovic-Kihic · Ahmed Kovacevic Editors
13th International Conference on Compressors and Their Systems Conference Proceedings
Editors Matthew Read Department of Engineering, School of Science and Technology City, University of London London, UK
Sham Rane Department of Engineering, School of Science and Technology City, University of London London, UK
Ivona Ivkovic-Kihic Department of Engineering, School of Science and Technology City, University of London London, UK
Ahmed Kovacevic Department of Engineering, School of Science and Technology City, University of London London, UK
ISSN 2352-2534 ISSN 2352-2542 (electronic) Springer Proceedings in Energy ISBN 978-3-031-42662-9 ISBN 978-3-031-42663-6 (eBook) https://doi.org/10.1007/978-3-031-42663-6 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Paper in this product is recyclable.
Contents
Screw Compressors Comparison of PV-Diagrams Between CFD and Experimental Results for Twin-Screw Compressors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jin Zhu and Vishnu Sishtla
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Model Validation of Twin Screw Compressor with Optimized Injection Port for Unit Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tasha Williams and Matthew Cambio
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Simplified Engineering Calculation Methods of the Temperature Distribution Along the Screw Compressor Rotors . . . . . . . . . . . . . . . . . . . . Timur Mustafin and Ruslan Yakupov
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CFD Analysis of Leakage Flow in Radial Tip Gap of Roots Blower . . . . . Neeraj Bikramaditya, Sham Rane, Ahmed Kovacevic, and Brijeshkumar Patel
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Thermodynamic Properties of Oil Droplets Impacting on Chamber Wall in Oil-Injected Screw Compressors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Di Yan, Bo Peng, and Guo Xiao
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Experimental Investigation of the Distribution of Two-Phase Flow in Oil-Injected Twin-Screw Compressors . . . . . . . . . . . . . . . . . . . . . . . . . . . . Matthias Heselmann, Ulrich Dämgen, and Andreas Brümmer
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Mesh Generation for Twin-Screw Compressors by Spline-Based Parameterization Using Preconditioned Anderson Acceleration . . . . . . . . Ye Ji and Matthias Möller
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Orthogonal Mesh Generation of Screw Compressors for Capturing Tip Leakage Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Samuel Ebenezer James, Karan H. Baliga, and Peter R. Eiseman
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Two Way Coupling of CFD Conjugate Heat Transfer Simulation with Solid Thermal Expansion in a Twin Screw Compressor . . . . . . . . . . . 101 Hui Ding, Haiyang Gao, and Xiaonong Meng Investigating Alternative Rotor Materials to Increase Displacement and Efficiency of Screw Compressor While Considering Cost and Manufacturability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 A. Kumar, K. Patil, A. Kulkarni, and S. Patil Investigation and Optimization of a Twin-Screw Compressor with Internal Cooling Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Abhignan Saravana, Haotian Liu, Nick Able, James Collins, Eckhard A. Groll, and Davide Ziviani Design of Hobbing Cutter for Variable-Pitch Screw Rotor . . . . . . . . . . . . . 139 Yuan Hao, Yao Tonglin, Liu Changfeng, and Shu Yue Influence of Bearing and Seal Design on Performance of an Oil-Injected Screw Compressor for Refrigeration Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 Thibaud Plantagenet, David Buckney, Lihini Seneviratne, and Matthew Read Theoretical Analysis of Hydrodynamic Water-Lubricated Plain Bearings for High-Speed Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 Sami Tuffaha, Thomas W. Moesch, Christiane Thomas, and Konrad Klotsche A Novel Screw Compressor with a Shunt Enhanced Decompression and Pulsation Trap (SEDAPT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 Paul Xiubao Huang, Sean Yonkers, and James Willie Scroll Compressors Preliminary Design and Performance Evaluation of Micro Scroll Compressor Used in Refrigeration Systems . . . . . . . . . . . . . . . . . . . . . . . . . . 193 Shuo Song, Yuanyang Zhao, Qichao Yang, Guangbin Liu, and Liansheng Li A Study to Improve Efficiency of a Variable Speed Scroll Compressor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 Mathew Pazhathara James, Alex Schmig, and Joe Ziolkowski Performance Anlaysis of Water-Cooled VRF System in Cooling Mode by Changing Scroll Compressor Geometry . . . . . . . . . . . . . . . . . . . . . 223 Dongwon Kim, Been Oh, Hosik Jeong, and Gyung-min Choi Experimental Testing of a Scroll Compressor with Two-Phase Refrigerant Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 Nicolas Leclercq, Benedikt G. Bederna, and Vincent Lemort
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Experimental Comparison into the Effect of Oversized Heat Exchangers on Seasonal Performance Improvements of a Two-Stage and a Variable Speed Compressor in an R410A Chiller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 Sugun Tej Inampudi and Stefan Elbel Experimental Investigation and Advanced Exergy Analysis of Different Factors That Can Affect Seasonal Performance in an R410A Chiller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 Sugun Tej Inampudi and Stefan Elbel CFD Simulation Motion Analysis of an Orbiting Scroll Bearing Hub . . . 275 Scott Branch CFD Simulation of an Orbiting Scroll Bearing Hub . . . . . . . . . . . . . . . . . . . 283 Scott Branch Hybrid Wrap-Based Shape Optimization of a Scroll Compressor with Deep Reinforcement Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 Janggon Yoo and Daegyoum Kim Integrated Optimization of High-Speed Motor Drive and Compressor System: A Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 Xin Ding, Carlos Castillo, Steven Pekarek, and Davide Ziviani Experimental Research of Pressure-Volume Diagrams in a Scroll Compressor at High Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 Xiaowen Li, Qiuhe Guo, Yusheng Hu, Huijun Wei, Yi Liao, Jia Yao, and Shuanglai Liu Numerical and Experimental Study of 120 °C Heat Pump Using a Scroll Compressor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 Sandeep Koundinya, J. Jothilingam, S. Rajendra Kumar Martin, and Satyanarayanan Seshadri Application of 1D Numerical Transient Compressor Model to Optimize Performance of Vapor Injection Heat Pump System . . . . . . . 339 Marek Lehocky, Nils-Henning Framke, Arne Heinrich, Gautham Ramchandran, and Rodrigo Aihara Reciprocating Compressors Feasibility Study on Two Novel Lubricants for a Carbon Dioxide Reciprocating Compressor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 Xin Ding, Justin Kontra, Frank-Olaf Mähling, Eckhard Groll, and Davide Ziviani
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Numerical Analysis of a Vapor-Injected Reciprocating Compressor for a Multi-evaporator Domestic Refrigerator/Freezer Application . . . . . 369 Changkuan Liang, Haotian Liu, Davide Ziviani, James E. Braun, and Eckhard A. Groll Numerical Analysis of the Dynamic Two-Phase Flow Behavior in the Ionic Compressor with a Novel H-shaped Piston . . . . . . . . . . . . . . . . 383 Zekun Liu, Xiang Kang, and Yun Li Development of Reduced Order Model for Performance Prediction of Reciprocating Compressor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395 Hosik Jeong, Been Oh, Dongwon Kim, Kwongi Lee, Hyungyul Kim, Jongsoo Kim, and Gyunmin Choi Numerical Investigation of the Effect of Cylinder Head Torque on Gas Leakage in Hermetic Compressors . . . . . . . . . . . . . . . . . . . . . . . . . . . 409 Emin Övünç Sengün ¸ Parametric Analysis in Crankshaft Design for the Reciprocating Compressors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421 Atacan Oral, Umar Ul Haque, Ozgur Yalcin, and Ismail Lazoglu Influence of 3D Printed Elastic Structures on the Pressure Pulsations in the Reciprocating Compressor Manifold . . . . . . . . . . . . . . . . 433 Damian Brewczy´nski, Kamil Chmielarczyk, Jarosław Bł˛adek, and Przemysław Młynarczyk Experimental and Numerical Investigation of the Discharge Valve Limiter Geometric Features Change on Compressor Thermal Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445 A. Ekemen, A. Pinarbasi, C. Sahin, and A. Yildirim New Concept for Electrically Driven Air Compressors for Commercial Vehicles—General Layout and Indicator Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457 Max Joswig, Konrad Klotsche, Thomas Mösch, Jörg Nickl, and Christiane Thomas Novel Machines Demonstration of Computationally Efficient Vapor Injection Optimization Method for Spool Compressor . . . . . . . . . . . . . . . . . . . . . . . . . 471 M. Mohsin Tanveer, Craig R. Bradshaw, Joe Orosz, and Greg Kemp Theory and Test of Expansion Power Recovery of Rotary Cylinder Compressor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481 Y. S. Hu, H. J. Wei, J. Xu, Z. C. Du, Z. Li, and L. P. Ren
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An Investigation of Internally Geared Screw Compressor Performance Using a Chamber Modelling Approach . . . . . . . . . . . . . . . . . . 491 Halil Lacevic, Ahmed Kovacevic, and Matthew Read Development of Numerical Grid and CFD Model for Analysis of Oil-Injected IGSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503 Sham Rane, Ahmed Kovaˇcevi´c, and Matthew Read Experimental Study of Conical Rotary Compressor for High Pressure Ratio Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515 Yang Lu, Nick Balodimos, Bryon Calder, James Adamson, Chris Bruce, David Noake, and Nicol Low Other Compressor Types Numerical Simulation and Experimental Research of Multi-stage Roots Vacuum Pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529 Kai Ma, Hongye Qiu, Dantong Li, Chongzhou Sun, Lantian Ji, Bingqi Wang, Weifeng Wu, and Zhilong He Numerical Analysis of Real Fluid Behavior Effects on a Sliding-Vane Compressor Comprehensive Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543 Stefano Gianoncelli, Andrea Genoni, Ida Costanzo, Stefano Murgia, Abdullah Bamoshmoosh, and Gianluca Valenti Performance Improvements of Scroll and Sliding Vane Expanders Via a Double Intake Port Technology for ORC-Based Power Units . . . . . 555 Fabio Fatigati and Roberto Cipollone Measured Reed Valve Dynamics of Diaphragm Pumps with Laser Doppler Vibrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567 L. Dür, A. Egger, M. Lang, R. Almbauer, F. Cloos, and F. Brugger CFD Studies on Ejectors Configured with Twisted Circular Profile Lobed Nozzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579 Kharsade Sachin Angad and Annamalai Mani Development and Performance Evaluation of a Micro Air Blower . . . . . . 591 Ahmed M. R. Elbaz, Nabil Mahmoud, Abdulnaser Sayma, Abdelrahman Abdeldayem, and Mohammed Ammar Active Magnetic Bearings, Variable-Speed Centrifugal Air Compressors Suitable to Reduce Carbon Footprint, is it Really the Case? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 609 Mihail Lopatin, Timo Pulkki, Igor Nagaev, Ramdane Lateb, and Joaquim Da Silva
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Noise and Vibration In-Line Sphere Arrays as Pressure Pulsation and Pipeline Vibration Dampers in Reciprocating Compressor Manifold . . . . . . . . . . . 627 ´ Przemysław Młynarczyk, Joanna Krajewska-Spiewak, Damian Brewczy´nski, Kamil Chmielarczyk, Jarosław Bł˛adek, and Paweł Lempa Acoustic and Energy Efficiency Analysis of Alternative Geometries of Plastic Suction Muffler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 637 Merve Baykal and Nuri Onur Çatak Multi-physical Modeling of Noise and Vibration Due to Refrigerant Discharge in Hermetic Compressors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 649 Dazhuang He, Yidan Cui, Davide Ziviani, and Yangfan Liu Mitigation of Fluid-Induced Noise Generated by Discharge Flow in a Hermetic Rolling Piston Compressor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 661 Yidan Cui, Dazhuang He, Davide Ziviani, and Yangfan Liu Prediction of Pressure Pulsation Damping Efficiency with the Use of Shaped Nozzles Based on Their Geometrical Parameters . . . . . . . . . . . 677 ´ Joanna Krajewska-Spiewak, Damian Brewczy´nski, and Przemysław Młynarczyk Hydrogen Compression Effects of Oil Compressibility on the Thermal Performances of Diaphragm Compressors Used in the Hydrogen Refuelling Station with a Mathematical Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 689 Yaling Zhao, Jiatong Zhang, and Xueyuan Peng Study of Effects of Hydraulic Parameters on the Motion of the Free Piston in Ionic Liquid Compressors in Hydrogen Refuelling Stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 703 Yi Jin, Jiacheng Jiang, and Xueyuan Peng Analysis and Enhancement of Heat Transfer of the Gas Head Cover of Hydrogen Diaphragm Compressors . . . . . . . . . . . . . . . . . . . . . . . . 715 Shengdong Ren, Xiaohan Jia, Jiatong Zhang, Jiacheng Jiang, and Xueyuan Peng Hydrogen Compressors: A Few Technical Challenges . . . . . . . . . . . . . . . . . 729 Enrico Scarpellini and Alessandro Traversari Working Fluid and System Analysis of R454B as a Low-GWP Refrigerant Alternative for R410A in a Vapor-Injected Rotary Compressor . . . . . . . . . . . . . . . . . . . 743 Tim Pfeiffer, Amjid Khan, and Craig R. Bradshaw
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Compressor Performance for Varying Compositions of High-Glide Mixtures R1233zd(E)/R1234yf and R1336mzz(Z)/R1234yf . . . . . . . . . . . . 753 Leon P. M. Brendel, Silvan N. Bernal, Dennis Roskosch, Cordin Arpagaus, Andre Bardow, and Stefan S. Bertsch Use of CFD and Geometry Optimization to Improve the Secondary Oil Separation of an Oil Flooded Rotary Vane Compressor . . . . . . . . . . . . 765 James Willie and Rumit Ganatra An Appraisal of the 1950 Festival Hall Heat Pump . . . . . . . . . . . . . . . . . . . . 781 Andy Pearson Development of a Digital Twin of an Oil-Flooded Screw Compressor Using Measurement Data and Numerical Simulations . . . . . 797 Lukas Richter, Michal Volf, Matej Jerabek, Zdenek Novotny, and Petr Salajka Sizing of Scroll and Rolling Piston Compressor for Low-Pressure Refrigerants in Residential Air Conditioning and Heat Pump Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 813 Haotian Liu, Eckhard A. Groll, and Davide Ziviani Numerical Simulation of Twin-Screw Expander and Its Effect on the Performance of ORC System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 825 Lantian Ji, Zhilong He, Xiao Wang, and Ziwen Xing Development of a Residential Scale, Economized, Compressor Load Stand to Measure Compressor Performance Using Low GWP, Flammable Refrigerants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 843 Amjid Khan and Craig Bradshaw Compressor Lubricants Study of Lubricant Compatibility with a Low-GWP Refrigerant as an Alternative to R410A in a Compressor Test Loop . . . . . . . . . . . . . . . . 857 Bong Seong Oh, Gilbong Lee, Bongsu Choi, Sun-Ik Na, Ho-Sang Ra, Eunseok Wang, Jongjae Cho, Beomjoon Lee, Hyungki Shin, and Junhyun Cho Solubility and Viscosity of Variably Miscible Mixtures of Refrigerant and Lubricant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 867 Anthony J. Barthel, Andrew D. Sumner, Haley L. Webster, and Matthijs Van De Wall Compressor Designs, Lubricant Options and Refrigerant Selections: Putting the Puzzle Together . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 877 Joe Karnaz
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Characteristics and Lubricity of Refrigeration Oil for R290 . . . . . . . . . . . 889 Tomohiro Takaki, Masaki Kawaguchi, Makoto Ando, Yuya Mizutani, and Yuji Shitara
Screw Compressors
Comparison of PV-Diagrams Between CFD and Experimental Results for Twin-Screw Compressors Jin Zhu and Vishnu Sishtla
Abstract As new technological advances emerge at breakneck speed, efficiency and robustness of design drives innovation in the field of compr- essors, expanders, and pumps. At the core of such exploration rests the notion that experimental validation is needed to prove the concept and efficacy of novel designs. Unfortunately, due to limits in instrumentation and experimental setup, it is sometimes infeasible to grasp the physics behind complicated phenomenon solely through experimentation. Experimentation results can provide an incomplete picture which may in turn force an incomplete solution to be incorporated into the product design. Using an experimentally validated CFD model in conjunction with exi- sting experimental results allows for an unexpurgated view of the broader system. One such instance of this problem is experimentally producing the pressure—volume (PV) diagram of a twin-screw compressor with an attached economizer. Due to instrumentation limitations caused by the geometry, the PV-diagram is created by adjoining several pressure transducers placed along the female rotor. However, drawing a conclusion from this PV-diagram is incomplete because comparing the result against the CFD model show that the pressure behavior exhibited in the experimentally created PV diagram is only local to the neighborhood of the pressure transducers, whereas the CFD model show that a continuous view of the compression process exhibits a smoother average pressure transition within the entire volumetric pocket. By combining experimental results along with the appropriate CFD model allows for a broadened understanding of the underlying physics that cannot be achieved solely through experimentation.
J. Zhu (B) · V. Sishtla Carrier Corporation, 13057 Syracuse, NY, USA e-mail: [email protected] V. Sishtla e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_1
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1 Introduction Applications of twin-screw compressors are widely used in refrigeration systems due to their compact nature, operational stability, design simplicity, and overall efficiency [1]. One component that can greatly affect the performance of a twin-screw compressor is the use of an economizer. The concept of the economizer was first patented by Edward Green in 1845 to be used with boilers. The use economizers in screwcompressor systems often results in an increase in the capacity and coefficient of performance (COP). Jonsson established a mathematical model to simulate a twinscrew compressor with an economizer and analyzed the compressor performance with several economizer alternatives [2]. Williams et al. showed that the economizer injection port should be placed farther away from the suction, and that the location of the port has a larger impact on the COP relative to its size [3]. Sjöholm reported that the strict isentropic efficiency of a compressor with an economizer at low pressure ratio is lower than that of a compressor without an economizer. This loss is mainly due to the leakage from the supercharged thread to the suction. However, at high pressure ratios, the strict isentropic efficiency of a compressor with an economizer is high than that of a compressor without the economizer because the addition of the economizer allows for the compressor to operate without under compression at a higher pressure ratio as compared to its counterpart without an economizer [4]. Wu et al. experimentally investigated the effects of superfeed pressure with economizer type on performance of twin screw compressors, and showed that economized compressors will have a higher pressure during the entire compression process which results in an increase in indicated power as compared to the a compressor without an economizer [5]. Unfortunately, it is often difficult to model the economizer through theoretical analysis due to its varied impact on compressor performance based on many factors such as economizer port shape and size, and location of the injection port. Thus, the designer or engineer often turns to experimentation to get more accurate information on the system. Unfortunately, experimentation lacks the flexibility that exists in modeling due to the constraining effects of instrumentation and the laboratory environment. To obtain transient pressure data within the screw compressor, pressure transducers are placed along the rotor housing, and it is assumed that the entire pressure of the pocket is equal to the instrumentation reading. However, since this approach only provides a local view, combining experimental results alongside 3-D CFD simulations often allows for the designer or engineer to better understand the nuances that exist in the system. Kohoff et al. proposed a method to set up the simulation of a dry screw compressor that accounts for gas flow with compressibility and turbulence effects, heat transfer bwtween gas and rotors, and leakage flow [6]. Ding et al. proposed using a volume of fraction approach to model the effects of oil injection within a twin-screw compressor [7]. Unfortunately, there is little research on the effects that an economizer have on the internal flow of a twin-screw compressor. This paper aims to closely examine the pressure distribution as it moves across
Comparison of PV-Diagrams Between CFD …
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the economizer port at various speeds. By using an experimentally validated CFD model, this papers shows that assigning singular pressure transducers as it moves across an active economizer port fails to properly capture the pressure distribution of the compression pocket.
2 CFD Simulation As the inner workings of a screw compressor are both geometrically and aerodynamically complex, it is advantageous to simulate the compression process using CFD. Figure 1a shows the full extracted compressor fluid volume used for the CFD simulation. The discharge pipe was extended to allow for better convergence in the discharge chamber. Figure 1b shows the locations of 7 monitor points placed along the female rotor. The location of each monitor point is analogous to the location of the pressure transducer probes placed on the compressor used for experimental validation. More detail about the pressure transducer probes will be given in Experimental Validation section. The most complicated aspect when performing CFD of a screw compressor is simulation of the rotor movement. In order to perform the rotor meshing, the commercial software SCORG developed by PDM analysis was used, as it can both generate the rotor meshes at each time step as well as create the appropriate pre-processing file for the CFD simulation downstream. Table 1 shows the parameters used for generating the rotor mesh that was used in this paper. The total number of vertices for the male
(a) Model used for CFD simulation
(b) Monitor points placed on female rotor analogous to the pressure probes placed on experimental compressor.
Fig. 1 3-D model of the compressor used for CFD simulation
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Table 1 Parameters used for generating the rotor mesh Parameter Value Circumferential division Radial divison Angular division Interlobe division
40 6 40 40
Table 2 Boundary conditions using for CFD simulation Pressure (PSIA) Suction Discharge Economizer
51.7 211.1 106.2
Temperature (.◦ F) 51 129.2 76.6
and female rotors respectively are 579,278 and 575,680. The total number of cells for the male and female rotors respectively are 494,592 and 491,520. The CFD simulation itself is performed using the commercial software SimericsMP+. In order to validate the simulation model, monitor points were placed at the same location as the pressure transducer probes that were placed in the experimental compressor. By imitating the method used to produce the PV-diagrams experimentally, the PV-diagram produced using the monitor points can be compared against the PV-diagram produced experimentally to ensure the validity of the model. As mentioned previously, a PV-diagram that is constructed using only local pressure values gathered from probes along the female rotor is insufficient to the understanding of the pressure distribution within a working chamber. A more complete approach is to continuously track the average pressure within the working chamber as the simulation progresses. To perform such an approach, custom code was developed to run alongside Simerics-MP+ that allows for continuous tracking of pressure and volume with a described working chamber. Simulations were performed at 3 different speeds: 30, 60, and 95 Hz, for both the economized and non-economized versions of the compressor. For the noneconomized simulations, the geometry of the economizer was not removed, but instead the inlet of the economizer was set as a wall. Table 2 shows the boundary conditions used for each of the 6 tests described above, and the refrigerant used was R134a.
3 Experimental Validation In order to validate the CFD model, an appropriate experiment was designed to create the PV diagram of a twin screw compressor. Seven pressure transducers, one per each
Comparison of PV-Diagrams Between CFD …
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male lobe, were selectively placed along the female rotor in order to capture the entire compression cycle. Figure 2 shows the 3D model of the full screw compressor. In the close up model shown on the right hand side, the green holes are made on the compressor housing to place the pressure transducers. The pressure transducer model used for this experiment was the PTX 600 Series Druck Precision Pressure Transmitter, with a sampling rate of 51 kHz. In order to guarantee that the gathered information were both accurate and complete during the capture process, each pressure transducer was placed so that it overlaps the previous pressure transducer by .10◦ . Figure 3 shows the unwrapped view of the twin screws and where the pressure probes are placed along the female rotor. The purple line represents the suction side, the brown line represent the discharge side, and the dark red dots are where the pressure transducers are placed relative to the female rotor. The first pressure transducer probe, probe 1, is placed approximately .30◦ after the suction cutoff. The location of the economizer is placed near the fourth probe (Counting upwards from probe nearest to the suction cutoff), thus more probes are focused around that area to ensure the correct data is captured. By setting up the pressure transducer probes in this manner, each probe will overlaps the previous probe by approximately .10◦ . A portion of the “head” from the data of the previous probe will approximately match the “tail” of the current probe. Therefore, using Eq. 1 to calculate the normalize absolute error at each data point between each successive sets of probe data will yield a portion with low relative error. Thus by using this method of matching successive probes head-to-tail and stitching them together at the positions of low error will generate the pressures of each working chamber as it goes through the compressor process. Since the suction and discharge pressures are known, the “tail” of probe 1 will match the suction pressure, and the “head” of probe 7 will match the discharge pressure.
Fig. 2 3D model of the full screw compressor showing location of pressure transducers
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Fig. 3 Placement of pressure transducer in unwrapped view of twin screw model
Fig. 4 Raw data gathered from pressure transducers
.
E=
xcurr ent − x pr ev ||xcurr ent − x pr ev ||
(1)
Figure 4 shows the data obtained from the pressure transducers. As the compressor is running at a fixed speed and the geometry of the rotors are well known, it is easy to represent crank angle as a function of time. Finally, using an internal geometry tool developed by carrier, crank angle can be represented as a function of volume.
Comparison of PV-Diagrams Between CFD …
9
4 Results and Discussion As previously discussed, the simulation and experimental results were obtained for both the economized and non-economized compressors at 30, 60, and 95 Hz. Note that for the purposes of this discussion, the effect of oil and 2-phase flow were not considered in the CFD simulation. The fluid was assumed to be a pure gas at all times and no oil was injected during the simulation. Figures 5, 6, 7 and 8 shows the simulation and experimental results at 30 Hz, 60 Hz, and 95 Hz respectively. For each Figs. 5, 6, 7 and 8, (a) shows the comparison between the experimental result and simulated result by probe point for the non-economized, (b) shows the comparison between the experimental result and simulated result by continuous tracking for the non-economized, (c) shows the comparison between the experimental result and simulated result by probe point for the economized, and (d) shows the comparison between the experimental result and simulated result by continuous tracking for the economized.
4.1 Simulation and Experimental Results at 30 Hz Figure 5 shows the experimental and simulated results of both the economized and non-economized compressor at 30 Hz. For a given PV-diagram of the twin-screw compressor, there are at least 2 points of interest: the area near the economizer port, and the area near the discharge port. Since the compressor is running at a low speed, the expected over compression near the discharge port did not occur. Looking at the comparison between the experimental results and the simulation results created from stitching together the monitor points, Fig. 5a and 5c, the simulation results exhibit the same overall characteristics as the experimental results proving the validity of the CFD results. It is evident from the experimental results shown that the added effects of economizer is located at the volume between 2 and 2.5 cc. As the compression pocket moves across the economizer port, the experimental results show that for a compressor running at low speed, a local over and under compression occurs near the economizer port. Note that for the non-economized result, the economizer port is still physically present, but the outside of the economizer is sealed. Thus, comparing the experimental results between the non-economized and economized models, the local over and under compression exists in the both results, but the peak magnitude of the over compression is greater in the economized result. If the economizer is either removed from the compressor completely, or if the economizer is sealed at port as opposed to the inlet, this behaviour will not occur. However, looking at the comparison between the experimental and continuously monitored results, Fig. 5b, d, it is plain that this local over and under compression cannot be generalized to include the entire compression pocket. If the average of the compression pocket is taken instead of a local probe point, the over and under compression is no longer
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(a) Non-Economized: experimental vs. monitor points
(b) Non-Economized: experimental vs. continuous monitoring
(c) Economized: experimental vs. monitor points
(d) Economized: experimental vs. continuous monitoring
Fig. 5 PV-diagrams at 30 Hz for experimental results, monitor points, and continuous monitoring
shown. Instead, the result is a smoother compression that exhibits behaviour more akin to a theoretical economizer model.
4.2 Examination of Pressure Near the Economizer Port Figure 6 shows a detailed looked of the compression pocket as it passes through the economizer port for the 30 Hz economized model as detailed in the previous section. It should be noted here that results that involve stitching together the pressures (the experimental and monitor point results), the over and under compression behaviour that occurs at the economizer port is exhibited through probe 4. The scale shown in the simulation results is normalized to the local pressure of between 105 and 115 psi. By fixating on the pressure at probe 4, it is clear that the behaviour shown in Fig. 5 can be reconstructed. Figure 6a shows the compression pocket before going through the economizer port. The pressure is shown as uniform due to the set scale.
Comparison of PV-Diagrams Between CFD …
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(a) Working chamber just before passing through economizer port area
(b) Working chamber as it’s passing through economizer port area
(c) Working chamber just before exiting the economizer port area
(d) Working chamber exiting the economizer port area
Fig. 6 Pressure of the working chamber as it passes through the economizer port area for the 30 Hz economized model
Figure 6b–d shows the compression pocket at various points as it goes through the economizer port. It can be seen that the pressure first increases at the female rotor end, translates through the pocket to the male rotor end, and returns as the economizer port passes. Looking at probe 4 isolation, the steps shown in Fig. 6a–d correlates exactly to the over and under compression shown Fig. 5. However, it is also clear that the compression pocket pressure is not uniform and thus assuming that entire pocket is equal to the 4th probe point pressure is inaccurate.
4.3 Simulation and Experimental Results at 60 Hz and 95 Hz Figure 7 shows the experimental and simulated results of both the economized and non-economized compressor at 60 Hz, and Fig. 8 shows the experimental and simu-
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(a) Non-Economized: experimental vs. monitor points
(b) Non-Economized: experimental vs. continuous monitoring
(c) Economized: experimental vs. monitor points
(d) Economized: experimental vs. continuous monitoring
Fig. 7 PV-diagrams at 60 Hz for experimental results, monitor points, and continuous monitoring
lated results of both the economized and non-economized compressor at 95 Hz. For compression at middle and high speed, the PV-diagrams for both the experimental and simulation results show the same key characteristics. As this compressor is no longer running at a low speed, the over and under compression observed at low speeds near the economizer port is not present at the high speeds. Instead, the transition over the economizer port behaves more similar to the theoretical model with a slight volume extension as the compression runs over the economizer port. In addition, the familiar over and under compression near discharge port occurs again. Looking at the comparison between the experimental and the monitor points, the results once again show that the simulation results exhibit the same overall characteristics as the experimental results. Both results show an over and under compression at the discharge port, and a slight volume extension in the economized model. However, the limitations of the continuously tracked PV-diagram appears to show here. Looking at the comparison between the experimental and continuously monitored results, the simulation results does not show the over and under compression at the discharge. Most likely, the volume calculator is overestimating the compression volume near
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(a) Non-Economized: experimental vs. monitor points
(b) Non-Economized: experimental vs. continuous monitoring
(c) Economized: experimental vs. monitor points
(d) Economized: experimental vs. continuous monitoring
Fig. 8 PV-diagrams at 95 Hz for experimental results, monitor points, and continuous monitoring
the discharge port. The over and under compression somewhat occurs in the 95 Hz result, Fig. 8b, d, but it is hardly conclusive due to the erratic nature of the discharge process. This behaviour is nonetheless isolated to the discharge port as the rest of the PV-diagram still show the same general characteristics as the experimental results.
5 Conclusion In this paper, the PV-diagrams that were generated from experimentation were compared against PV-diagrams from a validated CFD model. The CFD model was first validated by comparing the experimentally generated PV-diagrams against the CFD simulated PV-diagrams that used the same experimental methodology of adjoining data from adjacent pressure transducers. Next, the experimental PV-diagrams were compared against CFD simulations that continuously tracked the pressure and volume of the entire pocket as it moves from the compression process. The results show
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that although the experimentally generated PV-diagram show an over and under compression as it moves across the economizer port, this is only true with respect to the neighbourhood of the pressure transducer. A continuously tracked PV-diagram that averages the entire pressure of the working chamber pocket show a smoother transition across the economizer port. Future efforts for this work can add the effects oil injection and 2-phase flow to CFD simulation. Another area to explore is the determine the optimal placement of the pressure transducers so that collected data better reflects the internal flow of the compression pocket. Acknowledgements The authors would like to thank Carrier Global Corporation for the use of its resources in this research. The authors would also like to thank the Lab technicians and engineers for setting up and performing the experiments. Finally, the authors would like to thank Dr. Junfeng Wang of Simerics for helping with the initial setup of CFD simulations performed.
References 1. N. Stosic, I.K. Smith, A. Kovacevic, Optimisation of screw compressors. Appl. Thermal Eng. 23, 1177–1195 2. S. Jonsson, Performance simulations of twin-screw compressors with economizer. Int. J. Refrigeration 14 (1991) 3. T. Williams, M. Cambio, Selection of twin screw compressor economizer port location to optimize unit efficiency, in 25th International Compressor Conference at Purdue, May 24–28, 2021 4. Sjoholm, L., Important parameters for small, twin-screw refrigeration compressors (1986). International Compressor Engineering Conference, Paper 592 5. H. Wu, X. Peng, Z. Xing, P. Shu, P., Experimental study on p-V indicator diagrams of twin-screw refrigeration compressor with economizer. Appl. Thermal Eng. 24, 1494–1500 6. A. Spille-Kohoff, J. Hesse, A. El Shorbagy, CFD simulation of a screw compressor including leakage flows and rotor heating. in 9th International Conference on Compressors and their Systems 7. H. Ding, Y. Jiang, CFD simulation of screw compressors with oil injection, in 10th International Conference on Compressors and their Systems (2017)
Model Validation of Twin Screw Compressor with Optimized Injection Port for Unit Efficiency Tasha Williams and Matthew Cambio
Abstract A previously published paper examined the addition of an economizer to a twin-screw water chiller system with the intent of maximizing unit efficiency. The intent was to find the optimum economizer port within the twin-screw compressor. The port size and location were varied to understand how it affects the unit performance. The procedure developed to optimize the unit efficiency using internal modeling tools is reviewed within this paper. The selected port location was used to create a new screw compressor design predicted to achieve a 2–3% improvement in the unit coefficient of performance. The results of an experimental investigation of a twin screw compressor utilizing the optimized economizer port are also presented. From a compressor standpoint the inclusion of the economizer port increases compressor power, increases discharge mass flow, and reduces isentropic efficiency. However, the unit can achieve higher unit efficiency and capacity. The designed twin screw compressor has been tested on the gas cycle stand to validate economizer port optimization efforts. Tested compressor performance and system modeling was used to determine unit performance improvement of 3.6%. Keywords Screw compressor · Economizer port · Unit performance · Experimental
1 Introduction 1.1 Motivation Refrigeration and Air-conditioning systems were invented in the early 1900’s and has become extensively used all over the world today and the technology continues to evolve. Over the last few decades, several challenges have surfaced such as global warming, climate change, high electrical demand, and sustainability. Within the US, T. Williams · M. Cambio (B) Trane Technologies, LaCrosse, WI 54601, USA e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_2
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Roughly 75% of homes has air-conditioning systems [1]. Air conditioning and refrigeration systems account for about 20% of the energy demand today and expected to grow [2]. This has created a massive push in understanding the overall system and individual components. The basic system utilizes the vapor compression cycle. Many changes can be implemented to the system and compressor that contributes towards better environmental and economic conditions such as lower GWP refrigerant selection, optimized components i.e., compressor, and altering the vapor compression cycle [3]. The vapor compression cycle incorporates four components: compressor, condenser, evaporator, and expansion valve. The compressor has the largest influence on the overall system performance. Within this paper, the vapor compression cycle will be altered to include vapor injection and the compressor component will be a focal point, particularly the screw compressor. Screw compressors have been applied to numerous applications for many years. The addition of vapor injection (economizers) to a compressor has been studied and is understood to present an advantage to the overall cycle performance. Two benefits of the economizer port addition are the improvement to capacity [4] and coefficient of performance (COP). This paper uses compressor test data with optimized economizer port to examine the benefit of vapor injection on a water chiller system in an effort to improve unit efficiency.
1.2 Vapor Compression Cycle with Economizer Port The addition of vapor injection, also known as an economizer, into the vapor compression cycle will aid in decreasing the impact of the lost refrigeration effect. The lost refrigeration effect is defined as the loss of energy in vapor form resulting from an increase in vapor quality, which occurs as the enthalpy of the refrigerant rises during the expansion process. Additional benefits are lower compressor discharge temperature, capacity improvement, and lower power consumption [5–7]. This cycle is also referred to as flash-tank vapor injection cycle. The components of the modified vapor compression cycle include original components from the basic compression cycle along with the addition of a flash-tank and altered compressor with economizer port for injection of vapor (Fig. 1). This enhanced cycle (seen in Fig. 1) process starts where the refrigerant vapor enters the condenser (point 4). Next, the refrigerant is expanded after leaving the condenser (point 5) to an intermediate pressure and move into the flash-tank (point 6). Within the flash-tank, the refrigerant is separated into two individual states, vapor (point 9) and liquid (point 7), using both velocity reduction and gravity effect. The liquid continues to the evaporator (point 8) after further expansion. After exiting the evaporator coil, the refrigerant vapor enters the compressor through suction port (point 1). Vapor leaves the flash-tank and enters compressor economizer port (point 9) during the compression process. This starts the 2nd stage of compression (point 3). The assessed benefits are influenced by size and placement of the economizer port and should be optimized to take full advantage of modification.
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Fig. 1 Vapor compression cycle with vapor injection [8]
2 Economizer Port Optimization The addition of an economizer improves the total unit performance by increasing the capacity without increasing compressor power drastically. Economizer port size and location are two important design parameters of compressors. To determine the optimum size and location of the economizer port for unit performance, in-house analytical tools were used. The detailed analysis can be found in part 1 of this study [4]. However, a short summary is provided here. The port is evaluated at a range of size and placements. The saturated evaporator temperature (43 °F) and saturated condenser temperature (96 °F) conditions are held constant throughout analysis. The size is ranged from 0.2 to 1.2 in. while keeping the location constant at 25°. It is seen that as the port size shrinks, the unit performance increases. This is mainly caused by the reduction in leakage effect from the highpressure pocket to the low pocket as well as the moving the economizer injection pressure closer to the middle of the cycle. The evaporator and condenser pressures are used to define the middle of the cycle. The location ranges from 25 to 120° while keeping the size constant at 0.8 in. The range was limited by the suction and discharge of the compressor. Location of the port male angular position is translated to represent an axial distance along the axis of the rotation of the rotor due to the helical nature of the rotors seen in Fig. 2. It is seen that the location has a bigger impact than the size on the overall performance
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Earliest opening location. Need to avoid connection to suction.
Latest closing location. Need to avoid connection to discharge.
Fig. 2 Representation of economizer port location at the low-pressure and high-pressure end of rotors
of the unit. As the port moves further away from suction, the economizer injection pressure is increased which produces higher performance. The unit performance is significantly impacted by the economizer pressure. The maximum COP is found when the economizer pressure is around a ratio (r) of 50%. The optimum economizer port size and location that was determined is 1.22 in and 95°. r=
Pecon − Pevap (P_cond − P_evap)
(1)
3 Modified Screw Compressor Testing The modified screw compressor with optimized economizer port was tested on a compressor gas cycle stand. A wide range of data points were taken to span over the operating envelope on the compressor stand evaluating the economizer injection characteristics at various saturated suction and discharge conditions when the economizer is on and when it is off. The economizer injection is evaluated at three different flow conditions: low, medium, and high. The compressor test data is used to create a 23-coefficient compressor map. The compressor map is then used within a unit model to determine the impact that the addition of the optimized economizer port has on the overall unit performance.
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3.1 Experimental Setup A modified 400-ton screw compressor with optimized economizer port was tested on a gas cycle stand that was equipped with refrigerant injection (see Fig. 3). The refrigerant used is R134a with RL68 oil. The compressor was run at 50 Hz, 400 V, and 100% for all test points. The suction pressure, discharge pressure, and economizer superheat were controlled to reach each test condition. The low and high flow amounts were obtained by adjusting a regulating valve at the exit of the economizer to achieve different injection pressures. The high flow is found when the maximum stable leaving economizer saturated temperature is reached. The low is defined when the minimum stable leaving economizer saturated temperature is reached. The medium condition is determined by finding a point closest to the average of the low and high stable points. ASHRAE 23 method of test for positive displacement compressors standard is followed. The uncertainty flow and power is 1.4% and 0.6% respectfully.
4 Results and Discussion The results will consist of compressor with economizer performance data and unit performance data. The economizer pressure, efficiency, vapor injection flow rate, power, and pressure ratio will be evaluated at three different economizer flow conditions; low, medium, and high. In this paper, the low condition is defined as lowest economizer pressure possible within stable conditions and typically around 10% of suction flow. Similarly, the high conditions is defined as highest auxiliary flow possible within stable conditions. The medium condition is an average of the low and medium conditions.
Fig. 3 Simplified test stand schematic
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4.1 Compressor Results The compressor performance is evaluated at each flow condition (Figs. 5, 6, 7 and 8). The compressor power, efficiency, economizer pressure ratio (r), economizer pressure, and economizer injection flow rate is plotted versus low, medium, and high flow characteristics at three different saturated suction and discharge conditions (i.e. SST = 42 and SDT = 100) seen in Figs. 5, 6, 7 and 8. The low, medium, and high condition directly corresponds to the economizer injection flow rate caused by higher saturated temperatures and pressures at inlet of the injection port. Similarly, the economizer pressure increases and moves closer to condenser pressure. The economizer pressure ratio (r) directly correlates with the economizer pressure (1). This increase in economizer pressure and ratio indicates a unit improvement as it is theoretically proven that as r moves closer to the middle of compression, the unit COP increases. Power is seen to slightly increase as the economizer flow increases from low to high. Trane 23-coefficient curve fit A compressor map is generated using the compressor test data. This data is later used within an analytical unit model to determine the benefit of incorporating the vapor injection. Vapor injection compressor mapping introduces a new independent variable. To account for this, Trane’s 23-coefficient mapping model is created using ARI 10-coffiecient model as a base. The schematic of the full matrix is shown in Fig. 4. The full matrix consist of 64 total terms and the gray shaded areas are terms
Fig. 4 Schematic of full matrix of parameters for three-factor, third order equation [5]
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Fig. 5 Measure vapor injection flow versus economizer flow characteristic at various saturated suction and discharge conditions
Fig. 6 Ratio (r) versus economizer flow characteristic at various saturated suction and discharge conditions
that are excluded. The derived equation is shown in Eq. (2) where TS is saturated suction temperature, TD is saturated discharge temperature, and TE is economizer saturation temperature. X = C1 + C2 · T S + C3 · T D + C4 · T S 2 + C5 · T S · T D + C6 · T D 2 + C7 · T S 3 + C8 · T D · T S 2 + C9 · T S · T D 2 + C10 · T D 3 + C11 · T E + C12 · T E 2 + C13 · T S · T E + C14 · T E · T D + C15 · T E 3 + C16 · T S · T E 2 + C17 · T E · T S 2 + C18 · T D · T E 2 + C19 · T E · T D 2 + C20 · T S · T E · T D + C21 · T E · T D · T S 2 + C22 · T S · T E · T D 2 + C23 · T S · T D · T E 2
(2)
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Fig. 7 Measure economizer pressure versus economizer flow characteristic at various saturated suction and discharge conditions
Fig. 8 Measured power versus economizer flow characteristic at various saturated suction and discharge conditions
4.2 Unit Results The modified vapor injected compressor is optimized for an evaporator leaving coolant temperature of 44 °F and a condenser leaving coolant temperature of 86 °F rating condition. The generated compressor map determined using test data is implemented within an analytical system model to determine the improvement in COP. The basic vapor compression cycle with original compressor and no vapor injection is used at the baseline. Evaluated conditions are 44 °F/120 °F and 44 °F/86 °F for evaporator and condenser leaving coolant temperature. All input is the same for both baseline and vapor injection unit models and comparing capacity and COP to one another. The COP increased 5.3 and 3.6% while the capacity increase is 12.7 and
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Table 1 Unit performance comparison
Baseline
Evaporator lvg Coolant (°F)
Condenser lvg Coolant (°F)
COP
Capacity (ton)
44
120
2.95
311.86
3.10
351.61
Comp/w optimized Econ % Difference
5.3
12.7
5.83
401.07
Comp/w optimized Econ
6.04
417.46
% Difference
3.6
4.1
Baseline
44
86
4.1%. This is 1.9% below projected performance from theoretical work presented in part 1 of this paper however it meets the design target of 2–3% (Table 1).
5 Conclusions Many HVAC systems have a large impact on environmental factors. Globally scientist and engineers are working towards innovating new technologies to reduce environmental effects. A screw compressor with optimized economizer port size and location provides a solution to the challenges ahead. Compressor testing and system modeling techniques are used jointly to determine the unit improvement when applying a compressor with vapor injection capabilities. The optimized size and location of the economizer port allowed for COP design target to be reached. The amount of vapor injected within the compressor at a given condition has a larger impact on unit performance. Additionally, this experimental effort confirms that moving the injection port location further away from suction increases the performance as a result of the intermediate pressure becoming closer to the optimum economizer injection pressure. The newly designed compressor incorporated with optimized economizer port size and location produced a COP improvement of 3.6% at the design condition.
References 1. Air Conditioning, Energy.gov, https://www.energy.gov/energysaver/air-conditioning 2. IEA, The Future of Cooling Opportunities for Energy-Efficient Air Conditioning. Report (2018). https://iea.blob.core.windows.net/assets/0bb45525-277f-4c9c-8d0c-9c0cb5e7d 525/The_Future_of_Cooling.pdf 3. C.-U. Moon, K.-H. Choi, J.-I. Yoon, Y.-B. Kim, C.-H. Son, S.-J. Ha, M.-J. Jeon, S.-Y. An, J.-H. Lee, Experimental study on the performance of the vapor injection refrigeration system with an economizer for intermediate pressures. Heat Mass Transf. 54(10), 3059–3069 (2018)
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4. T. Williams, M. Cambio, Selection of Twin Screw Compressor Economizer Port Location to Optimize Unit Efficiency (2021) 5. M. Cambio, in Trane Internal Technical Note. Model for screw compressors with economizers. (La Crosse, WI, 2015). 6. X. Xu, Y. Hwang, R. Radermacher, Refrigerant injection for heat pumping/air conditioning systems: Literature review and challenges discussions. Int. J. Refrig. 34(2), 402–415 (2011) 7. B. Wang, W. Shi, L. Han, X. Li, Optimization of refrigeration system with gas-injected scroll compressor. Int. J. Refrig. 32(7), 1544–1554 (2009) 8. DuPont Company, Thermodynamic Properties of HFC-134a (1,1,1, 2-tetrafluoroethane) (Wilmington, Delaware, 1993)
Simplified Engineering Calculation Methods of the Temperature Distribution Along the Screw Compressor Rotors Timur Mustafin and Ruslan Yakupov
Abstract A purpose of a screw compressor experimental prototype development, rotor profiles design of optimization has many engineering problems. One of the main of them is trying to predict on this stage the compressor construction parameters, which are as close to the optimal as possible. Using of the compressor mathematical model for this aim sometimes is impossible, because of hardness of new mathematical model design and necessary of their accuracy checking. Therefore there is a necessary to have not only high-accuracy calculation tools, such as mathematical model, but also have some simplified engineering methods for the fast calculation of compressor parts’ conditions, which have enough accuracy for the first stage of the development at same time. These conditions also include the temperature field of the compressor rotors. The presented paper dedicated to the analyses of possibility to obtain approximation equations, which can be used for the calculation of the preliminary value of the screw compressor rotors’ temperature fields depending on the operation mode and construction parameters of the screw compressors. Keywords Screw compressor · Rotors’ temperature fields · Simplified engineering calculation methods
1 Introduction Setting safe gaps in displacement compressors is an important issue since this determines not only the reliability of the unit but also its thermodynamic characteristics. When designing compressors, one has to compromise between reducing the probability of jamming, which requires increased gaps between the operating components, T. Mustafin (B) · R. Yakupov Kazan National Research Tehnological University, 68 Karl Marx Str., Kazan’ 420015, Russian Federation e-mail: [email protected] R. Yakupov Chelyabinsk Compressor Plant, 14th Kilometer of the Chelyabinsk-Novosibirsk Highway, Krasnoarmeisky District, Chelyabinsk Region 456671, Russian Federation © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_3
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and reduced leakages, which is achieved by reducing the gaps. Setting safe gaps is impossible without calculating thermal deformations and, consequently, the temperature distribution among the compressor components. Even for compressors with simple-shape operating components, e.g. piston compressors, this is not a trivial task since it is required to correctly define the conditions in which heat exchange between the operating element and the walls of the working chamber occurs. In case of scroll or screw compressors, this task is further complicated by the complex shape of their operating elements. Thermal expansion of one scroll is compensated by thermal expansion of the second one in scroll compressors, screw compressors see the effects of thermal deformations of their rotors on the profile gaps added up. Two methods for calculating thermal deformations of rotors can be distinguished nowadays: the method of calculation based on empirical dependencies [1] and the one based on building a mathematical model of the thermal state of rotors [2–6]. The purpose hereof is to approximate the data suitable for a preliminary rapid assessment of the thermal state of rotors.
2 Calculation of Temperature Fields of Rotors and Their Thermal Deformations A whole range of works discusses the calculation of temperature fields of screw compressor rotors, with some of them revealing the impact of various factors on the temperature field of compressor rotors to some extent. The most comprehensive approach to calculating the temperature fields is presented in [2–8]. Thermal state of rotors is determined by the heat conduction equation: ∂T = α · ∇2T , ∂τ
(1)
where α is the thermal diffusivity coefficient of the rotor material, T is temperature, and ∇ is nabla. Thermal load on compressor rotors is cyclical. However, the period of a single cycle is rather short; as a result, the temperature field of the rotor does not virtually change with time. The latter is confirmed by the studies in [2, 3, 7]. This makes it possible to assume that thermal processes in a rotor are pseudostationary. Therefore, Eq. (1) can be simplified as follows: ∇ 2 T = 0.
(2)
The boundary conditions for Eq. (2) are determined based on equation λ M ∂∂nT = q, λ M is the heat conductivity of the rotor material, where ∂∂nT is the normal derivative with respect to the rotor surface which is affected by the heat flow q. However, one should distinguish between the heat gains from the heat exchange of the gasoil medium with the rotor surface in the working cavity, the heat exchange of the
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Fig. 1 Calculation scheme for determining the boundary conditions
end rotor surfaces with the gas-oil medium in the suction cavities through the end surfaces of the suction and discharge ports, the heat gain from the friction of the rotors against the gas-oil medium in the end surfaces and radial gaps, as well as the heat gain along the shaft sections from the bearings. All of these heat gains are reflected in the calculation scheme in Fig. 1 and are described in much detail in [7–12]. To set the boundary conditions when calculating the temperature field of the rotors, it is necessary to calculate the average gas temperature in the end section along the rotor length. The rotor is divided into n sections for this purpose. The distance between the sections is equal to Δz = Δφ · H,
(3)
where Δφ is the angular pitch of the mathematical model, and H is the screw pitch of the corresponding rotor (4). First, the temperature of the cavities at each angle of rotation of the rotor is determined for each rotor section. Since the same processes occur in the cavities shifted by a 90-degree angle, the temperature of one working cavity can be considered to determine the average gas temperature in each section. The average air temperature in each section is calculated as ∑360/Δφ TC P =
Ti i=1 , 360/Δφ
(4)
where Ti is the air temperature in the working cavity of the section at the i angle of rotation of the rotor. Figure 2 exemplifies the medium temperature distribution along the rotor length at each angle of rotation. Figure 3 exemplifies the distribution of the average medium temperature in the working cavity along the rotor length.
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T. Mustafin and R. Yakupov
Fig. 2 Medium temperature distribution in the working cavity along the length of the male (a) and female (b) rotors and the angles of rotation of the rotors
Simplified Engineering Calculation Methods of the Temperature …
29
Fig. 3 Average medium temperature in the working cavity along the rotor length
2.1 Impact of the Compressor Design Parameters, As Well As the Operating Mode on the Thermal State of the Rotors Figure 4 shows the impact of the design parameters as exemplified by the presence of the suction port on radial housing boring. The results of the temperature field calculations show that the radial tops of the rotors in the radial gap are subject to the most intense heating. It should be noted that the temperature of the gas-oil medium at the suction is lower; consequently, its viscosity is much higher, and therefore, the friction heat in the gap is also higher. This explains the higher temperature of the rotors in the housing without any suction port on the radial housing boring. Similar conclusions can be made by analyzing the effect of the geometric compression ratio of the compressor on the temperature fields of the rotors. Its effect reflects not only through a change in the temperature of the compressed medium but also determines the discharge port dimensions. Significant geometric compression ratio is achieved by the smaller dimensions of the discharge port, which consequently leads to greater friction of the end surfaces of the rotor against the gas-oil mixture on the discharge side. The latter leads to additional heating of the rotor ends on the discharge side. The impact of the values of the end and radial gaps on the temperature fields of the rotors is determined by the friction against the gas-oil mixture in them, which leads
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T. Mustafin and R. Yakupov
Fig. 4 Impact of the compressor design parameters on the temperature fields of the rotors (degree of compression P = 9, driving rotor speed of rotation n = 3000 rpm): a female rotor in a housing without any radial housing boring for the suction port; b female rotor in a housing with radial housing boring for the suction port; c male rotor in a housing without any radial housing boring for the suction port; d male rotor in a housing with radial housing boring for the suction port
to the conclusion that they are inversely proportional to the values of said gaps, all other things being equal. In fact, a smaller gap leads to an increased gas-oil mixture temperature in the gap and, therefore, to its viscosity drop. Thus, the smaller the gap the higher the friction heat, but its growth is non-linear. This article uses the profiles of the female rotor without any seal ledges as an illustration for the calculations. The presence of the latter reduces the friction area on the radial surface against the gas-oil mixture, while the main heating along the radial surface from the friction heat can be seen on said ledges, which reduces the unevenness of the temperature field of the rotor in the end section as a whole. The impact of the operating parameters on the temperature fields of the rotors is shown in Fig. 5 as exemplified by a driven rotor without any seal band in the housings and without radial boring for the suction port. It should be noted that their main effect shows through the temperature of the gas in the working cavities. This explains the higher temperature gradient between the suction and discharge ends of the rotors at high-pressure ratios. Reduced speed of rotation of the rotors leads to the equalization of the temperature of the rotors in different end sections, but the total rotor temperature increases at the same time. This can be explained by the fact that
Simplified Engineering Calculation Methods of the Temperature …
31
Fig. 5 Impact of the compressor operation mode on the temperature fields of the female rotor. a degree of compression P = 9, driving rotor speed of rotation n = 1500 rpm. b Degree of compression P = 4, driving rotor speed of rotation n = 3000 rpm. c Degree of compression P = 9, driving rotor speed of rotation n = 3000 rpm. d Degree of compression P = 9, driving rotor speed of rotation n = 3600 rpm
the smaller the rotor speed the higher the temperature of the compressed gas in the working cavities and the smaller the friction of the rotors against the gas-oil mixture in the gaps. Figure 6 shows the effect of the amount of injected oil on the temperature field of the female rotor. The screw compressor without radial boring of the suction port in the cylinder block as described above was selected for the analysis. The suction and oil parameters also correspond to those described, and the assumed compression ratio is equal to P = 9, and while the speed of rotation is n = 1500 rpm. A change in the amount and temperature of the injected oil affects not only the temperature of the compressed medium in the working cavity but also its viscosity. The latter, as noted above, has a strong effect on the friction heat in the gaps and consequently affects the unevenness of the temperature fields of the rotors in their end sections. Less oil injected leads to decreased gas temperature on the suction side and to increased discharge-side temperature, which results in an increased temperature gradient in the rotor between the suction and discharge ends. More oil injected leads to decreased discharge-side temperature and increased gas temperature on the suction side. Further increase in the amount of gas injected does not lead to any significant temperature decrease on the discharge side, however, slightly increases the gas temperature on
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T. Mustafin and R. Yakupov
Fig. 6 Effect of the amount of injected oil on the temperature field of the female rotor (degree of compression P = 9, driving rotor speed of rotation n = 3000 rpm): a gas-oil ratio: 1.95. b Gas-oil ratio: 3.9. c Gas-oil ratio: 7.8
the suction side due to the initial temperature of the injected oil. This results in a more even temperature field throughout the rotor.
2.2 Calculation Results As can be seen from the results, the thermal state of the rotors is determined by many factors, with their majority unable of being taken into account in the final empirical dependence. The central part of the rotor is affected by the heat gain from the bearings, beyond which the unevenness of the temperature field increases approaching the tops of the rotor lobes. This unevenness also decreases the higher the distances from the rotor ends. This is due to the effect of friction against the gas-oil mixture in the gaps. This makes it possible to determine—with some confidence—the following dependence for determining the average temperature of the rotors in the sections along the length of the rotor for any i section according to the following method: TMi
( ) ( )2 li li = (TS − 1.35) + 0.45(TD − TS ) + 20.76 − 10.15 lR lR
(5)
Simplified Engineering Calculation Methods of the Temperature …
( ) ( )2 li li TFi = (TS + 3.39) + 0.40(TD − TS ) + 32.49 − 26.76 lR lR
33
(6)
where TS , TD , are the suction and discharge temperatures, respectively; li is the distance from the suction end to i section of the rotor, and l R is the length of the profile part of the rotor. The Eq. (5) describes the male rotor average temperature in section, the Eq. (6) should be used for the female rotor average temperature in section calculation. All temperatures have °C dimension.
3 Conclusions The computational model discussed enables the calculation of the temperature fields of the rotors: it makes it possible to assess the impact of both individual factors and the combination thereof, including not only the operating mode but also the compressor design features. The dependences for the approximate calculation of the average temperature in the rotor section have been obtained based on the approximation of the calculation data.
References 1. I.G. Khisameev, V.A. Maksimov, Dvukhrotornye Vintovye I Pryamozubye Kompressory. Teoriya, Raschetiproyektirovanie (Twin Rotors Screw and Spur Compressors. Theory, Calculation and Design (in Russian)) (Fen, Kazan, 2000) 2. B. Weather, J. Sauls, G. Powell, in International Compressor Engineering Conference. Transient Thermal Analysis of Screw Compressors, Part II: Transient Thermal Analysis of a Screw Compressor to Determine Rotor-to-Housing Clearances (Purdue University, 2006), pp. C052,1–C052,8 3. S.H. Hsieh, W.H. Hsieh, C.S. Huang, Y.H. Huang, in International Compressor Engineering Conference. Numerical Analysis of Performance, Rotor Temperature Distributions, and Rotor Thermal Deformation of an R134a Screw Compressor (Purdue University, 2012), pp. 1387.1– 1387.10 4. S.H. Hsieh, Y.C. Shih, W.H. Hsieh, F.Y. Lin, M.J. Tsai, Calculation of temperature distributions in the rotors of oil-injected screw compressors. Int. J. Thermal Sci. 50, 1271 (2011) 5. T.Y. Gao, D.F. Yang, F. Cao, J.C. Jiao, Temperature and thermodynamic analysis of the rotors on a twin screw multiphase pump with high gas volume fraction. J. Zhejiang Univ. Appl. Phys. Eng. 12, 720 (2011) 6. J. Sauls, G. Powell, B. Weathers, in Proceedings of International Compressor Engineering Conference. Transient Thermal Analysis of Screw Compressors, Part 1: Use of Thermodynamic Simulations to Determine Boundary Conditions for Fine Element Analyses (Purdue University, West Lafayette, 2006) 7. T.N. Mustafin, R.R. Yakupov, A.V. Burmistrov, M.S. Khamidullin, I.G. Khisameev, in 9th International Conference on Compressors and their Systems (IOP Conference Series: Material Science Engineering), vol. 90. Analysis of the Screw Compressor Rotors’ Non-Uniform Thermal Field Effect on Transmission error (IOP Publishing, 2015) p. 012004
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8. T.N. Mustafin, R.R. Yakupov, A.V. Burmistrov, M.S. Khamidullin, I.G. Khisameev, Analysis of screw compressors’ constructive parameters and working conditions influence on rotors’ temperature fields. Proc. Eng. 152 (2016) 9. T.N. Mustafin, R.R. Yakupov, M.S. Khamidullin, I.G. Khisameev, V.A. Alyaev, O.Y. Paranina, in Oil and Gas Engineering (OGE-2017) (AIP Conference Proceedings 1876). The Analysis of Typical Profile Clearances Formation in Meshing Rotors of the Screw Compressor (AIP Publishing LLC, 2017), p. 020024 10. T.N. Mustafin, R.R. Yakupov, M.S. Khamidullin, I.G. Khisameev, I.G. Uybekova, O.Y. Paranina, in Oil and Gas Engineering (OGE-2018) (AIP Conference Proceedings 2007). Calculation and Experimental Analysis of Profile Clearance Values in Screw Compressor Rotors (AIP Publishing LLC, 2018), p. 030049 11. R.R. Yakupov, T.N. Mustafin, M.S. Khamidullin, I.G. Khisameyev, V.A. Alyayev, Comparison of Methods for Calculating Thermal Deformations of Screw Compressor Rotors. AIP Conference Proceedings (this link is disabled) (2020), pp. 2285, 030017 12. T.N. Mustafin, R.R. Yakupov, M.S. Khamidullin, I.G. Khisameev, I.G. Uybekova, O.Y. Paranina, Determining of Actual Profile Clearances and Screw Compressor Rotor Positions Depending on Working Condition. IOP Conference Series: Materials Science Engineering, vol. 232. (IOP Publishing, 2017), p. 012023.
CFD Analysis of Leakage Flow in Radial Tip Gap of Roots Blower Neeraj Bikramaditya, Sham Rane, Ahmed Kovacevic, and Brijeshkumar Patel
Abstract A Roots Blower is rotary positive displacement machine, commonly used for low pressure applications [3]. However, the gaps between the rotors and the housing are the main source of volumetric inefficiency and are required to be minimised. This has limits due to thermal expansion of compressor elements. Improvements can also be done by minimising leakage flows using different configurations of rotor tip profiles for which careful analysis is required. An optical Roots Blower from Howden is being investigated using experimental and numerical tools for the effects of heat transfer and tip geometry on leakage of gas. To closely study the leakage through the clearance gaps, a 2D simplification (Fig. 1b) of this 3D model is proposed in this paper. A local flow is evaluated in steady and transient state conditions using only through the tip leakage gap between the rotor and the housing on one rotor lobe. Using data from PIV measurements, the base tip design on the rotor profile is analysed and used for validation of the 2D model. Following this, variants of the tip-shape, namely equal-cavity and unequal-cavity tip profiles with alterations, have been numerically evaluated. These results will help in implementation of such a tip profile design in conventional oil free twin screw compressors to meet demands of efficiency improvements. Keywords CFD · PIV · Roots blower · Leakage · Clearance · PR (pressure ratio)
1 Introduction Roots blower is a Rotary PDM used for low pressure applications. It is also known as straight lobe compressor. This oil free air delivery machine is useful for the industries where contaminations plays an important role such as FMCG, Chemical, Pharmaceutical, textile etc. The Roots Blower has oppositely rotated and non-contacting pair of Rotors enclosed within a casing. One of the rotors is known as main/male rotor and other as gate/female rotor. There are three types of gaps in the blower, namely N. Bikramaditya (B) · S. Rane · A. Kovacevic · B. Patel City, University of London, London EC1V 0HB, UK e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_4
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inter-lobe or rotor-to-rotor gap, the tip or rotor-to-casing gap and the axial gap. They are separated by a precisely engineered gaps through which certain amount of air escape as losses. As shown in Fig. 1a, the Roots blower uses two straight-shaped lobe impellers mounted on parallel shafts. When the lobe passes over the blower inlet, a finite volume of air is trapped and is carried around the chamber by the lobes. The air is then discharged at the blower outlet. As the lobes continue to rotate, the pressure increases in the reservoir beyond the blower outlet. Thus, the pressure difference between discharge and suction causes air to flow back from the reservoir to the low-pressure regions through these clearances. To make flowing air be oil free and flow without lubrication, these clearances between the rotors (Lobe) and between the rotors and the casing (Tip and End plate) are kept. Researchers have been trying to study the physics of leakage flow to understand the flow phenomena in the clearance gaps. The gap management plays crucial role for better reliability and efficiency of the machine. Brijesh et.al [7] have developed and outlined the PIV method to capture important flow physics using the velocity and temperature field. Vimmr [1] have presented a numerical simulation of the leakage flow between the moving rotor and housing of a screw compressor. In their 2D moving mesh for analysis, they observed that rotor speed has negligible effect on velocity field at given pressure ratio. The fourth author of this paper has conducted the PIV test on roots blower for his PhD thesis, has found out that there is change in the velocity field in the leakage gap and in the downstream. In the present study, the goal was to develop a simplified model of the Roots blower which could validate the PIV results and efficiently be used for the modelling of different shapes of the Rotor tip.
Fig. 1 a Section view of roots blower clearances, b fluid flow in clearance roots blower
CFD Analysis of Leakage Flow in Radial Tip Gap of Roots Blower
37
2 Computational Fluid Dynamics Fluid flow is governed by three fundamental conservation laws of mass, momentum and energy. CFD employs numerical methods and algorithms to solve mathematical models which describe fluid flow using governing equations to a large set of algebraic equations. In the era of high computational capability, CFD has tremendous the ability to produce accurate solution for complex and realistic geometries. ANSYS Fluent commercial CFD code is used which is based on Finite Volume Method using conservation laws of fluids. More details can be found in ANSYS-FLUENT Theory guide [2].
2.1 Conservation Laws of Fluids Mass Conservation Equation. The mass conservation law states that the net mass crossing the boundary of a control volume must be balanced by an accumulation or depletion of mass in that control volume. For compressible flow, the mass can increase or decrease within the control volume. Mass conservation equation or equation of continuity is mathematically defined as: ∂ ρv j ∂ρ + =0 ∂t ∂x j
(1)
Momentum Conservation Equation. The momentum conservation equations are derived from the second Newton’s law of motion. It states that the sum of the forces acting on a fluid particle is equal to the mass of the element multiplied by its acceleration. The formulation below is a 3D transient formulation of the Naviers-Stokes equations for compressible flow in Eulerian frame of reference: ∂(ρvi ) ∂ ρv j vi ∂ + − pδ ji + ji + ρ f i = ∂t ∂x j ∂x j
(2)
Energy Conservation Equation. The energy conservation equation is derived from the first law of thermodynamics which states that energy can’t be produced or destroyed, just converted from one form to another. The change in energy over time is equal to the sum of the work done and the thermal energy generated: ∂v j ∂T ∂(ρCv T ) ∂ ρCv v j T ∂vi ∂ λ + φv + = −p + ji + ∂t ∂x j ∂x j dx j ∂x j ∂x j
(3)
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a)
b) Clearance between Tip & casing
Blowercasing
0.4 mm
Casing as Wall
Rotor Tip Y
6.4 mm
1 mm
X
Thickness (z-direction)
Fig. 2 a Computational domain (simplified 2D). b Schematic L/O of leakage region
The basic variables used in Eqs. (1), (2) and (3) ρ, v, p, f, Cv , T andλ are density, velocity, pressure, specific heat capacity, temperature and thermal conductivity respectively. For more details about notations, ANSYS [2] can be referred.
3 Computational Analysis of Roots Blower The ANSYS Fluent Commercial code is used for the simulation of the modified 2D of 3D Roots blower. The geometry is created using ANSYS Workbench and Mesh is created using ANSYS Mesh.
3.1 Computational Domain of Simplified Roots Blower Figure 2a is the simplified domain considered for the validation of the CFD set up. The modelling consists of defining input conditions and related boundary conditions, turbulence models, solution methods with both static and transient mode calculations. The Pressure inlet and pressure outlet boundary conditions is used for inlet and outlet respectively. Since the 2D model with thickness is considered, both side surfaces (yellow) are used as periodic BC. Figure 2b shows the dimensions of the modelling.
3.2 Simulation Set-Up Air has been used as a working medium. It is considered as a perfect gas which means that its density depends on temperature and pressure. It has density of ideal gas, specific heat of 1006.43 J/(kgK), thermal conductivity of 0.0242 W/(mK) and viscosity of 1.7894e − 05 kg/ms). Table 1. is the summary of the simulation cases considered same as PIV test.
CFD Analysis of Leakage Flow in Radial Tip Gap of Roots Blower
39
Table 1 Input conditions from PIV test Items
PR 1.6
RPM
Pin/Pout (kPa)
Tin/Tout (K)
Pin/Pout (kPa)
Tin/Tout (K)
Pin/Pout (kPa)
Tin/Tout (K)
2000
161.2/ 100.8
438/390
143/102
364.3/304.9
121.6/ 100.8
330.8/303.1
1800
PR 1.4
418/311
PR 1.2
333.6/306.2
1500
380.1/309.6
330.1/302.5 332.1/302.1
1000
329.1/302.1
Table 2 Solver setting Items
Specification
Items
Specification
Solver
Pressure based
Spatial discretization
2nd order upwind
Turbulence
K-ω SST, K-E, LES
Turbulence numeric
2nd order upwind
Fluid medium
Air
Gradient
Green-Gauss node
P–V coupling
Coupled
Flux-type
Rhie-chow: mom based
Transient
1st order implicit
Time-step size
0.001(s)
The simulation settings are shown in Table 2. The turbulence was modelled with the Shear Stress Transport (SST) k-ω model, K-E and LES. The k-ω SST turbulence model is selected mainly unless and otherwise stated differently in present calculations. The flow was assumed to be subsonic below an overall pressure ratio of 1.9 and sonic above it [3]. The current set up is considered after careful consideration of the transient setup of Roots blower by Sun. et.al [6]. The domain and solvers are different from Sun et. al. First the steady state calculation performed and after few iterations, transient simulations was adapted with Flow Courant number 20. This courant number is applied after investigating the convergence behavior. The Fluent default under-relaxation for body-force, k, omega, density and turb-viscosity is used.
4 Results and Discussion Roots blower geometry and simulation set-up were presented in the previous sections. In the first section, the numerical results will be validated with PIV data and in the second section, the results will be compared for the different rotor tip design concepts and their effect. The Physical phenomena and the related analysis are presented.
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4.1 Validation For the validation of the current CFD set up, the absolute maximum velocity at the exit of the tip and the averaged velocity profile through leakage (casing to rotor) is considered. The Leakage gap is maintained at the 400 μm. The comparison conditions are made at PR 1.6, 1.4 and 1.2 with RPM 2000, 1800, 1500, 1000 and 0. In order to validate the current CFD model, there were three basic turbulence modelling approach investigated at all Pressure ratio (PR) 1.6, 1.4 and 1.2, and Komega and LES was chosen at PR1.4. The PIV results shows that at one fixed Pressure Ratio, different Rotor speeds (RPM) show variation in the velocity profiles between rotor tip and casing (i.e., Leakage gap). This PIV result pattern is not observed in CFD results. CFD has shown almost no variation of the velocity profile for all the Rotational speed of the Rotor. At PR1.6, PIV showed higher velocity in leakage region for RPM1800 and RPM0 than RPM2000. CFD has shown (Figs. 3 and 4) a negligible variation in averaged velocity profiles for all the three Turbulence models (RANS (k-ω SST, K-E) and LES) (Fig. 3). Although, there was some change observed for K-Epsilon but cannot be validated as an improvement because this pattern was not observed at other PRs. For the PR1.4, PIV resulted in the similar trend as PR1.6 (Figs. 5 and 6). Averaged velocity profiles for the RPM1800 and RPM0 is higher than that of RPM2000 and RPM1500, but this flow characteristics is not visible in CFD for all the turbulence models (Fig. 5). Also, at the PR1.2, RPM1800, RPM1000 and RPM0 are higher in vel. magnitude than RPM2000 and RPM1500 (Figs. 7 and 8). CFD has not depicted this vel. profile for any of the turbulence model chosen (Fig. 7). There is a possibility that 2D-model and non-rotating mesh are combinedly unable to track the physics of the leakage flow and downstream flow field of tip. The mesh rotation usually impose fluctuation in the flow field through their complete rotation cycle (Figs. 3, 4, 5, 6, 7 and 8). At the exit of the rotor tip, the maximum velocities were investigated to compare them with the PIV results (Fig. 9). Exit velocity indicates the speed at which the flow is exiting as leak and tend to predict the volume flow of leak. The absolute max. velocity has also shown the better agreement for the RPM2000 at PR1.6. For all other cases, discrepancies exist within the range of 20%. At this particular case of PR1.6 and RPM2000, the averaged velocity profile through leakage and the abs. max. velocity at the tip exit are in closer agreement with PIV as shown in Fig. 10.
4.2 Tip Design Concept Study Considering the case of PR1.6 and RPM2000, the Roots blower tip concepts will ¯ be investigated in this paper. The mass flow rate (m ˙ = U*A) on the section plane at
CFD Analysis of Leakage Flow in Radial Tip Gap of Roots Blower
PR1.6/K-ω SST
300
Avg. Vel Mag(m/s)
41
250 200
PIV/RPM2000 CFD/RPM2000 PIV/RPM1800 CFD/RPM1800 PIV/RPM0 CFD/RPM0
150 100 50 0 50
100 150 200 250 300 350 400
Tip Clearance gap(mm)
PR1.6/K-ε
250 PIV/RPM2000
200
CFD/RPM2000
150
PIV/RPM1800
100
CFD/RPM1800 PIV/RPM0
50
CFD/RPM0 100
150
200
250
300
250 200
PIV/RPM2000 CFD/RPM2000 PIV/RPM1800 CFD/RPM1800 PIV/RPM0 CFD/RPM0
150 100 50 0
0 50
PR1.6/LES
300
Avg. Vel Mag(m/s)
Avg. Vel Mag(m/s)
300
350
400
Tip Clearance gap(mm)
50
100 150 200 250 300 350 400
Tip Clearance gap(mm)
Fig. 3 PR1.6/velocity profiles comparisons K-ω SST versus K-ε and LES
(a) RPM2000
(d)
RPM2000
(b) RPM1800
(c)
(e) RPM1800
(f)
RPM0
RPM0
Fig. 4 PR1.6/vel. contours comparison b/w PIV (a–c) and CFD k-ω SST model (d–f)
N. Bikramaditya et al.
PR1.4/K-ω SST
250
Avg. Vel Mag (m/s)
Avg. Vel Mag (m/s)
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200 PIV/RPM2000 PIV/RPM1800 PIV/RPM1500 PIV/RPM0 CFD/RPM2000 CFD/RPM1800 CFD/RPM1500 CFD/RPM0
150 100 50 0
50
100
150
200
250
300
350
PR1.4/K-ε
250 200
PIV/RPM2000 PIV/RPM1800 PIV/RPM1500 PIV/RPM0 CFD/RPM2000 CFD/RPM1800 CFD/RPM1500
150 100 50 0 50
400
100
150
200
250
300
350
400
Tip Cleance gap(mm)
Tip Cleance gap(mm)
Fig. 5 PR1.4/velocity Profiles comparisons K-ω SST versus K-E
(a) RPM2000
(e) RPM2000
(b) RPM1800
(c) RPM1500
(d) RPM0
(g) RPM1500
(f) RPM1800
(h) RPM0
Fig. 6 PR1.4/vel. contours comparison b/w PIV (a–d) and CFD k-omega SST (e–h)
PR1.2/K-
50 100 150 200 250 300 350 400
Tip Cleance gap(mm) PIV/RPM2000 PIV/RPM1500 CFD/RPM2000 CFD/RPM1500
PIV/RPM1800 PIV/RPM0 CFD/RPM1800 CFD/RPM0
Avg. Vel Mag (m/s)
Avg. Vel Mag (m/s)
PR1.2/K-ω SST 200 160 120 80 40 0
200 160 120 80 40 0 50 100 150 200 250 300 350 400
Tip Cleance gap(mm) PIV/RPM2000 PIV/RPM1500 CFD/RPM2000 CFD/RPM1500
Fig. 7 PR1.2/velocity profiles comparisons K-ω SST versus K-E
PIV/RPM1800 PIV/RPM0 CFD/RPM1800 CFD/RPM0
CFD Analysis of Leakage Flow in Radial Tip Gap of Roots Blower
(c) RPM1500
(b) RPM1800
(a) RPM2000
(f) RPM2000
(h) RPM1500
(g) RPM1800
43
(d) RPM1000
(e) RPM0
(i) RPM1000
(j) RPM0
CFD
2000
PIV
1800
0
280 240 200 160 120 80 40 0
PR1.4 CFD
PIV
2000 1800 1500
0
Abs. Max Vel (m/s)
PR1.6 320 280 240 200 160 120 80 40 0
Abs. Max Vel (m/s)
Abs. Max Vel (m/s)
Fig. 8 PR1.2/vel. contours comparison b/w PIV (a–e) and CFD k-omega SST (f–j)
200 160 120 80 40 0
PR-1.2 CFD
2000 1800 1500 1000 0
Rotor RPM
Rotor RPM
Rotor RPM
PIV
300 250 200 150 100 50 0
PR1.6
CFD/RPM2000 PIV/RPM2000 50 100 150 200 250 300 350 400
PR1.6 Abs. Max Vel (m/s)
Avg. Vel. Mag (m/s)
Fig. 9 Comparison of absolute max. vel at the tip exit
300 275 250 225 200 175 150 125 100
CFD
PIV
RPM2000
Tip clearance Gap(mm) Fig. 10 Comparison of averaged vel. profile through leakage and absolute max. vel at the tip exit
the exit of the rotor is considered as a main evaluation criterion. The corresponding results will be discussed and more efficient design will further be considered for the future designs. Figure 11 is current combination of tip concepts.
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Fig. 11 Tip and cavity concepts
4.3 Rotor Tip Design Study Three concepts of Tip are being analyzed using Even-cavity and Unevencavity. Figure 12(a) is Base-type, Fig. 12(b) is (b)-type even-cavity tip, Fig. 12(c) is (c)-type uneven-cavity tip with high tip at inlet side and Fig. 12(d) is (d)-type uneven-cavity tip with high at exit side (Fig. 12). The contour comparison (Fig. 13) and mass flow rate comparison (Fig. 14(a) and (b) results show that (b)-type concept (Q1-(a)-type) has least leakage (improved by 21%) in the gap compared to other concepts (Fig. 14(b)). The cavity between the tip is working as the flow reduction in the downstream as it creates the vortices. Also, the next best tip concept is (d)-type (Q3-(c)-type) which has decreased the leakage 15% compared to (a) Base type (Q (Base Cavity)). The sudden restriction of flow after the bigger entrance of flow was able to reduce the flow at tip exit. The (c)-type (Q2-(b)-type) concept has increased the flow speed at entrance and finds wider passage at the exit tip to the downstream. The mass flow rate comparison graph clearly indicated the improved result and which will be helpful in deciding future shapes (Fig. 14(b)). (a) Base-type
(b)-type
(c)-type
Fig. 12 Computational analysis domains of tip concepts (2D)
(d)-type
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5 Conclusion and Future Scope The presented simplified 2D model of Roots blower is aimed to develop a reliable CFD setup to study complex leakage flows thoroughly. Several cases were used for validation with PIV results and analyzed. Even though the average velocity profiles for most cases are not in very good agreement, Case with PR1.6 and RPM2000 is promising. Using this case, the cavity tip concepts were analyzed, and suitable tip to improve the leakage was found. As a future work, present CFD model will be improved to mimic the PIV test set-up using improved meshing techniques such as dynamics mesh and rotating mesh. Also, CHT [4, 5] with improved mesh model will be applied to make simulation more realistic. Acknowledgements Funding for this research was received from Royal Academy of Engineering, UK and Howden, UK towards the project Smart Efficient Compression: Reliability and Energy Targets (SECRET).
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References 1. J. Vimmr, Mathematical modelling of compressible viscous fluid flow in a male rotor-housing gap of screw machines. Proc. Appl. Math. Mech. 4(1), 454–455 (2004) 2. ANSYS, Fluent theory guide 3. S. Mcdougald, B.W. Imrie, B.N. Cole, An Investigation of the Volumetric Efficiency of a Roots Blower. Purdue E-pubs (1974) 4. M. Matuzovi´c, S. Rane, B. Patel, A. Kovaˇcevi´c, Ž. Tukovi´c, Analysis of conjugate heat transfer in a roots blower and validation with infrared thermography. Int. J. Thermofluids, 100234 (2022) 5. S. Rane, A. Kovaˇcevi´c, N. Stoši´c, I.K. Smith, Bi-directional system coupling for conjugate heat transfer and variable leakage Gap CFD analysis of twin-screw compressors. IOP Conf. Ser. Mater. Sci. Eng. 1180(1), 12001 (2021) 6. S. Sun, A. Kovacevic, C. Bruecker, A. Leto, G. Singh, M. Ghavami, Numerical and experimental analysis of transient flow in roots blower. 4(1), 3 (2020) 7. B. Patel, A. Kovacevic, A. Krupa, On measuring velocity and temperature in leakage flows of oil free rotary positive displacement machines, in New Technologies, Development and Application IV (Springer International Publishing, Cham, 2021), pp. 763–773
Thermodynamic Properties of Oil Droplets Impacting on Chamber Wall in Oil-Injected Screw Compressors Di Yan, Bo Peng, and Guo Xiao
Abstract As a typical type of positive displacement compressor, screw compressors are widely used in a variety of industrial sectors with a fast-growing trend, especially boosted by the application of oil injection technology. The oil injection process inside the screw compressor is complicated and difficult to observe directly by experiment, as is the accompanying heat transfer process. Since the contact time between the oil and the gas is very short due to the rotation of the rotors, the main object of study remains the heat transfer between the droplet and the chamber wall. In order to investigate the liquid–gas two-phase flow in the compression chamber after oil injection, the Level Set Method is adopted to simulate the impacting process of oil droplet on hot wall with oil film, the influence of oil injection parameters on the heat transfer between oil droplets and wall was analyzed theoretically. The present study contributes to further understanding and accurate prediction of the heat transfer process in oil-injected screw compressors, which is important for improving the energy efficiency of screw compressors. In addition, this research is not only relevant to screw compressor, but also has universal significance for liquid injection technology. Keywords Oil-injected screw compressor · Oil injection parameters · Oil film · Droplet impact · Heat transfer
D. Yan (B) · B. Peng · G. Xiao Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering, Wuhan University of Science and Technology, Wuhan 430081, China e-mail: [email protected] D. Yan · B. Peng Key Laboratory of Metallurgical Equipment and Control Technology, Ministry of Education, Wuhan University of Science and Technology, Wuhan 430081, China G. Xiao Precision Manufacturing Institute, Wuhan University of Science and Technology, Wuhan 430081, China © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_5
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1 Introduction Screw compressors are one of the most widely used rotary compressors. The most common type of screw compressor is the oil-injected compressor, which accounts for 88% of the total. The first oil-injected screw compressor was developed in 1954 and commercialized in 1957 [1, 2]. Oil-injected machines were preferred over oilfree and water-injected machines because they could reach high pressures in a single stage, are simple in structure, easy to maintain, and were stable and reliable. Therefore, since then, oil-injected twin-screw compressors have occupied an important position in the compressor market at a very fast pace. However, with the gradual improvement of technical requirements such as energy saving and environmental protection, the performance of oil-injected screw compressors is becoming more and more demanding. The energy efficiency has become a key indicator to determine its future development [3–6]. The object of this paper is to investigate the heat transfer in the compression chamber when the oil droplets impact on the chamber wall when the compressor is working. Although there is heat transfer between the gas in the chamber and the oil droplets, it is relatively small, because the contact time between oil and gas is very short due to the rotation of rotors [7]. Therefore, the research object of this paper is mainly about the heat transfer process between the oil droplets and the chamber wall. In addition to the heat transfer between the droplets and the gas, the heat transfer of the droplets impacting on the chamber wall is an important influence factor in the oil injection cooling process of screw compressors [8]. The heat transfer characteristics during the impacting are closely related to the dynamic characteristics. Therefore, this paper carried out numerical modelling on the impacting process of oil droplets on chamber wall with oil film, analyzed the heat transfer characteristics under different impact parameters, and explored the influence of droplet diameter, droplet velocity, droplet temperature and oil film thickness on heat transfer characteristics. It helps better understanding of heat transfer during the actual working process of oil injection screw compressor.
2 Computational Model 2.1 Model Parameters and Boundary Settings A two-dimensional model was adopted for numerical simulation, as shown in Fig. 1. The calculation space is a rectangle of 6 mm × 4 mm, the working medium is gas and oil, and the surface tension coefficient is 0.04 N/m. The boundary conditions of the upper side and the left and right sides were set as open boundary, the bottom was set as constant temperature hot wall boundary and was adiabatic and non-slip, the contact angle of the wall was 60°, and the initial shape of the oil drop was spherical.
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Fig. 1 Geometric model of oil droplet impact on wall oil droplet 4mm g,v y
Oil film Wall 6mm x
2.2 Governing Equations The numerical simulation of oil droplets impacting the wall follows three fundamental laws, namely, conservation of mass, momentum and energy. In the meantime, the surface tension and the Marangoni effect between the oil droplets and the hot wall surface should be taken into account. The Level Set Method in COMSOL is used to study the impact of oil droplets on the wall, assuming a gas–liquid two-phase flow as an incompressible flow. The mass and momentum transfer can be described by the incompressible Navier–Stokes equations as follows. ρ
δu + ρ(u · ∇)u = − p∇ · I + ∇ · μ (∇u)T + ∇u + ρg + Fst δt ∇·u=0
(1) (2)
In the above equations, ρ is density, u is speed, t is time, p is the pressure, μ is viscosity. Momentum equation contains gravity ρg and the surface tension component represented by F st . Surface tension is defined by the following formula. Fst = ∇ · T = ∇ · σ I + −nnT δ
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where σ is the surface tension coefficient, I is the identity matrix, n is the interface unit normal, δ is the Dirac delta function. This function is non-zero only at the fluid interface. The energy conservation equation is δ cp P T + ρ∇ · uc p T = ∇ · (λ∇T ) δt
(4)
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where T is temperature, cp is the specific heat capacity, λ is the heat transfer coefficient. In addition, considering that the oil droplet is heated by the hot wall surface during the impact process, which leads to the change of temperature inside the droplet. The temperature at the contact point with the wall is higher, and the temperature at the center of the oil droplet is the lowest. The uneven temperature distribution will lead to the formation of temperature gradient. The temperature gradient creates a surface tension gradient on the surface of the oil drop, resulting in the Marangoni effect, which can be expressed as follows, τ=
δσ ∇T δT
(5)
2.3 Grid Independence Verification Taking the numerical model of oil droplet impact on dry wall as an example, the numerical simulation results under different mesh numbers were compared and analyzed to test the grid independence. In this case, three kinds of mesh quantities, 17,817, 31,750 and 89,886, are adopted respectively. The initial diameter of the oil droplet D0 is 1 mm, the velocity of the oil droplet v0 is 1 m/s, the initial temperature of the oil droplet T o is 313 K, and the wall temperature T w is 373 K. The spreading diameter D of the oil droplet after impacting the wall under different grid division is calculated. The results are shown in Fig. 2. It can be found that when the number of grids is 31,750 and 89,886, the variation of oil droplet spreading diameter with time is very close. However, when the grid Fig. 2 Grid independence verification
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number is 17,817, there is an obvious difference in the spread diameter of oil droplets. Therefore, the numerical model adopts the division method of the grid number of oil droplets is 31,750, which can ensure the calculation accuracy and save the calculation time and cost. All the subsequent simulation calculations of oil droplets against the wall adopt the grid number of 31,750. Therefore, the numerical model adopts the grid division method with the mesh number of 31,750, which can ensure the calculation accuracy and save the calculation time and cost. The grid number of 31,750 is adopted in all subsequent simulations of droplet impacting.
3 Oil Film Heat Transfer with Droplet Impacting on the Wall The phenomenon of oil droplet impacting the wall is a continuous process in the actual working process of oil-injected screw compressor. When oil droplets impact the dry wall surface, some of the droplets break and splash, and the residual oil droplets adhere to the wall surface. After a period of time, the oil droplet will form an oil film on the wall surface, and then the subsequent oil droplet will impact oil film on the wall. Therefore, the heat flux of the wall can be written as: q = h × Tw − T f
(6)
where h is surface convective heat transfer coefficient; T w is wall temperature; T f is the average temperature of the oil film in contact with the wall. In this paper, a numerical study is carried out to reveal the heat transfer characteristics of the droplets impacting on the chamber wall under the action of the oil film. The relationship between dynamic characteristics of oil droplets and heat transfer characteristics is analyzed, and the effects of oil film thickness, oil drop temperature, initial velocity and diameter on heat transfer are obtained, which helps to understand the actual cooling process inside oil-injected screw compressor from the oil droplet’s point of view.
3.1 The Influence of Oil Film Thickness Oil film thickness is an important parameter that influences the heat transfer characteristics when oil droplets impact on the wall. The impacting process was analyzed numerically under different thickness of oil film, among which, the initial diameter of droplet is set as 1 mm and initial temperature 313 K. The thickness of the oil film is 0.1, 0.15 and 0.2 mm, the velocity of the oil drop is 1 m/s, and the temperature of the wall and the oil film is 373 K.
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Figure 3 shows the temperature changes after the oil droplets impact the film with thicknesses of 0.1 mm, 0.15 mm and 0.2 mm, respectively. It can be seen that, in the initial stage of impact, the maximum splashing height of jet generated when the oil droplet hits the oil film of 0.2 mm; the oil film of 0.15 mm follows behind; the lowest splash height is produced on the oil film of 0.1 mm. After the impact, the oil droplet disturbs the oil film under the action of force, which is the main reason for the generation of jet. For 0.1 mm oil film, the disturbance is the largest, so the jet flow is higher. On the contrary, the disturbance for 0.2 mm film is the smallest, so the jet flow is the lowest. On the other hand, the smaller the thickness of the oil film, the larger the spreading diameter of the oil droplet. This is because when the oil droplets hit the thinner oil film, they are less affected by the surface tension of the oil film. It can also be found from the figure that the smaller the thickness of the oil film, the faster the heat transfer between the droplet and the oil film, so the faster the internal temperature of the oil droplet rises. As shown in Fig. 4, the wall heat flux generally presents similar changes under different oil film thicknesses. The smaller the oil film thickness is, the larger the wall heat flux is, and the faster the increase is, the shorter the time it takes to reach the
Fig. 3 Temperature distribution diagram of oil droplet impacting oil film with different thickness a h = 0.1 mm; b h = 0.15 mm; c h = 0.2 mm
Thermodynamic Properties of Oil Droplets Impacting on Chamber Wall … Fig. 4 Influence of oil film thickness on wall heat flux
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maximum wall heat flux is. When h is 0.1 mm, 0.15 mm and 0.2 mm respectively, the corresponding maximum wall heat flux is 111.45, 79.81 and 54.02 kW/m2 . It can be seen that the wall heat flux is closely related to the oil film thickness. The smaller the oil film thickness is, the faster the wall heat flux increases, and the easier the heat transfer between the oil droplet and the wall surface is. According to the analysis, this is because the oil droplet impacts the oil film wall with a small thickness, the viscous resistance of the oil film is small, and the disturbance of the oil droplet to the wall is large. Therefore, the heat transfer capacity between the oil droplets and the wall is large, which increases the heat flux of the wall in the impact area of the oil droplet. In addition, the smaller the thickness of the oil film, the more obvious the spreading feature of the oil droplet. The greater the pressure at the interface between the impact zone and the non-impact zone of the oil droplet spreading edge, the greater the disturbance to the wall surface, so as to improve the wall heat flux at the interface of the spread edge.
3.2 The Influence of Oil Drop Temperature The heat transfer characteristic of droplet impacting on oil film is simulated by changing the initial temperature of oil droplets. The initial temperature of the oil droplet is 293 K, 313 K and 333 K respectively, and the temperature of the wall and oil film is set to 373 K. The oil droplet with diameter of 1 mm falls down at a speed of 1 m/s to impact the oil film with a thickness of 0.1 mm. The temperature distribution during the process of oil droplets impacting the oil film at different temperatures are as Fig. 5a–c. Because the time of oil droplets reaching the maximum spreading width
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Fig. 5 Temperature distribution diagram of oil droplet impacting oil film at different temperatures. a To = 293 K; b To = 313 K; c To = 333 K
after impacting the wall at different temperatures are different, sampling time of the three figures are inconsistent. It can be seen from the simulation results that the jet splashing heights generated by the oil droplet impacting the oil film at different temperatures are very close, which indicates that the correlation between the jet height and the temperature of the oil droplet is small, it also means that the Marangoni effect caused by heat transfer has negligible influence on the jet height during the process of droplet impacting. In addition, as the temperature of the oil droplet decreases gradually, the time for the oil droplet to reach the maximum spreading diameter becomes faster, reaching the maximum spreading diameter at 0.0032 s, 0.0030 s and 0.0028 s, respectively. From the perspective of heat transfer, with the impacting process of the oil droplet, the lower the temperature of the droplet, which also means the greater the temperature difference, the faster the heat transfer in contact area with the oil film. Moreover, with the decrease of the temperature of oil droplet, the temperature variation range of the oil film is also larger, so the heat transfer ability between the oil film and the wall is also larger.
Thermodynamic Properties of Oil Droplets Impacting on Chamber Wall … Fig. 6 Influence of oil drop temperature on wall heat flux
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Figure 6 shows the change of wall heat flux with time under different oil drop temperatures. On the whole, when oil droplets with different initial temperatures impact the oil film, the wall heat flux changes in the same trend with time, showing a trend of firstly increasing and then decreasing. The higher the oil droplet temperature is, the smaller the maximum wall heat flux value is. This is because the higher temperature of the oil droplets means the smaller the temperature difference. When the oil droplet contacts with the oil film, the oil droplet in the impact center has less disturbance to the wall surface, and the wall heat flux changes less. Specifically, at the initial stage when the oil droplets contact the wall, the temperature difference between the oil droplets and the wall surface is large. With the spread of the oil droplets, the heat flux of the wall surface gradually increases until it reaches a certain peak value. The corresponding maximum heat flux is 225.88 kW/m2 , 111.45 kW/m2 and 72.05 kW/m2 respectively. After that, because the oil droplet stays on the oil film, its temperature rises, which leads to the decrease of heat transfer, and the maximum heat flux under the temperature of the three oil drops decreases to a relatively small value.
3.3 The Influence of Oil Droplet Velocity In order to study the influence of the oil droplet velocity on the heat transfer characteristics of the oil droplet impacting the wall with oil film, the oil droplets with diameter of 1 mm and temperature of 313 K impact the oil film with thickness of 0.1 mm on the wall at the velocity of 0.8 m/s, 1.0 m/s and 1.2 m/s, respectively, and the impact process was studied by numerical simulation. Where, the wall contact angle is 60°, and the oil film temperature and wall temperature are both 373 K.
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Figure 7 shows the temperature distribution after oil droplets impact the oil film with different speeds. It can be seen that when the initial velocity of the oil drop is 1.2 m/s, the splash height is the highest; when the velocity decreases to 1 m/s, the splash height decreases slightly. This is because the kinetic energy of the droplet during impact decreases and the disturbance to the oil film decreases as a result of the decreased velocity, so the splash height decreases. When the velocity decreases to 0.8 m/s, there is no obvious splash. This is because at this time, the surface tension of the oil film is slightly stronger than the inertial force, and the oil droplets spread on the surface of the oil film, so only a “crown” shaped jet is generated. In addition, the larger the velocity of oil droplets, the larger the spreading diameter of oil droplets on the oil film. With the gradual increase of the velocity of oil droplets, the time for droplets to reach the maximum spreading diameter is faster, and the maximum spreading diameter is reached at 0.0034 s, 0.0030 s and 0.0028 s respectively. Based on the above two factors, it can be concluded that the larger the velocity of the oil droplet, the faster the temperature rise at the contact area of the wall. The oil droplet with a larger initial velocity has a larger impact kinetic energy and a larger heat transfer capacity between it and the wall. Figure 8 shows the changes of heat flux on the wall after the oil droplets hit the oil film at different speeds. As can be seen from the figure, wall heat flux changes with different initial velocities of oil droplets are similar. At the initial moment of wall collision, due to the effect of the surface tension of the oil film, the spread diameter of the oil droplets is relatively small, and the heat transfer between the oil droplets and the oil film is large, while the heat transfer between the oil droplets and the wall surface is small, so the wall heat flux is also relatively small. The maximum heat flux from small to large velocity is 85.20 kW/m2 , 111.45 kW/m2 and 156.77 kW/ m2 , respectively. With the gradual increase of the spread diameter of the oil droplet, the disturbance between the oil droplet and the oil film also increases correspondingly, and the wall heat flux increases gradually. However, when the wall heat flux reaches the maximum, it gradually decreases and becomes stable. It can be seen that increasing the droplet velocity can promote the heat transfer between the oil droplet and the wall surface. Meanwhile, the larger the initial velocity of the oil droplet is, the larger the heat transfer coefficient is. Therefore, the total heat flow corresponding to the oil droplet with a higher velocity rises faster and the heat flux also rises rapidly.
3.4 The Influence of Oil Droplet Diameter The change of oil droplet diameter directly affects its contact area with the wall surface, which is also closely related to the change of heat transfer characteristics. In order to analyze the influence of oil droplet diameter on heat transfer characteristics, t simulation was carried out for the impact of 0.6 mm, 0.8 mm and 1 mm oil droplets on 0.1 mm oil film with an initial temperature of 313 K and a velocity of 1 m/s. The
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Fig. 7 Temperature distribution of oil droplet impacting oil film at different speeds. a v = 0.8 m/ s; b v = 1 m/s; c v = 1.2 m/s Fig. 8 Influence of oil drop velocity on wall heat flux
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wall contact angle was 60°, and the oil film temperature was the same as the wall temperature, both being 373 K. Figure 9 shows the temperature distribution diagram during the impact of three oil droplets with different diameters on the oil film. It can be found that the larger the initial diameter of the oil droplets is, the higher the splash height will be. There is no obvious jet flow. This is because the diameter is small and the surface tension of the oil film is stronger than the inertial force, so the oil drops spread on the surface of the oil film. In addition, the increase of the diameter also increases the maximum spreading diameter of the oil droplet, and the spreading diameter of the oil droplet with a diameter of 1 mm is the largest when it hits the oil film. The spreading diameter of 0.6 mm oil drop is the smallest after hitting the oil film. From the perspective of heat transfer, at the same time (0.0024 s), the smaller the diameter of the oil droplet, its overall temperature is more affected by the oil film and wall surface, and the smaller the diameter of the oil droplet into the oil film faster, so the internal temperature of the oil droplet rises faster. As can be seen from Fig. 10, increasing the diameter of the oil droplet significantly increases the wall heat flux, among which the maximum heat flux reached by the
Fig. 9 Temperature distribution of oil droplet impacting oil film with different droplet diameters. a Do = 0.6 mm; b Do = 0.8 mm; c Do = 1 mm
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oil droplet with diameter of 0.6 mm, 0.8 mm and 1 mm after impacting the wall is 111.45 kW/m2 , 90.45 kW/m2 and 68.03 kW/m2 , respectively. The increase in the diameter of the oil drop brings more oil into contact with the wall, and thus more heat is exchanged. The reason for this situation is that the oil droplet with a large diameter has a larger inertia and is easy to form a larger spreading area on the oil film, which promotes heat transfer between the oil film and the oil film. The temperature rise of the oil film is higher, the temperature difference between the oil film and the wall decreases, and the heat flux of the wall is smaller. In the subsequent stage, due to the gradual integration of the oil droplets into the oil film over time, the temperature difference between the oil and the wall decreases, so that the corresponding wall heat flow of the oil droplets of these three diameters gradually decreases and eventually tends to be similar.
4 Conclusions In this paper, the heat transfer characteristics of the oil droplet impacting on the oil film wall under different conditions were numerically studied by the Level Set Method. The influence of oil droplet temperature, oil droplet velocity, oil droplet diameter and oil film thickness on heat transfer during the impact process was explored, and the variation law of the droplet morphology, temperature field and wall heat flux were analyzed. Similar to the process of oil droplet impacting the dry wall surface, under different conditions, after oil droplet impacting the wall with oil film, the heat flux of the wall surface changes with time in the same trend, showing a trend of firstly increasing and then decreasing. However, the difference is that the “crown” shaped jet splashing
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motion will be generated after the oil droplet hits the oil film. The shape and size of the splashing motion will also change with the change of the impact conditions. It is found that the thinner the oil film thickness is, the higher the relative jet height is, the more obvious the jet splash is, and the greater the impact disturbance of the oil droplet on the wall oil film is. Therefore, the greater the heat transfer capacity between the oil droplet and the wall surface is, and the greater the maximum heat flux of the wall surface is. The higher the temperature of the oil droplet is, that is, the smaller the temperature difference between the oil droplet and the oil film. When the oil droplet impacts the oil film, the smaller the splash height is generated. The disturbance of oil droplets in the impact center to the oil film on the wall is relatively small, so is the maximum wall heat flux. However, when the diameter and initial velocity of the oil droplet increase, the higher the height of the jet generated after the droplet impinging on the oil film of the same thickness, the larger the spreading area on the oil film, and the larger the disturbance to the oil film. This helps to promote the heat transfer between the oil film and the wall surface, and the peak value of the wall heat flux also increases. This research provides reference for the optimization of oil injection parameters and the improvement of energy efficiency of screw compressors. Acknowledgement This reasearch is supported by National Natural Science Foundation of China (Grant No. 52375061)
References 1. B. Peng, D. Yan, Current situation and prospects of energy efficient design of screw compressors. Hydraul. Pneum. 45(11), 12 (2021) 2. N. Stosic, On heat transfer in screw compressor. Int. J. Heat Fluid Flow 51, 285–297 (2014) 3. N. Basha, A. Kovacevic, S. Rane, Numerical investigation of oil injection in screw compressors. Appl. Thermal Eng. 193, 116959 (2021) 4. X.Y. Peng, Z.W. Xing, X.J. Zhang, et al., Experimental study of oil injection and its effect on performance of twin screw compressors. Int. Compress. Eng. Conf. 1003–1010 (2000) 5. G. Ramchandran, J. Harrison, A thermodynamic chamber modelling approach for oil free and oil injected twin screw compressors. IOP Conf. Ser. Mater. Sci. Eng. 1180(1), 012002 (2021) 6. J. Xie, J. Li, K. Lian, et al., in 2016 Purdue Conferences. 23rd International Compressor Engineering Conference at Purdue. Research on Injected Effect and Heat-Transfer Characteristics of Narrow-Slit Injection Orifice Used for the Screw Compressor (2016) 7. M. De Paepe, W. Bogaert, D. Mertens, Cooling of oil injected screw compressors by oil atomisation. Appl. Thermal Eng. 25(17–18), 2764–2779 (2005) 8. G. Melanie, B. Andreas, Influence of water and oil clearance flow on the operational behavior of screw expanders. Proc. Inst. Mech. Eng. Part E J. Process Mech. Eng. 23(1), 38–46 (2016)
Experimental Investigation of the Distribution of Two-Phase Flow in Oil-Injected Twin-Screw Compressors Matthias Heselmann, Ulrich Dämgen, and Andreas Brümmer
Abstract Oil-injected twin-screw compressors are the dominating compressor type in the industry. Compressors differ, depending on the manufacturer, in the rotor profile, the lobe number combination, the rotor diameter ratios, the wrap angle, the oil injection position, the oil injection quantity, etc. Historically, they all were probably mainly designed and optimised by trial and error, e.g. by experimentally varying the oil injection quantity, the injection nozzle and its position, or by modifying the profile. However, for some years now, computational modeling has taken an increasingly large part. Although the efficiency of the compressors is satisfying, there is still a remaining potential for improvements. In order to optimise machines by simulation a detailed knowledge of the loss mechanisms due to oil in the working chambers and approaches for their calculation are required. Therefore, for this work, as a first step for developing these models a series compressors’ housing is exchanged with a transparent glass housing in order to visualise the oil during the whole working process. First approaches for calculating the hydraulic losses are proposed and analysed in combination with the measurements. Keywords Twin-screw compressor · Oil-injection · Oil distribution · Hydraulic loss · Transparent housing
Nomenclature a A e h
acceleration [.m/s2 ] area [m.2 ] specific energy [W/kg] height [m]
M. Heselmann (B) · A. Brümmer TU Dortmund University, 44227 Dortmund, Germany e-mail: [email protected] URL: https://ft.mb.tu-dortmund.de/en/ U. Dämgen BOGE KOMPRESSOREN, Otto Boge GmbH, 33739 Bielefeld, Germany © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_6
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l m˙ n n p P R t u v .vi ˙ .V w W .β .β .γ˙ .Δ .η .ϑ .∏ .τ .ρ ˙ .Φ .
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length [m] mass flow rate [kg/s] rotational speed [1/s] polytropic exponent [–] pressure [Pa] power [W] radius [m] time [s] circumferential speed [m/s] velocity [m/s] inner volume ratio [–] volume flow rate [m.3 /s] width [m] work [J] angular range [.◦ ] lead angle [rad] shear rates [1/s] difference [–] dynamic viscosity [Pas] temperature [.◦ C] pressure ratio (compressor) [–] density [kg/m.3 ] shear stress [Pa] power loss [W]
Subscript acc c e FR fric g hp imp in kin lp m MR N n o
acceleration clearance effective female rotor friction gas high pressure side impulse injection kinetic low pressure side mixture male rotor standard condition (1013.25 hPa, 273.15 K) normal direction oil
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of full scale of reading in pipe behind filter relativ related to standard volume flow rate tangential direction oil tank rotor tip circumferential direction
1 Introduction Twin-screw compressors in general consist of two helical rotors enclosed in a tight housing. In wet-running application, an auxiliary fluid (usually oil) is injected into the working chambers. This compressor type dominates the market, used for compression of air, refrigerants, or process gas in industry. The injected fluid increases the efficiency of the compressor type significantly due to sealing the gaps and dissipating the compression heat. The biggest disadvantage are the so-called hydraulic losses, caused by the oil, which causes additional friction. These losses are responsible for the reduced circumferential speeds of wet-running screw compressors compared to dry-running screw compressors [1–3]. Beside the compressor’s geometry itself the amount of injected fluid, circumferential tip speed and the fluid viscosity significantly influence the compressor operation. To consider the influence of injected fluid in calculations Kauder introduced the surge hypothesis, which describes the formation of a liquid surge in front of the rotor teeth [4]. Further research can be divided mainly into two priorities; the loss mechanisms caused by the injected fluid and the distribution of the injected fluid in the working chambers. To investigate the loss mechanisms, the individual effects on the compressor performance are isolated. According to Deipenwisch, who considers oil as auxiliary fluid, the loss mechanisms are identified as frictional, momentum and acceleration losses [5]. Frictional losses occur due to the viscous shear of the fluid. The momentum loss describes the periodic acceleration of the fluid attached to the walls, by the passing rotor surface. The acceleration loss is the acceleration of the injected fluid to the circumferential tip speed. The influence of injected water into a screw expander has been investigated by Nikolov in terms of indicator diagrams [6]. It shows the same tendencies as injected oil. The latest study chose a more overall approach to describe the hydraulic losses in terms of a torque loss coefficient [7]. The loss coefficient is determined by experiment and depends as well on the circumferential tip speed and the amount of injected fluid. In order to investigate the fluid distribution it is necessary to observe the fluid behavior within the working chambers. This is a difficult task if the geometry should not be simplified. The investigation of the oil distribution includes the oil injection
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itself, e.g. if the injected fluid atomises, the movement of the fluid on the rotor surface and housing bores and the behavior of the fluid in the gaps. These issues were first addressed by Harling, who conducted extensive experimental studies on the distribution of the injected oil in the compressor. He validated his models by means of windows in his compressor housing and found in general good agreement even if he was not able to capture some issues, e.g. bubbles in the liquid surge, or sealing of the housing gap [8]. He described the restrictions of the optical analysis and proposed further investigation with improved optical tools. With increasing computing power it becomes possible to simulate positive displacement machines like the screw machine with computational fluid dynamics. Those simulations show good agreement with experiments in shaft power and mass flow rate of gas [9]. However, the currently available grids for twin screw compressors can not capture the oil film which affects sealing the gaps [10]. As the authors in [5, 10] propose, it is desirable to validate their models with experiments. In this work a test rig is presented containing a series oil-injected screw compressor with a transparent casing. High speed recordings are used to contribute to the validation of the developed models.
2 Experimental Setup To visualise the oil within the working chambers, a series, direct-drive, oil-injected screw compressor is modified and connected to the experimental test rig outlined in Fig. 1. The modifications mainly concern the space required for high-speed recordings and the installation of measuring equipment. This means electric motor and compressor are elevated to provide more space and the distance between electric motor and compressor is increased to install a torque measuring shaft to record the shaft power. To further explain the test rig, it is divided into the fluid paths air (black), oil (brown) and water (blue). The arrows symbolise the flow direction. The air is sucked in through an intake filter. At the suction port of the compressor pressure . plp,g and temperature .ϑlp,g of the gas are measured. At the high pressure side, the pressure . php,m and temperature .ϑhp,m are measured where the index .m indicates a mixture of air and oil. The mixture is fairly separated in the oil tank and than passes an oil filter, so that the remaining oil is reduced to a minimum. Pressure measurements. ptank,g in the oil tank and behind the oil filter. p pi pe,g gives information of the status of the filter. The delivery mass flow rate is measured with a Coriolis sensor. The valve is used to control the pressure in the system. At last the air is released in the atmosphere through a sound absorber. For the oil injection circuit no oil pump is needed. The circuit starts in the oil tank and is driven by the pressure difference between the oil tank . ptank,g and the injection nozzle at the compressor . pin,o . In order to control the oil temperature in the tank ◦ .ϑtank,o to about 78. C a thermostat is implemented. For higher temperatures the oil passes a heat exchanger with an additional cooling circuit and for lower temperatures the heat exchanger is bypassed. Pressure . pin,o and temperature .ϑin,o are measured
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water tank intake filter plp,g ϑlp,g electric motor
valve
heat exchanger (water - air)
pin,o
compressor
water pump
ϑin,o
M M,n
ϑhp,m php,m
mass flow meter ptank,g
oil tank
heat exchanger thermostat
ϑtank,o
oil mist removal filter sound absorber
ppipe,g mass flow meter
valve
Fig. 1 Schematic representation of the compressor test rig Table 1 Measuring range and uncertainty of the installed measuring devices Range Uncertainty Type (Manufacturer) Parameter p
.−1-16
.ϑ
.−185-300 .
bar(g) ◦C h.−1
Mass flow rate (oil)
0–6,500 kg
Mass flow rate (gas)
0–900 kg h.−1
Torque
.±200
Rotational speed
max. 13,500 min.−1
Nm
.±1
% o.f.s. ◦C
.±1 .
(.− 40-133 .◦ C) .±0.1 % o.r. (.m˙ > 200 kg h.−1 ) .< 0.35 % o.r. (.m˙ > 643 kg h.−1 ) .±0.05 % o.f.s. –
Danfoss MBS 3000 thermocouples type T Proline Promass F300 (Endress + Hauser) Proline Promass 83F (Endress + Hauser) ETH DRVL-III-200-n-1 (ETH-messtechnik)
directly before the injection and a Coriolis sensor is implemented to measure the mass flow rate of the oil. The circuit is closed when the gas-oil mixture enters the oil tank again. The water cooling circuit is driven by a centrifugal pump with a water tank, a heat exchanger and valve to control the flow rate. Detailed information about the range, uncertainty and type of the measuring devices are given in Table 1. The essential measuring device is a high-speed camera for recording the flow pattern of the oil within the working chambers of the screw compressor. The experimental procedure is designed for steady-state conditions in terms of pressure ratio, rotational speed and temperatures.
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Table 2 Geometric data of the compressor Designation Male rotor (MR) Number of lobes 5 Rotor lead 253.2 mm Rotor profile Built-in volume ratio Shaft center distance to male rotor diameter ratio Length to male rotor diameter ratio Female to male rotor diameter ratio Clearance heights
Female rotor (FR) 6 303.84 mm Developed by BOGE 4.3 0.72 1.66 0.8 0.04-0.08 mm
2.1 Operation Point and Compressor The baseline compressor package BS-62 SLF is provided by BOGE KOMPRESSOREN Otto Boge GmbH & Co. KG. It is a direct-drive compressor stage with a nominal power of 55 kW. For the investigations planned, the electric motor is bigger than the series application motor to ensure operation even at operating points far outside the series application. The outlet is designed for discharge pressures from 9 to 10 bar(a). The profile is carefully designed with respect to a small blowhole on the high pressure side. The lobe combination is 5 + 6 and the ratio of rotor length to rotor diameter is designed for relatively big outlet opening and low deflection of the rotors under pressure [11]. Table 2 summarises some key ratios of the compressor. As already mentioned the series housing is exchanged with a glass housing. This is shown in Fig. 2 with the depicted high pressure side of the compressor. On the left hand side the stage is shown direct after assembling. The right hand side shows a flash light photo during operation at driving speed of 50 Hz, respectively 20 m s.−1 circumferential speed of male rotor at a compression end pressure of 7 bar(a).
2.2 Reference Measurements In this section the compressor with the glass housing is compared to the series compressor. Therefore the pressure ratio is kept constant at a pressure ratio .∏ ≈ 7, which is low compared to the designed inner volume ratio. Figure 3 shows the shaft power. Pe , the standard volume flow rate.V˙ N and the specific power. Pspec as a function of the rotational speed .n. The standard volume flow rate as well as the shaft power of the series machine increases nearly linearly with increasing rotational speed. While the volume flow rate of the compressor with the glass housing is slightly below the
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Pe [kW]
series housing glass housing
V˙ N [Nm3 min−1 ]
Pspec [kW min Nm−3 ]
Fig. 2 Photographs of the glass compressor after assembling and during operation at 20 m s.−1 at compression end pressure of 7 bar(a)
n [Hz]
n [Hz]
n [Hz]
Fig. 3 Measurements and uncertainties comparing series and glass compressor
series compressor, its shaft power is slightly higher. This leads to a large deviation of the specific power for low rotational speeds that decreases for higher rotational speeds. The main part responsible for the uncertainties is the mass flow measurement, since the mass flow rate for rotational speeds of 15 and 20 Hz is at the lower range of the sensor. Furthermore, it should be mentioned that there were some manufacturing issues with the glass housing. This means that the housing bores are slightly larger than that of the series housing (approx. 0.24-0.26 mm). Therefore, the profile had to be modified (crown and root circle) with the given axis distance as boundary condition. It should be noted, that the standard volume flow rate of the compressor with the glass housing is nevertheless smaller than that of the series compressor. This could indicate a changed gap situation either due to the addressed changed profile or
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due to a mis-location of the housing to the rotors. The mis-location would change the gap situation in such a way, that the housing gap in particular would become smaller on the probably less important low-pressure side and larger on the high-pressure side.
3 Modeling Hydraulic Losses The need to model hydraulic losses results from the chosen simulation itself. If the simulation covers e.g. all containing fluids (gas and oil) with all their properties (film formation, momentum exchange, inhomogeneous distribution, etc.), the compressor stage can be calculated without extra models. This is the case when multiphase flow simulations are performed with computational fluid dynamics [9, 10]. However, the requirements for the mesh used are high and the solution of the system of equations computationally intense. As a result, this method is more suitable for detailed recalculation and for visualization purposes than for performing numerous geometric variations. For these purposes, the chamber model simulation is suitable. Basic equations here are only the conservation of mass and energy. The drawback is that several assumptions have to be made and submodels have to be developed. An overview of some submodels containing models for the mass flow rate and heat transfer is given in [12]. However, the complex calculation of non-miscible multiphase content in one chamber e.g. oil and air, is not yet fully implemented. The calculation of oil-injected compressors requires three further steps compared to dry running compressors. 1. The mass flow rates through all connections (front gaps, housing gaps, inter-lobe clearance, blowhole, suction and discharge port) must take into account two-phase flow models. This takes into account the sealing of the gaps by the auxiliary fluid. 2. Some model has to be chosen to take into account the heat dissipated by the oil. 3. A model that accounts for hydraulic losses must be used to account for the adverse effects of oil injection. In the following, the experiments with the compressor with the glass housing, the high-speed recordings are used to investigate the influence of the individual loss mechanisms. The loss models are taken from [5].
3.1 Acceleration Power Loss According to Deipenwisch, one part of the hydraulic power loss occurs immediately after injection, because the majority of the oil is injected in the radial direction. Smaller portions of the oil enter the working chambers elsewhere, e.g. oil disposal ˙ acc it is assumed that: holes of the bearing seats. To estimate this power loss .Φ
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• The injected oil has no circumferential velocity (.vr el = 0). • The whole amount of injected oil is accelerated to circumferential tip speed (.vr el = u ti p ). • The sucked in air needs to be accelerated, too (entire mass flow is considered). • The mass flow is equally distributed between male and female chambers. Using the specific kinetic energy .ekin and the entire mass flow rate .m˙ m the power ˙ acc can be expressed as: loss due to acceleration .Φ .
˙ acc = m˙ m · ekin = Φ
1 4
· m˙ m · u 2M R +
1 4
· m˙ m · u 2F R
(1)
The circumferential tip speed of the rotors is represented by .u M R of the male rotor and .u F R of the female rotor, respectively. This approach presents an upper estimation of the power loss, since the entire mass must be accelerated to tip speed. Therefore, the rotors are not wetted by the oil e.g. in the root circle area [5]. For the used glass housing oil injection takes place in the radial direction at the female rotor side near the discharge port. High speed recordings are done and analysed. Figure 4 visualises some impressions from the high pressure side at rotational speed of 50 Hz. The oil is represented by the white/foamy areas in the photographs due to the reflection of the light. Areas, where the oil builds a film at the housing are transparent. Each photo is supported by an image showing the main flow directions of the oil in the form of sketched arrows. As the rotor tip is visible, this indicates that the housing gaps of both rotors are well sealed. After passing the housing gap, the oil flow is decelerated and a border line between foamy and transparent areas is formed that slightly varies with the rotation angle. This border is represented by the black line. The red dashed line represents the border of the first image and thus, in comparison to the black line, the movement of the decelerated oil border. At the male rotor the border is approximately at a constant distance behind the rotor tip. This is not identified at the female rotor. It is observed, that the injected oil influences the oil film for more than one tooth gap, as the female rotor tip passes the injection port.
3.2 Fluid Friction Power Loss Fluid friction is considered in the narrow clearances with regard to the oil, due to the significant higher viscosity compared to air. Therefore, it is assumed that: • • • •
The clearance is completely filled with oil. Couette-flow is considered. Shear stresses .τ are superposed with a pressure gradient .Δp. The cross section relevant for the friction is formed by the width of the clearance .wc and effective length of the clearance .l c (. A c = wc · l c ). • The shear rates .γ˙ are calculated from the relative velocity .vr el of the boundary and the minimum gap height .h c (.γ˙ = vr el / .h c ).
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Fig. 4 Images from the high pressure side of the compressor (at oil injection) for a tip speed of ≈ 20 m s.−1 and oil mass flow rate of .m˙ o ≈ 23 kg min.−1
.u M R
The effective length .lc of the gap represents not only the area with minimum gap height, but also the area in front of the rotor tooth where an oil surge is formed. This forms, when the sum of the oil from the oil film on the housing surface in front of the gap and the oil flowing into the gap from the leading tooth flank is greater than the amount of oil that can flow out again through the housing gap [5]. The power ˙ f ric can be calculated as: loss due to fluid friction .Φ .
˙ f ric = Ac · τ · vr el = Φ
wc ·lc ·η·u 2 hc
+
Δp·h c ·wc ·u 2
(2)
The dynamic viscosity of the oil is represented by .η. The relative velocity .vr el corresponds to the circumferential speed of the considered clearance (housing gap β·π or front gap). The identification of .lc = 180 ◦ · Rti p , where . Rti p is the crown circle radius of the considered rotor, is described by Harling according to a lubrication gap flow. It is assumed, that a liquid surge forms in an angular range of .β = 15◦ in front of the male rotor, without violating the underlying model. It is mentioned that this angle is more valid for the male rotor than for the female rotor, because of the small curvatures of the female rotor contour [8]. More recent are experimental investigations of Vasuthevan. Herein, different profile contours are turning in a cylindrical housing, which is filled with a specified amount of liquid. The angle range is determined to .β = 30◦ for a rectangular profile. However, the experiments have been done at atmospheric pressure conditions (without pressure gradient) [7].
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Fig. 5 Impressions from the female rotor side of the compressor for a male rotor tip speed of .u M R ≈ 20 m s.−1 and oil mass flow rate of .m˙ o ≈ 23 kg min.−1
The calculation of the power loss due to friction is therefore dependent on the gap width and length as geometric parameters. To take a closer look at the assumptions made, Fig. 5 shows images of the female rotor at male rotor driving speed of 50 Hz. The first image on the left hand side depicts the chamber closure from the suction port. The foamy oil at the surface of the suction port indicates that oil distributes through the whole machine. Centrifugal forces throw the oil into the suction port, where it forms a film on the wall and runs back towards the chamber until it is collected by the female rotor tooth again; the same is observed for the male rotor which is not shown. From this point, there is an oil surge forming in front of the rotor tip sketched in the images below the photographs on Fig. 5. This oil surge in general moves normal to the rotor tooth. Due to the lead of the rotor, the circumferential acceleration can be decomposed in a normal and tangential component, shown in Fig. 6. Therefore the amount of oil within the oil surge increases towards the high pressure side. This decomposition depends on the lead of the rotor, the lead angle .β respectively. The transport in the axial direction therefore increases when the rotor lead decreases, respectively the wrap angle increases if the rotor length is constant. When it reaches the front end of the housing it is strongly redirected in an almost pure circumferential direction. Observing this oil accumulation, a flow is detected where it is not clear whether it flows through the housing gap or the front gap. However, this flow does not start directly, but only with further rotation and an associated increase in pressure difference over the gap.
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Fig. 6 Accelerations acting on an oil element in front of the rotor on unwound rotor
oil element
at β
au
an
wrap angle
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β
rotor length
As before, there is nearly no air flow through the housing gap visible. Thus it can be deduced, that the housing gap is completely filled with oil as no spray or foamy parts are observed. A further clue is given by the circumferential smear sketched by the dashed lines.
3.3 Momentum Power Loss The oil films on the housing and the rotors get periodically accelerated by the passing ˙ mom . rotor tooth and rotor flanks, respectively. This causes an impulse power loss .Φ Assumptions to express this loss by an equation are: • • • •
The gap is completely filled with oil. A linear flow profile forms until the end of the gaps. The entrance velocity of the oil in the gap is negligible. The gap flow is comparable with a plane wall that is suddenly moved.
˙ mom can be determined by: Thus, the momentum power loss .Φ .
˙ mom = Φ
dWacc dt
=
1 6
·
u 2 ·ρo ·h c ·wc ·lc lc u
(3)
For the housing gap, the relative velocity equals the circumferential tip speed of the rotor .u = u M R for the male rotor and .u = u F R for the female rotor, respectively. For the front gap, the circumferential speed increases with the radius of the gap segment considered (.u = u(r )) [5]. As already pointed out, there must be a film of oil on the housing bore surfaces, as the rotor tips are clearly visible. Therefore Fig. 7 focuses on the pockets between two rotor tips, of the male rotor at circumferential speed of .u M R = 20 m s.−1 . The black rectangle is a bracket against mis-location of the housing. The black and gray stained area is a glass chipping from the housing. For the interpretation of these impressions, the images are divided into two areas. The first in the suction area or at the start of compression (on the right hand side in each case).
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Fig. 7 Impressions from the male rotor side of the compressor for a male rotor tip speed of .u M R ≈ 20 m s.−1 and oil mass flow rate of .m˙ o ≈ 23 kg min.−1
In this area there is nearly no oil surge or pressure gradient. The dashed lines in the sketches accompanying the photos illustrate a slight oil smear in the corresponding area caused by the contact of the rotor tips with the oil film at the housing. This in turn causes a momentum power loss discussed in this section. Analysing the assumptions made, the assumption that a linear flow profile is formed up to the end of the gap is doubtful, since the considered male rotor housing gap has almost no length, especially when there is no oil surge. However, the assumption made represents an upper estimation of the loss in this section. The further the rotor rotation progresses, an oil surge forms and the pressure gradient along the gap increases. As illustrated by the arrows on the left hand side of each the flow through the housing gap becomes foamy, which means that there are some air inclusions or oil spray within the gap. Therefore, the gap cannot be completely filled with oil. Vasuthevan has already shown that the presence of a surge alone excludes a complete sealing of a gap against air, but for water [13]. The pictures shown here underline this also for an oil surge. However, the surge increases the effective length of the gap, so that the assumption of a linear flow profile at the gap outlet becomes more plausible. The line shown marks the area where the oil flow calms down again, i.e. becomes transparent again. This is approximately in the middle between the rotor teeth and it can therefore be assumed that the flow velocity in the oil film is small compared to the velocity in the gap.
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b
c
d
e
f
Fig. 8 Impressions from the suction side of the compressor for a male rotor tip speed of .u M R ≈ 20 m s.−1 and oil mass flow rate of .m˙ o ≈ 23 kg min.−1
3.4 Squeezed Oil One of the main objectives of oil injection is to lubricate the rotors to allow them to roll. Since the rolling takes place in the area of the inter-lobe clearance, it is obvious that there must be oil between the rotors. Taking a closer look to the interlobe clearance from the low pressure side towards the high pressure side, there are two main issues which might cause some serious power losses (see Fig. 8). The first issue is based on the large pressure gradient along the inter-lobe clearance due to the fact that at some point a connection from the machine’s high pressure side to the low pressure side is established. The circle in Fig. 8e shows, that there is still connection to the suction port, when a lot of oil enters the chamber through the inter-lobe clearance. The second issue is not that obvious considering just the pictures or videos showing the suction side of the compressor. But remembering the injection area (Fig. 4) directly below the area seen here, the amount of oil in the vanishing chambers seems huge. By design, there is a connection from the vanishing chambers to the high-pressure port, but it is conceivable that there is too much oil in the chambers. The forced flow through the moving rotors would then cause a massive increase in pressure. The fluid would be squeezed through the existing connections (gaps and discharge port) and could increase the power consumption significantly. So there are two effects which could be responsible for the sketched flow through the inter-lobe clearance. It is observed that the flow appears suddenly. Considering the
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compression process of a screw compressor, a steady flow can be expected through the inter-lobe clearance, except when the compressor is operated outside its design point. In that case, under or over compression occurs. The suddenly appearing flow requires an under compression, because otherwise the fluid would expand in the discharge port. Considering the inner volume ratio of .vi ≈ 4.3 and a pressure ratio of .∏ ≈ 7 an under compression could be likely using a polytropic exponent in the range .n ∈ [1.1; 1.3]. However, there are vanishing chambers anyway which cause a relatively large increase in pressure at the end of the working cycle, especially when there is some oil left in the chamber. This issue could be modified either by changing the outlet or by changing the direction of injection. The latter will be investigated in the future.
4 Conclusion In this paper, hydraulic losses in a twin-screw compressor with a glass housing are investigated. For this purpose, the cast housing of a commercial machine is replaced by a glass housing so that insights into the entire machine can be achieved. Highspeed recordings of the compressor in operation are made and the plausibility of the assumptions of the existing loss models is examined and an oil film is detected on the entire housing. An oil surge is formed almost immediately at the start of compression. The oil is mainly transported through the machine normal to the rotor tooth. Particularly in the area near the discharge port, large quantities of oil occur, some of which is squeezed through the inter-lobe clearance into working chambers that are still in connection with the suction port. So far the operation point was set to a relative small pressure ratio of .∏ ≈ 7 to avoid a break down of the glass housing. In future works it is planned to set the operation point to the design point of the compressor. Different injection nozzles will be analysed with respect to the oil distribution within the compressor. The overall aim is to generate a model which accounts for the oil distribution within a machine.
References 1. L. Rinder, Schraubenverdichter (Springer-Verlag, Wien New York, 1979) 2. H. Kauder, Das Öl im Schraubenkompressor - Ein Faktor für optimale Betriebsverhältnisse. Pumpen Vakuumpumpen Kompressoren ’87 71075, pp, 38–44 (1987) 3. J.S. Fleming, C.X. You, Y. Tang, Rotor Tip Design in Oil Injected Helical Twin Screw Compressors With Respect to Viscous Friction Loss (Institution of Mechanical Engineers Conference Publications, Medical Engineering Publications Ltd., 1994), pp. 115–121 4. K. Kauder, Energiewandlung in öleingespritzten Schraubenverdichtern. Technische Mitteilungen 72(6), 404–10 (1979) 5. R. Deipenwisch, Ein Beitrag zum Einsatz von Öl als Konstruktionselement in Schraubenmaschinen. Dissertation University Dortmund (2000)
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6. A. Nikolov, A. Brümmer, Analysis of indicator diagrams of a water injected twin-shaft screwtype expander, in International Compressor Engineering Conference. Paper 2492 (2016). https://docs.lib.purdue.edu/icec/2492/ 7. H. Vasuthevan, A. Brümmer, Generic experimental investigation of hydraulic losses within twin-screw machines, in The 9th International Conference on Compressor and Refrigeration (2019) 8. H.B. Harling, Untersuchung zur Ölverteilung in Schraubenkompressoren mit Schmiermitteleinspritzung. Dissertation University Dortmund (1993) 9. S.R. Rane, A. Kovacevic, N. Stosic, CFD Analysis of oil flooded twin screw compressors, in International Compressor Engineering Conference. Paper 2392 (2016). https://docs.lib.purdue. edu/icec/2392 10. N. Basha, Numerical Analysis of Oil Injection in Twin-screw Compressors. Ph.D. thesis City, University of London (2021). https://openaccess.city.ac.uk/id/eprint/26572/ 11. BOGE KOMPRESSOREN Otto Boge GmbH & Co. KG, Brochure BOGE airend (2012). https://www.boge.com/sites/default/files/360_en-bi_201212_effilence.pdf 12. M.M. Tanveer, C.R. Bradshaw, X. Ding, D. Ziviani, Mechanistic chamber models: a review of geometry, mass flow, valve, and heat transfer sub-models. Int. J. Refrigeration 142, 111–126 (2022). https://doi.org/10.1016/j.ijrefrig.2022.06.016 13. H. Vasuthevan, A. Brümmer, Multiphase-flow simulation of a rotating rectangular profile within a cylinder in terms of hydraulic loss mechanisms. IOP Conf. Ser. Mater. Sci. Eng. 425, 012002. https://doi.org/10.1088/1757-899X/425/1/012002 (2019)
Mesh Generation for Twin-Screw Compressors by Spline-Based Parameterization Using Preconditioned Anderson Acceleration Ye Ji and Matthias Möller
Abstract Constructing high-quality structured meshes is a crucial preprocessing step in the simulation-based analysis of positive displacement machines and, in particular, rotary twin-screw compressors. Instead of creating these meshes directly, we resort to the computational paradigm of IsoGeometric Analysis (IGA) that integrates geometric modeling and numerical simulations in a unified spline-based formalism. In this paper, we propose an efficient approach for generating high-order analysissuitable parameterizations of rotary twin-screw compressor geometries from their boundary representation adopting the concept of elliptic grid generation and applying the IGA formalism. As this approach involves the solution of nonlinear systems of equations, we speed up the computation by using a block-diagonal Jacobianpreconditioned Anderson acceleration algorithm. Our numerical results demonstrate the effectiveness and efficiency of the proposed workflow. The so-created parameterizations can be easily turned into high-quality structured meshes suitable for simulation-based compressor analysis. Keywords Isogeometric analysis · Rotary twin-screw compressors · Mesh generation · Analysis-suitable parameterization
1 Introduction Rotary-type positive displacement machines (PDMs), such as twin-screw rotary compressors, are prevalent in industrial applications for producing high-pressure air and gases. These machines work by using the mechanical power of two counter-rotating rotors to suck in a fluid at the inlet, transport it through the chambers formed between Y. Ji School of Mathematical Sciences, Dalian University of Technology, 116024 Dalian, China Y. Ji (B) · M. Möller Delft Institute of Applied Mathematics, Delft University of Technology, 2628CD Delft, The Netherlands e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_7
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Fig. 1 The basic structure of a rotary twin-screw compressor (adjusted from [3])
the rotors, and compress it by reducing the volume of these chambers through rotation. The compressed fluid is then released at the exit with a higher pressure. Figure 1 shows an example of such a machine. The widespread usage of PDMs makes them prime targets for design optimization, both for economic and environmental reasons. Small improvements in performance can result in substantial energy savings and reduced carbon emissions globally, emphasizing the need for the development of energy-efficient designs. Numerical simulation plays a crucial role in the analysis and optimization of twinscrew rotary compressors [1, 2]. Establishing a highly accurate and time-dependent geometry model of the fluid passage, the volume between the two counter-rotating rotors and the casing, is essential for conducting downstream simulations and structural design optimizations. Creating a high-quality structured mesh is therefore a critical pre-processing step. However, constructing such meshes is challenging for two main reasons. Firstly, the geometry of these compressors is complex, with extreme aspect ratios and features such as tiny clearances and sharp changes in gap sizes, making it difficult to construct high-quality meshes that are suitable for analysis. Secondly, the precise representation of the geometry requires a large number of mesh nodes, particularly in areas such as the clearance and the small gap between the rotors and the casing, which presents computational challenges to the efficient construction of meshes. To address the challenges in constructing high-quality structured meshes for rotary twin-screw compressors, the current best practice is to use specialized mesh generation tools such as TwinMesh™ [4] and SCORG™ [5]. These tools are designed specifically for rotary twin-screw compressors and pre-generate a sequence of computational meshes for both the fluid and solid parts of the domain at pre-selected time instances. Whereafter, commercial simulation packages like ANSYS CFX™ [6] can be applied. It is important to note that both of these mesh generators only produce linear meshes consisting of straight-sided cells.
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Isogeometric Analysis (IGA) is an innovative computational method aimed at bridging the gap between Computer-Aided Geometric Design (CAGD) and Computer-Aided Engineering (CAE) [7]. The central idea of IGA is to use the same basis functions for both geometry representation in the design stage and finite element analysis (FEA). This approach offers several benefits, including accurate geometry modeling capabilities and simplifying the mesh generation interaction between the design and analysis models. IGA, which utilizes smooth and non-negative basis functions such as B-splines and Non-uniform Rational B-splines (NURBS), has been demonstrated to be more accurate and efficient than conventional FEA with 0 .C shape functions. As a result, IGA has gained traction in various areas, including fluid-structure interaction [8] and structural design optimization [9]. In addition, the principle of IGA has been effectively utilized in the numerical simulation of rotary PDMs [10]. Our focus on the IGA approach leads us to develop high-order B-spline parameterizations for rotary twin-screw compressors from their boundary representation in point cloud form. This paper presents an efficient approach that involves the solution of elliptic grid generation (EGG) within the IGA framework, with the added advantage of a block-diagonal Jacobian-preconditioned Anderson acceleration (AA) algorithm to speed up the computation of nonlinear systems of equations. Our results showcase the effectiveness and efficiency of this method. Moreover, the resulting parameterizations can be easily converted into high-quality structured meshes for simulation-based analysis of compressors.
2 Workflow of Our Analysis-Suitable Parameterization Method for Rotary Twin-Screw Compressors In this paper, our starting point is the input point clouds of the two rotors and the casing, i.e., .{rimale } for the male rotor, .{rifemale } for the female rotor, and .{ci } for the casing. Our goal is to develop a high-order analysis-suitable spline-based volumetric parameterization of the form x: .
Ωˆ → Ω
(ξ, η, ζ ) |→ (x, y, z) =
n2 ∑ n3 n1 ∑ ∑
Pi1 ,i2 ,i3 Ni1 ,i2 ,i3 (ξ, η, ζ ),
(1)
i 1 =0 i 2 =0 i 3 =0
where .Ωˆ is the parametric domain, .Ω is the physical domain, and . Ni1 ,i2 ,i3 (ξ, η, ζ ) are tri-variate B-spline basis functions. Due to the inherent difficulty in constructing a parameterization for twin-screw geometries with small clearances and rapidly varying gap sizes, our basic idea is to first construct individual analysis-suitable parameterizations . x(ξ, η, ζi3 ) for each planar slice .ζ = ζi3 and glue these planar slices together along the .ζ -parametric direction to complete the entire parameterization process.
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Y. Ji and M. Möller Inputs: point clouds representing two planar rotors and the casing
Parameter matching between the male and female rotors and their casing circles
Constructing base O-type parameterizations using EGG with preconditioned AA
Fitting to obtain B-spline representations for the two rotors and their casing circles
Splitting the base parameterizations to obtain clearance profile and outer parts
Parameter matching for the clearance between male rotor and female rotor
No, then next slice Finished?
Yes
Gluing the current planar slice to z-axis in physical space
stop
Refitting of the ‘west’ boundary of the clearance to its ‘east’ boundary
Constructing parameterization for the clearance and combining with outer parts
Fig. 2 Main workflow of our method
For clarity, we summarize the main workflow of our method in Fig. 2: 1. Pre-processing steps: The first step of our method involves treating the male and female rotors as two independent rotors with their respective casing circles. We partition the original casing into two segments and complete them to a full circle. The quality of the resultant parameterization is heavily influenced by the parameter matching between the rotor and its corresponding casing circle. Therefore, we employ an outer boundary regularization subroutine to assign parametric values to the input point clouds and ensure high-quality results. Figure 3 (left) illustrates the outcome of this process for the male rotor. Next, we use constrained B-spline least-squares fitting that prescribes the end-points to convert the point clouds into B-spline representations. All subsequent manipulations are performed on these B-spline representations, thereby eliminating the need to interact with the original input point clouds. 2. Constructing high-quality analysis-suitable parameterization using EGG with preconditioned AA (Sect. 3): Having established the boundary representation of the computational domains, we adopt the principle of Elliptic Grid Generation (EGG) to generate an analysis-suitable parameterization. To enhance the quality of the parameterization, we introduce a novel discretization method in the Sobolev space . H 1 . Furthermore, we present an efficient preconditioned Anderson acceleration (AA) algorithm to solve the underlying nonlinear systems. Our approach initially generates base O-type parameterizations for the individual male and female rotors and their casing circles. This step is performed only once as the
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Fig. 3 Left: parameter matching result between the male rotor and its casing circle; Right: splitting the base O-type parameterizations to obtain the profile of the clearance and the C-type parameterization for outer parts
base parameterizations can be re-utilized repeatedly. We then apply our method to construct high-quality spline-based parameterizations for the clearance at each planar slice .ζ = ζi3 . 3. Constructing analysis-suitable parameterization for the clearance at each planar slice: Once the base O-type parameterizations are generated, we split them at the CUSP-points for each slice .ζ = ζi3 to obtain two C-type parameterizations, which are then combined to form the parameterization for the outer parts of the twin-screw geometry. This process is illustrated in Fig. 3 (right). To construct highquality parameterizations for the clearance at each slice, we first use a parameter matching technique to assign reasonable parametric values to the west and east boundaries. Then, we refit the west boundary and apply the EGG parameterization technique to generate a high-quality parameterization for clearance. These steps are repeated for each slice, and the resulting parameterizations for each slice are glued together to form the final parameterization for the entire twin-screw geometry.
3 Elliptic Grid Generation Using Preconditioned Anderson Acceleration In this section, we present a new discretization for EGG in the Sobolev space . H 1 . In addition, we introduce a novel preconditioned Anderson acceleration framework to increase the efficiency of solving the nonlinear systems involved.
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3.1 Elliptic Grid Generation (EGG) and Its . H 2 Discretization The fundamental idea of EGG is to find a harmonic mapping . x : Ωˆ → Ω through the solution of the following Laplace equations { Δξ(x, y) = 0 ˆ . (2) s.t. x −1 |∂Ω = ∂ Ω. Δη(x, y) = 0 Let .SΞp,q,H denote the spline space spanned by the bivariate B-spline bases of ξ ,H
degree . p and .q with knot vectors .Ξ and .H, respectively, and .(S p,q )0 = {Ni ∈ ξ ,H S p,q : Ni |∂ Ωˆ = 0} be those vanishing on .∂Ω. The variational principle leads to the following equivalent form of the nonlinear system (2) {∫ ~ dΩˆ = 0, N Lx ξ ,H 0 ∫Ωˆ .∀Ni ∈ (S p,q ) : (3) s.t. x|∂ Ωˆ = ∂Ω, ~ ˆ Ωˆ N Ly dΩ = 0, ξ ,H
where .N is the collection of B-spline basis functions in .(S p,q )0 , and ~= L
.
L , xξ · xξ + xη · xη
(4)
is the scaled version of the differential operator [11] L = (x η · x η )
.
∂2 ∂2 ∂2 + (x − 2(x · x ) · x ) . ξ η ξ ξ ∂ξ 2 ∂ξ ∂η ∂η2
(5)
3.2 Discretization in Sobolev Space . H 1 Figure 4a shows a base O-type parameterization of the female rotor. The color map shows the value of the scaled Jacobian, with higher values indicating better orthogonality. As seen, the orthogonality is poor near the rotor. To enhance the parameterization quality without increasing the number of control points, we introduce the following discretization in the Sobolev space . H 1 instead of . H 2 {∫ ∇ N · ∇ x ξ dΩˆ = 0, ξ ,H 0 ∫Ωˆ x .∀Ni ∈ (S p,q ) : (6) s.t. x|∂ Ωˆ = ∂Ω. ˆ Ωˆ ∇ x N · ∇ x η dΩ = 0, Figure 4b shows the parameterization of the female rotor from solving the system (6). It is evident that the parameterization quality has been significantly improved in terms of orthogonality.
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(a) Discretization in H 2 space
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(b) Discretization in H 1 space
Fig. 4 Base O-type parameterizations for the female rotor constructed by discretizing the differential Eq. (2) in the Sobolev spaces . H 2 and . H 1
3.3 Anderson Acceleration with Dynamic Preconditioning Strategy Problems (3) and (6) both resolve into a nonlinear system of the form F (x) = 0, x ∈ Rn , F : Rn → Rn .
.
(7)
Newton-type methods are often used to solve the above nonlinear system [12]. However, these solvers require calculation and updating of the Jacobian matrix in each iteration, which become computationally expensive for large-scale problems. To this end, we adopt a preconditioned Anderson acceleration (AA) algorithm to improve the numerical stability and convergence speed [13]. Specifically, we define a preconditioned fixed-point iteration scheme using a non-singular matrix, .Mk , called the preconditioner at iteration .k: x
. k+1
= xk − M−1 k F (xk ).
(8)
Here, the non-singular matrix .Mk is referred to as the nonlinear preconditioner. To strike a balance between convergence speed and computational efficiency, we use the diagonal blocks of the Jacobian matrix . jac(F k ) as the preconditioner [
] ∂Px,(k) F x 0 .Mk = diag Block ( jac(F k )) = , 0 ∂P y,(k) F y
(9)
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where .P x,(k) and .P y,(k) represent the .x- and . y-components of the control points .P at the .k-th iteration, respectively, and .F x and .F y denote the first and second groups of the nonlinear system in (3) or (6). Different from Newton-type and gradient-based solvers, the iteration of AA is a linear combination of several previous iterates. This enables us to avoid frequent updates of .Mk , which is computationally expensive. To accelerate our preconditioned AA solver, we update the preconditioners every . Nupdate steps instead of at each iteration. In our parameterization problems, our preconditioned AA scheme typically converges within .1 to .2 updates of the preconditioner.
4 Analysis-Suitable Parameterizations for Planar Slices With the base O-type parameterizations for both the male and female rotors obtained, we proceed to generate the topology information of the parameterization. For each slice.ζ = ζi3 , we split the base O-type parameterization for the male rotor by inserting the parameter values corresponding to the CUSP-points until their multiplicities reach . p + 1. This results in the profile of the clearance and two C-type parameterization for the outer parts, as illustrated in Fig. 3 (right). We have now obtained the profile of the clearance for the planar slice .ζ = ζi3 . However, the parameter matching between the west boundary and the east boundary is poor, resulting in skewed isolines or even inverted elements due to the tensorproduct structure of B-spline surfaces, as shown in Fig. 5a. To address this issue, we need to ensure that the same parameter values are assigned to both sides, especially near the tiny gaps. The basic idea is to keep the east boundary of the current slice fixed and allow the parameter velocity to vary along the west boundary. To begin, we perform a uniform
Fig. 5 a Poor boundary contour parameterization can result in skewed isolines; b our parameter mathing process; c improved parameterization result
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Fig. 6 Evolution of the planar parameterizations upon rotation of the rotors
sampling of the east boundary of the current slice and identify the closest points on the west boundary. Since the parameter values for points near small gaps are crucial, we designate point pairs with a distance less than a given tolerance .εdist (which we set to 1.0 in our experiments) as candidate point pairs. We then find the local minimum of the distances between the candidate point pairs, satisfying the condition .dist i−1 ≤ dist i ≤ dist i+1 . However, to improve the accuracy of parameter matching, we also take into account the tangent vectors of the candidate point pairs. Specifically, we calculate the normalized tangent vectors on each candidate point pair, and mark pairs of points with .tangi < εtang < tangi+1 or .tangi > εtang > tangi+1 as matching pairs. To enhance robustness, we disallow adjacent nodes from being the same. Figure 5b provides an illustration of our parameter matching process. The resulting parameterizations before and after the parameter matching process are displayed in Fig. 5c, where it is evident that our method greatly enhances the quality of the parameterization. With the boundary curves of the clearance in B-splines form, we proceed to generate an analysis-suitable parameterization using the method introduced in Sect. 3. The evolution of the constructed parameterizations are shown in Fig. 6. After constructing parameterizations for all the slices, the volumetric parameterization is achieved by connecting them along the .z-direction within the physical space. Figure 7 illustrates a portion of the volumetric parameterization, obtained by stacking a substantial number of planar slices in the .ζ -direction.
5 Conclusion and Future Work In this paper, we present a practical and efficient method for constructing analysissuitable spline-based parameterizations for rotary twin-screw compressors. In particular, we adopt a block-diagonal Jacobian-preconditioned Anderson acceleration scheme to balance convergence speed and computational overhead. The proposed AA iteration scheme eliminates the need for frequent updates of computationally
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Fig. 7 Resulting volumetric parameterization
expensive preconditioners, enhancing its computational efficiency. Our dynamic preconditioning strategy updates the preconditioners every few steps rather than every iteration, allowing our scheme to typically converge within one or two such updates. However, note that the resulting volumetric parameterization may not be bijective if the distance between two slices .ζ = ζi and .ζ = ζi+1 is too large. Constructing genuinely three-dimensional analysis-suitable spline-based parameterizations for rotary twin-screw compressors is one of our ongoing works. Acknowledgements Ye Ji was partially supported by the China Scholarship Council (No. 202106060082) for visiting Delft University of Technology.
References 1. N. Stosic, I. Smith, A. Kovacevic, Screw Compressors: Mathematical Modelling and Performance Calculation (Springer Science & Business Media, 2005) 2. A. Kovacevic, N. Stosic, I. Smith, Screw Compressors: Three Dimensional Computational Fluid Dynamics and Solid Fluid Interaction, vol. 46. (Springer Science & Business Media, 2007) 3. Gas Compressors Ltd (GCL): Oil Flooded Screw Compressor. https://www.gascompressors. co.uk/technologies/oil-flooded-screw-compressor/ 4. TwinMesh: reliable CFD analysis of rotary positive displacement machines. https://www. twinmesh.com 5. SCORG: screw compressor rotor grid generator. http://pdmanalysis.co.uk/scorg 6. ANSYS CFX: turbomachinery CFD software. https://www.ansys.com/products/fluids/ansyscfx
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7. T.J. Hughes, J.A. Cottrell, Y. Bazilevs, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput. Methods Appl. Mech. Eng. 194(39–41), 4135– 4195 (2005) 8. Y. Bazilevs, V.M. Calo, T.J. Hughes, Isogeometric fluid-structure interaction: theory, algorithms, and computations. Comput. Mech. 43, 3–37 (2008) 9. W.A. Wall, M.A. Frenzel, C. Cyron, Isogeometric structural shape optimization. Comput. Methods Appl. Mech. Eng. 197(33–40), 2976–2988 (2008) 10. M. Möller, J. Hinz, Isogeometric analysis framework for the numerical simulation of rotary screw machines. I. General concept and early applications. IOP Conf. Ser. Mater. Sci. Eng. 425(1), 012032 (2018). IOP Publishing 11. J. Hinz, M. Möller, C. Vuik, Spline-based parameterization techniques for twin-screw machine geometries. IOP Conf. Ser. Mater. Sci. Eng. 425(1), 012030 (2018). IOP Publishing 12. J. Hinz, M. Möller, C. Vuik, Elliptic grid generation techniques in the framework of isogeometric analysis applications. Comput. Aided Geometric Des. 65, 48–75 (2018) 13. Y. Ji, K. Chen, M. Möller, C. Vuik, On an improved PDE-based elliptic parameterization method for isogeometric analysis using preconditioned Anderson acceleration. Comput. Aided Geometric Des. 102191 (2023)
Orthogonal Mesh Generation of Screw Compressors for Capturing Tip Leakage Flows Samuel Ebenezer James, Karan H. Baliga, and Peter R. Eiseman
Abstract Structured meshes have been the industry standard for CFD simulations of positive displacement rotors for the last few years. There are many players in the market who offer structured meshes. However, current techniques have a few limitations. There is always a challenge in geometry capturing, mesh quality and the physics that needs to be resolved. The lack of a conformal meshing solution which offers robustness in geometry capturing and orthogonal tip gap resolution often poses a hurdle in obtaining accurate CFD predictions. This paper proposes a novel, automated, multi-block structured meshing technique for positive displacement machines. This approach proposes a structured conformal mesh which creates an orthogonal mesh around the tip gaps and accurately captures the rotor and housing as a single domain mesh. The mesh is also created orthogonal to the helical angle of the rotors, ensuring flow-alignment of the meshes up to a clearance of 4 microns, consequently reducing diffusion errors and giving better results of the tip leakage flows. This new technique will enable users to obtain far more accurate CFD results on positive displacement machines. Keywords Screw compressor · Normal rack grid generation · Orthogonal mesh · Tip leakage flow · Single domain mesh
S. E. James (B) · K. H. Baliga Program Development Company LLC, Bangalore 560037, India e-mail: [email protected] URL: https://www.gridpro.com/ K. H. Baliga e-mail: [email protected] P. R. Eiseman Program Development Company, 10601 New York, USA © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_8
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1 Introduction Over 200 million rotary compressors are manufactured annually in the domestic refrigeration and air conditioning industry. Increasing efficiency is the primary area of research and development in positive displacement machines. In a helical screw compressor, the presence of a clearance gap influences the efficiency and reliability of the screw compressor. The size of the clearance, the shape of the rotors, and the operating condition of the screw compressor influence the leakage flows through the tip gaps. Internal leakage flows in these clearances contribute to a 2–3% reduction in volumetric efficiency compared to an ideal scenario with no leakage. Since Computational Fluid Dynamic studies are commonly used while designing these machines, it becomes paramount to accurately discretise the fluid domain, especially regions of the internal leakage paths. Significantly less research has been conducted into accurately meshing the regions where these flow losses dominate. The popular approaches generate 3D meshes of the screw compressor by merging grids that are generated in a plane transverse to the axis of the rotors of the screw compressor. This prevents any possibility of smoothing the grids along the third dimension, ultimately leading to the development of a grid not aligned with the flow direction. This is especially so at the clearance gaps, where the CFD solution is susceptible to errors arising from numerical diffusion. This paper describes the development of an automated blocking technique for screw compressors using GridPro—an automatic, object-oriented multi-block hexahedral element grid generator. The grids generated are highly orthogonal to the rotor surfaces, at all regions of the mesh, especially at the tip clearances, which helps in accurately capturing the tip leakage paths.
1.1 GridPro’s Topology Paradigm At the heart of GridPro’s technology is its topology paradigm. With the help of this unique technology, a multi-block structured grid can be generated using a set of loosely defined corners around the domain to be meshed. This process defines a coarse, unstructured, hexahedral wireframe. Unlike the frames of other grid generation systems, the pattern-defining points do not need to be precisely positioned. The topology paradigm offers a high level of flexibility to create blocks, so much so that a user can create hundreds of blocks within a span of a few seconds. The topology based approach aids in the automation process of any given design space as long as it is topologically identical. GridPro with the aid of its DBC technology repositions the wireframe on the bounding surfaces to create a smooth mesh. Another advantage of the topology based approach is that it removes the user inten-
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Fig. 1 The input blocking for topologically identical geometries
Fig. 2 The output mesh for topologically identical geometries from Fig. 1
sive manual positioning and shaping of blocks by accurately positioning the block vertices around the geometry to be meshed (Figs. 1 and 2).
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1.2 Dynamic Boundary Conforming (DBC) Technology The input topology serves as a initial starting for the powerful proprietary Dynamic Boundary Conforming (DBC) technology, which automatically morphs the topology wireframe grid into conformity with the bounding geometry, generating a smooth, orthogonal, curvature clustered and evenly distributed multi-block grid. The process is driven by the algorithms that ensure the highest possible grid quality level available under the user’s constraints. This quality level is difficult, if not impossible, to attain by traditional methods of multiblock grid generation. The DBC technology projects the block faces onto the respective bounding surfaces, untangles them and uses an elliptic smoothing over the blocks created to produce a high quality grid. DBC technology enables high-quality design optimisation to proceed automatically. As users make changes in region boundaries to achieve the desired physical attributes, GridPro dynamically tracks the evolving boundary shapes (Fig. 3). With this technology, users are not required to generate a surface grid or build such items as block edges and their pointwise distributions. The user gets both surface and volume grids simultaneously and automatically. This approach to grid generation removes the labour-intensiveness of block creation and its dependence upon user judgement. GridPro’s unique methodology significantly increases productivity. Its mathematical engine relieves much of the tedious work of constructing the various parts of the grid and then correctly assembling them into a whole mesh.
2 Conformal Interface Approach GridPro only allows for grid generation of a single domain, conformal mesh. A conformal meshing approach has several key advantages over a non-conformal approach, as explained in [1]. A conformal grid refers to one where the male and female rotors have one-to-one connectivity at the interface between them. A conformal grid prevents any instabilities or inaccuracies from arising due to not having one-to-one connectivity in the grid. It also restates doubts about the conservativeness of the flux balance across the interface of the two rotors. A conformal grid is best suited for multiphase simulations, such as in liquid injection machines. A non-conformal grid limits the use of different types of solvers, as not all of them are suited to be used in the presence of a highly deforming, sliding interface, such as one present in a non-conformal, helical screw compressor grid.
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Fig. 3 The grids after 30, 40 and 50 sweeps, showing the movement of the blocks
3 Existing Approach—Transverse Plane Grid Generation The Transverse plane grid generation method is the most commonly used technique in generating the grid for many positive displacement machines. In GridPro we use a similar approach but the strategy changes as it is a topology-based grid generator. Commercially available tools on the market use Algebraic Grid Generation technologies, where the nodes are distributed on the rotors using boundary distribution methods [2]. GridPro, on the other hand, being a topology-based grid generator, uses a template—a loosely distributed set of corners around the 2D geometry (Fig. 4). The grid generator automatically projects and distributes the points for the initial 2D section. The meshes are generated for different sections along the z direction, using the nodal location of the previous mesh as a reference. These 2D grids, each located
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Fig. 4 The 2D wireframe template for a twin screw geometry
at different z locations, are then merged to form the 3D grid. In the process of mesh generation, users are provided options to keep a close monitoring of the mesh quality. GridPro can take either a 2D or 3D geometry as input. In either option, the user must input the total length and sweep angles of the rotors. Whether the user chooses a Rotor O-Grid approach or the Rotor-Housing O-Grid approach, the cusp points in the housing pose a challenge since the rotors move very close to the housing. As the two O-Grids meet at the cusp, special treatment and care are required to accurately discretise that region, which would otherwise lead to bad-quality cells, eventually hampering the accuracy of the solution. In GridPro we use a micron level filleted approach to alleviate this issue, which is discussed below.
3.1 Rounding the Housing Cusp In this approach, the housing cusp points are slightly rounded with a circular surface, which can be analytically created in GridPro. The circle can have a very small radius, such as 0.05 mm, which makes a very minimal impact on the result of the CFD simulation. With this, we can have a topology where the corners are distributed along the circle. This topology differs from the double O-Grid topology usually enforced by other software. It would include additional corners near the two circles (at the top and bottom cusp, respectively). Once again, given that GridPro is a topology-based mesh generation tool, the corners around the cusp need not be accurately placed. The smoother will automatically move the blocks around the circle to achieve the best possible fit (Fig. 5).
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Fig. 5 The rounding at the cusp. Left—zoomed out, right—zoomed in
Fig. 6 Warped cells along the rotor surface
4 3D Smoothing of the Transverse Grid The transverse grid, generated in the previous section, develops issues once merged along the third dimension. This happens because there is no smoothing applied to the grid after merging. This leads to distortion and in accurate capturing of the rotors, mainly along the high curvature regions (Fig. 6). A solution to this issue is to smooth the 3D grid using algorithms. The following sections will explain how this is implemented in GridPro.
4.1 3D Smoothing Results The 3D topology can be created from the 2D topologies. This method of 3D smoothing is only applicable if the 3D rotor and housing surfaces are available. The smoother is then run on the 3D topology which is created. As seen in the images, the warpage of faces along the regions of small radii is eliminated (Fig. 7).
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Fig. 7 Images of the merged grid before (left) and after (right) 3D smoothing
5 Rotor Helix Normal Grid Generation Method In the transverse plane grid generation method, the 2D meshes are created in planes perpendicular to the rotor axes. Since the flow direction—both the main flow and leakage flow paths, are usually aligned along the helix line [3], the transverse plane method does not generally give an orthogonal grid. This is especially detrimental at the tip gaps of the rotors, where it is essential to get an orthogonal grid to accurately predict tip leakage flows. Even with 3D smoothing of the blocks, the baseline topology is not best suited to give grids in which the cells are aligned to the flow direction. To get a grid in which the cells align themselves to the flow direction, and give a better grid orthogonal to the rotors at every location, entails changing the block structure used to generate the grid. We need to have blocks aligned to the rotor’s helix line while simultaneously being normal to the two ends on either side of the grid. GridPro has developed an algorithm to generate this topology from the 3D transverse plane topology.
5.1 Methodology The algorithm which has been developed works on this basic general methodology. Let us take a 2D quad corner sheet to explain this better. If we have a 2D quad cell aligned along the x–y plane, the algorithm creates a face centre at the centroid of the quad cell. These are then linked with the nodes of the faces, which creates triangles. The original links are then removed, to get a quad topology (Fig. 8).
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Fig. 8 The input to the algorithm (left) and the criss-cross output (right). The white nodes represent the newly created nodes
5.1.1
Topology and Grid
The algorithm takes in the 3D topology generated using the transverse plane approach as input and, using the quad conversion mentioned above, creates a valid topology in which the blocks are in the direction of the rotor sweep. The block structure to be created could have been easily implemented for a single rotor with a cylindrical housing, however, it gets complicated for a twin rotor system where the housing cusp is a straight feature. Special treatment is required for the cusp of the housing, without which it would lead to collapsed cells. A topology has to be generated which remains orthogonal to both the rotor and the housing of the screw compressor. A special treatment of blocks is carried out at the two rotor end planes and at the housing cusps, to generate orthogonal cells there. Since the blocks running along the helix line of the rotors, would not be aligned orthogonally to the to the two end planes of the rotors, a special block structure needs to be generated here. Additionally, because of the sharp cusp at the housing, further changes to the block structure is required all along the cusp line as well (Fig. 9). A modified block structure is created at the end planes as seen in Fig. 10. The block edges at the end plane are orthogonal to it, and the block faces opposite to it travel diagonally along the rotor helix line, maintaining orthogonality with the rotor surface too. This is how the block structure ensures that the cells maintain orthogonality at the end planes, which is perpendicular to the direction of the rotor axis, while also ensuring that the subsequent blocks propagate diagonally along the rotor helix. The preview depicts the cell structure before smoothing, and the orthogonality of the cells at the end plane is clearly seen.
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Fig. 9 A 2D sheet of nodes representative of the special treatment carried out along the cusp line (left) and on the boundary at the end planes (right)
Fig. 10 The topology (left) and preview of the mesh (right) at the end plane, showing the block structure at the end plane
Figure 11 shows the block structure and mesh preview at the cusp. Here, it can be seen that the blocks at the cusp maintain orthogonality all along the cusp line, which starts at one end plane and terminates at the other. The blocks then transform into the diagonal structure and start propagating along the rotor helix line a short distance away from the cusp line. The smoother ensures that the best possible mesh is generated with orthogonality at all surfaces being the primary concern while smoothing. Once the grid is generated, we can see that grid sheets travel along the helix line. Other sheets run perpendicular to these sheets, which is the ideal way the grid sheets need to be aligned to generate an excellent orthogonal grid (Figs. 12, 13 and 14).
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Fig. 11 The topology (left) and preview of the mesh (right) at cusp, showing the gradual progression into the diagonal topology away from the cusp
Fig. 12 The grid and blocks at the end plane and cusp
5.2 Suitability of the Mesh for Different Solvers GridPro has a large number of mesh output formats to which the generated mesh can be exported into. GridPro has users carrying out CFD simulations of screw compressor using its meshes on CFX and other solvers, however it is still in the testing phase.
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Fig. 13 The grid sheet which travels perpendicular to both rotors and straightens out at the cusp
Fig. 14 The generated grid. One sheet (white) travels along the sweep of the rotor, while the other (pink) travels perpendicular to it
References 1. S. Rane, A. Kovacevic, Algebraic generation of single domain computational grid for twin screw machines. Part I. Implementation. Adv. Eng. Softw. 107, 38–50 (2017). ISSN: 0965-9978. https:// doi.org/10.1016/j.advengsoft.2017.02.003 2. A. Kovacevic, Boundary adaptation in grid generation for CFD analysis of screw compressors. Int. J. Numer. Methods Eng. 64 (2005) 3. L. Yang, A. Kovacevic, M. Read, Normal Rack Grid Generation Method for Screw Machines with Large Helix Angles, IOP Conference Series: Materials Science and Engineering, vol. 604. https://doi.org/10.1088/1757-899X/604/1/012011
Two Way Coupling of CFD Conjugate Heat Transfer Simulation with Solid Thermal Expansion in a Twin Screw Compressor Hui Ding, Haiyang Gao, and Xiaonong Meng
Abstract Gas temperature changes due to compression can cause non-uniform thermal expansion in the compressor hardware, potentially impacting both its performance and lifespan. This paper proposes a fully-coupled simulation approach that incorporates gas compression, conjugate heat transfer (CHT), and solid thermal expansion. We will describe in detail the complete procedure for solving a twoway coupled computational fluid dynamics (CFD), conjugate heat transfer, and solid thermal expansion, including the technical challenges and proposed solutions. This approach has been applied to a twin screw compressor case. The simulation results indicate that the solid thermal expansion has significant impact on the performance of the compressor. This paper will also demonstrate that the approaches used are robust, fast, user friendly, making them readily applicable to industrial compressor systems. Keywords Twin screw compressor · Conjugated heat transfer · Thermal expansion · FSI · CFD
1 Introduction 1.1 Compressor Conjugate Heat Transfer and Thermal Expansion The temperature of a diatomic ideal gas can increase 32% when compressed to half in an adiabatic process. Gas temperature can raise further due to irreversible processes such as friction and mixing. These temperature changes can affect the solid components of the compressor and cause thermal expansion and stress, leading to excessive abrasion, changes in leakage gaps, and thermal-induced fatigue. Maintaining a small gap size in PD compressors is essential to separate gas pockets of high and low H. Ding (B) · H. Gao · X. Meng Simerics, Inc., Bellevue, WA 98004, USA e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_9
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pressure, and altering these gaps can have a significant effect on the compressor’s performance. Therefore, predicting and analyzing gap size changes due to thermal effects is crucial for compressor design and improvement. However, most CFD studies of twin screw compressors only consider the fluid part of the compressor due to technical difficulties and simulation costs. Solid thermal effects are often ignored or completely decoupled from the CFD simulation. Generating a proper moving mesh for the moving/deforming rotor fluid volume is a challenge. Due to issue in handling small gaps, the high cost of remeshing, and the loss of accuracy during result interpolation, general purpose moving mesh solutions which generate a totally new mesh at each rotor position are rarely used for PD compressor. Hence, conventional techniques involving the deformation of an existing mesh are generally preferred. Because of really complex geometry, the moving mesh for twin screw is often generated using 3rd party special software for a set of predetermined rotor positions. Besides complex geometry, another important issue is the cost of coupling slow heat propagation in solids with the very fast movement of the fluid machine. Ding et al. [1] have demonstrated that a simple direct coupling of conjugate heat transfer for twin screw is not practical. Coupling solid thermal expansion with geometry change in the rotor fluid volume requires deforming the fluid mesh based on local thermal expansion predictions. This is very difficult when using pre-created third-party rotor meshes. Literature search shows that only a few studies have considered CHT with solids in their simulations. Rowinski et al. [2] simulated a twin screw expander coupled with solid fluid heat transfer using a “semi-transient” method. Ding et al. [1] used “Mixed Time Scale” method simulated CHT of a twin screw compressor. Thermal expansion of the rotors was also solved in this study, but not coupled with fluid volume geometry change. The current study is a continuation of the work done by Ding et al. [1] and involves coupling solid thermal expansion with fluid simulation to alter the fluid domain’s geometry based on solid thermal expansion results. The following section will outline the simulation strategy, and the necessary capabilities utilized in the approach.
1.2 Proposed Simulation Approach with Required Capabilities/Tools The proposed approach consists of 3 independent simulations: fluid simulation, solid heat transfer simulation, and solid thermal expansion simulation as shown in a flow chart displayed in Fig. 1. These simulations are run separately due to significant differences in their time scales. The approach involves two nested iteration loops: the CHT inner loop and the thermal expansion outer loop. The solid temperature field and thermal expansion are initialized before simulation iteration to provide boundary conditions and an initial mesh for fluid simulation. During Simulation 1,
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Fig. 1 Flow chart of proposed procedure
the fluid domain mesh is created and deformed based on available thermal expansion information, and transient simulation of fluid flow and heat transfer is solved for a repeating period. Heat exchange data between fluid and solid are collected during this simulation. Simulation 2 runs solid heat transfer simulation using the collected data as boundary conditions. If heat exchange balance is not achieved, the procedure returns to Simulation 1 with updated solid surface temperature. Otherwise, the conjugate heat transfer loop ends, and Simulation 3 solves solid thermal expansion based on the temperature field obtained in Simulation 2. Then, the convergence of thermal expansion is checked, and if not converged, the outer loop starts again. The collected thermal expansion data are used for mesh adjustment in fluid simulation. To overcome the time scale issue, solid heat transfer simulation runs in steady state. This Mixed Time Scale Approach has been successfully used in many single phase and multiphase CHT simulations with high speed fluid machineries such as piston liquid cooling [3], e-motor liquid cooling [4], e-compressor CHT [5], and twin screw CHT [1]. The approach utilizes multiple innovative methods and tools, implemented in the commercial software Simerics-MP + . Rotor Mesher: This study utilized the General Gear Template, originally designed for gear set meshes in gearboxes, to generate the twin screw rotor mesh. The template features: (a) modeling of spur/helical, internal/external gears, and more than two gears connected together, as shown in Fig. 2 for a helical planetary gear set mesh; (b) on-the-fly mesh generation in any specified rotation angle during simulation; (c) generation of a viscous layer mesh on gear surface which can benefit CHT simulation; (d) generation of a fluid rotor mesh representing a deformed rotor solid using localized geometry deformation information, which is critical for this study; (e) gear overlap protection by enforcing a minimum gap between solids. The General Gear Template has been previously tested in many gear cases [6] and a few twin screw cases [7]. CHT Data Exchanger: The exchange of heat transfer data between the fluid simulation and the solid heat transfer simulation is facilitated by a Data Exchanger Module, which is integrated into the same solver. This module automatically gathers the
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Fig. 2 Mesh of a helical planetary gear set
necessary heat exchange data, calculates appropriate time averages with the specified interval at the fluid–solid interface, and maps the data to the corresponding coupled solid or fluid simulation on different meshes. The Data Exchanger Module has been employed in various CHT coupling simulations mentioned earlier [3–5]. Solid Thermal Expansion Solver: This study uses a recently developed FEA capability to simulate the thermal stress and expansion of the solid. This FEA solver is based on classical finite element technology and offers all the advantages of a finite element solver, with the added flexibility to handle complex geometries. The solver works on general polyhedron meshes, which can be generated using Simerics-MP + proprietary binary tree meshing technique. It allows a mixture of hexahedron, tetrahedron, pyramid, prism, and polyhedron cell types, resulting in a hex-dominant mesh that offers superior speed, robustness, and accuracy. As the FEA solver can operate on the same binary tree mesh utilized in the current CFD solver for fluid flow and solid heat transfer simulations, coupling the simulations together becomes more convenient for the users.
1.3 Governing Equations and Physics Models The CFD package, Simerics-MP + , used in this study solves conservation equations of mass, momentum, and energy of a compressible fluid using a finite volume approach. The standard two-equation κε model with wall function is used to account for turbulence. Those equations combine with fluid properties to form a closed system. In the solver, each of the fluid properties can be a function of local pressure and temperature, and can be prescribed as an analytical formula or in a table format. Heat conduction in solids is also solved using a similar energy conservation equation. Please refer to Ding et al. [1] for more details.
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Thermal Stress: The linear thermal stress problem can be solved by minimizing the potential energy of the system, I (u) =
1 2
∇ s u : D(∇ s u − ε0 )d −
u : bd −
u : td
(1)
u = Na (ξ )u a
(2)
ε0 = α(T − T0 )
(3)
In the above equations, u is the displacement, which can be approximated by shape functions and displacements at cell nodes, ε0 is the thermal strain, it is caused by temperature change from stress-free temperature.
2 Twin Screw Compressor Test Case The twin screw compressor studied in this research is an oil-free compressor with a 3/5 lobe arrangement [8]. It operates at male rotor speeds varying from 6000 to 14,000 rpm, with a male rotor diameter of 127.45 mm and a female rotor diameter of 120.02 mm. The center distance between the two rotors is 93.00 mm, and the rotors’ length to diameter ratio is 1.6, with a male rotor wrap angle of 285.0 deg. Three independent models are created for three separate simulations: a fluid model, a solid heat transfer model, and a solid thermal expansion model. These models are coupled iteratively as described above to solve CHT and corresponding thermal expansion.
2.1 Fluid Model The rotor section of the twin screw in the fluid model (Fig. 3) is meshed using Simerics-MP + General Gear Template. A 20-micron thick, two-layer boundary layer mesh is generated on the male and female rotor surfaces to capture CHT effects more accurately. The inlet and outlet ports of the fluid volumes are meshed using the Simerics binary tree unstructured mesher, and all fluid volumes are connected using the Mismatched Grid Interface (MGI). The fluid volume mesh comprises around 3.4 million cells, as shown in Fig. 4. A fixed total pressure and a fixed total temperature boundary conditions are set for the gas inlet, while the outlet is set to a fixed static pressure. The fluid–solid interface is set to a fixed temperature boundary condition with temperature values mapped from the solid model simulation results. Air is the simulated fluid, and the male rotor rotation speed is set at 8000 RPM. The fluid model takes approximately 2 h per male rotor revolution to run on an AMD workstation with 64 cores.
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Fig. 3 fluid volumes
Fig. 4 Fluid mesh: a fluid volume mesh b cross-section of the rotor mesh
2.2 Solid Heat Transfer Model The solid heat transfer model consists of three volumes: the case, the male rotor, and the female rotor, as illustrated in Fig. 5. All solid volumes are meshed using binary tree mesh with a total of about 0.4 million cells, as shown in Fig. 6. The solid–fluid interface is set as a fixed heat flux boundary with values mapped from the fluid model simulation results. The other boundaries of the solid rotor are assumed to be fully insulated. The outer surface of the case is set as a heat convection boundary. The solid model solves for steady-state heat conduction, and the simulation time for each run is less than one minute.
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Fig. 5 Solid volumes: a case b rotors
Fig. 6 Solid mesh: a case and rotor mesh in a cross section b rotor mesh
2.3 Solid Thermal Expansion Model The solid thermal expansion model in this study only considers the male and female rotors due to insufficient information about the case solid components. The same
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rotor mesh used in the solid heat transfer model is also used in the thermal expansion study (Fig. 6b). In the simulation, the top and bottom surfaces of the rotor axials are fixed with zero displacement. The thermal expansion model reads the temperature field from the solid heat transfer simulation, runs a thermal expansion analysis, and save the displacement of the rotors in a data file. Later, the fluid model reads the displacement file to deform the fluid mesh for the next simulation iteration. The simulation time for each thermal expansion run is less than one minute.
3 Results and Discussion In the simulation, the fluid inlet total pressure is 1 bar, outlet static pressure is 2 bar, and inlet total temperature is 300K. Both rotors are assigned proper rotational speed. Table 1 summarizes key simulation parameters. The solid case has a 10 W/m2 K heat convection on its outer surface with a 300 K environment temperature. Both fluid and solid are initially set to 300 K. A fixed number of iterations for the CHT inner loop is used. During the inner loop, the fluid model runs for one tooth rotation. The solid heat transfer model then runs a steady state simulation using the data from the fluid simulation. The CHT results from the solid simulation is used for the next fluid simulation. After 15 iterations or 5 revolutions of the male rotor rotation, the inner loop is considered complete. After that, the solid temperature field is passed to the thermal expansion model to calculate rotor expansion, which is used for the next iteration of the thermal expansion outer loop. In this study, the thermal expansion outer loop runs four iterations with total of 20 revolutions of male rotor rotation. The simulation is controlled by a Simerics-MP + batch file running in background without user interference. Table 1 Simulation parameters Parameters
Values
Gas
Air (using ideal gas law)
Gas inlet total pressure
1 bar absolute
Gas inlet total temperature
300 K
Outlet static pressure
2 bar absolute
Solid
Stainless steel
Solid density
7800 kg/m3
Solid conductivity
30 W/mK
Solid heat capacity
450 J/KgK
Solid Young’s Modulus
200 GPa
Solid Poisson Ratio
0.33
Solid thermal coefficient
1.2 × 10–5 /K
Compressor speed
8000 rpm (male rotor)
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Figure 7 shows the instantaneous and cycle-averaged heat flux between fluid and solid rotors during the 20 male rotor revolutions to demonstrate procedure convergence history. The maximum instantaneous heat flux is about 500 watts. Once the solution has converged, the average heat flux becomes zero, which is correct because there is no heat source inside solid rotors, and other boundaries of rotors are assumed adiabatic. The plot shows that the conjugate heat transfer converges quickly after the 1st outer loop iteration, and the 5-revolution inner loop iteration may not be needed for later outer loop iterations. The solid case carries about 90 watts of heat away from its outer surface by the environment. Figure 8 displays pressure contour of rotors at 5 different crankshaft angles in the final iteration. Pressure inside each fluid pocket has similar values. The pressure value increases as a pocket moves from inlet to discharge due to volume reduction. No abnormalities were found in the simulation results even with deformed rotor geometry, indicating proper handling of mesh deformation. The final averaged solid temperatures are 331.7 K, 355.7 K, and 352.4 K for the case, the male rotor, and the female rotor, respectively. Figure 9a displays solid temperature distribution in a cutting plane, while Fig. 9b shows rotor surface temperature. The temperature inside rotors has a layered distribution from low to high when moving from inlet to discharge. As noted in [1], this pattern is different from the temperature distribution assuming adiabatic rotor surfaces.
Fig. 7 Heat flux between fluid and solid rotors
Fig. 8 Pressure contour at different male rotor crankshaft angles: a 24 degree b 48 degree c 72 degree d 96 degree e 120 degree
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Fig. 9 Solid temperature a temperature in a cutting plane b rotor surface temperature
Figure 10 demonstrates the rotor thermal displacement in radial direction due to thermal expansion, increasing from center to out surface, with a maximum value of about 60 microns. Displacement also increases in the axial direction due to the temperature gradient. Figure 11 compares the rotor geometry before and after deformation, displaying a significant reduction in tip gap and a slight reduction in inter-lobe gap as a result of thermal expansion at one of the rotor positions. In the picture, grey area is the deformed fluid volume, and the red curves represent original geometry. Rotor thermal expansion significantly reduced tip gaps, assuming negligible case geometry thermal expansion. Figure 12 shows the compressor mass flow rate plotted against the male rotor revolution. During the first outer loop iteration, when there were no shape changes caused by thermal expansion, the mass flow rate stabilized at approximately 11.7 kg/ min. However, during the second iteration, when the rotor shape changed due to thermal expansion, the mass flow rate increased by more than 6% to 12.4 kg/min as a result of the reduction in gap size. The mass flow rate only underwent minor reduction during the third and fourth iteration. The reduction in mixing is attributable to less leakage, which results in lower gas temperature and, consequently, reduced thermal expansion. Eventually, the gap size slightly increased. The parameters listed in Table 2, which include mass flow rate, rotor average temperature, and rotor volume change due to thermal expansion, indicate that the coupling with thermal expansion has converged. Table 3 compares gas mass flow rate and rotor power for the simulation results at the end of the first and the fourth outer iterations against experimental data [8]. The predicted flow rates have about 1 to 6% differences, and predicted powers have about 1 to 2% differences from the test data. The table shows that the prediction from
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Fig. 10 Rotor displacement due to thermal expansion
Fig. 11 Comparison of original and deformed gap size
Fig. 12 Mass flow rate
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Table 2 Thermal expansion loop iteration convergence Iterations
1
2
3
4
Mass flow rate (kg/min)
11.70
12.43
12.39
12.40
Rotor average temperature (K)
357.80
354.14
354.05
353.89
Rotor volume change (mm3 )
0
6080
5690
5680
Table 3 Comparison of mass flow rate and rotor power 1st iteration
4th iteration
Experiment
Mass flow rate (kg/min)
11.7
12.4
11.8
Rotor power (kw)
21.9
21.7
22.2
“original” rotor geometry matches the test data significantly better than the one from deformed geometry. The reason is that the deformed geometry could have double counted the thermal expansion effects since the "original" geometry had already been modified to consider potential shape changes due to thermal expansion, as mentioned by Kovacevic et al. [8].
4 Conclusion and Future Works This study successfully attempted direct coupling of 3D CFD, CHT, and solid thermal expansion for twin screw compressors, with the aim of predicting thermal expansion effects on compressor performance. The method is divided into three coupled models: fluid flow and heat transfer, solid heat transfer, and solid thermal expansion. The solution procedure has a CHT coupling inner loop, nested in a thermal expansion coupling outer loop, and couplings are solved iteratively. Several new capabilities have been developed to fulfil the needs of this coupled procedure. With these added capabilities, setup and run such a simulation is very easy. The simulation results demonstrate stability and quick convergence of the proposed iterative procedure. The thermal expansion was found to cause a significant change in twin screw leakage gap size, which affected compressor performance, with a 6% increase in gas flow rate and 1% drop in power consumption for the simulated case. Added simulation time for solid heat transfer and thermal expansion was negligible compared to fluid simulation. Future work will include applying the procedure to twin screw compressor cases with more complete information to further evaluate the method’s accuracy and improve simulation efficiency. Acknowledgements The authors would like to express our gratitude to Dr. Kovacevic and Dr. Rane of City University London for letting us use their twin screw rotor geometry in this study.
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References 1. H. Ding, Y. Jiang, S. Dhar, CFD modelling of coupled heat transfer between solid and fluid in a twin screw compressor. IOP Conf. Ser. Mater. Sci. Eng. 604(2019), 012005 (2019) 2. D. Rowinski, A. Nikolov, A. Brümmer, Modeling a dry running twin-screw expander using a coupled thermal-fluid solver with automatic mesh generation. IOP Conf. Ser. Mater. Sci. Eng. 425, 012019 (2018) 3. Y. Chen, J. Schlautman, S. Dhar, Experimental and numerical investigation of the multiphase flow and heat transfer in an oil jet cooled engine piston. SAE Tech. Paper 2020-01-0165 (2020). https://doi.org/10.4271/2020-01-0165 4. C. Srinivasan, J. Wan, R. Saha, S. Dhar et al., Heat transfer analysis of an electric motor cooled by a large number of oil sprays using computational fluid dynamics. SAE Tech. Pap. 2022-01-0208 (2022). https://doi.org/10.4271/2022-01-0208 5. A. Ballani, M. Tao, C. Srinivasan, H. Gao, D. Maiti, S. Dhar, 3D conjugate heat transfer modelling of E-compressor. Int. Compressor Eng. Conf. Paper 2740. https://docs.lib.purdue.edu/icec/2740 6. U. Duzel, S. Dhar, M. Zecchi, H. Gao, H. Ding, CFD simulation of helical external gear pump with asymmetric tooth profile: Development of 3D helical mesh generation and motion algorithm and experimental validation. GFPS2022, Napoli Italy, Oct 12–14 (2022) 7. P. Borriello, E. Frosina, P. Lucchesi, A. Senatore, A study on a twin-screw pump for thermal management systems by means of CFD using SimericsMP+®: experimental validation and focus on pressure pulsation. GFPS2022, Napoli Italy, Oct 12–14 (2022) 8. Kovacevic, A., Rane, S., Stosic, N., Jiang, Y., Lowry, S., Influence of approaches in CFD solvers on performance prediction in screw compressors, Int. Compressor Eng. Conf. Purdue (2014)
Investigating Alternative Rotor Materials to Increase Displacement and Efficiency of Screw Compressor While Considering Cost and Manufacturability A. Kumar, K. Patil, A. Kulkarni, and S. Patil
Abstract Screw compressor, a rotary positive displacement machine, has gained popularity and is one of the most commonly used types of compressors across the globe due to better efficiencies and high reliability. The most vital component on which the screw compressor functions are the screw rotors, enclosed inside the housing with minimal clearances. Hence, the design of the rotors plays a significant role in affecting the thermodynamic performance. Also, it is found that profiles with a greater depth deliver a larger flow with higher volumetric and adiabatic efficiencies than their counterparts of the same size with a smaller profile depth [1]. In this paper, structural analysis of the screw compressor block is carried out to examine the effect of stresses, thermal gradients and deformation for different rotor materials for a 4/5 lobe combination. This alternative material investigation further influences the rotor profile depth for the same main rotor outer diameter, enhancing displacement and efficiency by 5.01% and 1.1%, respectively. Factors such as manufacturability and production cost of screw rotors have also been considered to fairly evaluate the commercial feasibility of alternative materials. Besides enhancing performance, the selected materials improve other essential properties, such as corrosion, bio-compatibility and wear resistance. The future study proposes a 3/6 lobe combination screw rotors to be considered for a significant amount of improvement in performance with smaller root diameter for numerical analysis and to be validated experimentally. Keywords Screw compressor · Structural analysis · Materials · Rotor profile depth · Manufacturability · Cost
A. Kumar (B) Centre for Compressor Technology, City, University of London, London, U.K. e-mail: [email protected] A. Kumar · S. Patil Kirloskar Pneumatic Company Limited, Pune, India K. Patil · A. Kulkarni Vishwakarma Institute of Information Technology, Pune, India © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_10
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1 Introduction 1.1 Exploring Lightweight Materials and Innovative Manufacturing Techniques for Screw Compressor Rotors In the age of high-power requirement applications that have gained widespread usage and demand, a lot of research is currently going into reducing the weights of the moving components, thus reducing their specific power consumption. The research on lightweight moving components have helped various industries including but not limited to the aerospace, automobile, power, and production to improve fuel efficiency, reduce cost of manufacturing as well gaining desirable mechanical properties for the components. Thus, researchers are focusing on finding suitable alternative materials to conventional types which include research on a wide range of alloys, plastics, composites, polymers, etc. Along with materials, the performance, manufacturing feasibility and production cost associated with the materials are also researched for optimum results. According to the report on the compressor market by Mordor Intelligence [2], the global compressor market value is supposed to be valued at USD 50.45 billion by 2027 from USD 38.28 billion in 2020, with a CAGR of 4.47% for the period 2022– 2027. The rotary screw compressor, a type of positive displacement machine, has a wide range of applications including but not limited to refrigeration, petrochemical, HVAC, and pharmaceuticals, and are classified as oil-injected, water-injected, and oil-free based on the quality of air requirement. The screw rotors being an integral part of the screw compressor, are responsible for the compression of the fluid in exchange for power consumption. To cope with this power requirement demand and achieve sustainability, researchers are focusing on alternatives to existing manufacturing and material used due to the limited scope of optimising screw performance from profile and design point of view. The current manufacturing technique used for these screw rotors is the conventional method of milling and grinding using a numerically controlled machine. Screw rotor having a complex shape, even with the precision machine tools, the associated manufacturing cost and cycle times are relatively large. According to the market survey [3], medium carbon steels are the most widely used materials in manufacturing screw rotors for screw compressors. EN8 is also a type of carbon steel that is widely used in most of the screw compressors. The current research focuses on alternatives to the currently widely used material with a purpose to enhance the displacement and efficiency of screw compressor, taking into account manufacturability and production cost. To find the best suitable material for the application, structural analysis is done using ANSYS Mechanical, followed by SCORPATH (Screw Compressor Optimal Rotor Profiling And THermodynamics) analysis for performance enhancement. Multiple recent studies have explored the additive manufacturing of screw rotors. Additive manufacturing (AM) has been a breakthrough in the manufacturing industry due to its feasibility to manufacture complex shapes without wasting material in the form of chips as in the conventional methods, with little to no human involvement
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and high accuracy. Bailas [4] presented an innovative way and researched the effect of injecting epoxy resin into the specially designed voids of additively manufactured parts by manufacturing specimens of varying infill using the FDM (Fused Deposition Modeling) process and injecting epoxy into the voids and concluded that the stiffness of the specimens could be enhanced by about 90 percent. The Eaton Intelligent power limited presented its additively manufactured screw rotors [5] and showcased the flexibility of various Additive manufacturing techniques by manufacturing them in vivid ways. Techniques such as 3D printing, Fused deposition modeling, Selective laser sintering can create internal voids in the rotors, which are unlikely to be formed using conventional ways. The advantage of creating internal voids is the reduction in the overall mass of the screw rotors, thus reducing their moment of inertia or providing possibilities to internally cool them to achieve near isothermal compression. Svenska Rotor Maskiner AB [6] successfully manufactured screw rotors using a metal shaft such as steel and polymeric body of lobes using polyurethane and inorganic filler silicate-containing fibers and demonstrated that they were able to eliminate drawbacks associated with conventional manufacturing. Do Suh [7] also implemented a unique way of manufacturing the screw rotors by implementing the resin transfer molding process. They used carbon fiber in chopped form with a tensile strength of fibers corresponding to 3528 MPa and epoxy resin (IPCO 2434/2310, National starch and chemical, USA). The publication demonstrated that short fibers suit complex products and shapes such as screw rotors. A mold of a helical shape resembling the screw rotor of material aluminum 6061T6 and manufactured using CNC machining was used. They successfully manufactured the composite screw rotor, weighing 52% as compared to the aluminum screw rotor. However, the publication didn’t demonstrate the testing part of the composite rotor, thus leaving scope for further investigation and research. Vacuum casting is also a type of additive manufacturing in which silicon molds are used to manufacture fully polymeric screw rotors. Thus with the technological advancements in manufacturing, additive manufacturing can be a breakthrough considering its innovative adaption and a wide variety of production techniques apart from 3D printing.
1.2 Metal Additive Manufacturing and Alternative Materials for Different Screw Compressor Applications The additive manufacturing of screw rotors for compressors is suitable, but a decision for shortlisting the correct type of AM and the suitable material for manufacturing plays a significant role. Materials like polymers for screw rotors are suitable for lower-pressure applications due to their lower yield strength and temperature resistance. However, the applications where the inner casing temperature exceeds (100– 125) .◦ C and pressure varying 7–13 bar, higher yield strength materials are suitable. According to the literature survey, materials other than metals have no significant practical advantage. The metals, however manufactured using Powder bed fusion, a
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Table 1 Tabular column showing alternative materials and their mechanical properties .UTS (MPa) .Yield stress .Hardness (HB) .Density (g/cc) .Material name (MPa) EN8 (normalised) 610 666 SS 316L 442 AISI10Mg-0403 1140 Maraging steel M300 Ti6Al4V 1133 ELI-0406
465 548 264 1016
180–220 183 114 342
7.85 7.9 2.68 8.1
1045
380
4.42
type of metal additive manufacturing technique, exhibit mechanical properties at par with conventionally manufactured metals if material properties are compared. As discussed earlier, Eaton Intelligent power limited [5] manufactured the screw rotors using selective laser sintering and stated that various metals like steel and aluminum could be similarly sintered. The screw compressor can be distinguished as oil-free and oil-flooded [8]. In oilfree compressors, based on the lubrication method used there are two types- waterinjected screw compressor and those with purely air in the compressor chamber. Patel [9], in their work on the tribological behavior of materials for compressors, stated that stainless steel has less wear property and suitable for compressor applications. For oilfree and water-injected screw compressors, the material implemented must be highly corrosion resistive and wear-resistant. SS 316L, a grade of stainless steel, is corrosion resistant due to chromium content and due to its lower carbon variation compared to standard SS 316; it can be implemented for water-injected compressors. Removing the heat from the screw rotors for oil-free compressors is vital, so materials with higher thermal conductivity could be used. AISI 10Mg-0403, a type of aluminum alloy which can be additively manufactured, has a thermal conductivity ranging from 130 to 190 W/mK, making it suitable for oil-free compressors. In natural gas compressors, where reactive materials like nickel, brass, or copper cannot be used and high strength is required, Maraging steel (with yield strength around 1000 MPa) can be utilised as it has properties of corrosion resistance. In pharmaceutical applications where biocompatibility is important, titanium alloy (Ti6Al4V ELI-0406) is a suitable option. Table 1 shows the material properties comparison of the materials obtained from additive manufacturing firms and the conventionally manufactured material EN8. The proposed study focuses on the finite element analysis of an industrial screw compressor block by varying the screw rotor’s material. Further, the SCORPATH analysis using the high-strength material is carried out to increase the displacement and efficiency by increasing the rotor profile depth keeping in account the rotor deflection and minimum shaft size requirement for bearings and seals fitment. The proposed materials can be manufactured additively and are widely accepted by metal additive manufacturers. For a clear understanding the cost breakdown structure of
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manufacturing screw rotors using the conventional machining method is presented along with a comparison table with the additive manufactured rotors. In the future study, the prototype of the additive manufactured rotors is to be produced in-house, followed by the performance validation.
2 Numerical Simulation Before implementing any new system or material in industrial applications, validating numerically and experimentally with the latest alternative has become critical. Finite element analysis has become the backbone of research and development in almost all industrial applications. As discussed in the previous sections, the materials EN8, SS 316L, AISI 10Mg-0403, and Maraging steel M300 are suitable for the screw rotors depending on the applications. The static structural analysis of the screw rotors incorporated into the compressor block has been carried out by varying the screw rotor materials mentioned. The Ansys static structural solver has been used to evaluate results like principal stresses, penetration, and clearance after deformation between the rotor and the casing.
2.1 Modelling Methodologies The machine considered in this work is KAS-100 oil-flooded air screw compressor (belt-driven) with built-in volume ratio of 4.6 operated at a pressure ratio of 8.5 and a tip speed of 20 m/s, manufactured at Kirloskar Pneumatic Company Limited, Pune (India). Since this is a commercial screw compressor product, information about the size and profile cannot be disclosed. Experimental testing has been conducted for this compressor, whose data will be used for modelling the screw compressor in the SCORG (Screw Compressor Rotor Grid Generation) software from the PDM Analysis [10].
2.2 Rotor Grid Generation .(SC O RG T M ) The SCORG is an industry leading grid generation and performance software for positive displacement screw machines. It performs the thermodynamic calculation based on the multi-chamber model using conservation equations of mass and internal energy to control volumes [11]. SCORG is used for the grid generation of temperature and pressure domains for the screw rotors, which is used as an input in the Ansys structural analysis as shown in Fig. 1 for reference. The procedure of analytical grid generation of screw machine working domain is explained in Kovacevic [12].
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Male: SCORG imported temperature (50o C max) Male: SCORG imported pressure (16 bar)
Female: SCORG imported temperature (50o C max)
Female: SCORG imported pressure (16 bar)
Fig. 1 Thermal and pressure boundary conditions on rotors using SCORG
2.3 Structural Analysis Boundary Conditions Temperature and pressure range are two essential factors in the analysis. Here two solvers have been used in the Ansys workbench environment. First is steady-state thermal, where the temperature input is given. The properties like thermal conductivity and coefficient of thermal expansion are specified in the engineering material section. The solution of the steady-state thermal is connected to the setup of the static structural. In static structural, the properties mentioned in Table 1 and other mechanical properties are specified in the engineering materials section. The temperature and pressure 3D grids of screw rotors generated from SCORG are imported into the Ansys mechanical as inputs. The design pressure considered for this structural analysis is 16 bar (g) at an ambient temperature of .30 .◦ C and operating temperature of .50 .◦ C. The KAS-100 compressor block is a belt driven screw, so the belt tension force of 1200 N is applied on the male rotor shaft. Other boundary conditions, such as gravity force, load, displacement and fixed supports, are then specified. The mesh size is 3 mm, generating 1186339 nodes and 759047 elements. Figure 2 shows the cross-sectional view of the meshing with the screw rotor visible.
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Fig. 2 Cross-sectional view of the meshing
2.4 SCORPATH Modelling The software developed for the conceptual and preliminary design of screw machines is called SCORPATH (Screw Compressor Rotor Profiling and Thermodynamics) [13]. It is used for the performance enhancement analysis of the same oil-flooded screw compressor with 4/5 lobe combination. The rotor profiles with both nominal and deeper profiles was designed for comparison. The deeper profiles were generated by reducing the centre distance keeping all other parameters constant except the main rotor profile addendum, that is being tweaked to maintain the main rotor outer diameter constant. Since the main rotor outer diameter is constant, which results in the same length of the rotors, i.e., same relative length ratio (L/D). The nominal centre distance was reduced by 3.5 mm to increase the rotor profile depth. The purpose is to show how the increased strength of rotor can be used to design deeper profiles and enhance their energy efficiency; a principle already known and presented in [1]. The influence of the changing of the distance between the centres of the rotors are the same for all materials of the rotors, even though the influence of centre distance is known and realised that at smaller centre distance a more efficient profile is achieved. This effect cannot be utilised fully for designing more efficient profiles unless higher strength materials are adopted. For existing rotor materials generally used, profile depth cannot be increased beyond a certain point without compromising the rotor rigidity and deflections. Hence from this point of view it is important to stress here how change of rotor materials with higher strength can be utilised to improve the efficiency of the machine (Fig. 3).
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Screw rotors with reduced centre distance
Screw rotors with nominal centre distance
Fig. 3 Screw rotor profile with nominal and reduced centre distance using SCORPATH Table 2 Tabular column showing structural analysis results for different rotor materials .Materials .Stress (MPa) .Penetration (mm) .Clearance (.µ) EN8 (normalised) SS 316L AISI10Mg-0403 Maraging steel M300 Ti6Al4V ELI-0406
11.621 7.7837 12.538 6.5438 6.4519
0 0 0 0 0
38 (M); 36 (F) 40 (M); 39 (F) 30 (M); 29 (F) 45 (M); 44 (F) 47 (M); 45 (F)
3 Result and Discussion The results from the structural analysis for different rotor materials is presented in Table 2. In this analysis, the casing material is kept constant, FG 260. The current rotor material used for conventional machining manufacturing rotors is normalised EN8. In the Ansys mechanical static structural set up, except the engineering material for screw rotors all others are assumed to be constant. From the structural analysis, the minimum stresses were found to be in Maraging Steel M300 and Ti6Al4V ELI-0406. Also, these materials show good amount of clearance (between rotors and housing i.e. radial clearance) left after deformation which is obvious as these are high strength materials. The critical point is that no penetration is observed with different rotor materials. All the comparison have been made concerning the currently used rotor material, i.e., normalised EN8. The clearance before deformation is found to be 60 .µ. On the other hand, from the SCORPATH analysis to generate the deeper profiles, the centre distance was reduced by 3.5 mm. The main rotor outer diameter and the relative length is kept constant. The rotor inner diameter decreased, and the rotor profile depth increased. The oil-flooded compressor’s average flow and specific power
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Fig. 4 Rotor manufacturing cost
with these rotors operating between 1 and 8.5 bar were improved 5.01% and 1.1%, respectively. The centre distance was reduced to its optimum point of 3.5 mm to achieve the maximum rotor profile depth. It is possible to further reduce profile depths or design rotors with smaller root diameters with lower number of lobes by taking advantage of the high strength materials. The only limitation could be in selecting suitable bearings and other components over the rotor shaft which is too small (practically rotor shaft diameter has to be smaller than root diameter of the rotor). In order to improve performance by increasing profile depth, one of the practical challenges is regarding the rotor deflection at high discharge pressures. If the current material (Normalised EN8) was used for this reduced centre distance profile, the deflection was beyond the optimum range and would lead to seizure of the compressor block. Therefore, using the high strength material from the above structural anlaysis, which gives minimum stress and has an optimum clearance left after deformation could be used. The deflection could be reduced by a significant amount of 32%. With the rotor deflection in check because of the high strength material, an improvement in performance is also achieved with 5.01% higher flow and and 1.1% lesser specific power. Thus, it is evident from the structural analysis using Ansys Mechanical and the SCORPATH analysis that high strength alternative rotor materials can lead to improved displacement and efficiency with minimum stress and optimum clearance after deformation. But this cannot be the only factor in using this alternative materials for the screw rotors without considering the manufacturability and cost. The pie chart in Fig. 4 presents the rotor manufacturing cost for the exact size of rotors using the conventional machining, i.e. milling and grinding process. The main cost is the milling and grinding machining cost, including the jigs and fixtures.
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Table 3 Tabular column showing comparison of normalised manufacturing cost for a single pair of screw rotors .Materials .Conventional manufacturing cost .Additive manufacturing cost EN8 (normalised) SS 316L AISI10Mg-0403 Maraging steel M300 Ti6Al4V ELI-0406
1.00 – – – –
– 1.83 1.50 3.00 4.12
The alternative materials mentioned above are high strength materials which can be manufactured conventionally using high strength tools, but in regards to this study, additive manufacturing is considered for comparison. Manufacturing the screw rotors using the metal additive manufacturing technique eliminates the milling tooling and machining cost, which requires a considerable investment in the jigs and fixtures. The surface roughness obtained after additive manufacturing is in the range of (5–10) Ra, which needs to be further ground using the conventional grinding operation. The comparison of production cost of screw rotors (both male and female) for the given compressor block using the conventional machining for the currently used material and the additive manufacturing for the alternative materials are presented in Table 3. All the cost have been normalised; and the cost of manufacturing screw rotors using the conventional machining is taken as reference. From the table, it is evident that the currently costlier AM is suitable over conventional method only if the advantages such as improved energy efficiency (achieved by reliably realising deeper profiles) cover the extra initial cost of manufacturing by saving in energy cost throughout the life cycle of the machine.
4 Conclusion A comparative analytical study was carried out to determine the effect of alternative rotor materials on screw compressor performance. The structural analysis was conducted to find the efficient material with minimum stress, zero penetration and optimum clearance left after deformation through Ansys Mechanical. In the SCORPATH analysis the effect of high strength material with deeper rotor profile by reducing centre distance improved average flow and specific power consumption by 5.01% and 1.1%, respectively. The female rotor deflection using this high strength material got reduced by 32%, thereby maintaining the optimal clearances and avoiding seizure. The manufacturability and production cost of screw rotors using additive manufacturing and conventional machining has also been presented. The selected materials not only improves the performance of the screw compressor but also improves other properties such as corrosion, wear resistant and biocompatabiliblity.
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5 Further Study In the current study a 4/5 lobe combination and deeper profile by 3.5 mm; the improvement observed is not very significant. However, considering a 3/6 lobe combination, the effect of smaller root diameter can be more strongly realized. 3 lobes on main rotor would reduce its root diameter significantly and the 6 lobes on gate rotor would allow for enough gate rotor shaft diameters for bearing fitments along with relatively deep profiles. In the future study, a 3/6 lobe combination screw rotors made of high strength materials proposed hereby are to be considered for further analysis. Acknowledgements We gratefully thank Kirloskar Pneumatic Company Limited, Pune, India for sponsoring this research. We also want to acknowledge the Centre for Compressor Technology, City, University of London (U.K.) and Vishwakarma Institute of Information Technology, Pune (India) for their continued guidance and support in this research.
References 1. N. Stosic, I.K. Smith, A. Kovacevic, Improving screw compressor displacement and efficiency by increasing the rotor profile depth, IOP Conf. Ser. Mater. Sci. Eng. 604(1) (2019) 2. Mordor Intelligence—Compressor Market—Growth, Trends, Covid-19 Impact, and Forecasts (2023–2028). https://www.mordorintelligence.com/industry-reports/compressormarket. Accessed 15 Jan 2023 3. G. Muiznieks, E. Gerins, A. Katasevs, J. Ozolins, G. Pikurs, Evaluation of coating material structure of screw type compressor rotor contact surface. Proc. World Congress Eng. 3 (2012) 4. K. Bailas, P. Papanikos, Injecting epoxy resin to specially designed voids of additively manufactured parts to improve mechanical properties. Procedia Manuf. 51, 692–697 (2020) 5. Eaton Intelligent Power Limited, Additively Manufactured Rotors for Superchargers and Expanders, US Patent No. US20220234106A1. https://patentimages.storage.googleapis.com/ 1d/3c/b3/610ece817df058/US20190070664A1.pdf. Accessed 10 Feb 2023 6. Polymer Rotor and Method for Producing Polymer Rotors, US Patent No. WO2001028747A1. https://patents.google.com/patent/WO2001028747A1/en. Accessed 15 Feb 2023 7. J. Do Suh, Manufacture of composite screw rotors for air compressors by RTM process. J. Mater. Process. Technol. 113(1–3), 196–201 (2001) 8. N. Stosic, I. Smith, A. Kovacevic, Screw Compressors: Mathematical Modelling and Performance Calculation (Springer Science & Business Media, 2005) 9. S.S. Patel, M.S. Shiva, T. Kataray, D. Srivastava, S. Maji, C. Kapruan, P.P. Kumar, B. Yarram, U. Chadha, S.K. Selvaraj, Trends in tribological behaviour of materials for compressors. J. Phys. Conf. Ser. 2272(1), 012023 (2022) 10. PDM Analysis Ltd., SCORG—screw compressor rotor grid generation, in Software Package for Design and Analysis of Positive Displacement Machines (City University, London, 2014). Retrieved from https://pdmanalysis.co.uk/scorg/ 11. A. Kumar, A. Kovacevic, S.A. Ponnusami, S. Patil, S. Abdan, N. Asati, On performance optimisation for oil-injected screw compressors using different evolutionary algorithms. IOP Conf. Ser. Mater. Sci. Eng. 1267(1), 012021 (2022) 12. A. Kovacevic, Three Dimensional Numerical Analysis for Flow Prediction in Positive Displacement Screw Machines (Doctoral dissertation, City University London, 2002) 13. N. Stosic, SCORPATH: Screw Compressor Optimal Rotor Profiling and THermodynamics (2005). Retrieved from http://www.staff.city.ac.uk/~ra600/DISCO/DISCO%20SCORPATH. htm
Investigation and Optimization of a Twin-Screw Compressor with Internal Cooling Channels Abhignan Saravana, Haotian Liu, Nick Able, James Collins, Eckhard A. Groll, and Davide Ziviani
Abstract Twin-screw compressors are used extensively in commercial and industrial applications. Profile optimization and capacity modulation solutions (e.g., slide valves, variable-speed, etc.) are continuously investigated to optimize the operation of the compressors and improve the performance. Previously, the authors have developed a detailed simulation model of a twin-screw air compressor with internal cooling channels to explore the feasibility of achieving quasi-isothermal compression process and prototype rotors were successfully 3D-printed. In this paper, further investigations are conducted at different operating conditions, including various pressure ratios, rotational speeds, and mass flow rates to improve the compressor efficiency. Since the compression process is coupled with heat transfer during the operation of the compressor, the interactions between solid (i.e., rotors) and fluid phases (i.e., air and coolant) are analyzed using a CFD model with conjugate heat transfer. The results of CFD model are used to quantify compression loads, assess the characteristics of the heat transfer processes, and optimize the internal flow through the cooling channels. The performance of the twin-screw compressor with internal cooling channels is compared with a conventional twin-screw compressor.
A. Saravana (B) · H. Liu · E. A. Groll · D. Ziviani Ray W. Herrick Laboratories, School of Mechanical Engineering, Purdue University, West Lafayette 47907-2099, USA e-mail: [email protected] H. Liu e-mail: [email protected] E. A. Groll e-mail: [email protected] D. Ziviani e-mail: [email protected] N. Able · J. Collins Ingersoll Rand, Davidson, NC, USA e-mail: [email protected] J. Collins e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_11
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Keywords Twin-screw compressor · Conjugate heat transfer · CFD · Air compressor · Efficiency optimization
1 Introduction Positive displacement machines are used extensively in various gas compression applications. Specifically, twin-screw compressors are characterized by high efficiencies, compact designs and feature wide range of operations [1]. The compression process in a screw compressor can be analyzed from a thermodynamic point of view by comparing it to a reversible adiabatic, polytropic or isothermal process [2]. Moreover, it is well known that an isothermal compression would require the least amount of work to accomplish the process. However, achieving an isothermal compression process is particularly challenging as it requires removing heat energy from the compression chamber in sync with the mechanical rotation of the rotors and the compression process. Therefore, heat transfer through the rotors and compressor shell plays a key role and requires technological advancements to be implemented. Despite several research efforts to develop transient 3D CFD simulation [3–6], it is still challenging to accurately simulate the conjugated heat transfer between temperature variations during the compression process and their interaction with the housing and compressor assembly. If active liquid cooling is being used in the cooling process, a full heat transfer analysis between the rotor and housing (solid), working fluids (gas) and coolant (liquid) must be conducted through the conjugated heat transfer (CHT). Usually, the solid side simulation takes longer to converge at a steady-state solution than the fluid side, which makes it computationally expensive. Ding et al. [7] addressed this by modelling CHT with mixed timescale coupling between the rotor walls and gas chamber. Willie [8] used combined CFD and CHT simulation method to optimize and improve the cooling within a screw compressor and validated the model against the experimental measurement. Rane et al. [9] conducted bi-directional coupling for CHT and CFD to analyze the variable leakage gap for an oil-free twin-screw compressors and quantitively provided the relation between gap size and efficiency. To actively cool down the twin-screw compressors to progressively reduce temperature difference between suction and discharge with the ultimate goal being to achieve isothermal compression, the authors proposed to use 3D printed shape-optimized hollow rotors. Coolant (water in this paper) will path through the hollow rotors to cool down the rotor as well as the working fluid. Prior to this paper, Saravana et al. [10–11] conducted preliminary studies on stress and heat transfer analyses on a 4–6 twin-screw compressor with internal cooling channels and showed that it is both safe and beneficial to use rotors with internal cooling channel. Continuing the research on this topic, this paper provides a comprehensive evaluation for hollow rotors with internal cooling channels to be used in twin-screw compressors. The CFD coupled CHT simulation is conducted to understand the complex heat transfer
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between working fluid, rotor metals and coolant within the internal cooling channels. Based on the CFD results, a comparison of the performance of the hollow rotor design is presented on range of operating conditions. The hollow rotor performances such as compressor efficiency, discharge temperatures are discussed and compared with conventional rotor design.
2 Twin Screw Compressor Model The twin-screw compressor considered in this study has a 4–6 configuration and both male and female rotors are modified to include internal cooling channels to allow coolant fluid to flow through. The compressor working fluid is wet air with 60% relative humidity and has been modeled as an ideal gas mixture with average specific heat of 1.021 kJ/(kg − K) and a polytropic coefficient of 1.4. Whereas the coolant flowing inside the rotors is water. All the simulations are run for a dry screw compressor with no fluid injection. Both rotors were additively manufactured with Inconel, but to be more conservative, the material considered in the conjugated heat transfer study is carbon steel as it has lower structural integrity properties than Inconel alloy.
2.1 Geometry Model The rotor geometries and the internal channels were optimized in a previous work carried out by Saravana et al. [10]. The rotor designs are shown in Fig. 1, and they have been employed in the CFD simulations. To enable comparisons, the baseline case with conventional solid rotors maintained same external rotor profiles.
Fig. 1 CAD model of a male and b female rotors with internal fluid domain projections
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2.2 Heat Transfer Model The hollow rotors consist of three phases interacting simultaneously: (1) solid rotor, (2) liquid coolant flowing inside the rotors and (3) working gas being compressed. The heat transfer problem is studied through a conjugated heat transfer approach implemented alongside CFD. The energy conservation equations and various models used within the study are described in more detail by Saravana et al. [11].
3 Simulation Setup The CFD simulations are performed with CONVERGE CFD 3.0 [12] and involved grid size optimization, governing equations, and solver setups (e.g., relaxation parameters) and boundary conditions. These aspects are summarized in the following sections for completeness, but the details are provided in previous work [11].
3.1 Geometry Setup and Operating Conditions This study involves two types of geometries: the conventional rotor assembly and the hollow rotor assembly. The hollow rotor assembly differs from the conventional simulation from the fact that it involves an internal fluid domain for a liquid coolant medium, whose boundary conditions are defined based on atmospheric pressure and an inlet mass flow rate which is tuned to arrive at steady state sooner. The inlet mass flow rate is decided based on several iterations, which is not discussed in this paper. Two and three cases were run on the conventional and hollow rotor simulations respectively. The internally cooled cases were run with different pressure ratios of 3.29–7 bar and rotational speeds of 19,000 RPM and 11,000 RPM whereas the conventional rotor simulation was run for 3.29–7 bar but for fixed rotational speed of 19,000 RPM. The built in volume ratio of the machine is 4.2, and no capacity modulation features were included for simplicity. Figure 2 illustrates the general twin-screw compressor assembly for solid (dry running) and hollow rotor (internally cooled) cases and (Table 1a, b) list the boundary conditions for hollow and solid rotors.
3.2 Simulation Methods and Meshing To simulate the transient CHT problem, an innovative “Super-Cycling” numerical technique has been employed. The numerical simulation allows to solve the interactions between solid, liquid and gas phases by iterating between transient and
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Fig. 2 Twin-screw compressor assembly with boundary conditions
Table 1 Heat transfer and flow boundary conditions for (a), hollow rotor and (b), solid rotor (a) All cases:
Gas inlet
Liquid inlet
Temperature (K)
293
278
Pressure (Pa)
101 325
101 325
Velocity (m/s)
Zero normalgradient
Zero normal gradient
Mass flow rate (kg/s)
0.8
Liquid outlet
Casing (wall)
Shaft (wall)
Convection T= 300 K h = 10 mW2 K
Insulated
Stationary
Rotating
0.8
(a)
Gas outlet pressure (Pa)
Rotational speed (Hz)
Case 1
329 200
19,040
Case 2
700 000
19,040
Case 3
329 200
11,000
(b) All cases:
Gas inlet
Casing (wall)
Shaft (wall)
Temperature (K)
293
Convection T= 300 K h = 10 mW2 K
Insulated
Pressure (Pa)
101 325
Velocity (m/s)
Zero normal gradient
Stationary
Rotating
Rotational speed (Hz)
19,040
steady-state solvers to achieve steady-state convergence within fewer cycles. Several meshing methods such as embedded layer and adaptive meshing refinement (AMR) were employed within the simulations. While the grid generation and simulation methods are described in more detail by Saravana et al. [11], a summary of the main parameters is provided in Table 2.
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Table 2 Table listing meshing strategies employed in the simulation Mesh resolution strategies
Description
Basic grid
Basic element size of 8 × 8×8 mm
Adaptive mesh refinement
Maximum embedding level of 3 for velocity and temperature
Embedded layer meshing
Upto 3 embedding layers to resolve flow conditions near the boundary and refine Y+ numbers
4 Results and Discussion 4.1 Model Verification The model was verified through three major methods: mesh verification through Y+ numbers, lumped heat transfer analysis, comparison between solid (dry running) and hollow (internally cooled) rotors. While Saravana et al. [11] described the verification analyses in more detail, a summary of the methods is listed. • Mesh verification: With more than 1 million cells and turbulence flow, it is important to verify that the turbulent flows are well resolved using Y+ numbers. By analyzing one internally cooled case with 3.29 bar and 19,000 RPM, the numbers were within the acceptable range of 120 and 420, concluding that the chosen mesh strategies are sufficient to run the simulations within this study. • Lumped Heat Transfer: The complex 3D heat transfer process is simplified into a 1D thermal resistance circuit. The lumped heat transfer is checked by back calculating the thermal conductivities of the male and female rotors (14.56 W/mK–36.72 W/mK, respectively) and comparing with the material properties. • Performance of Hollow rotors: A comparison between internally cooled and conventional rotors is presented in subsequent sections of this study. The comparison presented in Table 4 verifies the effect of internal cooling and reinforces the advantage of hollow internally cooled rotors over conventional rotors.
4.2 Rotor Discharge Temperature Slices Temperature contour slices can be a great way to observe temperature hot spots within the rotor assembly, since they involve a general temperature overview for all mediums, solids, liquids, or gases. Rotor temperature slices at discharge for three different internally cooled cases are presented in Fig. 3. As expected, the highest temperatures are in the discharge pipeline, due to compressed gas exiting at very high temperatures. The magnitude of the temperatures, however, varies with operating conditions. This study clearly shows that higher rotational speeds and higher-pressure ratios lead to higher temperatures, both in the discharge as well as the rotor surfaces. The coolest location in the slices is observed to be inside the hollow domain through
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Fig. 3 Discharge temperature contour slices with velocity vectors for a Hollow 11,000 RPM 3.2 bar; b Hollow 19,000 RPM 3.2 bar. c Hollow 19,000 RPM 7 bar
which internal coolant flows. The temperature hot spots higher than 450 K are on the discharge pipeline due to hot compressed gas exiting. However, the cool spots inside of the rotors due to internal cooling are very effective at maintaining the rotor temperatures consistently at less than 400 K even at the highest gas discharge temperatures. This further proves the need for internal cooling.
4.3 Rotor Surface Temperature Plots Rotor surface temperature contour plots with a line plot of average boundary temperatures are utilized to understand the heat transfer characteristics, as illustrated in Fig. 4. Similar observations can be made in the discharge slices presented earlier. The internal coolant, being water, has a limitation with its lowest possible temperature before freezing. As a result, the simulations were only run with a water coolant temperature of around 5 °C. The cooling effect provided is not sufficient to provide
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Fig. 4 Temperature contour plots inlaid with average boundary temperature line plots for a Hollow 11,000 RPM 3.2 bar; b Hollow 19,000 RPM 3.29 bar; c Hollow 19,000 RPM 7 bar. Rotor boundary temperatures are averaged across the length and summarized in the line plot
cooling at higher operating pressures, which results in significantly higher temperatures for the case with discharge pressure of 7 bar. The average boundary temperature line plot, inlaid into the contour plots, not changing significantly also serves as a verification for steady state. Clearly, the rotors reach their maximum surface temperatures near the discharge. By reducing these discharge temperatures, we can arrive at better efficiencies, as will be shown in subsequent sections.
4.4 Performance Parameters To prove the purpose of this study, it was important to perform a like for like comparison of efficiencies between conventional and internally cooled rotors. Indicated power values for each case are computed using total torque values obtained from CFD. Once they are computed, they are compared with the ideal isentropic and isothermal efficiencies that are calculated using basic thermodynamic relations, to
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develop efficiencies. The idea behind internally cooled rotors to reduce discharge temperatures, thereby reducing indicated power, is corroborated through the results in Table 2. It can be observed that there is a 2% improvement in efficiencies when compared to a solid rotor case without internal cooling for lower pressure ratios (case 1); but only around 1% improvement for higher pressure ratios (case 2), even though there is a higher drop in indicated power for the latter case. This difference can be explained due to lower inlet mass flow rates for hollow rotors over solid rotors resulting in lower isothermal and isentropic power which counteracts the improvement provided by lower indicated powers in the internally cooled case. Comparing internally cooled cases 1 and 3, it can also be concluded that the indicated power is lower for lower rotational speeds. This explains why lower rotational speeds result in the lowest efficiencies despite having the lowest indicated power. Although there could be additional pumping work required to circulate the coolant in the internally cooled case, this pumping power would only lead to a slight decrease in overall efficiency. Further, there is no additional cooling needed in an internally cooled case compared to a traditional compressor which could compensate for the added pumping needed for coolant.
4.5 Solid and Hollow Rotor Comparison Comparing Figs. 3 with 5 and Figs. 4 with 6, it can be concluded that the internal cooling is effective at reducing the overall rotor surface temperatures much lower than the dry running case without internal cooling. The overall rotor temperatures are much higher for the conventional rotor as compared to the internal cooling case. The magnitude of reduction in outlet temperatures can be observed from Table 3. There is a reduction of around 20 K for the lower pressure ratio case but about double that for the high-pressure ratio case. Looking at (Figs. 4b and 6b), it can be noted that the maximum rotor temperature for a certain crank angle reaches around 540 K for the solid rotor but remains as low as 460 K for the internally cooled hollow rotors. Similar observations can be made from (Figs. 4a and 6a), with around 400 K and 325 K respectively. The internal fluid cools down the rotors effectively and this cooling effect leads to lower discharge temperatures, which in turn improves efficiency. The magnitude of improvement differs with operating conditions, which is demonstrated from the broad range of pressure ratios and rotational speeds tested within this study. Although, it might appear that the mass flow rates within the simulation are not at steady state, this is not the case. The difference in mass flow rates can be accounted for by leakages, backflow due to adverse pressure gradient or due to temperature differences at the outlet, which affects density and thereby mass flow rates. The higher discharge pressures increase density and thereby mass flow rates. This explanation is corroborated through the significantly higher outlet densities of around 4.109 kg/m3 in case 2 compared to 1.204 kg/m3 in case 1 for the hollow rotors. The density change outweighs the increase in leakage flow and therefore the discharge mass flow rate is still higher. As explained in Saravana et al. [11], the inlet
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Fig. 5 Discharge temperature contour slices with velocity vectors for a Solid 19,000 RPM 3.2 bar; b Solid 19,000 RPM 7 bar
Fig. 6 Temperature contour plots along with average boundary temperature line plots for a Solid 19,000 RPM 3.29 bar. b Solid 19,000 RPM 7 bar
conditions are the same in both cases and therefore doesn’t change the suction density or the inlet mass flow rate, and hence the mass flow rates in the internally cooled case are not higher than the one in solid rotor simulation despite having higher discharge density at lower discharge temperatures. Despite the difference in inlet and outlet conditions, the difference is very similar for the solid rotor or the internally cooled simulations. This further proves the fact that internally cooled rotors perform better than conventional solid rotors under the same operating conditions.
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Table 3 Efficiency and power calculations for hollow and solid rotor configurations Data
Indicated power (kW) Isothermal efficiency (%) Isentropic efficiency (%)
Solid (case 1)
44.1
63.6
75.4
Hollow (case 1) 42.8
65.1
77.1
Solid (case 2)
92.69
42.7
57.3
Hollow (case 2) 90.93
43.5
58.3
Hollow (case 3) 39.9
40.36
48.12
Table 4 Compression conditions for hollow and solid rotor configurations Data
Outlet cycle average gas mass flow rate ( kg hr )
Inlet cycle average gas mass flow rate ( kg hr )
Suction pressure (bar)
Discharge pressure (bar)
Suction temperature (K)
Discharge temperature (K)
Solid (case 1)
950.00
−1000.00
1.013
3.33
293
440.0
Hollow (case 1)
889.45
−1000.71
1.013
3.33
293
422.6
Solid (case 2)
1429.23
−888.12
1.013
7.10
293
602.33
Hollow (case 2)
1520.09
−868.32
1.013
7.10
293
564.16
Hollow (case 3)
568.44
−578.43
1.013
3.31
293
410.4
5 Conclusion In this paper, a previously developed and verified CFD model is expanded to various operating conditions and the performance is compared. The hollow rotor with internal cooling has an increase in efficiency of 1% for higher pressure ratio and 2% for lower pressure ratio, with the highest efficiency at 19,000 RPM and 3.29 bar making it the optimal condition for improved performance under internal cooling. The extensive cooling costs and complex rotor manufacturing would be difficult to justify considering the modest 1–2% improvement in efficiency, however this technology has major potential as efficiency can be improved further by varying internal flow conditions and replacing the liquid with a refrigerant, which is an area currently being explored and will be presented in future studies. A future study could also include a deeper analysis into varying inlet mass flow rates for the coolant and observe how that affects performance.
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References 1. H.H. Patel, V.J. Lakhera, A critical review of the experimental studies related to twin screw compressors. Proc. Inst. Mech. Eng. Part E: J. Process Mech. Eng. 234(1), 157170 (2019) 2. N. Stosic, I. Smith, A. Kovacevic, Screw compressors: mathematical modelling and performance calculation (Springer, Heidelberg, 2005) 3. A. Kovacevic, Three-dimensional numerical analysis for flow prediction in positive displacement screw machines. Doctoral Thesis (2002) 4. A. Kovacevic, Boundary adaptation in grid generation for CFD analysis of screw compressors. Int. J. Numer. Methods Eng. 64(3), 401426 (2005) 5. Analysis PDM SCORG Retrieved from https://pdmanalysis.co.uk/scorg/ 6. H. Ding, Y. Jiang, in CFD simulation of a screw compressor with oil injection, IOP conference series: Materials science and engineering, Vol. 232 (1978) 7. H. Ding, Y. Jiang, S. Dhar, in CFD modelling of coupled heat transfer between solid and fluid in a twin screw compressor, IOP conference series: materials science and engineering, Vol. 5 (2002) 8. J. Willie, Conjugate heat transfer simulation and cooling optimization of the flow inside a screw compressor. IOP Conf. Series Mat. Sci. Eng. 1180(1), 012061 (2021) 9. S. Rane, A. Kovacevic, N. Stosic, I. Smith, Bi-directional system coupling for conjugate heat transfer and variable leakage gap CFD analysis of twin-screw compressors. IOP Conf. Series Mat. Sci. Eng. 1180, 012001 (2021) 10. A. Saravana, H. Liu, N. Able,J. Collins J, E.A. Groll, D. Ziviani, Rotordynamic and fatigue analyses of a twin-screw compressor with 4–6 configuration and internal cooling channels international compressor engineering conference 2792 (2022) 11. A. Saravana, H. Liu, N. Able, J. Collins, E.A. Groll, D. Ziviani, in Conjugate heat transfer analysis of a twin-screw compressor with 4–6 configuration and internal cooling channels, 11th international conference on screw machines (ICSM) (2022) 12. K.J. Richards, P.K. Senecal, E. Pomraning, CONVERGE 3.0*. Convergent Science Madison,WI (2022)
Design of Hobbing Cutter for Variable-Pitch Screw Rotor Yuan Hao , Yao Tonglin , Liu Changfeng , and Shu Yue
Abstract Innovatively extended a single-degree-of-freedom hobbing algorithm and proposed a low cost processing method for variable-pitch screw rotor of twin screw compressor and expander. Firstly, summarized the design method of hobbing cutter for constant-pitch screw rotor and derived the three-degree-of-freedom hobbing algorithm. Secondly, extended the algorithm to the design method of variable-pitch hob which can process the variable-pitch screw rotor. Finally, a design example which pitch has changed by a factor of 1.7 is given to verify the algorithm. Keywords Variable-pitch · Screw rotor · Hobbing cutter
1 Introduction The screw expander, which uses gas pressure energy to generate electricity, is an energy-saving product that can be widely used in petroleum, chemical and environmental protection fields to reduce enterprise energy consumption and improve energy utilization efficiency. Screw expander with variable-pitch screw rotor instead of constant-pitch screw rotor, can increase the maximum available inner volume ratio from the current 4.0–6.0 to 14.0, which can theoretically improve the efficiency of the expander by 10–15% [1], and thus can greatly improve its product competitiveness. However, variable-pitch screw rotor is currently usually machined by five-axis machining or turn-mill complex machining. The processing efficiency is low, the production cost is high, and the machine tools are usually very complex and expensive. The maximum processing size is limited, which further limits the size of the rotor. H. Yuan (B) · T. Yao · C. Liu Shanghai Marine Diesel Engine Research Institute (SMDERI), Shanghai 201108, China e-mail: [email protected] Y. Shu State Key Laboratory of Compressor Technology, Hefei General Machinery Research Institute Co., Ltd., Hefei 230031, Anhui Province, China © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_12
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Hobbing tools are used for manufacturing constant-pitch screw rotor by generation method, i.e. hobbing cutter and hobbing wheel. The hobbing cutter refers to the tool used for milling machines in the hobbing method and the hobbing wheel refers to the grinding wheel used for grinding machines in the hobbing method. The existing hobbing technology can only machine constant-pitch screw rotor but not variablepitch screw rotor. This paper extends the hobbing technique by proposing a technique for machining variable-pitch screw rotor by the generation method using variable-pitch hobbing tools. The machining can be done using a custom hobbing cutter or wheel in conjunction with simple gear machining machines, which can greatly improve machining efficiency, reduce production costs, and increase machining sizes. This technology can significantly reduce the cost of machining variable-pitch screw rotor, which in turn can be industrialized and applied to the whole field of screw rotor manufacture, extending the design methodology of screw compressors from the study of end profiles to the study of spatial rotor surfaces. In the field of gear research, a great deal of research has been carried out on hobbing machine and hob design, and several classic works have been compiled by experts in this field. For example, “Principles of Gear Meshing” by Litvin [2], “Principles and Calculations of Tool Design” by Ruxun [3], “Handbook of Tool Design” by Zhejun and Huaming [4], and “Theory and Practice of Accurate Tool Design” by Jiehua [5]. A variety of gear hob design algorithms (common rack method, Olivier principle, spatial tooth normal method, double-degree-of-freedom method, three-degree-of-freedom method) introduced in the above-mentioned monographs and hobbing algorithms from the screw compressor industry: “Screw Compressors— Mathematical Modelling and Performance Calculation” by Stosic et al. [6] have been programmed for verification. The programming results show that in the hob design for constant-pitch screw rotor, the calculation results of the multiple methods are very close (error less than 1 µm), indicating that all can be used in the engineering design of compressor rotor hobs. In the process of expanding the hobbing algorithm to variable-pitch screw rotor, the author found that the three-degree-of-freedom method, is most suitable algorithm. The relative rotation of the hob and rotor is considered as one degree of freedom, the axial feed of the hob as one degree of freedom and the axial feed of the rotor as one degree of freedom. When processing on a machine, the method of keeping all these three degrees of freedom in motion is called the three-degree-of-freedom method.
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2 Constant-Pitch Hobbing Algorithm 2.1 Coordinate Systems and Coordinate Transformation In order shape, a right-handed coordinate system is introduced. to study the hobbing σ p O p ; X p , Y p , Z p is a coordinate fixed in space. The basis vectors of this coordinate are i p , j p , kp . σ2 (O2 ; X 2 , Y2 , Z 2 ) is a moving coordinate linked with the rotor. The basis vectors of this coordinate are i 2 , j 2 , k2 . σ (O; X, Y, Z ) is a coordinate fixed in space. The basis vectors of this coordinate are i, j , k. σ3 (O3 ; X 3 , Y3 , Z 3 ) is a moving coordinate linked with hob. The basis vectors of this coordinate are i 3 , j 3 , k3 . The relative position of the hob and the rotor depends on the following two parameters: The mounting angle : the minimum angle between the hob axis and the rotor axis; The center distance A: the minimum distance between the hob axis and the rotor axis, is equal to the sum of the radius of the pitch circle of hob r1 and the radius of the pitch circle of rotor r2 , that is A = r1 + r2 . Define the rotor lead for unit rotation angle as p2 , the rotation angular speed of rotor as ω02 , the feed speed along the axial direction of rotor as v02 , the hob lead for unit rotation angle as p1 , the rotation angular speed for hob as ω01 , the feed speed along the axial direction of hob as v01 , the tooth number of hob as z 1 , the tooth number of rotor as z 2 . Then the hob rotor tooth ratio is: i 21 = z 1 z 2 = ω02 ω01 . Total angular speed of the hob and rotor are: ωI = ω01 + v01 / p1 and ω I I = ω02 + i v02 , where i will be calculated. After a period of time δt from the initial position, the rotor turns through angle ϕ I I = ω I I δt and ϕ2 = ω02 δt, the hob turns through angle ϕI = ωI δt and ϕ1 = ω01 δt, the rotor moves axially l2 = v02 δt, and the hob moves axially l1 = v01 δt. Then there are: ϕI = ϕ1 + l1 / p1 and ϕII = ϕ2 + i l2 . From coordinate system σ2 to σp : ⎡
⎤ ⎡ ⎤ ⎡ xp x2 cos ϕII − sin ϕII ⎢y ⎥ ⎢y ⎥ ⎢ sin ϕII cos ϕII ⎢ p⎥ ⎢ 2⎥ ⎢ ⎥ = M2 · ⎢ ⎥, where M2 = ⎢ ⎣ 0 0 ⎣ zp ⎦ ⎣ z2 ⎦ 0 0 1 1
⎤ 00 00⎥ ⎥ 1 l2 ⎦ 01
(1)
⎤ ⎡ ⎤ ⎡ ⎤ ip i2 cos ϕII − sin ϕII 0 ⎢j ⎥ ⎢ ⎥ ⎣ p ⎦ = M02 · ⎣ j 2 ⎦, where M02 = ⎣ sin ϕII cos ϕII 0 ⎦ 0 0 1 k2 kp
(2)
⎡
From coordinate system σp to σ :
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⎡ ⎤ ⎡ ⎤ ⎡ xp x − sin ⎢y ⎥ ⎢ y⎥ ⎢ 0 ⎢ p⎥ ⎢ ⎥ ⎢ ⎥ = Mp · ⎢ ⎥, where Mp = ⎢ ⎣ cos ⎣ zp ⎦ ⎣z⎦ 0 1 1
⎤ 0 − cos 0 1 0 −A ⎥ ⎥ 0 − sin 0 ⎦ 0 0 1
(3)
⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ip i − sin 0 − cos ⎢ ⎥ ⎢ ⎥ ⎦ 1 0 ⎣ j ⎦ = M0 p · ⎣ j p ⎦, where M0 p = ⎣ 0 cos 0 − sin k kp
(4)
Then there are: [x, y, z, 1]T = M p · M2 · [x2 , y2 , z 2 , 1]T
i, j, k
T
(5)
T = M0 p · M02 · i 2 , j 2 , k2
(6)
From coordinate system σ to σ3 : ⎡ ⎤ ⎤ ⎡ x x3 cos ϕ I sin ϕ I 0 0 ⎢ y⎥ ⎢y ⎥ ⎢ − sin ϕ I cos ϕ I 0 0 ⎢ ⎥ ⎢ 3⎥ ⎢ ⎥ = M · ⎢ ⎥, where M = ⎢ ⎣ 0 0 1 −l1 ⎣z⎦ ⎣ z3 ⎦ 0 0 0 1 1 1 ⎡
⎤ ⎥ ⎥ ⎦
(7)
2.2 Meshing Equation During the meshing process of the hob and the rotor, at any moment, the surfaces are in tangential contact and the velocity vector of the relative motion of the tangent point is perpendicular to the normal vector, i.e. n · v I −I I = n · (v I − v I I ) = 0
(8)
The angular and axial velocities of the hob and rotor are expressed as:
ω I = ωI k v 01 = v01 k
(9)
ω I I = ω I I k2 = −ω I I cos i − ω I I sin k v 02 = v02 k2 = −v02 cos i − v02 sin k
(10)
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ωI , ωII , v01 , v02 are the norms of each velocity vector. Let there be a contact point M in space with coordinate value (X, Y, Z ) in a fixed coordinate system σ , there is
r I = O M = xi + y j + zk r I I = O M + O p O = O M + A j = x i + (A + y) j + zk
(11)
The velocity of the point M moving with the rotor and hob respectively are:
v I I = ω I I × r I I + v 02 v I = ω I × r I + v 01
(12)
Combining the two functions, the velocity vector of the relative motion can be calculated.: v I −I I = [−(x2 sin ϕ I I + y2 cos ϕ I I )(ω I + ω I I sin ) + ω I A + v02 cos ]i + [−(x2 cos ϕ I I − y2 sin ϕ I I )(ω I sin + ω I I ) − ω I (z 2 + l2 ) cos ] j + [ω I I cos (x2 sin ϕ I I + y2 cos ϕ I I ) + v02 sin + v01 ]k
(13)
The equation of end face
profile of the rotor and it’s derivative with respect to t x0 = x0 (t) x0 = x0 (t) are and . The rotor surface is formed by the left spiral y0 = y0 (t) y0 = y0 (t) movement of this section around the Z axis and it’s function is: ⎧ ⎪ ⎨ x2 = x0 cos θ − y0 sin θ y2 = x0 sin θ + y0 cos θ (14) ⎪ ⎩ z 2 = − p2 θ Assume that, a point M2 (X 2 , Y2 , Z 2 ) of the rotor has the radius vector: r 2 = x2 i 2 + y2 j 2 + z 2 k2
(15)
and normal vector: n2 = where,
∂ r2 ∂ r2 × = n x2 i 2 + n y2 j 2 + n z2 k2 ∂t ∂θ
(16)
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⎧ ⎪ n x2 = ⎪ ⎪ ⎪ ⎪ ⎨ n y2 = ⎪ ⎪ ⎪ ⎪ ⎪ ⎩n = z2
∂z 2 ∂ y2 ∂ y2 ∂z 2 − = − p2 x0 sin θ + y0 cos θ ∂t ∂θ ∂t ∂θ ∂ x2 ∂z 2 ∂z 2 ∂ x2 − = p2 x0 cos θ − y0 sin θ ∂t ∂θ ∂t ∂θ ∂ x2 ∂ y2 ∂ y2 ∂ x2 − = x0 x0 + y0 y0 ∂t ∂θ ∂t ∂θ
(17)
The component of the normal vector n2 in the fixed coordinate σ can be obtained by formula (11): ⎧ ⎪ ⎨ n x = − n x2 cos ϕII − n y2 sin ϕII sin − n z2 cos n y = n x2 sin ϕII + n y2 cos ϕII ⎪ ⎩ n z = n x2 cos ϕII − n y2 sin ϕII cos − n z2 sin
(18)
By substituting formula (14) and formula (18) into formula (8), the meshing equation can be obtained: ωII y2 n x2 − x2 n y2 + v01 · cos n x2 cos ϕII − n y2 sin ϕII − n z2 sin − v02 n z2 ⎤ ⎡ − sin n x2 cos ϕII − n y2 sin ϕII A + sin y2 n x2 − x2 n y2 ⎥ ⎢ + ωI · ⎣ + n z2 cos (x2 sin ϕII + y2 cos ϕII − A) ⎦=0 − cos (z 2 + l2 ) · n x2 sin ϕII + n y2 cos ϕII (19)
2.3 Three-Degree-of-Freedom Hobbing Method The three-degree-of-freedom method has the most variables and is the most complex method, yet it provides a clear description of the mathematical equations and physical meaning of the hob and rotor machining process. It is therefore more suitable for the extension of variable-pitch. The hobbing process can be viewed as the meshing of the three degrees of freedom: ωI , v01 , v02 . After substituting them into formula (19), we can obtain: v02 · B + ωI · C + where:
v01 (C + D) = 0 p1
(20)
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⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩
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B = i y2 n x2 − x2 n y2 − n z2 C = − sin n x2 cos ϕII − n y2 sin ϕII A + sin y2 n x2 − x2 n y2 +n z2 cos (x2 sin ϕII + y2 cos ϕII − A) − cos (z 2 + l2 )· n x2 sin ϕII + n y2 cos ϕII + i 21 y2 n x2 − x2 n y2 D = p1 cos n x2 cos ϕII − n y2 sin ϕII − p1 n z2 sin − i 21 y2 n x2 − x2 n y2 (21)
Since ωI , v01 , v02 are independent of each other and there is no functional relationship between them, to satisfy the meshing Eq. (20), they must simultaneously satisfy: B=C =D=0
(22)
Substituting formula (14 – 17) into B = 0, we can obtain: i =
n z2 1 =− y2 n x2 − x2 n y2 p2
(23)
Substituting formula (23) into D = 0, we can obtain: n x2 cos ϕII − n y2 sin ϕII =
p1 sin − p2 i 21 · n z2 p1 cos
(24)
Substituting formula (23) into formula (24), and defining: tan μ = y0 x0 , we can obtain: p1 sin − p2 i 21 (25) f 1 (t) = θ + ϕII = arcsin (x0 cos μ + y0 sin μ) − μ − p1 p2 cos Substituting formula (14), (17), (23) into C = 0, we can obtain: f 2 (t) = z 2 + l2 =
− p2 n z2 (i 21 + sin ) + n z2 cos (x2 sin ϕII + y2 cos ϕII − A) − sin n x2 cos ϕII − n y2 sin ϕII A cos n x2 sin ϕII + n y2 cos ϕII
(26)
Then, formula (25) minus formula (26)/(− p2 ), we have f 1 (t) −
f 2 (t) = (θ + ϕII ) − − p2
z 2 + l2 − p2
l2 l2 = (θ + ϕII ) − θ + = ϕII − − p2 − p2
From formula (1) and formula (15), we have, ⎧ ⎪ ⎨ xp = x0 cos(θ + ϕII ) − y0 sin(θ + ϕII ) yp = x0 sin(θ + ϕII ) + y0 cos(θ + ϕII ) ⎪ ⎩ z p = − p2 θ + l 2
(27)
(28)
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From formula (3) and formula (28), we have the equation of the meshing surface, ⎧ ⎪ ⎨ x = − sin [x0 cos(θ + ϕII ) − y0 sin(θ + ϕII )] − cos (− p2 θ + l2 ) y = x0 sin(θ + ϕII ) + y0 cos(θ + ϕII ) − A ⎪ ⎩ y = cos [x0 cos(θ + ϕII ) − y0 sin(θ + ϕII )] − sin (− p2 θ + l2 )
(29)
There is only one parameter t in the above formula (29), which represents the meshing line. The equation of hob tooth surface can be obtained from formula (7), ⎧ ⎪ ⎨ x3 = x cos ϕI + y sin ϕI y3 = −x sin ϕI + y cos ϕI ⎪ ⎩ z 3 = z − l1
(30)
Substituting the angle relationship gives, l2 f 2 (t) = i 12 f 1 (t) − ϕ1 = i 12 ϕ2 = i 12 ϕII − − p2 − p2 l1 f 2 (t) + ϕI = i 12 f 1 (t) − − p2 p1
(31) (32)
Substituting the formula (25), formula (26) into formula (29 – 32) and other equations, we can get the hob tooth equation. From formula (30), we can see, there are only two independent parameters t and l1 . In order to calculate the axial profile of the hob, the following condition is needed: z 3 = 0.
3 Variable-Pitch Hobbing Algorithm The hob design for variable-pitch rotors can be achieved by adapting the constantpitch of the rotor in the above algorithm to the parametric equation of variable-pitch. The analysis reveals that the individual differential elements of cross-sections of the variable-pitch rotor are not identical (different pitches for each differential section element). Therefore, the cutting tools are not identical, indicating that the design of the tool cannot be simplified by the axial feed of the rotor or the tool. The machining problem of variable-pitch rotor degenerates into a single degree of freedom problem. Therefore, we named this extended algorithm as “single-degree-of-freedom hobbing method”. Physically it means that each differential section element of the rotor requires a separate section of hob for machining. Once the sections of the rotor have been combined and shaped, the hobs for each section are combined and shaped to a “unique” variable-pitch hob. The term “unique” means that the hob structure is
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unique when the hob design parameter is determined. When the tool parameter is adjusted, the shape of the hob will change accordingly. After replacing the variables of the three-degree-of-freedom method, which expresses the axial feed motion of the rotor and hob, with zero, and giving the equations for pitch and rotor height, the constant-pitch hobbing algorithm can be extended to variable-pitch hobbing algorithm. Eliminate the axial feed of the hob and the rotor, i.e. v01 = v02 = 0, so that l1 = l2 = 0, then formula (20) is reduced to ωI · C = 0
(33)
Let the rotor lead for unit rotation angle of a variable-pitch rotor be renumbered as the function of rotation angle, that is p2 (θ ). Thus, the rotor height coordinates z 2 can θ be rewritten as:z 2 (θ ) = 0 p2 (θ )dθ . Let the hob lead for unit rotation angle of the variable-pitch hob be renumbered as the function of rotation angle, that is p1 (θ ). The derivation of Eq. (25) does not involve the variation of pitch. So that any differential section element, still satisfies it’s equation condition, which can be rewritten as p1 (θ ) sin − p2 (θ )i 21 (34) θ + ϕII = arcsin (x0 cos μ + y0 sin μ) − μ − p1 (θ ) p2 (θ ) cos Denote it as: θ + ϕII = f 1 (t, θ ). Then, the Eq. (26) can be simplified as,
θ 0
p2 (θ )dθ =
− p2 (θ )n z2 (i 21 + sin ) + n z2 cos [x0 sin( f 1 ) + y0 cos( f 1 ) − A] + p2 (θ ) sin x0 sin( f 1 ) + y0 cos( f 1 ) A p2 (θ ) cos y0 sin( f 1 ) − x0 cos( f 1 )
(35)
It is very difficult to solve this integral equation theoretically, thus numerical method can be used instead. Since the rotor no longer adds axial feed, the hob and rotor must move in a rotational motion at an axially fixed position. It is recommended that the zero position (i.e. z(θ0 ) = 0 position) of the rotor should be placed near the axial geometric center. Define the workpiece torsion angle is τ , and the total length is L, then we have ⎧
⎪ ⎨ z(θ1 ) = L 1 , θ1 < 0, L 1 < 0 |θ1 | + |θ2 | = τ z(0) = 0 , where ⎪ |L 1 | + |L 2 | = L ⎩ z(θ2 ) = L 2 , θ2 > 0, L 2 > 0
(36)
This zero position of integration can be adjusted according to different pitch variations of rotors.
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4 Example of Variable-Pitch Hob Design In order to keep the outer diameter of the male and female rotors consistent, this paper gives the following end profile design example (Fig. 1): Number of teeth of male rotor and female rotor: 3, 5; Rotor center distance: 120 mm; Outer diameter of male rotor and female rotor: 160 mm. The variation of lead with rotor length is shown in Fig. 2. The design parameters of the hobs are shown in Table 1. The calculated tools are shown in Fig. 3.
Fig. 1 Design example of rotor profile
Fig. 2 Design example of variation lead
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Table 1 Design parameters of the hobs Rotors
Center distance between the hob and rotor: A/mm
Number of teeth of hob:z 1
Mounting angle: /°
Length between the z(θ0 ) = 0 position and the z(θ1 ) = L 1 position: |L 1 |/mm
Male rotor
195
7
17.1887
207.8697
Female rotor
270
7
22.9183
207.8697
Fig. 3 3D views of the hobbing cutter of the male rotor and female rotor
5 Conclusions The variable-pitch hob can be regarded as a conjugate rotor with the staggered shaft of the variable-pitch rotor. When the angle of the staggered shaft is 0° (i.e. parallel), the hob is a conjugate rotor of the machining rotor, which can be used in a screw compressor. That is, the female rotor or male rotor can be regarded as a hob of each other. However, due to the size limitation of the actual machine, it is difficult to achieve the 0° mounting angle, which also provides the possibility for the industrial application of the variable-pitch hob in this paper. At present, the design of the pitch variation and axial profile of the rotors is not considered in the design of the hob, some profiles can not even design variable-pitch hobs, that makes the design of variable-pitch hob very difficult, and the selection range of design parameters very narrow. At the same time, there are certain restrictions on the range of the pitch variation. The maximum and minimum value of pitch, which seems to be within 4 times. Another problem of single-degree-of-freedom hobbing for variable-pitch rotor is that we couldn’t design the hob for a very short section of the rotor and process the whole rotor through axial feed. Theoretically, in order to complete the machining, one point on the rotor needs to correspond with one point on the hob. The blades of hobbing cutter cannot cover the whole cutters profile, so in theory, only rough machining can be carried out by it. Finish machining should be carried out through hobbing wheel. However, it is possible to change the teeth number of hob (greater than 1 and not equal to the teeth number of workpiece rotor), and design different
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blade positions for different teeth, to reduce the machining error as much as possible and to enable engineering applications. It is hoped that through further research into various areas such as machining machines, hobbing tools and rotor profiles, industrialised processing and mass application of variable-pitch rotors can eventually be realised. This will further improve the efficiency of screw compressors and expanders, increase energy efficiency and at the same time boost the screw industry by reducing the production cost for such compressors.
References 1. C. Huang, New Twin Screw Compressor Design by Deviation Function Method. UCLA. ProQuest ID: Huang_ucla_0031D_13328. Merritt ID: ark:/13030/m59k6k3p. Retrieved from https://escholarship.org/uc/item/7fj942k5 (2015) 2. F.L. Litvin, Teoria zubchatiih zaceplenii (Theory of Gearing), 2rd ed. by Nauka Moscow (1968) 3. Li. Ruxun, Principles and Calculations of Tool Design (Jiangsu Science and Technology Press, Jiangsu, China, 1985). ((in Chinese)) 4. Y. Zhejun, L. Huaming, Handbook of Tool Design (China Machine Press, Beijing, China, 1999). ((in Chinese)) 5. L. Jiehua, Theory and Practice of Accurate Tool Design (National Defense Industry Press, Beijing, China, 2005). ((in Chinese)) 6. N. Stosic, I. Smith, A. Kovacevic, Screw Compressors (Springer, Berlin, 2005)
Influence of Bearing and Seal Design on Performance of an Oil-Injected Screw Compressor for Refrigeration Applications Thibaud Plantagenet , David Buckney, Lihini Seneviratne, and Matthew Read
Abstract Screw compressors are key components in a range of refrigeration and air conditioning applications. It is essential that the design and operation of these systems is optimised to ensure energy efficiency and reliability. An important aspect of the compressor design is the choice of bearings used to support the twin helical rotors. These bearings must be capable of providing the reaction forces required to accurately locate the rotors across a defined range of inlet and discharge pressures for machines with a range of volume ratios and operating speeds. This paper explores the selection process for both rolling element and hydrodynamic bearings. The influence on compressor performance of these bearings can be defined in terms of the frictional power losses and required oil supply flow rates. Bearings can also have indirect influence on overall compressor efficiency, due to the potential introduction of leakage paths of process gas through low-pressure bearing oil drains. Therefore, additional sealing requirements for each bearing type are investigated, allowing an assessment of leakage flow and frictional power loss of bearing/seal systems and their influence on the overall performance of different compressor configurations in terms of energy efficiency, lifespan and maintenance requirements. Keywords Refrigeration twin-screw compressor · Oil-injected · Hydrodynamic bearing · Cylindrical roller bearing · Annular oil seal
T. Plantagenet · M. Read (B) Department of Engineering, City University of London, London, UK e-mail: [email protected] D. Buckney · L. Seneviratne Mayekawa UK Ltd, Glasgow, UK © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_13
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1 Introduction Screw compressors are used for a wide range of applications including air, refrigeration and process gas compression. These machines are required to operate with high efficiency and reliability, and significant research has been conducted on their geometrical design, operation, and performance optimization. While areas such as rotor profiling and geometry are well characterized, there is relatively little literature focusing on the various mechanical losses that occur in these machines. These losses can be a significant percentage of the power input, and consist of frictional losses in bearing, seals, fluid shearing in clearance gaps and contact between rotors. The selection of bearing and seal components is therefore an important element of machine design influencing the volumetric efficiency and specific energy consumption. The ultimate aim of the current research is to enable the future integration of bearing and seal models with existing thermodynamic models, which would allow holistic optimization of the compressor geometry and components. The present paper focus only on the design methodology for both hydrodynamic and cylindrical roller bearings (CRBs) for supporting radial loads and oil seal, allowing an estimate of the power losses and leakage flows within the compressor. The example of an ammonia (R717) refrigeration application has been used and is described in the following section.
2 Definition of Test Cases Two rotor sizes have been considered in the current study: 127.5–321.3 mm rotors with the same N46 rotor profile, a diameter to centre distance ratio of 1.275, a L/ D ratio of 1.65 and a rotational speed of the male rotor of 3600 rpm. The criteria were considered to be representative of refrigeration applications (Ammonia, with non-soluble oil), and allow an initial assessment of the bearing and seal design for two operating conditions presented in Table 1. The choice of bearing type used to support loads in the screw compressor has an influence on the required oil supply, and the sealing requirements necessary between the working chamber and bearings. In the current study, two different bearing/seal configurations are considered and presented in Fig. 1: hydrodynamic bearings only, and cylindrical roller bearing + oil seals. Moreover, axial bearings supporting axial load are not considered in this stage of the study. Table 1 Definition of machine operating conditions for test cases
Volume index
2.63
5.8
Evaporating temperature [°C]
−5
−25
Condensing temperature [°C]
35
35
Evaporating pressure [MPa]
0.355
0.155
Condensing pressure [MPa]
1.35
1.35
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Fig. 1 Schematics of oil flow paths and pressures (supply, chamber, evaporating pressures) for a Hydrodynamic bearing and b Cylindrical roller bearing and dual oil seal
Initial bearing load analysis has been performed using the SCORG chamber modelling software using the data in Table 1 and the following assumptions: • Model input parameters were adjusted to target typical performances (volumetric efficiency, oil flow rate, discharge temperatures…) of existing refrigeration compressors. • Radial bearing loads act at rotor end faces. This is considered a logical starting point as it is a design objective to minimize the bearing span, and this quantifies the maximum possible force on the highly loaded female radial bearing. The resulting rotor forces allow an estimate of the maximum bearing loads for a particular combination of machine geometry and operating conditions described in each test case. The results show that higher loads occur for the larger rotor size and low Vi , which is due to the earlier opening of the discharge port (resulting in high pressure acting over a larger area of the rotor surfaces). High pressure bearings are two to three times more loaded than low pressure bearings. Finally, the heavily loaded bearing in every case is the female bearing on high pressure side. Regarding the variation of the direction of radial forces, in most cases, it doesn’t exceed 5°. Based on these results the variation of direction of radial forces was neglected in the study, and only minimum and maximum loads where extracted.
3 Bearings and Seals Selection and Design To select appropriate bearings for a given application, it is important to understand the working principles and physical mechanisms involved in different technologies. In this paper, only rolling element bearings and hydrodynamic bearings are considered. The rolling element bearings are composed of one inner ring fixed to a (usually) rotating shaft, an outer ring fixed in a housing bore (casing), rolling elements (balls or cylinders) that are disposed between the two rings and a cage which avoids contact between rolling elements. In addition, the bearing is very often filled with lubricant (oil, grease) and sometimes sealed to avoid contamination and lubricant leakage. Thus, this technology uses rolling elements to allows the rotation of the shaft and carry the load from the shaft to the casing. Physically, rolling element bearings can be defined using Hertz contact theory for deformation of solids and lubrication to
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describe the behaviour of the flow. This is usually referred as Elasto-Hydrodynamic Lubrication (EHL). However, rolling element bearings can work in all regimes of lubrication. Hydrodynamic bearings are composed of one rotating shaft (or journal) mounted in a housing bore (bearing/bushing) with a clearance gap partially filled with a fluid (usually oil). When the shaft is not rotating, the load applied to the shaft (W ) pushes the journal into contact with the bushing. As the shaft starts to rotate, the journal begins to roll inside the bushing. After a certain speed is reached, the hydrodynamic fluid film is established, and the journal finds its equilibrium position. At this stage, the static load is compensated by generation of a pressure field in the fluid film mainly due to restriction of the film thickness along the circumference and the shear stress of the flow. This is known as the wedge effect and the full mathematical model of hydrodynamic lubrication (including wedge, stretch and squeeze effects) was developed by Reynolds in the late nineteenth century. In some cases, hydrodynamic bearing can also work in EHL conditions, and in a lesser extent in boundary and mixed lubrication regimes during start up and shut down.
3.1 Bearing Design Constraints The constraints limiting and defining the boundaries of the current study are discussed. Constraints can be based on design rules, material properties or application. Neale in “The Tribology Handbook” [1] graphically present the limits of different bearing technologies for a given load capacity, a rotational speed and a shaft diameter as shown in Fig. 2. As can be observed, hydrodynamic bearings are suitable for higher speed and load than rolling element bearings. The limit between rolling element and hydrodynamic bearings for any diameter is defined by a red line in Fig. 2. Another constraint for the design of both technologies is inherent to the machine design and defined by the bearing envelope which limits the size of the bearing. Moreover, there are specific constraints for each bearing, as the bearing rating life for the roller bearings and minimum film thickness for the hydrodynamic bearing to cite only two. All constraints are listed and detailed. Bearing Envelope An important consideration when designing or selecting the type of bearing to use in a screw compressor is whether it can be assembled and physically fit in the compressor, without interfering with other compressor functions. Then, the bearing envelope represents the limits of what can comfortably be arranged for normal screw compressor function. An exercise was undertaken to review existing compressor designs so that common screw compressor geometry constraints could be identified and defined in a simple way, whilst allowing as much design flexibility as possible. The presented design envelope on the defined test cases is for the purposes of radial bearing and, where applicable, seal design. Wherever possible, a larger shaft
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Fig. 2 Selection by load capacity of bearings with continuous rotation [1] m, f
diameter (I Db ) is preferred for rigidity and for easier design of additional shaft features that are outboard of the radial bearings. Additionally, a smaller bearing m, f outer diameter (O Db ) is advantageous as it allows more material thickness in the casings and/or larger port flow areas. Envelope limits are all referenced to the rotor outer diameter (O D) to make these rules generic for both rotor sizes. f The male and female bearing outer diameter (O Dbm , O Db ) must satisfy the following constraints:
f
O Dbm + O Db < 2 A m, f O Db ≤ 0.84O D
(1)
The first constraint is driven by the fact that there is limited space between rotor axes (centre distance A), while the second constraint is for each individual rotor to ensure that there is sufficient clearance and material thickness for Vi and capacity slide valve actuation. m, f The male and female bearing inner diameters I Db must satisfy the following constraints: m, f
0.26O D ≤ I Db
≤ 0.49O D
(2)
The upper limit on the inner diameter is restricted by the maximum shaft size that will fit through the casing once material allowance has been added to allow for design of suction and discharge ports. The lower limit on the shaft size is more subjective
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and is based on analysis of the drive shaft diameter on existing compressor designs with this 4/6 rotor design. Cylindrical Roller Bearing Limits CRBs have several limits which are related to the size, rotational speed, load, lubricant, etc. Bearing manufacturers provide limits on maximum rotational speed and minimum bearing load, which need to be satisfied for the selection of the CRB. Moreover, the maximum bearing load is not directly limited but based on the bearing rating life for a given application. For this analysis, the minimum bearing life has been selected to be higher than 30000 h and if possible higher than 50000 h. There are various models to estimate the bearing life of rolling element bearings, but they are mainly based on the fatigue limit of the bearing. The standard ISO 281 [2] presents calculation of basic rating life and modified rating life. SKF, applied ISO rating and modified rating life to their bearings, with some modification for SKF Explorer bearings range. Moreover, the ISO rating life calculation is also detailed by Harris and Kotzalas [3]. Hydrodynamic Bearing Limits Four limits can be distinguished for the operating region of a hydrodynamic bearing based on the applied load and on the rotational speed [1]. These limits are related to temperature, stability, wear and oil degradation. In order to satisfy these limits and restrict the study, assumptions have been applied in this paper: • The bearing geometry is restricted to cylindrical journal bearing. • The normal range of specific pressure (Load/L D) for the hydrodynamic bearing calculation has been defined between 2 and 4 MPa. • The L/D ratio is restricted to 0.5, 0.75 and 1, as the lower values satisfy lightly loaded bearings and upper value offers a compromise between load capacity and misalignment [4]. • To ensure hydrodynamic lubrication, it is initially assumed that the film thickness parameter λ ≥ 10 [5]. The minimum film thickness can then be expressed as shown in Eq. (3) with an assumed value of composite roughness σ . h min ≥ λσ → h min ≥ 8.5μm
(3)
• The allowable maximum surface pressure in the bearing is very dependent to the bearing material. It is assumed that a layer of white metal is used in the bearing. After consideration of material thickness and the temperature dependence of compressive yield strength, the maximum allowable peak pressure in the journal bearing has been limited to 11 MPa. • Maximum temperature is dependent of material and lubricant degradations. An assumed limit of 120 °C is used based on practical compressor operation. As the stability and dynamic behaviour of bearings and rotors is not in the scope of this study an initial way to avoid instability is to ensure a minimum eccentricity of the
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Fig. 3 Dual oil seal configuration
journal in the bearing (journal bearings can present whirl and whip instability when totally centred). A minimum eccentricity ratio is of 0.4 has been judged to ensure safe design for lightly loaded bearing in an initial analysis. Moreover, in future analyses, calculation of bearing dynamic coefficients and stability as well as implementation of preloaded bearings (lemon bore, tilting pad) should be considered. Dual Oil Seal Design In order to provide a similar level of sealing between roller and hydrodynamic bearings, an oil seal configuration has been considered at the high-pressure side only. The oil seal design corresponds to a dual oil seal shown in Fig. 3, for which the diameter (D) is based on the inner diameter of the CRB for each case. The dual oil seal is divided into two seals: Seal 1 between the oil supply at supply pressure (Ps ) and the process gas at compressor chamber pressure (Ps1 ); Seal 2 between the oil supply (Ps ) and the bearing chamber at evaporating pressure (Ps2 ). To simplify the calculation, the compressor chamber pressure (Ps1 ) was taken as the average of condensing and evaporating pressure at the high-pressure side, and as the evaporating pressure at the low-pressure side. Based on incompressible and viscous flow for an annular seal perfectly centred [6], the volume flow rate in each annular seal can be expressed by Eq. (4). Q s1,s2
π DCr3 Ps − Ps1,s2 = 12μ L
(4)
where D is the journal diameter, Cr the radial clearance, μ the dynamic viscosity, P the differential pressure and L the seal length. For the design of oil seal, the amount of leakage flow has been selected based on a proportion (30%) of the side leakage flow observed in the journal bearing. It is assumed that all parameters except differential pressure have been set to be identical for both seals, then the proportion of leakage flow between each seal is known. The radial clearance is selected to be slightly bigger than the clearance in the CRB, which is fixed at approximately 1.5 times the CRB mean clearance. For both seals (Seal 1 and Seal 2), the length is calculated as well as power losses due to shear and extrusion, temperature increases along the oil flow path of the seal.
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3.2 Bearings and Seals Loss Modelling This section aims to present the models used to estimate the bearing power loss for rolling element bearing (especially CRB) and hydrodynamic bearings (cylindrical journal/sleeve bearing). Two models have been used to estimate the CRB power losses: Palmgren model and SKF model. Power loss of hydrodynamic bearing is extracted from the finite length bearing theory. For the dual oil seal, power loss is based on dissipated power by the shear of lubricant due to rotational speed and power used to “push” the oil axially into the seal due to the differential pressure. CRB Loss Models For Palmgren and SKF models the frictional moment is calculated, which multiplied by the rotational speed give power loss. Palmgren’s model is well known and documented in many books such as Harris and Kotzalas handbook [7]. The model was developed based on experimental tests for various load conditions and slow to moderate rotational speeds. In this model, friction torque is divided into three terms, one load dependent, one lubricant dependent and an additional one in case of axial load applied to the CRB. SKF developed a more sophisticated model to calculate the frictional moment of rolling element bearing include several sources of losses which are rolling and sliding friction, seal and drag losses. These four components of the total frictional moment account for a large variety of properties and are based on several empirical coefficients. Power loss models will not be further detailed here, and reader can find extensive model description in the previously cited book and in SKF website [8], for Palmgren and SKF models, respectively. Oil flow rate in the CRB is estimated based on the allowed temperature increase (Tlim ) in the bearing based on the power loss and lubricant properties by Eq. (5). Q=
κ Ploss ρC p T
(5)
where, κ, is the proportion of heat convected by the flow, set to κ = 0.8 in first instance and ρ and C p , which are the density and specific heat of the fluid, respectively. Hydrodynamic Bearing Loss Model Hydrodynamic bearing calculation is based on solution of Reynolds equation, which in many cases has no analytical solution and must be solved numerically. This analysis is simplified by using tables for specific cases available in the literature, providing numerical solution of static characteristics of hydrodynamic journal bearing for several L/D ratios and different lubrication conditions. In this study the L/D ratio was previously constrained to 0.5, 0.75, and 1, thus the dimensionless journal bearing parameters for these ratios have been extracted from [5]. To apply this data, the Sommerfeld number S is calculated. This is a nondimensional parameter formed using all relevant parameters of the journal bearing
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as presented in Eq. (6). S=
μNs DL R 2 W Cr
(6)
where μ is the dynamic viscosity, Ns the rotational speed in rotation per second, D the journal diameter, L the bearing length, W = Fr the applied radial load, R the journal radius and Cr the radial clearance. The radius is kept in the equation to show the ratio Cr /R which is an important design parameter. As an initial value, Cr /R ∼ 10−3 . With calculation of the Sommerfeld number, all other parameters can be linearly interpolated, and the following dimensional characteristics calculated: • • • • •
Eccentricity (e), minimum (h min ) and maximum (h max ) film thickness. Leakage (Q L ) and inlet (Q i ) flow rates in m3 /s for full film starting from h max . Friction coefficient ( f ), friction force (F) and power loss (Ploss ). Specific (Pspec ) and maximum surface pressure (Pmax ). Temperature rise (T ), average temperature of oil inside the bearing (Toil ) and maximum temperature (Tmax ).
The calculation of static characteristics of journal bearing is an iterative process as the lubricant’s properties (viscosity, density, specific heat) change with the temperature which are known from −20 to 100 °C. The iterative process can be stopped when the difference of T between two iterations is inferior to 1 °C. Moreover, the oil supply arrangement (size and position) has an influence on the leakage flow (Q L ). It was decided to use two axial grooves at ± 90° for this analysis, using the same reference [5] the side leakage flow is calculated based on L/D ratio, eccentricity ratio and empirical coefficients. Seal Loss Model The power loss of the seal can be defined by the power needed to ensure the rotation of the shaft to counteract the Couette flow (shear of the fluid layers in the seal due to the rotation) and the power needed to extrude the flow axially (to push the fluid out of the seal). This modelling of seal power loss is fully detailed in San Andres lecture note 11 [6].
3.3 Bearing Selection Methodology A simplification of the bearing and dual oil seal selection methodology is depicted in the Fig. 4. For each bearing location the minimum and maximum radial forces are extracted from SCORG. Maximum load and size constraints based on bearing envelope are used as inputs for CRB selection using basic and modified rating life (ISO 281 and SKF Explorer). Power losses are calculated for the CRB using Palmgren
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Fig. 4 Selection and calculation methodology for bearings and oil seal
and SKF models. Oil injection in CRB is estimated based on temperature increase in lubricant to dissipate heat loss. For hydrodynamic bearing, the static characteristics are calculated using finite length bearing theory for a given L/D ratio and satisfying all hydrodynamic bearing limits for maximum and minimum radial load. Power loss is extracted and side leakage flow is calculated for twin-groove design for the maximum load case. Dual oil seal length is calculated based on an incompressible viscous flow for a given leakage oil flow (proportion of JB oil flow) and geometry based on CRB selected size. Seal power loss is then calculated as well as temperature increase along the seal (similarly to CRB). Total power loss and oil consumption are calculated by the sum of the four bearings (on low-pressure and high-pressure side and on male and female rotors), for cylindrical roller bearing + oil seal and hydrodynamic bearing. Finally, both configurations are compared in terms of power loss, oil consumption and size.
4 Performance Analysis of Bearing-Seal Configurations In this section the results from the bearing and seal analysis will be presented for the screw compressor test cases with both CRB and hydrodynamic bearing options.
4.1 Cylindrical Roller Bearing Results of the CRB selection process are presented in Table 2 for the two rotor sizes. For each bearing position, i.e., Low Pressure Male (LPM), High Pressure Male (HPM), Low Pressure Female (LPF) and High Pressure Female (HPF), the selected
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Table 2 Selection results of cylindrical roller bearing for the two rotor sizes 127.5 mm
321.3 mm
Bearing position
LPM
HPM
LPF
HPF
LPM
HPM
LPF
HPF
Minimum load (VI 5.8) [kN]
1.20
3.08
1.63
4.43
7.61
20.56
10.27
29.16
Maximum load (VI 2.63) [kN] 2.32
5.26
3.10
7.15
14.34
34.39
18.85
45.67
Bearing reference NU…
2207
2207
2207
2307
2217
2317
2217
2317
d [mm]
35
35
35
35
85
85
85
85
D [mm]
72
72
72
80
150
180
150
180
B [mm]
23
23
23
31
36
60
36
60
Cr range [µm]
25–35 25–35 25–35 25–35 50–85 50–85 50–85 50–85
Palmgren power loss [W]
42
59
26
54
482
1070
314
736
Palmgren CRB oil flow [l/min] 0.115
0.164
0.073
0.149
1.336
2.966
0.870
2.040
SKF power loss [W]
66
85
38
63
811
1766
446
914
SKF CRB oil flow [l/min]
0.183
0.235
0.106
0.176
2.248
4.894
1.236
2.533
bearing reference and corresponding geometry is shown. Power and oil consumption are calculated using the Palmgren and SKF models based on the maximum load. For the small rotor size, the same bearing reference (NU2207) can be used for 3 bearing positions and only on the highest loaded position the NU2307 should be used in order to satisfy the bearing life requirements. Rolling elements are bigger (length and diameter) in NU23## series in comparison of NU22##, which allows the extension of bearing life for identical conditions. On the 321.3 mm rotor size, NU2317 are used for high pressure (discharge) side and NU2217 for low pressure side. Overall, the SKF model shows higher power losses than Palmgren model, however, this model appears to give more accurate results by more precisely taking account of the different friction sources. Moreover, it can be observed in. Table 2 that CRBs on male rotor generate more power losses than those on female rotor while loads are higher on the female rotor. This is explained by the rotational speed of the female rotor which is 4/6 times lower than male rotor.
4.2 Hydrodynamic Bearing Table 3 presents the designed journal bearings for the two rotor sizes based on the finite length bearing theory with twin grooves located at ± 90° of the load. Similarly to CRB selection, journal bearing power loss and oil flow have been calculated for the maximum load. However, the selected design is based on satisfaction of all criteria presented in Sect. 0 for minimum and maximum loads.
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Table 3 Selection results of hydrodynamic bearing for the two rotor sizes 127.5 mm
321.3 mm
Bearing position
LPM
HPM LPF
HPF
LPM
HPM
LPF
Minimum load (VI 5.8) [kN]
HPF
1.20
3.08
1.63
4.43
7.61
20.56
10.27 29.16
Maximum load (VI 2.63) [kN] 2.32
5.26
3.10
7.15
14.34 34.39
18.85 45.67
D [mm]
35
40
35
50
85
95
85
110
L/D [mm]
¾
1
1
1
¾
1
¾
1
Cr [µm]
25
29
25
35
60
65
45
60
Power loss [W]
92
181
59
179
1331
2541
809
2142
Side oil leakage flow [l/min]
1.114 1.673 1.093 3.133 15.64 19.471 6.958 15.001
The selection is very different between bearing location as there is a wide range of variation in the applied loads. Thus, lightly loaded bearings (on low pressure side) are designed with the minimum journal diameter and with, when required, a reduction of L/D ratio from 1 to 0.75. This is done to avoid stability issues appearing for lightly loaded bearings (centred journal in the bearing). On the contrary, on high pressure side, bearings are heavily loaded, resulting in an increase of journal diameter as L/ D ratio is limited to 1.
4.3 Dual Oil Seal Table 4 present the calculated results for the dual oil seal sized to provide sufficient sealing for use with the cylindrical roller bearings described in Sect. 4.1. The oil seals have been sized to achieve 30% of the side oil leakage flows identified above for the hydrodynamic bearing cases.
4.4 Bearing Configuration Comparison A direct comparison can now be made for the performance of the two bearing systems, hydrodynamic and CRB + dual oil seals. These overall performance results are presented in Table. 5. The comparison of total power loss suggests that the choice of seal configuration is an important factor when using CRBs. When seals are only used for the high-pressure side bearings the power loss is predicted to be around 65% of the journal bearing losses. However, the addition of seals at the low-pressure side increases losses to around 175%. The dual oil seals used with CRBs are also seen to significantly reduce the oil flows relative to the journal bearing case. Further insight can be gained by considering these results relative to the results of thermodynamic chamber modelling. As shown in Table 6, the predicted mechanical
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Table 4 Selection results of dual oil seal for the two rotor sizes 127.5 mm
Seal 1 (Oil supply—Process gas)
Seal 2 (Oil supply—Bearing chamber)
321.3 mm
Bearing position
LPM
HPM LPF
HPF
LPM
HPM LPF
HPF
Cr [µm]
45
100
45
45
45
100
100
100
Length [mm] 25.5
13.3
25.9
7.1
48.3
30.5
108.5 39.6
Differential pressure [MPa]
1.4
0.8
1.4
0.8
1.4
0.8
1.4
Targeted leakage flow [l/min]
0.167 0.183 0.163
0.342 2.346 2.124 1.044 1.637
Power loss [W]
47
25
23
10
584
363
554
214
Oil 7.8 temperature increase [°C]
3.8
3.9
0.8
6.9
4.7
14.7
3.6
Differential pressure [MPa]
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
Targeted leakage flow [l/min]
0.167 0.319 0..164 0.598 2.346 3.717 1.044 2.864
Power loss [W]
47
30
23
19
584
419
554
258
Oil 7.8 temperature increase [°C]
2.6
3.9
0.9
6.9
3.1
14.7
2.5
0.8
power loss in the bearing/seal system is small compared to the indicated power for the compression process. The bearing/seals oil flow rates are however a significant proportion of the total oil injection required for efficient operation. These results suggest that further attention should be paid to the design and performance of the bearings and seals in order to better understand the influence of these power losses and internal flows on the thermodynamic performance of the compressor system.
5 Conclusions This paper summarised progress made in defining the selection and sizing process for bearings and seals in screw compressor applications. The influence on compressor performance has been characterised for specified test cases in terms of the frictional power losses and required oil supply flow rates, and related to predicted overall
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Table 5 Comparison of hydrodynamic and CRB + seals bearing systems 127.5 mm Bearing position
321.3 mm
LPM
HPM
LPF
HPF
LPM
HPM
LPF
HPF
Cylindrical roller Shaft bearing + dual oil diameter seal (on both side) [mm]
35
35
35
35
85
85
85
85
CRB outer diameter [mm]
72
72
72
80
150
180
150
180
Total length [mm]
73.9
49.6
74.8
45.2
132.6 121
253.1 139.1
Power loss (SKF) [W]
161
140
85
92
1978
1553
2547
1386
Total oil 0.518 0.737 0.434 1.116 6.940 10.736 3.323 7.033 flow (SKF) [l/ min] Cylindrical roller bearing + dual oil seal (on high pressure side)
Shaft diameter [mm]
35
35
35
35
85
85
85
85
CRB outer diameter [mm]
72
72
72
80
150
180
150
180
Total length [mm]
23
49.6
23
45.2
36
121
36
139.1
Power loss (SKF) [W]
66
140
38
92
811
2547
446
1386
Total oil 0.183 0.737 0.106 1.116 2.248 10.736 1.236 7.033 flow (SKF) [l/ min] Journal bearing
Journal diameter [mm]
35
40
35
50
85
95
Total length [mm]
26.25 40
35
50
63.75 95
85
110
63.75 110
(continued)
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Table 5 (continued) 127.5 mm
321.3 mm
Bearing position
LPM
HPM
LPF
HPF
LPM
HPM
LPF
HPF
Power loss [W]
92
181
59
179
1331
2541
809
2142
Total oil flow [l/ min]
1.114 1.673 1.093 3.133 15.64 19.471 6.958 15.001
Table 6 Comparison of bearing configurations power loss and oil flow to compressor indicated power and oil injection 127.5 mm
321.3 mm
Power loss (%) Oil flow (%) Power loss (%) Oil flow (%) CRB + Dual oil seals on both 0.82 side
14
0.8
15
CRB + Dual oil seals on high 0.58 pressure side
11
0.56
11
Hydrodynamic bearing
35
0.74
30
0.88
machine performance metrics. A direct comparison has been made between hydrodynamic and cylindrical roller bearings for application in a refrigeration compressor application. The findings of this study support the presupposition that rolling element bearings are low friction and have lower oil consumption than journal bearings. However, it has been further demonstrated that the overall performance difference can be much closer when the influence of auxiliary components for a specific bearing configuration are considered. This work is part of an ongoing project to better understand the selection and design of bearing/seal systems and their influence on the overall performance of different compressor configurations in terms of energy efficiency, lifespan, and maintenance requirements.
References 1. 2. 3. 4. 5.
M.J. Neale, Tribology Handbook, 2nd ed. (Butterworth-Heinemann, 1995) ISO 281:2007(E), Rolling bearings—Dynamic load ratings and rating life (2007) T.A. Harris, M.N Kotzalas, Advanced Concepts of Bearing Technology (2007 in press CRC) M.E. Leader, Underst. J. Bearings M.M. Khonsari, R.E. Booser, Applied Tribology: Bearing Design and Lubrication, 3rd ed. (Wiley, 2017) 6. L. San Andrés, Modern lubrication theory, “High pressure long oil seals,” Notes 11, Texas A and M University Digital Libraries (2010) 7. T.A. Harris, M.N. Kotzalas, Essential Concepts of Bearing Technology (2007 in press CRC)
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8. SKF, The SKF model for calculating the frictional moment. http://www.skf.com/binaries/ pub12/Images/0901d1968065e9e7-The-SKF-model-for-calculating-the-frictional-moment_ tcm_12-299767.pdf. Last Accessed 28 May 2023
Theoretical Analysis of Hydrodynamic Water-Lubricated Plain Bearings for High-Speed Applications Sami Tuffaha, Thomas W. Moesch, Christiane Thomas, and Konrad Klotsche
Abstract Oil is usually used for the lubrication of plain bearings due to its high viscosity, which is the essential parameter in the bearing designing process. However, the oil-free operation seems desirable in a growing number of industrial applications to eliminate complex separation processes of the lubricant from the working fluid after the compressor or various disadvantages of the lubricant in the process downstream of the compressor, e.g. oil traps and reduced heat transfer in the heat exchangers. In addition to the dry-running approach familiar to the process gas industry, the use of the working fluid itself as a lubricant is a possible approach to solve this problem. This paper analyses the feasibility of using a plain radial bearing for a high-speed spindle screw compressor that uses water as a working fluid, internal coolant, and lubricant. Based on calculations, this paper discusses the possible rotational speed and temperature range as well as other challenges and their impact on the minimum acceptable water film thickness and flow in the plain bearing gap. Keywords Water lubrication · Refrigerant lubrication · Dry-running · R-718 · Spindle screw compressors
S. Tuffaha · T. W. Moesch (B) · C. Thomas (B) · K. Klotsche (B) Technische Universität Dresden, Dresden, Germany e-mail: [email protected] C. Thomas e-mail: [email protected] K. Klotsche e-mail: [email protected] S. Tuffaha e-mail: [email protected] S. Tuffaha · T. W. Moesch Combitherm GmbH, Fellbach, Germany © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_14
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1 Introduction Hydrodynamic bearings are widely used in various industrial applications because they support high loads and provide low friction with minimum wear. However, the selection of an appropriate lubricant is critical for the proper operation of hydrodynamic bearings. The lubricant’s viscosity affects the bearing’s load-carrying capacity and its performance in terms of friction, wear, and thermal stability. This paper provides an overview of the challenges of designing a hydrodynamic bearing for a compressor that uses water (R-718) as the refrigerant and the lubricant for the bearing. A hydrodynamic bearing is a type of bearing that uses a fluid film that is created due to the relative motion between non-parallel surfaces, to separate the bearing surfaces from each other, thus reducing friction. The fluid film is generated by the relative motion of the rotating and stationary components, which creates a pressure differential supporting the load and separating the surfaces. Hydrodynamic bearings are commonly used in high-speed and high-load applications where conventional bearings may fail due to excessive friction and wear. Since the fluid film separates the surfaces, hydrodynamic bearings offer low friction and high load-carrying capacity, allowing them to be used in various applications, including rotating machinery, pumps, and compressors. Water has been widely used as a coolant in various industrial applications, including refrigeration and air conditioning systems. Its widespread availability, low cost, and high heat capacity make it an attractive alternative to traditional refrigerants such as hydrofluorocarbons (HFCs), i.e., potent greenhouse gases. Using water as a lubricant adds the structural simplicity of an oil-free refrigerant cycle; however, its viscosity is very low compared to conventional lubricants such as polyalkylene glycol (PAG), polyol ester (POE) or mineral oil. This makes it challenging to maintain a stable lubricating film in hydrodynamic bearings, especially at high speeds and loads. The paper discusses the various factors that influence the performance of these bearings, including the viscosity, bearing geometry, operating conditions, and lubricant film thickness formulation. The validity of the calculations depends on several assumptions, including the absence of disturbing forces, dimensional deviations from ideal geometry, and lubricant contamination. Additionally, it is assumed that the lubricant and bearing material are compatible with one another.
2 Layout and Operational Bearing Forces The investigated screw spindle rotors are shown in Fig. 1. The rotors are mounted horizontally, and the bearings A and B are within the rotor bore at either end of the rotor.
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Fig. 1 Hollow screw spindle rotor pair
The bearing loads result from the weight of each rotor m r otor = 57.9 kg and the gas forces arise from the pressure in each working chamber during operation. The gas forces were calculated for a compression of R-718 for a chiller application with an evaporation temperature ϑevap = 5 ◦ C, a condensation temperature ϑcond = 50 ◦ C, and a rotor speed of n S = 16,000 min−1 . A detailed thermodynamic calculation of the pressure conditions in the working chamber p(ϕ) for the investigated rotor was conducted by Moesch et al. [1]. The gas pressure-induced bearing loads were calculated using the approach of Rinder [2], as shown in Fig. 2, by evaluating the line loads f x and f y for each length control variable z and integrating them over the length of the rotor L r otor . The line load f x and f y are calculated for each rotor as shown in Eqs. (1) and (2).
Rotor II
f x (ϕ, τ ) = −p(ϕ) · [y2 (ϕ, τ ) − y1 (ϕ, τ )]
(1)
f y (ϕ, τ ) = p(ϕ) · [x2 (ϕ, τ ) − x1 (ϕ, τ )]
(2)
Rotor I
Fig. 2 Resulting line load from pressures within a working chamber (left) and calculation approach for bearing loads (right)
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Fig. 3 Loads on the screw spindle compressor bearings on the suction side (FA ) and pressure side (FB ) for R-718 with ϑevap = 5 ◦ C, ϑcond = 50 ◦ C and n = 16,000 min−1
where τ is the wrap angle, ϕ is the crank angle, x1 and y1 are the coordinates of point P1 , and x2 and y2 are the coordinates of point P2 . The gas pressure induced bearing loads F for bearing A and B result from an integration of the line loads for each chamber as shown in Eqs. (3) and (4). ⎡ ⎤ τi,e (ϕ) N L r otor − z(τ ) b(τ ) ⎥ ⎢ FA,x,y (ϕ) = f x,y (ϕ, τ ) dτ ⎦ ⎣ L r otor 2π i=1 τi,s (ϕ)
⎡
FB,x,y (ϕ) =
N i=1
⎢ ⎣
⎤
τi,e (ϕ)
f x,y (ϕ, τ ) τi,s (ϕ)
(3)
z(τ ) b(τ ) ⎥ dz⎦ L r otor 2π
(4)
where τi,s (ϕ) and τi,e (ϕ) mark the start and end of each chamber i, N is the total number of working chambers, and b(τ ) is the rotor lead. The results for the gas pressure induced bearing loads are shown Fig. 3. The calculation shows that the maximum radial load occurs on bearing B on the pressure side of the rotor and it reaches up to 97.8N. The figure also shows that the radial load on each bearing is almost constant and therefore very well suited for hydrodynamic bearing application.
3 Materials for Water-Lubricated Journal Bearings Water-lubricated journal bearings typically require unique materials to ensure proper function and durability. In this case, these materials must be compatible with water and able to withstand the harsh operating conditions of the bearing, such as high contact stresses, high temperatures, and corrosive environments. Commonly used materials for water-lubricated journal bearings include ceramics and hard-faced composites. These materials have good wear resistance, high hardness, and good
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Table 1 Applicability of different bearing materials and coatings [3] Material or coating Parameter
Cast iron
Sintered metal
Cast Cu Cast Cu Pb Sn Sn Pb alloys
Plastics
Graphite
SSiC
Sliding property
2
2
3
4
4
4
4
3
Emergency running behavior
2
4
2
3
3
4
4
2
Wear resistance
4
2
4
2
1
2
1
4
High sliding speeds
1
0
3
4
4
0
3
4
Heat conductivity
2
2
3
2
1
0
3
4
Low thermal expansion
4
4
3
2
2
0
4
4
Water lubrication
0
0
0
0
0
4
4
4
Dry run
0
0
0
0
0
4
4
1
Corrosion resistance
1
2
2
2
1
4
4
4
4—very well applicable, 3—well applicable, 2—possibly applicable, 1—limited application, 0— not applicable
corrosion resistance, making them suitable for use in water-lubricated bearings. The choice of material depends on the application’s specific operating conditions and requirements. Table 1 shows a comparison of materials and coatings that are used for journal bearings and their applicability [3]. Graphite and sintered silicon carbide can be used for this application because they can be lubricated with water, resist corrosion, and be used for high sliding speeds.
4 Flow Characteristics and Gap Tolerance In journal bearings, it is ideal for maintaining a laminar flow of the lubricant rather than a turbulent flow. Laminar flow refers to a smooth and predictable flow pattern, whereas chaotic and unpredictable flow patterns characterise turbulent flow. Laminar flow also helps to maintain a stable and consistent lubricating film between the bearing and shaft. This reduces friction and wear and extends the lifespan of the bearing. In contrast, turbulent flow increases the frictional forces as well as the temperature and decreases the load carrying capacity [4]. Therefore, maintaining
η [mPa·s]
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1,75 1,50 1,25 1,00 0,75 0,50 0,25 0,00 0
10
20
30
40
50
60
70
80
90
100
ϑ[ ]
Fig. 4 Dynamic viscosity—temperature diagram for water at 1bar [5]
laminar flow conditions is necessary to operate a journal bearing. The design and geometry of the bearing and the viscosity of the lubricant can control the flow. The flow of a fluid is characterised by the dimensionless Reynolds number: Re =
u·l , ν
(5)
where u is the relative velocity between the journal and the bearing, l is the characteristic length and ν the dynamic viscosity. Figure 4 shows the dependence of the viscosity of water on temperature. The viscosity drops significantly with a slight increase in temperature. To ensure a smooth run of the bearing, the water temperature should be kept as low as possible. To avoid vaporous cavitation, a suitable pressure must also be selected for the lubricant water. The pressure has almost no influence on the viscosity. The temperature also causes the aluminum spindle to expand according to the coefficient of thermal expansion (α), causing a relative gap ΔΨ: ΔΨ = α · (TO − TR )
(6)
The spindle screws rotate at n S = 16,000 min−1 . To keep the flow laminar, the diameter of the bearing should be as small as possible. Therefore, it is advantageous to design the journal of the bearing in the screw spindle’s bore with the diameter D and thus to lower the peripheral speed u S : uS = π · nS · D
(7)
where n S is calculated in Hz. The bearing surfaces must be precisely machined to narrow tolerances to ensure proper clearance between the bearing and shaft as well as to form a uniform and consistent lubricating film between the two surfaces. Deviations from the specified tolerances can result in leaks, compromising the integrity of the lubricating film and leading to bearing failure. In this specific case, the inner diameter of the hollow shaft is D = 32mm. The gap tolerance is selected according +3.5 µm to the ISO standards (ISO 286). In this case, js4 32−3.5 µm for the journal and
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µm G4 32+16 for the bearing, leading to a maximum clearance Smax = 19.5 µm +9 µm and minimum Smin = 5.5 µm. The maximum effective relative bearing clearance Ψe f f,max can be calculated according to (8): Ψe f f,max =
Smax + ΔΨ D
(8)
The Reynolds number for the flow in the bearing gap is: Regap
u = · ν
1 (smax + ΔΨ · D) 2
(9)
Substituting n S from Eq. (7) and Ψe f f,max from Eq. (8) in Eq. (9), Regap is calculated: Regap =
π · D 2 · nS · Ψe f f,max 2ν
(10)
The critical Reynolds number Recrit for a laminar flow in a gap according to [6] is: / Recrit ≈ 41.3 ·
1 Ψe f f,max
(11)
The layout and the dimensioning of the journal bearing is valid for a laminar flow which is fulfilled when Recrit > Regap . In this layout Regap = 817 and Recrit = 945. Thus, this condition is met. Should this not be the case for a layout, the parameters D, n, and S should be iterated until a laminar flow is assured. Figure 5 shows the turbulence of the flow as a function of the dynamic viscosity. In (a) the influence of the bore diameter is shown; the larger the diameter, the greater the Reynolds number and the flow approaches a turbulent behavior. On the other hand, (b) shows the influence of the rotational speed. Briefly, a smaller bearing with a lower rotational speed is safer to design for a water-lubricated journal.
5 Minimum Lubricant Film Thickness 5.1 Hydrodynamic Lubrication The designing process for journal bearings aims at full lubrication through a sufficient size of the minimum lubricant film thickness h min . Its size determines the requirements to be met by the surface roughness of the journal and bearing to be used. h min is displayed in Fig. 6a. To understand the tribological effects, the Stribeck curve
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Turbulent
Turbulent
Laminar
Laminar
(a)
(b)
Fig. 5 The influence of D (a) and the n S (b) in a flow type—viscosity diagram
needs to be analysed, see Fig. 6b [7]. The curve is a graphical representation of the relationship between friction and Hersey number in a tribological system. It typically shows three zones of friction behaviour: boundary lubrication, mixed lubrication and hydrodynamic lubrication. At low speeds, boundary lubrication occurs where the fluid film is insufficient to separate the contacting surfaces and direct metal-to-metal contact occurs between the surfaces. This lubrication is present when the fluid film is thin or when the load is high, resulting in a significant amount of surface-to-surface contact. An increasing velocity leads to mixed lubrication. This lubrication occurs when the velocity and load are intermediate resulting in a partially developed fluid film that cannot fully separate the surfaces. In the zone of hydrodynamic lubrication, the friction is low. It decreases as the velocity increases due to the development of a complete film that separates the moving surfaces and reduces friction. However, with increasing velocity, the hydrodynamic friction increases due to the viscous friction part that can be seen in the Stribeck curve.
(a)
(b)
Fig. 6 Designations on the journal bearing [6] and Stribeck curve, according to [7]
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Mixed friction is unavoidable during the start-up and run-down of a compressor, even in hydrodynamically lubricated plain bearings. With the correct choice of material and after a successful running-in process and not too frequent start-up and rundown, the resulting wear is low, i.e., harmless. In operation, the surface asperities of the journal and bearing should not touch.
5.2 Allowable Minimum Lubricant Film Thickness hl i m The allowable minimum film thickness required to prevent metal-to-metal contact and ensure reliable operation varies in the literature. With a sufficiently rigid or deformation-compliant design of the components and good surface finish as well as high-performance bearing materials, the limit value for the allowable minimum lubricant film thickness h lim can be defined as a function of the mean roughness depth Rz [6]: h lim (Rz ) = (0.5 . . . 1.0) · (Rz,J + Rz,B )
(12)
The allowable minimum lubricant film thickness can be determined using empirical data [8, 9] as a function of the arithmetical mean roughness Ra of the contact partners journal (J) and bearing (B). The allowable minimum film thickness should be at least 10 times the combined conjunction surface roughness values for the surfaces [7]: / h lim (Ra ) ≥ 10 Ra,J 2 + Ra,B 2
(13)
In addition to this correlation, DIN 31652 [6] allows the minimum permissible thickness to be determined as a function of rotational speed and diameter h lim (n, D) when a surface roughness within acceptable limits is achieved. In this case, the allowable minimum thickness h lim is set to 7 µm. Note that the allowable minimum thickness is smaller than the average clearance Savg = 12.5 µm for the tolerances chosen in Sect. 4.
5.3 Ratio of Length and Diameter and Relative Eccentricity The ratio of the length and diameter of the bearing L/D is used to describe the geometry of the bearing and it is used to describe the characteristics of the bearing regarding load-carrying capacity, friction, and stability. A large value of L/D generally indicates a broader bearing. The ratio is used to optimise the performance and stability of journal bearings for a given application. L/D is used for calculating the Sommerfeld number So, which is a dimensionless number enabling assessment of
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the load-carrying capacity of journal bearings. The Sommerfeld number describes a dimensionless bearing load in addition to the relative bearing clearance Ψe f f and the relative eccentricity ε, while taking the viscosity η of the lubricant into consideration as well: So =
p · Ψe f f 2 , η·ω
(14)
where ω is the angular velocity and p the pressure between the journal and bearing, which is defined as: p=
D2
F . · (L/D)
(15)
Having determined the Sommerfeld number, the relative eccentricity ε can be calculated as defined by [6]. It is imperative to exercise caution when using this approach for designing water-lubricated bearings, given that it is based on empirical data primarily derived from oil-lubricated bearings. The lubricant film thickness h 0 is a function of the relative bearing clearance and the relative eccentricity: h 0 Ψe f f , ε = 0.5 · D · Ψe f f · (1 − ε).
(16)
Figure 7 shows the minimum lubricant film thickness as a function of the viscosity and the bearing diameter D for L/D = 1 in (a) and as a function of viscosity η and L/D in (b) for D = 32 mm. A larger bearing diameter causes a larger minimum film thickness; however, as seen in Sect. 4, it also creates a more turbulent flow. A balance must be met for the bearing diameter that limits turbulence and builds up a sufficient film thickness h 0 . On the other hand, L/D can theoretically be chosen as large as possible, because it will increase the lubricant thickness without altering other variables. However, further increases in the parameter makes bearing misalignments more likely and no longer yield significant improvements in a thicker lubricant film beyond a threshold. As mentioned in Sect. 5.1 the film thickness builds up in the hydrodynamic region. Therefore, the minimum rotational speed is determined for the diameter D = 32 mm and a reasonable length/diameter ratio L/D = 1. Figure 7c shows this correlation. Assuming the temperature was kept constant at ϑ = 20 ◦ C, resulting in a constant dynamic viscosity η = 1000 µPa, a rotational speed of about 3500 min−1 would be enough to build a sufficient lubricant film thickness.
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(a)
(b)
177
(c)
Fig. 7 h 0 as a function of η for varying bearing diameters D (a), varying L/D (b) and varying rotational speeds (c)
6 Conclusion As part of the research that preceded this paper, the possibility of using water both as a working fluid and as a lubricant for a spindle screw compressor was to be investigated. The bearing loads of screw spindle compressors have a low deviation from the average load, making hydrodynamic journal bearings suitable for this compressor type. Due to the corrosive properties of water and the high rotational speed of the compressor presented, the suitable materials for a journal bearing for this application are limited. Water has a lower viscosity compared to regular compressor lubricants; an increased temperature decreases the viscosity and can lead to metal-to-metal contact, excessive friction, and wear. Therefore, maintaining a constant temperature for the supplied water is necessary. Water with higher viscosity ensures proper function and extended lifespan. A high value of L/D means a larger film thickness and needs to be considered while designing a bearing, unlike the bearing diameter and rotational speed for which a balance needs to be met. A greater diameter and speed allows forming a greater film thickness in the bearing. However, it increases the turbulence in the lubricant flow, making it unreliable. The calculations presented in this paper show that to run the compressor at 16,000 min−1 , the journal’s diameter D could be a maximum of 32 mm to prevent turbulence in the gap. Based on the calculations, it can be inferred that the bearing is better suited for applications involving slower rotating spindles and smaller diameters. This is because these conditions provide a greater buffer for ensuring the safety of the application. The theoretical investigations show that water can also be used as a lubricant under suitable conditions. Further studies as well as experimental investigations are the next steps in future research projects.
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Symbols and Units b
Rotor lead
mm
Re
Reynolds number
1
d
Bore diameter
mm
S
Clearance
µm
e
Eccentricity
mm
So
Sommerfeld number
1
f
Force
N
u
Peripheral speed
m/s
h
Lubricant thickness
µm
z
Length control variable
mm
L
Bearing length
mm
α
Coeff. of thermal expansion
K−1
l
Characteristic length
mm
ε
Relative eccentricity
1
L r otor
Rotor length
mm
η, μ
Dynamic viscosity
mPa · s
m
Mass of the rotor
kg
ϑ
Temperature
◦C
nS
Rotational speed
min−1
ν
Kinematic viscosity
mm2 /s
N
Num. of working chambers
1
τ
Wrap angle
1
p
Pressure
Pa
ϕ
Crank angle
1
Ra
Arithm. Mean roughness
µm
Ψ
Relative gap
1
Rz
Mean roughness depth
µm
ω
Angular frequency
rad/s2
References 1. T.W. Moesch, H. Pleskun, K. Klotsche, C. Thomas, U. Hesse, Thermodynamic analysis of a conical screw spindle compressor for R718, in Proceedings of 26th IIR International Congress of Refrigeration, Paris, 2023 (to be published) 2. L. Rinder, Schraubenverdichter (Springer-Verlag, 1979) 3. H. Wittel, D. Muhs, D. Jannasch, J. Vossiek, Roloff/Matek Maschinenelemene (Springer-Verlag, Berlin, Heidelberg, New York, 2009) 4. K.R. Mehta, Turbulence in Journal Bearings. Thesis (University of Missouri at Rolla, 1965) 5. I. Bell, J. Wronski, S. Quoilin, V. Lemort, Pure and Pseudo-pure fluid thermophysical property evaluation and the open-source thermophysical property library CoolProp. Ind. Eng. Chem. Res. 53(6), 2498–2508 (2014) 6. DIN 31652-1, 2, 3, Hydrodynamic radial plain bearings in stationary operation, 2017-01 7. M.M. Khonsari, R. Booser, Applied Tribology. Bearing Design and Lubrication, 3rd ed. (John Wiley & Sons Ltd., 2017) 8. Engineering Science Data Unit (ESDU), General Guide to the Choice of Thrust Bearing Type, Item 67033 (Institution of Mechanical Engineers, London, 1994) 9. B. Hamrock, Fundamentals of Fluid Film Lubrication (McGraw-Hill Book Co., New York, 1994)
A Novel Screw Compressor with a Shunt Enhanced Decompression and Pulsation Trap (SEDAPT) Paul Xiubao Huang, Sean Yonkers, and James Willie
Abstract When operating at pressures outside of their design point of a screw compressor, under- or over-compression would occur due to the deviation of the compressor cavity pressure from outlet pressure, and compressor efficiency suffers and pulsation and noise worsen. To solve the discharge pressure mismatch issue, some sort of control system is necessary, such as a variable volume ratio (commonly referred to as variable Vi) slide valve design. These systems, however, frequently have complex structural design, high price, large size, and significant dependability issues. Additionally, they are ineffective for commonly used dry screw applications in which oil is not allowed to lubricate the moving slide-valve parts. It has been widely known that a bicycle tire pump or rotary piston or scroll compressor equipped with an automatic discharge valve (one way valve), such as a reed valve, can operate over a wide range of pressures without suffering either an under-compression or an over-compression. The underlining principle of the bicycle pump has thus far NOT been fully explored for controlling the over compression or under compression problems of a screw compressor in general. This paper introduces a self-sensing and self-correcting screw compression process that can be derived or deduced from the Perfect Gas Law by optimizing for multiple design criteria such as best compression efficiency, pulsation/noise abatement, and cost and footprint reduction when operating over a wide range of pressures. The resulting schemes, called SEDAPT (Shunt Enhanced Decompression And Pulsation Trap), in contrast to an alternative scheme called SECAPT (Shunt Enhanced Compression And Pulsation Trap) (Huang et al. in A novel screw compressor with a shunt enhanced compression and pulsation trap (SECAPT), 2022), is then investigated and further honed numerically by a proprietary COMPUTATIONAL MODEL code for a dry screw case: a bulk truck loading P. X. Huang (B) Hi-Bar MC Technologies, LLC, Fayetteville, GA, USA e-mail: [email protected] S. Yonkers Hi-Bar Blowers, Inc., Fayetteville, GA, USA J. Willie CVS Engineering GmbH, Rheinfelden, Germany e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_15
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application where compressor pressure varies from no pressure rise to maximum load. The numerical simulations illustrate that SEDAPT is tentatively capable of achieving multiple targets as theorized from the Gas Laws. Keywords SEDAPT · SECAPT · Internal volume compression · One way valve · Over-compression · Under-compression
1 Introduction Refer to the INTRODUCTION of a sister paper [1] by the same authors Huang, Yonkers and WILLIE, entitled “A Novel Screw Compressor with a Shunt Enhanced Compression and Pulsation Trap (SECAPT)” for more detailed description of the background of the problem in various applications, idea origin and reasoning for a different approach from traditional slide valve solution in the 2022 Dortmund paper in contrast to the SEDAPT discussed in this paper. However, some figures are kept the same as the SECAPT paper but with shortened description in order to keep a smooth context flow while passing plagiarism checker.
2 Process Analysis of Two Parallel Compression Schemes 2.1 Arrangement of Screw Compression in Parallel: UC Only Scheme—SECAPT Refer to Sect. 2.2 of the sister paper [1] by the same authors for more detailed description of the SECAPT scheme.
2.2 Arrangement of Screw Compression in Parallel: OC Only Scheme—SEDAPT [2, 3] In contrast to the parallel scheme for UC-Only mode as shown in Fig. 1 as the SECAPT, Fig. 2 shows an alternative parallel scheme for OC-Only mode called the SEDAPT (Shunt Enhanced Decompression And Pulsation Trap—pending patents [2, 3]) that uses a shunt feedback flow loop with a one directional valve (ODV) to communicate with the outlet and compensate the IC before the discharge port opens in such a way that the pressure difference ΔPOC would be minimum (determined by ODV opening pressure difference) during the process of internal compression and at discharge over a wide range of operating pressures shown in Fig. 2 between Min Poutlet and Max Poutlet as required by application.
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Fig. 1 Phases of a screw compression cycle for a parallel arranged IC and UC mode
As illustrated in Fig. 2a, SEDAPT involves changing a fixed Vi screw compression cycle from the serial mode, i.e. from the violent transient decompression AFTER the discharge port opens, to a more gentle parallel mode BEFORE the discharge port opens. In this configuration, IC is playing the dominant compression role while a slight OC is only needed to help monitor and relieve cavity OC during a much longer time interval ΔtOC during the compounded compression phase as shown in Fig. 2b. Any small deviation of the pressure in the compressor cavity higher than the target outlet pressure, i.e. ΔPOC (= Pcavity − Poutlet ) would immediately trigger the shunt ODV to open to release some mass inside the cavity to outlet to diminish the pressure difference ΔPOC during the compound compression process BEFORE the discharge port opens. For example for outlet pressure at point B as shown in Fig. 2b, the IC would continue to work alone until reaching point A when ODV opens to discharge, starting the OC process that is in parallel with the IC process. Above all, SEDAPT is capable of automatically eliminating OC over a wide range of operating pressures, just like a bicycle tire pump or rotary piston or scroll compressor [4] equipped with ODVs, hence improving overall compressor efficiency and reducing discharge pulsation and noise.
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Fig. 2 Phases of screw compression cycle for parallel arranged IC and OC mode
2.3 A One-Stage SEDAPT Example and Design Rules Screw compressor is very different structurally from a bike pump by possessing a series of fast moving cavities that constantly change its shape, position and volume (hence gas pressure trapped inside) between the suction and discharge port as described by Soren Edstrom [5]. To fulfill the SEDAPT idea for a screw compressor, specific design issues have to be addressed for optimization such as: what discharge pressure is targeted and where to locate ODV on casing with respect to discharge port? How many ODVs are needed between suction and discharge? How to connect different ODVs to discharge? The following will answer these questions by a specific SEDAPT example employing a one stage ODV. COMPUTATIONAL MODEL simulations will be applied in the next chapter for two industrial cases. Figure 3a shows an example of a screw compressor with a one-stage SEDAPT design with just one ODV equipped orifice while Fig. 3b illustrates the unwrapped view of the rotor bore showing the possible locations of ODVs for orifices interfacing the cavity and the orifice cross-sectional shape, for example, slot transitioned into circle shown on the left and circular all the way on the right. The slot shape is for better conforming to and communicating with the cavity shape that is essentially a twisted oblong body. The relative position of the orifice with respect to the inlet and
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Fig. 3 a An example of a one-stage SEDAPT design with ODV, b unfolded view of a one-stage SEDAPT with ODV locations and shapes
discharge ports of the compressor is defined by its thread pitch (t) direction which is perpendicular to the screw cavity orientation. As a rule of thumb, the discharge port of a screw with SEDAPT is always designed for the maximum required outlet pressure (or maximum required pressure ratio) so that there will never be UC mode while slight OC is allowed during operation. When the compressor runs below the maximum pressure, the sideway ODV will be activated relieving any OC inside the cavity as from point A → B as illustrated in Fig. 2b. Hence the optimal ODV orifice locations are designed for the minimum required outlet pressure. While the orifice size associated with the shunt flow amount & flow rate to be subtracted from the cavity is designed for the minimum required outlet pressure in order to release the maximum mass flow. A more detailed operation of a one-stage SEDAPT is described as follows using a twin screw compressor. As shown in Fig. 3, a series of moving cavities, such as C1– C2–C3, are formed for trapping, compressing, and propelling the trapped gas from a suction port to a discharge port. An ODV equipped orifice location is designed for the minimum required discharge pressure P2 of an application AND is equal or less than one pitch distance away from the discharge port. As shown in Fig. 3a when P1 > P2, the moving cavity C1 with slightly higher gas pressure P1 forces the ODV orifice to open to the diffusing chamber with slightly lower pressure P2, relieving any excessive pressure generated inside the compressor cavity C1 by internal compression. Since the IC process is gradual in nature corresponding to gradual volume reduction of the cavity, the induced outflow is gentle and small in magnitude as indicated by small flow arrows in Fig. 3a, not causing large gas pulsations [4, 6] downstream and eliminating a significant energy waste associated with over-compression. If the range of pressure ratio variation or the extent of OC is small, a onestage SEDAPT with at least one ODV equipped OC orifice is enough to cover the compounded compression phase when the distance between the orifice opening to discharge port opening is smaller than one lobe span or screw pitch t as shown in Fig. 3b. However, for some applications where the range of pressure ratio variation
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of OC is large, a two-stage SEDAPT with at least two ODV equipped outflow OC orifices can be used to cover the compounded compression phase when the distance between the closing of the first orifice opening to the discharge port opening is larger than one lobe span or screw pitch. The general design rule is that each SEDAPT cavity C1 or C2 should always be in communication with the compressor outlet at any instant after being activated by ODV opening, but cavities C1 and C2 should never be allowed to communicate with each other. Based on this rule, the start of the 2nd stage orifice should be located about one screw pitch away, or totally sealed or isolated, from the end of the 1st orifice and within the last screw pitch before the discharge port opening. Likewise, if a two-stage SEDAPT is not enough to cover the compounded compression phase, a three-stage SEDAPT ensues.
3 Design Optimization of SEDAPT Scheme by Computational Model Analysis 3.1 Computational Model Simulation—Code Description In this section, the SEDAPT scheme is simulated numerically by a COMPUTATIONAL MODEL code developed by Mazzawy [7] for a dry screw example: a bulk truck loading/unloading case where screw pressure varies from no pressure rise (14.5 PSIA) to maximum load up to 58 PSI absolute. The code is set up to deal with multiple PD compressor models of mainly three types (Screw, Vane and Roots) with specific geometry templates to enable the necessary analysis of the compression process for each type. In order to optimize the SEDAPT design, multiple cases are run for different PD compressor operating points with or without SEDAPT orifices. Options include the selection of the operating gas (Air, Oxygen, Nitrogen or R134A refrigerant). SEDAPT orifice location(s) and geometry are easily varied to determine the best combination of operating efficiency and minimization of UC/OC exit pressure mismatch.
3.2 Computational Model Simulation Example—Optimization Procedure In this example, the pressure level vs degrees of rotation for the dry screw compressor is shown with no SEDAPT in Fig. 4a. In the base calculation, there is observed a sudden adjustment to the exit pressure at all pressures except the 58 PSIA case which is the design level. The optimization process starts with selecting the number of SEDAPT orifice (equipped with ODV) locations required to cover the range of most frequently used exit pressure which for this example will be between 14.5 PSI and 58 PSI absolute.
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Fig. 4 a Base pressure rise with no SEDAPT at 4 levels of exit pressure, b pressure rise with SEDAPT at 4 levels of exit pressure
Based on the screw compressor design, there is a range of rotor rotational angle over which the screw cavity will be exposed to any one SEDAPT orifice. For most of the range (29 PSIA to 58 PSIA) the addition of a SEDAPT orifice located at 50% of the volume reduction (approximately the 29 PSIA exit pressure of the range) will work well for this example. A second SEDAPT orifice located at 25% of the volume reduction is also needed to include the lowest exit pressure of 14.5 PSIA. Once the locations are defined, the orifice area can be varied within a range consistent with the size of the screw compressor hardware to minimize the level of OC. Figure 4b demonstrates that the addition of SEDAPT orifices is able to greatly improve the match to the exit pressure over the range of interest, hence minimizing gas pulsations at the compressor discharge. Optimization is targeted for minimizing power consumption and leakage for various locations and sizes of the SEDAPT orifices for the exit pressure of interest. The power requirement as shown in Fig. 5 has been greatly reduced at lower than design exit pressure level. Comparing with SECAPT scheme as discussed in the sister paper [1], the power saving for SEDAPT is much better across the whole operating range with the most gain from low exit pressures. If the pressure loss of a downstream dampener is taken into account for the Base case but not SEDAPT generally, the overall power savings of SEDAPT will be even greater compared to the Base scenario. Figure 6 shows the volumetric efficiency is affected little with the addition of the SEDAPT orifices equipped with ODVs when compared with the Base.
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Fig. 5 Power Requirement with and without SEDAPT
Fig. 6 Volumetric Efficiency with and without SEDAPT
3.3 Comparison of the Pros and Cons of Several Compression Schemes with SEDAPT Table 1 is a Best-In-Class comparison of some commonly used compression strategy with SECAPT and SEDAPT with the criteria of whether they are competent of
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accomplishing numerous targets at the same time, such as reasonable applications (oil injected or dry or both), energy saving, pulsation/noise reduction, cost and size, and dependability when working over a wide load range. Some commonly used compression strategies of screw compressors designed with or without a variable Vi slide valve and SECAPT as detailed in the sister paper [1] will be compared and rated with the SEDAPT for their individual benefits and drawbacks. Table 1 shows that SEDAPT or SECAPT is a better way to accomplish the various design goals than the widely used variable Vi design, or at least an alternative. It differs from the later approach by utilizing fluid gas to compensate for changeable load circumstances as opposed to moving solid mechanical elements (slide valves), which are vulnerable to friction, heat, fatigue failure, and response frequency. In control terms in analogy with a comparison of an unguided rocket with guided missile for self-propelled weapons, the serial IC + UC (or OC) combo strategy for screw, shown as ABC-1 and ABC-2 in Table 1 [1], is an unguided and self-propelled one pressure-ratio IC process which only homes in to the design pressure at the last moment at discharge by UC or OC. The variable Vi technique, in contrast, uses a slide valve to mechanically zero in on its goal pressure. Hence it is an externally directed and powered IC process with electronic-sensing and external power-driven feedback. SEDAPT or SECAPT, by contrast, is a self-guiding and self-propelling process with an autonomous compensating shunt flow loop to home in on a wide range of goal pressures (ΔP → 0). It achieves this by moving fluid gas instead of solid mechanical parts. The inherent built-in detecting and rectifying capability of Table 1 Best-in-class comparison of commonly used compression strategy with SECAPT and SEDAPT Screw without variable Vi
Screw with variable Vi
Applications
For wet and dry screw
Not for dry screw For wet and dry screw
For wet and dry screw
Energy consumption
High loss due to OC or UC and serial dampener
Little loss due to OC or UC or serial dampener
Little losses due to OC or UC or serial dampener
Pulsations/ noise
Discharge dampener required
No discharge No discharge dampener needed dampener needed
Cost and footprint
Large footprint and extra high cost by adding dampener
Large footprint and extra high cost by adding slide valve system
Small footprint and Small footprint and medium cost by medium cost by adding SECAPT adding SEDAPT
Reliability
Potential failure of serial dampener
Potential failure of slide valve system
Robust, no moving Potential fatigue and fatigue parts failure of ODV valves
Very slow
Fast
Response time Fast
Screw with SECAPT
Little loss due to OC or serial dampener. Slight loss from UC
Screw with SEDAPT
No discharge dampener needed
Fast
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the SEDAPT or SECAPT is a lot similar to PDs furnished with pressure-differenceactivated valves that are continually detecting the pressure difference between the cavity gas and the outlet, and consequently opening.
4 Conclusions and Recommendations for Future Work 4.1 Conclusions Since SRM re-invented screw compressors in the 1930s, automatic elimination of UC and OC for screw compressors operating over a wide range of pressures has been a persistent challenge because they are the causes of gas pulsations and energy losses. This paper investigates a wide range of alternative compression schemes as opposed to the conventional methods of using a variable Vi slide valve and develops an optimized configuration called SEDAPT (Shunt Enhanced Decompression And Pulsation Trap) that shows most advantageous and promising as follows: 1. Unlike PD compressors with simple automatic discharge valves that have continued to be successful for their ability to operate under variable loads without experiencing UC or OC, screw compressors do not have the same option, as of now, because they have a fixed built-in volume ratio determined by porting positions. This problem in turn results from the limitations of the conventional design paradigm, which uses a volume reduction strategy as the only method of increasing gas pressure, as seen by the enormous efforts made in the last 60 years to develop the variable Vi concept for screws. 2. SEDAPT departs from the volume reduction only paradigm by utilizing a different efficient method of adjusting gas pressure: direct, automatic, synergistic exchange of gas molecules between the compressor outlet and cavity. It is a combination compression technique designed for various design objectives, such as optimal compressor efficiency, pulsation/noise abatement, and cost and footprint reduction for a screw to work over a wide range of pressures. Its basic idea can be derived or inferred from the Perfect Gas Law. By utilizing the flowing gas and one-directional valve to compensate for the over-pressure circumstances rather than by moving the solid mechanical elements, which are expensive and sensitive to friction, SEDAPT is further demonstrated to be superior to the popular variable Vi design in terms of cost and reliability. 3. According to the COMPUTATIONAL MODEL simulations, SEDAPT is shown tentatively to be capable of meeting numerous design targets as intended.
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4.2 Recommendations for Future Work The project’s next step is to conduct an experimental investigation phase to validate the SEDAPT design for screw compressors. We’ll also look at how it applies to the developing Fuel Cell technology. It is envisaged that improved compression schemes can be developed and applied to the design of future generations of screw compressors that will have more energy savings, smaller sizes, and smoother operation. This will be possible as we continue to understand and enhance screw compression mechanism. Acknowledgements The authors would like to thank Robert Mazzawy for reviewing this paper and providing valuable feedbacks. Moreover, he has developed a proprietary COMPUTATIONAL MODEL simulation code as employed in this paper, by applying his programming skill and gas dynamics expertise, capable of optimizing both SECAPT and SEDAPT designs.
Nomenclature d IC OC ODV P PD SECAPT SEDAPT t UC Vi
Distance from orifice to rotor axis Internal compression Over compression One directional valve Absolute gas pressure Positive displacement Shunt enhanced compression and pulsation trap Shunt enhanced decompression and pulsation trap Time, or screw thread pitch Under compression Compressor design volume ratio
Subscripts 1 2 cavity inlet outlet
Cavity pressure of compressor Outlet pressure of compressor Compressor cavity Compressor inlet Compressor outlet
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References 1. P. Huang, S. Yonkers, J. Willie, A novel screw compressor with a shunt enhanced compression and pulsation trap (SECAPT), in The 2022 International Conference for Screw Machinery (Dortmund/Germany, 2022) 2. P. Huang, S. Yonkers, SEDAPT allowed patent: USA, Filed on Sept 26, 2021, Patent Application No. 17/485, 432 3. P. Huang, S. Yonkers, SEDAPT pending patent: Europe, Filed on Sept 23, 2022, Patent Application No. EP22197450.4 4. C. Rohleder, E. Groll, Measurement of pulsation at the discharge of positive displacement (PD) compressors, in 11th International Conference on Compressors and Their Systems, City (University of London, 2019) 5. S. Edstrom, Unwrapped Views of Rotor Bores of Twin-Screw Compressors. Design Notes from private communications, 2000 6. P. Huang, Gas pulsations: a shock tube mechanism, in The 2012 International Compressor Engineering Conference at Purdue, 2012 7. R.S. Mazzawy, Positive Displacement Compressor Analysis Computational Model Code Users Manual, Trebor Systems, LLC Report, Sept 25, 2021
Scroll Compressors
Preliminary Design and Performance Evaluation of Micro Scroll Compressor Used in Refrigeration Systems Shuo Song, Yuanyang Zhao, Qichao Yang, Guangbin Liu, and Liansheng Li
Abstract Micro refrigeration systems can be used in many applications. Micro scroll compressors have the potential for application in these refrigeration systems. With its miniaturization, the clearance and geometry parameters have become more influential in the performance of scroll compressors. In this paper, several threedimensional flow models with different pitches, thicknesses, and leakage clearances are established. These models are designed by the control volume method with R134a as the working fluid. By using the CFD method, the temperature distribution, pressure distribution, and flow characteristics in the working chamber are analyzed. By comparing compressors with different pitches and thicknesses, the effect of pitch and thickness on the volumetric efficiency and isentropic efficiency is obtained. By changing the radial and axial clearances, the change trends of the efficiency are obtained. The results provide a reference for the design of micro scroll compressors. Keywords Micro scroll compressor · Design · Thickness · CFD · Efficiency
1 Introduction In recent years, as fossil energy consumption increases and climate warming becomes more and more serious, energy conservation, emission reduction, and green development have become important issues for the sustainability of society [1]. As a necessary piece of modern technology for human existence, refrigeration has recently gained popularity as a research topic. Due to their compact size, lightweight, low noise, great volumetric efficiency, and other benefits, scroll compressors are frequently employed in refrigeration and air conditioning systems [2–4]. Compressors used in micro refrigeration systems have recently made some advancements as a result of the advancements in micro refrigeration system technology. In general, a compressor with a volume flow rate of less than 10 cm3 / S. Song · Y. Zhao (B) · Q. Yang · G. Liu · L. Li College of Electromechanical Engineering, Qingdao University of Science and Technology, Qingdao 266061, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_16
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rev is defined as a micro compressor. Yang et al. [5–7] developed different microrefrigeration systems in which the compressor components were micro-volumetric compressors. Sathe et al. [8, 9] tested the volumetric efficiency of a mini rotor compressor at varying pressure ratios to lay the foundation for the application of miniature compressors. As a volumetric compressor, scroll compressors have the potential to be used in micro refrigeration systems. With the development of Computational Fluid Dynamics (CFD) techniques, it has been used to study the working process and performance of scroll compressors. Zheng et al. [10–13] studied the internal flow of compressors and investigated the effects of parameters such as scroll wall roughness, speed, evaporation temperature, and pressure on compressor performance using CFD methods. Song et al. [14] analyzed the internal flow at different suction port positions based on the CFD method and analyzed the effect of suction ports on the mass flow rate of compressors. Wang et al. [15] investigated the variation of base circle radius and spreading angle of variable thickness scroll compressor on the length of leakage line, but the effect on leakage volume and performance parameters was not analyzed. Pereira et al. [16] investigated the leakage of compressors with different working fluids and geometrical parameters and concluded that the inlet loss of the axial clearance and the curvature of the radial clearance have a significant effect on the leakage. Zheng et al. [17] analyzed the effect of the number of slots and slot depth on the scroll teeth on the radial leakage and obtained that both the volumetric efficiency and isentropic efficiency of the compressor increased and then decreased with the increase of the slot depth. Bell et al. [18] researched the empirical friction factor of the isentropic nozzle model, calculated the leakage mass flow rate of the model, and concluded that the compressor leakage rate is related to the Reynolds number and the geometry of the leakage clearance. The above studies provide references for studying the flow and performance effects of scroll compressor leakage. But most of them do not quantify the effects of clearance and scroll parameters on the performance of scroll compressors systematically. When scroll compressors are used in miniature refrigeration systems, the miniaturization of the compressor makes its performance more sensitive to the change of structural parameters. Therefore, an in-depth study of the effect of geometric parameters on the performance of miniature scroll compressors is needed. In this paper, a numerical analysis model with radial clearance and axial clearance is established and transient flow simulations are finished by the CFD method. The flow field characteristics and the influence of geometric parameters on the compressor leakage line length and volumetric efficiency are studied.
Preliminary Design and Performance Evaluation of Micro Scroll … Table 1 Main performance parameters of the system under air-conditioning conditions
Table 2 Micro scroll compressor structure parameters
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Parameters
Number
COP
2.93
Power/W
104
Volume ratio
3.63
Structural parameters
Number
Suction volume (cm3 /r)
2.0
Thickness (mm)
1.2/1.3 /1.4/1.5
Pitch (mm)
5.6/5.8/6.0/6.2
Involute final spreading angle (° )
1980
Radial clearance (mm)
0.010
Axial clearance (mm)
0.007
2 Preliminary Design of Micro Scroll Compressor 2.1 Basic Parameters The working fluid of the micro refrigeration system is R134a, and the working conditions of the system are standard air conditioning conditions, the design conditions for the scroll compressor are shown in Table 1. The suction volume of the micro scroll compressor is 2.0 cm3 /r, and the rotation speed is 4500 r/min. The scroll profile is a circle involute. The detailed profile parameters are shown in Table 2.
2.2 Structure Design The design structure of the micro scroll refrigeration compressor is shown in Fig. 1. The compressor adopts the low-pressure chamber structure, and the refrigerant in the suction state enters the inside of the compressor through the suction port located on the side of the compressor shell. The refrigerant cools the motor first, and then it is sucked into the suction chamber composed of orbiting and fixed scroll. Then with the rotation of the orbiting scroll, the refrigerant is compressed to the high-pressure state in the space between the orbiting and fixed scrolls. Finally, it flows out from the compressor through the discharge tube located on the top of the compressor and flows into the condenser of the refrigeration system.
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Fig. 1 Micro scroll compressor structure
3 Performance Analysis Model 3.1 Physical Model A physical model was developed to estimate the performance of the micro scroll compressor, as seen in Fig. 2. The suction fluid domain, the discharge fluid domain, the working chamber fluid domain, and the axial clearance fluid domain were the four segments of the fluid domain in the physical model. Five monitoring sites were set up close to the wall of the fixed scroll, 90° apart from one another, to make it easier to analyze pressure change in the operating chamber of the scroll compressor (Fig. 3). To study the influence trends of geometric parameters on the performance of micro scroll compressors, this paper adopts the control variates to ensure that the compressor displacement and the turn number of scrolls are constant. The pitch is fixed at 5.8 mm, and the compressor models with the thickness of 1.2, 1.3, 1.4, and 1.5 mm are established; the thickness is fixed at 1.5 mm, and the compressor models with pitches of 5.6, 5.8, 6.0, 6.2 mm are established. the specific structural parameters of the compressor are shown in Table 2.
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Fig. 2 Scroll compressor fluid domain model Fig. 3 Monitoring points in the working chamber
3.2 Meshing The moving region of the scroll compressor has meshed as the high-quality hexahedral structured grid. The inlet and outlet regions and the connection part are meshed by a common mesh template to generate a high-quality Cartesian mesh. The compressor mesh and the axial clearance mesh are shown in Fig. 4. To verify the grid independence, the fluid domain model with a pitch of 5.8 mm and a thickness of 1.5 mm is selected as an example. The grid parameters and calculation results are shown in Table 3. When the grid number is 480,000, the mass flow rate of the compressor is 1.7198 g/s, and the mass flow rate changes very little when the grid number continues to increase. Therefore, the 480,000 grid model was used in the numerical simulation.
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Fig. 4 Compressor calculation grid and axial clearance grid
Table 3 Grid independence and calculation time Number of grids
Calculate the number of laps
Calculation time/h
Mass flow rate/g/s
280,000
5
11
1.5813
370,000
5
15
1.6768
480,000
5
18
1.7198
690,000
5
27
1.7203
3.3 Calculation Method and Boundary Conditions R134a is used as the working fluid for the 3D transient simulation, and the thermophysical properties of R134a are called from the NIST database. The standard k-ε turbulence model is used to describe the refrigerant flow in the working chamber of the compressor. The compressor rotation speed is set to 4500 r/min. The pressure inlet and outlet conditions are chosen as the boundary conditions, where the inlet pressure is 0.3772 MPa, the inlet temperature is 291.45 K, and the outlet pressure is 1.4698 MPa. The first-order windward format is used, the pressure solver is chosen as the solver, and the pressure–velocity coupling equation is solved by the SIMPLES method. Since the compression process is very fast, the wall surface is regarded as an adiabatic wall surface.
4 Results and Discussion 4.1 Analysis of Internal Flow of Compressor A micro scroll refrigeration compressor with a pitch of 5.8 mm and a thickness of 1.5 mm is selected in this part.
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0°
60°
255°
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270°
Fig. 5 Pressure distribution in working chambers
(1) Pressure distribution Figure 5 shows the pressure distribution of the scroll compressor during one working cycle. Since the suction tube is not centrally symmetric, the pressure distribution in each pair of working chambers is not the same. When the crank angle is 0°, the pressure difference between the two suction chambers is about 5000 Pa. When the compressor rotates to 60°, there is pressure fluctuation in the discharge chambers because the volume of the discharge chambers changes more drastically and the connection area between the discharge chambers and the discharge channel is small, and the pressure rises steeply to 1.55 MPa. The region near the radial clearance is the same as a leakage channel with convergent and expansion parts. With the movement of the orbiting scroll, the pressure difference of the working chambers at two sides of the contact point is changing, the closer to the center, the greater the pressure difference between the two working chambers. (2) Temperature distribution Figure 6 shows the temperature distribution of the scroll compressor. The temperature distribution of each pair of working chambers is not uniform, and the temperature distribution in a working chamber is not uniform too. Comparing the distribution of pressure and temperature distributions, the leakage flow has a certain influence on the mass flow in the working chambers of the compressor. And the influence of leakage flow on the temperature distribution is much larger than that of the pressure distribution. (3) Velocity distribution Figure 7 shows the velocity distribution in the scroll compressor. Except for the radial clearance area, the fluid in the whole compression chamber is in a lower velocity motion. To better show the overall velocity distribution of the flow distribution, the upper-velocity limit is set to 15 m/s in the following section, while the actual maximum velocity in the leakage clearance is up to 204 m/s. When the suction process is finished, the velocity distribution in the two suction chambers is not uniform. The suction flow channel is closed at this time and some
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0°
60°
255°
270°
Fig. 6 Temperature distribution in working chambers
0°
135°
255°
270°
Fig. 7 Velocity distribution of working chamber
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gas leaks through the clearance from the suction chamber. And the vortex V1, V2 is generated in the suction channel. At the radial clearance, the direction of leakage flow is from the chambers near the scroll center to the outside chambers. With the movement of the moving scroll, the pressure difference between the two sides of the clearance increases, and tangential leakage flow gradually obvious. The leakage in the radial clearance leads to the vortex V3, V4 in the working chamber of compressors. It is found that the intensity of vortex V4 is always greater than that of V3. This is because the gas flow velocity of WC1A in the two suction chambers is always greater than that of WC1B. The gas in the WC2A chambers is more violent than that of WC2B. For the discharge chamber, the vortex V5 has always existed. As the moving scroll continues to move, the vortex V5 intensity gradually decreases. (4) Working process of scroll compressor Figure 8 shows the pressure change curves of the scroll compressor with different scroll thicknesses. During the compression process, the pressure in the working chamber rises with the increase of the scroll thickness. During the discharge process, the pressure rises faster when the scroll thickness is small, as shown in Fig. 8a. When the rotation angle of about 600°, the pressure fluctuation appears firstly in the compressor chamber with a big scroll thickness, as shown in Fig. 8b. Figure 9 shows the pressure change curves of the compressor at different scroll pitches. During the compression process, the gas pressure with a smaller pitch rises
Fig. 8 Pressure variation during compressor operation with different thickness
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Fig. 9 Pressure variation during compressor operation at different pitches
faster, which means there is smaller leakage when the scroll pitch decreases. At the start of the discharge process, the pressure change trend changes. The larger the pitch, the faster the pressure rise, as shown in Fig. 9a. These may be caused by the change in the leakage flow during the discharge process. When the rotation angle is about 585°, the pressure fluctuation with a smaller pitch appears first, as shown in Fig. 9b. The effect of the scroll pitch on the working process is bigger than that of the scroll thickness.
4.2 Performance Analysis Under Variable Working Conditions The volumetric efficiency is a key parameter to express the performance of refrigeration compressors. The volumetric efficiency is defined as: ηv =
m ac m id
(1)
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Fig. 10 Schematic diagram of internal leakage of scroll compressor
where mac is the actual mass flow rate, mid is the design mass flow rate. The isentropic efficiency is defined as: ηs =
Pad Pis
(2)
where Pis is the actual compression work, and Pad is the isentropic process work. The leakages of scroll compressors mainly are composed of tangential leakage through the radial clearance and radial leakage from the axial clearance (Fig. 10). The length of the tangential leakage line is the height of the scroll, which can be defined as: L f = 2h
(3)
The length of the radial leakage line is related to the length of the scroll profile and the rotation angle, which can be defined as: ϕi + 1
Lr = 2 ∫ ϕi
√
x 2 + y 2 dϕ
(4)
where ϕ i , ϕ i+1 are the starting and ending angles of the scroll profile. (1) Effect of scroll thickness Figures 11 and 12 show the volume efficiency with different thicknesses and axial clearances when the scroll pitch is 5.8 mm. In the actual design, scroll compressors can use an axial sealing mechanism such as a sealing strip to reduce the influence of axial clearance. Therefore, in the numerical simulation, this case can be simplified to the axial clearance of 0 µm. From Table 4 it can be obtained that the radial leakage line length of compressors with different thicknesses is the same, and the tangential leakage line length increases with the increase of thickness. When the
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axial clearance is 0 µm and the scroll thickness increases from 1.2 to 1.5 mm, the compressor volumetric efficiency decreases from 86.66 to 82.06%. Axial clearance(0μm)
Volumetric efficiency (%)
Fig. 11 Volumetric efficiency at different thicknesses without axial clearance
Thickness (mm)
Axial clearance(7μm)
Volumetric efficiency (%)
Fig. 12 Volumetric efficiency at different thicknesses for an axial clearance of 7 µm
Thickness (mm)
Table 4 Leakage line length at different thickness Thickness/mm
Radial leakage line length/mm
Tangential leakage line length/mm
1.2
139.6812
8.074
1.3
139.6812
8.579
1.4
139.6812
9.147
1.5
139.6812
9.800
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When the axial clearance is 7 µm and the thickness increases from 1.2 to 1.5 mm, the compressor volumetric efficiency decreases from 68.57 to 67.55%. It means that the leakage through the axial clearance has a greater impact on the volumetric efficiency. And the leakage caused by changing the thickness and the leakage through the radial clearance is small. (2) Effect of scroll pitch The scroll pitch is one of the important structural parameters and is directly related to the outer diameter of the compressor motor scroll. In the initial design of the compressor, the height-pitch ratio is recommended in the range of 1.0–2.5 to ensure the stability of the compressor. In this paper, the length of the leakage line is calculated for different pitch models which are shown in Table 5. The larger the pitch, the longer the radial leakage line and the shorter the tangential leakage line with the same thickness and number of scroll turns. Figures 13 and 14 show the change in volumetric efficiency at different pitches and axial clearances when the scroll thickness is 1.5 mm. The compressor volume efficiency shows an increasing trend under different axial clearances. When the axial clearance is 0 µm and the pitch increases from 5.6 to 6.2 mm, the volume efficiency increases from 78.48 to 88.43%. When the axial clearance is 7 µm and the thickness increases from 5.6 to 6.2 mm, the volume efficiency increases from 65.69 to 70.74%. The effect of leakage through the axial clearance on the volumetric efficiency is much greater than that of the radial clearance, which leads to an increase in volumetric efficiency. The above simulation results show that the effect of leakage through the axial clearance on the volumetric efficiency of the compressor is much greater than that of the radial clearance leakage. When designing a micro scroll compressor, a suitable thickness should be selected and the pitch should be increased as much as possible under the condition that the capacity and clearance remain unchanged. (3) Effect of clearance The leakage clearance has an important impact on the performance of micro scroll refrigeration compressors. A compressor model with a pitch of 6 mm and a thickness of 1.5 mm was established, and CFD simulations were conducted for different axial clearance and radial clearance, and the results are shown in Figs. 15 and 16. When the axial clearance is 5 µm and the radial clearance is gradually increased from 5 to 11 µm, the volumetric efficiency of the compressor decreases from 86.38% Table 5 Leakage line length at different pitches Pitch/mm
Radial leakage line length/mm
Tangential leakage line length/mm
5.6
134.8648
10.931
5.8
139.6812
9.800
6.0
144.4977
8.842
6.2
149.3141
8.022
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Fig. 13 Volumetric efficiency at different pitches without axial clearance Volumetric efficiency (%)
Axial clearance(0μm)
Pitch (mm)
Axial clearance(7μm)
Volumetric efficiency (%)
Fig. 14 Volumetric efficiency at different pitches for an axial clearance of 7 µm
Pitch (mm)
to 75.11% and the isentropic efficiency decreases from 67.78 to 56.18%. When the axial clearance is 0 µm, the volumetric efficiency of the compressor decreases from 92.06 to 84.67% and the isentropic efficiency decreases from 78.35 to 64.19% when the radial clearance increases from 5 µm to 11 µm, and the changing trend is the same as that of the axial clearance. According to the comparison of the data without axial clearance and with axial clearance of 5 µm, the difference between the two volumetric efficiencies gradually increases with the increase of radial clearance, and the maximum difference can reach 9.56%. The difference between the isentropic efficiencies gradually decreases, and the maximum difference is up to 10.57% when the radial clearance is 5 µm.
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Volumetric efficiency (%
Axial clearance(0μm) Axial clearance(5μm) Axial clearance(6μm) Axial clearance(7μm) Axial clearance(8μm)
Radial clearance (μm)
Fig. 16 Effect of clearance on isentropic efficiency
Isentropic efficiency (%)
Axial clearance(0 Axial clearance(5 Axial clearance(6 Axial clearance(7 Axial clearance(8
Radial clearance (μm)
Compared with the radial clearance, the axial clearance has a greater impact on the volumetric efficiency and isentropic efficiency of the micro scroll compressor because the leakage channel of the axial clearance of the compressor is longer than that of the radial clearance. During the operation of the scroll compressor, due to the machining accuracy, it is impossible to ensure that the two scroll plates are completely tight, so there must be radial clearance and axial clearance between the scroll plates, which will lead to radial leakage and tangential leakage. According to the above results, it can be seen that the axial clearance has more influence on the compressor performance, so in the actual design, other sealing methods are usually adopted to reduce the influence of the clearance, such as sealing strips and labyrinth seals. Since the size of the micro compressor is much smaller than the normal compressor, it is more difficult to take suitable axial sealing measures for the micro compressor, which is an important
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direction development for the future [19]. In this paper, to make the compressor volume efficiency reach 80% or more, the axial clearance should be less than 6 µm and the radial clearance less than 9 µm based on the calculation results.
5 Conclusions In this study, the R134a micro scroll refrigeration compressor was modeled and analyzed using CFD numerical methods, and the influence trends of the scroll thickness, clearance, and scroll pitch on the compressor performance were analyzed. There is always a vortex phenomenon inside the compressor, the existence of vortex and clearance leakage cause the flow change in the working chamber. Comparing the distributions of pressure and temperature, the influence of leakage flow on the temperature distribution is much larger than the pressure distribution. In the ideal case of no axial clearance, the volumetric efficiency decreases slightly with the increase in the scroll thickness. After adding 7 µm of axial clearance, the compressor volumetric efficiency decreases from 68.57% to 67.55%. Ensuring the same thickness and number of scroll turns, the increase of the scroll pitch has a significant effect on the improvement of the volumetric efficiency. When the axial clearance is 7 µm and the scroll pitch increases from 5.6 to 6.2 mm, the volume efficiency increases from 65.69 to 70.74%. With the increase in clearance, the volume and isentropic efficiencies show a decreasing trend. When the radial clearance changes from 5 to 11 µm and the axial clearance is 5 µm, the volume efficiency decreases from 86.38 to 75.11% and the isentropic efficiency decreases from 67.78 to 56.18%. For the compressor prototype in this paper, when we wish to increase the volumetric efficiency up to 80%, the axial clearance should be less than 6 mm and the radial clearance should be less than 9 mm. Acknowledgements This work was supported by the Taishan Scholar Program of Shandong (No. tsqn201812073).
References 1. M.C. Barma, R. Saidur, S. Rahman et al., A review on boilers energy use, energy savings, and emissions reductions. Renew. Sustain. Energy Rev. 79(C), 970–983 (2017) 2. P. Bin, A. Legros, V. Lemort et al., Recent advances on the oil-free scroll compressor. Recent Pat. Mech. Eng 09(999), 1–1 (2015) 3. P. Song, M. Wei, L. Shi et al., A review of scroll expanders for organic Rankine cycle systems. Appl. Therm. Eng. 75, 54–64 (2015) 4. L. Wang, Y. Zhao, L. Li et al., Research on oil-free hermetic refrigeration scroll compressor. Proc. Inst Mech Eng Part J Power Energy 221(7), 1049–1056 (2007)
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5. Y. Yang, W. Yuan et al., Development of a miniature vapor-compression refrigeration system for personal cooling, 23rd IIR international congress of refrigeration (Czech Republic, Praha, 2011) 6. Z. Wu, R. Du, Design and experimental study of a miniature vapor compression refrigeration system for electronics cooling. Appl. Therm. Eng. 31(2–3), 385–390 (2011) 7. S. Trutassanawin, L. Cremaschi, E.A. Groll et al., Performance analysis of a miniature-scale vapor compression system for electronics cooling: bread board setup, in 2006 Purdue Conferences. 18th International Compressor Engineering Conference at Purdue & 11th International Refrigeration and Air-Conditioning Conference at Purdue [CD-ROM] (2006) 8. A. Sathe, E. Groll, S. Garimella, Experimental evaluation of a miniature rotary compressor for application in electronics cooling. Australas. J. Educ. Technol. 23(3), 350–370 (2008) 9. S. Trutassanawin, E.A. Groll, S.V. Garimella et al., Experimental investigation of a miniaturescale refrigeration system for electronics cooling. IEEE Trans. Compon. Packag. Technol. 29(3), 678–687 (2006) 10. S. Zheng, M. Wei, C. Hu et al., Flow characteristics of tangential leakage in a scroll compressor for automobile heat pump with CO_(2). Sci. Chin. Technol. Sci. 64(5), 971–983 (2021) 11. B. Peng, Y. Li, S. Zhao, Unsteady numerical simulation of scroll expander based on CFD(2018). in International Compressor Engineering Conference. Paper 2641. 12. X. Zhang, L. Su, K. Li, A study of a low pressure ratio vapor injection scroll compressor for electric vehicles under low ambient conditions. Int. J. Refrig. (2021) 13. S. Sun, K. Wu, P. Guo, et al., Analysis of the three-dimensional transient flow in a scroll refrigeration compressor. Appl. Therm. Eng. S1359431117330946 (2017) 14. P. Song, M. Wei, Z. Liu et al., Effects of suction port arrangements on a scroll expander for a small scale ORC system based on CFD approach. Appl. Energy 150, 274–285 (2015) 15. J. Wang, Y. Wu, Z. Jing et al., Influence of profile parameters on radial leakage line length of variable tooth thickness scroll compressor. J. Phys. Conf. Ser. 1676, 012171 (2020) 16. E. Pereira, C.J. Deschamps, Numerical analysis and correlations for radial and tangential leakage of gas in scroll compressors. Int. J. Refrig. 110 (2019) 17. S. Zheng, M. Wei, C. Hu et al., Impact of micro-grooves in scroll wrap tips on the performance of a trans-critical CO2 scroll compressor. Int. J. Refrig. (2021) 18. I. Bell, E. Groll, J. Braun et al., A computationally efficient hybrid leakage model for positive displacement compressors and expanders. Int. J. Refrig. 36(7), 1965–1973 (2013) 19. C. Rong, W. Wen, Discussion on leaking characters in meso-scroll compressor. Int. J. Refrig. 32, 1433–1441 (2009)
A Study to Improve Efficiency of a Variable Speed Scroll Compressor Mathew Pazhathara James, Alex Schmig, and Joe Ziolkowski
Abstract A study using a 1D chamber model was done to improve isentropic efficiency of a variable speed scroll compressor and then testing was conducted to validate. It was noticed in the initial analysis that the economizer location, sizing, and timing optimization gave an efficiency improvement of 0.5–2.5% depending on the operating point. Since the economizer was optimized for location, area and timing or activeness, the back flow was reduced, hence the mass flow through the port and efficiency improved. A study with focus on speed resulted in an improvement in weighted efficiency to the tune of 4–6%. Investigating the effect on port delay showed, improvement was on a rising trend as the discharge port delay was increased until around 110° and then efficiency started to decline. The improvements for different operating conditions were in the range of 2–4%. An improvement in involute start angle also resulted in improvement in efficiency to the tune of 0.7–1.3% depending on the operating condition. Changing this parameter affected the structural integrity, hence not adapted. A new compressor was built with new economizer port geometry to understand the effect. The results were promising with variation in efficiency from − 0.6 to 5.1% for different operating conditions investigated. Speed sweeps showed there are peak efficiency points, which can be used to decide the speed for operating condition. Keywords Variable speed scroll · Efficiency · Economizer · Speed
M. P. James (B) · A. Schmig · J. Ziolkowski Trane Technologies, Applied Compression-NOE, Bangalore, India e-mail: [email protected] A. Schmig e-mail: [email protected] J. Ziolkowski e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_17
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1 Introduction A hermetically-sealed, variable-speed, asymmetric-involute scroll compressor, for transport application, was under consideration for this work. The main intent was to improve efficiency of an existing R452A compressor (baseline compressor), which was manufactured and tested with an elliptical profile injection port. A GTsuite chamber model was used for predicting the behaviour of the manufactured compressor. Five different operating conditions were considered for targeting efficiency for the compressor. These are provided in Table 1. The geometric parameters of the scroll were proprietary, hence were not included in this paper. The isentropic efficiency was calculated using ASHRAE standard 23–2022 [1]. The equation based on above standard is shown below. ηisen P m1 m2 h21s h22s h31s
h32s
m˙ 1 h 31s − h 21s + m˙ 2 h 32s − h 22s = P
(1)
Total power input to the unit under test (hence motor power) (kW). total mass flowrate entering the compressor (kg/s). refrigerant mass flow rate after mixing the injection and inlet flow (kg/s). Specific enthalpy of refrigerant vapor at suction pressure and temperature entering compressor (kJ/kg). specific enthalpy of refrigerant vapor after mixing the intermediate pressure flow at State Point 5 with the flow at State Point 31s (kJ/kg). Specific enthalpy of refrigerant vapor at intermediate pressure following an isentropic compression of the refrigerant from compressor suction pressure (kJ/kg). Specific enthalpy of refrigerant vapor at compressor discharge pressure following an isentropic compression of the refrigerant from state point 22s (kJ/kg).
Table 1 Operating points considered for comparison Refrigerant: R452A Point name
P1
P2
P3
P4
P5
Compressor speed (Hz)
120
75
75
45
15
Suction pressure (PSIA)
18
22
55
23
71
Discharge pressure (PSIA)
300
230
270
226
168
Economizer pressure (PSIA)
50
80
N/A
60
N/A
Suction temperature (°F)
− 19
−4
29
14
44
Economizer temperature (°F)
26
52
N/A
41
N/A
Suction mass flow normalized
0.5
0.4
1.0
0.2
0.1
Economizer mass flow normalized
0.7
1.0
0.0
0.3
0.0
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Fig. 1 Cycle and pressure-enthalpy diagram
The cycle schematic and pressure-enthalpy diagram [1] for the system under consideration is shown in Fig. 1. The system makes use of a heat exchanger-based economizer. This addition imparts a subcooling to main cycle defined by state points 42 to 41 . This sub-cooling improves the capacity and hence the COP of the cycle. The data presented in this study is mainly from compressor alone testing, with test points (P1–P5) obtained from cycle’s balance points. The cycle balance point determination is not part of current study.
2 Optimization In this application, the compressor had to meet capacity and efficiency requirements at multiple operating conditions, hence efficient use of design parameters was necessary. While conducting initial assessment [2–6] it was understood that economizer sizing, compressor speed, discharge port geometry and timing had a significant influence on the efficiency of the compressor. A detailed study using a chamber model is presented below in conjunction with test results.
2.1 Economizer Vapor injection and refrigerant selection was necessary for this design in order to improve system capacity, efficiency, and operating envelope. The different geometries considered are shown in Fig. 2. Initially, a circular vapor injection port was used. It was intuitive in the design process that, to increase the area, the diameter of the circle had to increase. The consequence of this was that the economizer port initialized while the suction chamber was still active. In addition to this the cycle duration or crank angle for which the economizer is active, started increasing. Hence as the area increased, the cycle duration of the economizer increased and the start angle advanced more. Both resulted
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Fig. 2 Circular and elliptical injection ports in red color
in increasing the injection pressure. This posed a challenge since the target injection pressure was held constant. Increased backflow was also noted (Fig. 4). For some of the operating points, the additional area acted as a clearance volume which negatively impacted efficiency. Another candidate geometry was an ellipse. This reduced cycle duration of the economizer and improved control of the area. Still, the dependency of area and cycle duration was higher. As area was increased to achieve more flow through the economizer, the start angle was changed and the port was moved to a more inefficient zone. A novel method (patent pending) was devised to break the area and cycle duration relationship by making use of involute geometry itself (Fig. 5). This method ensured better control of start of economizer and could make the start angle constant, unlike other profiles discussed earlier. This novel profile can be defined such that it can be used to control end of injection of the economizer in the direct and indirect chambers. A plot of different geometric candidates with crank angle is shown in Fig. 3. The novel design better utilized injection pressure ensuring higher flow, hence higher capacity for smaller economizer. Reduction in reverse flow through the injection port for different port geometries is evident in Fig. 4. Economizer mass flow is plotted for four operating conditions in Fig. 6. It should also be noted here that, the port area was lowest for novel design. There was improvement in efficiency with the novel design as shown in Fig. 7. The last operating point (P5) corresponds to a point where economizer was inactive. But efficiency improved mainly due to the fact that the clearance volume created by the novel design was less as indicated by the area curve cycle duration or activeness in Fig. 3. The improvement from a typical circular port is in the range of 0.2–8.66 points in efficiency depending on the operating condition.
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Fig. 3 Area comparison of different geometry
Fig. 4 Mass flow through Injection port during compression cycle
Fig. 5 Areas with same start angle
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Fig. 6 Economizer mass flow
Fig. 7 Normalized concept isentropic efficiency comparison
The study was done on different geometries to improve isentropic efficiency of the baseline compressor, which was underperforming at some of the operating points. Having seen improvement with novel geometry, a new compressor was made with this profile and tested to see whether the analytical prediction aligned with test results. The efficiency comparison for two profiles are shown in Fig. 8. The comparison of mass flow at different conditions are also shown in Fig. 9. The mass flow for the elliptical port was less by 5–70%. The main reason for this change was that the location and cycle duration of the existing injection port was not optimum. When the location was corrected and changed to the novel design, the mass flow, capacity and efficiency improved.
2.2 Speed Optimization Compressors behave differently at different speed. As speed increases, so does power monotonically (see Fig. 10). While running speed sweeps, however, it was noticed
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Fig. 8 Normalized tested isentropic efficiency
Fig. 9 Normalized mass flow comparison
that the compressor efficiency does not change monotonically with speed, but rather there was a peak efficiency. Also, the speed corresponding to peak efficiency for each operating condition was different. A plot of efficiency versus speed for different operating condition is shown in Fig. 11. The compressor under discussion was tested at different speeds to validate this as shown in Fig. 11. From the plot it is clear that there are optimum speeds for an operating condition. Hence to extract maximum performance, it is necessary to size the compressor such that it provides design capacity and isentropic efficiency at an optimized speed. At lower speeds the inertia force (orbit scroll rotation) will decrease and hence the contact force arising from this will decrease, resulting in scrolls line contact length along the height of the flank to decrease, resulting in more leakages across chambers, motor efficiency and torque in the chamber model are based on prediction, which has error, etc. are some of the reasons for this behavior.
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Fig. 10 Normalized power variation with speed
Fig. 11 Normalized efficiency variation with speed
2.3 Discharge Port Delay During the compressor optimization process it was noticed that, when the discharge port was delayed (see Fig. 12), or volume ratio was changed, the efficiency improved. Like other parameters, this depended on operating condition as evident from Fig. 13. An optimized discharge port geometry, considering different operating condition, was selected. In this case a 110° port delay from the typical discharge timing prescribed by the theoretical maximum circular discharge port was used. Also, from Fig. 13 it was clear that operating point P5 had a decreasing efficiency, due to the low speed producing relatively higher leakage [7]. The improvement in efficiency was approximately 2–5 points depending on the operating point under consideration. This was incorporated in the baseline design.
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Fig. 12 Discharge port position with different port delay
Fig. 13 Variation of efficiency with port delay
2.4 Involute Start Angle Involute start angle along with trim details [8] determines the leading-edge thickness. Figure 14 shows start angle, trim details and the variation of leading edge of scroll as the start angle and trims are changed. It was noticed that the behavior was like port delay. The efficiency increased as start angle reduced, but as the thickness of the leading side of the scroll involute decreased, structural reliability decreased [9]. For the above reason start angle was not reduced further from the baseline design. Sensitivity of efficiency can be seen in Fig. 15. Change in start angle can bring an improvement to the tune of 0.7–1.3 points in isentropic efficiency.
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Fig. 14 Geometry nomenclature and examples with different start angle and trims
Fig. 15 Effect of start angle on efficiency
3 Conclusion It is clear from above study that • A suitably sized and positioned injection port has significant effect on isentropic efficiency of a compressor with injection port. • Injection port using the novel geometry has a superior performance compared to other port geometries. • By suitably selecting the speed and economizer port improvement can be seen in the compressor isentropic efficiency in comparison to other port geometries. • An optimum discharge port delay or volume ratio has significant effect on the isentropic efficiency. • Though involute start angle affect the reliability, it can still be optimized by suitably selecting the scroll material and thus can add to the compressor efficiency. Hence different economizer port designs result in different compressor performance. It can be sized to maximize capacity and efficiency for a given type of operating point and reduce the capacity and efficiency for others. Hence this economizer can be sized and tuned based on the requirement of the operation allowing trade offs based on the target operating points.
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Acknowledgements I would like to express my gratitude to Trane Technologies for sponsoring this effort. Also, would like to place on record my sincere thanks to Eric Mlsna for his guidance and suggestion.
References 1. ASHRAE standard 23-2022, Methods for Performance Testing Positive Displacement Refrigerant Compressors and Compressor Units 2. J. Sauls, Optimization of Scroll Compressor Performance with Manufacturing Capability and Reliability Constraints, International Compressor Engineering Conference. Paper 1633 (Purdue University, 2004) 3. X. Xing, Y. Hwang et al., Refrigerant injection for heat pumping/air conditioning systems: literature review and challenges discussions. Int. J. Refrig. 34(2), 402–415 (2011) 4. F.M. Tello Oquendo, et al., A Methodology for Characterization of Vapor injection Compressors, International Compressor Engineering Conference. Paper 2424 (Purdue University, 2016) 5. Y. Song, et al., An Experimental Study of a Multi-port Vapor Injected Scroll Compressor, International Compressor Engineering Conference. Paper 2376 (Purdue University, 2014). 6. R. Baumgart, et al., Optimization of the Pre-Outlet and Main-Outlet Bores in Scroll Compressors, International Compressor Engineering Conference. Paper 2763 (Purdue University, 2022) 7. D. Gross, et al., Scroll Wrap Additional Stress in Variable Speed Application, International Compressor Engineering Conference. Paper 2584 (Purdue University, 2018) 8. Y. Liu et al., Study on involute of circle with variable radii in a scroll compressor. Mech. Mach. Theor. 45(11), 1520–1536 (2010) 9. C. Ancel, et al., Fatigue Design for Scroll Compressor Wraps, International Compressor Engineering Conference. Paper 2034 (Purdue University, 2010)
Performance Anlaysis of Water-Cooled VRF System in Cooling Mode by Changing Scroll Compressor Geometry Dongwon Kim, Been Oh, Hosik Jeong, and Gyung-min Choi
Abstract In this study, the performance of water-cooled variable refrigerant flow (VRF) system was evaluated through static numerical simulation by changing scroll compressor geometry. The parameters used in the evaluation are the wrap height of the scroll compressor and the basic circle radius. To determine the best combination of geometry under given conditions, the mass flow rate, condensation pressure, evaporation pressure, power consumption, COP, and IEER were calculated. As a result of the analysis, the VRF performance was evaluated to be better where the height of the compressor is lower, and the radius of the basic circle is smaller. However, considering the COP, the optimal variable combination is the wrap height of 4 mm, which is 1 mm higher than the previous value, and the basic circle radius of 1.6 mm which is the previous value. In the optimal parameter combination, COP improved by 3.73% and the IEER by 5.04%. Keywords VRF · Scroll compressor · Numerical modelling
D. Kim · B. Oh · H. Jeong Graduate School of Mechanical Engineering, Pusan National University, Busan 46241, Republic of Korea e-mail: [email protected] B. Oh e-mail: [email protected] H. Jeong e-mail: [email protected] G. Choi (B) Department of Mechanical Engineering, Pusan National University, Busan 46241, Republic of Korea e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_18
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1 First Section The Variable refrigerant flow (VRF) is an air conditioning system in residential and commercial buildings consisting of one or more outdoor units and several indoor units. The VRF system is one of the representative systems in the heat pump system. The VRF system has many advantages. The first feature is its high energy efficiency. The variable speed compressor using inverter is included in VRF system, and these systems can adjust the refrigerant flow according to load. By using an inverter compressor, it is possible to efficiently manage energy by continuously operating without using the conventional on–off operation principle. The second is that accurate indoor temperature control is possible. The part load is distributed by the user’s set temperature. Third, it is easy to install. The module size of the indoor unit does not significantly affect the interior space. In addition, it is possible to repair individual indoor units, not all. Recently, the power consumption of refrigeration systems is increasing. And HVAC systems use a very large amount of energy consumption in buildings (50% of building consumption and 20% of total consumption in the USA) [1]. Therefore, researchers are paying more attention to energy consumption. However, it takes a lot of time and money to carry out a VRF experiment. Therefore, many studies have been conducted using numerical calculations to solve this problem for HVAC. Min et al. [3] studied on the performance of a VRF system by comparing the bypass cycle and the vapor injection cycle. They derived that bypass cycles and injection cycles represent improved energy efficiency and cooling capacity. In addition, they observed that the input power of the injection cycle was reduced by up to 4.45% under the same cooling capacity condition [2]. Cho et al. [2] analyzed the heat pump cycle performance of R410A and R32 refrigerants using vapor injection in variation of compressor speed and injection ratio. They demonstrated that cooling capacity, heating capacity, and COP incresed when vapor injection was applied. Furthermore, they conducted that vapor injection can play an important role in improving performance at extreme temperatures [3]. Choi et al. [4] analyzed the performance of the water-cooled VRF system by changing the geometry of the plate type outdoor heat exchanger. They derived that the optimal vertical length of a plate heat exchanger is 1 m when considering the load in cooling mode. Also, they showed that there was no significant difference in energy efficiency ratio between heating and cooling modes [4]. The compressor is a key part of the refrigeration system and accounts for more than 80% of the system’s energy consumption. Among them, scroll compressors are mainly used in parts of the air conditioning system due to their high efficiency and low torque fluctuation compared to other compressors. The geometry of the compressor affects the performance of system as well as the performance of the compressor. The scroll compressor has various parameters that affect performance. Among them, the warp height of the scroll compressor affects the Radial Leakage Area, and the radius of the basic circle affects the Axial Leakage Length. Therefore, the two compressor parameters affect the leakage of the compressor, and thus have a great influence on
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the compressor performance. Etemad and Nieter [5] analyzed that the effect on the various parameters of the scroll compressor from an energy loss and manufacturing perspective. They derived that the starting angle and height are the most important parameters in scroll compressor optimization studies [5]. Ishii et al. [6] studied that the optimal combination of key parameters for high mechanical efficiency at a fixed cylinder diameter. They explained that the more compact the parameter combinations of the compressor, the better the cooling capacity and mechanical efficiency [6]. Ishii et al. [6] studied that the effect of heat transfer on the efficiency of the compressor. In addition, it was confirmed whether there is an effect on it in the optimal parameter combination. They showed that the resultant efficiency decreased when considering heat transfer, and that the combination of parameters was not affected by heat transfer [7]. However, in previous studies, performance analysis of VRF due to changes in scroll compressor geometry were not mainly conducted. Therefore, in this study, the performance analysis of the water-cooled VRF system according to the geometry change of the scroll compressor is performed.
2 Measurement Device The schematic of the VRF test device consisting of a combination of water-cooled outdoor unit and 12 indoor units is shown in Fig. 1. The outdoor unit consists of a scroll compressor, plate heat exchanger, pump, water tank and fan. The scroll compressor has a displacement volume of 61.1 cm3 /rev and has a frequency from 30 to 120 Hz. As a cassette type unit for the indoor unit, a louvered fin-tube type heat exchanger was used. Detailed specifications of the system are shown in Table 1. The performance of the VRF system was evaluated according to AHRI Standard 1230 [8]. The experimental conditions according to the AHRI Standard 1230 are summarized in Table 2. IEER is calculated by Eq. (1). The uncertainty of IEER measuring devices is shown in Table 3. I E E R = (0.02 · A) + (0.617 · B) + (0.238 · C) + (0.125 · D) where A B C D
EER at 100% Capacity at AHRI Standard Rating Conditions. EER at 75% Capacity at reduced condenser temperature. EER at 50% Capacity at reduced condenser temperature. EER at 25% Capacity at reduced condenser temperature.
(1)
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Fig. 1 Measurement device of the water-cooled VRF systems Table 1 Table captions should be placed above the tables Specifications ODU
• Scroll compressor • • • • • • •
IDU
(Suction Volume = 61.1cm3 /rev) (Frequency = 30–120 Hz) Plate type heat exchanger (Plate type: L 0.47 × W 0.119) ODU fan Water tank Pump
• Cassette types of IDU • (Finned type (Louver fin—tube) •: L 1.8 × W 1)
Table 2 Environmental conditions of water-cooled VRF simulation Mode
Cooling
Load (%)
100 75 50 25
Indoor
Outdoor
Air-source
Water-source
Dry bulb temperature (°C)
Wet bulb temperature (°C)
Inlet temperature (°C)
27
19
30.0 23.1 16.7 12.8
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Table 3 Uncertainty analysis of a measurement device Suction pressure Discharge pressure Air temperature Water temperature Input power cooling capacity EER (cooling mode)
Unit
Accuracy of measurement device
Uncertainty
kPa kPa °C °C kW kW Btu/Wh
± 0.25% ± 0.25% ± 0.05 °C ± 0.05 °C ± 0.2 °C
± 0.31 ± 0.31 ± 0.27 ± 0.27 ± 0.44 ± 0.24 ± 0.52
3 Mathematical Model 3.1 Water-Cooled VRF System Figure 2 shows a flowchart of the water-cooled VRF system used in this study. Input values are the super-heating temperature, the sub-cooling temperature. Then, the calculation is started assuming condensation pressure, evaporation pressure, suction super-heating temperature, and Heat ratio. In the calculation process, three types of convergence (subcooling temperature, super-heating temperature and compressor inlet enthalpy) are checked. In the second convergence process, calculate the heat transfer and pressure drop of the indoor unit using the evaporator inlet pressure and the inlet enthalpy at the expansion. valve assumed at the starting of the calculation. At the evaporator outlet, pressure converges because of the super-heating temperature calculation. Heat Indicator (HI) and Mass flow rate Indicator (MI) variables are used to determine the mass flow rate of refrigerant distributed to individual indoor units. MI represents the mass flow distribution ratio of the indoor device. HI is the tracking variable for input sub-cooling temperature and super-heating temperature, which is the variable used to calculate MI. The mass flow rate of each indoor device is calculated by Eqs. (2)–(5). H Ii = H Ii,n−1 · M Ii =
h eva,out h eva,out,set
H Ii H Itotal
(2) (3)
m˙ I DU,i = m˙ I DU,total · M Ii
(4)
m˙ O DU = m˙ total · m˙ I DU,total
(5)
In the third convergence process, calculate the heat loss and pressure drop of the gas pipe. The enthalpy at the inlet of the compressor is converged by the suction
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Fig. 2 Flowchart of the water-cooled VRF system calculation
super-heating temperature. The iteration of the simulation is repeated until a value within an acceptable error range is reached. When all values converge, the VRF simulation calculation is finished.
3.2 Scroll Compressor Figure 3 is a flowchart of the scroll compressor used in this study. The Simulation of scroll compressor is modeled with a geometry-based thermodynamic approach proposed by Yanagisawa et al. [9]. The input values are scroll compressor geometry and the condensation pressure, evaporation pressure, and suction super-heating temperature assumed in the VRF simulation. The volume of the scroll compressor can be obtained by multiplying the difference between in the area formed by the
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inner and outer involute curves by the height of the scroll wrap. In addition, the volume can be calculated by Eqs. (6)–(8) using the following equation through the three processes of suction, compression, and discharge. Vsuction = 2h
⎧ ϕ ⎨1 e ⎩2
ϕk
Vcompr ession
Vdischarge = 2h
ϕa
1 2
lb2 dϕ + Ar easuction opening ϕk −π
⎫ ⎬ (6)
⎭
⎧ ϕ +2π ⎫ ϕe +π ⎨ 1 k ⎬ 1 = 2h la2 dϕ − lb2 dϕ ⎩2 ⎭ 2
⎧ ϕ ⎨1 1 ⎩2
la2 dϕ −
ϕe −π
ϕk
la2 dϕ −
1 2
ϕk +π
ϕ1 −π
lb2 dϕ + Ar eadischarge opening ϕa −π
(7) ⎫ ⎬ ⎭
(8)
As compression proceeds, the internal leakage occurs between the gaps due to the pressure difference. Leakage can be classified into cases where it flows into the chamber and cases where it flows out of the chamber. Also, the leakage of the scroll compressor can be defined into radial leakage through the wrap length and axial clearance, and tangential leakage through the gap between the wraps. The leakage area for each leakage direction and inflow and outflow can be calculated with the following Eqs. (9)–(11) and the mass flow rate due to leakage is calculated by the Eq. (12) for the leakage area.
Fig. 3 Flowchart of the scroll compressor calculation
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Aaxi in
⎛ ϕ2 ⎞ = ⎝ la dϕ ⎠ · δaxi
(9)
ϕ1
Aaxi out
⎛ ϕ2 ⎞ = ⎝ lb dϕ ⎠ · δaxi
(10)
ϕ1
Arad = h · δrad / m˙ = Aleak · Cv · Pu ·
(11)
2·k · (k − 1) · Rgas · Tu
/
2
(Pr ) k − (Pr )
k+1 k
(12)
The mass flow rate and Properties are defined by the law of conservation of mass and conservation of energy, as Eqs. (13)–(15). dm i dm o dm = − dθ dθ dθ dT dv ∂P ∂P dP = + dθ ∂ T v dθ ∂v T dθ dv 1 dm i o − h) − dm − h) − ∂h − ∂∂vP T v dθ dT m dθ (h i dθ (h o ∂v T ∂h = dθ − ∂∂ TP v v ∂T v
(13) (14)
(15)
The indicator work of compressor was calculated from the results of temperature and pressure calculation from suction to discharge processes, as Eq. (16). Windi =
Pd V
(15)
The input power consumed by the scroll compressor was finally obtained with motor and mechanical efficiency data from the experiments, as Eq. (17). Additional, enthalpy of discharge is obtained by Eq. (18). Wcomp = Windi · ηmotor · ηmech
(17)
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The calculation is determined by the convergence of the compressor discharge temperature. Iterations of the simulation are repeated until an acceptable error range calculator value is reached. When all values converge, the compressor mass flow rate, compressor work, and compressor discharge enthalpy become output values, and the calculation is finished.
3.3 Other Components Heat Exchanger. In a VRF system, several heat exchangers are located inside the condenser and evaporator. A louvered fin-tube heat exchanger was used for the indoor unit, and a plate heat exchanger was selected for the outdoor unit. The indoor unit heat exchanger was modeled by Eq. (19) using the ε-NTU method. Q = m˙ air C p,air Tair,in − Tair,out = m˙ r e f h r e f,in − h r e f,out
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The outdoor unit was modeled by Eqs. (20) and (21) according to the ε-NTU method. Q = εCmin (Tr e f,in − Twater,out )/(1 − h r e f,out = h r e f,in +
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The heat transfer between refrigerant and air within each tube is simulated with average characteristics at the inlet and outlet of each tube, considering energy and mass conservation in the heat exchanger model. The correlation between heat transfer and pressure drop between the outdoor and indoor units is summarized in Table 4. Expansion Valve. The mass flow through the expansion valve is calculated by the orifice equation of Eq. (22). √ m˙ main,E E V = Cv A ρ E E V,i ΔPE E V
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The inlet condition of the Expansion Valve was determined from the results of IHX calculation, and the outlet condition was determined with assuming the expansion process to be isentropic.
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Table 4 Correlation between heat transfer and pressure drop between the ODU and IDU Fin-tube type heat exchanger Heat transfer coefficients
• Refrigerant side — Single phase: Gnielinski — Two phase Condensation: Goto Evaporation: Jung-Radermacher • Air side: Wang
Pressure drop coefficients • Refrigerant side — Single phase: Churchill — Two phase Condensation: Goto Evaporation: Jung-Radermacher • Air side: Wang Plate type heat exchanger
Heat transfer coefficients
• Refrigerant side — Single phase: Kumar — Two phase Condensation: Han Evaporation: Han • Air side: Han
Pressure drop coefficients • Refrigerant side — Single phase: Kumar — Two phase Condensation: Han Evaporation: Han
4 Results and Discussion 4.1 Validation of the Simulation Figure 4a, b show the validation results of the cooling capacity and input power according to the compressor frequency (30, 60, 90, 120 Hz). The experiment of scroll compressor performance was performed based on ISO 917 (International Organization of Standardization, 1989). Each result was included within a 10% error rate (Fig. 5). Validation between the simulation calculation result and the experimental data was performed based on the AHRI Standard 1230. The energy performance of the VRF system has less than 10% deviation between simulation and experimental data, so it can be evaluated as reasonable in simulation.
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4.2 Analysis of VRF System Performance by Changing Geometry of Scroll Compressor The performance change of the water-cooled VRF system was performed according to the change in the height of the scroll wrap and the radius of the basic circle. The height of the scroll wrap was shown at every 0.2 mm interval change from 3 to 5 mm. The basal radius was shown at every 0.1 mm interval change from 1.6 to 1.8 mm. Figure 6 shows the change in mass flow rate according to the change in compressor height and the basic circle radius. The height of the scroll compressor has a relationship proportional to the radial leakage area. Therefore, as the height increases, the leakage amount increases as the radial leakage area increases. In addition, the radius of the basic circle is proportional to the leakage length. As the value of the radius of the basic circle increases, the leakage length increases, which affects the axial leakage area. Therefore, as these two values increase, the mass flow rate increases.
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height of the wrap increases and the radius of the basic circle increases. However, when a certain point is reached, the increase in slope is almost not changes. Figure 10 shows the change in the input work of the system according to the change in the height of the scroll wrap and the radius of the basic circle. The input work increases as the height of the wrap increases, and the radius of the basic circle increases. Because, mass flow rate increases, and the pressure ratio increases, which results in an increase in the input work of the compressor. Figure 11 shows the change in the COP of the system according to the change in the height of the scroll wrap and the radius of the basic circle. COP shows a tendency that rises until the height of the wrap increases to 4 mm and then decreases thereafter. Fig. 9 IEER
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COP tends to increase because the rate of increase in cooling capacity is larger than the rate of increase in input work, but after a certain height of the wrap, the rate of increase in power consumption of the compressor is larger than the rate of increase in cooling capacity, so COP decreases. Therefore, in this study, the results of the best COP are shown when the height of the warp is 4 mm and the radius of the basic circle is 1.6 mm within a given condition. 7.0
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5 Conclusions In this study, the performance of water-cooled variable refrigerant flow (VRF) system was evaluated through static numerical simulation by changing scroll compressor geometry. The mass flow rate, condensation pressure, evaporation pressure, power consumption, COP, and IEER were calculated by changing the wrap height and the radius of basic circle. • Considering COP, the optimal warp height is 4 mm, and the optimal base circle radius is 1.6 mm. • In optimal parameter combination, the mass flow increases by 4.76%, the compression ratio increases by 2.03%, the IEER increases by 5.04%, input work increases by 3.54%, and COP increases by 3.73%. Acknowledgments This work was also supported by the Technology Innovation Program (RS2022-00143968, Development and Demonstration of Eco-friendly Ocean Clean-up Vessel) funded By the Ministry of Trade, Industry and Energy (MOTIE, Korea) and This work was supported by Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government (MOTIE) (20214000000140, Graduate School of Convergence for Clean Energy Integrated Power Generation).
References 1. L. Pérez-Lombard, J. Ortiz, C. Pout, A review on buildings energy consumption information. Energy Build. 40(3), 394–398 (2008) 2. I.Y. Cho, H. Seo, D. Kim, Y. Kim, Performance comparison between R410A and R32 multi-heat pumps with a sub-cooler vapor injection in the heating and cooling modes. Energy 112, 179–187 (2016) 3. B. Min, S. Jang, T. Lee, H. Bae, C. Moon, G. Choi, Performance comparison between bypass cycle and injection cycle for sub-cooling methods in multi-split variable refrigerant flow (VRF) system in hot seasons. Int. J. Refrig. 107, 202–213 (2019) 4. J. Choi, B. Oh, S. Na, B. Min, Y. Park, G. Choi, Evaluation of the performance of water-cooled VRF system for heat exchanger geometry under part-load operation. Appl. Therm. Eng. 215, 118921 (2022) 5. S. Etemad, J. Nieter, Computational parametric study of scroll compressor efficiency, design, and manufacturing issues, in International Compressor Engineering Conference. Paper 602–611 (1988) 6. N. Ishii, M. Yamarnura, S. Muramatsu, S. Yamada, M. Takahashi, Efficiency simulations with consideration of heat losses of a r410a compact scroll compressor for its optimal performance, in International Compressor Engineering Conference, 1598–1607 (1994) 7. N. Ishii, S. Kawamura, S. Yamamoto, K. Sawai, A. Hiwata, H.K. Nakomoto, T. Seng, Efficiency simulations with consideration of heat losses of a r410a compact scroll compressor for its optimal performance, in International Compressor Engineering Conference, 1598–1607 (2002)
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8. AHRINET, 2021, AHRI Standard 1230, 2021 Standard for Performance Rating of Variable Refrigerant Flow (VRF) Multi-Split Air-Conditioning and Heat Pump Equipment, Air-conditioning, Heating and Refrigeration Institute. https://www.ahrinet.org/standards. Last accessed 2021 9. T. Yanagisawa, M.D. Cheng, M. Fukuta, T. Shimizu, Optimum operating pressure ratio for scroll compressor, in International Compressor Engineering Conference, 732–741 (1990)
Experimental Testing of a Scroll Compressor with Two-Phase Refrigerant Flows Nicolas Leclercq, Benedikt G. Bederna, and Vincent Lemort
Abstract The present paper introduces an experimental investigation of a scroll compressor working with two-phase refrigerant flows, in the frame of a novel thermodynamic cycle making use of two-phase compressions/expansions called REGENBY-2. The design of the test bench dedicated to two-phase compression will first be explained. The objective of this test bench is to assess the performances of the compressor working with a two-phase refrigerant-oil mixture (R1233zd(E)—Emkarate RL32 MAF) under varying conditions such as inlet pressures, inlet vapor qualities, oil circulation ratio, pressure ratios and speeds. In order to investigate losses that could come from an unperfect compression, the pressure ratio can be manipulated to reach over and under compression. The vapor quality can go down to 35% in mass fraction. Finally, the post-processing methodology is detailed and the results of the test bench analyzed, showing the influence of the pressure ratio, the speed, the vapor qualities and the oil circulation ratio on the isentropic and volumetric efficiencies. Keywords Two-phase compression · Experimental testing · Oil-refrigerant mixture
1 Introduction REGEN-BY-2 is a Horizon 2020 EU-funded project, that aims to develop a first-ofits-kind lab-scale prototype of a novel thermodynamic cycle and related plant for the revalorisation of renewable thermal energy sources, unlocking their large potential to supply electric, heating and-or cooling energy vectors. The ideal investigated thermodynamic cycle, about which more details can be found in [1], is highly efficient as it is constituted by a proper combination of cycles close to the Carnot cycle N. Leclercq (B) · V. Lemort Energy Systems Research Unit, University of Liège, 4000 Liège, Belgium e-mail: [email protected] B. G. Bederna Cryogenics and Compressor Technology, Technische Universität Dresden Bitzer Chair of Refrigeration, 01062 Dresden, Germany © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_19
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Fig. 1 REGEN-BY-2 cycle architecture
Fig. 2 REGEN-BY-2 cycle temperature-entropy diagram
operating with a two-phase fluid circulating in novel two-phase expanders and twophase compressors. The working fluid selected for the lab-scale prototype is the HFO R1233zd(E). The lubrication of the compressors is ensured by the oil EMKARATE RL32 MAF. The architecture of the REGEN-BY-2 prototype is depicted in Fig. 1 and the corresponding Temperature-Entropy diagram in Fig. 2. The loop 1-2-2*-3-4-5-5*-6-7-8-1 consists in a two-stage vapor expansion cycle, where the high pressure is reached with the help of two compressors and a regenerator in between. Likewise, the power is recovered by three expanders, the two first being separated by the same regenerator as the compressors. The low temperature thermal source, allowing to vaporize the working fluid between points 3 and 4 can come from waste heat recovery or any renewable power source. Two condensations are then performed: between points 6 and 7 in order to provide the end-user with heating and between points 13 and 1 with an air-cooled condenser. Finally, a conventional
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refrigeration loop is realized between points 1-9-10-11-12-13-1 where an air-cooled condenser allows to reach a saturated liquid state before the expansion valve. In order to investigate the feasability of the REGEN-BY-2 cycle, a test bench has been developed to test a commercial scroll compressor with two-phase regimes. The description of this test bench and the results of the experimental campaign will be described in the subsequent sections.
2 Test Bench Description The layout of the test bench is inspired from a heat pump and can be found in Fig. 3. This test bench is dedicated to the characterization of the compressor performance, namely, its volumetric and isentropic efficiencies over a wide range of operating conditions. The compressor is an open-drive automotive scroll compressor with a displacement volume of 86 cm.3 and a built-in volume ratio of 2.3. It is powered with an electric motor and a torquemeter is used to measure the compressor power consumption. Moreover, its lubrication is ensured by an independant oil loop allowing to regulate the oil circulation ratio (OCR) using the valve V3. To separate the oil from the refrigerant, the two-phase oil-refrigerant mixture is vaporized by a heating resistor at the outlet of the compressor, the oil is then recovered by an oil separator. The oil is then cooled and directed at the inlet line of the compressor, called "mixing line". After the oil separator, a part of the vapor is redirected directly towards the mixing
Fig. 3 Test bench layout
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line while the remaining part is condensed and subcooled. By varying the opening of the three controlled discharge valves (V1, V2, V3), a wide range of conditions can be met, allowing to test different pressure ratios, inlet pressures, inlet vapor qualities and OCR. Furthermore, the compressor speed can also be controlled using a variablefrequency drive. A pulley ratio of 1.7 between the motor and the compressor allows to run the compressor with a speed up to 5000 RPM. Regarding the instrumentation of the test bench, lots of temperature/pressure measurements are taken, mainly to check the energy balances all over the test bench. Furthermore, the mass flow rates of each line (refrigerant vapor, refrigerant liquid and oil) are measured, using Coriolis flowmeters for the oil and the liquid lines and a rotameter for the vapor line. The cooling water mass flow rates are also measured using electromagnetic flowmeters to check the energy balances of the three heat exchangers. A cylindrical sight glass has been placed in the mixing line in order to see the flow, particularly useful for the start-up of the test bench, to check the presence of liquid before increasing the speed of the compressor. Finally, the inlet vapor quality is figured out using an energy balance on the mixing line, the details of this energy balance will be shown in the subsequent section.
3 Results Post-processing In this section, the post-processing methodology will be detailed. First, the assumptions governing the post-processed results will be explained. Then, the procedure to figure out the vapor inlet quality will be detailed, an energy balance is applied on the mixing line, taking into account the OCR. The performance indicators, i.e., the volumetric and isentropic efficiencies will also be defined.
3.1 Assumptions For the results analysis, the following assumptions have been made: • No refrigerant is flowing in the oil line. A minimum superheat of 15 K is set at the outlet of the heating resistor. It allows to minimize the quantity of liquid refrigerant trapped in the oil. • Thermal equilibrium is assumed before the compressor where the temperature of the mixture is measured. This assumes that the liquid phase and the vapor phase have the same temperature. This assumption has been partially verified by checking the temperature evolution in the mixing line and creating some additional pressure losses to check the effect on the results. However, depending on the operating point measured, it may be possible that this equilibrium is not reached. For instance, in the points where a high vapor quality and a high speed are tested the vapor phase is so fast compared with the liquid phase that it is impossible to guarantee
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the thermal equilibrium. This points will be detected and removed by the postprocessing algorithm, as explained further in the paper. • No thermal losses are taken into account in the mixing line (between the mixing point of the oil, the subcooled liquid and the superheated vapor and the inlet of the compressor). This allows to compute the inlet vapor quality using an energy balance on this line. This assumption should be valid as the line is well insulated and the mixture reaches temperature close to the ambiance temperature (.≈ 20 ◦ C) in the low-pressure side (R1233zd(E) has a boiling point of 19 .◦ C).
3.2 Inlet Vapor Quality Calculation As already mentioned, the inlet vapor quality is calculated assuming an energy balance on the mixing line, i.e., the equality .h mi x = h su should be respected. The enthalpies are calculated using the ideal mixture assumption between the oil and the refrigerant (neglected mixing term) [2], moreover, the fraction of oil in the vapor phase is neglected as the saturation pressure of the oil is extremely low compared with the refrigerant. This gives: ⎧ .
h mi x = Q mi x h r,v (Pv , Tv ) + z o h o (To ) + (1 − Q mi x − z o )h r,l (Pl , Tl ) σ (Tsu ) h su = Q su h r,v (Psu , Tsu ) + z o h o (Tsu ) + (1 − Q su − z o )h r,l
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where the conditions (temperatures, pressures and mass flow rates) coming from the three main lines (refrigerant vapor (.r, v), oil (.o) and refrigerant liquid (.r, l)) and the supply (.su) of the compressor are known. Moreover, the mixing quality ˙o m˙ v . Q mi x = , the OCR.z o = mm and the total mass flow rate.m˙ tot = m˙ r,v + m˙ r,l + m˙ o m˙ tot ˙ tot σ are also coming from the measurements. The compressor inlet enthalpy uses .h r,l , the liquid saturation (.σ ) enthalpy of the refrigerant. The refrigerant properties are computed using CoolProp and the oil properties are retrieved from [3]. Finally, the only unknown in (1) is the inlet vapor quality of the compressor . Q su .
3.3 Volumetric Efficiency The volumetric efficiency of the compressor compares its mass flow rate with its theoretical mass flow rate and can be computed using the following equation: ε =
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Again, (3) considers an ideal mixture with a neglected mixing term.
3.4 Isentropic Efficiency The isentropic efficiency compares the ideal power consumption of the compressor with its real power consumption and can be obtained from: ε =
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with .h ex,is the outlet enthalpy following an isentropic (adiabatic and reversible) compression and .W˙ sha f t,cp , the power consumption of the compressor shaft. As already said, the compressor is driven by a motor connected with a belt. Unfortunately, it was impossible to place the torquemeter on the compressor shaft, it has thus been placed on the motor shaft, and the friction torque generated by the belt is inevitably measured by the torquemeter. To address this issue, a measurement of the power consumed by the belt without the compressor has been performed with a varying speed as can be seen in Fig. 4. This power is subtracted from the motor shaft measurement and the power of the compressor shaft is thus approximated. The definition of the isentropic compression outlet enthalpy for a two-phase oilrefrigerant mixture is inspired from the definition of [4], where the entropy exchange between the oil and the refrigerant is taken into account. However, they did not consider the part of refrigerant under the liquid phase, as their inlet superheats were high enough to neglect it. A new definition is therefore proposed, for which two unknowns have to be defined: • The isentropic temperature .Tis • The isentropic vapor quality . Q is . Those two unknows will allow to compute the isentropic enthalpy as follows: σ h = Q is h r,v (Pex , Tis ) + z o h o (Tis ) + (1 − Q is − z o )h r,l (Tis )
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Two equations are necessary to solve the system with the two previously defined unknowns: the conservation of entropy along the compression and the oil-refrigerant solubility equation. The oil-refrigerant solubility equation will be obtained using the Raoult law as done in [5], although [6] stated that this assumes that the polarity and the molecular size are similar for the two components, which is not the case for an oil-refrigerant mixture. It thereby constitutes an approximation. The system to solve is therefore the following, with .ssu = sex,is : ⎧ σ (Tsu ) ⎨ ssu = Q su sr,v (Psu , Tsu ) + z o so (Tsu ) + (1 − Q su − z o )sr,l σ (Tis ) sex,is = Q is sr,v (Pex , Tis ) + z o so (Tis ) + (1 − Q is − z o )sr,l . ⎩ ¯ ( Q is − 1 − z¯ oil )Prσ (Tis ) = Pex ( Q¯ is − 1)
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where the last equation, coming from the Raoult law, uses molar fractions (. ¯ ) instead of mass fractions. This can be converted assuming a molar mass of 500 g/mol for the oil, an averaged value for POE oil, as no data is available for the selected oil. The isentropic work determination process is illustrated in Fig. 5. The crossing point between the two temperature lines defines the isentropic quality. It thus finds the temperature and vapor qualities allowing to respect the conservation of entropy and the solubility equation of the mixture.
4 Results and Discussions In order to get rid of the dependency of the inlet quality. Q su on.z o (the higher the OCR the lower the vapor quality), all the results will be plotted as a function of a refrigerantonly vapor quality (varying between 0 and 1), defined as: . Q r,su = Q su /(1 − z o ). In total, 5 variables can influence the compressor performances:
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The compressor inlet pressure . Psu tested between [1 and 2] bar The oil circulation ratio .z o tested between [0.05 and 0.20] The compressor speed . Ncp tested between [1500 and 5000] RPM The inlet vapor quality . Q r,su tested between [0.35 and 0.95] The compression ratio .r p tested between [1.5 and 6].
All those variables have varying degrees of impact on both isentropic and volumetric efficiencies of the compressor. However, it is impossible to get a high number of tested values for each variables for two reasons. First, the test bench limitations do not allow to test any conditions, for instance, the mass flow rate varies from 4 g/s (high quality with a low speed) to 90 g/s (low quality with a high speed), meaning that the pressure losses in the test bench will only allow to test high compression ratios at high speeds. Then, too many points are needed to test each variable with many values, for instance, if 4 values were to be tested for each variable, it would need .45 = 1024 points to record, which is unfeasible. Therefore, instead of targeting all possible points, a useful predictive tool has been used to predict points that were not recorded. The tool is called GPExp [7] and is a machine learning tool using Gaussian processes to predict data in the 5 dimensions given a set of points. It is able to get rid of the outliers and to perform a cross-validation with the dataset used. This method is applied for every point and if the total error is below a fixed tolerance, the dataset is accepted. If too much error is resulting from the cross-validation, it means that some data are missing to get accurate predictions. In total, 106 points have been validated by GPExp, the fitting error as well as the cross-validation error on the volumetric and isentropic efficiency can respectively be seen in Figs. 6 and 7. The mean absolute error (MAE) on the isentropic efficiency predictions is 1.47% and on the cross-validation is 2.54% while the MAE on the volumetric efficiency is 3.09% and on the cross-validation 4.07%. The sample (isentropic and volumetric efficiencies) are normalized in the following way: yi − min(y) . yi,nor m = (7) max(y)
4.1 Volumetric Efficiency The evolution of the volumetric efficiency for two different speeds can be observed in Fig. 8. In general, for low vapor qualities and high pressure ratios, the volumetric efficiency is reduced considerably. It could be explained by the heat transfer going from the shell of the compressor to the two-phase mixture, therefore increasing the vapor quality and decreasing considerably the density inside the compressor. The higher the pressure ratio, the higher the temperature of the shell, which increases the heat transfer to the mixture. Furthermore, it can be seen that for low qualities, increasing the speed considerably improves the volumetric efficiency, while for high
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qualities, the efficiency is decreased. It seems that with a higher speed, a sealing effect of the liquid is decreasing the losses. Moreover, the heat transfer have less effect due to the inlet speed being higher. Therefore, the maximum volumetric efficiency (0.95) can be found for a vapor quality of 0.48.
4.2 Isentropic Efficiency The variables having the most influence on the isentropic efficiency have been identified as being the inlet vapor quality and the pressure ratio. An example of the isentropic efficiency as a function of the pressure ratio and the inlet quality can be found in Fig. 9. It can clearly be seen that the isentropic efficiency is decreasing when the inlet quality decreases. Another tendency is the under-compression losses that are emphasized with low vapor qualities, this can be explained by the shift of the ideal pressure ratio towards lower value when lowering the qualities, due to the inlet-outlet volume ratio being further to the built-in volume ratio of the compressor.
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4 e rat 5 io [-]
6
0.8 ] 0.6 ity [ l u 0.4 t q a e Inl
.5 42 0 . 45 47.5 0.0 5 5 52.
3
65
67.5
.5 62
6
.0
55.0 0 0.
47.5
57
.5
40.0 32.5
2 52.5
0.4
Isentropic efficiency [%]
35.0
.5 37
32.5
62.5
.0
.0
40
4
40
55
50
Pressure Ratio [-]
60
Isentropic efficiency [%]
70.0 5
50.0 47.5
0.6 Inlet Quality [-]
0.8
25.0
Fig. 9 Evolution of the isentropic efficiency with the inlet quality and the pressure ratio for an inlet pressure of 1.5 bar, an OCR of 10% and a compressor speed of 3000 RPM
Therefore, when lowering the vapor quality, undercompression losses are increased and overcompression losses decreased. Moreover, the decrease in isentropic efficiency can also be justified with the decrease of the volumetric efficiency with low vapor qualities and the increase of pressure losses through the discharge port, as investigated in [8]. The influence of the speed and the OCR can be observed in Figs. 10 and 11. For a high vapor quality, increasing the speed decreases the isentropic efficiency, this is certainly due to the additional discharge port pressure losses faced with the higher mass flow rate. For low vapor qualities, the reverse effect is observed, it can be explained by the higher volumetric efficiencies as already shown in the previous section. Regarding the effect of the OCR, it can be seen that the presence of oil increases the efficiency for a high vapor quality and low pressure ratio, while decreasing it for a low vapor quality. This follows the tendency of the volumetric efficiency, that is generally improved when the OCR is increased.
Experimental Testing of a Scroll Compressor with Two-Phase Refrigerant Flows
249
90 N N N N
Isentropic efficiency [%]
80
= 1500 = 1500 = 5000 = 5000
RPM, RPM, RPM, RPM,
Q = 40.0% Q = 90.0% Q = 40.0% Q = 90.0%
70 60 50 40 30 2
3 4 Pressure ratio [-]
5
6
Fig. 10 Isentropic efficiency for a varying pressure ratio for an inlet pressure of 1.5 bar and an OCR of 5% 90 N N N N
Isentropic efficiency [%]
80
= 1500 = 1500 = 5000 = 5000
RPM, RPM, RPM, RPM,
Q = 40.0% Q = 90.0% Q = 40.0% Q = 90.0%
70 60 50 40 30 2
3 4 Pressure ratio [-]
5
6
Fig. 11 Isentropic efficiency for a varying pressure ratio for an inlet pressure of 1.5 bar and an OCR of 20%
5 Conclusion In the present paper, a test bench dedicated to the investigation of two-phase compression using a commercial scroll machine has been introduced. The need for two-phase compression has been explained by introducing the REGEN-BY-2 European project consisting in the development of a trigeneration prototype, making use of two-phase compressions and expansions. Then, the methodology to analyze the performance of the compressor has been shown, considering an oil-refrigerant two-phase mixture in the calculations. Eventually, 106 points have been used to generate 3D maps, showing the evolution of the efficiencies for varying pressure ratios and inlet qualities. Those maps have been analyzed checking the influence of the speed and the OCR. The results have shown a decrease in efficiency for low vapor qualities, especially for high pressure ratios, where under-compression occurs. Generally, when increasing
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the speed, both volumetric and isentropic efficiencies are increased for low pressure ratio, while they are decreased for high pressure ratio. Some explanations have been found to interprete the results, however, a deeper analysis is necessary to confirm the presented tendencies. The validation of a model could help in confirming this analysis. Acknowledgements The project source of the results presented in this paper has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement N.◦ 851541.
References 1. S. Briola, R. Gabbrielli, A. Baccioli, A. Fino, A. Bischi, Thermo-economic analysis of a novel trigeneration cycle enabled by two-phase machines. Energy 227, 7 (2021) 2. M. Youbi-Idrissi, J. Bonjour, The effect of oil in refrigeration: Current research issues and critical review of thermodynamic aspects, 3 (2008) 3. R. Hanna, A. Zoughaib, Atomization of high viscosity liquids through hydraulic atomizers designed for water atomization. Exper. Thermal Fluid Sci. 85, 140–153 (2017) 4. S. Ramaraj, B. Yang, J.E. Braun, E.A. Groll, W.T. Horton, Experimental analysis of oil flooded r410a scroll compressor. Int. J. Refrigeration 46, 185–195 (2014) 5. J. Bock, Vapor-liquid equilibria of a low gwp refrigerant, r-1234ze(e), mixed with a POE lubricant (2015) 6. F. Dawo, J. Fleischmann, F. Kaufmann, C. Schifflechner, S. Eyerer, C. Wieland, H. Spliethoff, R1224yd(z), r1233zd(e) and r1336mzz(z) as replacements for r245fa: experimental performance, interaction with lubricants and environmental impact. Appl. Energy 288, 4 (2021) 7. S. Quoilin, J. Schrouff, Assessing steady-state, multivariate experimental data using gaussian processes: the GPExp open-source library. Energies 9, 423 (2016) 8. N. Leclercq, V. Lemort, Modeling and simulation of a two-phase scroll compressor, in International Compressor Engineering Conference (2022)
Experimental Comparison into the Effect of Oversized Heat Exchangers on Seasonal Performance Improvements of a Two-Stage and a Variable Speed Compressor in an R410A Chiller Sugun Tej Inampudi and Stefan Elbel
Abstract There is an increased focus on improving the seasonal performance (SEER, IPLV.SI) of HVAC&R systems. Many studies suggest enhancing the efficiency and capacity modulation capabilities of the compressor to achieve higher seasonal performance. The improved compressor can better match the required cooling demand, undergo fewer cycling losses, and have lower power consumption in general. A larger heat exchanger improves the COP by lowering the operating pressure ratio and power consumption. This current paper focuses on the effect of using an oversized Brazed Plate Heat Exchanger (BPHX) as condenser on the seasonal performance of a similarly sized two-stage and a variable speed compressor in an R410A water ethylene glycol (WEG) chiller. The seasonal performance of this 8 kWchiller is estimated using IPLV.SI according to AHRI 551/591. Experimental results indicate that a condenser having 70% more plates than the nominally sized condenser improves the COP by 18% for a two-stage compressor (with lower stages of capacity modulation) at the part load conditions while this is only 4% for the variable speed compressor. Additionally, the overall IPLV.SI improves by 18% for the two-stage compressor and by 12% for the variable speed compressor. These results show that the positive impact of condenser oversizing diminishes at part load conditions for variable speed compressors. Additionally, the effect of charge optimization is also explored. Keywords Two-stage · Variable speed · Seasonal performance · BPHX size S. T. Inampudi · S. Elbel Department of Mechanical Science and Engineering, Air Conditioning and Refrigeration Center, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, IL 61801, USA e-mail: [email protected] S. Elbel Creative Thermal Solutions, Inc., 2209 North Willow Road, Urbana, IL 61802, USA S. Elbel (B) FG Wärmeübertragung und -wandlung, Institut für Energietechnik, Technische Universität Berlin, Sekr. KT 2, Marchstr. 18, 10587 Berlin, Germany e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_20
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1 Introduction Due to the new energy regulations, there is an increasing focus on seasonal performance improvement in HVAC&R. There are many studies which suggest using compressor capacity modulation strategies while others suggest improving the compressor motor efficiencies [1–4]. A compressor with better capacity modulation will undergo fewer cycling losses, reduced power consumption by operating at lower pressure ratios at the part load conditions [3]. On the other hand, a better compressor motor with higher isentropic efficiency will reduce the power consumption at all the operating conditions [3]. An HVAC system can operate at lower pressure ratio by better matching the refrigerant temperature profile to the secondary fluid temperature profile. This lowers the LMTD and the operating pressure ratio. A heat exchanger can reduce the LMTD by increasing the overall heat transfer coefficient or the available heat transfer surface area. This current study explores the idea of improving the seasonal performance of a two-stage and a variable speed compressor by using an oversized condenser. The seasonal performance of this 8 kW-chiller with BPHX is estimated using IPLV.SI according to AHRI 551/591 [5]. Initially, optimum operating charge is estimated by a charge optimization study. In the later sections, the relative improvements in a twostage and a variable speed compressor with this oversized condenser. Additionally, the effect of charge optimization and BPHX oversizing on the seasonal performance is studied with a two-stage compressor. Finally, the improvements in IPLV.SI are estimated for all the different compressor modulation strategies.
2 Experimental Facility Description An R410A WEG chiller with a mixture of 20% water and ethylene glycol as the secondary fluid is used for this study. Two closed WEG loops are connected to the evaporator and condenser. Variable speed pumps and electric heaters are used to control the WEG flow rate and temperature. All the heat exchangers used in the facility are brazed plate heat exchangers. A 0.9 L receiver is connected between the condenser and the subcooler. Superheat is controlled by an Electronic Expansion Valve (EEV) while the subcooling is a function of the charge. The geometric dimensions of the evaporator, different condensers, and subcooler can be found in Table 1. The compressors used are scroll compressors with a nominal speed of 1800 min−1 . Additional details and the schematic of the experimental facility, instrumentation used can be found in [4]. The uncertainty of the sensors used in the experimental facility is presented in Table 2. Capacity is calculated on the refrigerant side and WEG side. For the WEG side, mass flow rate, temperature, and specific heat are used to calculate capacity as shown in Eq. (1). For the refrigerant side, temperature and pressure are used to calculate the enthalpy which is then used with the mass flow rate to calculate the capacity as
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Table 1 Dimensions of the BPHX Heat exchanger
Length (mm)
Width (mm)
Number of plates
Evaporator
311
111
28
Subcooler
207
77
14
Condenser (C-14)
311
111
14
Oversized condenser (C-24)
311
111
24
Table 2 Summary of measured and calculated property uncertainties Instrument
Thermocouple (°C)
Pressure transducer (kPa) (%)
Mass flow Wattmeter meter (g/ (kW) (%) s) (%)
Capacity (kW) (%)
COP (−) (%)
Uncertainty
± 0.2
± 0.2
± 0.2
± 3.0
± 3.2
± 0.5
shown in Eq. (2). The capacity reported is the average of the refrigerant side and WEG side capacity given by Eq. (3). The difference between the two capacities is indicated by the error given by Eq. (4). This error is always less than 3% for the part load rating tests. Power consumed by the compressor is measured using a wattmeter. The ratio of the average capacity and power consumed by the compressor is used to calculate the C O P test as shown in Eq. (5). Q˙ ev,W E G = m˙ W E G C p T
(1)
Q˙ ev,r e f = m˙ r e f h
(2)
( Q˙ ev,W E G + Q˙ ev,r e f ) Q˙ ev,avg = 2
(3)
ε Qev =
( Q˙ ev,avg − Q˙ ev,W E G ) · 100 Q˙ ev,avg
C O Ptest = Q˙ ev,avg /W˙ cp
(4) (5)
3 Standard Used for Testing AHRI 551/591 is used for the determination of the part-load performance of water chillers [5]. The standard defines a single number part-load efficiency figure of merit called Integrated Part Load Value (IPLV.SI) calculated at part load rating conditions. These part load rating conditions are shown below in Table 3. As seen in the table,
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Table 3 AHRI 551/591 part load conditions for IPLV.SI Condition
Part load ratio [%]
Condenser inlet/outlet [°C]
Evaporator inlet/outlet [°C]
A
100
30/35
12/7
B
75
24.5/*
**/7
C
50
19/*
**/7
D
25
19/*
**/7
* Same condenser WEG mass flow rate as A condition ** Same evaporator WEG mass flow rate as A condition
condenser inlet, outlet, and evaporator inlet, outlet are mentioned for A condition while for the B, C, and D conditions, only the condenser inlet and evaporator outlet temperature are mentioned. Standard required that the condenser and evaporator WEG flow rate used for the A condition be used for the B, C, and D conditions. IPLV.SI is the weighted average of the C O P R = C O P test /C D , (where C D is the cycling degradation factor) measured at these standard rating conditions as shown in Eq. (6). These factors in Eq. (6) are based on the weighted average of the most common building types and operations using average weather in 29 U.S cities. Additional details of how cycling losses and C D are estimated using this standard are available in [3, 4]. I P L V .S I = 0.01 · A + 0.42 · B + 0.45 · C + 0.12 · D
(6)
A = C O P R at 100% B = C O P R at 75% C = C O P R at 50% D = C O P R at 25%
4 Results and Discussion 4.1 Charge Optimization with Oversized Condenser The chiller used in this study has a condenser followed by a receiver and a dedicated subcooler. Charge optimization with normal sized condenser (C-14) in the same experimental facility was conducted and analyzed [6]. There was a peak COP before the receiver starts filling up. This peak occurs due to the relative sizing of the
Experimental Comparison into the Effect of Oversized Heat Exchangers …
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condenser and subcooler and the optimum charge corresponds to the scenario when some portion of the two-phase heat transfer is happening in the subcooler [6]. Charge optimization was conducted with an oversized condenser (C-24) and variable speed compressor operating at 50% capacity to see if a similar peak is observed. The results are shown in Fig. 1. Like the study with normal sized condenser, there is a peak in COP at 1.25 kg of refrigerant charge in region 2 [6]. The entire charge optimization curve is divided into four regions. In region 1, the system is undercharged, and any refrigerant added goes to the evaporator to reduce the excess superheat. At the end of region 1, there is sufficient charge for the EXV to operate properly and maintain the required superheat. In region 2, the added refrigerant distributes between the condenser and dedicated subcooler such that some portion of two-phase condensation happens in the dedicated subcooler. In region 2, the additional refrigerant charge increases the cooling capacity (due to additional subcooling and reduction in evaporator inlet enthalpy) and power consumption (higher condensation pressure and pressure ratio). However, the relative increase in cooling capacity is higher than the relative increase in power consumption. When refrigerant charge is added beyond region 2, the amount of two-phase condensation in dedicated subcooler reduces and the relative increase in power consumption is higher than the increase in cooling capacity. In region 4, the additional refrigerant added gets accumulated in the receiver and no significant change is observed in the system performance. When the added charge exceeds the receiver holding capacity, the system is overcharged. The excess refrigerant charge starts backing up in the condenser causing an increase in condensation pressure, power consumption and a drop in COP. The system is typically operated with 1.50 kg of refrigerant charge (in region 4) with some charge in the receiver. This will safeguard the system against any potential refrigerant leaks and minor changes in the refrigerant charge do not affect the system
Fig. 1 Variation of COP, cooling capacity and condensation pressure with charge
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performance. In Sects. 4.2, 4.3 and 4.4 the system operates in region 4 of the charge optimization curve. In Sect. 4.4, the effect of charge optimization and heat exchanger oversizing is studied in the case of a two-stage compressor.
4.2 Seasonal Performance of a Variable Speed Compressor with Different Condensers The system operating with a variable speed compressor is tested with two condensers, normally sized condenser with 14 plates (C-14) and oversized condenser with 70% more plates (C-24). The system is charged with 1.50 kg of refrigerant in both cases such that the system operates in Region 4 as shown in Fig. 1. The seasonal performance is estimated according to AHRI 551/591 [2]. The seasonal performance with C-14 and C-24 is shown in Figs. 2 and 3 respectively. Additionally, the change in L M T D co , pressure ratio and compressor power input with an increase in the number of condenser plates is shown in Table 4. The compressor in both the cases can match the required cooling load by changing the motor frequency. Hence, there are no cycling losses and both C O P test and C O P R are equal. Additionally, since the size of the evaporator does not change the compressor operates at the same frequency, the cooling capacity shown in Figs. 2 and 3 are the same. However, the C O P R is higher for the case with C-24. This higher C O P R can be explained by the lower pressure ratio and power consumption as shown in Table 4. The higher heat transfer area due to increase in the number of condenser plates reduces the temperature difference between the two fluids (R410A and secondary fluid). The lower temperature difference (indicated by L M T D co ) causes the refrigerant to operate with a lower condensation pressure (indicated by
Fig. 2 Seasonal performance of a variable speed with a normal sized condenser (C-14)
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Fig. 3 Seasonal performance of a variable speed with an oversized condenser (C-24)
Table 4 Variation of different parameters with condenser size when using a variable speed Parameter L M T D co [K]
A condition
B condition
C condition
D condition
C-14
C-24
C-14
C-24
C-14
C-24
C-14
C-24
14.8
7.7
12.0
5.0
8.5
3.5
5.0
2.0
π [−]
3.5
3.0
2.7
2.3
2.0
1.8
1.8
1.7
Wcp [kW]
2.44
2.18
1.20
1.03
0.55
0.49
0.26
0.25
π ). The compressor requires less power to operate at this lower pressure ratio leading to a higher C O P R . The IPLV.SI when the variable speed compressor is operating with C-14 and C-24 are 5.8 and 6.5 respectively. Interestingly, the effect of this oversized condenser drops as we reduce the part load ratio. At A and B conditions, the pressure ratio drops by 14 and 15%, while it only drops by 11 and 7% at C and D conditions. This causes the power consumption to decrease by a lower percentage at the C and D conditions compared to the A and B conditions. When a variable speed compressor reduces its operating frequency to match the required load, it reduces its refrigerant mass flow rate. At the C and D conditions, the refrigerant mass flow rate is too low to take advantage of this oversized condenser. The refrigerant temperature profile is as close as possible to the secondary fluid profile with a normal sized condenser (C-14) that any oversizing will not benefit this operating condition. However, at the higher part load conditions, the refrigerant mass flow rate is higher and there is still some potential improvement with the condenser oversizing.
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4.3 Seasonal Performance of a Two-Stage Compressor with Different Condensers A two-stage compressor has two bypass ports which enable it to operate at either 67% of the capacity (low stage) or 100% capacity (high stage) [4]. The seasonal performance of this two-stage compressor with C-14 and C-24 is shown in Figs. 4 and 5 respectively. In both these configurations, the compressor operates at high stage for A condition and low stage for the part load conditions. The capacity provided by the low stage at the B condition is equal to the required load and hence there are no cycling losses included. However, the compressor cannot operate below the low stage, hence cycling losses are included for both C and D conditions. Additionally, since the secondary fluid temperatures and mass flow rates are the same for B and C conditions, the cooling capacity provided and C O P test are comparable for these two conditions. The cooling capacity provided with these two configurations are comparable as shown in Figs. 4 and 5. The change in L M T D co , pressure ratio and compressor power input with an increase in the number of condenser plates is shown in Table 5. C O P test and C O P R are higher for the case with C-24 (Fig. 5). This can be explained by the lower pressure ratio and compressor power input. Due to the higher heat transfer area available, the L M T D co is lower by 30% at A condition and around 36% lower at the other part load conditions. This leads to a 10–12% lower pressure ratio and 7–14% lower compressor power input. Interestingly, unlike the variable speed compressor, the reduction is power consumption is higher at the C&D conditions compared to the higher load conditions. This can be attributed to the compressor modulation strategy. Unlike the variable speed compressor, the two-stage compressor cannot unload to 50 and 25% part load capacity. It still operates at its minimum possible low stage. This low stage provides a
Fig. 4 Seasonal performance of a two-stage with a normal sized condenser (C-14)
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Fig. 5 Seasonal performance of a two-stage with an oversized condenser (C-24)
Table 5 Variation of different parameters with condenser size when using a two-stage compressor Parameter
A condition
B condition
C & D condition
C-14
C-24
C-14
C-24
C-14
C-24
14.5
10.3
12.1
7.7
12.7
8.2
π [−]
3.6
3.2
2.8
2.5
2.5
2.2
Wcp [kW]
2.6
2.4
1.6
1.4
1.4
1.2
L M T D co [K]
mass flow rate which is 60% higher than required at 50% condition (C condition) and three times higher at 25% condition (D condition). There is still potential improvement possible through the condenser oversizing due to these higher refrigerant mass flow rates unlike the variable speed compressor.
4.4 Effect of Charge Optimization and Condenser Sizing on the Two-Stage Compressor Seasonal Performance The seasonal performance of a two-stage compressor when operating with a refrigerant charge of 1.25 kg and oversized condenser is shown in Fig. 6. This 1.25 kg of refrigerant charge corresponds to the peak COP seen in Fig. 1. Compared to performance without optimum charge, i.e., Fig. 6, the C O P test is 2% higher at B, C and D conditions while C O P R is 4% higher at C and D conditions. C O P R at B, C and D conditions contribute to 99% of the IPLV.SI.
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Fig. 6 Seasonal performance of a two-stage with an oversized condenser (C-24) and optimum refrigerant charge (1.25 kg)
4.5 Comparison of IPLV.SI for Different Compressor Modulation Strategies and Condenser Sizes The seasonal performance of different compressors tested using the AHRI 551/591 standard and the experimental facility described in Sect. 2 is shown in Table 6. Additional discussion on the performance of the tandem combinations, single speed compressor is provided in [3]. All these compressors have comparable cooling capacity at full load conditions; hence the seasonal performance of these compressors can be compared. The two-stage compressor with C-14 has a lower IPLV.SI than the single speed compressor with improved motor showing that a better motor might be more significant than being able to modulate the capacity. However, when the same two-stage compressor is used with oversized condenser, the IPLV.SI increases by 18% for the case without charge optimization and 20% when operated with optimum charge. This puts the two-stage compressor IPLV.SI above the single speed compressor with improved motor showing that oversizing BPHX might yield better results than improving the compressor motor efficiency. IPLV.SI for the variable speed compressor increases by 12% with C-24 compared to C-14. This lower improvement than two-stage compressor is because the two-stage compressor operates with higher refrigerant mass flow rates at part load conditions and oversized BPHX benefit this.
Experimental Comparison into the Effect of Oversized Heat Exchangers … Table 6 IPLV.SI for different compressors and condenser sizes
261
Compressor
IPLV.SI
Single speed (C-14)
3.6
Two-stage (C-14)
3.9
Single speed (improved motor) (C-14)
4.0
Two-stage (C-24)
4.6
Two-stage (charge optimized) (C-24)
4.7
Even tandem combination (C-14)
4.9
Uneven tandem combination (C-14)
4.9
Variable speed (C-14)
5.8
Variable speed (C-24)
6.5
5 Conclusions This current study focused on the effect of using an oversized BPHX on the seasonal performance of a similarly sized two-stage and a variable speed compressor in an R410A WEG chiller. The seasonal performance of this 8 kW-chiller is estimated using IPLV.SI according to AHRI 551/591. Experimental results indicate that a condenser having 70% more plates than the nominally sized condenser improves the COP by 18% for a two-stage compressor (with lower stages of capacity modulation) at the part load conditions while this is only 4% for the variable speed compressor. Additionally, the overall IPLV.SI improves by 18% for the two-stage compressor and by 12% for the variable speed com-pressor. These results show that the positive impact of condenser oversizing diminishes at part load conditions for variable speed compressors. Additionally, IPLV.SI of a two-stage compressor when operating with oversized BPHX and optimum charge increased by 20% showing that the impact of BPHX oversizing might be more than the compressor motor efficiency.
References 1. L. Cecchinato, Part load efficiency of packaged air-cooled water chillers with inverter driven scroll compressors. Energy Convers. Manage. 51(7), 1500–1509 (2010) 2. E. Kinab, D. Marchio, P. Rivière, A. Zoughaib, Reversible heat pump model for seasonal performance optimization. Energy Build. 42(12), 2269–2280 (2010) 3. S.T. Inampudi, F. Botticella, S. Elbel, Comparative experimental analysis of different compressor capacity modulation strategies in R410A chiller with focus on seasonal performance, in 19th International Refrigeration and Air Conditioning Conference, Purdue, West Lafayette, IN, USA, July 11–14, Paper 1198 (2022) 4. S.T. Inampudi, F. Botticella, S. Elbel, Experimental comparison of seasonal performance in R410A chiller using single speed and two stage compressor, in 18th International Refrigeration and Air Conditioning Conference, Purdue, West Lafayette, IN, USA, May 23–28, Paper 1484 (2021)
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5. AHRI, AHRI Standard 551/591 (SI): 2020 Standard for Performance Rating of Water-Chilling and Heat Pump Water-Heating Packages Using the Vapor Compression Cycle (Air-Conditioning, Heating, Refrigeration Institute, Arlington, VA, USA, 2020) 6. S.T. Inampudi, S. Elbel, Study of charge optimization and compressor modulation strategies effect on the seasonal performance in a R410A chiller, in 19th International Refrigeration and Air Conditioning Conference, Purdue, West Lafayette, IN, USA, July 11–14, Paper 1199 (2022)
Experimental Investigation and Advanced Exergy Analysis of Different Factors That Can Affect Seasonal Performance in an R410A Chiller Sugun Tej Inampudi and Stefan Elbel
Abstract Due to the new energy regulations, there is an increased demand for higher efficiency HVAC&R equipment. Improvements in compressors and heat exchangers (BPHX) can lead to a higher system COP. Compressors are compared using efficiency and BPHX are evaluated based on their LMTDs and pressure drops. It is difficult to compare the contribution of these two on the system COP using traditional first law analysis. Advanced exergy analysis (AEA) can help with this estimation by using exergy destruction as a metric. In the current paper, AEA framework is used to analyze the different factors that can impact the system performance and seasonal performance. The study is done on an 8-kW R410A water ethylene glycol chiller (WEG) and the results from seasonal performance of three different scroll compressors are used for this analysis. Three factors included are compressor motor efficiency, condenser size and compressor capacity modulation strategy. AEA shows that optimizing the compressor followed by condenser has the highest potential of improving system performance. E˙ DE X,total drops by 18% with upgraded compressor while it drops by 28% with oversized condenser showing that that the condenser has higher impact on the exergy destruction. AEA comparison of a two-stage compressor and a variable speed compressor show that E˙ DE N of the two-stage compressor is 39% higher indicating that variable speed compressor is more efficient at matching the cooling load. Based on the relative magnitude of E˙ DAV ,E N , compressor upgrade and condenser upgrade would yield higher system performance in two-stage and variable speed compressor systems respectively. S. T. Inampudi · S. Elbel Department of Mechanical Science and Engineering, Air Conditioning and Refrigeration Center, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, IL 61801, USA e-mail: [email protected] S. Elbel Creative Thermal Solutions, Inc., 2209 North Willow Road, Urbana, IL 61802, USA S. Elbel (B) FG Wärmeübertragung und -wandlung, Institut für Energietechnik, Technische Universität Berlin, Sekr. KT 2, Marchstr. 18, Berlin 10587, Germany e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_21
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S. T. Inampudi and S. Elbel
Keywords Exergy · Compressor · Variable speed · Seasonal performance · BPHX
1 Introduction There is an increased demand for higher efficiency HVAC&R components to meet the new energy regulations. The performance of a system can be increased by improving the compressor and the heat exchangers. The compressors are compared using isentropic efficiency while the heat exchangers are assessed based on the temperature difference between the two working fluids and pressure drops. It is difficult to compare the contribution of a compressor and heat exchanger on the system COP using traditional first law and energy balance. An exergy analysis which calculates the exergy destruction within the compressor and heat exchangers can help with this comparison. In Conventional Exergy Analysis (CEA), the exergy is split among the different components, however, the exergy destruction in the components may neither be caused by their imperfections and nor be reduced by the optimization of that component. Splitting the exergy destruction into parts (avoidable and unavoidable, or endogenous and exogenous) can improve the quality of the conclusions from an exergy analysis and this type of analysis is called Advanced Exergy Analysis (AEA). eal Splitting the actual exergy destruction of the kth component ( E˙ rD,k ) into endogeE N r eal E N E X nous ( E˙ D,k ) and exogenous ( E˙ D,k = E˙ D,k − E˙ D,k ) makes it possible to separately estimate the exergy destruction in a component caused by the component itself and EN part of the exergy destruction is associated with by the remaining components. E˙ D,k only the irreversibilities occurring in the kth component when all the other components operate in an ideal way and the component being considered operates with its EX includes the exergy destruction caused by the irreversibilities current efficiency. E˙ D,k EN is used as an indicator of the theoretical that occur in the remaining components. E˙ D,k EN and maximum potential of the system by optimizing the concerned component. E˙ D,k EX are calculated using the hybrid cycles [1, 2] and is further discussed in Sect. 4. E˙ D,k eal Splitting the actual exergy destruction of the kth component ( E˙ rD,k ) into unavoidU N AV r eal U N able ( E˙ D,k ) and avoidable ( E˙ D,k = E˙ D,k − E˙ D,k ) provides a realistic measure of the potential for improving the thermodynamic efficiency of a component [1, 2]. The exergy destruction rate that cannot be reduced due to technological limitations such as availability and cost of materials and manufacturing methods is the E˙ UD,kN [3]. AV is the remaining part of the exergy destruction. E˙ UD,kN will always be there if this E˙ D,k component is being used in the system [3]. The two approaches of splitting the exergy destruction can be combined to calculate the part of the total exergy destruction that depends on the inefficiencies within the kth component and that cannot be reduced because of technical limitations for the kth E N ,U N ) part of the exergy destruction. component, i.e., endogenous unavoidable ( E˙ D,k E N , AV Endogenous avoidable ( E˙ D,k ) part of the exergy can be reduced through changes
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E X, AV in the component being considered whereas the exogenous avoidable ( E˙ D,k ) part of the exergy destruction describes the part that can be reduced by improving the efficiency of the remaining components or by improving the structure of the overall E N ,AV of the kth component, in general will lead to a system [1, 2]. Decreasing E˙ D,k E X, AV E N , AV ˙ decrease of E D of the other components. E˙ D,k indicates the real maximum improvement potential at the current technical level [3]. In the current paper, AEA framework is used to analyze the different factors that can impact the system performance and seasonal performance. The results from seasonal performance of three different compressors single speed, two-stage and variable speed compressor are used for this analysis. The study is done on an 8-kW R410A water ethylene glycol chiller (WEG) and seasonal performance (IPLV.SI) is measured using AHRI 551/591. The three factors included in this analysis that impact the system performance are compressor motor efficiency, heat exchanger size and compressor capacity modulation strategy. The improvement in system COP due to improved compressor motor and increased condenser size are analyzed using the single speed and the two-stage compressor in Sects. 5.1 and 5.2. While the effect of different ways to modulate capacity is studied using the two-stage and variable speed compressor in Sect. 5.3.
2 Experimental Facility Description An 8-kW R410A WEG chiller with a mixture of 20% water and ethylene glycol as the secondary fluid is used for this study. Two closed WEG loops are connected to the evaporator and condenser. Variable speed pumps and electric heaters are used to control the WEG flow rate and temperature. All the heat exchangers used in the facility are brazed plate heat exchangers (BPHX). A 0.9 L receiver is connected between the condenser and the subcooler. Superheat is controlled by an electronic expansion valve (EXV). The system is charged with enough refrigerant to fill the receiver halfway and thus subcooling is a function of the charge. The geometric dimensions of the evaporator, different condensers, and subcooler can be found in Table 1. Compressors used are scroll compressors with a nominal speed of 1800 min−1 . Additional details and the schematic of the experimental facility, instrumentation used can be found in [4]. Uncertainty of the sensors used in the experimental facility is presented in Table 2. Table 1 Dimensions of the BPHX Heat exchanger
Length (mm)
Width (mm)
Number of plates
Evaporator
311
111
28
Subcooler
207
77
14
Condenser (C-14)
311
111
14
Oversized condenser (C-24)
311
111
24
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Table 2 Summary of measured and calculated property uncertainties Instrument
Thermocouple (°C)
Pressure transducer (kPa) (%)
Mass flow Wattmeter meter (g/ (kW) (%) s) (%)
Capacity (kW) (%)
COP (–) (%)
Uncertainty
± 0.2
± 0.2
± 0.2
± 3.0
± 3.2
± 0.5
Capacity is calculated on the refrigerant side and WEG side. For the WEG side, mass flow rate, temperature, and specific heat are used to calculate capacity as shown in Eq. (1). For the refrigerant side, temperature and pressure are used to calculate the enthalpy which is then used with the mass flow rate to calculate the capacity as shown in Eq. (2). The capacity reported is the average of the refrigerant side and WEG side capacity given by Eq. (3). The difference between the two capacities is indicated by the error given by Eq. (4). This error is always less than 3% for the part load rating tests. Power consumed by the compressor is measured using a wattmeter. The ratio of the average capacity and power consumed by the compressor is used to calculate the C O P test as shown in Eq. (5). Q˙ ev,W E G = m˙ W E G C p T
(1)
Q˙ ev,r e f = m˙ r e f h
(2)
( Q˙ ev,W E G + Q˙ ev,r e f ) Q˙ ev,avg = 2
(3)
ε Qev =
( Q˙ ev,avg − Q˙ ev,W E G ) · 100 Q˙ ev,avg
C O P test = Q˙ ev,avg /W˙ cp
(4) (5)
3 Standard Used for Testing AHRI 551/591 is used for the determination of the part-load performance of water chillers [5]. The standard defines a single number part-load efficiency figure of merit called Integrated Part Load Value (IPLV.SI) calculated at part load rating conditions. These part load rating conditions are shown below in Table 3. As seen in the table, condenser inlet, outlet, and evaporator inlet, outlet are mentioned for A condition while for the B, C, and D conditions, only the condenser inlet and evaporator outlet temperature are mentioned. The standard required that the condenser and evaporator WEG flow rate used for the A condition be used for the B, C, and D conditions. IPLV.SI is the weighted average of the C O P R measured at these standard rating
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Table 3 AHRI 551/591 part load conditions for IPLV.SI Condition
Part load ratio (%)
Condenser inlet/outlet (°C)
Evaporator inlet/outlet (°C)
A
100
30/35
12/7
B
75
24.5/*
**/7
C
50
19/*
**/7
D
25
19/*
**/7
*Same condenser WEG mass flow rate as A condition **Same evaporator WEG mass flow rate as A condition
conditions as shown in Eq. (6). These factors in Eq. (6) are based on the weighted average of the most common building types and operations using average weather in 29 U.S cities. Additional details of how cycling losses are estimated using this standard are available in [4, 6]. I P L V .S I = 0.01 · A + 0.42 · B + 0.45 · C + 0.12 · D
(6)
A = C O P R at 100% B = C O P R at 75% C = C O P R at 50% D = C O P R at 25%
4 Advanced Exergy Analysis (AEA) The exergy destruction of each component is split into endogenous/exogenous and unavoidable/avoidable exergy destruction using the three different cycles shown in Fig. 1. The theoretical cycle includes the assumption that the exergy destruc˙ th tion within the component, E˙ th D is minimum or zero. The E D of the EXV and the compressor are set to be zero by considering an isentropic expansion and compression. E˙ th D of the condenser (and evaporator) are set to the minimum possible by considering the minimum temperature difference between the secondary fluid and refrigerant T CthO (and T th E V ) to be zero [1–3]. To split the exergy destruction into unavoidable and avoidable parts, separate cycle with only unavoidable exergy destructions occurring in each component should be considered. The unavoidable exergy cycle is built using the theoretical cycle but also includes the irreversibilities caused by unavoidable temperature difference in the
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Fig. 1 Cycles used to calculate the different parts of exergy destruction in a component
heat exchangers (T UC ON , T UE VN ), compressor efficiency (ηCU PN ) and throttling in the EXV. For the current analysis, the following parameter values for the unavoidable efficiencies were assumed: T UC ON = 0.5K , T UE VN = 0.5K and ηCU PN = 95%. These values represent the technological limitations [1–3]. To calculate the endogenous part of the exergy destruction within each component, the following hybrid cycles should be analyzed. In each of these hybrid cycles, there is only one irreversible component. These cycles are shown in Fig. 2. • • • •
Compressor (Fig. 2a): 1T − 2 H − 3T − 4T (ηCr eal P from experiment) Condenser (Fig. 2b): 1T − 2 H ∗ − 3 R − 4 H (T rCeal O from experiment) Evaporator (Fig. 2c): 1T − 2 H ∗∗ − 3T − 4 H ∗∗ (T rEeal V from experiment) EXV (Fig. 2d): 1T − 2T − 3T − 4 H ∗ (Isenthalpic process from experiment)
To calculate the unavoidable endogenous part of the exergy destruction within each component, the approach for calculating the endogenous part of the exergy destruction is used with the efficiency of each component being equal to the efficiency used to calculate its unavoidable exergy destruction [1–3].
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Fig. 2 Cycle used to calculate the endogenous exergy destruction within a compressor, b condenser, c evaporator and d EXV
5 Results and Discussion 5.1 Effect of Improved Compressor Motor (Higher Isentropic Efficiency) A single speed compressor does not have any capacity modulation. It can operate at its maximum possible speed at all the conditions and whenever the load is less than the provided capacity, it undergoes cycling losses. A single speed compressor with a baseline compressor motor and a similar capacity single speed compressor with an improved motor were tested according to AHRI 551/591. Improved compressor motor has higher isentropic efficiency at all the tested conditions [4, 6]. Entropy destruction of different components at full load conditions when operating with these two different compressors are shown in Tables 4 and 5. Since, the load matches the capacity, the single speed compressor does not encounter any cycling losses at this A condition. Comparing the E˙ DAV,E N , compressor (0.37 kW) followed closely by condenser (0.30 kW) have the highest potential to improve the performance of the system. Though a similar trend is observed by comparing the E˙ rDeal , the relative magnitudes of the E˙ rDeal might lead to a conclusion that upgrading the compressor (0.82 kW) will
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Table 4 Exergy destruction when using a single speed compressor at A condition (C O P test = 3.0; I P L V .S I = 3.6) Component
Exergy destruction (kW) E˙ rDeal
EN E˙ D
EX E˙ D
N E˙ U D
E˙ DAV
E˙ DAV,E N
Compressor
0.82
0.51
0.31
0.14
0.68
0.37
Condenser
0.43
0.36
0.09
0.06
0.39
0.30
Evaporator
0.23
0.23
0.00
0.08
0.15
0.15
EXV
0.21
0.11
0.10
0.11
0.09
0.00
Total
1.69
0.51
Table 5 Exergy destruction when using a single speed compressor with an improved motor at A condition (C O P test = 3.3; I P L V .S I = 4.0) Component
Exergy destruction (kW) E˙ rDeal
EN E˙ D
EX E˙ D
N E˙ U D
E˙ DAV
E˙ DAV,E N
Compressor
0.65
0.40
0.25
0.14
0.50
0.26
Condenser
0.41
0.36
0.05
0.06
0.35
0.30
Evaporator
0.24
0.23
0.01
0.08
0.16
0.15
EXV
0.21
0.11
0.11
0.11
0.10
0.00
Total
1.51
0.42
yield the maximum improvement and the E˙ rDeal of the compressor is almost twice the E˙ rDeal of condenser. This shows the potential insights that can be gained through AEA which are not evident through the traditional exergy analysis. Note that the E˙ DE N , E˙ DAV,E N remain constant between Tables 4 and 5 for the condenser, evaporator and EXV. The E˙ UD N is constant for the components. The E˙ rDeal of the compressor drops by 21% while E˙ rDeal of the other components remain the same when the compressor motor is improved. This causes the total r eal,total ) drops by 11%. The E˙ DAV,E N of the compressor drops exergy destruction ( E˙ D by 30%. Due to the improved compressor motor, the total E˙ DE X which accounts for the interdependence between the components drops by 18%. Interestingly, only the E˙ DE X of the compressor reduced significantly from 0.31 to 0.25 kW. The compressor improvement did not cause the exergy destruction to drop in the other components showing that the interdependence of compressor on the other components is not significant.
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5.2 Effect of Upgrading the Condenser (Oversized Condenser) A two-stage compressor can operate at either 100% capacity or 67% capacity depending on the opening or closing of the internal bypass ports [4, 6]. The two-stage compressor has similar compressor motor as the single speed compressor shown in Table 4 and the cooling capacity provided at the full load conditions are also comparable. Experiments were conducted with this two-stage compressor operating at high stage at A condition with a 14-plate condenser and another 24-plate condenser with similar plate geometry. The exergy destruction for these two cases is shown in Tables 6 and 7. By analyzing the results from Sect. 5.1 and 5.2, it is possible to compare the effect of upgrading a compressor motor and increasing the size of condenser. From Tables 6 and 7, it is seen that the E˙ rDeal,total drops by 13% when the size of the condenser increases by 70%. This 13% drop in E˙ rDeal,total with condenser upgrade is like the 11% drop with upgraded compressor motor. E˙ rDeal of the condenser drops by 31% which is significantly higher than the 21% drop in E˙ rDeal of the upgraded compressor. E˙ DAV ,E N of the condenser drops by 27% which is comparable to the E˙ DAV,E N drop of the compressor. Interestingly, upgrading the condenser drops the E˙ DE X,total from 0.53 to 0.38 kW (28% drop) while this drop was only Table 6 Exergy destruction when using a two-stage compressor at A condition (C O P test = 3.0; I P L V .S I = 3.9) Component
Exergy destruction (kW) E˙ rDeal
EN E˙ D
EX E˙ D
N E˙ U D
E˙ DAV
E˙ DAV,E N
Compressor
0.84
0.51
0.33
0.15
0.69
0.37
Condenser
0.45
0.39
0.09
0.06
0.41
0.33
Evaporator
0.25
0.25
0.00
0.09
0.16
0.16
EXV
0.22
0.11
0.11
0.12
0.10
0.00
Total
1.76
0.53
Table 7 Exergy destruction when using a two-stage compressor with an oversized condenser at A condition (C O P test = 3.3; I P L V .S I = 4.6) Component
Exergy destruction (kW) E˙ rDeal
EN E˙ D
EX E˙ D
N E˙ U D
E˙ DAV
E˙ DAV,E N
Compressor
0.79
0.51
0.28
0.15
0.64
0.37
Condenser
0.31
0.30
0.01
0.06
0.25
0.24
Evaporator
0.24
0.24
0.00
0.09
0.16
0.16
EXV
0.20
0.11
0.09
0.12
0.08
0.00
Total
1.54
0.38
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18% with the upgraded compressor. This difference in the drop of E˙ DE X,total shows that the condenser has higher impact on the exergy destruction than upgrading the compressor. This impact of oversized condenser can be different at part load conditions with a compressor which can match the required cooling load by reducing the refrigerant mass flow rate.
5.3 Comparison of Two Compressor Modulation Strategies A variable speed compressor can match the required cooling load by reducing their refrigerant mass flow rates at the 75% part load condition (B condition). The variable speed compressor reduces its operating speed from 72.5 to 45.5 Hz while the twostage compressor operates at low stage (the bypass ports are opened) to reduce the refrigerant mass flow rate. Both the compressors do not undergo the cycling losses and since the refrigerant mass flow rate across the heat exchangers are same, the only contributing factor to the difference in the system performance must be the compressor [6]. The exergy destruction with a two-stage compressor and a variable speed compressor when operating at B condition is shown in Tables 8 and 9 respectively. The E˙ rDeal of the two-stage compressor is 40% higher than that of the variable speed compressor. Interestingly, E˙ DE N of the two-stage compressor and variable speed compressor is 60% of the E˙ rDeal indicating that improving the compressor efficiency is the best way to reduce the compressor exergy destruction. E˙ DE N of the two-stage compressor is 39% higher and the E˙ DAV,E N is twice that of the variable speed compressor. This shows that variable speed compressor has lower overall and endogenous exergy destruction and thus is more efficient at matching the required cooling load than the two-stage compressor. Additionally, the higher E˙ DAV,E N of the two-stage compressor indicates that in a system with this compressor, improving the efficiency of this compressor will yield higher performance. On the other hand, the higher E˙ DAV,E N for the condenser in the case of variable speed compressor shows that priority should be given to condenser upgrade. The AEA shows that different components should be prioritized for upgrading depending on the compressor and capacity modulation strategy used.
6 Conclusions In the current paper, AEA framework is used to analyze the different factors that can impact the system performance and seasonal performance. Comparing the avoidable endogenous exergy destruction ( E˙ DAV,E N ) of the single speed compressor, optimizing the compressor followed closely by condenser has the highest potential of improving system performance. With an upgraded compressor motor E˙ rDeal of
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Table 8. Exergy destruction when using a two-stage compressor at B condition (C O P test = 3.6; I P L V .S I = 4.0) Component
Exergy destruction (kW) E˙ rDeal
EN E˙ D
EX E˙ D
N E˙ U D
E˙ DAV
E˙ DAV,E N
Compressor
0.60
0.36
0.24
0.08
0.52
0.28
Condenser
0.29
0.23
0.06
0.04
0.25
0.19
Evaporator
0.15
0.12
0.03
0.05
0.10
0.08
EXV
0.09
0.05
0.05
0.05
0.04
0.00
Total
1.13
0.37
Table 9 Exergy destruction when using a variable speed compressor at B condition (C O P test = 4.5; I P L V .S I = 5.8) Component
Exergy destruction (kW) E˙ rDeal
EN E˙ D
EX E˙ D
N E˙ U D
E˙ DAV
E˙ DAV,E N
Compressor
0.36
0.22
0.15
0.08
0.28
0.14
Condenser
0.23
0.23
0.01
0.04
0.20
0.19
Evaporator
0.12
0.12
0.00
0.05
0.08
0.08
EXV
0.09
0.05
0.04
0.05
0.04
0.00
Total
0.81
0.20
the single speed compressor reduced by 21% while the E˙ rDeal,total drops by 11%. When the condenser is oversized by 70%, E˙ rDeal,total with a similar sized two-stage compressor drops by 13%. E˙ rDeal of the condenser drops by 31% which is significantly higher than the 21% drop in E˙ rDeal of the upgraded compressor. Interestingly, only the E˙ DE X (which accounts for the interdependence between the components) of the compressor reduced significantly while it remained constant for other components with the compressor upgrade causing the E˙ DE X,total to drop by only 18%. On the other hand, upgrading the condenser dropped the E˙ DE X,total by 28%. This difference in the drop of E˙ DE X,total shows that the upgrading/oversizing condenser has higher impact on the exergy destruction than upgrading the compressor and that interdependence of compressor on the other components is not as significant. The exergy destruction with a two-stage compressor and a variable speed compressor are compared at 75% load condition. E˙ DE N of the two-stage compressor is 39% higher and the E˙ DAV,E N is twice that of the variable speed compressor. This shows that variable speed compressor is more efficient at matching the required cooling load than the two-stage compressor. Based on the relative magnitude of E˙ DAV,E N compressor upgrade and condenser upgrade would yield higher system performance in two-stage and variable speed compressor system respectively.
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References 1. T. Morosuk, G. Tsatsaronis, Advanced exergetic evaluation of refrigeration machines using different working fluids. Energy 34(12), 2248–2258 (2009) 2. S. Kelly, G. Tsatsaronis, T. Morosuk, Advanced exergetic analysis: approaches for splitting the exergy destruction into endogenous and exogenous parts. Energy 34(3), 384–391 (2009) 3. T. Morosuk, G. Tsatsaronis, in ASME International Mechanical Engineering Congress and Exposition, vol. 54907. Advanced Exergoeconomic Analysis of a Refrigeration Machine: Part 1—Methodology and First Evaluation (2011), pp. 47–56 4. S. Inampudi, F. Botticella, S. Elbel, in IOP Conference Series: Materials Science and Engineering, vol. 1180, no. 1. Part Load Performance of Single and Two Stage Compressors—A Comparative Experimental Study in a R410A Chiller Unit (IOP Publishing, 2021), p. 012050 5. AHRI, AHRI Standard 551/591 (SI): 2020 Standard for Performance Rating of Water-Chilling and Heat Pump Water-Heating Packages Using the Vapor Compression Cycle (Air-Conditioning, Heating, Refrigeration Institute, Arlington, VA, USA, 2020). 6. S.T. Inampudi, F. Botticella, S. Elbel, in 19th International Refrigeration and Air Conditioning Conference at Purdue. Comparative Experimental Analysis of Different Compressor Capacity Modulation Strategies in R410A Chiller with Focus on Seasonal Performance (West Lafayette, IN, 2022) (Paper 1198)
CFD Simulation Motion Analysis of an Orbiting Scroll Bearing Hub Scott Branch
Abstract There are major areas that need to be considered when creating a chamber model of a scroll compressor, including the motor and the compression process. Minor energy losses need to be modeled as well, such as bearing losses, line losses, heat losses, and windage losses. One of these windage losses is the orbiting scroll bearing hub that moves around inside the scroll compressor housing. Computational fluid dynamics (CFD) simulations were used to investigate the differences in power between different methods of motion. One of these motions is in a rotating frame of reference and the other is in an orbiting frame of reference. The orbiting frame of reference is the correct motion but modelling it in a rotating frame of reference is easier to set up and does not require an advanced user to create the orbiting motion. This study will provide power comparisons at one dynamic viscosity and at three different speeds. For this study it will be conducted in a single fluid of oil only. Keywords Scroll compressor · CFD · Mesh motion
1 Introduction There are many CFD tools available. For this study ANSYS CFX was used. The differences in power between using a rotating reference frame and an orbiting reference frame were investigated to make it easier for a casual user to simulate the analysis. An option available in CFX is to turn the domain into a rotating reference frame, making it much easier to setup and simulate a rotating frame of reference. Another advantage is the rotating reference frame can simulate the rotating motion much faster than the orbiting reference frame. For the orbiting reference frame, a mesh motion model and a set of velocity terms were applied to the orbiting scroll bearing hub. The issue with using the rotating reference frame is that it is not the S. Branch (B) Trane Technologies, La Crosse, WI 54601, USA e-mail: [email protected]
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_22
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motion of the orbiting scroll, but how much difference there is between the two methods. That is the focus of this paper. To make the simulations easier, they were run as an oil-only analysis.
2 Simulation Setup The setup for these simulations is similar to the analysis when modelling the scroll oil pump analysis Branch [1] in 2015. The rotating and orbiting motion simulations were analyzed to determine the power differences between the two movement processes. The torque and power of the orbiting scroll bearing hub was found using the same technique as Branch [2] in 2014.
2.1 Geometry Preparation Figure 1 explains the solid parts used to setup the negatives for the simulation. It also shows the fluid inlet. Figure 2 shows the negative used for these simulations. Figure 3 shows a meshed cross section of the simulation. The inside domains were meshed as a hexahedral meshes where the outside domain was meshed as a tetrahedral mesh. The total mesh size is 3.7 million nodes.
Fig. 1 Simulation geometry
CFD Simulation Motion Analysis of an Orbiting Scroll Bearing Hub
Fig. 2 CFD simulation setup
Fig. 3 Simulation cross section showing the mesh
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2.2 CFD Setup • ANSYS CFX Version V2022R1 was used for the CFD Analysis • Transient Simulation—one degree of movement per time step • Heat Transfer method used = Isothermal • Oil Temperature = 187.3 °F • Simulation Initial Static Pressure = 88.94 psia • Outlet Static Pressure = 87.94 psia • • • • •
Turbulence Model = SST All walls are adiabatic Compressor rotational speed = 900, 3600, 7200 rev/min Fluid = RL32H Oil Oil Viscosity = 14 cP
The simulation was set up in three domains. There is the outside stationary domain which connects the thrust surface, angled pipe, and the outlet together. The stationary domain has the angled pipe and the thrust surface exit. It also connects the moving domain to the outside stationary domain. The inside domain is the moving domain which contains the inlet and the orbiting scroll bearing hub. The moving reference frame was created so it could apply a rotating reference frame and an orbiting motion. To aid in the motion, the moving domain was created so it can rotate about the global z-axis. The moving reference frame is highlighted in green in Fig. 2. To create the orbiting motion, a mesh motion process was used. Then an orbiting velocity was applied on the orbiting scroll bearing hub. Rotating Reference Frame • Orbiting Scroll Bearing Hub • Motion is rotating. • Velocity profile is rotating. Orbiting Reference Frame • Orbiting Scroll Bearing Hub • Motion is rotating. • Velocity profile is orbiting. The orbiting velocities are shown below.
CFD Simulation Motion Analysis of an Orbiting Scroll Bearing Hub Table 1 Simulation oil flow rates
279
RPM
900
3600
7200
Oil Flow rate (kg/s)
0.004645
0.020845
0.04169
Vx = −V T heta × sin(oa + dT heta)
(1)
Vy = V T heta × cos(oa + dT heta)
(2)
oa orbiting angle = Starting angle of the orbiting scroll dTheta compressor rotational speed in rev/min × time VTheta crank shaft throw (offset) × compressor speed in rev/min The inlet to the simulations is an oil mass flow rate and is shown in Table 1. These were determined from a bearing flow model.
3 Results The results will show the differences in velocity profiles of the orbiting scroll bearing hub between the rotating and orbiting simulations. The process used to evaluate the windage power of the simulations will be explained. Finally, the windage power differences are shown in Table 2 between the rotating and orbiting reference frames at various speeds. Figure 4 shows the orbiting scroll bearing hub rotating motion which was taken from the 900 rev/min rotating simulation. Figure 5 shows the orbiting scroll bearing hub motion orbiting from the 900 rev/min orbiting simulation. Instantaneous power was calculated by measuring the torque of the orbiting scroll bearing hub multiplied by the speed at every time step. Results were averaged over a full revolution to determine the power. The torque was obtained by offsetting the axis shown on Fig. 6 by the crank shaft throw times the force in the y-direction. Figure 6 shows locations at zero degrees and one hundred and eighty degrees where the instantaneous torque/power values were obtained. Table 2 Orbiting scroll bearing hub power
Speed
Rotating
(rev/min)
Average Power (W)
900
1.0
Orbiting 1.8
3600
39.8
69.6
7200
293.6
474.4
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Fig. 4 Orbiting scroll bearing hub rotating motion
The orbiting power is the correct form of motion, and it was compared to the rotating motion to see how closely they compared. Table 2 shows the simulation power calculated for the orbiting scroll bearing hub at various speeds.
CFD Simulation Motion Analysis of an Orbiting Scroll Bearing Hub
Fig. 5 Orbiting scroll bearing hub orbiting motion
Fig. 6 Torque calculation process at 0° and 180°
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4 Conclusion Even though the rotating method is faster and easier to set up, the results were less accurate than the moving mesh orbiting movement. The next step will be to model this simulation as an oil/ refrigerant gas multiphase process using the moving mesh orbiting motion process. Acknowledgements The author acknowledges Eric Mlsna for providing the oil flow rate information. The author thanks Trane Technologies for allowing this information to be shared at this conference.
References 1. S. Branch, in International Conference on Compressors and their Systems 2015. Scroll Compressor Oil Pump Analysis (London, England, 2015) 2. S. Branch, in International Compressor Engineering Conference. Methods of Fluid Properties for Compressible Refrigerant CFD Analysis (West Layfette, Indiana, USA, 2014)
CFD Simulation of an Orbiting Scroll Bearing Hub Scott Branch
Abstract There are major areas that need to be considered to create a chamber model of a scroll compressor, including the motor and the compression process. Minor energy losses need to be modeled as well, such as bearing losses, line losses, heat losses, and windage losses. One of these windage losses is the orbiting scroll bearing hub that orbits inside the scroll compressor housing. Computational fluid dynamics (CFD) simulations with oil and refrigerant will be modeled as an isothermal multiphase analysis to determine the power of the orbiting scroll bearing hub. These CFD simulations will investigate different dynamic viscosities at multiple speeds. The results of these CFD simulations will also be used to see if the oil reaches the thrust surface of the scroll compressor. Keywords Scroll compressor · CFD · Multiphase
1 Introduction There are several sources of power consumption in a scroll compressor. A minor one is the windage losses from the orbiting scroll bearing hub. The results from this study will be added to GT Suite to enhance its power predictions. This paper will show the power created by the orbiting scroll bearing hub at various speeds and multiple dynamic viscosities. The simulation tool used is ANSYS CFX. The orbiting scroll bearing hub is used to hold the orbiting scroll bearing and orbits inside the compressor housing. The gap between the housing and the orbiting scroll is called the thrust surface and a small film of oil is used between the two to prevent damage. The orbiting action from the bearing hub helps drive oil into the thrust surface. The oil is fed through the crankshaft and moves through the orbiting and housing bearings and then reaches the inlet in this simulation. The flow through the crankshaft and bearings was not modeled for these simulations. S. Branch (B) Trane Technologies, La Crosse, WI 54601, USA e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_23
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2 Simulation Setup The setup for these simulations is similar to one done when modeling the scroll oil pump analysis Branch [1] in 2015 where both oil and refrigerant were modeled in the same simulation and the time it took to reach the top of the crankshaft was investigated. During these simulations the flow times were not a concern, but the power and oil distribution into the thrust surface was one focus of the analysis. The same technique as Branch [2] in 2014 was used to determine the torque and power of the orbiting scroll bearing hub.
2.1 Geometry Preparation Figure 1 shows the solid parts used in the setup to create the negatives for the simulation. It also shows the fluid inlet location. Figure 2 shows the negative setup used. Figure 3 shows a meshed cross section of the simulation. The inside domains were meshed as a hexahedral meshes where the outside domain was meshed as a tetrahedral mesh. The total mesh size is 3.7 million nodes.
Fig. 1 Simulation geometry
CFD Simulation of an Orbiting Scroll Bearing Hub
Fig. 2 CFD simulation setup
Fig. 3 Simulation cross section showing the mesh
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2.2 CFD Setup There are several approaches that could have been used to model the oil and refrigerant in ANSYS CFX. There is an option to treat one of the fluids as partial tracking. There is an option to treat one of the fluids as a dispersed fluid. There is an option to treat both fluids as continuous fluids. The best option for this analysis was to use a Euler-Euler approach with both the oil and refrigerant being treated as two continuous fluids. This is the same technique as used in Branch (1) in 2015. • ANSYS CFX Version V2022R1 was used for the CFD Analysis • Transient Simulation—one degree of movement per time step • Heat Transfer = Fluid dependent Isothermal – R452A = 52 °F – Oil = 187.3 °F • Simulation Initial Static Pressure = 88.94 psia – Outlet Static Pressure = 87.94 psia • • • • • • •
Turbulence Model = SST Buoyancy is turned on All walls are adiabatic Compressor rotational speed = 900, 3600, 7200 rev/min Fluid = RL32H Oil, and R452A refrigerant gas Oil Viscosity = 15, 14, 40 cP Multiphase analysis setup – Drag Coefficient = 0.44 – Interface Length Scale = 0.05 mm
The orbiting motion was created by moving the meshes by a mesh motion process. An orbiting velocity profile was applied to the orbiting scroll bearing hub. • Orbiting Reference Frame • Orbiting Scroll Bearing Hub – Motion is rotating – Velocity profile is orbiting The orbiting velocities are shown in the equations below. Vx = −V T heta × sin(oa + dT heta)
(1)
Vy = V T heta × cos(oa + dT heta)
(2)
orbiting angle = Starting angle of the orbiting scroll oa dTheta compressor rotational speed in rev/min × time VTheta crank shaft throw (offset) × compressor speed in rev/min
CFD Simulation of an Orbiting Scroll Bearing Hub Table 1 Simulation oil flow rates
287
RPM
900
3600
7200
Oil flow rate (kg/s)
0.004645
0.020845
0.04169
The inlet to the simulations is an oil mass flow rate and is shown in Table 1. These were determined from a bearing flow model.
3 Results The results will show the power that was created due to the orbiting scroll bearing hub. The simulation will show the flow reaching the thrust surface. The process used to evaluate the windage power of the simulations will be explained. Figure 4 shows the orbiting velocity profile of the orbiting scroll bearing hub. Instantaneous power was calculated by measuring the torque of the orbiting scroll bearing hub multiplied by the speed at every time step. Results were averaged over a full revolution to determine the power. The torque was obtained by offsetting the axis shown on Fig. 5 by the crank shaft throw times the force in the y-direction. Figure 5 shows the locations at zero degrees and one hundred and eighty degrees where the instantaneous torque/power values were obtained.
Fig. 4 Orbiting scroll bearing hub orbiting motion
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Fig. 5 Torque calculation process at 0° and 180°
Table 2 shows the simulation power calculated for the orbiting scroll bearing hub at various speeds. A curve fit program was used to fit the data in Table 2 to an equation. This is graphically represented in Fig. 6. The curve fit equation is then modelled in GT Suite to predict the power of the orbiting scroll bearing hub. Figure 7 shows that the oil is reaching the thrust surface in all cases. The red is the oil, and the blue is the refrigerant. The other colors are a mixture of the oil and refrigerant.
Table 2 Orbiting scroll bearing hub power
Speed
Dynamic viscosity
Multiphase oil and gas power
(rev/min)
(cP)
(W)
900
5
0.37
900
14
0.60
900
40
1.14
3600
5
17.26
3600
14
24.28
3600
40
38.10
7200
5
104.11
7200
14
138.87
7200
40
211.44
CFD Simulation of an Orbiting Scroll Bearing Hub
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Fig. 6 Curve fit plot of speed and viscosity to get the power
Fig. 7 The red is the oil and shows it leaving the thrust surface
4 Conclusion These simulations predicted the orbiting scroll bearing hub power in oil/refrigerant multiphase simulations. It also showed that the flow reached the thrust surface in all cases. For future simulations, increasing the resistance at the thrust surface will provide more accurate flow rates through the thrust surface.
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Acknowledgements The author acknowledges Eric Mlsna for providing the oil flow rate information. The author thanks Trane Technologies for allowing this information to be shared at this conference.
References 1. S. Branch, in International Conference on Compressors and their Systems 2015. Scroll Compressor Oil Pump Analysis (London, England, 2015) 2. S. Branch, in International Compressor Engineering Conference. Methods of Fluid Properties for Compressible Refrigerant CFD Analysis (West Layfette, Indiana, USA, 2014)
Hybrid Wrap-Based Shape Optimization of a Scroll Compressor with Deep Reinforcement Learning Janggon Yoo and Daegyoum Kim
Abstract Designing the profile of a scroll compressor to maximize its capacity within a given maximum diameter of a scroll compressor is crucial for the performance enhancement of the refrigeration cycle. To maximize the volume of suction chambers, a hybrid wrap that consists of nodes connected with multiple curves is applied for the scroll profile. However, the shape of the hybrid wrap is hard to optimize because of the many degrees of freedom. Therefore, this research aims to automate and optimize the shape of the scroll compressor with proper wall thickness, using deep reinforcement learning which is a proper optimization method with unknown constraints and nonlinear objective functions. During the optimization process, the nodes are displaced by the agent of the learning process and connected with smooth curves automatically to reconstruct the scroll profile. As the environment, an analytical pressure model based on mass and energy balance equations is established to derive leakage and structural stress on the scroll compressor. The proximal policy optimization method is adopted to maximize capacity and avoid structural damage, by adopting a penalty on a reward function. The reward evolution of the training and the transition of scroll shape are presented to show optimization results. The optimization method proposed in this study is expected to greatly reduce the difficulty and cost of designing the hybrid wrap-based scroll compressor. Keywords Deep reinforcement learning · Scroll compressor · Hybrid wrap · Design optimization
1 Introduction Designing the scroll profile of a scroll compressor to make proper the coefficient of performance, displacement, and compression ratio (the ratio between discharge and suction pressure) is one of the key processes for developing the compressor. An involute profile, which requires several parameters, is widely used to study and J. Yoo · D. Kim (B) Department of Mechanical Engineering, KAIST, Daejeon 34141, Republic of Korea e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_24
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develop the compressor. Efficiency and performance of the involute-based scroll compressor have been researched with respect to the parameters of the involute, such as base circle radius, scroll height, orbiting radius, and scroll turns [1–5]. Also, the design of the central part of the compressor has been developed to reduce the clearance volume and structural stress [6, 7]. However, the involute-based scroll compressor requires a large roll angle for a high compression ratio and displacement. A large roll angle induces large leakage and small displacement for a given circular design domain [8]. To overcome the limitation of the involute profile, a variable wall thickness scroll compressor, composed of multiple curves or an involute with the radius of curvature proportional to the k-square of the angle, is used for industrial purposes. Bush et al. [9], Tanaka et al. [10], Liu et al. [11], Shaffer and Groll [12], and Bin et al. [8] presented asymmetric hybrid wraps and showed that the capacity of the scroll compressor is increased, while the rotational torque applied on the scroll is similar to the involute-based scroll. Bin et al. [8] introduced the hybrid wrap with circular arcs, involutes, and higher-order curves, and a thermodynamic model based on mass and energy balance equation is presented. To have maximum displacement and to adjust target pressure from a given circular domain, shape optimization of the hybrid wrap is required. At the same time, the shape of the scroll profile should satisfy conditions that the profile is designed within the circular domain and the stress applied on the scroll profile is smaller than the allowable value. However, optimizing the hybrid wrap-based scroll compressor is time-consuming because of many degree-of-freedom and non-linear objective functions with required conditions. To overcome the limitations mentioned above in the shape optimization of the hybrid wrap, we introduce a new optimization method based on deep reinforcement learning (DRL), which can deal with non-linear problems properly. The general objective of DRL is to construct proper actions from a given environment for maximum rewards using an interaction loop with the agent. DRL uses neural networks for the agent to choose actions and predict rewards. Deep learning allows the DRL to provide reasonable solutions for complicated shape optimization for non-linear and multiple degrees-of-freedom (DOF) systems [13–15]. This paper presents a method to design a hybrid wrap profile to maximize the displacement and adjust the target compression ratio using DRL. The methodology chapter will treat the node-based scroll profile generation, the analytic model for the compression process, and the optimization method. The example of the analytic model and the optimization results with reward evolution will be suggested in the results section, followed by the conclusions section summarizing the study’s key findings.
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Fig. 1 a Midline of the scroll compressor profile with node and b An involute connecting two nodes
2 Methodology 2.1 Geometry of the Scroll Compressor The hybrid wrap is composed of multiple involute curves and connecting nodes with directions (Fig. 1a). An involute curve requires six degree-of-freedom to be specified, and two nodes with position and direction information satisfy the condition [(.xi , yi , ψi ) and (.xi+1 , yi+1 , ψi+1 ) in Fig. 1a]. Then, the coordinates of the involute .(x, y) are as follows: x = xi + a(sin ψ − sin ψi ) + b(ψ sin ψ − ψi sin ψi + cos ψ − cos ψi ) (1a) . y = yi + a(− cos ψ + cos ψi ) + b(−ψ cos ψ + ψi cos ψi + sin ψ − sin ψi ), (1b) .
where .ψ is the tangential angle of involute, subscripts 1 and 2 mean the two nodes. a and .b are the coefficients that consist of the radius of curvature (.r = a + bψ), and the coefficients can be derived using node 2.
.
.
D = 2 + (ψi+1 − ψi ) cos(ψi+1 + ψi ) − 2 cos(ψi+1 − ψi ) 1 [(−ψi+1 cos ψi+1 + ψi cos ψi + sin ψi+1 − sin ψi )(xi+1 − xi ) .a = D . − (ψi+1 sin ψi+1 − ψi sin ψi + cos ψi+1 − cos ψi )(yi+1 − yi )] 1 [(cos ψi+1 − cos ψi )(xi+1 − xi ) + (sin ψi+1 − sin ψi )(yi+1 − yi )]. .b = D
(2a) (2b) (2c) (2d)
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Fig. 2 Schematics for movement of the orbiting scroll when orbiting angle ◦ ◦ ◦ .φ = 0 , .φ = 90 , .φ = 180 , and .φ = 270◦
Then, the scroll profile is generated automatically with the coordinates of nodes (xi , yi , ψi ), where .i is the index of the node. The nodes are sampled along an involute profile whose maximum tangential angle .ψn is .600◦ and maximum distance from the origin point is 53 mm. The tangential angles are selected at every .120◦ . A copy of the scroll profile, which is 180-degree rotated, is connected to the original scroll line at the origin point. The fixed scroll and orbiting scroll are generated with spacing from the midline with deviation .ror /2 and .−ror /2, respectively, where .r or is orbiting radius (5 mm) (Fig. 1b). As a result, the distance between elements of fixed and orbiting scrolls become .ror before orbiting as Fig. 1b. The thickness of the profile .t can be estimated numerically by finding the nearest points between orbiting and fixed scroll for every degree. The orbiting scroll orbits with the orbit radius .ror without rotating as Fig. 2. When the orbiting angle .φ = 0, the tips of the orbiting and fixed scroll are connected to each other, and two suction chambers are generated at the tip of the fixed and orbiting scroll profiles. The chamber with outer wall of the fixed scroll is the A chamber, and the chamber with outer wall of the orbiting scroll is the B chamber. The chambers are displaced and compressed during the compressor operation. At .φ = φe − 360◦ , the mixing occurs so the A and B chambers are merged to form the M chamber, and the discharge port starts to open. The M chamber disappears when .φ becomes .φe . The tangential angle of the scroll profile is transformed to the normal angle starting from the suction tip (.θ = ψmax − ψ) to compare with the orbiting angle .φ. The volume of the compression chamber is evaluated using the area between infinitesimal arcs of the fixed and orbiting scrolls. The area between two arcs within the infinitesimal change in the normal angle, .Δθ , is expressed by the area between con.
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Fig. 3 An infinitesimal area of the compression chamber
centric arcs and the size of a trapezoid induced by a displacement of the orbiting scroll. The summation of the area can be expressed by using orbiting angle .φ and the infinitesimal length of the midline (.Δs = rmid Δθ ) (Fig. 3b). φ+360◦ .
V =h
∑
ror [1 − cos(φ − θ )]Δs.
(3)
θ=φ
where .h is the height of the compressor. At the M chamber (.φ > φe − 360◦ ), the volume .V is doubled, and the maximum angle of the summation in Eq. 3 become .φe .
V = 2h
φe ∑
ror [1 − cos(φ − θ )]Δs.
(4)
θ=φ
2.2 Analytic Model for Compression Process Using the mass and energy balance equations with open control volume, we can predict pressure . P inside the compression chamber during the compressor operation. The refrigerant is assumed to be air, whose material properties can be acquired from the CoolProp library in Python, and lubrication oil is not considered in the compression process. Changes in specific volume .v(= V /m) and specific entropy .s in the chamber during operation can be derived from the mass and energy balance equation with open control volume.
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[ ] 1 ∂V v ∂v = + (m˙ d + m˙ lo − m˙ li ) , ∂φ m ∂φ ω ] 1 [˙ ∂s = Q ext + m˙ li (h li − h) . ∂φ mT ω
(5a)
.
(5b)
where . f or b means orbiting frequency and .ω is orbiting speed (.2π f or b ). .T , .h, and . Q˙ ext are the temperature, enthalpy, and heat influx from the scroll wrap to the refrigerant, respectively. Subscripts .d, .lo, and .li mean discharge, outflux leakage, and influx leakage, respectively. Then, the pressure. P, temperature.T , and enthalpy.h are derived as follows: k ∂v αT ∂s ∂P =− + , ∂φ βv ∂φ βcv ∂φ αT ∂v T ∂s ∂T =− + , . ∂φ βcv ∂φ c ∂φ ( v ) k ∂v k−1 ∂s ∂h =− + +T , . ∂φ β ∂φ α ∂φ
(6a)
.
(6b) (6c)
where .cv , .α, and .β are the specific heat capacity at constant volume, isothermal compressibility, and isobaric expansion coefficient, respectively. Or, . P, .T , and .h can be acquired from CoolProp library with .v and .s. (. P = P(v, s), .T = T (v, s), .h = h(v, s)) The leakage from high pressure chamber 2 to low pressure chamber 1 is modeled with isentropic and one-dimensional compressible nozzle flow. The mass flow rate .m˙ of the leakage is determined by the lower and higher pressure .(P1 , P2 ), temperature at the higher pressure chamber .T2 , and the gap area . A for a compression chamber: /
k+1 [( ) 2 ( ) k+1 ]− 2(k−1) P1 k 2k P1 k .m ˙ = P2 A − (k − 1)RT2 P2 P2 k+1 )1/2 ( )− 2(k−1) ( k+1 k .m ˙ = P2 A RT2 2
if
P2 < Pcr P1
(7a)
if
P2 > Pcr , P1
(7b)
where .k means an isentropic expansion coefficient, and . R is a specific gas constant. k ( k+1 ) k−1 . Pcr is the critical pressure ratio that makes the Mach number one (. Pcr = ). 2 Two types of leakage are considered: radial leakage through the top and bottom of the scroll wall and tangential leakage through the side tip of the chamber wall. The gap area for radial leakage is calculated by using numerical integration, and the gap width is assumed to be 20.μm. The gap area for tangential leakage is the gap width of 1.μm times the height of the scroll (.l = 40mm). At the mixed chamber where.φ > ψmax − 360, the A and B chambers are merged, and the refrigerant inside the chamber is mixed. Because of the symmetry design and identical volume of the A and B chambers, the pressure of the chambers should be the
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same. Therefore, the pressure of the M chamber is the same as the A and B chambers at .φ = φe − 360◦ . After .φ = φe − 360◦ , we assume that the pressure is assumed to be constant. Then, the discharge mass flux can be derived by using constant pressure condition (.m˙ d = −m˙ lo − ω/v × ∂ V /∂φ). Then, the total discharge mass flux can be derived by integrating .m˙ d . From the pressure difference applied on the wall of the scroll profile, bending stress .σ1 , which is proportional to .(l/t)2 , and normal stress applied on the axial direction .σ2 , which is proportional to .l 4 /r t 3 , can be estimated.
2.3 Optimization with DRL The proximal policy optimization (PPO) algorithm, one of the actor-critic methods, is applied in this study to give continuous actions. In the actor-critic method, the critic network, the value-based method, predicts the value of the current states and actions with reward, and the actor-network, policy-based method, is updated with the predicted value and changes the policy of action during the episode. Then, the action is determined by the policy in a probabilistic manner. In our model, degenerated version of the PPO method, which has a running step per episode, is applied because the shape optimization is not affected by the sequential procedure [15] (Fig. 4). In our model, the positional and directional changes of the nodes from the base design.(xi − xib , yi − yib , ψi − ψib ) are calculated from the action.ai =[ai1 , ai2 , ai3 ], and the compression ratio and displacement are applied to design the reward .r . Subscript .i means the node number, and .b denotes the base design. The base design is derived from an involute profile whose base circle radius is .rb = 5 mm, and the radius of the circular design domain is .rmax = 53 mm. The node is selected every 120 degrees. . i
x = xib + ai1 cos ψib − ai2 sin ψib
(8a)
. yi = yib + ai1 sin ψib + ai2 cos ψib ψi = ψib + ai3 ,
(8b) (8c)
.
where .ai1 and .ai2 is bounded from .−(πrb − ror ) to .πrb − ror , and .ai3 is bounded from .−30.◦ to 30.◦ .
Observation Environment Initial state
Episode i Agent Actions Environment Reward Actor Changed state
Fig. 4 Reinforcement learning framework
Agent Critic
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.r
=
c1 0
Pd,target −|Pd,target −Pd | Ps
∑
m˙
+ c2 ∑ m˙ d
d,b
2 if all σ1 , σ2 < σmax and x 2 + y 2 < Rmax 2 2 2 if any σ1 , σ2 > σmax and x + y > Rmax
(9)
where subscripts.d,.s,.target, and.b imply discharge, suction, target, and base design, respectively. .c1 and .c2 are the coefficients of the multi-objective optimization. In this study, we set both values as 1.
3 Results 3.1 Analytic Model Result The volume and pressure of the compression chamber are first estimated through the methods described in Sects. 2.1 and 2.2. For example, the base design, when the actions are zero (Fig. 1a), is considered in this subsection (Fig. 5a and b). The suction pressure is 1 bar, and the orbiting frequency . f or is 60 Hz. The mass flux for a single orbit is 5.406 .×10−5 kg/rev, and the compression ratio is 2.770. The chamber volume and compression ratio are applied to design the reward at Sect. 2.3.
3.2 Shape Optimization Results The DRL system is trained by changing the shape of the scroll profile with the action (Sect. 2.3) and running the analytic model with 1 bar of suction pressure and 4 bar of target discharge pressure to maximize the mass flux through a single orbit (Fig. 6). The reward evolution shows the penalty rewards as zero value, and the frequency of the penalty rewards decreases during the training. The reward evolution shows that the training for the non-linear objective function is successfully conducted, and the objective function converges during the training.
(a) ×103
(b)
60 P/Ps
Vch (mm3)
80
40 20 0 0 100 200 300 400 500 600 Orbit angle φ (°)
2.75 2.50 2.25 2.00 1.75 1.50 1.25 1.00 0 100 200 300 400 500 600 Orbit angle φ (°)
Fig. 5 a Sum of the volume with respect to the orbit angle .φ and b Pressure example with base scroll design
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(a)
299
(b) 4
Reward
3 2 1 0 2500 5000 7500 10000 Episode
0
(d)
80
3.5
60
3.0 P/Ps
Vch (mm3)
(c) ×103
40 20
2.5 2.0 1.5
0
1.0 0 100 200 300 400 500 600 Orbit angle φ (°)
0 100 200 300 400 500 600 Orbit angle φ (°)
Fig. 6 a Reward evolution of the optimization process, b Optimal scroll design, and corresponding c sum of the chamber volume and d the ratio between the pressure inside the chamber and suction pressure
The optimal results are shown in Fig. 6b, c, and d. At the optimal condition, the compression ratio is 3.793 (Fig. 6d), and the mass flux for a single orbit is 5.301. The mass flux of the optimal condition is slightly decreased compared to the base design, but the compression ratio is improved significantly. The coefficient of the multiobjective optimization causes the mass flux to decrease. If the coefficient applied to the mass flux is larger than 1, the mass flux can be improved rather than the compression ratio. Theoretically, to have a large compression ratio and mass flux, the size of the suction chamber should be maximized, and the size of the mixed chamber should be minimized. In Fig. 6b, The outer profile of the scroll almost shows a circular shape, which can use the limited space properly. Also, the mixed chamber is designed to be as small as stress allows. The minimum value of the thickness and the radius of the curvature are restricted because of the stress applied to the wall. At the optimal condition, the decreasing rate of the chamber volume is increased at the early stage compared to the base design. The volume profile is reasonable since the compression ratio is directly affected by the ratio between .V (φ = 0◦ ) and ◦ . V (φ = φmax − 360 ). As a result, for the constraint design space, the volume change ◦ from.φ = 0 to.φ = φmax − 360◦ should be maximized, and the volume change from ◦ .φ = φmax − 360 to .φ = φmax should be minimized.
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4 Conclusions In this work, we propose an optimization method for the shape of the hybrid wrap profile based on the node-connection method using DRL and the low-order analytic models for the compression process. The objective function is designed to consider the mass flux, discharge pressure, design domain, and durability of the compressor by comparing the base design and using the zero reward as a penalty. The PPO is then applied to maximize the rewards. As a result, an optimal scroll design is found to maximize the mass flow rate, adjust the discharge pressure to the target, and avoid geometric restrictions. Despite the complicated geometries of the scroll compressor, this study demonstrates that the simple analytic models to estimate the pressure and mass flux are successfully coupled with DRL to produce optimization results efficiently. Admittedly, for practical industrial applications of our optimization method, more accurate analytic or empirical models validated by experiments should be adopted for the environment of DRL. Although we have considered only mass flux and pressure ratio, the optimization method can be improved and applied to develop the efficient scroll design by applying lab-based empirical relations. Moreover, the design parameters for manufacturing, such as minimum radius of curvature for the cutting tool size, maximum involute angle, and outer shell size, can be considered by adding the parameters into the reward design. The comparison of the optimization results for different refrigerant parameters is in future work.
References 1. S. Etemad, J. Nieter, Design optimization of the scroll compressor. Int. J. Refrig. 12, 146–150 (1989) 2. N. Ishii, M. Sakai, K. Sano, S. Yamamoto, T. Otokura, I. Noriaki Ishii, M. Sakai, K. Sano, S. Yamamoto, T. Otokura, A fundamental optimum design for high mechanical and volumetric efficiency of compact scroll compressors. Int. Compressor Eng. Conf. (1996) 3. B. Wang, X. Li, W. Shi, A general geometrical model of scroll compressors based on discretional initial angles of involute. Int. J. Refrig. 28, 958–966 (2005) 4. C.H. Tseng, Y.C. Chang, Family design of scroll compressors with optimization. Appl. Therm. Eng. 26, 1074–1086 (2006) 5. B. Blunier, G. Cirrincione, Y. Hervé, A. Miraoui, A new analytical and dynamical model of a scroll compressor with experimental validation. Int. J. Refrig. 32, 874–891 (2009) 6. Y.R. Lee, W.F. Wu, On the profile design of a scroll compressor. Int. J. Refrig. 18, 308–317 (1995) 7. J. Wang, Q. Liu, C. Cao, Z. Wang, Q. Li, Y. Qu, Design methodology and geometric modeling of complete meshing profiles for scroll compressors. Int. J. Refrig. 91, 199–210 (2018) 8. P. Bin, V. Lemort, A. Legros, Z. Hongsheng, G. Haifeng, Variable thickness scroll compressor performance analysis—part ii: Dynamic modeling and model validation. P. I. Mech. Eng. E-J. Pro. 231, 641–649 (2017) 9. J. W. Bush, W. P. Beagle, M. E. Housman, J. W. Bush, S. Program, M. Wayne, P. Beagle, Maximizing scroll compressor displacement using generalized wrap geometry. Int. Compressor Eng. Conf. (1994)
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10. J. Tanaka, N. Morozumi, M. Araki, M. Fujino, M. Furukawa, Development of the hybrid scroll compressors. Int. Compressor Eng. Conf. (2002) 11. Y. Liu, C. Hung, Y. Chang, Study on involute of circle with variable radii in a scroll compressor. Mech. Mach. Theory 45, 1520–1536 (2010) 12. B.R. Shaffer, E.A. Groll, Parametric representation of scroll geometry with variable wall thickness parametric representation of scroll geometry with variable wall thickness. Int. Compressor Eng. Conf. (2012) 13. S. Qin, S. Wang, L. Wang, C. Wang, G. Sun, Y. Zhong, Multi-objective optimization of cascade blade profile based on reinforcement learning. Appl. Sci. 11, 1–27 (2021) 14. X. Yan, J. Zhu, M. Kuang, X. Wang, Aerodynamic shape optimization using a novel optimizer based on machine learning techniques. Aerosp. Sci. Technol. 86, 826–835 (2019) 15. J. Viquerat, J. Rabault, A. Kuhnle, H. Ghraieb, A. Larcher, E. Hachem, Direct shape optimization through deep reinforcement learning. J. Comput. Phys. 428, 110080 (2021)
Integrated Optimization of High-Speed Motor Drive and Compressor System: A Case Study Xin Ding, Carlos Castillo, Steven Pekarek, and Davide Ziviani
Abstract Climate change and decarbonization challenges are forcing the HVAC&R industry to transition to low Global Warming Potential (GWP) and natural refrigerants. Despite the environmental benefits, low-GWP refrigerants often yield to tradeoffs in system performance, flammability and volumetric capacity. Compressors need to be optimized to adapt working chambers and displacement volume requirements to the thermophysical properties of the refrigerants. In addition, to meet capacity targets under full- and part-load conditions, variable-speed operation also plays an important role especially during heating conditions. This paper describes an integrated optimization approach that couples the optimization of both compressor geometry and electrical motor for residential heat pump applications with emphasis on colder climates. The modelling framework includes a generalized semi-empirical compressor model as well as a multi-objective electric driver optimization toolbox (EDOT). The two sub-models were trained and validated with an R410A scroll compressor dataset and a detailed Method-of-Moments (MoMs) engine, respectively. A case study of a scroll compressor using Minneapolis weather data and low-GWP replacements has been considered to demonstrate the utilization of the modelling framework and the design trade-offs. The new-designed compressor was found to be 30% smaller in volume than the original design while maintaining a comparable performance. Keywords Heat pumps · Low-GWP · V-shape interior PMSM · Coupled optimization X. Ding (B) · D. Ziviani School of Mechanical Engineering, Purdue University, West Lafayette, IN 47906, USA e-mail: [email protected] D. Ziviani e-mail: [email protected] C. Castillo · S. Pekarek School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47906, USA e-mail: [email protected] S. Pekarek e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_25
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1 Introduction In recent years, the HVAC&R industry is urged to replace existing hydrofluorocarbons (HFCs) with near-zero GWP or natural refrigerants by regulatory changes (US Department of Energy 2021). Recent phase-down proposal (U.S. Department of Energy 2021) issued by the U.S. Department of Energy’s (DOE) emphasised the importance to complete the transition and ensure energy efficiency requirements. Compressor designs need to be optimized for air-conditioning and heat pumping systems, which are typically designed for a specific working fluid, to overcome the trade-offs brought by the transitioning to low-GWP fluids and inherently yield to lower volumetric capacities. A common solution to address the challenge is increasing the compressor size. However, this approach increases the manufacturing and operating costs, without addressing the need for optimized compressors. As an alternative approach, this study aims at exploring the potential for increasing the speed range of variable-speed hermetic compressors for heat pump applications to meet capacity requirements at low ambient conditions. Such an approach requires an integrated optimization and redesign of the electric drive (motor/inverter) and the compressor. This study extends the feasibility of the method presented in the previous work and expands the design space [1]. An integrated optimization framework is proposed in the study as a generalized method for designing of low-GWP and natural refrigerants compressors.
2 Modelling of the Integrated Optimization Framework The optimization is built by coupling two well-established tools: a generalized semiempirical compressor model and a population-based electric drive optimization tool (EDOT) based on the Method-of-Moments [2], which are coupled to enable the integrated design of variable-speed compressors. On the compressor side, a mechanistic compressor modelling tool called positive displacement simulator (PDSim) [3, 4] is used to generate the compressor envelope based on given working conditions. The envelope trains a generalized semi-empirical compressor model which takes the desired working ranges and other machine specifications as inputs and computes the corresponding torque force and power consumption. On the electric motor drive side, EDOT is used to perform a rigorous multi-physics evaluation of suitable motor designs using a method-of-moments engine, which is used afterwards to test and validate the performance of the newly designed high-speed compressor. The proposed framework takes the desired operation ranges, rotating speed, and displacement of a compressor as inputs and calculates the required torque and power input of the compressor as intermediate results. The framework then conducts a multiobjective design optimization of the electric drive and provides a Pareto-optimal front of possible designs. A user-defined objective function is then used to select the mostfavoured design from the obtained front. The updated compressor design is then fed
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(a) Schematic of the framework
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(b) Schematic of the semi-empirical model
Fig. 1 Schematic drawings of the framework and the compressor model
into the framework again to generate new designs. The framework iteratively solves for the optimized compressor-motor design until the pre-defined error threshold is met. The schematic of the optimization framework is shown in Fig. 1a.
2.1 Semi-Empirical Compressor Model To simulate the compressor, a PDSim model was considered for its high accuracy and capability of providing comprehensive solution space. However, it requires high computational costs because the PDSim model is a physical-based model that implements comprehensive analytical methods and numerical methods. Therefore, a light-weight semi-empirical model was chosen to be implemented in the framework. The semi-empirical model follows the method presented in Nelson et al. [8] with various modifications to compressor structures to fit the geometric settings of the compressor selected in the case study. It consisted of a total 8 sub-models that described the various physical processes and thermodynamic properties of a compression process with energy balance equations, heat transfer and pressure drop correlations and a set of empirical coefficients. The model was trained and validated by a R410A scroll compressor dataset generated by the PDSim model. After training and validation, the semi-empirical model was integrated into the optimization process. The conceptual schematic diagram of the semi-empirical scroll compressor is presented in Fig. 1b. A total of 15 parameters were used in the semi-empirical model. Inlet temperature, pressure, outlet pressure, ambient temperature, and rotating speed were used as model input variables. The mechanical power consumption, discharge temperature, mass flow rate, and shaft torque force were calculated as the output variables. Other variables were tuned based on experimental training datasets by minimizing a pre-defined error function. Additionally, the model is able to extrapolate performance predictions with various drop-in refrigerants (e.g., from R410A to R454B or R454C) with minor modifications to its variables. The modifications are made only based on refrigerant thermophysical properties. The model extrapolation accuracy can be further improved by
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developing a detailed relationships between the leakage area (. Aleak in the model) and the refrigerant/lubricant interactions in lieu of treating it as constant, because the physical properties of the refrigerant and lubricant can cost a significant impact on the internal leakage flow in some cases. The effect of leakage flows can be investigated with PDSim. In this work, we are limiting the discussion to showcase the optimization framework.
2.2 Motor Model The chosen motor topology for the coupled optimization procedure is the V-shaped interior permanent magnet synchronous machine, whose name is garnered by the shape and disposition of the magnets which can be seen in Fig. 2. The use of V-IPMSMs offers potential advantages in comparison with other types of machines, including surface-mount permanent magnet machines (SPMSM), which makes them a relatively popular choice for compressor motors and other HVAC applications. Among the advantages is a higher rotor robustness, which can expand the motor’s speed range compared with SPMSMs without the need for armored sleeves. Furthermore, the presence of a saliency-based torque can enhance torque production capabilities at similar stator current levels [5]. Although V-IPMSMs have several characteristics that make them desirable, modelling the V-IPMSM for design introduces challenges compared to SPMSMs. Specifically, since the steel regions next to the flux barriers (also known as bridges) work to create short circuit paths for the magnetic flux produced by the permanent magnets and since they are relatively narrow, the steel in these bridges usually has very high levels of saturation. This implies that the magnetic permeability in this region cannot be considered constant and the electromagnetic models of the the system become
Fig. 2 V-shape PMSM motor topology
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nonlinear. If applying tools such as the Method of Moments (MoM) [6], this implies the existence of bound currents inside the material, making it necessary to mesh the volume that saturates, unlike the SPMSM which can often be accurately modelled using only a surface mesh [6]. In order to evaluate the performance of a machine within the design optimization, a nonlinear hybrid MoM developed in [2] has been used. Specifically, in the hybrid approach considered, a surface mesh is used to model all magnetic materials except for the rotor bridge regions which are discretized using triangular elements [2]. After meshing the material, the tangent component of the magnetization at each element of the surface mesh, and x- and y-components of magnetization at each element of the volume (triangular) mesh are used as unknowns. The formulation can be expressed in the form show in Eq. 1 [ .
][ L ] ] [ L ,L L L FBtot,tan Mtan Mtan FBNML ,L FB M ( ) = NL N L + FB I f I f + FB I pm I P M NL L ,N L N L ,N L M M FBtot,x F F xy xy y BM BM
(1)
L where . Mtan is a vector containing the tangent components of the magnetization at each of the edges of the surface elements, . MxNyL is a vector containing the .x- and . y- components of the magnetization at the triangular elements. . I f is a vector containing the free currents of the stator windings and . I P M is a vector of free currents representing the equivalent current generated by the residual magnetization of the ,L ,N L , . FBLM , . FBNML ,L , . FBNML ,N L , . FB I f , . FB I P M are permanent magnet. The matrices . FBLM derived by determining the contribution to magnetic flux density ( N L )from each of the NL L relate the mag, . FBtot,x free- and bound-current sources. Finally, . FBtot,tan y Mx y netic flux density inside a material with its magnetization. Details of these matrices are provided in [2] and [6]. Since the system of equations is nonlinear, a Newton-Raphson method is used to solve the system of equations. Additional details on how to calculate the matrices and the application of the MoMs can be found in [2] and [6].
2.3 Objective Function The optimization tools described in the previous sections provide the user a considerable amount of new designs with different emphases. The toolbox has to identify the most desired design that satisfies customized needs for different users from the obtained results. To enable user-defined selection judging criteria in the identifying process, a method call Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) [7] is implemented to form the objective selecting function. To demonstrate the method, the best design that minimizes the overall power losses and machine weight (mass) from the design space is identified with TOPSIS. A 40% and 60% weight is assigned to the normalized power losses and mass variables, respectively. The best and worst cases are identified from the weighted values of
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both variables and are used as reference to calculate the relative overall distance between each design The design that has the smallest relative value is identified as the optimization result.
3 Results and Discussion 3.1 Compressor Model In this section, validation results of the established semi-empirical compressor model are shown. A comprehensive dataset was generated by the PDSim model. 48 points were selected throughout the entire compressor envelope, within which 18 points were randomly selected to train the semi-empirical model. The model accuracy was validated with the rest 30 points in the R410A dataset. Moreover, datasets of R454B and R454C as drop-in replacement refrigerants were generated with the PDSim model and utilized to demonstrate the extrapolation capabilities from training fluid to low-GWP refrigerants. 10 fictitious parameters and their determined values are listed in Table 1. The results provided by the two solvers were combined and cross validated to get a global optima parameter set. Figure 3a, b show the torque force and power consumption results for R410A with training in red and validating in blue. All the predicted points were within a 10% error bar. . R 2 , relative mean square error (RMSE), and maximum average percentage error (MAPE) were used as critical indicators to evaluate the model prediction accuracy. The . R 2 , MAPE, and RMSE for the torque and power consumption are both 99.9%, 1.0% , and 1.2%, respectively; Overall, the model shows a good prediction accuracy through all conditions. The results proved that the well-trained semi-empirical model is capable of providing accurate predictions at various conditions. The R454B and R454C datasets were fed to the R410A-trained semi-empirical model to validate the extrapolation accuracy. Torque and power consumption validation results of R454B are shown in Fig. 3c, d. All points are within the 5% error bar. 2 . R , RMSE and MAPE values were 99.9%, 2.3%, and 1.7% for both torque and power, respectively. The . R 2 value is same as the results of R410A, and MAPE and RMSE values are around 1% higher than that of R410A. Similar accuracy can be found for
Table 1 Identified parameters of the semi-empirical model Parameter Value Parameter .U
Asuc Adis .U Aamb .V R . Asuc
.U
39.75 26.76 4.67 4.07 6.218e.−5
. Adis . Aleak . Vsuc .ηmotor .τloss
Value 3.257e.−5 7.769e.−7 6.989e.−5 0.9 1.8
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(a) Torque
(b) Power consumption
(c) R454B Torque
(d) R454B Power consumption
(e) R454C Torque
(f ) R454C Power consumption
Fig. 3 Validation plots of torque force and power consumption of R410A, R454B and R454C results Table 2 Example motor specifications Value Description Para
Para
Value
Description
.as
.ar
M19 Ferrite AC-12 34.2 mm .−8.68A
Rotor material Magnet material
.ac .P
r
. Iqs
M19 Copper
Stator material Conductor material
.am
16 10.75A
Number of poles Q-axis stator current
. Ids
.l
r
Machine length D-axis stator current
R454C extrapolation results in Fig. 3e, f. Most of the points lie in the 5% error bar. R 2 , RMSE and MAPE values were 99.8%, 2.5%, and 2.5% for torque, and 99.8%, 2.5%, 2.6% for power consumption, respectively. In general, the model showed a high extrapolation accuracy for both R454B and R454C, with R454B slightly higher (1%) than R454C. The validation results proved that the developed semi-empirical model is capable of extrapolating accurately to other refrigerants.
.
3.2 Motor Model Prior to optimization, the proposed MoM-based model used in the optimization was validated using an example motor geometry taken from [2] which had been previously been evaluated using a Finite Element Algorithm (FEA). The specifications for the machine can be seen in Table 2.
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The machine was evaluated using the hybrid methodology over 8 rotor positions. The RMSE value of the backiron and teeth flux densities with respect to the FEA baseline model were 0.0871 and 0.0857, respectively. Additionally the average electrical torque on the rotor on each of the rotor positions was obtained with an error of 3.16% relative to the FEA model. This results show that the method of moments is successful in evaluating V-IPMSMs with high levels of saturation in the core.
4 Case Study A household heat pump application in Minneapolis was identified as a cold climate benchmark application case study to demonstrate the feasibility of the optimization framework. A total of 10 d were selected from the typical annual weather data (TMY3) as representative working conditions of the heat pump application, in which 4 d were picked from winter (Jan, Feb, Dec) and 2 d were picked from the rest three seasons, respectively. If 70% of a day that has an hourly-averaged outdoor dry bulb temperature lower than 20.◦ C, then the heat pump was set in heating mode in such a day. Whereas if 70% hours in a day that have a temperature higher than 20.◦ C, then the heat pump was set in cooling mode. Based on hourly temperatures throughout a day, 7 out of 10 d were determined as in heating mode while 3 d (1 d in spring and 2 d in summer) in cooling. A matrix of compressor working conditions was determined and a compressor envelope with 38 test points was established. The indoor temperature was assumed to be 26.◦ C in winter and 20.◦ C in summer. Therefore, the evaporating and condensing temperature of the compressor was assumed ranging from .−36.◦ C to 20.◦ C and 15.◦ C to 55.◦ C, respectively. A hourly compressor working schedule was determined by knowing the hourly temperature distribution throughout a day. The hourly schedule coupled with the working condition matrix were used to generate a compressor map and a motor operating schedule using R454B as working fluid. The proposed methodology is able to optimize machines with an hourly schedule, but in this case only 3 operating conditions that have maximum, minimum and average electric power requirements were extracted out to set the nominal characteristics of the machine. A single run of the optimization framework was applied to the established schedule. A Pareto-front (Fig. 4a) of non-dominated designs was obtained, where each point in the Pareto-Plot represents a different motor design. Among the 500 designs in the Pareto-front, the 85th design was selected using TOPSIS as the objective function. Comparing to the radius and height of the original motor module, 9.75 cm and 8.5 cm respectively, the radius and height of the selected optimized motor design, 8.85 cm and 6.25 cm respectively, are 9.2% and 26.5% less. The volume and mass of the selected design are therefore around 39.4% less than the original module. It can be seen from Fig. 4, that for the obtained set of designs, increases in mass lead to a decrease in the relative contribution of resistive losses of the conductors and the core loss, indicating most of the improvement is coming from increasing the stator
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(a) Pareto-front
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(b) losses by parts vs. mtotal
Fig. 4 Pareto-Optimal Front of the Minneapolis heat pump application Fig. 5 Overall isentropic efficiency comparisons for the original module and the updated design
volume to accommodate winding with increased cross-sectional area and reducing flux density levels in the teeth and back-iron. Interestingly, the total contribution of semiconductor losses has relatively little variation. Further analysis will be necessary to evaluate the impact of the optimization process for multiple operating conditions in comparison to alternative design approaches. As a preliminary result, this study choose the overall isentropic efficiency of the compressor as the indicator to showcase the performance improvements that can be gained from the framework. Figure 5 shows the overall isentropic efficiencies comparisons for 10 test points between the original module and the updated design. The updated design has a higher overall isentropic efficiency comparing to the original design from 4.55 to 5.49%. Comparisons of other thermodynamic performance indicators will be conducted in the furture works.
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5 Conclusions In this study, an integrated optimization framework consists of a generalized semiempirical compressor model and a multi-objective motor design toolbox EDOT is introduced. The compressor model was constructed and validated to enhance the extrapolation ability of the optimization framework while maintaining a fast computing speed. A V-IPMSM model was implemented into EDOT to enhance the capabilities of the toolbox. A preliminary case study was done to showcase the whole working process of the coupled optimization. Main conclusions were summarized as follows: • For R410A, R454B, and R454C, . R 2 were 99.9%, 99.9% and 99.8%, respectively; MAPE values were 1.0%, 1.7%, and 2.5%, respectively; and RMSE values were 1.2%, 2.3%, 2.5%, respectively. The semi-empirical model was proved having high accuracy for all three fluids. • The RMSE for the magnetic flux density in the stator backiron an stator teeth was 0.0871 and 0.0857 respectively. RE of the torque was 3.16%, which indicate that the updated V-IPMSM model is able to provide accurate predictions. • The integrated optimization framework showed significant improvements compared to the original design with around 39.4% less weight while maintaining similar electric power losses. The proposed optimization framework proved being able to provide design guidance and detailed analyses to the target compressor.
References 1. X. Ding, C. Castillo, M. Dickerson, Pekarek, S., Ziviani, D.: Coupled design of high-speed motor drive and shaped optimized compressor systems. In: International Compressor Engineering Conference. Paper 2780. https://docs.lib.purdue.edu/icec/2780 2. D.C. Horvath, Analysis and Design of Electric Machines Using 2D Method of Moments (Purdue University Graduate School, Thesis, 2020). https://doi.org/10.25394/PGS.12730976.v1 3. I.H. Bell, D. Ziviani, V. Lemort, C.R. Bradshaw, M. Mathison, W.T. Horton, E.A. Groll, PDSim: A general quasi-steady modelling approach for positive displacement compressors and expanders. Int. J. Refrig. 110, 310–322 (2020). https://doi.org/10.1007/11823285_121 4. D. Ziviani, I.H. Bell, X. Zhang, V. Lemort, M. De Paepe, J.E. Braun, E.A. Groll, PDSim: Demonstrating the capabilities of an open-source simulation framework for positive displacement compressors and expanders. Int. J. Refrig. 110, 323–339 (2020). https://doi.org/10.1016/ j.ijrefrig.2019.10.015 5. Lin, R., A design paradigm for V-shape interior permanent-magnet machines using multiobjective optimization (dissertation). ProQuest Dissertations & Theses, Ann Arbor (2017) 6. R. Howard, S. Pekarek, Two-dimensional Galerkin magnetostatic method of moments. IEEE Trans. Mag. 53(12), 1–6, Dec 2017, Art no. 7002406. https://doi.org/10.1109/TMAG.2017. 2741449 7. E.K. Zavadskas, A. Mardani, Z. Turskis, A. Jusoh, K.M. Nor, Development of TOPSIS method to solve complicated decision-making problems-An overview on developments from 2000 to
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2015. Int. J. Inf. Technol. Decis. Making 15(03), 645–682 (2016). https://doi.org/10.1142/ S0219622016300019 8. N.A. James, J.E. Braun, E.A. Groll, W.T. Horton, Semi-empirical modelling and analysis of oil flooded R410A scroll compressors with liquid injection for use in vapor compression systems. Int. J. Refrig. 66, 50–63 (2016). https://doi.org/10.1016/j.ijrefrig.2015.12.011
Experimental Research of Pressure-Volume Diagrams in a Scroll Compressor at High Speed Xiaowen Li, Qiuhe Guo, Yusheng Hu, Huijun Wei, Yi Liao, Jia Yao, and Shuanglai Liu
Abstract The Experiment of pressure-volume (PV) diagrams is carried out to study the pressure distribution in a scroll compressor throughout the whole compression process, which is important to demonstrate the real status of the compressor during compressing operation. The analysis of pressure and efficiency based on the PV method of scroll compressor operating at high speed is presented. The composition of various loss, such as the pressure loss in suction and exhaust process, overcompression loss and indicated efficiency at different speeds and operation conditions are finally obtained. The results show that the suction and exhaust pressure loss increase rapidly with the rising of rotation speed, which leads to the decrease of indicated and volumetric efficiency. The composition of loss is quite different from low speed to high speed. The research is useful to understand various important phenomena and improve our design of scroll compressor at high speed. Keywords Scroll compressor · PV diagram · High speed
1 Introduction The development of commercial refrigeration system takes energy saving and environmental protection as the main melody. Compressor is the core component of refrigeration system, and its performance directly affects the energy-saving efficiency of the whole system. Inverter scroll compressors are widely used in domestic X. Li (B) · Y. Hu · H. Wei · Y. Liao State Key Laboratory of Air-Conditioning Equipment and System Energy Conservation, Jinji West Rd, Zhuhai 519070, People’s Republic of China e-mail: [email protected] X. Li · Y. Hu · H. Wei · J. Yao Guangdong Key Laboratory of Refrigeration Equipment and Energy Conservation Technology, Zhuhai 519070, People’s Republic of China X. Li · Q. Guo · Y. Hu · H. Wei · S. Liu Gree Electric Appliances, Inc. of Zhuhai, Zhuhai 519070, People’s Republic of China © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_26
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and commercial refrigeration systems with large capacity, due to their high efficiency, low torque variation, noiseless operation, low vibration and smooth operation. Finding out the internal operating characteristics of inverter scroll compressors at different frequencies is particularly important for high-efficient optimization design of compressors. Pressure and volume change law test (PV diagram measurement) on the inside of the compressor is an important means to understand the internal working characteristics of the compressor. At present, the existing papers mainly focus on rotary compressors, and there are relatively few studies on inverter scroll compressors. In this paper, by testing the PV characteristics of the inverter scroll compressor with high and low frequencies, the characteristics of scroll compressors are compared and the relative variation law is analyzed, which provides the basis and reference for the optimization design of scroll compressors at high speed.
2 Theory of Experiment 2.1 Thermodynamic Model of Compression Chambers For compression chamber, mass and energy conservation equations are deduced to describe the thermodynamics state. And between chambers, an isentropic nozzle model of one-dimensional compressible flow is used to determine the mass and energy exchange from flank and radial clearance. According to the conservation of mass and energy [1], the equations can be written as: 1 • dm • = mi − mo dθ ω • • ∂p V 1 ∂h dV − m − h) − m − h) − − (h (h i i o o ω ∂υ T ∂υ T m dθ dT = dθ m ∂∂hT v − V ∂∂Tp
(1) V dm m eθ
(2)
v
The isentropic nozzle model is used to calculate the mass flow rate through the clearances between fixed and orbiting scroll wrap [2], which can be written as
2γ pup m = Cd ρup A γ − 1 ρup •
pdown pup
γ2
−
pdown pup
γ γ+1 21
pdown for ≥ pup
2 γ +1
γ γ−1 (3)
21 γγ +1 γ γ−1 −1 γ pup 2 pdown 2 m = Cd ρup A for < ρup γ + 1 pup γ +1 •
(4)
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2.2 Efficiency of Compression Chambers Based on the law of thermodynamics, the enthalpy difference change during the suction process satisfies the relation of Δh = Δq + Δw. If the heat exchange between the refrigerant and the environment in the suction process is ignored, the flow loss Δw caused by the viscous friction of the refrigerant during the charging process are all converted into heat and absorbed by the refrigerant, now the equation is known as Δq + Δw = 0, so the enthalpy value remains unchanged during the flow process. In addition, the temperature remains constant if h (h = C p * T ) keeps invariant. The pressure of the refrigerant decreases while the temperature remains unchanged, thus the density of coolant decreases. Besides, the aspirated volume of the compressor is fixed, it will inevitably lead to a decrease of inspiratory mass and volumetric efficiency when the density of the refrigerant decreases. The theoretical mass of refrigerant is denoted by ms = ρ s V s . The pressure (P) somewhere in the suction process can be obtained by PV diagram measurement, subsequently, the density (ρ) can be calculated from the pressure (P), temperature (T s ) and physical property of the refrigerant, then the actual mass can be written as m = ρ V s [2, 3]. Volume efficiency loss due to flow losses is given by / ηi = (ρs Vs − ρVs )/ (ρs Vs ) = 1 − ρ ρs
(5)
Figure 1 shows the indicated work division diagram of compressor, where Ps is the theoretical suction pressure, Pd is the theoretical exhaust pressure, Ps1 is the measured suction pressure, Pd1 is the measured exhaust pressure, V h is the actual effective volume of the compressor, V d is the discharge port open volume of the compressor, n is the rotary speed, ➀ is the theoretical work of adiabatic compression, ➁ is suction pressure loss. ➂ represents other losses in the compression process (mainly including under-compression loss, leakage loss, heat loss, etc.), and ➃ is the exhaust pressure loss (including loss of over compress, loss of pump body‘s discharge port, the loss of exhaust flow).The pressure loss during the suction and discharge process of the compressor is as follows / Vh ΔPi = n 60 ∫ [PS − Ps (θ )]dV
(6)
/ Vd ΔP0 = n 60 ∫ [Pd (θ ) − Pd ]dV
(7)
0
0
According to the pressure calculation formula, P is defined as P = Ps (Vs /V )n
(8)
Taking the closure pressure (P0 ) of suction process and compression index n as unknowns, the P–V data of the compression stage of the test can be used to fit the
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Fig. 1 P-V schematic diagram of scroll compressor
closure pressure (P0 ) of suction process and compression index (n) at each operation condition. By substituting the fitted parameters into the pressure calculation formula, the actual pressure change of the compression chambers in the compression stage can be calculated more accurately.
3 Test Method and Equipment 3.1 Testing Compressor Multiple displacement and pressure sensors need to be installed to monitor pressure and volume changes in PV diagram measurement. The compressor needs to be specially made, which is a detachable compressor with upper and lower covers, as shown in Fig. 2. The data of pressure (P) and displacement (V ) are respectively collected by the acquisition card (NI: 9239), and the PV curve diagram of the operation process is obtained by post-processing method.
3.2 Pressure Measurement Pressure sensors (Kulite: XTL-142B-190 M-50barA, USA) are inserted into the fixed scroll of the pump body. Four pressure sensors are arranged in the inner and outer compression chambers of the pump body respectively, and every four sensors monitor a complete compression cycle, as shown in Fig. 3. The connecting wire is connected from the flange plate on the upper cover of the compressor and the experiment is tested in multiple groups.
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Fig. 2 Picture of testing compressor
Fig. 3 Location of pressure sensors
3.3 Volume Measurement By sensing the rotation angle of the gear flange mounted on the compressor with a displacement sensor (Del: DT3010-M, Germany), and then the volume can be obtained by the relevant calculation. The newly designed displacement induction gear flange is assembled on the shafting system, meanwhile, the pressure sensor goes deep into the shell and the wire is connected from the shell flange, as shown in Fig. 4.
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Fig. 4 Illustration of location sensor
Table 1 Operation condition for experiments Load condition
Suction pressure (MPa)
Discharge pressure (MPa)
Suction temperature (°C)
Frequency (Hz)
Refrigerant
1 2 3
0.634 0.850 0.877
2.086 1.788 1.652
−2 7 8
123/199 65/106 28/46
R410A
4 Results and Discussion 4.1 Experiment Condition According to the enterprise standard, the conditions in Table 1 are selected for test comparison, and the pressure ratio is from large to small. The ultrahigh electric motor frequency(Full text abbreviation: frequency) of 199 Hz is taken as the upper limit, and the PV curves of high and low frequencies under various working conditions are compared respectively to analyze the loss ratio changes of each module with high and low frequencies(unit volume:98 cc). All experiments are implemented in a compressor calorimeter.
4.2 Data Analysis The test results are shown in Figs. 5, 6 and 7 (All the measurement results of an inner compression chamber). Under the high-frequency working condition 1 (Fig. 5), and the actual exhaust pressure at the theoretical discharge angle is lower than the theoretical exhaust pressure. Meanwhile, the pressure rises sharply after the opening of the discharge port, there is an under-compression phenomenon of high-pressure gas return, and the under-compression phenomenon is aggravated under ultra-high frequency condition. On the other hand, the actual suction pressure is lower than
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the theoretical suction pressure and with suction loss. Under the condition of ultrahigh frequency, suction loss increases. The actual exhaust pressure at the theoretical discharge angle of working condition 2 and 3 is higher than the theoretical exhaust pressure. When the pressure reaches the exhaust pressure, the orbiting scroll does not reach the exhaust angle, and there is the over-compression phenomenon. With the increase of frequency, the over-compression phenomenon becomes worse [4]. The actual suction pressure in low frequency is higher than the theoretical suction pressure, and the “precompression” characteristic phenomenon of scroll is obvious, and the “precompression” phenomenon decreases with the increase of frequency. (Precompression: When the suction chamber of scroll compressor is close to closure, the volume of chamber gradually decreases, and the gap at the closure point of the profile line also gradually decreases. When the gap decreases to a certain extent, the influence of leakage through the gap is small, and the suction chamber can be considered as a closed chamber. With the rotation of the orbiting scroll, the volume Fig. 5 PV diagram of condition 1
Fig. 6 PV diagram of condition 2
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Fig. 7 PV diagram of condition 3
of the chamber gradually decreases and the pressure gradually rises, that is, the compression has begun before the inspiratory closure. By calculating the area of each loss module in Figs. 5, 6 and 7 and summarizing statistics, the comparison Figure of loss ratio is obtained, as shown in Figs. 8, 9 and 10. The ratio of over (under)-compression and the discharge loss of pump body keepsz direct ratio with frequency, the loss of exhaust flow keep direct ratio with frequency and only occurs in mid-low frequencies. The other losses (leakage and heat loss, etc.) are keep inverse ratio with frequency. Under the ultra-high-frequency condition 1, the over (under)-compression and discharge loss account for the main part of the total loss. The indicated efficiency (The ratio of theoretical work of adiabatic cycle to actual cycle) does not change significantly in low frequency, decreases in high frequency, and decrease range enhances in ultra-high frequency, as shown in Fig. 11.
5 Conclusions (1) The over-compression and under-compression of scroll compressor are difficult to avoid under various working conditions. With the increase of frequency, the actual discharge angle increases. (2) Different frequencies have a great impact on suction-exhaust process. The deviation of suction and exhaust conditions increases in ultra-high frequency conditions, so the suction and exhaust structures need to be redesigned and optimized.
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Fig. 8 Loss ratio of condition 1
Fig. 9 Loss ratio of condition 2
(3) The proportion of exhaust loss and over (under)-compression loss are keep direct ratio with the frequency, and the proportion of ultra-high frequency accounts for the main part of the total loss. There is no significant change in indicated efficiency at low frequencies, while indicated efficiency decreases at high frequency and it decreases intensified at ultra-high frequency.
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Fig. 10 Loss ratio of condition 3
Fig. 11 Indicated efficiency comparison
Nomenclature p T V m ρ A
Pressure (Pa) Temperature (K) Volume (m3 ) Mass (kg) Density (kg × m−3 ) Area (m2 )
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n η CP m h u θ ω γ v C
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Compress exponential (–) Efficiency (%) Mobar heat capacity at constant pressure (J/(mol × K)) Mass flow rate (kg × s–1 ) Specific enthalpy (J × kg−1 ) Specific volume (m3 × kg−1 ) Orbiting angle (rad) Angular speed (rad × s–1 Polytropic index (–) Velocity (m × s–1 ) Efficiency (%)
Subscripts i O n S Up down s h
In Out Natural frequency Suction gas Upstream Downstream Suction gas Heat
References 1. X. Jia, L. Shuanglai, L. Yun, S. Caixia, The experimental and numerical study of discharge valves in scroll compressor. J. Chem. Eng. 50(12), 43–44 (2022) 2. Y.C. Park, Y. Kim, H. Cho, Thermodynamic analysis on the performance of a variable speed scroll compressor with refrigerant injection. Int. J. of Refrigeration 25(8), 1072–1082 (2002) 3. Wu. Jianhua, Y. Li, G. Wang et al., Measurement of Indicated Diagram and Performance Analysis of Propane Rolling Piston Compressor. J. Xi’an Jiaotong Uni. 3, 6–11 (2014) 4. K.C. Moun,Y. Tae-Hwan, K. Tae-Jong et al., Performance evaluation of rotary compressor with special attention to the accuracy of P-V diagram, in Proceedings of the International Compressor Engineering Conference. (Purdue University, USA 1990), pp. 442–449
Numerical and Experimental Study of 120 °C Heat Pump Using a Scroll Compressor Sandeep Koundinya , J. Jothilingam, S. Rajendra Kumar Martin, and Satyanarayanan Seshadri
Abstract Numerous industrial process require hot air or hot water at temperatures below 120 °C and diesel or LPG-fired boilers are often used to generate it. The use of a high-temperature heat pump can help reduce emissions and lower the CO2 footprint by eliminating these fired sources. This study reports on the development and continuous operation of a high temperature heat pump with a heating capacity of 60 kW that generates hot water at 120 °C at a heating COP of 2.27. Using this hot water, hot air at 100 °C is generated using a heat exchanger. The high temperature heat pump increased carbon emissions by 20.3% compared to diesel, based on India’s emission factor of 790 gCO2 /kWh. However, considering the emission factor of the European Union, the high temperature heat pump has the potential to reduce carbon emissions by 57.8%. Keywords High temperature heat pumps · Decarbonization · Hot air dryer · Energy conservation
1 Introduction In recent years, the issue of energy conservation and environmental concerns has received a lot of attention, leading to the implementation of various government policies aimed at lowering carbon emissions. With many countries committing to achieving carbon emission reduction targets at international events such as COP26 [1], industries are also exploring technologies to reduce their energy consumption and carbon footprint. Process heating, which primarily uses hot water, hot air and steam, is a common energy requirement in many industrial processes and is typically met by the use of fossil-fired boilers [2]. In India, the industrial sector consumes 55.85% of total primary energy, with 16–20% used for process heating at temperatures ranging from S. Koundinya · J. Jothilingam · S. R. K. Martin · S. Seshadri (B) Energy and Emissions Research Group (EnERG), Department of Applied Mechanics and Biomedical Engineering, Indian Institute of Technology Madras, Chennai 600036, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_27
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50 to 250 °C [3]. The use of alternative technologies to replace fossil-fueled boilers for process utility could result in significant reductions in carbon emissions. Hightemperature heat pumps (HTHP) have emerged as a promising technology in this regard, receiving significant research attention over the last decade, with efforts to achieve operating temperatures of up to 160 °C. Ongoing research aims to increase operating temperatures even further by utilising different refrigerants and HTHP architectures. The choice of a suitable refrigerant is an important aspect of HTHP design. For optimal performance, it is preferable for the critical temperature of the refrigerant to be slightly higher than the desired operating temperature range. The potential refrigerants for HTHP applications are listed in Table 1. Many studies have been conducted in recent years on HTHP, particularly on the use of natural refrigerants such as CO2 and hydrocarbons, as well as synthetic refrigerants such as R245fa, R1233zd(E), R1224yd(Z), R1234ze(E), R1234ze(Z), R717, R365mfc, R1336mzz(Z), and R600. Fukuda et al. [5] investigated the thermodynamic, numerical, and experimental properties of R1234ze(E) and R1234ze(Z) for HTHP and discovered that the COP was maximised when the operating temperature was 20 K below the critical temperature. The simulations revealed that R1234ze(E) had lower pressure drop losses at higher temperatures of 105 and 125 °C, resulting in a higher COP. Kondu and Koyama [6] evaluated the thermodynamic properties of R717, R365mfc, R1234ze(E), and R1234ze(Z) using four different cycle configurations and sink temperatures of 160 °C and source temperatures of 80 °C. Among the refrigerants studied, the Cascade cycle of R1234ze(Z) and R365mfc had the highest COP. Nilsson et al. [7] created an HTHP by modifying a reciprocating compressor to use R1336mzz(Z) as the working fluid, achieving a heating COP of 2.5 at 60 °C source temperature and 120 °C sink temperature. Studies have demonstrated that when utilized appropriately, natural refrigerants have exhibited comparable or superior performance compared to synthetic refrigerants. White et al. [8] built a transcritical CO2 heat pump with a heating COP of 2.46 Table 1 Properties of HTHP refrigerants [2, 4] ASHRAE number
Boiling point (°C)
Mass composition (%)
Critical temperature (°C)
Critical pressure (bar)
R1234ze(E)
−18.97
Pure fluid
109.36
36.34
R1336mzz(Z)
33.45
Pure fluid
171.35
29
R1224yd(Z)
14.62
Pure fluid
155.54
R1233zd(E)
18.26
Pure fluid
166.45
R245fa
15.05
Pure fluid
R600a
−11.75
R600
−0.49
R1234ze(Z) R365mfc
GWP 100 yr
ODP
Safety group
6
0
A2L
2
0
A1
33.4
1
0.00012
A1
36.2
1
0.00034
A1
153.86
36.5
858
0
B1
Pure fluid
134.66
36.29
4
0
A3
Pure fluid
151.98
37.96
4
0
A3
9.728
Pure fluid
150.12
35.31
6
0
A2L
40.193
Pure fluid
186.85
32.66
782
0
A2
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and hot water temperature of 120 °C. Stavset et al. [9] studied HTHP using hydrocarbons at temperatures up to 115 °C, whereas Bamigbetan [10] studied HTHP using ammonia, hydrocarbons, and their mixtures in a simple cycle, double stage with intercooler, and cascade cycle. The study found that the cascade cycle of hydrocarbon mixtures showed an 11.8% increase in COP compared to pure fluids at a sink temperature of 110 °C. The literature on scroll compressor based HTHP is scarce, with only a handful of articles exploring laboratory-based studies. Despite its potential, there has been a lack of field-level application of HTHP. This study aims to address this gap by presenting the development of an HTHP using a scroll compressor to generate hot water utilizing condensate water that is available in few industries and also to generate hot air at a temperature of 100 °C using the developed HTHP, which has many industrial applications. The choice of R245fa as the refrigerant for this research project was motivated by its well-established performance in high-temperature cycles, as evidenced by previous studies. By opting for R245fa, the intention is to minimize result variability and conduct a comprehensive assessment of the HTHP.
2 System Simulation The heat pump system uses vapour compression technology with a scroll compressor that can withstand temperatures of up to 150 °C. Brazed-type plate heat exchangers are used in the evaporator, economizer, and condenser. The economizer is used to heat the vapour injection line as it travels through the main line. To reduce the pressure from the condenser to the intermediate vapour injection line pressure, an expansion valve is used. The temperatures of the source and sink water are 60 °C and 120 °C, respectively, DWSIM [11], an open-source sequential modular steady-state simulator that produces results comparable to commercial software [12], was used to simulate the system. The simulation was run under steady-state conditions, with adiabatic pipes and zero pressure drop, and the heat exchangers were assumed to be 100% efficient with no fouling. The Peng Robinson equation of state was used to calculate the thermodynamic properties of the refrigerant. Figure 1 depicts the DWSIM system simulation model.
3 Pilot Study Due to the continuous availability of waste heat, a pilot-scale experiment was conducted at a sugar processing facility in Hariawan, Uttar Pradesh, India. The source for the HTHP was hot water condensate at 60 °C. The HTHP was tested for 24 h of uninterrupted continuous operation. Figure 2 depicts the commissioning of HTHP. The experimental setup was built using the numerical model’s specifications. With the exception of the compressor, which was a pre-market sample, all components
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Fig. 1 Theoretical model of HTHP in DWSIM
Fig. 2 Pilot study experimental setup
were commercially available (provided as an application engineering prototype to facilitate faster technology penetration into the market). The hermetically sealed scroll compressor with a displacement of 444.5 cc/rev was used. Scroll compressors are known for its high efficiceny, less number of moving parts, smooth operation and enhanced reliability. The compressor has a two pole three phase induction motor. The maximum allowable winding temperature is 135 °C. The maximum continuous current (MCC) and locked rotor amperage (LRA) are 62.3 A and 290 A, respectively. The maximum allowable discharge pressure is 25 barg. The manufacturer suggests
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using RFL68FA oil to ensure the long life of the compressor. This specific lubricant is compatible with R245fa refrigerant, guaranteeing proper lubrication while minimizing the risk of any negative interaction between the lubricant and refrigerant. By using RFL68FA, the compressor receives the necessary protection against corrosion, oxidation, and other forms of degradation, thereby enhancing its overall durability and reliability. SWEP heat exchangers with 60 plates were chosen for the condenser and evaporator. The circulating water pump in the sink was linked in a closed-loop configuration. The circulating water pump was chosen for its high head and special seals that can withstand temperatures of up to 120 °C. To ensure the safety of the components, the HTHP was outfitted with high and low-pressure switches. The PLC was programmed with high and low pressure limits that would automatically shut down the machine if they were exceeded. To prevent pump dry runs, flow switches were installed in both the source and sink water loops. To protect the compressor and other electrical components, the machine was also outfitted with protection devices such as a phase reversal protection device, phase loss protection device, 3-phase protection device, over voltage protection device, and high current protection device. An internal protection switch was also installed to prevent compressor winding failure. Preliminary experiments determined that the optimum charge for the HTHP was 15 kg. The circulating water volume flow rates of the condenser and evaporator ranged from 6 m3 /h to 8 m3 /h and 2 m3 /h to 5 m3 /h, respectively. The source temperature, which varied between 50 and 60 °C depending on waste heat in the industry, was monitored to ensure it did not exceed 60 °C for proper operation within the compressor envelope. Six calibrated thermistors, four PT-100 temperature sensors, and six pressure transmitters were used to measure temperature and pressure at various state points. The uncertainty of the temperature and pressure sensors is ± 1.1 K and ± 0.5% FS, respectively. Three endress and hauser vortex mass flow metres were used to measure the flow rates of source and condenser water, with an uncertainty of 0.5% of the measured value. An energy metre was used to calculate total electricity consumption. Data from these measuring devices was collected by a PLC (IPG215D) and sent to the cloud via a gateway using RS485 communication and a cellular network, with data being logged and pushed every 5 s.
4 Performance Parameters The two important performance parameters studied in this paper are compressor efficiency and coefficicent of performance (COP). The research focuses on two compressor efficiency measures: isentropic efficiency and total compressor efficiency. The ratio of the theoretical enthalpy change during an ideal, isentropic compression process to the actual enthalpy change during the compression process is defined as isentropic efficiency. It is calculated as the ratio of isentropic to actual
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enthalpy change. Total compressor efficiency is defined as the ratio of the theoretical work input required for an ideal, isentropic compression process to the actual electrical power input required for the compression process. It is defined as the ratio of isentropic work input to actual electrical power input. Equations 1 and 2 give the mathematical expressions for isentropic efficiency and total compressor efficiency, respectively. h 2,isen − h 1 h2 − h1 m r e f h 2,isen − h 1 = E comp
ηisen = ηtotal
(1)
(2)
The mass flow rate of the refrigerant is calculated using the manufacturer’s AHRI polynomial [2]. REFPROP 10 [4] was used to calculate the enthalpies for the measured temperatures and pressures. The heating COP is calculated by dividing the amount of heat delivered by the amount of electrical work done. The system COP, on the other hand, is calculated by dividing the total electrical work by the sum of heat delivered in the condenser and heat absorbed in the evaporator. The heating and system COP is given by Eq. 5 and 6, respectively, which uses Eq. 4 and 3, respectively. Q evap,r e f = m r e f (h 1 − h 4 )
(3)
Q cond,r e f = m r e f (h 2 − h 3 )
(4)
C O Pheating = C O Psys =
Q cond,r e f E total
Q cond,r e f + Q evap,r e f E total
(5) (6)
5 Hot Air Generation Numerous industries require hot air for drying applications. An experimental setup was built to generate hot air and was supplied to a chamber having a dimension of 1.31 × 1.53 × 1.5 m at a temperature of around 100 °C. Hot water at 120 °C was first generated using the developed HTHP. This hot water was passed through a fin and tube heat exchanger which transferred the heat from water to air. The heat exchanger has 40 number of tubes with 6 rows. The developed HTHP requires a source temperature of 60 °C. Hence, another low temperature heat pump (LTHP) of
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Fig. 3 Experimental setup of hot air generation using HTHP
40 kW of heating capacity with a heating COP of 4.3 was used to generate water at 60 °C. R417A refrigerant was used in the LTHP. An air blower at a rated flow rate of 1.1 m3 /s was installed along the duct of cross section 0.4 m × 0.4 m. Figure 3 shows the experimental setup for hot air generation. Calibrated k type thermocouple was installed in the chamber which was measured and recorded using a KEYSIGHT data aquisition system (DAQ 970A). A detailed experiments and analysis is yet to be performed to obtain the drying characteristics of various materials and the energy, exergy, economic and environmental benefits of using the HTHP in hot air generation.
6 Results and Discussion The performance of the compressor is assessed by the compressor discharge temperature. The discharge temperature affects the solubility and viscosity of the lubricant. The manufacturer has set a maximum limit of 150 °C and 60 °C for the maximum discharge and suction temperature, respectively. Suction temperature is a crucial parameter that affects the compressor’s performance. RFL68FA oil was used in the compressor, and its average temperature remained below 100 °C. Although the oil’s color changed slightly after a few months of operation, the compressor’s performance was not affected. However, detailed analysis of the oil must be performed in the future. The experiment’s average suction and discharge temperatures were 48.14 °C and 124.4 °C, respectively, and the simulations’ temperatures were 50.17 and 131.1 °C. Both were within the safe limits specified by the compressor manufacturer. The maximum hot water outlet temperature observed in the experiments was 120.83 °C. Pressure sensors were installed in both the low and high-pressure sides of the compressors to measure the pressure. For added security, low and high-pressure switches were installed. The high-pressure values, on the other hand, were found to be sensitive to small fluctuations in the flow rate of the source and sink water, and occasionally exceeded the safety limits, causing the compressor to trip. As a result, maintaining a consistent flow rate of the source and sink is critical for ensuring the
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Fig. 4 shows the suction and discharge temperature and pressure values
heat pump’s safe and efficient operation. Figure 4 shows the suction and discharge temperature and pressure values. The experimental and simulation values were found to be consistent. There is some variation in the pressure values compared to the simulation due to the position of the pressure sensor and pressure drop in downstream components. The maximum discharge pressure measured during operation was 20 barg, which was within the manufacturer’s maximum limit of 25 barg. During the experiments, the maximum pressure ratio recorded was 11.74, which was less than the manufacturer’s specified maximum of 17. The consistency of experimental and simulation pressure and temperature values suggests that simulations can accurately predict compressor performance over a wide range of operating conditions beyond the limits of the experimental setup. Based on the experimental results of pressure and temperature, the total compressor efficiency and isentropic efficiency have been calculated. On average, the total compressor efficiency was found to be 63%, while the isentropic efficiency was 71.7%. The difference between these values is due to losses in the electric motor, frequency converter, transmission, and heat. Figure 5 illustrates the compressor efficiencies heating COP and compressor power for various source temperature. Notably, the high-temperature premarket scroll compressor efficiencies were found to be comparable to those of existing industrial standard heat pump compressors. The heating COP of the heat pump is influenced by the source temperature. When the source temperature is lowered, the temperature lift increases, causing the compressor to consume more power. Consequently, the heating COP of the heat pump decreases. Note that the study did not take into account the power consumption of the circulating water pumps, as the same pumps used in the existing process were utilized for the pilot demonstration. The focus of the study was on the performance of the compressor. During the pilot testing, the HTHP was tested for 24 h of continuous operation using the available condensate water as the source. Figure 6 shows the variation of the source and sink temperatures during the continuous operation. During the 24-h continuous operation of HTHP the available condensate water was used as the source. The system’s performance was stable, with an average
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Fig. 5 Experimental results of compressor efficiencies, heating COP and compressor power Fig. 6 Variation of source and sink temperature during continuous operation
heating COP of 2.27 and an average compressor power consumption of 26.8 kW was recorded. However, there were some fluctuations in the system’s performance due to interruptions in the supply of condensate water at the desired temperature.
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6.1 Emission Study Heat pumps are recognised as a potential decarbonization solution, but their effectiveness is dependent on the emission factor of the country where they are installed or whether the location of installation has a green source of electricity production. Regardless, electrification is the first step towards decarbonization, and heat pumps can be a viable option. To compare CO2 emissions, HTHP with waste heat of 60 °C as source were compared to 85% efficient fossil-fired boilers. CO2 emissions were discovered to be dependent on the country’s emission factor. The European Union, Germany, Norway, and India were found to have emission factors of 276 gCO2 /kWh, 450 gCO2 /kWh, 22 gCO2 /kWh, and 790 gCO2 /kWh, respectively [13, 14]. Figure 7 depicts CO2 emissions per kW of heating capacity for various countries and fuels. In all countries studied, the HTHP emitted 55.3% less CO2 than electric boilers. Due to the current high emission factor, replacing LPG would increase carbon emissions by 49% in India. The HTHP was found to emit 55.3% less CO2 than electric boilers in all countries studied. In countries like Norway, where electricity generation is mainly from hydropower, HTHP would reduce emissions by at least 95, 14, and 47% in Norway, Germany, and the European Union (EU), respectively, by replacing LPG. However, in India, replacing LPG with HTHP would increase carbon emissions by 49% due to the high emission factor in the country. It is important to note that “greening the grid” is a more feasible solution compared to finding alternatives for combustion sources. Despite the slightly higher emissions from HTHP in India, it still has potential for the future as the country moves towards cleaner sources of electricity. Additionally, the benefits of HTHP, such as reduced energy consumption and lower operating costs, make it an attractive option for many applications. Fig. 7 gCO2 /kWh for various fuels
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7 Conclusion Finally, this study highlights the design, numerical and experimental evaluation of a 60 kW HTHP capable of producing hot water at 120 or hot air at 100 °C. The pilot scale experiments and numerical studies yielded similar results, with an average heating COP of 2.27 when using waste condensate water at 60 °C. Furthermore, the carbon emissions of any technology are heavily influenced by the emission factor of the country or location of installation. Due to its high emission factor of 790 gCO2 /kWh, the HTHP was found to emit 20.3% more carbon than diesel in India, while it has the potential to reduce carbon emissions by 57.8% when compared to the EU emission factor. When calculating the carbon emissions of HTHPs, it is critical to consider the emission factor of the country or installation location. Future research can look into the potential of HTHP for applications such as steam generation and drying. The drying properties of various products must be investigated because they have a significant potential for energy conservation and decarbonization in industries. Furthermore, additional experiments with other potential natural and synthetic refrigerants can be conducted to investigate the possibilities of performance improvement, which will increase the economic and environmental benefits of HTHP technology. Acknowledgements The authors would like to thank the management of DCM Shriram for allowing us to conduct pilot scale testing at their facilities. The authors gratefully acknowledge the Ministry of Human Resource Development (MHRD), the Government of India, and Aspiration Energy Pvt Ltd for financial assistance under grant number 35-8/2017-TS.1. The authors would like to express their appreciation to Emerson’s management for providing a pre-market sample of a high-temperature compressor. Sandeep Koundinya appreciates the PM fellowship from SERB-CII and Aspiration Energy Pvt Ltd. Sandeep Koundinya is also thankful to SERB for the international travel support.
Nomenclature Comp Cond COP E EU Evap FS h isen m Q ref sys
Compressor Condenser Coefficient of performance Electrical power (kW) European Union Evaporator Full scale Specific enthalpy (kJ/kg) Isentropic Mass flow rate (kg/s) Rate of heat transfer (kW) Refrigerant System
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Compressor suction Compressor discharge
References 1. Action, C.S.R. on C.C. and H.T.H.A. for C, COP26 Special Report on Climate Change and Health. The Health Argument for Climate Action (2021) 2. S. Koundinya, S. Seshadri, Energy, exergy, environmental, and economic (4E) analysis and selection of best refrigerant using TOPSIS method for industrial heat pumps. Therm. Sci. Eng. Prog. 36, 101491 (2022). https://doi.org/10.1016/j.tsep.2022.101491 3. N.S. Suresh, B.S. Rao, Solar energy for process heating: a case study of select Indian industries. J. Clean. Prod. 151, 439–451 (2017). https://doi.org/10.1016/j.jclepro.2017.02.190 4. E.W. Lemmon, I.H Bell, M.L. Huber, M.O. McLinden, E.W. Lemmon, H.B. Ian. M.L. Huber, M. O. McLinden, NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 10.0, National Institute of Standards and Technology (2018) 5. S. Fukuda, C. Kondou, N. Takata, S. Koyama, Low GWP refrigerants R1234ze(E) and R1234ze(Z) for high temperature heat pumps. Int. J. Refrig. 40, 161–173 (2014). https://doi. org/10.1016/j.ijrefrig.2013.10.014 6. C. Kondou, S. Koyama, Thermodynamic assessment of high-temperature heat pumps using low-GWP HFO refrigerants for heat recovery. Int. J. Refrig. 53, 126–141 (2015). https://doi. org/10.1016/j.ijrefrig.2014.09.018 7. M. Nilsson, H.N. Rislå, K. Kontomaris, Measured performance of a novel high temperature heat pump with HFO-1336mzz (Z) as the working fluid, in 12th IEA Heat Pump Conference (2017) 8. S.D. White, M.G. Yarrall, D.J. Cleland, R.A. Hedley, Modelling the performance of a transcritical CO2 heat pump for high temperature heating. Int. J. Refrig. 25, 479–486 (2002). https:// doi.org/10.1016/S0140-7007(01)00021-4 9. O. Stavset, K. Banasiak, A. Hafnar, Analysis of high temperature heat pumps applying natural working fluids, in 11th IIR Gustav Lorentzen Conference on Natural Refrigerants (2014) 10. O. Bamigbetan, T.M. Eikevik, P. Nekså, M. Bantle, C. Schlemminger, Theoretical analysis of suitable fluids for high temperature heat pumps up to 125 °C heat delivery. Int. J. Refrig. 92, 185–195 (2018). https://doi.org/10.1016/j.ijrefrig.2018.05.017 11. D. Medeiros, DWSIM (2021) 12. K. Tangsriwong,P. Lapchit, T. Kittijungjit, T. Klamrassamee, Y. Sukjai, Y. Laoonual, Modeling of chemical processes using commercial and open-source software: A comparison between Aspen plus and DWSIM. IOP Conf. Ser. Earth Environ. Sci. 463 (2020). https://doi.org/10. 1088/1755-1315/463/1/012057 13. D.H. Kang, S.I. Na, J.W. Yoo, J.H. Lee, M.S. Kim, Experimental study on the performance of a steam generation heat pump with the internal heat exchanging effect. Int. J. Refrig. 108, 154–162 (2019). https://doi.org/10.1016/j.ijrefrig.2019.09.003 14. CEA, CO2 Baseline Database for the Indian Power Sector, User Guide Version 17.0, October 2021, Government of India Ministry of Power (2021)
Application of 1D Numerical Transient Compressor Model to Optimize Performance of Vapor Injection Heat Pump System Marek Lehocky, Nils-Henning Framke, Arne Heinrich, Gautham Ramchandran, and Rodrigo Aihara
Abstract In heat pump systems operating with high pressure ratios and extended environmental conditions, vapor injection compressor systems are used in order to increase the system COP and lower the operating expenditure. Such systems consist of a two-stage throttling process in which injection gas for the compressor is provided via an internal heat exchanger or a flash tank. To maximize COP further, such heat pump systems offer multiple opportunities for optimization ranging from matching of an existing compressor to a specific heat pump system over compressor design modifications to expansion control strategies. Exploring the large design space that can be available to improve the overall system performance is only feasible by means of simulation considering economic constraints. Often though simulation tools focusing only on the macroscopic system performance are steady state and driven by empirical correlations and measurement data or focus on the compressor unit only. This approach however neglects possible dynamic system and compressor interactions that could lead to performance diminish. This holistic system optimization methodology can be implemented in the commercial simulation software GT-SUITE. In this study, a transient capable, detailed 1D scroll compressor model is integrated with a transient system model to demonstrate the capability of simulation methodology for the optimization of vapor injection heat pump systems. The developed model is compared to currently available empirical models to investigate the benefits of the proposed methodology. Keywords Compressor · Simulation · Heat pump · Optimization · Scroll
M. Lehocky (B) · N.-H. Framke · A. Heinrich Gamma Technologies GmbH, Stuttgart, Germany e-mail: [email protected] G. Ramchandran · R. Aihara Gamma Technologies LLC, Westmont, USA © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_28
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1 Introduction The demand for residential heat pump systems has been growing significantly in the past years. The increased energy prices together with governmental subventions are considered to be the main effects driving the market growth. Together with the tightened governmental regulations on non-natural refrigerants, this increases the pressure on the heat pump systems providers to deliver more efficient systems in a shorter time. To increase the operational range and efficiency of heat pump systems, vapor injection systems have been established recently. Previous studies have shown, that by utilizing it, the Coefficient of Performance (CoP) can be increased by 4–30% depending on the boundary conditions, refrigerant, and types of vapor injection [6–8]. Scroll compressors are being used often in heat pump systems, providing benefits in performance and silent operation. When used in vapor-injected systems, the position and size of the vapor injection port needs to be defined. These parameters define the injection port mass flow rate. Numerical simulation has proven to be an integral part of the compressor and heat pump system development process allowing accurate predictions of the system performance under various operating conditions [7]. For the system optimization however, often compressor and refrigeration system are being considered separately which potentially neglects component interaction effects leading to efficiency loss in the final product. In this study, an optimization process has been developed that connects a detailed one-dimensional compressor model to the one-dimensional heat pump system model. The commercial software package GT-SUITE has been used to optimize the compressor geometry in terms of injection port size and position to achieve the best system CoP while maintaining the target heating performance.
2 Compressor Model The vapor-injection model used in this optimization study is assembled from a geometry generation and discretization engine that is feeding the required input to a one-dimensional flow simulation of the compressor.
2.1 Geometry Generation The geometry for the symmetrical scroll wrap shape is mostly derived from [2] using the two-arc method to define the wraps tip geometry in the discharge region. The geometry of the scroll wraps is defined by points along the involute where: x = rb (cos φ + (φ − φ0 ) sin φ), y = rb (sin φ + (φ − φ0 ) cos φ)
(1)
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with base circle radius rb , involute angle φ and the starting angle φ0 being located on the base circle radius. The thickness of the scroll wrap ts governs the starting angle of the outer and inner warp race respectively: ts = rb φi,0 − φo,0 .
(2)
For the one-dimensional transient simulation of the scroll compressor, chamber volumes and a number of flow areas have to be known as a function of the machines chamber volume angle θc . We define the θc in the interval [0, 2π N V ] where N V is the number of distinct volumes separated by the contact points of fixed and orbiting scroll. N V is similar to the maximum number of the compression chambers os −π NC,max = f loor ( φie −φ ) in [2]. In difference to [2] we do not strictly differentiate 2π between compression and discharge region for means of volume and area derivation and therefore N V = Nc,max + 1 for both fixed and orbiting scroll. Due to the symmetrical geometry N V exists for orbiting and fixed scroll respectively. Figure 1 shows an example of the profiles that are used by the one-dimensional model. The volume, suction, discharge and vapor port area as well as the fixed to orbiting scroll communication area profiles are derived from a three-dimensional geometry using GT-SUITE geometry preprocessor. As demonstrated in [4] the preprocessor utilizes a geometry kernel and different search and geometry identification methods to process arbitrary scroll wrap and especially port geometries. The creation of the required three-dimensional geometry for the GT-SUITE preprocessor begins with the calculation of the scroll wrap points. The actual three-dimensional geometry of the scroll wraps as well as the geometry of discharge and vapor ports are then created programmatically using the CadQuery 2 package from [3]. Figure 2 shows a representation of a sample geometry created during the optimization process. For this work, we focus on driving the geometry creation based on the compressor displacement Vdisp to satisfy the heat pump systems heating capacity target. The
Fig. 1 Volume of one chamber and flow areas of the scroll compressor
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Fig. 2 Example of the parametrically created CAD geometry
vapor port location is optimized to maximize the systems COP. All geometrical quantities required to build a three-dimensional parametric representation of a geometry variant need to be calculated based on the compressor displacement. We use ts = 5 mm and follow the assumptions and methodology for a minimal leakage scroll wrap geometry presented by Bell et al. in [1] to calculate the base circle radius rb , scroll height and other required quantities.
2.2 1D Dynamic Flow Model Within GT-SUITE the compressible 1D Navier–Stokes equations are solved at each sub-volume. This includes the conservation of mass, momentum and energy at each time step. Additionally, the conservation of the species is also given throughout the system. For the discretization of the system a staggered grid approach is applied, meaning the scalar variables are solved at the center of each sub-volume and vector quantities at the boundaries between the sub-volumes. For the compressor model in Fig. 3 each chamber, the inlet and outlet and volumes distributing from the vapor injection line to the ports in fixed and orbiting scroll are solved as those sub-volumes. The thermodynamic state at all boundaries is either imposed or dynamically created by a connected vapor compression system. The time integration was done using a variable timestep size explicit Euler scheme to resolve θc and accordingly, the chamber volume and area changes at about one degree increments. The fluid properties of the refrigerant are calculated by utilizing. NIST REFPROP which ensures the correct properties for the liquid, two-phase, gaseous or supercritical region.
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Fig. 3 Model map representation of a compressor model in GT-SUITE, consisting of the suction boundary conditions and volumes (blue), the vapor injection boundary condition and geometry (cyan), the compression chambers of fixed and orbiting scroll (black) and the discharge volumes and boundary conditions (red)
2.3 Vapor Injection Port Geometry Optimization The parametrical scroll geometry is used for the optimization of compressors with candidate displacements. The geometry creation is flexible to change any parameter changing the scroll wrap and tip geometry or port. For this work, we limit the number of optimization design variables to the vapor port position φv and the total vapor port area Av,tot . Both design variables are constrained by functional requirements. The upper and lower limit of φv is constrained to ensure that for no θc the compressor chamber connected to the suction or discharge ports and the vapor injection ports. The injection port radius rv is limited by wrap thickness ts to prevent internal short circuiting of compression chambers. In difference to φv the total port area is not constrained within bounds. Instead, the geometry generator detects the condition. 2rv,tot ≥ ts and calculates the required number or ports m and port diameters rv so that Av,tot = mπrv2 . The m port injection ports are positioned using Eq. (1) with φ = φv and repurposing Eq. (2) φv,0 = φi,0 −
ts + r v . rb
(3)
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3 Heat Pump System Model The brine-to-water heat pump used in this investigation is typically for the European and German markets. It can be installed indoors and is suitable for both new construction and renovation. The data and size of the heat pump used here are based on the commercial conventional heat pump found in [9]. With a heating power of about 10 kW, it is used in single-family or two-family houses. According to EN 14511, case B0/W35 the CoP is 4.5. Based on that the vapor injection compression cycle was constructed. The operation conditions are summarized in Table 1.
3.1 System Layout: Heat Pump with Vapor Injection The heat pump system with vapor injection is shown in Fig. 4. The layout consists of a scroll compressor, condenser, thermal expansion valve, evaporator and an internal plate-type heat exchanger, often called economizer. Additionally, the refrigerant flow at the condenser outlet m˙ c is split into two paths. One goes through the first expansion valve before entering the economizer (m˙ e ). The refrigerant gets superheated and enters the injection port of the compressor. The other flow path (m˙ ev ) is further subcooled inside the economizer. After that, its pressure is reduced due to the TXV and then it flows through the evaporator and enters the compressor at the suction port. The corresponding T-s and p-H diagrams of such a system can be seen in Fig. 5. For the sake of simplicity, these results are taken from an optimized solution with the boundary conditions taken from the conventional heat pump system. The CoP has increased by about 30%.
3.2 1D Dynamic Flow Model The heat pump system schematic shown in Fig. 4 together with the boundary conditions from Table 1 is implemented in the simulation software GT-SUITE. The Table 1 Summary of the heat pump system data at B0/ W35 (EN 14511)
Quantity
Value
Refrigerant
R410A
Brine
EGL-30/70
Brine mass flow rate
2314 kg/h
Brine inlet temperature
0 °C
Water mass flow rate
1000 kg/h
Water inlet temperature
30 °C
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Fig. 4 Scheme of the heat pump system with vapor injection
Fig. 5 Operating point of the heat pump system with vapor injection; Left: T-s diagram, right p-H diagram
resulting model map is presented in Fig. 6. The model utilizes the same physics and fluid properties models discussed in Sect. 2.2 except that the implicit Euler is used for the time integration. This results in a larger time step for the system model simulation. Additionally, it includes model representations for the expansion devices and heat exchangers. The heat exchangers capture the pressure drop, the heat transfer performance and the thermal inertia of the component. Geometry type and function-specific Nusselt and pressure loss correlations are used, for which relevant quantities such as heat exchange surface areas are derived based on the geometry of the heat exchanger. The simulation model also includes controls of the heat pump system. These can control or target a specific superheat of a refrigerant stream, or
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Fig. 6 Model map representation of the heat pump system model in GT-SUITE, consisting of the condenser, evaporator, economizer, TXV, compressor control and a compressor sub-assembly (highlighted in green)
the compressor flow rate, directly or by means of compressor speed. Nevertheless, the applied control strategies are dependent on the test case and the compressor modeling option chosen. The heat pump system model in Fig. 6 is used consistently for all optimizations and tests where the direct interaction of the heat pump system and a compressor is required. The modeling fidelity of a compressor representation changes for different steps of the simulation and optimization workflow presented in this work. Therefore, highlighted compressor sub-model in Fig. 6 can consist of components imposing fixed mass flow rates per branch, a performance map of a compressor or the detailed compressor model shown in Fig. 3.
4 Compressor and Heat Pump System Optimization Loop We are proposing a simulation workflow to perform the selection of the compressor displacement and the system informed optimization of the vapor injection ports with those compressors to best match the requirements of the heat pump system under arbitrary operating conditions. The full simulation and optimization workflow is shown in Fig. 7 and consists of running the heat pump system model with different representations of the compressor. The detail of the compressor submodel is based on the information availability and runtime performance requirement of the respective step in the simulation workflow. As part of the workflow, the optimization of the vapor injection port location of the geometry-based compressor is performed. The full workflow consists of a large number of sequential simulations as well as data pre-, transfer and postprocessing
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Fig. 7 Overview of the automated simulation workflow
tasks. Therefore, the full workflow is automated using GT-SUITE ProcessMap that allows to control sequential and parallelized branches of model preprocessing, solution, optimization and postprocessing. This allows for the full workflow to run from beginning to end without any user interaction.
4.1 System Preliminary Performance Optimization Based on the described layout of the heat pump system with economizer vapor injection, the optimization loop has been started to obtain maximum CoP by varying the mass flow ratio Rsys =
m˙ e m˙ c
(4)
of the injection port, where m˙ e is the mass flow rate through economizer injected into the compressor and m˙ c the mass flow rate through the condenser. For this simulation, an idealized compressor model has been used with imposed mass flow rate for the main and injection flow and constant isentropic efficiency estimated to be 80%. The
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Table 2 Preliminary system optimization results Heat source temperature CoP Ts
ps
(°C)
(−)
(°C)
(bar) (°C) (bar) (−)
−5
4.4
−5.2 5.3
26.3 15.0
0.104 53
0
5.0
−0.1 6.3
27.5 15.4
0.096 46
5
5.6
4.9
29.4 16.3
0.082 40
7.5
Ti
pi
Rsys
Compressor displacement (cm3 )
The indices “s” and “i” represent the values at the compressor suction and injection port, respectively
compressor mass flow rate is controlled so that the target heating performance of 10 kW is reached. Optimization has been performed for several heat source temperatures, however, due to the usage of single fixed injection port in the compressor, only the design from the B0/W35 has been used further. From the system optimal operating conditions, compressor size has been derived considering fixed compressor speed of 3000 RPM.
4.2 Compressor Design Optimization The preliminary design conditions at the compressor main and vapor injection inlets as shown in Table 2 were used as boundary conditions in the detailed one-dimensional compressor model. The injection port position was optimized to reach the desired mass flow ratio. Compressors of two different displacements, 45 and 55 cm3 have been considered further to account for products available off-shelve. The optimized detailed compressor model has then been used to generate performance maps for system-level compressor model (Fig. 8).
4.3 System-Level Compressor Model For the compressor design validation in the system model, map-based compressor model is being used. In this study, main and injection compression paths are modeled in parallel. This simplifies the handling of performance data and provides advantages for the creation of performance maps while keeping the necessary accuracy. The performance data coming from the detailed compressor model are processed into tables where the compressor volumetric, isentropic and mechanical efficiency is being stored. During the system simulation, the operating point is selected based on suction temperature and pressure ratio for both main and injection branch. The map-based compressor model flow rate and discharge temperature validation data are shown in Fig. 9. The dashed lines show + 5% and − 5% difference.
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Fig. 8 Compressor performance maps
Fig. 9 Map-based compressor performance results compared to detailed compressor results
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It is apparent that while the evaporator branch flow rate and the discharge temperature can be well predicted by the map-based model, the economizer flow rate show more significant differences mainly at low flow rates.
4.4 Heat Pump System Results After integrating the map-based compressor model into the heat pump system, the final compressor choice can be made. The simulation results from the different automated simulation workflow process stages (Fig. 7) are presented in Fig. 10. In the design point, 45 cm3 compressor does not reach the desired heating performance, therefore the 55 cm3 compressor has been selected for further investigations. The heat pump system model with integrated map-based compressor model shows significantly decreased CoP compared to the idealized pre-design model. This is mainly contributed by the overestimated isentropic efficiency and neglected mechanical loss of the idealized model. At the same time, the heating capacity at the design
Fig. 10 System performance results under varying heat source temperature
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conditions is about 20% higher than the target. To further test the system performance, the simulation was performed for several off-design heat source temperatures (−10 °C, −5 °C, 5 °C). The heating capacity of the system at −10 °C is about 5% below the target. To further validate the design, detailed one-dimensional compressor model can be integrated into the heat pump system model. This provides the highest level of insight into the interaction between the compressor and the system. The results of this model are shown in Fig. 10 in violet. It is apparent that the map-based compressor model in this case is not able to completely predict the behavior of the real compressor. This can be contributed to the fact that the map-based compressor model does not take the dynamic flow conditions into account that impact the compressor itself, but also the system control response. For the low economizer flow rates also the accuracy of the map-based model in terms of flow rate prediction is limited. On the other hand, the runtime of the system with detailed compressor is significantly higher than for the map-based variant. The integrated detailed compressor model further offers the opportunity to investigate results within single compressor cycle. Figure 11 shows the injection port mass flow rates of the optimized design model standalone and the system model where detailed compressor is integrated. While the shape of the injection profile is similar for both variants, the dynamic boundary conditions in the system model contribute to different integrated mass over the cycle leading to variation in the system mass flow rate. Dynamically oscillating pressure in the economizer outlet pipe (compressor injection port inlet) is shown in Fig. 12. Compared to the constant boundary condition used in the design model this will contribute to results differences between the design point and the final system integration.
Fig. 11 Detail of vapor injection process in the design model and design model integrated in system
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Fig. 12 Pressure oscillation at different position of the economizer outlet pipe
5 Conclusions In this study, a process has been developed allowing optimization of scroll compressor vapor injection port geometry based on the performance demand of the system where the compressor is being used. This allows better matching of the compressor design to the system where the compressor is integrated. The process is integrated in the single simulation software GT-SUITE allowing a direct exchange of data between different process steps and a full automation without user-interaction needed during the process. Varying compressor model fidelity levels have been utilized at different process stages to ensure necessary results accuracy at reasonable simulation speed. In the investigated operating conditions, the map-based compressor model has shown limited accuracy in terms of economizer flow rate. Further investigations will be needed to reduce the accuracy loss. The integration of one-dimensional compressor and system models has been introduced to validate previous results and increase the accuracy of the system performance predictions. While this level of simulation is computationally intensive, it has been shown that it allows valuable insights in the compressor and system interaction which can be utilized to further improve system efficiency.
References 1. I. Bell, E. Groll, J. Braun, T. Horton, Derivation of optimal scroll compressor wrap for minimization of leakage losses, in International Compressor Engineering Conference, paper 2111 (2012) 2. I. Bell, Theoretical and Experimental Analysis of Liquid Flooded Compression in Scroll Compressors (Publications of the Ray W. Herrick Laboratories, 2011), paper 2 3. CadQuery 2 Homepage. https://cadquery.readthedocs.io/en/latest/. Last accessed 2023/02/10
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4. J. Harrison, S. Koester, R. Aihara, D. Ratner, From CAD to 1D: a direct approach to modeling scroll compressors with multi-physics simulation, in International Compressor Engineering Conference, Paper 2539 (2018) 5. S. Ramalingam, A. D’Amico, M. Strand, M. Rutan, G. Ramchandran, Numerical prediction of gas pulsation in a scroll compressor using 1-D modeling: a validation study based on AHRI Standard 530-2011, in International Compressor Engineering Conference, Paper 2770 (2022) 6. X. Xu, Y. Hwang, R. Radermacher, Control strategy of vapor injection cycle, in International Refrigeration and Air Conditioning Conference, Paper 1066 (2010) 7. D. Kim, et al., Optimization of the injection-port geometries of a vapor injection scroll compressor based on SCOP under various climatic conditions. Energy 135, 442–454 (2017) 8. D. Lumpkin, N. Spielbauer, E. Groll, Performance measurements and mapping of a R-407C vapor injection scroll compressor. IOP Conf. Ser. Mater. Sci. Eng. 232, 012049 (2017). https:// doi.org/10.1088/1757-899X/232/1/012049 9. STIEBEL ELTRON WPF 10 cool—232918, Bedienung Und Installation, p. 64. https://www. stiebel-eltron.com/en/home.html. Downloaded 04 Jan. 2023 from https://www.manualslib.de/ manual/699150/Stiebel-Eltron-Wpf-5-E.html
Reciprocating Compressors
Feasibility Study on Two Novel Lubricants for a Carbon Dioxide Reciprocating Compressor Xin Ding, Justin Kontra, Frank-Olaf Mähling, Eckhard Groll, and Davide Ziviani
Abstract In recent years, increasing research efforts have been made on modeling and testing positive displacement compressors with low global warming potential (GWP) working fluids and their systems. The ongoing HFC phase-down is forcing the HVAC&R industry to investigate low-GWP refrigerant alternatives as well as natural refrigerants (e.g., water, hydrocarbons, .CO2 ). The transition to low-GWP and natural refrigerants requires research efforts on cycle configurations and components including compressors. More specifically, most of the existing positive displacement compressors employed in HVAC&R systems rely on lubricant oils to ensure correct operation and performance. To better understand the potential research directions in lubricant oils, a reciprocating compressor with .CO2 as refrigerant was selected as the case study to investigate alternative lubricant oil formulations. In this study, a baseline POE reference and two alternative lubricant oils were evaluated on a transcritical .CO2 reciprocating compressor with respect to performance enhancement and potential issues and challenges. A hot gas bypass test stand was used to carry out the experimental studies. A total of 66 steady-state data points were collected, and control tests were performed after each alternative oil formulation to ensure correct operation of the compressor. The alternative lubricant oils showcased comparable performance data to the baseline lubricant oil under a wide range of operating conditions without sign of decomposition and wear. X. Ding (B) · E. Groll · D. Ziviani Purdue University, West Lafayette IN 47906, USA e-mail: [email protected] E. Groll e-mail: [email protected] D. Ziviani e-mail: [email protected] J. Kontra Evonik Oil Additives USA Inc., Horsham PA 19044, USA e-mail: [email protected] F.-O. Mähling Evonik Operations GmbH, Darmstadt 64293, Germany e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_29
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Keywords .CO2 · Reciprocating compressor · Lubricant oil · Energy efficiency
1 Introduction In recent years, increasing research efforts have been made on modelling and testing positive displacement compressors with low global warming potential (GWP) working fluids and their systems. The transition to low-GWP and natural refrigerants requires research efforts on cycle configurations and components including compressors. More specifically, most of the existing positive displacement compressors employed in HVAC&R systems rely on lubricant oils to ensure correct operation and performance. Several research studies can be found in literature that investigated the impact of lubricants in a .CO2 refrigeration system both numerically and experimentally and tried to identify the best-fit lubricant for the .CO2 system. Hauk and Weidner [1] reported experimental measurements for .CO2 -lubricant binary mixture solubility and fluid dynamic properties in a conventional refrigeration system. Pensado et al. [2] conducted an experimental measurement of viscosity and density of binary mixtures of .CO2 -PEC5, .CO2 -PEC7, and .CO2 -PEC8. Dang et al. [3] reported experimental tests of lubricant impacts on heat transfer and flow patterns for PAG, PVE, and ECP oils in a supercritical .CO2 system. Wang et al. [4] experimentally studied the flow behaviors of .CO2 and PAG-68 mixture during the start-up and the shut-down process. Stockel et al. [5] conducted experimental tests of a groups of binary and ternary refrigerant-lubricant mixtures, which includes .CO2 and POE VG68 oil, to study the interaction properties and impacts on heat transfer. Most of the works were investigating the refrigerant-lubricant thermodynamic and fluid dynamic properties as well as the impacts of different lubricant formulations on heat transfer. The systematic energy analysis and impacts on compressor performance were, however, less mentioned. To better understand the potential research directions in lubricant oils, this study aims to assess and identify the current state-of-the-art of lubricants employed in .CO2 compression systems for commercial applications with respect to the system performance. A reciprocating compressor with .CO2 as refrigerant was selected as the case study to investigate alternative lubricant oil formulations. Three types of lubricant oil formulations were evaluated on a transcritical .CO2 reciprocating compressor with respect to performance enhancement and potential issues and challenges.
2 Experimental Setup 2.1 System Descriptions A hot gas bypass setup with .CO2 as refrigerant was used to conduct the experiments. The schematic of the system with main components and locations of the sensors
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Fig. 1 Piping and instrumentation diagram of the hot gas bypass system
is shown in Fig. 1. Two manually controlled needle valves of different sizes were installed in parallel in the bypass line (N3 and N4) and the condensing line (N1 and N2) as expansion devices. Mass flow rates and mixing ratio between condensing line and bypass line were also controlled by these four valves. The cooling water was supplied by the building at a constant temperature of 11.2 .◦ C. A stainless-steel oil separator and a high-pressure oil gauge with side glass were installed vertically after the bypass line needle valves. The compressed .CO2 -oil mixture undergoes phase separation in the oil separator. The oil level in the compressor was monitored by three sight glasses on the compressor and was maintained by the oil management module installed at the compressor sump to prevent oil starvation during compressor operation. The compressor used was a constant speed, transcritical.CO2 four-cylinders reciprocating compressor. The nominal displacement of the compressor was 53.09 cm.3 and the nominal rotating speed was 60 Hz. The factory-charged lubricant type was POE reference. The compressor operated at condensing pressures between 50 and 110 bar and evaporating pressures between 20 and 51 bar. In the rest part of the content, sc represents subcooling, sh represents superheating, dis represents discharge, suc represents suction, disp represents displacement, .ηoi is overall isentropic efficiency, and .ηvol is volumetric efficiency.
2.2 Instrumentation The sensors installed in the experimental setup included 8 T-type thermocouples, 5 pressure transducers, 1 mass flow meter and 1 wattmeter. The mass flow rate of the refrigerant in the bypass line, the power consumption of the compressor, pressures of the refrigerant, and temperatures of the refrigerant as well as the cooling water in the system were measured. The measureing range and uncertainty of the sensors are listed in Table 1 as well as the derived measurements in Table 1b. The thermocouple uncertainty is .± 0.5 K or .±0.4%, whichever is greater. An Agilent Agent 34980A DAQ unit was used to collect voltage signals from the sensors with a sampling
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Table 1 Uncertainty of measurements in the test a Uncertainty of direct measurements Direct Mea Range 0–260 .◦ C
Temp Pres 0–172.36 bar Mass – 0–40 kW Power b Uncertainty of derived measurements Derived Mea .ΔTsc .ΔTsh .ηoi .ηvol
Uncertainty .±
0.5 K or .± 0.4% 1.0% of reading .± 1.0% of reading .± 2.0% of reading
.±
Mean uncert 1.1 K .± 1.1 K .± 1.75% .± 1.1% .±
frequency of 1 Hz. The digital signals were collected and processed in LabVIEW 10.0 software1 . The CoolProp2 plug-in was used in the LabVIEW project to retrieve thermophysical properties of .CO2 and process the data.
3 Data Collection and Processing The overall isentropic efficiency and volumetric efficiency were selected as the performance indicators of the compressor. Formulas of the overall isentropic and volumetric efficiency are given in Eqs. 1 and 2, respectively. m˙ · (h dis,s − h suc ) W˙ m˙ · ρsuc (Psuc , Tsuc ) = Vdisp N
η =
. oi
η
. vol
(1) (2)
As reported in Table 2, four groups of tests were conducted to investigate the impacts of two new oil formulations on the compressor operation with respect to the baseline oil. A total of 88 steady state points was collected with 22 points gathered from each testing group. The 22 points were selected on a basis of the points provided by the compressor map. All four groups were charged with 1600 cm.3 of lubricant oil. Two control groups were charged with reference POE type oil whereas other two groups utilized two novel lubricants which are combinations of a base oil and an acronym polyalkylmethacrylate (PAMA) oil, respectively. The PAMA is shear stable and has passed ASHRAE-97 screening. 1 2
https://www.ni.com/en-us/shop/labview.html. http://www.coolprop.org/.
Feasibility Study on Two Novel Lubricants for a Carbon Dioxide .. . . Table 2 List of lubricants used during the testing Group Oil component 1 Oil component 2 Name 1 2 3 4
POE#1 POE#2 POE#1 PAO#1
PAMA#1 PAMA#2
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KV at 40 .◦ C .ρ at 15 .◦ C in cSt in kg m.3
Reference Formulation 1 Reference repeat Formulation 2
66.6 69.8 66.6 65.8
890.0 901.1 890.0 899.2
Table 3 Charging amounts of subgroup A, B, and C in four test groups Subgroups Sets Charging amount A B C
20 bar .< Pevap < 27 bar 27 bar .< Pevap < 35 bar 35 bar .< Pevap < 45 bar
31.03 bar 38.61 bar 45.85 bar
The testing capabilities were limited by two major factors: • The cooling water was supplied by the laboratory water pump throughout the entire laboratory. The condensing temperature and pressure in the condenser were therefore fixed at 14 .◦ C and 4965 kPa. The pressure drop between the suction port and the condenser outlet was insufficient to provide desired temperature drop at some extreme cases. The issue could cause large superheat (.> 40 K) and compressor overheating at high condensing pressure conditions. A solution to the issue was increasing the refrigerant charging amount to enlarge the maximum control range of the superheat by providing larger cooling capacity in the condenser. • Although charging more refrigerant helped maintaining a desired superheat and suction temperature, it became challenging for discharging state achieving desired pressure, especially for points that have low condensing pressure. A solution to this issue was to use different refrigerant charging amount in different operating conditions. Therefore, the 22 points were split into 3 subgroups with different refrigerant charging. The superheat was maintained at around 11 .◦ C at most of the points. Table 3 shows the testing range of the subgroups in each test and their charging amount.
4 Results and Discussion 4.1 Consistency of Operating Conditions To conduct a meaningful comparison across the oil formulations, consistent and repeatable testing conditions must be achieved. To this end, compressor suction
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(a) Tsuc
(b) Psuc
(c) Tdis
(d) Pdis
(e) m ˙
˙ (f ) W
Fig. 2 Operation condition comparisons between Test 2, Test 3, and Test 4
and discharge temperatures and pressures, mass flow rates and power consumptions were compared for each test point. Figure 2 provides an overview of all the operating conditions for each oil formulation. During Test 1 of the base oil, the discharge temperatures of the Test Group 1 were higher than 20 .◦ C in the high evaporating pressure range B and C (Table 3) due to insufficient refrigerant charging amount. The operation conditions were not aligned with normal operation causing potential damages to the compressor. Therefore, the data of Test 1 was dropped. Experimental comparisons were mainly conducted with the remaining three test groups. Figure 2 shows the comparison of operation conditions between Test 2, Test 3, and Test 4. The measured variables have been plotted with the uncertainty bands for all the points. For most of the points, suction pressures, discharge pressures, mass flow rate, and power consumption are overlaid within the uncertainty band. In general, the consistence between operating conditions of Test 3 and Test 4 is better than Test 2 versus Test 3. For Test 2 and Test 4, errors of pressures, mass flow rate and power consumption are negligible for most of the points, whereas the difference of temperatures were relatively large for a few points. Overall, the differences for all measured variables were smaller than 7.5%. It can be noticed that the relative errors of temperature generally are larger than that of pressures and power consumption. This is because the temperature was impacted more directly by the ambient than other variables and the system was not completely thermal-isolated from the ambient, which caused a noticeable heat flux between tubes and the ambient. Another reason is that temperature is more sensitive to fine tuning while operating the system to achieve the desired operating point. The mass flow rate is almost identical for all three tests in each point, which indicates that the charging amounts of the refrigerant
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were consistent. In general, suction and discharge temperatures at a few points in Test 2 are higher than the other two tests. Overall, based on the comparison analysis, it can be concluded that the operation conditions are consistent for all the experiment test groups.
4.2 System Performance Comparisons The compressor performance for each test group was evaluated using overall isentropic efficiency and volumetric efficiency as two critical indicators. More specifically, uncertainty propagation calculations were performed for the two indicators by Engineering Equations Solver (EES)3 to investigate the variances in indicator calculation results. Comparisons were made between every two test groups to restrict the objects and avoid over-complexity. In the following sub-sections, uncertainty propagation results were firstly introduced, then comparisons and analyses between test groups were explained in details. Overall isentropic efficiency The overall isentropic efficiency uncertainty is propagated from 6 variables: inlet temperature and pressure, outlet temperature and pressure, power consumption, and mass flow rate. The 6 variables were fed into an EES model to perform a break-down calculation of the uncertainty in the results. The pressure measurements contributed around 35% of the uncertainty, which is made up by suction and discharge pressure for approximately 20% and 15%, respectively. In addition, mass flow rate and power consumption measurements uncertainty was approximately 10% and 55% of the total uncertainty, respectively. The temperature measurements only accounted for less than 1% of total uncertainty. The overall isentropic efficiencies of each group were plotted against pressure ratios. Figures 3 and 4 present the comparisons between every two test groups. The 22 points were categorized into 7 groups by evaporating pressure. Each group was differentiated by a color bar in the plot. The surface color of markers indicates different evaporating pressure groups, and the edge color indicates different test groups. The uncertainty of each point was indicated by vertical error bars. Figure 3 shows the overall isentropic efficiency comparison between Test 2 and Test 3. The pressure ratio ranges from 1.6 to 3.9. The overall isentropic efficiency varies from 51 to 59%. It can be seen from Fig. 3 that the differences between the two test results are smaller than the uncertainty bars at every point, which indicates that the compressor performances in the two tests are very close. Although no significant performance gap is observed, a consistence can be found throughout the comparison that Test 3 overall isentropic efficiency are higher than Test 2. Similar results can also be found for the comparisons of Test 3 versus Test 4 and Test 2 versus Test 4 in Fig. 4, respectively. Almost all differences are smaller than the acceptable uncertainty range. In general, the differences between Test 3 and Test 4 3
F-Chart Engineering Equation Solver (EES): https://fchartsoftware.com/ees/.
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Fig. 3 Pressure ratio versus overall isentropic efficiency between Test 3 and Test 2
(a) ηoi B2F 2
(b) ηoi F 1F 2
Fig. 4 Pressure ratio versus overall isentropic efficiency between Test 3 and Test 4, and Test 2 and Test 4
are smaller comparing to the differences between Test 2 and Test 3. The differences between Test 2 and Test 4 are around 0.5–1% respectively, which is the smallest in the three compared pairs. Every point in Test 4 is lower than that in Test 3 at the same pressure ratio, while the differences between Test 3 and Test 4 do not have a consistency. It can be concluded that overall isentropic efficiency difference between the three groups are very small (around 0.5–1.5%), and the three tested oils are compariable to each other. Volumetric efficiency Uncertainties in volumetric efficiency of each test point is directly affected by measurements of mass flow rate and inlet specific volume, which is a function of the inlet temperature and pressure. The three variables were included into the EES model for analyses of uncertainty contributions to the volumetric efficiency. The largest uncertainty contribution comes from inlet pressure measurements,
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Fig. 5 Pressure ratio versus volumetric efficiency between Test 2 and Test 3
which are around 60% of the total uncertainty. Mass flow rate measurement contributes around 40% of total uncertainty. The inlet temperature measurement only builds up 1–2% of the total uncertainty. Figure 5 shows the volumetric efficiency comparison between Test 2 and Test 3. The pressure ratio and volumetric efficiency range from 1.6 to 3.9 and from 65.1% to 80.4%, respectively. Test 2 results are almost identical to Test 3 results when pressure ratios are lower than 2.8. In subgroups that evaporating pressures are 20 and 23 bar, Test 2 points are slightly lower than Test 3 points. Whereas, for evaporating pressure higher than 23 bar, the results of two test groups are almost overlapped. This suggests that Test 2 and Test 3 have a comparable impact on compressor volumetric efficiency in low pressure ratio range (.< 2.8), while Test 3 performs slightly better Test 2 in high pressure ratio range (.> 2.8). Figure 6a shows volumetric efficiency comparisons between Test 3 and Test 4. The pressure ratio and volumetric efficiency in the two groups range from 1.6 to 3.9, and 65.4% to 80.4%, respectively, which are close to the comparison results of Test 2 and Test 3. The efficiency differences between the two test groups are generally larger in region where pressure ratio is higher than 2.6 and very close in region where pressure ratio is lower than 2.6. In subgroups with evaporating pressure smaller than 31 bar, the efficiency differences between the two test groups are relatively noticeable. Whereas the efficiency differences between the two test groups are negligible in subgroups with evaporating pressure larger than 31 bar. This suggests that performance of Test 4 is comparable to Test 3 when pressure ratio is smaller than 2.6 but slightly lower when pressure ratio is higher than 2.6. The comparisons between Test 2 and Test 4 can be found in Fig. 6b. The volumetric efficiency varies from 65.2 to 79.7%. It is noticed that the distribution of the points are more compact between Test 2 and Test 4 comparing to previous pairs. The volumetric efficiency difference between the two test groups is negligible. Points of the two test groups are overlapped in every evaporating pressure groups. The results suggest that Test 2 and Test 4 can be considered as identical regarding to impacts on compressor volumetric efficiency.
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(a) ηv B2F 2
(b) ηv F 1F 2
Fig. 6 Pressure ratio versus volumetric efficiency between Test 3 and Test 4, and Test 2 and Test 4
5 Conclusions In this study, experimental studies were conducted investigating the impact of lubricant oil formulations on compressor performance with .CO2 as working refrigerant. Four groups of experimental tests were conducted on a transcritical .CO2 reciprocating compressor to evaluate the impacts of two new designed lubricants on compressor performances. Two tests were performed with POE reference oil as reference groups and two tests were performed using two new formulated oils, 1 and 2. The composition of the new oil formulations was not optimized yet. Critical comparisons were performed between each group of tests based on collected operation data such as temperature, pressure, and mass flow rate. The experimental results demonstrated that the system is capable of testing the compressor performance using different lubricants and evaluating the compatibility of lubricants with .CO2 and different compressor designs. • The operation conditions between Test 3 and Test 4 are closer comparing to Test 2. In general, suction and discharge temperatures at a few points in Test 2 are higher than the other two tests. But the differences are small in absolute values. The operation conditions can be considered consistent for each test group. • The efficiency differences between test groups are within the uncertainty variance for all points, indicating that the compressor performance of the three tests is relative close to each other. Test 2 and Test 4 performs identically. • In general, no significant performance difference was observed between the three lubricants regarding to volumetric efficiency. More specifically, Test 3 is nearly identical to Test 2 and 4 when pressure ratio is lower than 2.8 and 2.6, respectively, but slightly higher than Test 2 and 4 when pressure ratio is higher than 2.8 and 2.6, respectively. Test 2 and Test 4 are consistently comparable throughout all conditions with respect to volumetric efficiency.
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• The additional lubricant component in Test 2 and 4, Poly(alkyl)methacrylate, did not cause any harm to compressor operation. Steady state conditions were achieved as quickly as with the reference fluids. The new lubricant formulations were fully compatible and no accumulation of substance took place in any part of the system.
References 1. A. Hauk, E. Weidner, Thermodynamic and fluid-dynamic properties of carbon dioxide with different lubricants in cooling circuits for automobile application. Ind. Eng. Chem. Res. 39(12), 4646–4651 (2000) 2. A.S. Pensado, A.A. Padua, M.J.P. Comuñas, J. Fernandez, Viscosity and density measurements for carbon dioxide+pentaerythritol ester lubricant mixtures at low lubricant concentration. J. Supercrit. Fluids 44(2), 172–185 (2008) 3. C. Dang, K. Hoshika, E. Hihara, Effect of lubricating oil on the flow and heat-transfer characteristics of supercritical carbon dioxide. Int. J. Refrig. 35(5), 1410–1417 (2012) 4. D. Wang, Z. Zhang, B. Yu, X. Wang, J. Shi, J. Chen, Experimental research on charge determination and accumulator behavior in trans-critical CO.2 mobile air-conditioning system. Energy 183, 106–115 (2019) 5. K. Stöckel, R. Nosbers, R.B. Barta, C. Thomas, Measurement of vapour pressure, miscibility and thermal conductivity for binary and ternary refrigerant lubricant mixtures in the context of heat pump tumble dryers. Int. J. Refrig. (2023)
Numerical Analysis of a Vapor-Injected Reciprocating Compressor for a Multi-evaporator Domestic Refrigerator/Freezer Application Changkuan Liang, Haotian Liu, Davide Ziviani, James E. Braun, and Eckhard A. Groll
Abstract Domestic refrigerators account for ~6% of the energy consumed worldwide and mainly rely on vapor compression cycles to operate. To enable smart and versatile systems, advanced cycle architectures are necessary to optimize their operation and reduce energy consumption. In this paper, a modern threeevaporator domestic refrigerator/freezer using R600a as refrigerant is investigated. To enhance the performance of the cycle, a variable-speed vapor-injected reciprocating compressor has been analyzed and integrated into the cycle architecture. Initial cycle modeling results showed a 12.9% decrease in power consumption. To evaluate additional performance improvements, a detailed mechanistic compressor model of the baseline variable-speed compressor was developed and validated with experimental data. Next, a vapor-injection line was added to the compressor model as an additional flow path to the compression chamber. The injection line has been modeled as a tube connected to an opening on the cylinder wall, which is uncovered during the compression stroke. The injection tube is controlled by a fast-acting solenoid valve to separate injection and suction flow for the compressor. Parametric studies have been carried out to assess the effects of injection timing and injection port diameter on power consumption and overall isentropic efficiency with respect to the baseline compressor. It was found that vapor-injection in the reciprocating compressor can reduce specific work required by up to 10.7%. Based on parametric studies, opening time of the fast-acting solenoid valve directly impacted the compressor efficiency and mass flow rate. An optimal design of the compressor exists by careful selection of the pressure inside the cylinder before injection to reach maximum efficiency. Keywords Reciprocating compressor · Domestic refrigerator/freezer · Vapor injection · Compressor optimization
C. Liang (B) · H. Liu · D. Ziviani · J. E. Braun · E. A. Groll Ray W. Herrick Laboratories, Purdue University Mechanical Engineering, West Lafayette, IN, USA e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_30
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1 Introduction Domestic refrigerators/freezers are essential appliances in modern households and contribute to a significant amount of energy consumption around the world. In fact, ~6% of all energy consumed worldwide is attributed to domestic refrigerators according to the study done by Caglayan et al. [1]. High energy demand can be attributed to the large number of units running as well as low thermodynamic efficiency values (of ~15% of Carnot COP) as mentioned by Hermes et al. [2]. To reduce the energy consumption of these systems, advanced cycle architectures such as multi-stage vapor-injected cycle were considered in previous studies [3]. For instance, Liang et al. [4] investigated a triple-evaporator bypass circuit domestic refrigerator/freezer as the baseline system. By modifying a validated dynamic model of the baseline system, a multi-stage vapor injection cycle was analyzed and the average power consumption of the modified system was reduced by up to 12.9% when compared to the baseline while maintaining the same temperature set points in all the cabinets. The previous study [3] used a simplified two efficiency-based compressor model with a mixing section in between as shown in Fig. 1. In order to understand the full benefits of the proposed cycle, it is of most importance to accurately predict the vapor-injected compressor performance. In this work, a mechanistic vapor-injected reciprocating compressor model employing R600a as the working fluid was developed to be coupled with the established model for the modified multi-stage vapor injection cycle for a domestic refrigerator/freezer. The vapor-injected mass flow is controlled and separated from the suction flow by a fast-acting solenoid valve. It was identified that injection opening time of the injection flow is a key factor for overall compressor performance and a parametric study was carried out to investigate this factor. The compressor isentropic efficiency improvement was optimized and compared with the baseline compressor. It was concluded that optimization of the compressor needs to be based on the cylinder pressure when injection occurs.
2 Vapor Injection in Reciprocating Compressor To model a vapor-injected reciprocating compressor, it is important to understand the dynamics associated with both compression and vapor injection processes. In a typical suction stroke of a reciprocating compressor, the inside cylinder pressure is lower than the suction pressure to allow a reed valve to open due to a pressure difference. During the suction process, the piston reaches bottom dead center (BDC) when it is closest to the crankshaft. The piston then moves towards top dead center (TDC) and the volume of the compression chamber decreases and the pressure inside the cylinder increases. For vapor injection with multi-stage operation, the injection should occur at a point in the compression stroke where the intermediate injection pressure is close to, but greater than the cylinder pressure. One approach for
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Fig. 1 Schematic of the modified multi-stage vapor-injected cycle used in Liang et al. [4]
achieving this goal would be to locate an always-open injection port at a location that is only revealed for a fixed time period during the compression stroke. This approach has previously been developed for vapor-injected scroll compressors [5]. However, for a reciprocating compressor, when the piston is at BDC, all the area is open to the chamber and an open injection port would continuously mix injection flow and suction flow until the cylinder pressure reached the intermediate pressure and then there would back flow. For a vapor-injected reciprocating compressor, a fact-responding control valve is necessary in the injection line as shown in Fig. 2 to control the timing and duration of refrigerant injection. A good example is a fast-acting solenoid valve controlled by an electronic signal based on the angle of the crankshaft. An additional check valve should also be used in the injection line to prevent any backflow through the line if cylinder pressure is greater than the intermediate pressure.
3 Modeling Approach To accurately model the compression process of a vapor-injected reciprocating compressor, a mechanistic model was developed based on the PDSim open-source modeling platform. PDSim was developed by Bell et al. [6] and further enhanced by Ziviani et al. [7] to enable steady-periodic simulations of the performance of various compressor types, including reciprocating compressors. PDSim is coded in an object-oriented fashion within Python, where individual model elements, such as heat transfer and mass flow models, in the various compression and expansion machines are objects that can be used in a plug-and-play manner to develop an integrated compressor model. A detailed description of the PDSim framework can be found in Ziviani et al. [7].
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Fig. 2 Illustration of the compression cylinder for the vapor-injected reciprocating compressor
Vapor injection is modeled using an open system control volume method with mass and energy conservation as shown in Fig. 3. The control volume in this figure refers to the refrigerant within the compression cylinder. There are a total of three tubes connected to the control volume. The subscript tot refers to total flow exiting the control volume or the discharge flow. The subscript suc and in j refers to suction and injection flow, respectively. The inlet, injection, and outlet of the control volume are modeled using tube and flow path models. The tube and flow path models in PDSim were used to handle the pressure, heat transfer and mass flow rate calculations. The energy and mass balance convergence criteria used by PDSim take into account the additional injection flow. The mass balance of the control volume is shown in the equation below. m˙ tot = m˙ suc + m˙ in j Fig. 3 Control volume of the vapor-injected reciprocating compressor
(1)
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The energy balance of the control volume in Fig. 3 is as follows: W˙ = m˙ tot h dis − m˙ suc h suc − m˙ in j h in j + Q˙
(2)
where W˙ refers to the total rate of work entering the control volume while Q˙ is the ambient heat transfer rate from the control volume. As discussed in Sect. 2, the injection flow is controlled using a valve that opens and closes at the specified times during the compression process. To model the control valve and calculate the injection flow in the developed compressor model, the area of injection is tied to the crankshaft angle. Before the specified injection moment in the compression process, the injection area is zero in the PDSim model to simulate the valve being close. After the specified injection moment, the injection area is calculated based on radius of the injection line. The flow path model in PDSim is used to calculate the mass flow rate of a certain flow in/out of the control volume. In this study, the flow path model uses the isentropic nozzle model presented by Bell et al. [6] where the mass rate is given by: m˙ tube = Ctube Atube
√
/ pup ρup
2k 2/k (k+1)/k ( pr − pr ) k−1
(3)
where pup and ρup are the upstream pressure and density, k is the ratio of the upstream specific heat (k = c p /cv ), pr is the pressure ratio of the upstream and downstream pressure, and Ctube is a tunable flow coefficient. Tube models in PDSim are used to simulate the flow by predicting the pressure drop and the heat transfer process. As detailed in Bell et al., the flow through the tubes in a compressor is assumed to be turbulent and the friction factor of the flow is found in Church [8, 9]. The pressure drop is then calculated using the equation below: Δp = −
f G2 L 2ρ D
(4)
where f is the turbulent flow friction factor, G is the mass flux found by G = m˙ tube /Atube . The tube model handles the heat transfer of the flow by using the equation found in Gnielinski [10]. By combining the flow path model’s calculation of mass flow rate and the tube model’s calculation of heat transfer and pressure drop, the injection flow’s mass flow rate and outlet condition can be determined since the inlet condition is known. Isentropic efficiency is evaluated for the vapor-injected compressor using the method presented in Bahman et al. [11]. To calculate the isentropic work, the low stage compression process (from low pressure to injection pressure) and the high stage compression process (from injection pressure to discharge pressure) are each assumed to be isentropic but with different flow rates and an entering state to the second stage that is based on adiabatic mixing of the low stage discharge and injection flows. Based on these assumptions, the overall compression process isentropic is determined as:
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ηoa,isen
( ) m˙ suc h in j,isen − h suc + m˙ tot (h dis,isen − h in j,isen,mi x ) = W˙ comp
(5)
where m˙ suc and m˙ tot refer to suction and discharge mass flow rate. h in j,isen refers to the enthalpy at the pressure of the injection flow with the specific entropy at low stage suction. This describes the first stage compression as reversible and adiabatic. h in j,isen,mi x refers to the mixture state that begins the second stage compression. It is calculated using Eq. 6. It should be noted that the enthalpy of this point is determined based on isentropic compression in the first stage and adiabatic mixing at injection pressure. The entropy at this point must be determined using its enthalpy and pressure. It is then used to calculate the h dis,isen , the enthalpy of the refrigerant at discharge pressure after isentropic compression. W˙ el,comp refers to the total electric power consumed by the compressor. The enthalpy h in j,mi x is calculated using the below equation: h in j,mi x =
m˙ suc h in j,is + m˙ in j h in j m˙ tot
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It must be noted the vapor injection process reduces both the isentropic and actual work, the numerator and denominator in Eq. 5. The reduction of the work comes from the cooling effect of the injected refrigerant. This increases the density of the refrigerant entering the second stage compression and reduce the specific work required. The isentropic efficiency of the vapor-injected compressor does not increase but the specific work required decreases. The reduction of specific work is the main benefit of using the vapor-injected compressor in a refrigeration system.
4 Results and Discussion 4.1 Baseline Compressor For this study, PDSim was first employed to build a comprehensive model of a hermetic R600a variable-speed reciprocating baseline compressor. The baseline compressor model in this study follows closely the methodology used to model a R-410A reciprocating compressor model described in Ziviani et al. [7]. The main parameters of the compressor can be found in Table 1. The PDSim model was used to predict performance of the compressor across a range of condensing temperatures and evaporation temperatures at an operating frequency of 50 Hz. The results were then compared to the performance map provided by the manufacturer for validation. Both power consumption and mass flow rate predictions by the mechanistic compressor model fall within a ± 10% error range with respect to the performance map data shown in Appendix. This validates the baseline compressor model. This verified model was then modified to predict performance of a vapor-injected compressor.
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Value
Unit
Displacement volume
11.4
cm3
Piston stroke
21
mm
Piston diameter
26
mm
Crank length
10.4
mm
Connecting rod length
31.8
mm
4.2 Vapor Injection Compressor Simulation Results For results presented in this section, the suction and discharge pressures corresponding to the evaporating and condensing temperatures considered in the refrigerator system level study [4] were employed, which are 60.52 and 482.07 kPa, respectively. The evaporation pressure for the medium temperature cabinet was used as the injection line pressure for compressor vapor injection, which is 174.32 kPa. The behavior of the model under different operating pressures will be considered in future studies once the compressor model is integrated with the system model. The injection line diameter was chosen to be 6.35 mm (0.25 inch), consistent with the suction and discharge line sizes. The injection was assumed to start at 4.9 rad during the compression process. This particular crank angle was chosen to demonstrate the results of the vapor-injected compressor. At this particular crank angle, the piston is rising to the TDC position and the refrigerant is being compressed inside the cylinder. The selection of different injection opening time has a large impact on the compressor’s performance, which will be discussed in detail in Sect. 4.3. Model predicted vapor-injected reciprocating compressor results are shown in Figs. 4 and 5. Compression cylinder pressure versus crank angle is plotted in Fig. 4 where the dotted lines represent pressures of the vapor-injected model and the solid lines represent pressures of the baseline compressor. When the injection line opens, the cylinder pressure and the injection line pressure quickly equalize and then the refrigerant continues to be compressed. The suction process is the same for the baseline compressor and vapor-injected compressors since the injection line only opens after the suction process is finished. Similarly, the refrigerant temperature vs crank angle is shown in Fig. 5. The temperature of the cylinder is lower for the vapor-injected compressor due to the cooling effect brought by the injection refrigerant. The discharge temperature of the vapor-injected compressor is also lower compared to that of the baseline due to the same reason. Table 2 summarizes the performance of the vapor-injected compressor for the simulated case. The power consumption of the vapor-injected compressor is higher than that of the baseline compressor due to the increased refrigerant mass flow. The isentropic efficiency of the vapor-injected compressor increased 1.64% compared to the baseline. This slight increase in isentropic efficiency needs to be validated with experimental results in future works. The specific work is also reported in the table.
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Fig. 4 Pressure versus crank angle plot for the vapor-injected reciprocating compressor model at 40 Hz
Fig. 5 Temperature versus crank angle plot for the vapor-injected reciprocating compressor at 40 Hz
Table 2 Performance comparisons for vapor-injected and baseline compressors
Vapor-injected Discharge temperature (°C) Mass flow rate (g/s) Power consumption (W) Specific work (J/g) Overall isentropic efficiency (–)
79.11
Baseline 86.86
0.59
0.50
69.61
65.99
117.87
131.98
72.87
71.13
Specific work is determined as the work per unit mass flow. There is a 10.7% reduction in the specific work of the compressor. As discussed in the previous sections, vaporinjection increases the refrigerant density of the high-stage compression through the cooling effect of the injection flow.
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4.3 Parametric Study of Injection Opening Time
Injection Mass Flow Rate (g/s)
Parameters of the injection include injection diameter, injection height and injection opening time. Among them, injection opening time is the only parameter that can be controlled during the compression process. This section will focus on a parametric study of injection opening time for compressor performance optimization. Injection opening time is expressed in terms of crank angle and describes when injection starts during the compression process through the opening of the control valve in Fig. 2. For the parametric study, the injection opening time was varied between 4 and 5 rads. The rest of the operating conditions and parameters were kept the same as described in Sect. 4.2. Figure 6 shows a plot of the injection mass flow rate at different injection opening times for the vapor-injected compressor at 40 Hz operating frequency. The injection mass flow rate decreases as injection starts later in the compression. The injection always closes when the piston covers the injection area regardless of the opening time. Thus, the earlier that injection occurs, the longer the injection process is, which explains the trend in the injection mass flow rate. The injection opening time’s effect on the overall isentropic efficiency is shown in Fig. 7. There is an optimal injection timing that leads to a maximum compressor isentropic efficiency. If the timing is too early, then there is a significant difference between the injection and cylinder pressures that causes irreversibility’s that must be overcome by additional compressor work. If the timing is too late, then the amount of refrigerant injection is less than ideal. Figure 8 shows a P–h diagram of the compression processes for injection opening times at 4.5 and 4.9 rads. When the injection opening time is at 4.5 rads, the injection occurs at a point when the compression cylinder pressure is low leading to a process line is quite difference than the isentropic compression process with lower isentropic efficiency. On the other hand, the compression process line for an injection opening time at 4.9 rads, is closer to the isentropic compression process. 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 4
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Fig. 6 Injection mass flow rate versus injection opening time at 40 Hz
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Isentropic Efficiency (%)
73 72 71 70 69 68
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Fig. 7 Isentropic efficiency versus injection opening time at 40 Hz
Fig. 8 P–h diagram of the compression process at different injection opening times at 40 Hz
The optimum injection pressure for maximum isentropic efficiency will vary with compressor operating frequency as seen in Fig. 9. At lower injection cylinder pressure, the isentropic efficiency increases rapidly with the increase of the injection cylinder pressure. As the injection cylinder pressure keeps increasing, the isentropic efficiency reaches an optimum. After this optimum point, the isentropic efficiency stops increasing and starts decreasing in some cases. This can be explained by the fact the injection flow is a pressure driven flow. When the injection cylinder pressure is higher, the pressure difference that drives the injection flow is lower as the injection line pressure is constant in this case. Lower pressure difference in the injection line results in less refrigerant being injected into the compression cylinder. This leads to a decrease in the cooling effect of the compression cylinder by the injection flow and thus a less efficient compression process. This means that for the vapor-injected
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Isentropic Efficiency (%)
75 73 71
35 Hz 40 Hz
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67 65 65
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Fig. 9 Isentropic efficiency versus injection cylinder pressure at different frequencies
compressor, there exists an optimal point for the injection opening time that results in a maximum overall isentropic efficiency that balances injection mass flow and injection cylinder pressure. As a result, it will be necessary to determine an approach for adjusting the injection timing to ensure optimal isentropic efficiency can be reached for different operating frequencies.
5 Conclusion and Future Work In this study, a mechanistic model of a vapor-injected reciprocating compressor was developed and studied. The vapor-injected compressor model was developed for the purpose of applying a multi-stage vapor injection cycle in domestic refrigerator/ freezer applications. Vapor injection in the reciprocating compressor was enabled using a control valve in order to separate the suction flow and the injection flow during the compression process. The injection mass flow rate and the isentropic efficiency were studied with respect to injection opening time during the compression process. The analysis of the injection opening time led to an understanding of the effect that injection cylinder pressure has on the overall performance of the vapor-injected reciprocating compressor. Based on this analysis, an optimal injection opening time exists that maximizes efficiency. A performance map-based model of the mechanistic model shown in this study will be developed in the next step. This performance map-based model will then be integrated into the dynamic model of the system shown in the introduction for a detailed system level study of the multi-stage vapor-injected cycle for domestic refrigerator/freezers. The mass flow rate of the compressor, including the injection line, must be determined based on the load requirement of the system model. Further, a prototype of a vapor-injected reciprocating compressor will be developed employing the control valve mentioned in this study. The performance of the vapor-injected compressor can then be experimentally determined.
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Appendix
Basline Model Power Consumption (W)
See Figs. 10, 11. 150 135 120 105 90 75 60 60
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Performance Map Power Consumption (W)
Baseline Model Mass Flow Rate (g/s)
Fig. 10 Comparison of power consumption between baseline compressor model results and performance map result at 50 Hz
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Performance Map Mass Flow Rate (g/s) Fig. 11 Comparison of mass flow rate between baseline compressor model results and performance map result at 50 Hz
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References 1. A Caglayan SM Husain M Ipek NA Tolga S Cadirci 2022 Dynamic modeling and experimental validation of a domestic refrigeration cycle J. Thermal Sci. Eng. Appl. 14 7 405253 2. CJL Hermes C Melo 2008 A first-principles simulation model for the start-up and cycling transients of household refrigerators Int. J. Refrig. 31 1341 1357 3. S Choi U Han H Cho H Lee 2018 Review: recent advances in household refrigerator cycle technologies Appl. Therm. Eng. 132 560 574 4. C. Liang, J.E. Braun, E.A. Groll, D. Ziviani, Dynamic modeling and validation of a tripleevaporator domestic refrigerator/freezer with R-600a, in 19th International Refrigeration and Air Conditioning Conference at Purdue, July 10–14, Paper 2501 (2022). 5. X Zhang B Zhang J Cao L Su K Li 2022 Numerical investigation on the performance and vapor injection process of a scroll compressor with different injection features Appl. Therm. Eng. 217 119061 6. I.H. Bell, V. Lemort, E.A. Groll, J.E. Braun, Development of a generalized steady-state simulation framework for positive displacement compressors and expanders, in International Conference on Compressors and their Systems 2013 (2013) 7. D Ziviani IH Bell X Zhang V Lemort MD Paepe JE Braun EA Groll 2020 PDSim: Demonstrating the capabilities of an open-source simulation framework for positive displacement compressors and expanders Int. J. Refrig 110 323 339 8. IH Bell EA Groll JE Braun WT Horton 2013 A computationally efficient hybrid leakage model for positive displacement compressors and expanders Int. J. Refrig 36 1965 1973 9. IH Bell D Ziviani V Lemort CR Bradshaw M Mathison WT Horton JE Braun EA Groll 2020 PDSim: a general quasi-steady modeling approach for positive displacement compressors and expanders Int. J. Refrig. 110 310 322 10. S Churchill 1977 Friction factor equation spans all flow regime Chem. Eng. 84 91 92 11. A Bahman D Ziviani EA Groll 2018 Vapor injected compression with economizing in packaged air conditioning systems for high temperature climate Int. J. Refrig. 94 136 150
Numerical Analysis of the Dynamic Two-Phase Flow Behavior in the Ionic Compressor with a Novel H-shaped Piston Zekun Liu, Xiang Kang, and Yun Li
Abstract With the development of the hydrogen energy industry, it is crucial for hydrogen refueling stations that compressors can work efficiently and flexibly with a longer life span. Adopting ionic liquid as a liquid piston to compress hydrogen is a feasible method. The high stroke frequency of ionic compressor prevents the liquid piston from maintaining a stable shape, leading to the generation of the additional clearance volume and hydrogen sealing failure. In this article, a novel H-shaped piston was proposed and a 3D numerical model of an ionic compressor cylinder with it was established. The dynamic simulation of the two-phase fluid behavior in the cylinder during three cycles was performed using the volume of fluid method and the dynamic mesh technique. The effect of this piston on the variation of the two-phase interface and the clearance volume of the compressor has been discussed for optimizing the design of the ionic compressor. Results show that: the clearance volume of the cylinder with a H-shaped piston was smaller than that of the cylinder with a normal piston in all three compression cycles, which indicated that the higher volumetric efficiency could be obtained with the H-shaped piston. In addition, the application of the H-shaped piston allowed sufficient ionic fluid to be retained in critical sealing locations of the cylinder to keep hydrogen sealing and piston lubrication well. Keywords Ionic compressor · H-shaped piston · Clearance volume
1 Introduction As pollution-free and sustainable green energy, hydrogen has received increasing attention in the energy industry over the past few years. Hydrogen fuel cell electric vehicles (HFCEV) is an essential part of hydrogen energy industry. The popularization of HFCEVs is limited by the driving mileage, which depends Z. Liu · X. Kang · Y. Li (B) Xi’an Jiaotong University, Xi’an, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_31
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on the hydrogen filling pressure. Thus, efficient, high-pressure, stable and highdisplacement hydrogen pressurization equipment is crucial to the advancement of the HFCEV industry. Hydrogen compressor is one of the most important equipment in a hydrogen refueling station, the cost of which usually accounts for more than 30% of the total construction cost of a hydrogen refueling station [1]. The development of high-pressure hydrogen compressors can promote the popularity of hydrogen refueling facilities significantly. Ionic compressor is a novel compressor that utilizes ionic liquid as a liquid piston to compress hydrogen gas. Ionic liquids can offer good thermal stability, low compressibility, suitable viscosity, and excellent frictional properties. They have low solubility with hydrogen gas so that hydrogen gas can’t be contaminate. Benefiting from the excellent physicochemical properties of ionic liquids, ionic liquids can be used in ionic compressors for both sealing and lubrication functions, solving the problem of hydrogen sealing and oil-free lubrication at high pressure in piston compressors. Ionic compressor is a kind of liquid piston compressor in terms of working principle. Van de Ven et al. [2] developed several heat transfer models for liquid piston compressors corresponding to different applications and demonstrate by CFD methods that liquid pistons would effectively improve the heat transfer efficiency in the cylinder of compressors and lead the compression process closer to isothermal compression. Saadat et al. [3] obtained the optimal compression/expansion profile for a specific geometry of cylinder in a liquid piston air compressor by numerical methods, and demonstrated the effectiveness of the optimal profile to improve the compression efficiency. Patil et al. [4, 5] proposed various methods to improve the heat transfer efficiency of liquid piston compressors, including the application of porous media, optimized cylinder profile, in-cylinder spray, and investigated the ability of these methods to improve the compression efficiency experimentally. Kermani [6] presented a numerical model for the heat transfer process in an ionic compressor and devised an experimental prototype of a single-stage low-speed ionic compressor. Guo et al. [7] established a two-dimensional cylinder model of an ionic compressor and simulated the two-phase behavior in a single cycle to investigate the effects of liquid viscosity on the turbulent kinetic energy in the ionic compressor cylinder. To meet the demand for large compressor displacements in commercial hydrogen refueling stations with the limited reciprocating volume of compressors, ionic compressors have a stroke frequency as fast as 5.8 Hz, while liquid piston compressors for air storage have a stroke frequency of only 0.2–0.5 Hz. High speed reciprocating motion leads to deformation of the liquid piston. During the movement of the liquid piston, droplets and bubbles continuously generate and break up in the cylinder due to the interaction between the ionic liquid and the hydrogen gas, which could hinder the normal discharge of hydrogen gas in the discharge process. The hydrogen gas trapped in the cylinder prolongs the expansion process of the compressor and increases the clearance volume of the cylinder, leading to a reduction in compressor efficiency. In addition, there should be enough ionic liquid in the critical sealing part of the cylinder such as the contact surface between the solid piston and the cylinder
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wall for sealing and lubrication during the compressor operation. Nevertheless, it has been found by CFD simulations that when the piston moves to the bottom dead center, it often fails to maintain a complete liquid film on the piston surface, which could lead to the failure of the compressor sealing and lubrication. In this article, a numerical model of the ionic compressor cylinder with a novel Hshaped piston was established. 3D dynamic simulations were performed to obtain the behavior of the gas–liquid two-phase flow in the cylinder during multiple compression cycles by means of the dynamic grid technique and the volume of fluid (VOF) method. The variation of the two-phase interface and the compressor clearance volume was analyzed to demonstrate the positive influence of the H-piston on the compressor sealing process and volumetric efficiency.
2 Methodology 2.1 Physical Model The ionic compressor for hydrogen refueling station normally consists of five stages with minimum suction pressure of 0.5 MPa and maximum discharge pressure of 90 MPa. The first stage of a five-stage ionic compressor was studied in this article. The simplified model is shown in Fig. 1, and the basic design parameters of cylinder are shown in Table 1. The diameter Dj of the cylinder and the piston stroke S are given by Eqs. (1) and (2), respectively. / Dj = Fig. 1 Simplified physical model
4V s πS
(1)
Discharge valve
Suction valve
Piston
ω
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Table 1 Design parameters of the cylinder Parameters
Suction pressure (MPa)
Discharge pressure (MPa)
Volume flow rate of hydrogen gas (Nm3 /h)
Value
0.5
1.4
370
Parameters
Stroke frequency (Hz)
Gas temperature in suction valve (K)
Relative clearance volume (%)
Value
5.8
300
5
S=
30Cm n
(2)
where Cm is the average velocity of piston (m/s), n is the rotation speed of the compressor (rpm), Vs is the stroke volume of compressor (m3 ), which is given by Eq. (3). Vs =
qv ηvn
(3)
where qv is the volumetric flow rate of the compressor (m3 /min), ηv is the discharge coefficient. The displacement of the solid piston x can be obtained from Eq. (4). √ 1 2 2 x = r (1 − cos θ ) − (1 − 1 − λ sin θ ) λ
(4)
where r is crank radius, l is the length of the connecting rod, λ is the ratio of the crank radius to the length of the connecting rod, θ is the crank angle, and the curve of the piston displacement is shown in Fig. 2. Fig. 2 Piston displacement
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Table 2 Geometric parameters of the physical model Parameters
Value
Diameter of the cylinder (mm)
180
Stroke of the piston movement (mm)
179
Height of the liquid layer in the cylinder (mm)
38
Effective diameter of both suction and discharge valves (mm)
40
Crank radius (mm)
89.5
Connecting rod length (mm)
400
Table 3 Geometric parameters of the physical model (298.15 K) Property
Density (kg/m3 )
Heat capacity (J/mol K)
Valve
1436.8
524
Property
Thermal conductivity (W/m K)
Dynamic viscosity (mPa s)
Valve
0.128
50.8
The geometry parameters of cylinder model can be calculated, as shown in Table 2. The physical parameters of the ionic liquid employed in this research are shown in Table 3.
2.2 Numerical Model and Solution Method The main challenge in simulating two-phase behavior in a compressor cylinder is to capture the two-phase interface accurately. The VOF method is an excellent way for dealing with two-phase flow problems. Two or three immiscible fluids can be simulated by the VOF method through tracking the volume fraction of each phase in each grid and solving a single momentum equation. The VOF method has been reported to be one of the most powerful tools to deal with stratified compressible two-phase flows. Thus, this research used the VOF model to calculate the complex two-phase flow in the cylinder during the operation of the ionic compressor. The control equations were discretized in the Fluent software [8] by the finite volume method (FVM). The k–ω SST turbulence model was applied to calculate the turbulence flow. The convective term, turbulent kinetic energy and specific dissipation rate were discretized with the second order upwind format. Further, the pressure staggering option (PRESTO) method was adapted to interpolate the pressure gradient of the source term in the momentum equation. The upper surface of the solid piston is a moving boundary. The motion of the moving boundary is controlled by the UDF through the dynamic mesh technique. The boundary conditions of the inlet and the outlet are shown in Eqs. (5) and (6), respectively.
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W all, p ≥ 0.5 M Pa Pr essur e inlet(0.5M Pa), p < 0.5 M Pa
W all, p ≤ 1.4M Pa Pr essur e outlet(0.5 M Pa), p > 1.4 M Pa
(5)
(6)
The basic assumptions in the numerical model are as follows. (1) The ionic liquid is considered as incompressible fluid. (2) There is no mass transfer between hydrogen and ionic liquid. (3) No phase change occurs for both ionic liquid and hydrogen gas during the compressor operation process. (4) Cylinder walls are adiabatic and no relative sliding occurs between the fluid and the walls. The moving mesh was realized by the laying method, which requires all grids in the model to be structural grid. Thus, the mesh type was determined as hexahedral type mesh. After verification of grid independence, the total number of grids is determined to be one million.
3 Results and Discussions Figures 3, 5 and 7 show the phase fields in cylinder during the first three compression cycles, demonstrating the variation of the two-phase interface. The red area in the phase field represents hydrogen gas, the blue area is filled with ionic liquid, and the green area refers to the interface of two phases. The velocity field in the cylinder of the ionic compressor during the first three cycles is presented in Figs. 4, 6 and 7. The single reciprocating cycle lasts 0.2 s. The first half cycle is the compression and discharge process followed by the expansion and suction process in the second half cycle. The initial ionic liquid height is 5 mm, above the top surface of the H-shaped piston. It can be seen in Figs. 3 and 4, the shape of the liquid piston remained stable and no gas vortices were generated in the cylinder during compression and discharge process of the first cycle. When the liquid piston contacted the top surface of the cylinder, a part of the ionic liquid was discharged through the outlet along with the gas, when the piston was close to the top dead center. Several bubbles appeared in the liquid piston near the left cylinder wall, due to the viscous effect between the ionic liquid and the cylinder wall, as shown in the phase field at the time of 0.1 s. As shown in Fig. 4, the fluid flow rate in the cylinder is as low as 1.8 m/s during the expansion process from 0.1 to 0.1039 s. The hydrogen gas flowed into the cylinder with a maximum velocity of 39.6 m/s during the suction process from 0.1029 to 0.2 s, when the liquid was moving at a low speed because of the viscous effect with the cylinder wall, and there was an obvious separation between the liquid piston and the solid piston. As shown in Fig. 4, two small vortexes were observed on the either side of the intake gas flow at the time of 0.1375 s, the sizes of which increased during the movement of the solid piston to the bottom dead center. As a result of the interaction
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0.0000s
0.0489s
0.0650s
0.0850s
0.1000s
0.1000s
0.1039s
0.1375s
0.1708s
0.2000s
Fig. 3 Phase field in the cylinder during the first compression cycle
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0.0489s
0.0650s
0.0850s
0.1000s
0.1000s
0.1039s
0.1375s
0.1708s
0.2000s
Fig. 4 Velocity field in the cylinder during the first compression cycle
between the gas vortex and the liquid, part of the liquid adhered to the right cylinder wall in the form of a liquid film, part of the liquid transformed into small droplets and moved towards the liquid film, and a small part of the gas enters the ring gap of the H-shaped piston to generate bubbles. The distribution and movement trend of the liquid in the cylinder conforms to the distribution of the vortex in the cylinder, as shown in Fig. 4. The transition of the interface between two phases during the second compression cycle is presented in Figs. 5 and 6. The gas vortexes developed during the suction process of the previous cycle was still existing in the cylinder throughout the compression process from 0.2 to 0.2504 s and gradually disappeared after the start of the discharge process, as shown in Fig. 6. It can be found in Fig. 5 that the liquid on the right side of the cylinder wall accompanying with part of the gas quickly went
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0.2504s
0.2650s
0.2850s
0.3000s
0.3000s
0.3057s
0.3375s
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Fig. 5 Phase field in the cylinder during the second compression cycle
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0.2504s
0.2650s
0.2850s
0.3000s
0.3000s
0.3057s
0.3375s
0.3708s
0.4000s
Fig. 6 Velocity field in the cylinder during the second compression cycle
back to the ring gap of the H-shaped piston, and the liquid in the left side of ring gap moved quickly upward along the cylinder wall pushed by the solid piston during the movement of the solid piston to the top dead center. There was no bubble in the left side of ring gap while several bubbles existed in the right side of ring gap at the end of discharge process as shown in phase field at 0.3 s. During the movement of the solid piston to the bottom dead center, sufficient ionic liquid was still observed in the sealing position between the piston and the cylinder wall to perform the sealing and lubricating function, although a large amount of gas entered ring gap due to the difference in velocity of the liquid movement and the solid piston movement. As shown in the Fig. 6, two gas vortexes were found on the either side of the intake gas flow at the time of 0.3375 s, when the maximum velocity of 47.3 m/s during the suction process was obtained. During the movement of the piston to the bottom dead
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0.4s
0.4509s
0.4650s
0.4850s
0.5000s
0.5000s
0.5083s
0.5375s
0.5708s
0.6000s
Fig. 7 Phase field in the cylinder during the third compression cycle
center, the size of the right vortex kept increasing, while the left vortex splits into two small vortexes with the restriction of the liquid on the cylinder wall. The transition of the interface between two phases during the third compression cycle is presented in Figs. 7 and 8. As shown in Fig. 7, part of gas trapped in the ring gap of the H-shaped piston left the ring gap in the process of the piston moving to the top dead center. It can be seen in the phase flied at 0.5 s that there was still a small part of gas trapped in the ring gap at the end of the discharge process. As shown in the Fig. 8, two gas vortexes were observed on the either side of the intake gas flow at the time of 0.5375 s, sizes of which kept increasing during the suction process from 0.5375 to 0.6 s. The maximum velocity of the two-phase flow was 41.7 m/s in the expansion and the suction process. The vortex on the left side of the cylinder by the action of the liquid on the cylinder wall tended to split into two vortices, but the second vortex did not succeed in forming at the end of the suction, which was different compared to the second cycle. The vortex in the left side of the cylinder tended to split into two small vortexes with the restriction of the liquid on the cylinder wall, but the second vortex did not succeed in generation until the end of the suction process, which was different compared to the second cycle. It can be seen in the velocity field that the ionic liquid in the ring gap of Hshaped piston always maintained a low velocity over multiple compression cycles. Consequently, there was always sufficient ionic fluid at the critical sealing location between the piston and the cylinder, even though some gas would enter the ring gap during the entire compression cycle. The liquid piston cannot maintain a stable shape under the interaction with cylinder walls and gas vortexes. Part of the liquid adhered to the cylinder wall to form a liquid film, and part of the liquid was transformed into small droplets dispersing in the cylinder. It was apparent that the distribution of the liquid in the cylinder corresponds to the distribution of the vortexes. As can be found in Figs. 4, 6, and 8, a part of the ionic liquid left the cylinder accompanying with the hydrogen gas during the discharge process of each compression
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0.4509s
0.4650s
0.4850s
0.5000s
0.5000s
0.5083s
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Fig. 8 Velocity field in the cylinder during the third compression cycle
cycle, while some of the gas was trapped in the cylinder and could not be discharged in time, which caused an increase in the clearance volume of the compressor. The increase in the clearance volume led to a longer expansion process and a reduction in the volumetric efficiency of the compressor. Figure 9 illustrates the duration of the expansion process at different cycles for the case with an H-shaped piston and the case with a normal piston. The duration of the expansion process in the first compression cycle with an H-shaped piston was 0.0047 s, which was much shorter than 0.0076 s for a normal piston cylinder. During the second and third compression cycles, the duration of the expansion process increased in both cases as a result of the continuous loss of ionic liquid, but it was obvious that the duration of the expansion process in the case with a H-shaped piston was always lower than that in the case with normal piston. It is demonstrated that the application of the novel H-shaped piston can effectively reduce the clearance volume and improve the efficiency of the compressor comparing with the normal piston, while the H-shaped piston can keep sufficient ionic liquid in the sealing location between the piston and the cylinder wall to perform the sealing and lubricating functions throughout the compression cycles.
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Fig. 9 Duration of the expansion process at different cycles for the case with an H-shaped piston and the case with a normal piston
4 Conclusion In this article, a numerical model of an ionic compressor cylinder with a novel Hshaped piston has been established, and dynamic 3D simulations has been carried out to investigate the two-phase behavior in the cylinder by the VOF method and the dynamic mesh technique. The effect of the H-shaped piston on the variation of the two-phase interface and the clearance volume of the compressor has been discussed for optimizing the design of the ionic compressor. Main conclusions of this study can be summarized as follows: The shape of the liquid piston could not remain stable during all three compression cycles. A part of the ionic liquid leaked out of the cylinder in the discharge process of each compression cycle, resulting in an increase in the clearance volume of the compressor. There was always sufficient ionic liquid retained in the sealing location between the piston and the cylinder wall to perform the sealing and lubrication functions of the compressor. Two gas vortexes were observed and increased in size with the movement of the solid piston in the suction process of all three compression cycles. The vortex in the left side of the cylinder split into two small vortexes due to restriction of the liquid on the cylinder wall, which occurred in the late second cycle. It was demonstrated that the distribution of the liquid in the cylinder corresponded to the distribution of the gas vortex. The clearance volume of the cylinder with an H-shaped piston was smaller than that of the cylinder with a normal piston in all three compression cycles, which indicated that the higher volumetric efficiency of the compressor could be obtained with the H-shaped piston.
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References 1. N.A. Kermani, Evaluation of ionic liquids as replacements for the solid piston in conventional hydrogen reciprocating compressors: a review. Int. J. Hydrogen Energy 45(33), 16337–16354 (2020) 2. J. Ven, Liquid piston gas compression. Appl. Energy 86(10), 2183–2191 (2009) 3. M. Saadat, Optimal trajectories for a liquid piston compressor/expander in a Compressed Air Energy Storage system with consideration of heat transfer and friction, in American Control Conference (ACC), pp. 2725–2730. IEEE, Montreal (2012) 4. V.C. Patil, Experimental investigation of heat transfer in liquid piston compressor. Appl. Thermal Eng. 146, 169–179 (2018) 5. V.C. Patil, Experimental study of heat transfer enhancement in liquid piston compressor using aqueous foam. Appl. Therm. Eng. 164(3), 114441 (2019) 6. N.A. Kermani, Design and prototyping of an ionic liquid piston compressor as a new generation of compressors for hydrogen refueling stations (Technical University of Denmark, Copenhagen, Denmark, Doctor, 2017) 7. G. Yi, Numerical analysis of the dynamic two-phase flow behaviour in the ionic liquid compressor for hydrogen refuelling stations. Appl. Thermal Eng. 219, 119607 (2023) 8. A. Flunet, 2020R2 (Ansys Inc., Canonsburg, 2020)
Development of Reduced Order Model for Performance Prediction of Reciprocating Compressor Hosik Jeong, Been Oh, Dongwon Kim, Kwongi Lee, Hyungyul Kim, Jongsoo Kim, and Gyunmin Choi
Abstract The reduced order model (ROM) is one of the methods for quickly monitoring the response results when operating conditions change in complex systems. In the conventional method, human and numerical costs are incurred in pre-treatment, interpretation, post-processing to monitor the results of a response under a specific operating condition using numerical analysis. A simplified model is developed that faithfully reproduces higher-order models while lowering the degree of freedom (DOF) of complex systems. Training data should be collected for ROM configuration to predict the performance of the compressor. After setting the operating conditions inside and outside the actual operating area of the compressor as the analysis conditions of the 3D Fluid–Structure Interaction simulation results are collected as H. Jeong (B) · B. Oh · D. Kim · K. Lee Graduate School of Mechanical Engineering, Pusan National University, Busan 46241, Republic of Korea e-mail: [email protected] B. Oh e-mail: [email protected] D. Kim e-mail: [email protected] K. Lee e-mail: [email protected] G. Choi Department of Mechanical Engineering, Pusan National University, Busan 46241, Republic of Korea e-mail: [email protected] H. Kim LG Electronics Kitchen Appliance Lab., 391-2, Gaeumjeong-Dong, Changwon, Gyeongnam, Republic of Korea e-mail: [email protected] J. Kim H&A R&D Center, LG Electronics Inc., 327-23, Kasan-Dong, Geumchon-Gu, Seoul 153-082, Republic of Korea e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_32
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training data. The ROM for predicting the performance of the compressor is generated based on the training data. Although a large amount of data is required for high accuracy ROM generation, simulation can only obtain a small amount of training data with a long analysis time. Artificial Neural Network Method complements small amounts of training data by extending to large amounts of data. This paper is a study to establish a methodology for making ROM for predicting the performance of reciprocating compressor. The accuracy of the ROM is verified by comparing it with the experimental data. Keywords Reciprocating compressor · Reduced order model (ROM) · Artificial neural network · Performance prediction
1 Introduction General numerical analysis methods for performance analysis of compressors can be divided into 1D, a low-dimensional analysis, and 3D, a high-dimensional analysis. 1D analysis takes less time to analyze, but due to dimensional limitations, it is limited to accurately simulate the fluid characteristics inside the compressor, while 3D analysis uses high-order equations, so it can simulate the internal behavior of the compressor close to natural phenomena, but it takes a long time to interpretation. There are difficulties in selecting the analysis model because there are advantages and disadvantages of each analysis model. To solve this problem, a solution is proposed to generate the reduced order model (ROM) based on high-accuracy 3D analysis results and connect the 1D analysis model with the ROM. As a result, the long analysis time, which is a disadvantage of the 3D analysis model, is shortened, and the low accuracy, which is a disadvantage of the 1D analysis model, is increased. Lucia et al. [1] discussed the development of reduced order modeling techniques and their applicability in computational physics, especially in the multi-disciplinary field of computational aeroelasticity. Nayfeh et al. [2] presented the reduced order models for microbeams and rectangular and circular microplates. They validated these models by comparing their results with theoretical and experimental results. Yi-dong et al. [3] proposed a strategy to develop the reduced order model based on CFD results. The results showed the benefits of using ROM methodology for process simulation and optimization. Stabile et al. [4] compared and tested the accuracy of two different pressure stabilization strategies for POD-Galerkin ROMs based on a finite volume approximation. The ROMs are used to approximate the parametrised unsteady Navier–Stokes equations for moderate Reynolds numbers. In many previous studies, researchers did not discuss about the use of ROM when predicting the performance of reciprocating compressors. It is necessary to use the ROM because the ROM can reduce the shortcomings of numerical analysis methods. The objective of this study is to establish a methodology for development of reduced order model for performance prediction of reciprocating compressors.
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Fig. 1 Input and output parameters of training data
2 Training Data 2.1 3D FSI Data The training data required for reduce order model (ROM) configuration to predict the performance of the compressor is collected. After setting the operating conditions inside and outside the actual operating conditions of the compressor as the analysis conditions of the 3D analysis simulation, the analysis result, 3D Fluid–Structure Interaction (FSI) Data, is collected as training data.
2.2 Input and Output Parameter The input parameters of training data include six parameters, and the output parameters of training data include nine parameters. The input parameters and output parameters are shown in Fig. 1. The case of training data is determined according to the combination of the input parameters. In this study, RT has four conditions, RPS has four conditions, and the combination of Te , Tc , Ps , Pd has five conditions. So, the training data has 80 conditions. The meanings, ranges, and the number of conditions of input parameters are displayed in Table 1.
2.3 Reliability Verification of Training Data Two methods are used to verify the reliability of training data. One is to compare mass flow rate with the experimental results under seven conditions, and the other is to compare discharge average temperature with the experimental results under four
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Table 1 Range of input parameters Input parameters
Range
Number of conditions
RT (°C)
Compressor inlet temperature
10 to 43
4
RPS (Hz)
Compressor rotation speed
10 to 80
4
Te (°C)
Evaporating temperature
−27 to −17
5
Tc (°C)
Condensing temperature
32 to 58
Ps (kPa)
Suction pressure
53.45 to 82.10
Pd (kPa)
Discharge pressure
428.0 to 829.7
conditions. Table 2 shows the error rate of mass flow rate under seven conditions, and Table 3 shows the error rate of discharge average temperature under four conditions. The reliability of training data is verified because the error rate is < 10% under all eleven conditions. To verify the reliability of the training data, the additional data is generated. The additional data is used for data extending and ROM generation. Table 2 Error rate of mass flow rate RT = 32 °C RPS = 30 Hz 1
2
3
4
5
6
7
Te (°C)
−23.3
−25
−20
−25
−20
−25
−20
Tc (°C)
54.4
55
55
40
40
35
35
Ps (kPa)
63.06
58.43
72.48
58.43
72.48
58.43
72.48
Pd (kPa)
761.3
773.0
773.0
531.2
531.2
464.8
464.8
Error (%)
6.1
5.7
6.8
7.2
8.1
7.7
8.0
Table 3 Error rate of discharge average temperature
RT = 25 °C Te (°C) RPS
−29
Tc (°C)
31
Ps (kPa)
48.61
Pd (kPa)
517.1
20
Discharge average temperature error (%) 7.83
25
Discharge average temperature error (%) 4.97
30
Discharge average temperature error (%) 2.24
40
Discharge average temperature error (%) 2.74
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3 Data Extending 3.1 ANN Method The artificial neural network (ANN) method is chosen to extend a small amount of training data. This is because the ANN method is a specialized method for predicting figures by inputting figures. The ANN model receives input parameters from the input layer, multiplies by weights, and adds them all, and predicts output parameters from output layer through hidden layers containing activation function. Figure 2 represents an example of ANN model and the process of obtaining the output value. In Eq. (1), ykl−1 is the output value of the previous layer and the input value of the current layer. akl−1 is multiplied by the weight ωljk , and bias blj is added to the sum of the weight products. After that, the output value y lj is obtained after passing the activation function f [5]. y lj
= f
( ∑
) ωljk ykl−1
+
blj
(1)
k
In this study, the ANN model consists of one input layer, one output layer, and four hidden layers. The input layer has six nodes, the output layer has nine nodes, and each hidden layer has fifty nodes. The function tanh and sigmoid are selected as the activation functions. The error is calculated through the root mean square error (RMSE) of Eq. (2). ANN method proceeds in the direction in which the value of RMSE is minimized, and the value of the weight and bias of ANN model is optimized as the error is minimized. [ ) | n ( |∑ y i − yi 2 √ (2) Root Mean Squar e Err or (R M S E) = n i=1 ⌃
(a) ANN model
Fig. 2 Structure of artificial neural network
(b) Artificial neuron unit
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3.2 Data Extending Method Using ANN Method The reduced order model (ROM) is generated based on the training data. Although a large amount of data is required for high-accuracy ROM, 3D FSI simulation can only obtain a small amount of training data due to its long interpretation time. It complements a small amount of training data by expanding a small amount of training data to a large amount of data through ANN model. Figure 3 shows the flow chart for ANN model development and data expansion. Training data is trained on ANN model. When new input parameters are entered into the developed ANN model, the output parameters are predicted. The prediction results are obtained as extended data [6]. The range of the new input parameters cannot be outside the range of the training data used for ANN model development. This is because ANN model cannot accurately predict data from untrained areas. A small amount of training data is supplemented by using data expansion by ANN model, and extended data is applied when ROM is generated.
4 Reduced Order Model 4.1 Concept of Reduced Order Model The reduced order model (ROM) is one of the methods for quickly monitoring the corresponding response results when operating conditions change in the complex system. In the numerical analysis, human and numerical costs are incurred in pretreatment, interpretation, post-processing to monitor the response results under specific operating conditions. To address the shortcomings of numerical analysis in the development and monitoring of complex systems, simplified model is developed that faithfully reproduces high-dimensional analysis model while lowering the degree of freedom (DOF) of the complex systems.
4.2 Development of Reduced Order Model Figure 4 shows the process of generating ROM in the ANSYS Workbench. The ANSYS Workbench supports the generation of ROM that can analyze the system in short simulation time. In the ANSYS Workbench, training data and extended data are entered to generate ROM. The ANSYS Workbench provides a variety of response surface type. There is a difference in the accuracy and calculation time of the ROM according to the response surface type. There are many methods for verifying the accuracy of ROM, but in this study, the accuracy is verified by comparing the cooling capacity of the experimental results with the cooling capacity predicted by ROM. The ROM is converted into Functional Mock-up Unit (FMU). The reason for converting
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Fig. 3 Flow chart of data extending
to FMU is that ROM is implemented within the Ansys Workbench, but ROM cannot be directly linked to the 1D analysis model. The function that enables this connection is to convert ROM into FMU. By connecting FMU to the 1D analysis model, the 1D analysis model can apply 3D analysis results with high accuracy without long analysis time [7].
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Fig. 4 Flow chart of generating ROM
4.3 Response Surface Type Genetic Aggregation. Genetic Aggregation is method that optimizes predictions for input values using genetic algorithm. Equation (3) represents the mathematical model of Genetic Aggregation. ⌃
y ens (x) =
NM ∑
⌃
wi · y i (x)
(3)
i=1 ⌃
⌃
y ens is the prediction of the ensemble, y i is the prediction of the ith response surface, th N M is the number of met models used and N∑ M > 1, wi is the weight factor of the i NM response surface. The weight factors satisfy: i=1 wi = 1 and wi ≥ 0, 1 ≤ i ≤ N M . The weight factors are optimized through the genetic algorithm [8].
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(b) Kriging
(a) Non-parametric Regression Fig. 5 Behavioral pattern of response surface
Non-parametric Regression. The mathematical model of Non-parametric Regression is represented as Eq. (4). The function f is a fitting equation for output values. By adding and subtracting the margin of tolerance ε to the function f , all output values are included within the range of predicted values. Figure 5 shows the behavioral pattern of Non-parametric Regression. y = f (x) ± ε, f (x) − ε ≤ out put values ≤ f (x) + ε
(4)
Kriging. Kriging is method that represents predicted values for input values by adding a term of deviation to a quadratic polynomial function as shown in Eq. (5). The function f represents the general behavior of the model as a quadratic polynomial function, and the function z represents the local behavior of the model as a term of deviation. The term of deviation can be obtained by solving the covariance equation [9]. Figure 5 shows the behavioral pattern of Kriging. y = f (x) + z(x)
(5)
Standard Response Surface. Standard Response Surface is very similar to Kriging. Standard Response Surface is expressed only as a quadratic polynomial function without a term of deviation as shown in Eq. (6). y = f (x)
(6)
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Fig. 6 Training results of ANN model
5 Results and Discussion 5.1 Results of ANN Figure 6 shows the training results of the ANN model for nine output parameters. The x-axis is the output parameter of the training data, and the y-axis is the result calculated by the trained ANN model. The points line up on the graphs because the output parameters of the training data and the calculated results match. However, among the nine output parameters, a large error occurred at the maximum torque. The reason is that the input parameter of the result of the large error is an extreme condition in which it is difficult to form a normal refrigeration cycle.
5.2 Reliability Verification of Extended Data After learning the training data, entering new input parameters into the trained ANN model yields predictive results considering nonlinearity. Among these predictive results, results that are outside the margin of error are excluded. In this study, the
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Fig. 7 Cooling capacity predicted by ANN method
margin of error is 10%. The new input parameters input to the trained ANN model are the input parameters of the experimental conditions. The trained ANN model predicts the output parameters under the corresponding experimental conditions. There are two reasons for entering the experimental conditions into the new input parameters. First, the experimental conditions are within the range of the training data used for ANN model development. Second, the accuracy of the predicted data can be verified by comparing the cooling capacity of the experimental results with the cooling capacity of the predicted data. Figure 7 is a graph showing the cooling capacity of predicted data. The x-axis is the cooling capacity of the experimental results, and the y-axis is the cooling capacity predicted by the trained ANN model. Since there are 100 experimental conditions, ANN model predicts 100 data. Of the 100 data, 93 data are selected as extended data. The reason is that 93 data are within 10% of the error rate, and the remaining seven data exceed 10% of the error rate.
5.3 Accuracy of Reduced Order Model The method for verifying the accuracy of ROM is to compare the number of cases with an error rate of < 10% by comparing the cooling capacity of the experimental results with the cooling capacity predicted by ROM. The ROM Accuracy represents the number of cases with an error rate of < 10%. Since the experimental conditions are 100 cases, the ROM Accuracy is expressed as an integer from 0 to 100. Another method to verify the accuracy of ROM is to compare the average error rate and the maximum error rate for 100 cases. The inclusion of extended data in the ROM reduces the average error rate from 4.656% to 4.318% and the maximum error
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Fig. 8 Accuracy of reduced order model according to the amount of data
Table 4 Accuracy of reduced order model according to response surface type Number of data
184
Response surface type
Genetic aggregation
Non-parametric regression
Kriging
Standard response surface
ROM accuracy
100/100
97/100
93/100
96/100
Average error rate (%)
4.318
4.620
5.052
4.407
Maximum error rate 9.777 (%)
12.99
12.54
11.10
Standard deviation of error rate
2.808
3.273
2.806
2.355
rate from 11.77% to 9.777%. As the error rate is 50, where, .Vdisp is the maximum displacement volume of a compression chamber in .in 3 . Figure 1 compares the results from the calibrated model with the experimental results and suggests that the model can predict the mass flow rate, volumetric efficiency and power within Mean Absolute Error (MAE) of 1.9%, 2.9%, 2.6% and isentropic efficiency 2.04%, respectively. This validates that the model is sufficiently accurate in its base formulation and will need to be updated to include vapor injection.
3 Model Updates to Include Vapor Injection in Mechanistic Chamber Model To incorporate the simulation of vapor injection in the spool compressor, updates were made to the existing, validated, mechanistic chamber model. A sub-model was added to the overall model to calculate the injection mass flow rate into the different chambers of the spool compressor, based on the pressure difference across the port and the port’s angular location. At any given moment, there are two or three different chambers, which are dependent on the angular position of the vane. The detailed formulation of these chambers and their movement is described in [7]. In the vapor injection sub-model, the model first identifies the chamber that is interacting with the injection port (Fig. 2), and then calculates the mass flow rate across the injection
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Fig. 1 Spoolcompressor predicted performance compared to the experimental results for two compressor sizes and two refrigerants
Fig. 2 Three different injection port locations and their interaction with suction, compression and discharge chamber
port using the isentropic nozzle flow model. This calculated injection mass flow rate is used in the mass and energy balance equations to calculate the refrigerant state at the next integration step [6]. The addition of an injection port to the compressor stator introduces another leakage path as the vane travels across the injection port. To account for this, a
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leakage model has been added to calculate the mass flow rate from the high-pressure chamber to the low-pressure chamber. In the optimization model, the model iterates over the injection angle, which represents the central position of the port. Using, θ
. in j,s,e
= θin j ±
din j , 2Rstator
(7)
the leakage model calculates the starting and ending angle of the injection port using the port diameter and stator radius, where .θin j,s,e and .din j represent the starting and ending angle of the injection port and the injection port diameter, respectively, and . Rstator is the stator radius. The leakage area is modeled to vary in a sinusoidal pattern between the starting and ending angles of the injection port. This variation is calculated using,
.
Aleak,in j = (Amax − Amin )/2(sin(2(θvane − θin j ) + pi/2) + 1) + Amin ,
(8)
where . Amax equals the half of the cross-sectional area of the port, . Amin is set to zero, and .θvane represents the instantaneous angular position of the vane in the integration process. The location of the vane relative to the injection port is determined and, when the vane passes over the injection port, the model calculates which two of the three chambers are present and calculates the instantaneous mass flow rate from the high-pressure chamber to the low-pressure chamber using the isentropic nozzle flow model. The leakage mass flow rate is then incorporated into the mass and energy conservation equations to predict the next state of the refrigerant in each chamber. The isentropic efficiency of the compressor is calculated according to the ASHRAE standards 23 [8] and can be represented as, η
. o,is
=
m˙ 1 (h 2 s − h 1 ) + m˙ 3 (h 3 s − h 2' ) , P
(9)
where .m˙ 1 is the suction mass flow rate, .m˙ 3 is the discharge mass flow rate and refrigerant state points are shown in Fig. 3. The compressor power is calculated as,
Fig. 3 P-h plot of flash tank based simple vapor compression cycle
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P = m˙ 1 (h 3 − h 1 ) + m˙ 2 (h 3 − h 2 ),
477
(10)
where, .m 2 is the injection mass flow rate.
4 Optimization Model A schematic of the optimization algorithm is shown in Fig. 4. The algorithm starts with the assumptions of port diameter, injection angle, and injection pressure. The guess port diameter is linked with the discharge port size to ensure the model is suitable for different compressor sizes and falls between 1/3 to 2/3 of the discharge port diameter. The injection angle is varied between 260 and 280.◦ , as preliminary analysis shows a rapid drop in volumetric efficiency below 260.◦ and discharge ports lie a little over 280.◦ . The two extremes of injection pressure are 150 kPa above and below the suction and discharge pressure, respectively. Using these ranges, the mechanistic chamber model predicts compressor performance for different combinations of these parameters. The mechanistic chamber model predicts the injection mass flow rate based on the pressure difference between injection pressure and chamber pressure by using an isentropic nozzle flow model. This predicted mass flow rate could be more or less than the mass flow rate available from the flash tank. A complete iterative solution of the Vapor Compression Cycle (VCC) is required for an accurate prediction of mass flow rate, but this leads to high computational time. To reduce computation time, a simplified method is employed that finds the equilibrium injection pressure. The process starts by calculating the injection mass flow rate and discharge mass
Fig. 4 Flow chart for the optimization model
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flow rate using the mechanistic chamber model at the two extreme injection pressure values. The quality of the refrigerant at these pressures is calculated using the cycle analysis shown in Fig. 3. The quality and discharge flow rate are used to calculate the injection mass flow rate available in the flash tank for each injection pressure. The equilibrium pressure is found at the intersection of the calculated injection mass flow rate and the cycle analysis. The compressor performance parameters are predicted at this point using a linear curve fit between the two extreme results obtained from the mechanistic chamber model. This process is repeated for all port diameter and angle combinations and a 3-D surface plot and curve fit equations are developed for performance parameters. The optimum port diameter and angle are found and used to predict performance.
5 Results and Discussion In this study, a novel optimization model is presented to determine the combination of vapor injection port diameter, port angle, and pressure that maximizes the heating coefficient of performance (COP) of a spool compressor. The analysis is conducted for 132 in3 displacement volume and R1234yf refrigerant. The two operating conditions (.−30.◦ F/110.◦ F and 35.◦ F/110.◦ F) were chosen for preliminary analysis which represent two extremes of conditions for heat pump application. The model leverages a mechanistic chamber approach to simulate the compressor performance. The mechanistic chamber model is validated for different compressor sizes, refrigerants and operating ranges. A simplified modeling technique is developed to ensure that the injection mass flow rate, predicted by the mechanistic chamber model, is in balance with the vapor compression cycle. Figure 5 presents the impact of injection port diameter and angle on the heating COP, displayed through contour plots for two different operating conditions. The results indicate that for this particular compressor, the optimum injection diameter is
(a) -30/110F
(b) 35/110F
Fig. 5 Contour plots representing the change in the heating COP w.r.t injection port diameter and angle
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around 0.4 in, yielding a heating COP variation of up to 0.2 for various injection port diameters. Additionally, the best heating COP is independent of the injection port angle within the optimized range of 260–280.◦ . This range was selected to avoid a reduction in volumetric efficiency, which occurs when the injection port and suction port intersect, causing backflow. The developed methodology can be used to explore the optimum injection port specifications for a wide range of compressor sizes, refrigerants and operating conditions. Also, the results from this study will be used to develop a spool compressor prototype with vapor injection.
6 Conclusion A simplified method is developed that calculates the equilibrium vapor injection mass flow rate of VCC in a very short time and iterates over injection port diameter, port angle and injection pressure to find the optimum combination of parameters to achieve the best heating COP. A mechanistic chamber model based spool compressor model is validated with the experimental results and is used for performance evaluation. The preliminary results suggest that the 0.4 in injection port diameter is desirable to achieve the best performance with the vapor injection cycle. The demonstrated model will be used to find the optimum injection port design for future low-GWP refrigerants and heat pump applications.
References 1. D. Kim et al., Performance comparison among two-phase, liquid, and vapor injection heat pumps with a scroll compressor using R410A, in: Applied Thermal Engineering 137. Sept 2017 (2018), pp. 193–202. ISSN: 13594311. https://doi.org/10.1016/j.applthermaleng.2018. 03.086. https://doi.org/10.1016/j.applthermaleng.2018.03.086 2. A. Khan, C.R. Bradshaw, Quantitative comparison of the performance of vapor compression cycles with various means of compressor flooding. 2739 (2022) 3. S. Jain et al., Vapor injection in scroll compressors. Int. Compressor Eng. Cof. 1642 (2004). ISBN: 2173337734. https://docs.lib.purdue.edu/icec 4. M.G. Yuan, Z.H. Xia, Experimental study of a heat pump system with flashtank coupled with scroll compressor. Energy Buildings 40(5), 697–701 (2008). ISSN: 03787788. https://doi.org/ 10.1016/J.ENBUILD.2007.05.003 5. A. Redón et al., Analysis and optimization of subcritical two-stage vapor injection heat pump systems. Appl. Energy 124, 231–240 (2014). ISSN: 03062619. https://doi.org/10.1016/ j.apenergy.2014.02.066 6. M. Mohsin Tanveer et al., Mechanistic chamber models: a review of geometry, mass flow, valve, and heat transfer sub-models. Int. J. Refrig. 142(June 2022), 111–126. ISSN: 01407007. https://doi.org/10.1016/J.IJREFRIG.2022.06.016 7. C.R. Bradshaw, E.A. Groll, A comprehensive model of a novel rotating spool compressor. Int. J. Refrig. 36(7) (Nov. 2013), 1974–1981. ISSN: 0140-7007. https://doi.org/10.1016/J. IJREFRIG.2013.07.004 8. ANSI/ASHRAE, Methods for performance testing positive displacement refrigerant compressors and compressor units, in ANSI/ASHRAE Standard 23-2022 vol. 23(2) (2022)
Theory and Test of Expansion Power Recovery of Rotary Cylinder Compressor Y. S. Hu, H. J. Wei, J. Xu, Z. C. Du, Z. Li, and L. P. Ren
Abstract After the exhaust of rotary cylinder compressor, the refrigerant in the clearance volume will expand during the suction process of the next cycle, resulting in loss of power consumption. The paper proposes a scheme to recover the expansion power of high pressure refrigerant in the clearance volume by setting an expansion chamber, and carries out theoretical analysis and experimental evaluation. The test results show that the larger the pressure ratio is, the more expansive power is recovered. Compressors using expansion power recovery technology can improve energy efficiency by up to 3.3%.
1 Introduction The Rotary Cylinder Compressor (RCC) is a novel displacement compressor [1], its pump body mainly contains seven parts: main bearing, shaft, cylinder, piston, cylinder sleeve, spacing board, and sub bearing as shown in Fig. 1. The piston reciprocates relative to the cylinder, and the cylinder moves in a circular motion relative to the cylinder sleeve; Under the joint action of the above two relative movements, RCC completes the suction, compression and exhaust processes, as shown in Fig. 2. RCC adopts face sealing, with less leakage, high volumetric efficiency and significant advantages in medium and low frequency mechanical efficiency. The test results show that RCC has advantages in volumetric efficiency and electrical efficiency compared with rotor compressor. Y. S. Hu · H. J. Wei · J. Xu · Z. C. Du (B) · L. P. Ren State Key Laboratory of Air-Conditioning Equipment and System Energy Conservation, Zhuhai 519070, Guangdong, China e-mail: [email protected] H. J. Wei · J. Xu · Z. C. Du · L. P. Ren Guangdong Key Laboratory of Refrigeration Equipment and Energy Conservation Technology, Zhuhai 519070, Guangdong, China Y. S. Hu · H. J. Wei · J. Xu · Z. C. Du · Z. Li · L. P. Ren Gree Electric Appliances, Inc., Zhuhai 519070, Guangdong, China © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_39
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Fig. 1 Structure decomposition diagram Suction channel
1.Start suction,
Suction chamber
2.Suction process
End of exhaust
4.Compression process
3.Inhale end, start compression
5.Compresion process
Fig. 2 Schematic diagram of suction and exhaust process
6.Start exhausting
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The over compression of positive displacement compressor has great influence on the performance. Xiong et al. [3] studied the compound gear compressor and showed that, under the appropriate clearance volume, expanding the flow area of the diversion groove can solve the exhaust over compression. Huang et al. [4] realized synchronous monitoring of the rotation Angle and pressure of the rotor compressor by positioning the rotation Angle of the rotor compressor. Hu et al. [5] carried out CFD simulation analysis on the pressure pulsation of the refrigerant inside the rolling rotor compressor, and combined with the experimental study, obtained the relationship between the pressure inside the compressor pump and the Angle, so as to calculate the indicating power of the compressor. In order to evaluate the impact of over compression on the rotary compressor, we conducted an experimental study on the PV characteristics of RCC in the early stage [2]. According to the test results, adding a pressure relief port on the compressor reduces the exhaust loss from 5.5 to 0.5%. However, when the pressure relief port is added, the clearance volume increases at the same time, which affects the compressor efficiency. During the exhaust process of the rotary compressor, the volume of the compression chamber gradually decreases. When the volume decreases to the minimum, the compression process is completed, then the exhaust is finished. The compression chamber is separated from the exhaust port, and there is still a part of high pressure refrigerant in the compression chamber; with the operation of the compressor, the volume of the compression chamber begins to increase, and the suction channel is connected and converted into the suction chamber. At this time, the refrigerant in the suction chamber is still in the high pressure state at the end of exhaust gas. When the suction chamber is connected with the suction channel, this part of refrigerant will expand from the exhaust pressure to the suction pressure. The power in the expansion process cannot be recovered by the compressor, resulting in energy loss.
2 Test Method and Principle 2.1 Test Principle The PV test system of RCC is composed of compressor performance test bench, compressor, angle positioning system and pressure test system. The relationship between pressure and Angle (P-θ) can be obtained by testing the pressure at each Angle of the RCC compressor. The relationship between pressure and Angle (P-θ) can be obtained by testing the pressure at each Angle of RCC compressor. Combined with the relationship between volume and Angle, the pressure and volume curve (P– V) of the compressor can be obtained. By integrating the figure, the indicating work of the compressor can be obtained and the loss distribution can be further evaluated. Detailed test methods are shown in reference paper [2] (Figs. 3 and 4).
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w=
n
Vi Pi
(1)
i=1
In this test, three pressure sensors are arranged at different radial angles of the cylinder. Sensor 1 is installed in the suction channel to monitor the pressure value in the suction cavity at different angles during the suction process; Sensor 2 is mainly responsible for monitoring the pressure value in the suction chamber at different angles during compression; Sensor 3 is mainly responsible for monitoring the pressure state during the exhaust process, which is used to evaluate the loss of the valve disc during the opening stage and the over-compression loss. At the same time, it can monitor the expansion process of the high pressure refrigerant in the clearance volume and calculate the recovery of expansion power (Fig. 5; Table 1). Fig. 3 Compressor for PV test
Fig. 4 Schematic diagram of indicated power calculation
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S2 connection angle
S2 separation angle
S3 connection angle
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Fig. 5 Schematic diagram of the position of the pressure sensor
Table 1 Pressure test angle range of pressure sensor
Sensor
Starting angle (°)
Ending angle (°)
S1
0
180
S2
175
290
S3
280
390
Fig. 6 Complete P–θ curves
By combining the pressure curves of the three pressure sensors, a complete P-θ curve can be obtained, and then a P–V curve can be obtained by the relationship between Angle and volume (Figs. 6 and 7).
2.2 Test Conditions Based on the PV test scheme designed above, PV test of rotary cylinder piston compressor is carried out. The test conditions are shown in Table 2. Through PV test, we can study the valve disc opening stage loss, over compression loss and inspiratory
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Fig. 7 P–V curve
Table 2 Compressor working condition
Working condition number
1
2
Refrigerant
R410A
R410A
Condensation temperature (°C)
44
42
Evaporation temperature (°C)
15
2
Polytropic exponent
1.2
1.2
Volume (cc) (MPa)
9.6
9.6
Operating frequency (Hz)
50
50
loss of RCC compressor. This paper mainly studies the refrigerant expansion process in RCC clearance volume, and other characteristics of PV test are discussed in detail in other papers.
2.3 Theoretical Calculation of Expansion Angle The relationship between the volume of the working chamber and the rotation Angle of the rotary cylinder compressor is as follows: Vθ = Vco (1 − cos θ ) + Va
(2)
The relation between the pressure in the expansion cavity and the Angle is: n Pθ V0 = P0 Vθ
(3)
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Working condition number
1
2
Suction pressure (MPa)
1.28
0.86
Exhaust pressure (MPa)
2.73
2.60
Expand angel (°)
15
20
Expansion work/indicated work
1.3%
3.5%
Fig. 8 Expand angle
Without considering over compression, according to formulas (2) and (3), the angle from the expansion of high-pressure gas in the expansion chamber to the suction pressure can be calculated under each working condition (Table 3). The connection angle between the expansion chamber and the suction channel has a direct impact on the recovery effect of expansion power. If the connection angle is front, the recovery of expansion power is insufficient; If the connection angle is behind, there will be over-expansion. Based on the theoretical calculation results of the expansion end angle, the refrigerant pressure in the expansion cavity is connected with the suction channel at the moment of reaching the suction pressure by adjusting the connection angle between the suction channel of the compressor and the expansion cavity (Fig. 8).
3 PV Test Analysis of Expansion Process The Angle range of connecting the working chamber of sensor 3 is 280–390° (Fig. 11), where 360–390° is 0–30° in the next working cycle, and this Angle range is the working range of the expansion chamber (Figs. 9 and 10). There are two test conditions set in this test. The pressure ratio of working condition 1 is 2.1 and that of working condition 2 is 3.0. The test results show that the expansion angle of working condition 1 is 19° and that of working condition 2 is 27°. The larger the working pressure ratio, the larger the expansion angle. Fig. 12
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Fig. 9 P–θ curve of S3 of working condition 1
Fig. 10 P–θ curve of S3 of working condition 2
Fig. 11 PV curve of S3 of working condition 1
shows the P-θ relationship of expansion stages in two working conditions. When the pressure in the expansion chamber is lower than the inspiratory pressure, the gas in the expansion chamber will continue to expand because the expansion chamber is still not connected with the suction channel. This stage is called over expansion, and the process of over expansion will consume power.
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Fig. 12 PV curve of S3 of working condition 2
The P-θ curve is converted into a P–V curve, and the expansion power is calculated through the P–V curve. The expansion power under condition 1 is 6.5 W, accounting for 1.4% of the indicated power; In condition 2, the expansion power is 20.7 W, accounting for 3.7% of the indicated power. The greater pressure ratio is, the more the expansion power is recovered.
4 Compressor Optimization Design and Experimental Results Based on the PV test results, the expansion chamber is set on the compressor. In order to avoid over expansion, the angle of the expansion chamber is designed according to the expansion ratio under the condition of small pressure ratio. The compressor test results show that under this expansion angle, the compressor efficiency in condition 1 increases by 1.5%, and the compressor efficiency in condition 2 increases by 3.3% (Fig. 13).
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Fig. 13 Compressor improvement
5 Conclusion The rotary cylinder compressor has the characteristics that the suction chamber and the exhaust chamber are independent of each other. An expansion chamber can be set between the suction chamber and the exhaust chamber to recover the expansion power of the high pressure refrigerant in the clearance volume. Test results and theoretical analysis results show that setting expansion chamber on RCC can improve compressor energy efficiency. During the actual operation of the compressor, the working pressure ratio is variable, and the existing expansion chamber structure can only ensure the recovery efficiency of specific working conditions, not all working conditions. The follow up plan is to study the expansion power recovery scheme applicable to different pressure ratios.
References 1. Y.S. Hu, H.J. Wei, J. Xu, Z.C. Du, S. Yang, L.P. Ren, The theoretical and experimental research of a novel rotary cylinder compressor. IOP Conf. Ser.: Mater. Sci. Eng. 604(1), 012073 (2019) 2. Y.S. Hu, H.J. Wei, J. Xu, Z.C. Du, P.L. Zhang, Analysis and optimization of over compression for rotary cylinder compressor based on PV test. IOP Conf. Ser.: Mater. Sci. Eng. (2021) 3. W. Xiong, Q.K. Feng, X.Y. Peng, X.M. Li, Mathematical calculation and experimental study of compound gear-type compressor. J. Mech. Eng. 40, 189–194 (2004) 4. W.C. Huang, W.H. Yin, J.Q. Geng, Experimental study on rotation angle monitoring of rotary compressor. Refrig. Air-Condition. 15, 35–38 (2015) 5. Y.S. Hu, S.B. Liang, Simulation and experimental study of refrigerant pressure fluctuation in rolling rotor compressor. Electr. Appl. 8, 48–51 (2011)
An Investigation of Internally Geared Screw Compressor Performance Using a Chamber Modelling Approach Halil Lacevic, Ahmed Kovacevic, and Matthew Read
Abstract Gerotor machines are commonly used as oil and fuel pumps, and as hydraulic pumps and motors. They also have the potential to be used as positive displacement compressors, which is the focus of current research. The mechanism consists of an inner and outer rotor which rotate in the same direction but are each centred on offset parallel axes. The rotor profiles are specified such that multiple continuous contact points occur between them forming several separate working chambers, whose volume varies from minimum to maximum and back to minimum during rotation of the rotors. For a gas or two-phase working fluid, varying the discharge port geometry allows internal compression to occur prior to discharge. Furthermore, adding helical twist to the rotors allows the forces and torques acting on the rotors to be modified in order to minimize contact forces and power transfer between the driven and idler rotors. Previous research has investigated the operation of these internally geared screw machines via characterization of key geometrical properties and simplified analysis of the compression process. The current paper describes progress made on incorporating the geometrical analysis of these machines with the existing quasi one-dimensional chamber model within the in-house performance prediction software. This has allowed the compression process to be analysed in detail, including consideration of leakage flows and port flow losses. The influence of a range of factors including rotor profile, dimensions, built-in volume index and wrap angle have been considered via a parametric study over a range of inlet and discharge conditions. Keywords Chamber modelling · Internally geared screw machine · screw compressor
H. Lacevic (B) · A. Kovacevic · M. Read Department of Mechanical Engineering and Aeronautics, City, University of London, London, UK e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_40
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1 Introduction Internally geared positive-displacement machines have not been extensively investigated for compressor applications, but are relatively common as liquid gerotor pumps. The gerotor pump consists of two straight-cut rotors which rotate in the same direction about non-coincident parallel axes [1] and are commonly used in fuel and oil pumping applications and as hydraulic motors. The profiles of gerotor pump rotors are generated such that the continuous contact between the rotors is achieved. Porting in the casing then controls the period during which fluid is allowed to enter or leave the working chambers. While these ports are largely symmetrical in gerotor pumps, they can be sized to allow compression or expansion of a trapped mass of fluid to be achieved [2]. A 3D model and a cross-sectional view of a prototype internally geared screw machine are shown in Fig. 1. Previous studies on the internally geared screw machine investigated different geometries and methods to generate internally geared profiles with continuous contact between them and potential advantages have been presented [3, 4]. Apart from understanding the geometry of the machine, an important factor determining the compressor performance is the effect of internal leakage flows. The internally geared screw machine has axial, radial, interlobe and end face leakage paths. The length of the leading and trailing edges of the volume contained between two rotors can be found by tracking the contact points throughout the working chamber. However, unlike conventional twin-screw machines, the internally geared machines have no ‘blow-hole’ leakage area as the helix on both rotors has the same orientation [3]. The objective of this study is to, for the first time, use chamber modelling approach in order to investigate thermodynamic results for different configurations of internally geared screw machines for oil injected applications for compression of air between .1 and.8 bar. A performance calculation and design software for rotary positive displacement machines, SCORG, which was developed at City, University of London [6] is
(a) Internally geared screw machine model[5]
(b) Cross-sectional view of the internally geared screw machine prototype
Fig. 1 Internally geared screw machine
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used for thermodynamic calculations in this paper. Calculation procedures for the internally geared profile generation as well as geometry calculations were developed and integrated with the SCORG software allowing the usage of existing quasi onedimensional chamber thermodynamic modelling feature with the internally geared screw machine geometry.
2 Thermodynamic of the Compression-Expansion Process To perform thermodynamic calculations, SCORG software solves a nonsteady flow internal energy equation and calculation of the remaining thermodynamic and fluid properties within the machine through several cycles until the solution converges [7], as follows: dU dV .ω ˙ out + Q˙ − ωp (1) = (mh) ˙ in − (mh) dφ dφ ˙ in represents the energy gain due to the gas inflow into the working where .(mh) volume by the mass inflow, while the energy loss due to the gas outflow is defined by ˙ out . Variables.ω and the product of the mass outflow and its average gas enthalpy.(mh) .φ represent the angular velocity and angle of rotation of the main rotor respectively. Internal energy is represented by .U and the . Q˙ is the heat transfer between the fluid and the compressor surrounding. The used mass continuity equation is: ω
.
dm = m˙ in − m˙ out dφ
(2)
m˙ in and .m˙ out are the mass inflow and outflow rates, respectively, while each of the mass flow rates are calculated as:
.
m˙ = wρ A
(3)
.
The instantaneous density .ρ is obtained from the instantaneous mass trapped in the control volume and the size of the corresponding instantaneous volume .V as m and .w is the fluid velocity. The equations of energy and continuity are solved .ρ = V to obtain .U (φ) and .m(φ). Together with .V (φ), the specific internal energy .u = U/m and specific volume .v = mV are now known and temperature .T as well as the pressure inside the working chamber . p can be calculated for an ideal gas: .
u T = (γ − 1) , R
p=
RT v
(4)
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Adiabatic exponent .γ , gas constant . R, specific volume .v and specific internal energy are predetermined. Expressing the clearance flow leakage .m˙ l in terms of local variables (discharge coefficient .cd , fluid velocity .wl and flow cross-sectional area . Al ) at a particular position in the machine can be obtained using the following equation: .m ˙ l = cd wl ρl Al (5) The leakage gas velocity is calculated from the differential momentum equation, accounting for the fluid-wall friction as: wl dwl +
.
w 2 dx dp =0 + f l ρ 2 De
(6)
The friction coefficient . f is dependent on the local Reynolds and Mach numbers, as well as the shape of the clearance gap. Assuming constant enthalpy throttling process, the working fluid temperature will change only slightly, thus it’s density may be treated as a pressure function only. The continuity equation may then be integrated between the high and low pressure sides of the gap to yield: / m˙ l = cd Al
.
p22 − p12 RT2 [ζ + 2 ln( p2 / p1 )]
(7)
where . R is the gas constant, .T2 is the fluid temperature at high pressure side, .ζ is the flow resistance and . p2 , . p1 are pressures on high and low pressure side, respectively. The thermodynamic process of a compressor is described in detail by Hanjalic, Stosic [7] and the model used to perform the calculations in this paper is based on these equations. Injecting oil inside the compressor chambers has several advantages, such as cooling the compressing fluid, lubricating the meshing rotors and other clearance gaps, and preventing internal leakages. The interaction between the oil films and the rotors does however lead to a drag power loss [8]. In conventional twin-screw machines, oil creates drag losses through three different leakage paths: axial (casing-to-end face), interlobe (rotor-to-rotor), and radial (rotor tip-to-casing). However, since the internally geared rotors co-rotate with continuous contact, there is no equivalent of the radial drag. All drag occurring in rotor-to-rotor contact points has relatively low sliding velocity, and can be considered equivalent to drag in the interlobe gap in conventional machines, which is often neglected. The oil drag power (i) . Po is calculated using the Eq. 8 where . Fd and . Fd(a) represents interlobe and axial drag forces respectively, while .W(i) and .W(a) represent the corresponding velocities related to interlobe and axial drag force. .
Po = Fd(i) · W(i) + Fd(a) · W(a)
(8)
Drag force is calculated based on the shear stress of oil .τoil and the area on which that shear stress is applied to, . A gap . The drag forces . Fd(k) (.k = i, a) are related only
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to the interlobe and axial gaps. The relation used to calculate the shear stress in these gaps is presented in Eq. 9 where .ρgap and .μgap represents density and viscosity of the fluid in the gap respectively and .δgap is the actual size of the clearance gap. The fluid in the clearance gaps is assumed to be a homogeneous mixture of oil and gas with mass fraction equal to the overall oil-gas mass flow ratio for the compression process. ρgap · μgap · Wti p .τoil = (9) δgap Drag force, . Fd , calculation for axial and interlobe drag force is based on Eq. 10 where . A gap represents the surface area of the gap calculated by gap length and depth. .
Fd = τoil · A gap
(10)
The oil drag power calculation takes into account the main rotor (inner) tip speed Wa = Wti p in order to calculate axial shear stress and oil drag loss. Since interlobe drag force occurs between the inner and outer rotors providing different relative velocity between the two surfaces, the shear stress and drag loss calculation is a function of the sliding velocity between the two rotors .Wi = W12 at the contact point. Sliding velocity equations and detailed explanation used in this research are presented by authors [9, 10]. For the purpose of this research, sliding velocity .W12 is calculated for a contact point between the two rotors in one full rotational cycle and the root mean square (RMS) method is used in order to find a mean value used for radial drag force calculation.
.
3 Thermodynamic Analysis of Internally Geared Screw Machine Previous work has contributed to the understanding the internally geared screw machine geometry [3, 5] which allows further studies on thermodynamic of internally geared screw machines to be performed. Initial thermodynamic analysis of internally geared screw machines is a key requirement for understanding the overall performance of the machine and identifying areas where more detailed analysis may be appropriate. For this initial analysis, a configuration is chosen from previous research [5], referred as Case A in further text, that has been shown to limit power transfer between the rotors while achieving high swept volume. This Case A configuration is inner rotor driven and the parameters used to produce internally geared rotor profiles are presented in Table 1 (Case A) while the profiles are generated using the pin-generation method described by authors [5, 9]. Software implementing the pin-generation method as well as the geometry calculations for internally geared rotor profiling is developed and integrated with the SCORG software allowing a convenient means of generating internally geared profiles and performing geometry calculations.
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Table 1 Internally geared screw machine configuration parameters for compared cases Case A Case B Number of lobes for outer rotor . N1 Number of lobes for inner rotor . N2 Non-dimensional pin-center .λ parameter Non-dimensional pin-radius .σbar parameter Inner rotor length-to-diameter . L 2 /D2 ratio Inner rotor diameter . D2 Volume index .VI Inner rotor wrap angle .Φ2
.5
.5
.4
.4
.1.4
.1.4
.0.99
.0.99
.1.2187
.1.2187
.151.79 mm
.118.97 mm
.5
.4
◦
.261.25
.65.312
◦
Fig. 2 Magnitude of the sliding velocity for internally geared Case A configuration showing the obtained RMS value of the sliding velocity
It should be noted that the particular profile shape parameters chosen for the current study are based on previous studies which do not consider the effects of leakage, and future work will focus on full geometrical optimisation of the internally geared machine. The aim of the current study is to demonstrate the functionality of the software that will be used for optimisation and identify aspects of the machine performance modelling that may require further attention. Thermodynamic calculations were performed for the internally geared screw machine Case A configuration and gas mass flow rate of .m˙ 0 = 0.0951 is obtained. Sliding velocity magnitude as well as the calculated RMS value used in oil drag loss calculation for radial gaps for the Case A configuration are shown in Fig. 2.
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The pin-generation method for profile generation is based on the outer rotor geometry parameters, and hence these input parameters were varied in the current parametric study. Results, however, are presented in terms of the driven main rotor (in this case the inner) as for conventional screw machines. The parametric study was based on the same profile shapes as Case A (non-dimensional parameters .λ = 1.4 and .σbar = 0.99) and number of lobes (. N1 = 5, . N2 = 4) with different values of the outer rotor length-to-diameter ratio (. L 1 /D1 ) and wrap angle (.Φ1 ). In order to compare different configurations, the same gas mass flow rate .m˙ 0 is maintained (within the accepted error of .5%) by varying the outer rotor diameter. Additionally, volume index.VI has been varied for each case in order to achieve the lowest specific power for the specified operating conditions. Outer rotor length to diameter ratio (. L 1 /D1 ) values considered are . L 1 /D1 = 0.25 · i + 1, i ∈ {0, 1, 2, 3, 4}, outer rotor wrap angle (.Φ1 ) values are .Φ1 = j · Φn , j ∈ {0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75}, Φn = 209◦ and volume index values are .VI = 0.5 · k + 2, k ∈ {0, 1, 2, 3, 4, 5, 6}. Geometry calculations consisting of the geometry of the suction, discharge and fluid injection ports, chamber volume area and leakage paths with respect to the rotor position are used as the input data for the existing quasi one-dimensional chamber modelling approach. Careful study of the lines of rotor-to-rotor contact in internally geared machines allows leakage paths which connect different working chambers to be identified. The pressure difference across these sealing lines is a key factor in determining the internal leakage to and from a chamber during the compression process. ‘Blow hole’ leakage path is not present in the internally geared screw machine geometry, thus it is not considered in the geometry calculations [3], however for the purposes of the initial thermodynamic calculations, geometry simplifications have been made for the interlobe and axial end-face leakage paths. The loci of contact points between the rotors bifurcates close to the region of the minimum volume. These two branches of the contact loci connect the working chamber to the . N ’th and .(N − 1)’th chambers ahead and behind. In order to use the same chamber model structure as for the conventional compressor, these path have been combined into a single leakage path equivalent to the interlobe leakage, which connects to the .±N ’th chambers. The axial end face leakage has been estimated by assuming a leakage line length of half of the exposed working chamber perimeter for the two chambers immediately ahead and behind. Thermodynamic calculations for all the internally geared screw machine configurations have been performed using fixed working conditions shown in Table 2 considering an ideal gas with an adiabatic exponent of .γ = 1.4, gas constant of J . R gas = 287 and real gas factor of . Z = 1. kgK Based on the thermodynamic analysis, a ‘total’ power is calculated as the sum of indicated power and the estimated oil drag power loss. Other mechanical losses are not considered in the this study, but will be investigated as part of the current research programme. The internally geared screw machine .4/5 configuration with the outer rotor diameter of . D1 = 145 mm, outer rotor-to-length ratio of . L 1 /D1 = 1, outer rotor wrap angle of .Φ1 = 52.25◦ and volume index of .VI = 4, referred as Case
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Table 2 Thermodynamic working conditions Discharge Main rotor tip Suction Suction temperature pressure .(bar) pressure .(bar) speed (m/s) ◦ .( C) 1
8
32
19.85
0.08
0.08
0.06
0.06
0.04
0.04
0.02
0.02
0
0
-0.02
-0.02
Discharge temperature ◦ .( C)
36.85
70
-0.04
-0.04 Inner rotor centrode Outer rotor centrode Sealing line Inner rotor Outer rotor
-0.06 -0.08 -0.1
Oil temperature ◦ .( C)
-0.05
0
Inner rotor centrode Outer rotor centrode Sealing line Inner rotor Outer rotor
-0.06 -0.08 -0.1
0.05
(a) Internally geared screw machine
-0.05
0
0.05
(b) Internally geared screw machine
profiles for Case A
profiles for Case B
Fig. 3 Internally geared screw machine profiles for compared cases Table 3 Thermodynamic results for compared machines Configuration
Discharge temperature .(◦ C)
Indicated power .(kW)
.(kW)
Oil drag power Total power .(kW)
.(
Specific power Volumetric kW efficiency .(%) ) 3
Case A
70.14
27.86668
0.99601
28.86269
6.013
75.72
Case B
70.06
24.65756
0.19865
24.85621
5.403
85.41
(m /min)
B in further text, is found to achieve the lowest specific power, thus it is chosen for comparison with configuration obtained from the previous studies referred as Case A. Case B inner rotor diameter is . D2 = 119.0 m, inner rotor length-to-diameter ratio is . L 2 /D2 = 1.219 and inner rotor wrap angle is .Φ2 = 65.31◦ . Both Case A and Case B configuration parameters in terms of the main, inner, rotor are shown in Table 1 and generated rotor profiles for the Case A and Case B configurations are shown in Fig. 3. Oil injection angle is .60◦ with respect to the main rotor rotational position for all configurations while oil injection port diameter is varied in order to achieve the fixed discharge temperature of .70 ◦ C. Thermodynamic results for the Case A and B configurations are shown in Table 3. It can be seen that with variations of the port diameters, the same discharge temperature of .≈ 70 ◦ C is achieved. It can also be observed that the Case B internally geared configuration has greater volumetric efficiency and significantly lower indicated power as well as the lower oil drag power resulting in lower specific power.
An Investigation of Internally Geared Screw Compressor Performance .. . . Table 4 Mass flow rates and oil injection port diameter Configuration Gas mass flow Oil mass flow Oil-to-gas (kg/s) (kg/s) ratio Case A Case B
0.0951 0.0912
0.3485 0.2846
3.664 3.121
499
Oil injection port diameter (mm)
Rotational speed (RPM)
5.04 5.09
4026.3 5137
Table 5 Comparison of the Case A and Case B machine rotor diameters, lengths and volumes Inner/main Machine Machine Chamber Configuration Outer/gate rotor diameter rotor diameter length (mm) volume .(m3 ) volume .(m3 ) (mm) (mm) Case A Case B
185 145
151.79 118.97
185 145
0.004973 0.002394
0.000393 0.000262
Mass flow rates as well as the oil injection port diameters and rotational speeds for both configurations are shown in Table 4. The Case B configuration has slightly lower gas mass flow rate (.≈ 4%) and lower oil mass flow rate resulting in lower oil-to-gas ratio. The Case A configuration requires greater oil mass flow rate in order to achieve the same discharge temperature (.70 ◦ C) as the Case B configuration, while Case B operates at higher rotational speed in order to achieve the similar gas mass flow rate. Comparison of machine sizes for two cases showing the rotor diameters, machine lengths, overall volume of the compressor, calculated from the outer diameter and length, and the displacement volume of a single chamber are presented in Table 5. Both configurations have the same inner rotor length-to-diameter ratio . L 2 /D2 = 1.219. However, the significantly lower wrap angle in the Case B configuration leads to a smaller diameter . D2 = 119.0 mm and machine length. The Case B configuration has lower machine volume and lower chamber displacement volume, as the lower diameter allows higher operating speed with the same fixed tip speed of 32 m/s. Additionally, volume curves for a single working chamber for both configurations are presented in the Fig. 4. Based on the presented results it can be seen that Case B internally geared screw machine is smaller in overall size than the Case A configuration. As well as leading to a more compact compressor package, this has the advantages of lower manufacturing time and cost, and reduced sealing line lengths relative to the working chamber volume. The reduced influence of leakage flows in Case B is the main cause of the increase in volumetric efficiency seen in Table 3. Thermodynamic results for the Case A internally geared configuration showing the pressure as well as the mass flows in the working chamber with respect to the main rotor rotational position are shown in Fig. 5a, b respectively. Thermodynamic results for the Case B internally geared configuration showing the pressure as well as the mass flows in the working chamber with respect to the main rotor rotational position are shown in Fig. 6a, b respectively. Figures show that the leakage in the
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Fig. 4 Working chamber volume with respect to the main rotor rotational position for Case A and Case B configurations
working chamber for the Case B internally geared configuration is lower than the leakage in the working chamber for the Case A configuration. Furthermore, there is significantly less oil in the machine for the Case B configuration. Pressure diagrams show that both configurations are slightly under-compressing while the peak pressure is higher for the Case B configuration. This is due to the fact Case B has both a lower wrap angle and a higher rotational speed, which together result in a higher maximum rate of change of volume for a working chamber. The reduced wrap angle combined with the reduction in profile diameter will together tend to decrease the maximum discharge portflow area. The net effect of the increase rate of change of volume and the reduced port flow area is a larger build up of pressure in the working chamber during discharge. This needs to be balanced against the benefits of reducing leakages, highlighting the need for rigorous optimisation of machine geometry for a particular application.
4 Conclusion This paper describes the thermodynamic analysis of internally geared screw compressors. The capability to integrate geometrical data with the one-dimensional chamber model functionality of the software SCORG has been demonstrated, and used to investigate machine performance. The Case A configuration, obtained from the previous study, was selected as a basis for thermodynamic analysis presented in this paper. A parametric study of the outer rotor diameter, wrap angle and length-todiameter ratio using chamber thermodynamic model has characterised their influ-
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Fig. 5 Thermodynamic results for the Case A configuration of internally geared screw machine
Fig. 6 Thermodynamic results for the Case B configuration of internally geared screw machine
ence on performance. For a fixed rotor tip speed, an improved Case B geometry has been identified which achieves similar mass flow rate with smaller inner and outer rotor diameters, and higher rotational speed. The influence of volume index on specific power has been investigated. The Case B configuration has lower leakage flow rate and .≈ 10.15% lower specific power compared to the Case A configuration, leading to more efficient compressor. Additionally, the Case B configuration reduced the outer and inner rotor diameters and machine length by .≈ 21.6% resulting in a more compact machine. The thermodynamic model presented in this paper will be developed for use in performance prediction of internally geared screw machines. Future work will focus on experimental validation of the performance prediction and full optimization of the internally geared screw machine for selected applications. Full comparison of the internally geared and conventional twin screw compressors will then be performed.
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Acknowledgements Funding for this research was received from Carrier Inc., USA and PDM Analysis Ltd., UK.
References 1. M. Rundo, Models for flow rate simulation in gearpumps: a review. Energies 10, 1261 (2017) 2. M.G. Read, I.K. Smith, N. Stosic, Internally geared screw machines with ported end plates. IOP Conf. Ser. Mater. Sci. Eng. 232, 012058 (2017). https://doi.org/10.1007/11823285_121 3. M.G. Read, I.K. Smith, N. Stosic, Influence of rotor geometry on tip leakage and port flow areas in Gerotor-type twin screw compressors. Proc. Inst. Mech. Eng. Part E J. Process Mech. Eng. 236(1), 94–102 (2020) 4. M. Read, Basic design procedure for an internally geared screw compressor. IOP Conf. Ser. Mater. Sci. Eng. 1180(1), 012055 (2021) 5. M.G. Read, N. Stosic, I.K. Smith, The influence of rotor geometry on power transfer between rotors in gerotor-type screw compressors. J. Mech. Des. 142(7) (2019) 6. A. Kovacevic, N. Stosic, I.K. Smith, Screw Compressors: Three-Dimensional Computational Fluid Dynamics and Solid Fluid Interaction (Springer, Berlin Heidelberg, New York, 2006). ISBN 3-540-36302-5 7. K. Hanjalic, N. Stosic, Development and optimization of screw machines with a simulation model-PART II: thermodynamic performance simulation and design optimization. J. Fluids Eng. 119(3), 664–670 (1997). https://doi.org/10.1115/1.2819296 8. S. Abdan et al., Experimental validation of the screw compressor oil drag model for various rotor profiles. Proc. Inst. Mech. Eng. Part E J. Process Mech. Eng. 095440892311635 (2023). https://doi.org/10.1177/09544089231163514 9. D. Vecchiato, A. Demenego, J. Argyris, F.L. Litvin, Geometry of a cycloidal pump. Comput. Methods Appl. Mech. Eng. 190(18–19), 2309–2330 (2001) 10. L. Ivanovi´c, D. Josifovi´c, A. Ili´c, Modelling of trochoidal gearing at the Gerotor Pump. Power Transm. 553–562 (2013). https://doi.org/10.1007/978-94-007-6558-0_44
Development of Numerical Grid and CFD Model for Analysis of Oil-Injected IGSM Sham Rane, Ahmed Kovaˇcevi´c, and Matthew Read
Abstract A novel prototype design of an internally geared twin screw compressor for air, with oil injection has been analysed using a custom developed numerical grid. A two-fluid Eulerian-Eulerian CFD model has been applied for the calculations. Compressor performance at various operating conditions has been evaluated together with an analysis of the flow at the suction, discharge, and injection ports. Over the calculated range of speed and pressure, a specific power of 2–4 kW/m3 /min was estimated with a maximum volumetric efficiency of 95%. The adopted CFD model could be further used to optimize the oil injection and evaluate design modifications such as rotor profiles, variable lead rotors, etc. Keywords CFD · Dynamic mesh · Screw compressor · Oil injection · IGSM
1 Introduction A novel design of a positive displacement compressor is the internally geared configuration. In this arrangement, the conventional compressor housing is eliminated, and the second screw rotor is internally lobed in a conjugate action with the inner conventional screw rotor. To improve the volumetric and adiabatic efficiency of the compressor, oil is injected during the compression process. Numerical models using CFD can be used to evaluate such oil injection design and help in achieving an improved performance at various operating conditions. Figure 1 shows the layout of a 5–6 configuration that is being prototyped [1, 2]. Two end plates house the bearings for the 5-lobed inner rotor and have cut-outs for the suction and discharge port. The 6-lobed outer rotor is also rotating about an offset parallel axis, and it is held within a housing not shown here. The port shapes are important for controlling the closing of suction and opening of discharge, also to avoid any direct connection between the two ends. S. Rane (B) · A. Kovaˇcevi´c · M. Read City, University of London, London EC1V 0HB, UK e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_41
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Fig. 1 Prototype model of 5–6 IGSC with end plates showing the suction and discharge ports
A design procedure for IGSM for applications to compressors has been reported in [1]. The parameters such as flow rate, flow velocity in the ports were considered. A more detailed evaluation of such rotor geometry is presented in [2]. Swept volume, port flow areas and leakage areas were studied with respect to the rotor’s geometrical variation such as profile and wrap angles. Respective advantages of IGSM were identified. In this work, an in-house grid generator tool SCORG has been used for generating the computational grid of the deforming rotor domain. A two-fluid EulerianEulerian model has been applied for calculations of oil injection during the compression process. Compressor performance such as flow, indicated power, efficiencies at various operating conditions have been evaluated. Additionally, the suction and discharge port configuration has been studied for timing, filling, and built-in compression characteristics.
2 Grid Generation for Internally Geared Screw Rotors 2.1 Rotor Grid Generation Procedure The rotor grid generation has been implemented in the customised grid generator SCORG [3]. The procedure uses a combination of analytical and differential mesh generation. The cross-section grid is controlled using a distribution factor, number of nodes on the profile and in the radial space. Figure 2 represents the main steps in the generation of the 2D cross section mesh. By setting an angular increment to the rotor movement, the time advancement of the grid nodes and helical shape of the rotor is obtained [3].
2.2 Profile Adaptability The developed grid generator can adapt to profile variations such as shapes, different lobe combinations, depth of chambers, axis offset and wrap angles. Figure 3 shows three examples of 2–3, 4–5 and 8–9 lobes with small differences in profile parameters.
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Fig. 2 Procedure of the rotor grid generation in the cross-section and control parameters
Fig. 3 Few examples of IGSM rotor profiles and cross-section grid
The corresponding IGSM applications can range from low pressure ratio blowers to Gerotor type liquid pumps [1].
2.3 Lead Variation Another type of rotor design variation under investigation is its lead. By applying a variable lead on the IGSM rotors, it will be feasible to eliminate the ports, while still achieving the built-in compression ratio. A relative advantage is offered for bearing sizing and arrangement, etc. The CFD model was required to be capable of evaluation of such design variations, for which the rotor grid generator has been adopted. Using rotor lead variation, the axial spacing between the cross-section grids is calculated and the 3D grid is modified [4]. The 2D grid data remains the same as it was for an unform lead rotor. Figure 4 shows two examples of lead variations. In Fig. 4a, the low-pressure end pitch is 80 mm and that at the high-pressure end is 20 mm, there-by reducing the lobe spacing axially. In Fig. 4b, this has been reduced further to 10 mm. In both cases, the wrap angle of the rotor increases proportionally.
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Fig. 4 Examples of lead variation on the IGSM rotors
3 CFD Model of Oil Injected IGSC Unlike the classical twin screw compressor, where the housing is available for positioning the oil injection ports, in case of IGSM’s the outer rotor poses a challenge to design the oil injection system. In this case study, the prototype IGSM was evaluated with an oil injection located on the high-pressure end plate. The injection was timed to begin at 30° past the suction closure. Table 1 presents the main parameters of the prototype design and Fig. 5 represents the CFD model. Main parts of the CFD model are the rotors, suction, discharge, and oil injection ports. Additionally axial gaps were introduced. The operating clearance between the rotors was specified as 100 µm, the axial clearance at suction side was set at 100 µm and that at the discharge end was set at 50 µm. Oil injection hole size was 5 mm and the injection pressure was set to be equal to the discharge pressure. The description of the two fluid CFD model suitable for oil injected compressors has been reported in [5]. The same parameters for the solver, air and oil properties have been used. Table 2 shows the main settings of the ANSYS CFX solver. Table 1 The 5–6 IGSC prototype design
Variable
Value
Description
N1 (–)
6
Outer rotor lobe number
N2 (–)
5
Inner rotor lobe number
D (mm)
100
Diameter of outer rotor
L (mm)
130
Length of both rotors
E (mm)
6.712
Axis spacing distance
λ (–)
1.4
Profile shape parameters
σ (–)
0.8
(deg)
234
Wrap angle
v (–)
2
Built-in volume ratio
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Fig. 5 Schematic of the CFD model
Table 2 ANSYS CFX solver setup Mesh deformation
User defined nodal displacement
Advection scheme
High resolution
Mesh in ports
Tetrahedral with boundary layer refinements (ANSYS Mesh)
Transient scheme
Second order backward euler
Turbulence model
SST—k Omega (Standard wall functions)
Transient inner loop coefficients
Up to 5 iterations per time step
Inlet boundary condition
Opening (Specified total pressure and temperature)
Convergence criteria
r.m.s residual level 1e−03
Outlet boundary condition
Opening (Static Relaxation parameters pressure, backflow acts as total pressure and temperature)
Solver relaxation fluids (0.1)
4 Results and Discussion The test compressor was analysed over a speed range of 1000–4000 rpm and at two discharge pressures of 200 and 300 kPa. At the suction, the pressure was set at 100 kPa and temperature of 25 °C. The oil injection pressure was set equal to the discharge pressure and temperature of 40 °C. The results have been presented here to study the characteristics of compression and interaction of injected oil during the cycles.
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Fig. 6 Chamber pressure variation with rotor angle and a sample instantaneous distribution
4.1 Pressure Distribution The variation of pressure in the chamber with rotation of the inner rotor is presented in Fig. 6 at different operating conditions. An instantaneous distribution of pressure on the inner rotor has also been shown at 2000 rpm and 200 kPa discharge pressure. The suction port is closed at 90°. Oil injection starts at 120° inner rotor angle and for a built-in volume index of 2.0, the discharge port opens at 220° inner rotor angle. It can be observed that for 200 kPa and 2000 rpm, the internal pressure rise matches the discharge pressure. With increase of speed, over-compression is seen. At higher pressure of 300 kPa, there is under-compression when the port opens. The pressure continues to rise with further rotor rotation and the peak is about 25 kPa higher at 4000 rpm.
4.2 Rotor Torque Variation The 5–6 profile of the test compressor was designed such that transmission torque is minimum. Under ideal conditions the outer rotor is running free with zero torque. However, due to leakage and diffusion of pressure across adjacent chambers, there is a resultant transmission torque. This has been evaluated from the CFD model. Figure 7 presents the cyclic variation of torque on the inner and outer rotor with rotation angle of the inner rotor. Due to five lobes on the inner rotor, a full rotation consists of five cycles. For the inner rotor, which is the main drive element, the torque at 200 kPa, 2000 rpm is 2.5 Nm. With higher speed of 4000 rpm, there is an increase in the torque to 3.0 Nm. This is related to the over-compression seen in the pressure distribution plot of Fig. 6. At 300 kPa discharge pressure the average torque increases to 4.5 Nm. The difference between the two speeds reduces. In case of the outer rotor, relatively there is a lower average torque. At 200 kPa, 2000 rpm, it is 1.75 Nm, and
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Fig. 7 Rotor torque variation
a small increase is seen at 4000 rpm. At 300 kPa, 2000 rpm, the average torque increases to 2.0 Nm and at 4000 rpm it further increases to 2.25 Nm.
4.3 Compressor Performance Analysis The compressor calculations were performed such that stable pressure and flow distribution is observed. Data from the final five flow cycles was averaged to evaluate the performance of the compressor, presented in Table 3 for the various operating conditions. The air flow and indicated power variation with inner rotor speed is presented in Fig. 8. Specific power, efficiency and discharge temperature data is presented in Fig. 9. Air Flow. As shown in Fig. 8a, at 1000 rpm, 200 kPa discharge pressure, the flow through the compressor is 0.14 m3 /min. As the speed increases, there is a proportional increase in the flow to 0.862 m3 /min at 4000 rpm. With increase in pressure to 300 kPa, there is a reduction in the air flow which is 0.32 m3 /min at 2000 rpm and increases to 0.808 m3 /min at 4000 rpm. Indicated Power. Similarly, from Fig. 8b, at 1000 rpm, 200 kPa discharge pressure, compressor’s indicated power is the lowest at 360 W. As the speed increases, the indicated power increases to 1.74 kW at 4000 rpm. This is also seen in the internal pressure distribution from Fig. 6. At higher discharge pressure of 300 kPa there is significant increase in power. With 1.28 kW at 2000 rpm, it increases to 2.76 kW at 4000 rpm. Specific Power. Plot of specific power in Fig. 9a shows that the lowest specific power is 2.0 kW/m3 /min at 4000 rpm, 200 kPa pressure. Both flow and indicated power have increased at 4000 rpm, however the increase in flow is more as compared to the increase in power. This results in a better specific power. At 1000 rpm, 200 kPa the specific power increases to 2.6 kW/m3 /min. At 300 kPa, overall specific power is higher and varies from 4.0 kW/m3 /min at 2000 rpm to 3.42 kW/m3 /min at 4000 rpm.
Inner rotor speed
(rpm)
1000
2000
3000
4000
2000
3000
4000
Discharge pressure
(kPa)
200
200
200
200
300
300
300
0.808
0.548
0.320
0.862
0.601
0.349
2763.79
1995.40
1278.49
1739.74
1227.71
774.03
360.97
(W)
(m3 /min)
0.140
Power
Air flow rate
Table 3 5–6 IGSC performance results.
89.82
81.17
71.11
95.80
89.09
77.46
62.05
(%)
Volumetric efficiency
5.560
4.176
3.543
2.864
2.188
1.562
1.321
(kg/min)
Oil flow rate
0.17
0.15
0.11
0.35
0.32
0.26
0.12
(–)
Air-to-oil mass ratio
94.4
83.4
71.6
101.5
81.5
72.5
53.3
(C)
Discharge temperature
3.419
3.642
3.995
2.018
2.042
2.221
2.585
(kW/m3 / min)
Specific power
62.9
59.1
53.8
63.3
62.6
57.5
49.4
(%)
Isentropic efficiency
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Fig. 8 Air flow and Indicated power
Fig. 9 Specific indicated power, volumetric and isentropic efficiency, and discharge temperature
Volumetric and Isentropic Efficiencies. Plots of volumetric and isentropic efficiencies of the compressor are also presented in Fig. 9a. The volumetric efficiency is maximum of 95% at 4000 rpm, 200 kPa pressure. At 2000 rpm is drops down 33%. At 300 kPa pressure, the volumetric efficiency varies from 71% at 2000 rpm to close to 90% at 4000 rpm. For a small size of the IGSM, this volumetric efficiency is in an acceptable range and can be improved further by clearance control and improvement to the oil injection. Due to oil injection heat transfer and leakage flow re-compression effects, the isentropic efficiency of the compressor is in a lower range from 50 to 63%. Air Temperature. The suction air temperature was set to 25 °C. During the compression temperature rises. The leakage of gas also contributes to further rise in chamber temperature due to re-compression. Oil injection temperature was set to 40 °C, 30° after the closure of suction, so initial heat transfer rate depends on the difference between local gas temperature, and this injected oil. Local air temperature in the compression chamber can be highly non-uniform as seen in Fig. 10. Figure 10 is a comparison of the instantaneous temperature distribution on the inner rotor at 200 kPa pressure and speed of 2000, 3000 and 4000 rpm. It can be seen from Fig. 10 that the temperature ranges from 25 to 120 °C. The cycle average discharge temperature
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Fig. 10 Instantaneous air temperature at various operating speeds
was lower than this local peak as seen in Fig. 9b. As the speed increases, there is an increase in the quantity of oil getting injected (Table 3), however the mass of oil distributed into each chamber has reduced, together with the time available for heat transfer between oil and air. This results into an increase in the air temperature with speed.
4.4 Port Flow Dynamics Suction Flow. The suction port spans from the root of the inner rotor to the tip of the outer rotor and can connect 2–3 chambers over its circumference. As the rate of change of volume can vary between successive chambers, the distribution of air within the port is highly non-uniform and turbulent. The cyclic variation of suction flow over a rotation of the inner rotor is presented in Fig. 11. Figure 11 also shows an instantaneous velocity distribution in the port at 200 kPa, 2000 and 4000 rpm. At both speeds, the flow with 300 kPa pressure is lower than at 200 kPa. The average flow increases from 0.4 kg/min at 2000 rpm to 0.9 kg/min at 4000 rpm. The flow velocity is seen to increase from 6 m/s at 2000 rpm to 12 m/s at 4000 rpm. At locations of axial leakage, the velocity of gas exceeds 20 m/s.
Fig. 11 Air flow pulsation at the suction port and gas velocity distribution
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Discharge flow. Circumference of the discharge port is smaller and covers only 1–2 chambers simultaneously. The presence of a differential pressure between the chamber and the ports creates a very non-uniform flow field in the discharge ports. High magnitude pulsations are experienced. The cyclic variation of suction flow over a rotation of the inner rotor is presented in Fig. 12, together with an instantaneous velocity distribution in the port at 200 kPa, 2000 and 4000 rpm. In Fig. 6, over-compression and under-compression was observed with 200 kPa and 300 kPa pressure respectively. This causes a strong flow reversal in the discharge port in case of 300 kPa as shown in Fig. 12. At both pressures, pulsation of the flow is stronger at 4000 rpm. From the velocity distribution, the flow velocity is seen to increase from 10 m/s at 2000 rpm to 18 m/s at 4000 rpm. At locations of axial leakage, the velocity of gas exceeds 20 m/s. Oil Injection Flow. The oil injection port is located on the high-pressure end plate. Due to the movement of the rotors, the injection hole is blocked from the chamber during operation and the flow is intermittent in nature. The formation of the oil pattern within the chamber is presented in Fig. 13 over a complete cycle of 72°. With a reference of zero as closure of the suction port, the oil injection is timed to start at 30°. As the rotors move and the chamber is exposed, oil starts flowing in axial direction, comes in contact with the outer rotor surface and is pushed radially inwards towards the inner rotor surface (seen at 45°). At 60°, injection hole is disconnected from the chamber. On further rotation, oil contacting inner rotor surface is seen at 75° and the patch area keeps increasing. At 102°, the next oil injection cycle begins into the successive chamber.
Fig. 12 Air flow pulsation at the discharge port and gas velocity distribution
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Fig. 13 Oil injection pattern over a cycle
5 Conclusions A prototype design of a 5–6 IGSM compressor for air, with oil injection has been analysed using a custom developed numerical grid. A two-fluid Eulerian-Eulerian CFD model has been applied for the calculations. Compressor performance at various operating conditions has been evaluated together with an analysis of the flow at the suction, discharge, and injection ports. Over the calculated range of speed and pressure, a specific power of 2–4 kW/m3 /min was estimated with a maximum volumetric efficiency of 95%. The adopted CFD model could be further used to optimize the oil injection and evaluate design modifications such as rotor profiles and lead of the rotors. Acknowledgements Funding for this research was received from Carrier Corporation, USA and PDM Analysis Ltd., UK.
References 1. M. Read, Basic design procedure for an internally geared screw compressor. IOP Conf. Ser. Mater. Sci. Eng. 1180, 012055 (2021). https://doi.org/10.1088/1757-899X/1180/1/012055 2. M. Read, I.K. Smith, N. Stosic, Influence of rotor geometry on tip leakage and port flow areas in gerotor-type twin screw compressors. Proc. IMechE Part E J. Process Mech. Eng. 236(1), 94–102 (2022). https://doi.org/10.1177/0954408920962412 3. S. Rane, A. Kovacevic, Algebraic generation of single domain computational grid for twin screw machines. Part I. Implementation. Adv. Eng. Softw. 107, 38–50 (2017). https://doi.org/10.1016/ j.advengsoft.2017.02.003 4. S. Rane, Grid generation and CFD analysis of variable geometry screw machines. Doctoral thesis, City, University of London (2015) 5. S. Rane, A. Kovacevic, N. Stosic, CFD analysis of oil flooded twin screw compressors. In: International Compressor Engineering Conference, Purdue, p. 11023 (2016)
Experimental Study of Conical Rotary Compressor for High Pressure Ratio Applications Yang Lu, Nick Balodimos, Bryon Calder, James Adamson, Chris Bruce, David Noake, and Nicol Low
Abstract The Conical Rotary Compressor (CRC) is a positive displacement machine characterized by internal meshing, variable pitch, and variable rotor profile. Compared to twin screw machines, the CRC has a shorter leakage line length, no leakage triangle, no discharge port, and co-directional thermal expansion, providing advantages when operating at high pressure ratios (Pi). Over-compression or undercompression can be avoided by matching external Pi with internal Pi, which depends on the volumetric index (Vi) of the CRC. However, higher Vi values lead to increased manufacturing complexity and cost. For this study, a CRC with Vi 6.8 was selected, and Vi was modified by reducing the inner rotor length from the discharge side. Experiments were conducted at five different Vi values (6.8, 5.8, 4.6, 4, and 3) with Pi varying from 11 to 41. The results showed that 75% isentropic efficiency and 95% volumetric efficiency were achieved at a pressure ratio of 21. The isentropic efficiency and volumetric efficiency remained higher than 45% and 75%, respectively, even at a pressure ratio of 41. Performance began to decrease when Vi was lower than 4, resulting in significant under-compression. The efficiency contour and Vi contour obtained from this study can be used for performance prediction and optimization of CRC design. Keywords Conical rotatory compressor · Volume ratio · High pressure ratio · Experimental study
Y. Lu (B) · N. Balodimos · B. Calder · J. Adamson · C. Bruce · D. Noake · N. Low Vert Technology, Edinburgh, UK e-mail: [email protected] D. Noake e-mail: [email protected] N. Low e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_42
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Nomenclature q wrap number D1 L omega Vi Pi
Diameter ratio (/) Number of rotations of outer rotor profile over length (/) Pitch diameter (mm) Rotor length (mm) Cutting tool coefficient (/) Volume ratio = VV _suc (/) _dis P_out Pressure ratio = P_in (/)
1 Introduction The transportation of natural gas through pipeline networks is an environmentally friendly and cost-effective method of delivery. However, in the past, natural gas was often wasted through flaring or venting during pipeline maintenance and construction, resulting in both financial and environmental losses. To minimize waste and pollution, natural gas can be recompressed back into the pipeline section or tanks. Typically, a Pressure Index (Pi) of 20–40 is required for this application, which can be achieved using high Volume Index (Vi) in Positive Displacement Machines (PDM) such as piston and twin-screw compressors. Nevertheless, it can be challenging to attain high Pi in a single stage due to leakage and high discharge temperatures in both piston and twin-screw compressors. Pi of twin screw compressor in one stage can reach up to approximately 15:1 with oil cooling [1]. High Pi could be achieved by multistage, but this will add complexity and cost to the system. The Conical Rotary Compressor (CRC) is an innovative rotary compressor that utilizes a variable pitch and rotor profile to achieve high Vi, thereby improving performance at high Pi operating conditions. Its working mechanism, rotor profile design [2], and quasi one-dimensional chamber model [3] have been described. While chamber model analysis is effective for predicting PDM performance [4, 5], the leakage and heat transfer models need to be fine-tuned with experimental results to accurately predict high pressure ratio conditions. Choked flow can occur when the pressure ratio exceeds the critical pressure ratio, which is 0.53 for air. Computational Fluid Dynamics (CFD) is another powerful tool used for PDM performance prediction [6, 7]. However, both the chamber model and CFD require experimental validation to produce reliable results. This study conducted experiments to investigate the capability of the CRC with different Vi for high Pi applications. The performance of the CRC with five different Vi (3, 4, 4.6, 5.8, and 6.8) at Pi between 11 and 41 was evaluated to aid the selection of suitable Vi for different Pi applications.
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Table 1 Suction chamber volume and Vi changing with design parameters Parameters
Symbol
V _suc
Vi
Cutting tool
omega
Increase
Constant
Diameter ratio
q
Decrease
Increase
Wrap number
Lambda
Decrease
Increase
Pitch diameter
D1
Increase
Constant
Rotor length
L
Increase
Constant
2 Rotor Design The design of CRC rotor profile and its geometry calculation has been explained [2]. In this section, the suction chamber volume and Vi of the CRC are analyzed based on the design parameters. Five different Vi values are selected, and the rotor length is calculated accordingly. Additionally, the sealing line length, a key factor in performance, is quantified for all five cases.
2.1 Rotor Geometry Seven parameters are defined for CRC rotor design, which are lobe combination, pitch diameter, variable or constant pitch type, cutting tool coefficient, wrap number, rotor length and diameter ratio. Table 1 shows suction chamber volume and Vi changing with design parameters. Geometrical parameters such as suction chamber and discharge volume, volume index, sealing line length can be calculated with in-house software VertSim [2]. Normalized chamber volume is calculated with changing of rotational angle as shown in Fig. 1. The working process of CRC consists of suction, compression and discharge. Because the rotor pitch and rotor diameter decrease along the rotor length, the chamber volume decreases with the rotational angle. Around 50% suction chamber volume is sacrificed because suction chamber is not closed at the point maximum chamber volume reached. Therefore, it is necessary to design suction and discharge port plates to further increase suction chamber volume and Vi.
2.2 Vi Calculation As shown in Table 1, Vi is only dependent on diameter ratio and wrap number. The relationship between Vi, diameter ratio and wrap number are illustrated by Fig. 2. Vi increases with increasing wrap number and diameter. At wrap number 1.5, Vi is equal to diameter ratio. Any of the three parameters can be interpolated from the known two parameters.
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Fig. 1 Normalized chamber volume changing with rotational angle
Fig. 2 Vi contour
For the convenience of this experimental study, instead of making new pair of rotors with different Vi, inner rotor was reduced in length from discharge end. Discharge chamber volume increases with reducing the inner rotor length while suction chamber volume stays the same. In this way, Vi decreases with a shorter inner rotor. The relationship between Vi and rotor length is shown in Fig. 3. Five Vi cases were selected for this test, which were 3.0, 4.0, 4.6, 5.8 and 6.8. In this study, Vi is calculated without considering oil volume fraction which also occupied the chamber volume. Therefore, Vi could be higher when running with high oil volume flow rate. For example, Vi could increase from 6.8 to 8.0 with oil flow rate of 5 lpm. This will not be introduced here considering the length of this paper.
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Fig. 3 Vi changing with rotor length
(a) Side view
(b) Bottom view
Fig. 4 Contact band between inner and outer rotor with enlarged inner rotor surface
2.3 Sealing Line Length Leakage can negatively impact the performance of CRC. Sealing line should be continuous between inner and outer rotor and as short as possible. CRC has two types of leakage paths which are axial path and radial path. The contact band is amplified by offset inner rotor surface as shown in Fig. 4. Continuous sealing lines are formed between inner and outer rotors and the sealing line length between chambers is decreasing along rotor length. Six leakage paths were defined as shown in Fig. 5. Considering C1 is the control chamber, which can connect with maximum six neighbor chambers. Discharged side paths C12, C22 and C3 have a more significant effect on volumetric efficiency and isentropic efficiency. The discharge side sealing line length of C12, C22 and C3 are calculated for five different Vi cases as illustrated by Fig. 6. The leakage line length increases with the decreasing of Vi.
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Fig. 5 Leakage paths
Fig. 6 Leakage line length comparison
3 Experimental Results An experimental study of conical rotary compressor for high Pi applications is presented in this session. In theory, optimal performance of positive displacement machine is reached when internal Pi matches with external Pi. External Pi is defined as discharge pressure over suction pressure and internal pressure ratio for air testing is calculated based on Vi as Pi internal = V i 1.4 . However, the internal pressure ratio could be higher than theory because of internal leakage. The experimental parameters explored consists of Pi and Vi. The pressure ratio is varied between 11 and 41 and the Vi is varied between 3 and 6.8.
3.1 Test Rig The test rig schematic is outlined in Fig. 7. Same CRC is used for the test which starts from initial Vi of 6.8. CRC with Vi of 5.8, 4.6, 4 and 3 is modified by reducing the length of inner rotor. Air volume flow rate is measured at compressor suction side. Discharge pressure is regulated with pressure relief valve, symbol 15. In the
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Fig. 7 Test rig schematic
Table 2 Operating condition
Parameters
Unit
Value
Speed
rpm
3000
Suction pressure
barG
0
Discharge pressure
barG
10–40
Suction temperature
K
288
Discharge temperature
K
333–363
Oil injection temperature
K
313
Oil flow rate
lpm
3–5
meantime, torque, oil flow rate, oil injection pressure and discharge temperature are measured. The operating conditions are presented in Table 2. Suction pressure is atmosphere pressure. Discharge pressure sweep tests were operating from 10 to 40 barG. Oil injection flow rate is from 3 to 5 lpm and temperature is 313 K.
3.2 Performance Comparison of CRC with Different Vi Volumetric efficiency and isentropic efficiency varying with discharge pressure are compared for CRC with Vi of 3, 4, 4.6, 5.8 and 6.8 as shown in Fig. 8. Both volumetric efficiency and isentropic efficiency have optimal operating point which are 97.52% and 76.98% respectively at around 20 barG.
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Fig. 8 Efficiency changing with discharge pressure
For isentropic efficiency, when discharge pressure is lower than 35 barG, Vi of 4.6 is better than other cases. Vi of 3 has the lowest performance because of undercompression. Vi of 5.8 and 6.8 cases have lower efficiency comparing with lower Vi case when discharge pressure is lower 30 barG. As discussed in Sect. 2.3, cases with higher Vi values have shorter sealing line lengths, which typically results in better sealing. Therefore, lower efficiency in cases with high Vi values is possible for over-compression to occur. Vi of 5.8 and 6.8 cases only have better efficiency after 35 barG. For volumetric efficiency, all cases have comparable values higher than 90% at pressures below 30 barG. Volumetric efficiency drops quickly after 30 barG and higher Vi have higher volumetric efficiency beyond 35 barG.
3.3 Efficiency Comparison at Same Pressure Ratio All five Vi cases have optimal volumetric efficiency and isentropic efficiency at discharge pressure 20 barG. Therefore, efficiency changing with Vi at this pressure is compared in Fig. 9. In theory, all five cases are under-compression at this discharge pressure. Therefore, the best efficiency should be achieved at Vi of 6.8 where less under-compression than other cases. However, isentropic efficiency increases with Vi then decreases and approaches 80% at Vi of 4.6. Over-compression could happen due to leakage at Vi of 5.8 and 6.8. Volumetric efficiency stays higher than 90% and peaks at Vi of 4.
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Fig. 9 Efficiency changing with Vi at pressure ratio 21
3.4 Efficiency Contour Efficiency contours with different Vi and Pi are compared as shown in Fig. 10. These contours can help for selection of Vi and Pi to achieve better volumetric efficiency and isentropic efficiency. Volumetric efficiency can be higher than 93% for all cases operating at pressure ratio between 13 and 27. As high as 97% volumetric efficiency can be achieved when Vi between 3.2 and 4.1 operating at pressure ratio between 19 and 22. The optimal volumetric efficiency is achieved when the external pressure ratio is 2.0–2.5 times that of the internal pressure ratio. Isentropic efficiency of 76% is achieved when Vi is between 4.1 and 5.0 operating at pressure ratio around 20. Volumetric efficiency and isentropic efficiency drop quicker at low Vi side than high Vi side which can be visualized from the density of contour lines.
(a) Volumetric efficiency Fig. 10 Efficiency contour
(b) Isentropic efficiency
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4 Conclusions This paper details the selection of an initial CRC with a volumetric index (Vi) of 6.8, which was subsequently modified by reducing the length of its inner rotor to obtain different Vi values of 5.8, 4.6, 4, and 3. The resulting sealing line lengths were calculated and compared across all five cases. To investigate the impact of Vi and pressure index (Pi) on CRC performance, experiments were conducted at varying Pi values between 11 and 41, and volumetric efficiency and isentropic efficiency were compared, resulting in the generation of efficiency contours. Based on the experimental findings, the authors conclude that: • The CRC demonstrates capability for high Pi applications. • Over-compression may occur when the theoretical internal Pi is lower than the external Pi due to leakage. • The optimal volumetric efficiency (greater than 95%) envelope can be achieved with a Vi between 3.2 and 4.1 and operating at Pi between 19 and 22. • The optimal isentropic efficiency (greater than 74%) envelope is achieved when Vi is between 4.1 and 5.0, and operating at Pi between 18 and 22. • The CRC can achieve high volumetric efficiency (greater than 90%) across a wide range of Vi at Pi of 21. • A CRC with a lower Vi may be selected for Pi values lower than 35 to reduce manufacturing complexity. In future work, the experimental results will be utilized to refine the chamber model, with consideration given to the calculation of the volumetric index (Vi) by incorporating the oil volume fraction. Acknowledgements I would like to thank reviewers for their comments to this paper. My thanks also to Vert Rotors for permission to prepare and publish this paper. Finally, thanks to City, University of London for providing the conference for presentation of this work.
References 1. A. Kovaˇcevi´c, Three-Dimensional Numerical Analysis for Flow Prediction in Positive Displacement Screw Machines (University of London, City, 2002) 2. Y. Lu, K. Hoang, D. Noake, N. Low, Design and analysis of conical rotary compressor. IOP Conf. Ser. Mater. Sci. Eng. 1267, 012001 (2022). https://doi.org/10.1088/1757-899X/1267/1/ 012001 3. Y. Lu, H. Khoi, D. Noake, N. Low, Quasi 1D modelling of conical rotary compressors, in International Compressor Engineering Conference. Purdue e-Pubs (2022), p. 2713 4. I.H. Bell, D. Ziviani, V. Lemort et al., PDSim: a general quasi-steady modeling approach for positive displacement compressors and expanders. Int. J. Refrig. 110, 310–322 (2020). https:// doi.org/10.1016/j.ijrefrig.2019.09.002 5. D. Ziviani, I.H. Bell, X. Zhang et al., PDSim: demonstrating the capabilities of an open-source simulation framework for positive displacement compressors and expanders. Int. J. Refrig. 110, 323–339 (2020). https://doi.org/10.1016/j.ijrefrig.2019.10.015
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6. S. Rane, A. Kovacevic, Algebraic generation of single domain computational grid for twin screw machines. Part I. Implementation. Adv. Eng. Softw. 107, 38–50 (2017). https://doi.org/10.1016/ j.advengsoft.2017.02.003 7. A. Kovacevic, S. Rane, Algebraic generation of single domain computational grid for twin screw machines Part II—Validation. Adv. Eng. Softw. 109, 31–43 (2017). https://doi.org/10.1016/j.adv engsoft.2017.03.001
Other Compressor Types
Numerical Simulation and Experimental Research of Multi-stage Roots Vacuum Pump Kai Ma, Hongye Qiu, Dantong Li, Chongzhou Sun, Lantian Ji, Bingqi Wang, Weifeng Wu, and Zhilong He
Abstract Multi-stage roots pump is generally used as vacuum pump, which have medium tolerance and high gas flow. Multi-stage roots vacuum pump (MSRVP) is often used in the semiconductor and photovoltaic industries. The rotor of the MSRVP is a straight-blade rotor, so the theoretical internal pressure ratio of MSRVP is 0, and the pressure distribution in the cavity is established by leakage. One-dimensional working process simulation is difficult to predict its performance and internal flow. It is necessary to intuitively understand the mechanism of internal flow heat transfer in multi-stage roots through experiments and three-dimensional simulation. The MSRVP studied in this paper is six-stage rotor with two-lobes. A three-dimensional internal flow field model of a MSRVP is established, and a performance test bench is built to measure its performance. The experimental results are in good agreement with the three-dimensional simulation results. The simulation results reflect the fluid flow inside the MSRVP, and the pressure established by the internal leakage can be obtained more clearly.
1 Introduction Dry vacuum pumps continue to improve with the rapid development of high-tech semiconductors. As one of the MSRVP, it is widely used in industries such as semiconductors, scientific instruments, and biological products. MSRVP has the advantages of wide pumping speed range, stable operation, low vibration and noise, etc. Compared with single-stage vacuum pumps, MSRVP differ in that the internal structure is 3–5 stages of rotors connected in series on the rotor shaft. The rotors of each stage are connected through inter-stage channels [1, 2]. The connected chamber can be realized by radial bypass or axial connection. The rotors of MSRVP mainly have two-lobes, three-lobes and five-lobes rotor forms, and the diameter or phase angle of the rotor can vary [3, 4]. In addition, the profile of the Roots vacuum pump rotor can be symmetrical or asymmetrical [5]. K. Ma (B) · H. Qiu · D. Li · C. Sun · L. Ji · B. Wang · W. Wu · Z. He School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_43
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The mathematical model of the MSRVP can predict the working characteristics of the vacuum pump when the operating or structure parameters is changed. It’s necessary to the research the performance of the MSRVP. There are mainly two ways to study the MSRVP [6–9]. One is to establish a reasonable Roots vacuum pump leakage model through theory or experiment, so as to establish a reasonable pressure distribution and obtain its performance. Laurent-Charles et al. [10] used semi-empirical Knudsen-Dong law to calculate the conductance of each clearances to peridiction the internal leaks of dry Roots vacuum pump. In et al. [11] estimated the different leak channels as a rectangular channel with a circular profile of short duct length, and analysed the impact of different structural and operating parameters on performance. Raykov et al. [12] developed the conductance calculation procedure of radial channels of Roots vacuum pump. Isaev et al. [13] proposed the method based on energy balance of thermodynamic system to calculate the characteristics of Roots Pump. In addition to theory, a more commonly used tool is to use CFD to calculate the performance of Roots pumps [14, 15]. Hsieh et al. [16] analysed the flow characteristics of a gerotor type vacuum pump connected in serial and parallel. Li et al. [17] used unstructured grids to calculate the effects of pressure angle on the performance of Roots Pump. Sun et al. [18] established a 3D model and compared the difference between the 2D and 3D models. The result prove the accuracy of the 2D model in flow and pressure distribution. There are few numerical studies on MSRVP, and numerical models are often limited to a single machine. Furthermore, no detailed study of the flow field inside the MSRVP. In order to better study the internal pressure building process of the pump, this paper established a three-dimensional numerical model of the MSRVP by structured grids, and simulated the performance of the MSRVP by using CFD technology. The flow characteristics of the internal fluid inside the pump are analyzed, and the pressure distributions are obtained. The simulation and experimental results are in good agreement. And the model can be used for MSRVP with different stages, different lobes, variable diameters and variable phase angles.
2 Geometric Structure The multi-stage Roots rotor studied in this paper is a six-stage Roots rotor, and its profile is shown in Fig. 1. The rotor has a six-stage structure, and the rotor profile of each stage is the same. The profile of the Roots rotor is composed of circular arcs and conjugate curves of the circular arcs. Due to the compact structure and the need for a larger suction flow area, the first stage rotor is located in the second position. The structure of the MSRVP rotor is shown in Fig. 2. The rotors are 2nd, 1st, 3rd, 4th, 5th, and 6th stage rotors from left to right. The gap of the PZ refers to the positive direction of the Z direction, which is the gap between the rotor and the suction side. The MZ refers to the gap in the oppositive direction of the Z direction. The specific structural parameters of the multistage Roots rotor are shown in Table 1.
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Fig. 1 The rotor profile of the multi-stage Roots vacuum pump
Fig. 2 The structure of multi-stage Roots rotor
Table 1 The parameters of the multi-stage Roots rotor Stage
Rotor length (mm)
Gap of the PZ (mm)
Gap of the MZ (mm)
Cylinder diameter (mm)
1
31.8
0.05
0.05
70
2
12.8
0.05
0.05
70
3
9.8
0.05
0.05
70
4
7.85
0.05
0.05
70
5
6.85
0.05
0.05
70
6
5.9
0.05
0.05
70
Table 1 show that the rotors of each stage have the same gap of MZ and PZ, and the center distance between the two rotors is 48 mm. There are two connection methods between the roots of each stage. The connection methods of the different stage are shown in Fig. 3. One is that the gas connection path is in the radial direction of the rotor. The path of each stage is air intake on the upper
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(a) The gas radially connected between different stage rotors
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(b) The gas axially connected between different stage rotors
Fig. 3 The method of gas connection between different rotors
side and exhaust on the lower side. The intake and exhaust passages are connected outside the cylinder. The other is that the rotors of different stages are connected axially, and the connection path is located in the housing between the rotor stages. After the exhaust gas from the lower side enters the upper side of the next stage through the interstage casing, the connection between the stages is realized. The MSRVP studied in this paper adopts the method of radial connection.
3 Mesh Generation and Simulation Setup There are multiple working chambers in the MSRVP, and the working process is very complicated. In order to simulate the working process of MSRVP, the fluid model is divided into two parts. One is static fluid domain and the other is rotating fluid domain. The static fluid domain of the MSRVP is shown in Fig. 4. Among them, the static flow domain includes the suction flow domain, the exhaust flow domain and five inter-stage connected flow domains. The rotating flow domain is divided into 1–6 lobes of rotating flow domain. In the calculation process, connect all the parts and exchange data information through the interface. The control volume domain of the MSRVP is shown in Fig. 5. The mesh of static fluid domain of the MSRVP is generated by ANSYS-Mesh, and all the static fluid mesh is generated by the same method. For the inlet, outlet and inter-stage connected domain have complex shape, so the mesh size function of Proximity and Curvature is used. For the rotating fluid domain, the mesh is generated by the software TwinMesh. The 2D rotating grids is generated with 20 radial nodes and 61 Interface nodes. The rotating grids can meets the quality requirements through node settings. The meshing of the 2D seciton is shown in Fig. 6.
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Fig. 4 The static fluid domain of the MSRVP
Fig. 5 The control volume fluid domain of the MSRVP
Due to the different lengths of the rotors of different stages, the number of mesh layers in the axial direction is different. The number of axial grid layers of the multistage Roots rotor is proportional to the length of the rotor, and the grid length is less than 1 mm. The rotating fluid grids of the chamber volume is shown in Fig. 7. The internal fluid in the chamber should comply with the laws of conservation of physics, including the law of conservation of mass, the law of conservation of momentum and the law of conservation of energy. The system also needs to comply with additional turbulent transport equations. For the numerical simulation of rotating
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Fig. 6 The meshing of the 2D section
Fig. 7 The rotating fluid grids of the chamber volume
machinery, the shear pressure transmission (SST) k-ω model combines the far-field k-ε model and the near-wall k-ω model the SST (Shear Stress Transport) model, which can obtain more accurate results. ∂ ∂ω ∂ ∂ k + G ω − Yω + Dω + Sω (1) (ρku i ) = (ρk) + ∂t ∂ xi ∂x j ∂x j ∂ ∂k ∂ ∂ ω + G k − Yk + Sk (2) (ρωu i ) = (ρω) + ∂t ∂ xi ∂x j ∂x j The boundary conditions of the suction and exhaust ports is set to opening conditon. The inlet pressure is set to 0.01 bar, and the temperature is 293.15 K. The outlet pressure is set to 1.0 bar, and the return temperature is 293.15 K. The surface temperature of the pump body is an isothermal boundary, and the temperature is 60 °C. Since the dynamic mesh of the rotation domain in this paper is generated by TwinMesh, the time step is related to the angular step of rotation, and this mesh is generated with 2° angular step.
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4 Case Studies This paper use a six-stage MSRVP to build a vacuum pump performance test bench. The MSRVP performance test bench system diagram is shown in Fig. 8. The system is composed of MSRVP, mass flow meter, vacuum test chamber, and vacuum gauge. In this experiment, by adjusting the opening of the valve and the reading of the vacuum gauge, the pumping speed curve of the MSRVP at the rated speed is measured. The pumping speed curve of the MSRVP is shown in Fig. 9. The pumping speed of the MSRVP rises to the maximum value first, and the maximum suction speed is maintained at 100–1000 Pa at about 500 L/min. At 50,000–100,000 Pa, the pumping speed is about 170 L/min. Arrange temperature measuring points on the surface of each chamber of the MSRVP, and monitor the change of body surface temperature with time. After the MSRVP runs for 30 min, record the temperature of the measuring point at intervals
Fig. 8 The MSRVP performance test bench
Pumping speed[L/min]
Gas ballast valve:OFF
Pressure[Pa]
Fig. 9 The S-P curves
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45min 60min 90min 120min 150min
Rotor Stage Fig. 10 The relationship between the shell surface temperature and time
of 15 min. After running for 60 min, record the temperature of the measuring point at intervals of 30 min. The change curve of the surface temperature of the body with time is shown in Fig. 10. Within 90 min of running time, there is a large temperature rise on the surface of the chamber. From 45 to 60 min, the temperature rise is about 7 °C, and from 60 to 90 min, the temperature rise is about 3 °C. After subsequent operation, the temperature rise of the surface temperature of the chamber changes little. The average surface temperature of the cavity is about 60 °C. Under different conditions, measure the temperature of the surface of each cavity, and the average value of the surface temperature measurement points is the temperature of the chamber in the numerical simulation.
5 Results The MSRVP s adopts the method of radial connection. It’s hard to punch holes to measure icacity pressure. In order to verify the accuracy of the three-dimensional flow field model of the MSRVP, this paper compares the experimental and simulated values of the pumping speed. As shown in Fig. 11, the figure shows the difference between simulated value and the experimental value at rated speed and the different inlet pressures. The error between the simulated value and the experimental value is shown in Table 2.
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Pumping speed[L/min]
S-P Experiment Simulation
0.1
1
10
100
1000
10000
100000
Pressure[Pa] Fig. 11 Comparison of simulated data and experimental data
Table 2 The comparison results of the MSRVP simulated values and experimental values Suction pressure (Pa)
Experimental pumping speed (L/min)
Simulated pumping speed (L/min)
Error (%)
Experimental electric power (W)
Simulated shaft power (W) 231.71
1000
490.8
523.9
6.74
342
2000
472.6
493.5
4.42
354
243.42
3000
425.7
436.3
2.49
365
255.64
There are two main reasons for the difference between the simulation and the experiment. One is that the inlet pressure is low, and the flow state of the fluid is molecular-viscous flow, which leads to inaccurate CFD calculations. Another reason is that the temperature on the surface of the chamber adopts an isothermal wall, and the simulation uses an average temperature of 60 °C, rather than the actual wall temperature, which basically follows a linear distribution ranging from 56 to 64 °C. The inlet mass flow rate and rotor shaft power when the inlet pressure is 1000 Pa are shown in Figs. 12 and 13. Due to the asymmetrical rotation of the rotor, the mass flow at the inlet has asymmetrical periodic fluctuations. There are two peaks in the mass flow of the inlet, the peaks are 0.000124 kg/s and 0.0001515 kg/s respectively. The shaft power is only generated by the gas acting on the rotor, excluding mechanical and frictional losses. However, the electric power includes the power of the transformer, the power of the cooling fan and the input power of the MSRVP. This is the difference between the electrical power and the shaft power. The difference
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between the experimental electric power and the simulated shaft power is close to a fixed value, which is 110 W. The pressure distribution of the flow field in the MSRVP is calculated by CFD software. The MSRVP can be analyzed according to the axial pressure distribution of the rotor. The rotor of the MSRVP is a two-lobes rotor, and the rotor rotation period is 180°. At intervals of 30°, analyze the variation of intracavity pressure within a cycle. The pressure range in the MSRVP chamber is from 1000 to 100,000 Pa. In order to clearly reflect the pressure range of different stages of the chamber, the logarithmic coordinate system legend is used. Figure 14 reflects the change of pressure in the cavity and the connecting chamber in a period. The pressure in the chamber shows an upward trend from the first stage to the sixth stage. Since the rotor profiles of different stages are the same and the phase angles are the same, the suction and exhaust of the six stages are carried out Fig. 12 The mass flow rate changes with rotating angle
Inlet Pressure: 1000Pa
MassFlow[kg/s]
0.000150
0.000125
0.000100
0.000075
0.000050 0
Fig. 13 The shaft power changes with rotating angle
45
90
Rotating Angle[°]
135
180
Shaft Power[W]
Inlet Pressure: 1000Pa 270 265 260 255 250 245 240 235 230 225 220 215 210 205 200 195 0
45
90
Rotating Angle[°]
135
180
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at the same time. And the pressure fluctuation in the connected chamber is affected by the exhaust pressure of the previous stage, the suction pressure of the subsequent stage and its length and shape. The monitoring points are set at the beginning and end of the connecting cavity, and the pressure fluctuations also change periodically. The pressure change in the chamber of the six-stage Roots vacuum pump is shown in Fig. 15. For the change in the chamber of each stage, the change rule is the same as that of the single-stage Roots pump, which changes periodically, and only the inlet and outlet pressures are different. This article does not analyse the pressure change of a single stage, but mainly analyses the axial pressure change. The pressure range of the 1st chamber of the MSRVP is about 1000–2800 Pa, 2nd chamber of 2800–3600 Pa, and 3rd chamber of 3600–5800 Pa. The pressure difference range of the first three stages is about 2000 Pa, and from the fourth stage, the pressure
(a) Angle=30°
(b) Angle=60°
(c) Angle=90°
(d) Angle=120°
(e) Angle=150°
(f) Angle=180°
Fig. 14 The pressure distribution in the MSRVP
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100000
Pressure[Pa]
10000
1000
0
45
90
Monitor 11 Monitor 12 Monitor 13 Monitor 14 Monitor 21 Monitor 22 Monitor 23 Monitor 24 Monitor 31 Monitor 32 Monitor 33 Monitor 34 Monitor 41 Monitor 42 Monitor 43 Monitor 44 Monitor 51 Monitor 52 Monitor 53 Monitor 54 Monitor 61 Monitor 62 Monitor 63 Monitor 64
Rotating Angle[°]
Fig. 15 The pressure changes of the six-stage chamber
difference between the two stages becomes larger. The suction and exhaust pressure difference is about 10,000 Pa at the fourth stage, about 30,000 Pa at the fifth stage, and about 55,000 Pa at the sixth stage. The relative value of the pressure fluctuation in the connected chamber gradually decreases with the increase of the number of stages. Figure 16 reflects the distribution of the pressure on the rotor surface. The boundary line of different colors on the surface of the rotor is the leakage line when the gap between the rotor and the casing is the smallest. Outside the area affected by the non-inlet and non-exhaust ports, the boundary line is a straight line. The boundary line is affected by the intake and exhaust fluctuations, and the shape of the boundary is similar to that of the intake and exhaust ports.
6 Conclusions This paper establish a three-dimensional numerical model of the MSRVP, built a performance test bench and analyse the internal fluid field of the pump. The conclusions are as follows. (1) The internal flow field model of MSRVP is established and the performance test bench was built to test the pumping speed and surface temperature. The simulated and experimental values are in good agreement. So the model can be
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(a) Angle=30°
(b) Angle=60°
(c) Angle=90°
(d) Angle=120°
(e) Angle=150°
(f) Angle=180°
Fig. 16 The pressure distribution on the rotor surface
used for MSRVP with different stages, different lobes, variable diameters and variable phase angles; (2) The axial pressure of MSRVP increases according to the number of stages, showing a trend of slow first and then fast. The relative value of the pressure fluctuation in the connected chamber gradually decreases with the increase of the number of stages.
References 1. S.K. Sun, X.H. Jia, L.F. Xing, X.Y. Peng, Numerical study and experimental validation of a Roots blower with backflow design. Eng. Appl. Comput. Fluid Mech. 12(1), 282–292 (2018) 2. C.F. Hsieh, Y.C. Deng, A design method for improving the flow characteristics of a multistage Roots pumps. Vacuum 121, 217–222 (2015) 3. C.F. Hsieh, Q.J. Zhou, Fluid analysis of cylindrical and screw type Roots vacuum pumps. Vacuum 121, 274–282 (2015) 4. G. Singh, S. Sun, A. Kovacevic, Q. Li, C. Bruecker, Transient flow analysis in a Roots blower: experimental and numerical investigations. Mech. Syst. Sig. Process. 134, 106305 (2019) 5. J. Wang, S. Yang, R. Sha, H. Li, C. Xu, Geometric design and analysis of novel asymmetrical rotors for Roots vacuum pumps. J. Mech. Des. 142(6) (2020) 6. Y.R. Wu, V.T. Tran, Generation method for a novel Roots rotor profile to improve performance of dry multi-stage vacuum pumps. Mech. Mach. Theor. 128, 475–491 (2018)
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7. A.M. Joshi, D.I. Blekhman, J.D. Felske, J.A. Lordi, J.C. Mollendorf, Clearance analysis and leakage flow CFD model of a two-lobe multi-recompression heater. Int. J. Rotating Mach. 2006 (2004) 8. Q. Guo, K. Luo, D. Li, C. Huang, K. Qin, Effect of operating conditions on the performance of gas-liquid mixture Roots pumps. Energies 14(17), 5361 (2021) 9. Y. Li, D. Guo, Z. Fan, J. Du, Effects of different blade numbers on radial exciting force of Lobe pump Rotor. Int. J. Fluid Mach. Syst. 13(2), 281–291 (2020) 10. L.C. Valdès, B. Barthod, Y. Le Perron, Accurate prediction of internal leaks in stationary dry Roots vacuum pumps. Vacuum 52(4), 451–459 (1999) 11. S.R. In, S.P. Kang, Analysis of pumping characteristics of a multistage Roots pump. Appl. Sci. Converg. Technol. 24(1), 9–15 (2015) 12. A.A. Raykov, A.V. Tyurin, A.V. Burmistrov, S.I., Salikeev, M.D. Bronstein, M.G. Fomina, Calculation of backward flow in channels with moving walls in oil free non-contact vacuum pumps. AIP Conf. Proc. 2141(1), 030024 (2019, August). AIP Publishing LLC 13. A. Isaev, A. Raykov, A. Burmistrov, S. Salikeev, E. Kapustin, Development of calculation method based on energy balance of thermodynamic system of variable mass body for roots pumps. AIP Conf. Proc. 2285(1), 030042 (2020, November). AIP Publishing LLC 14. Y.B. Li, J. Du, D.S. Guo, Numerical research on viscous oil flow characteristics inside the rotor cavity of rotary lobe pump. J. Braz. Soc. Mech. Sci. Eng. 41, 1–11 (2019) 15. W. Xing, F. Zhang, F. Zhao, J. Song, X. Zhu, X. Tang, Influence of different reflux groove structures on the flow characteristics of the Roots pump. Machines 10(11), 1087 (2022) 16. C.F. Hsieh, T. Johar, Y.T. Li, Flow characteristics of gerotor vacuum pumps with multistage designs. Vacuum 196, 110787 (2022) 17. Y.B. Li, K. Jia, Q.W. Meng, H. Shen, X.H. Sang, Flow simulation of the effects of pressure angle to lobe pump rotor meshing characteristics. IOP Conf. Ser. Mater. Sci. Eng. 52(3), 032022 (2013, December). IOP Publishing 18. S.K. Sun, B. Zhao, X.H. Jia, X.Y. Peng, Three-dimensional numerical simulation and experimental validation of flows in working chambers and inlet/outlet pockets of Roots pump. Vacuum 137, 195–204 (2017)
Numerical Analysis of Real Fluid Behavior Effects on a Sliding-Vane Compressor Comprehensive Model Stefano Gianoncelli, Andrea Genoni, Ida Costanzo, Stefano Murgia, Abdullah Bamoshmoosh, and Gianluca Valenti
Abstract This work presents a simulation model on a sliding vane compressor based on a lumped parameter model. The model is capable of predicting the performance of sliding-vane compressors. The model is divided into different sub-sections to evaluate the compressor’s geometry, kinetics, thermodynamics, and rotor dynamics. The output of the tool includes the compressor unit’s performance, such as volumetric flow rate, mechanical power, and process efficiency. The study examines the tool’s ability to perform quick and efficient analyses using using either ideal or real fluid characterization, based on the REFPROP code. The code is validated against one experimental point. Simulations were conducted on a mid-size sliding-vane rotary compressor operating with three different types of working fluids from 20 °C and 1 bar (absolute) to 11 bar at 1500 rpm. In the ideal fluid case, simulations took 10– 27 s, while real fluid assumptions took 1038–4329 s. The volumetric flow rate was influenced by the gas used, but changes among fluid models were not substantial, with a mean absolute percent difference of 0.5%. Mechanical power consumption was affected by the fluid choice and gas model, leading to a mechanical power difference between 0.4 and 1.1% in the ideal gas case. The specific mechanical work showed greater deviations among the fluids, with methane molar mass coherently increasing its value. Results show that the model developed is able to assess the major phenomena of sliding-vane compressors, and the ideal fluid model should be preferred when possible since computational times are significantly reduced with comparable results. Keywords Sliding-vane compressor · Numerical simulation · Compressor performance · Fluid model
S. Gianoncelli · A. Genoni · A. Bamoshmoosh · G. Valenti (B) Department of Energy, Politecnico di Milano, Via Lambruschini 4/A, 20156 Milano, Italy e-mail: [email protected] I. Costanzo · S. Murgia Ing. Enea Mattei S.p.A, Strada Padana Superiore 307, Vimodrone, 20055 Milano, Italy © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_44
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1 Introduction The consumption of compressed air in the industrial, commercial, and residential sectors accounts for a significant percentage of electrical energy usage, ranging from 6 to 20% [1]. As a result, manufacturers in these sectors must prioritize energy efficiency and reliability to ensure a sustainable and affordable future for end-users. Given that the rotary compressors play a significant role in the compressed air market, this article focuses on the development of a comprehensive model for simulating the primary phenomena of sliding-vane compressors to enhance their performance. The computer model has been developed over several years with a continuous effort to improve its completeness, accuracy, and robustness. The article examines its ability to perform quick and efficient analysis with both ideal and real fluid models by presenting and comparing the results of case studies that simulate three slidingvane compressors using different types of working fluid, namely, air, methane, and a methane-carbon di-oxide mixture. The article starts by describing the numerical tool’s structure, followed by an explanation of the implementation of the ideal and real fluid models. Then, the simulated compressor geometry, working conditions, and working fluids are presented to provide a comprehensive characterization of the experimental and numerical analysis. The results are subsequently presented, highlighting the most interesting outcomes of the simulations, followed by a summary of schematic and direct conclusions.
2 Comprehensive Model The SVEC (Sliding Vane Efficient Compressor) software has been developed using MATLAB environment to simulate sliding-vane compressors and expanders. The software follows a multidisciplinary approach and is based on a comprehensive model divided into different sub-sections for theoretical and numerical analysis. The overall flow diagram is illustrated in Fig. 1, which is described in the next sections.
2.1 Input Modules Input structure includes two modules. The first module is CALL_SVEC, which is the user interface for inputting data either manually or by retrieving them from precompiled databases. The input parameters required by the software include machine geometry, thermodynamic boundaries of the process, and working fluid and lubricant properties. The input interface is divided into different sections, and the input data is packed into structures based on the information they contain. Additionally, the user can activate or deactivate additional controls and define simulation boundaries
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Fig. 1 Flow diagram of SVEC, the simulation tool for sliding-vane compressors performances evaluation. Each block in the diagram represents one of the internal functions of the software and is dual to a part of the theoretical comprehensive model characterising the compression process
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in a dedicated section, such as deciding whether to include inlet and outlet line components in the simulation. The input parameters are then converted into SI units and packed in the SVECpreProc module.
2.2 Main Model The core of the numerical model is included in SVECmodelMain. This module contains all the code subsections described below building a tiered execution structure. S1-Input Check and Unpacking This module unpacks the input data previously gathered, loading them in the simulation workspace. All the data are checked for both logical and numerical consistency. S2-Geometry and Kinematics This section performs an angular and temporal discretization of the process allowing to simulate the vane, stator and rotor motion in each angle and to compute velocities. Referring to Fig. 2, the vane center of gravity (F) position against time is computed via vector kinematic equations in exponential form and results are extended for symmetry to all vanes. Angle θ describes the vane kinematics relying on two reference systems: the inertial one along the vane axis and the absolute one fixed in the rotor center. Vane tip angles are defined according to [2], R is the stator radius, while r the rotor one. S3-Process and Pressure This is the core of the thermodynamic model evaluating the working fluid temperature and pressure evolution according to Sect. 2.3. Due to the computational complexity, different submodules are defined to cooperate with the main one, CHAMBER, able to compute the cell thermodynamic quantities in each point of a full revolution. Their purposes are to evaluate the oil injection inside the compression chamber and to compute the exploited mass flow rate and volumetric efficiency including leakages through main clearances. The effects of the suction and discharge processes outside the chamber are then included as well. Energy and mass balances are solved according to the fluid model selected, which can use ideal gas laws or real gas solution through the integration of REFPROP. S4-Mechanics S4 oversees dynamic quantities evaluation. Once the pressure evolution inside the chamber is known, and the geometry, forces magnitude can be computed also including inertial effects [3]. The module is based on an adaptation of Huang et al. [4].
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Fig. 2 Representation of the main geometrical quantities used for kinematic quantities evaluation. The inertial reference system is placed in point Z while the absolute one is in point O
Referring to Fig. 3, forces are reported to the absolute reference system through the transfer equations below. Firstly, resulting forces on a rotating reference system placed on vane axis are computed both in the perpendicular direction (Rθ x ) and on the tangential one (Rθ y ) starting from forces on the inertial reference system (i, j): slot slot cos θtilt + Tm + Tv − F pslot sin θtilt Rθ x = −Fm + Fv − F p1 + F p2
(1)
slot slot sin θtilt + Tm + Tv − F pslot cos θtilt (2) Rθ y = − −Fm + Fv − F p1 + F p2 where θtilt is the vane tilt angle with respect to radial direction while forces definition can be found in the related bibliography [4]. Equations 3 and 4 allow to compute the absolute horizontal (Rx ) and vertical (R y ) forces resultant on the fixed reference system placed on rotor center i.e., point O in Fig. 2: Rx = Rθ x sin θvane − Rθ y cos θvane
(3)
R y = Rθ x cos θvane + Rθ y sin θvane
(4)
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Fig. 3 Graphical representation of the forces acting on a vane. Pressure forces are labeled with p, friction ones with t
where θvane is the vane center of gravity angular position with respect to the horizontal. S5-Power and Efficiency Once the forces magnitude and their application points are known, the expected power consumption is computed. The shaft torque due to a single vane Cvane is computed via: s s − sgnTv rv − sgns2 Cvane = Fm AMi − Fv AVi − sgnTm rv + sgns1 2 2 slot slot A xi − F p2 A yi + sgnF pslot rv (5) + F p1 where subscript i points to a projection on the corresponding axis while sgn is a service coefficient allowing to extend the approach also for inclined vanes. In the right-hand side of the equation forces and their arms can be found, according to Fig. 3 and related bibliography. The overall resistant torque on the rotor, Ctot , is given by this contribution multiplied by the actual number of vanes and, finally, the overall power consumption Pmecc is computed through the mean integral of Ctot ∗ ω over an entire revolution. S6-Internal Actions This is an elective module where the 3D state of stress of the vane is evaluated, and the equivalent mono dimensional value is computed for material stress–strain analysis.
2.3 Fluid Models In this section, the two different approaches used to simulate the behavior of the fluids are described. Both approaches have separated models for the calculation of
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thermodynamic and transport properties. The first approach is the ideal gas approach. In the ideal gas approach, the density of the fluid is calculated through the ideal gas law, while the specific heat is equal to the ideal gas specific heat. The ideal gas specific heat is calculated through a fourth-degree polynomial which is a function of temperature [5]. The model for transport properties is based on the rarified kinetic gas theory. The formulation used in this work is the one given by Chung et al. [6]. The thermodynamic and transport models can be coupled easily as the assumptions for rarified kinetic gas theory and the ideal gas assumption are relatively similar. The second approach relaxes the real gas assumption. The thermodynamic properties are calculated using real fluid equations of state. The employed equations of state are the one present in the REFPROP routine. The three equations of state are Helmholtz free energy equations of state [7–9]. Air is treated as a pseudo-pure fluid. A specific equation of state is used for pure methane, while the natural gas standard GERG2008 is used for the carbon dioxide-methane mixture. Transport properties for air are calculated through a corrected kinetic gas theory model [10], while transport properties for methane and carbon dioxide are fitted from experimental data [11, 12]. The leakage model used for these simulations is based on Poiseuille-Couette flow theory [13], which depends on the gas-oil mixture viscosity, evaluated basing on Awad et al. [14].
3 Case Studies The software needs data on the machine geometry, working conditions and exploited fluids; therefore, these aspects are here presented in order to furnish the useful context before discussing the simulations results. Both the experimental and the numerical campaign used the same compressor type. Due to the inflammability of working fluids 2 and 3 from Table 2, these latter are only tested numerically for safety reasons.
3.1 Machine Geometry A mid-sized sliding-vane rotary compressor is considered, consisting in a cylindrical stator (D = 136 mm) hosting an eccentric rotor (d = 111 mm), tangent to the former inner wall defining a contact line. This line divides suction and delivery regions, where inlet and outlet ports are carved inside the cast-iron stator. The sliding-vanes are seven and positioned inside of radial slots. When the machine is operating, vanes slide out from their slots, making contact with the stator inner wall and forming a closed volume named cell. The cell capacity varies depending on the angle of rotation, determining the pressure variation of the fluid. As schematized in Fig. 4, suction phase lasts from 30.3° to 162.4° while discharge one spans from 326.1° to 356.1°. Vanes are 38 mm long and 4.72 mm thick, with an optimized tip radius equal to 9.5 mm.
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Fig. 4 Sliding vane compressor representation
Table 1 Simulation parameters (pressures are absolute) Test
Inlet pressure (barA)
Outlet pressure (barA)
Inlet temperature (°C)
1, 2, 3
1
11
20
Table 2 Working fluid composition Test Working fluid
Elements
Gas molar Molar mass (kg/ Dynamic composition (%) kmol) viscosity (μPa s)
1
Air
N2 , O2 , Ar, CO2 78, 21, 0.93, 0.03
28.96
21.6
2
Methane
CH4
100
16.04
13.2
3
Methane—CO2 CH4 , CO2
50, 50
30.03
13.5
3.2 Numerical Campaign The numerical campaign assumed a standard rotational speed of 1500 rpm, while the working conditions and the exploited fluids are reported respectively in Tables 1 and 2. Both the ideal and the real fluid models are tested.
3.3 Experimental Validation The experimental validation followed standards ISO 5167 and ISO 1217. The validation here presented is a test at 1500 rpm with air as working fluid with ambient conditions of 1 bar and 20 °C, with delivery pressure set at 7.5 barA. Table 3 compares the numerical data against the experimental ones: the three parameters proved the goodness of the comprehensive model, validating its implementation. The volumetric flow rate is the closest to the experimental data, with a percentage difference of 0.4%, proving the consistency of the cell volume evolution evaluation, the leakage models and the suction and discharge processes influence.
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Table 3 Results of the experimental campaign, compared with numerical results using ideal gas model Test
Volumetric flow rate (l/ min)
Mechanical work (kW)
Specific mechanical work (kJ/kg)
Experimental
3544.5 ± 0.7%
24.3 ± 0.2%
346.1 ± 0.8%
Numerical
3529.3 (−0.4%)
23.5 (−3.1%)
343.3 (−0.8%)
The percentage difference between the two values is reported in parenthesis
Mechanical power is the less accurate with an error equal to 3.1% which is however considered acceptable.
4 Results and Discussion This chapter presents and discusses the results of the numerical campaign. Common performance parameters of interest in compressors testing coming from the numerical campaign are presented in Table 4.
4.1 Numerical Results Simulations took 10–27 s in the ideal fluid case, 1038–4329 s with real fluid assumptions using REFPROP for properties evaluation on a 11th Gen Intel® Core i5-11600 K @3.90 GHz. The slowest test was number 1, due to the air molecular composition and complexity when compared to other gases. Basing on the process definition air, methane and CO2 can be in principle reasonably modelled as ideal fluids during the whole compression for every test. Regarding the volumetric flow rate, the first and third test results are very similar (1.4% different) despite the fluid difference, which in general should not implicate a considerable disparity of performance since volumetric flow rate value is Table 4 Results of the numerical campaign, obtained with both ideal and real gas modelling Test
Volumetric flow rate (l/min)
Mechanical power (kW)
Specific mechanical work (SMW) (kJ/kg)
Ideal
Real
Ideal
Real
Ideal
Real
1
3513.1
3508.2 (−0.1%)
27.35
27.23 (−0.4%)
393.2
391.9 (−0.3%)
2
3290.6
3273.1 (−0.5%)
25.85
25.70 (−0.6%)
716.1
714.4 (−0.2%)
3
3465.4
3490.6 (+0.7%)
25.83
25.56 (−1.1%)
363.1
355.5 (−2.1%)
The percentage difference between the two models is reported in parenthesis
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mainly influenced by the volume available in the first closed chamber and the rotational speed. The largest losses of volumetric efficiency are represented by the leakages between the three main clearances and to the fluid complexity. Differences in this value are mainly attributed to the rotor–stator leakage model selected. Despite Poiseuille-Couette is considered [15] to be the best overall performing model for sliding-vanes machinery, in this campaign it has shown to be quite sensible to the selected type of fluid, especially in scenarios where the viscosity and density of the fluid are particularly different from one another, leading to the result of test 2. Regarding the difference between the ideal and real gas thermodynamic model, volumetric flow rate changes among fluid models are not substantial, with the mean absolute percent difference being 0.4%. A peculiar case is found in test number 3, where the real gas volumetric flow rate is higher than the ideal one. This is a consequence of the highly detailed heat exchange model in the real gas model, leading to an increased heat exchange between gas and oil and, consequently, a lower outlet gas temperature (27 °C lower) and a higher and increased average viscosity due to the better molecules cohesion and, finally, a lower leaking flow rate in the real case scenario for this test. The mechanical power results are greatly affected by the working fluid choice, with the highest difference being 6.1% between the air and the mixture cases with real fluid assumption. Even if the methane flow rate is generally the lowest, its specific heat capacity leads to a higher compressing work and thus the required power in the ideal case is more similar (0.1% higher) to the one necessary for the mixture compression than to the air one. In the case of mechanical power, the fluid model choice has an appreciable influence due to the impact of pressure evolution on forces and related power consumption and dissipation. In the meantime, adopting the real gas assumption instead of the ideal one shows deviations comparable to the ones encountered in the volumetric flow rate with the same assumptions, proving a good scaling effect between the two values. As a matter of fact, applying the real gas model led to a difference between 0.4 and 1.1% compared to the ideal gas case, similar to the 0.7% maximum difference encountered for the flow rate. Real gas scenario offers a mechanical power which is always lower than the one predicted in the ideal case, differently to the volumetric flow rate trend. Lastly, the specific mechanical work (SMW) is directly related to the two previous parameters, being computed as the ratio between the mechanical power (Pmech ) and ˙ In the simple fluid scenario results show greater the elaborated mass flow rate (m). deviations among fluids, with the value of the second test being almost doubled with respect to the other two comparable results. In this case, differences are mainly due to the lower molar mass of the methane, causing a lower density and hence a lower mass flow rate that drastically increase the SMW. Comparing ideal and real fluid models, the maximum discrepancy is 7.6 kJ/kg absolute or 2.1% relative in the third test, due to the combined influence of the differences in volumetric flow rate and mechanical power.
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5 Conclusions In this work, a comprehensive model able to simulate sliding-vane compressors performances has been presented and experimentally validated, highlighting the implementation of both the models for ideal fluid and real fluid characterization. • The model can properly assess main phenomena characterizing sliding-vane compressors and provide quick and accurate estimate of their performance parameters. • Volumetric flow rate values are sensibly affected by the leakages path models. Fluid viscosity and molecular complexity have a considerable impact on results. • Mechanical power consumption is both affected by the fluid choice and the gas model, being directly related to pressure evolution in the chamber and related forces. • Ideal fluid model should be preferred when reasonable, depending on the process and fluid parameters since computational times are sensibly reduced with comparable results. When necessary, real fluid behavior can be assessed by choosing the proper equation of state model and using REFPROP for properties evaluation.
References 1. R. Cipollone, Sliding vane rotary compressor technology and energy saving. Proc. Inst. Mech. Eng. 230, 208–234 (2016) 2. C. Hong, L. Lianseng, G. Bei, S. Pengcheng, Research on tip profile of vane for rotary vane compressor. National Engineering Research Center for Fluid Machinery and Compressors (2005) 3. X. Tojo, T. Kan, A. Arai, Dynamic behavior of sliding vane in small rotary compressors, in International Compressor Engineering Conference (1978) 4. Y.M. Huang, C.L. Li, Analysis of forces acting on compressor sliding vanes, in Spring Technical Conference of the ASME Internal Combustion Engine Division (2002) 5. B.E. Poling, J.M. Prausnitz, J.P. O’Connel, Properties of Gases and Liquids, 5th ed. (McGrawHill, 2001) 6. T.H. Chung, L.L. Lee, K.E. Starling, Applications of kinetic gas theories and multiparameter correlation for prediction of dilute gas viscosity and thermal conductivity. Ind. Eng. Chem. Fundam. 23, 8–13 (1984) 7. E.W. Lemmon, R.T. Jacobsen, S.G. Penoncello, D.G. Friend, Thermodynamic properties of air and mixtures of nitrogen, argon and oxygen from 60 to 2000 K at pressures to 2000 MPa. J. Phys. Chem. Ref. Data 29, 331 (2000) 8. U. Setzmann, W. Wagner, A new equation of state and tables of thermodynamic properties for methane covering the range from the melting line to 625 K at pressures up to 1000 MPa. J. Phys. Chem. Ref. Data 20, 1061 (1991) 9. O. Kunz, W. Wagner, The GERG-2008 wide-range equation of state for natural gases and other mixtures: an expansion of GERG-2004. J. Chem. Eng. Data 57(11), 3032–3091 (2012) 10. E.W. Lemmon, R.T. Jacobsen, Viscosity and thermal conductivity equations for nitrogen, oxygen, argon and air. Int. J. Thermophys. 25, 21–69 (2004) 11. B.A. Younglove, J.F. Ely, Thermophysical properties of fluids. II. Methane, ethane, propane, isobutane, and normal butane. J. Phys. Chem. Ref. Data 16, 577 (1987)
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12. V. Vesovic, W.A. Wakeham, The transport properties of carbon dioxide. J. Phys. Chem. Ref. Data 19, 763 (1990) 13. N. Nervegna, S. Mancò, Simulation of an external gear pump and experimental verification. Politecnico di Torino (1987) 14. M.M. Awad, Y.S. Muzychka, Effective property models for homogeneous two-phase flows. Exp. Therm. Fluid Sci. (2008) 15. F. Fatigati, M. Di Bartolomeo, D. Di Battista, R. Cipollone, Experimental validation of a new modeling for the design optimization of a sliding vane rotary expander operating in an ORC-based power unit. Energies 13 (2020)
Performance Improvements of Scroll and Sliding Vane Expanders Via a Double Intake Port Technology for ORC-Based Power Units Fabio Fatigati
and Roberto Cipollone
Abstract Sliding Vane Rotary (SVRE) and Scroll machines are the most referenced Expanders for small scale Organic Rankine Cycle (ORC)-based power units. Indeed, volumetric expanders are generally preferred to the dynamic ones as they better address severe off-design conditions. Nevertheless, they present some intrinsic limitations related to friction, volumetric performance and geometrical constraints. Moreover, these machines behave like an “equivalent rotating valve” and their permeability (relationship between flow rate and pressure drop) primarily depends on the in taken mass flow rate. In this paper a Double Intake Port (DIP) technology is considered to achieve important benefits in terms of expander performance. DIP involves that after the closure of the main intake port, an additional port is opened fed by the working fluid at the same thermodynamic conditions of the first port. Thanks to this new aspiration, the pressure inside the vanes increases and, therefore, the indicated power as well as the capability of the machine to aspirate a greater quantity of fluid. A lumped effect of the DIP technology is the increase of the permeability of the expander able to elaborate a higher mass flow rate for a given pressure difference. The efficiency of the original and DIP machines is discussed as well as the effects on the on the power produced. To perform this analysis, comprehensive theoretical models of both expanders were carried out and experimentally validated. Subsequently, the models were used as a software platform to assess a best design of the DIP expanders in terms of performances. Keywords Small scale ORC based power unit · Scroll expander · Sliding Rotary Vane expander · Dual intake port · Design optimization
F. Fatigati (B) · R. Cipollone Department of Industrial and Information Engineering and Economics, University of L’Aquila, Piazzale Ernesto Pontieri, Monteluco di Roio, 67100 L’Aquila, Italy e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_45
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1 Introduction Organic Rankine Cycle (ORC)-based power units are interesting and promising solutions to produce mechanical power recovering low and medium grade heat, [1]. These power plants allow to exploit low temperature renewable heat sources such as solar [2], geothermal [3] and biomasses combustion [4]. Moreover, it is widely used for Waste Heat Recovery in Internal Combustion Engines [5] and in the Industrial Sector [6] too. In such application, volumetric expanders are chosen for the low rotational speed, the capability to elaborate two-phase working fluids and low mass flow rates for high pressure ratio, [7]. The selection of a volumetric expander depends by many factors, and it is not possible to define an optimal technological solution for every situation, [7]. The most important technological alternatives are those based on Scroll [8], Screw [9], Piston [10] and Sliding Rotary Vane machines [11]. Among these technological alternatives, Scroll and Sliding Rotary Vane expander are widely used but they present low capacity, [9]. Among the technology allowing to improve the performance of these machines and in general of all volumetric devices, the Dual Intake Port (DIP) is one of the most effective [11–13]. The authors demonstrated in previous works as, when it was introduced in Sliding Rotary Vane Expander, DIP technology ensures to increase the mass flow rate elaborated by the machine and consequently the power produced, [11, 12]. In [13] the authors provide a feasibility analysis of DIP technology when it was applied to scroll expanders. In the present paper, the benefits of the DIP technology were assessed when this technology was applied to SVRE and Scroll expander employed in a solar driven ORC-based unit for micro-cogeneration, and more in general, in those application characterized by a low temperature of the hot source and in all the cases of very reduced mechanical power recovered.
2 Materials and Methods A wide experimental characterization was carried out on Sliding Rotary Vane and Scroll expander introduced on a fully instrumented ORC-based power unit (Fig. 1a) where the working fluid is R245fa. An amount of ISOVG 68 POE oil (5% of the working fluid mass) was mixed to the working fluid to fulfill the lubrication and sealing requirements of the pump and the expander. The analyzed recovery unit was developed for micro-cogeneration purposes. Indeed, it was conceived to be integrated to flat solar thermal collector for the simultaneous production of heat and electric power. In the experimental facility, the solar power is reproduced by two electric resistances (i) (12 kW each one) heating up 135 L of hot water stored in a Thermal Storage Tank (TES) (p). The hot water represents the hot source of the ORC power unit. It is delivered by a water pump (q) towards a Heat Recovery Vapor Generator (HRVG) (q) thus providing thermal power to the working fluid (R245fa) entering the HRVG cold side. R245fa leaves the HRVG as a 15 °C superheating
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degree vapor and enters the expander (f). According to the choice of the expander machine (SVRE of Scroll) the experimental layout slightly changes. If SVRE is employed (Fig. 1b), the expander is externally linked to the electric motor (l) through mechanical joint (o) and torquemeter (m). The electric motor is then connected to the electric network. Such architecture together the adoption of a regenerative inverter, ensures to control the expander speed which is an important degree of freedom in the recovery plant regulation. Indeed, the speed variation allows to regulate the machine permeability, defined as the ratio of pressure difference at expander sides and mass flow rate entering the machine. So, the higher is the revolution speed the higher is the permeability and lower the expander intake pressure for a given mass flow rate and expander outlet pressure. In fact, a volumetric expander can be seen as a revolving valve defining the evaporating pressure of the ORC unit, [14]. If scroll expander is adopted, the plant layout changes in the expander section (Fig. 2). Indeed, as reported in Fig. 2, the scroll machine shares the shaft with the electric motor and both elements are enclosed in the same shaft being the machine hermetic. The electric motor is connected to a dissipative electric load without any link to the electric network. In this case the revolution speed is not externally controlled but is demanded to the dynamic equilibrium between the motor and resistance torque on the expander shaft. In both configurations at the outlet of the expander is placed a further heat exchanger (REX) (g) to perform a regeneration stage. It is important to notice how before to be sucked by the pump, the working fluid exiting the condenser (a) is gathered in a 3 L plenum (b) placed to dump the mass flow rate fluctuation, [14]. The wide experimental database ensures to assess the expanders performance and to validate their models. So, after the model validation, the two models are used as software platform to analyze the benefits introduced by the DIP technology in SVRE and Scroll expanders. The SVRE theoretical model was obtained updating for the expander at hand (Fig. 3) the one developed by the authors in [11, 12]. The scroll model was instead
(b)
(a)
(a).condenser; (b) plenum, (c) pump, (d) expander section, (e) HRVG, (f) expander, (g) recuperator, (h) Control system, (i) resistance, (l) electric generator, (m) torquemeter, (n) Coriolis flow meter fm, (o) joint, (p) TES, (r) Magnetic fm, (s) hot water pump;
Fig. 1 ORC-based power unit a, Sliding Rotary Vane expander configuration b
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Fig. 2 Scroll expander configuration
obtained updating a previous version [13] for the analysed scroll expander (Fig. 4). Both models are developed in GT-Suite™ software platform thus integrating a zero 0-D and mono dimensional 1-D thermo-fluid-dynamic approach. The GT-Suite ™ model (Fig. 5) adopts the 1-D analysis to assess the dynamic phenomena taking place at intake (b) and exhaust pipes (d). Indeed, intake and exhaust pipes were discretized in multiple sub-elements and for each one the mass, momentum and energy equations are solved through an explicit integration method. Thus, the filling and emptying of the chambers (c) can be reproduced. The 0-D thermo-fluid-dynamic analysis was used to reproduce the volumetric losses. Three main leakages paths are considered: the leakages trough the gap between the blades tip and stator inner surface (element f), between the blades side and rotor slot (element g) and between the rotor face and machine casing (element h). The (f) and (g) leakages are treated through the Poiseuille-Couette equation whereas (h) is assessed thanks to the equivalent orifice approach [11, 12]. Leakages, however, influence the pressure angular (or volume Vi ) trend inside the chamber pi during rotation (time tcycle ) and consequently the indicated power Pind (1). Once the indicated power was evaluated, the net expander power Pexp can be achieved subtracting the mechanical losses Plosses due to friction. The mechanical power losses are physically represented in SVRE model following a 0-D approach. All the mechanical losses source has been considered through subroutines reported in the element (l). Anyway, the power lost due to the dry contact between blades tip and stator inner surface represents the 95% of all mechanical losses. This contribution is evaluated according to Eq. (2) where f is the friction factor, rv is the distance between the blade tip and rotor centre and ω the expander speed. It is worth to mention that in (2) Fc represents the centrifugal force pushing the blade against the stator inner surface whereas Fp is the pressure force that that fluid
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Fig. 3 Sliding Rotary Vane expander Fig. 4 Scroll expander
enclosed under the blades exerts. Once the mechanical power is known, the expander efficiency can be evaluated as the ratio between Pexp and reference power Pad , is that produced by the expander if the expansion is adiabatic isentropic. The ratio between mass flow rate m ˙ WF and the inlet/outlet expander pressure difference Δpexp defines the machines permeability α (3). Similarly to the SVRE, also the scroll theoretical model
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Fig. 5 SVRE theroetical model
was developed in GT-Suite™ environment following the same procedure with some difference due to the more complex geometry (Fig. 4). The fixed and orbiting scrolls define six chambers. The intake phase happens axially filling chambers when are in 1a and 1b positions. The intake phase ends after a complete rotation. After the intake phase, the chambers branch off and are in correspondence of 2a and 2b positions. As the expansion going on the chambers proceeds towards position 3a and 3b in correspondence to which the exhaust phase takes place. Therefore, such behaviour suggests a symmetric structure for the model as reported in [13]. Concerning the mechanical power losses modelling it was considered according to a map of the mechanical efficiency following the approach of [13]. Both the models were validated against experimental data. Concerning SVRE, the experimental analysis was carried out for different values of mass flow rate provided by the pump which varies from 56 g/s up to 74 g/s. In order to keep the expander intake pressure close to the design value, the revolution speed was properly increased between 1245 and 1770 RPM following the m ˙ WF growth [14]. Such approach ensures intake pressure varies in a narrow range (9.5–10.5 bar) despite the mass flow rate increase. Hence, the expander works close to the design conditions thus producing a Pexp ranging from 608 W up to 716 W. The comparison of these experimental data with the corresponding theoretical predictions shows a good agreement. Indeed, maximum relative errors in terms of expander intake pressure and power produced are equal to 5% and 8% respectively. A similar validation approach was carried out for the scroll expander. Pind =
∑ Nv ∮ i=1
pi dVi
tcycle
( ) Plosses = f Nv Fc + F p rv ω
(1) (2)
Performance Improvements of Scroll and Sliding Vane Expanders Via …
α=
ΔW F Δpex p
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(3)
In this case, despite the expander speed is not controlled, the expander intake pressure linearly grows from 7.6 bar up to 10.7 bar when the mass flow rate varies from 32 g/s up to 54 g/s thus increasing the produced power from 398 W up to 545 W with mass flow rate enhancement. This is since the permeability α (3) can be retained constant (0.06 kg MPa−1 s−1 ) [14]. Also this case, the model can reproduce the experimental behaviour as demonstrated by the low maximum relative errors in terms of expander intake pressure (7%) and produced power (10%).
3 Results Once the SVRP and Scroll model were validated, they were used to assess the benefits introduced by DIP in the two cases. The introduction of DIP involves a slight modification of the machine and consequently of the model. Indeed, as observed in Figs. 3 and 4 the geometry remains the same. For SVRE case (Fig. 3) the only difference is that a further intake port is done angularly spaced from the main intake one (SIP) in the sense of the rotation. The DIP was introduced in correspondence of the expansion as it can be observed from Fig. 3. This position indeed allows to achieve a best compromise between the power produced and the machine efficiency [11]. As it can be observed in Fig. 2, the DIP port opening angle λ is equal to 91°, measured with respect to the reference line. Hence, considering that the distance of SIP port closing angle from the reference line τ is equal to 37°, the angle difference ε is 54°. Considering that DIP port presents an angular extent of 6°, the phase of the DIP presents an angular duration of 60°. The introduction of DIP technology port in also in the case of Scroll involves slight modifications (Fig. 4). Indeed, the only variation is the introduction of two symmetric ports. This is performed according to the approach developed in [13]. In fact, it was observed as the Scroll structure leads to pair of chambers (1a and 1b, 2a and 2b, 3a and 3b) whose volume symmetrically varies during rotation. Hence, two symmetric DIP technology ports should be introduced to avoid disequilibrium in the machine filling. The DIP technology can be done in a Scroll expander just introducing the ports on the fixed orbiting scroll as observed in Fig. 4. So, no adduction pipes are required being the intake phase axial and performed through the same intake manifold. As it was demonstrated in [13], the DIP technology should present a diameter lower than the spiral thickness to prevent that the DIP technology feeds simultaneously two consecutive chambers (i.e. 2a and 3a) in the sense of the expansion. Hence, the spiral thickness (3.5 mm) is equal to the maximum DIP diameter Φ. In the analysis also a lower Φ is considered (1.5 mm) to observe its impact on DIP Scroll performance. For the considered scroll expander, a rotation of 996° is needed to complete the whole cycle. After 360° the intake phase was completed. Subsequently, the expansion phase takes place up to 720° and finally
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the discharge phase happens. The DIP reported in Fig. 4 were installed to keep the machine filling even during the expansion phase. So, the DIP starts at 360° (after the SIP phase) and ends at 720°. Hence, in both SVRE and Scroll cases, the aim of DIP is to delay the pressure reduction during the expansion thus increasing the indicated power and consequently the mechanical power. This is achieved introducing a further amount of working fluid during the expansion phase. Hence, the extra mass flow rate elaborated by the expander produces a pressure boosting with the increase of the area of indicated cycle. Such effects can be observed for SVRE in Fig. 6a by the comparison between SIP and DIP indicated cycle. Figure 6a clearly shows as in correspondence of the DIP intake opening angle the pressure increases despite the chamber volume is growing. Such action delays the pressure reduction with respect to the SIP machine. In this way an increase of the area of the indicated cycle (1) was achieved. The indicated cycle area represents the power exchanged by the working fluid and the machine components, so DIP ensures an increase of power produced by the machine as it can be observed in Fig. 6b. The power benefit is significant for all the operating range considered. Indeed, increasing the pressure difference at the expander side from 4 bar up to 13 bar, the power enhancement decreases from 150% up to 77%. This power increase is due to the higher mass flow rate elaborated by the machine (+86%) as it can be noticed from Fig. 6c. This result shows a permeability increase of DIP SVRE. So, keeping constant Δpexp , it can be observed as DIP machine allows to elaborate a higher mass flow rate. In fact, the permeability of DIP SVRE is equal to 0.11 kgs−1 MPa−1 at 1500 RPM whereas it is 0.09 kgs−1 MPa−1 in SIP case at the same speed. DIP technology allows also to introduce efficiency benefits demonstrating that the power increase is not simply related to a higher mass flow rate elaborated by the expander. This can be observed, in Fig. 6c where the two efficiencies of the DIP and SIP technologies are compared. DIP SVRE efficiencies varies from 50% up to 40% for a Δpexp , ranging between 4 and 10 bar. In the same interval, the SVRE presents a maximum value of 40%. The SIP allows to achieve a slightly higher efficiency (+4%) only for pressure rise higher than 10 bar. This is since the efficiency of the DIP SVRE presents a higher reduction with Δpexp , than SIP case which shows a flatter curve. Anyway, in this point the DIP SVRE produces a 77% higher power so the benefits of DIP machine still apply. It is worth to mention that the introduction of a DIP (Fig. 7a) is different from the case of a SIP with an extended port (and greater intake volume), Fig. 7b. DIP technology avoids that multiple chambers would be opened toward the main intake port (as it happens when an extended SIP is done) preventing that the pressure, and consequently the power (Fig. 7c), decreases too much when lower mass flow rates are aspirated by the machine. Hence the adoption of a greater intake volume—Fig. 7b— shifts the operating region to higher mass flow rate which are suitable to completely fill the intake volume whereas the adoption of a DIP solution allows to manage in a similar way the higher flow rates but also the situations of lower flow rates avoiding the decrease of the pressure inside chambers. The operating region of the machine is, therefore, widened. DIP in Scroll expander produces the same phenomenological effect on the indicated cycle of the SVRE case (Fig. 8a). Nevertheless, the pressure boosting is significant only for the case of Φ equals 3.5 mm. This behaviour is
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Fig. 6 Indicated cycles a, power b, mass flow rate and efficiency c as function of expander pressure difference for SIP and DIP SVRE technology expander
reflected on the power increase as Fig. 8b shows. In fact, for Φ equal to 1.5 mm the power increase is slight. It ranges from 8% up to 1% when the Δpexp varies from 4 up to 11 bar. After 11 bar, the DIP technology produces a power decrease with respect SIP solution (−0.5%). If the DIP technology with Φ of 3.5 mm is considered, the power boosting is higher but also in this case it applies until to a Δpexp equal to 11 bar is reached. Indeed, in the same Δpexp range the power increase diminishes from 27 to 2%. After 11 bar, with DIP solution a power decrease up to 17% is observed. Such results confirm that despite the effects of DIP technology introduction is the same for both expanders the benefits on the two machines are different. For SVRE the power boosting is significant, and it applies for all Δpexp which results from different flow rates crossing the first and the second port. In the case of scroll expanders, the power increase is reduced (but it is still present) and it applies only for a limited Δpexp range.
Fig. 7 DIP a and extended SIP b configurations and produced power comparison c
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Fig. 8 Indicated cycles a, power b, mass flow rate and efficiency c as function of expander pressure difference for SIP and DIP Scroll technology expander
This is because in SVRE the further mass flow rate sucked through second port plays a more effective role due the lower volume in which is introduced. Indeed, for SVRE, the volume during which the second port is opened varies from 3.79 cm3 till to 10 cm3 ; In the scroll case, the second port feeds the corresponding scroll chamber when the volume varies from 6 cm3 up to 11 cm3 . Also DIP Scroll expander can elaborate more mass flow rate than SIP one keeping constant Δpexp (Fig. 8c). The flow rate increases when Φ of second port grows. Indeed, permeability raises from 0.06 kgs−1 MPa−1 of the SIP technology case up to 0.11 kgs−1 MPa−1 and 0.16 kgs−1 MPa−1 respectively when Φ is 1.5 mm and 3.5 mm. Nevertheless, this permeability increase provides lower benefits on power boosting as the extra mass flow rate is introduced in a larger volume and the effect on the pressure inside the chamber is reduced (Fig. 8a). It appears clear that if the diameter of the port could have been larger, the effect on power would have been greater as a larger flow rate was introduced to increase the pressure until to the main intake value. Hence, being the power boosting weak, the extra mass flow rate leads to an efficiency decrease for DIP technology solution as observed in Fig. 8c. Here, it can be seen how the SIP solution presents a higher efficiency varying from 70% up to 40% for a Δpexp ranging from 4 bar up to 13 bar. When DIP is considered, the efficiency decreases from 53% up to 30% and from 40% up to 20% in the same operating range. So, the Scroll expander produces more power but its efficiency is lower. This result is due to the higher volume of Scroll machine when DIP feeds the machine. So, a reduction of this volume through an optimization of machine spirals could allows to overcome this issue. For both SVRE and SVRE cases, the adoption of DIP ensures to reduce the pressure difference among two adjacent chambers [15], with respect to the more conventional SIP machine. This provides a reduction of the ratio between the leakages flow and the elaborated mass flow rate by the machine. From a quantitative
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point of view, from 5.8% up to 4.6% and for 0.08% up to 0.06% respectively for SVRE and Scroll expander.
4 Conclusion In the present paper the benefits introduced by the introduction of DIP technology for a Sliding Rotary Vane and Scroll Expander were assessed when they are operated in a small-scale ORC-based power unit. Thanks to the experimental characterization carried out on both expanders, theoretical models of the two machines were built and validated. The results show the same fluid-dynamic behaviour of the two machines when DIP technology is introduced. In both expanders, the DIP technology introduction provides a permeability increase causing, for the same pressure difference at the expander side, an aspiration of a higher mass flow rate thus boosting the pressure inside the vanes, increasing indicated work. DIP SVRE elaborate up to 84% of mass flow rate which allows to increase the power up to 150% than the original SIP expander. Benefits are observed also for the machine efficiency for a wide operating range where the DIP efficiencies range from 50% up to 38% and the SIP ones between 36 and 40%. DIP introduction provides a permeability increase also when it was applied to scroll expanders. In fact, for the same inlet/outlet expander pressure, the mass flow rate elaborated by the machine grows up to 30% and 100% according to the dimension of the circular port (1.5 mm and 3.5 mm respectively). So, the produced power increases up to 8% and 27% respectively with a DIP port equal to 1.5 mm and 3.5 mm. This reduced effect on power with respect to SVRE is due to the higher chamber volume than SVRE when DIP ports feed the machine thus limiting the pressure boosting inside the chamber. To overcome this issue, the geometry of the spiral can be modified to reduce the volume of the chamber fed by the DIP port. Acknowledgements The authors are grateful to SIVAM S.r.l., Ing. Enea Mattei S.p.A and Sanden S.p.A for the support given during this activity.
References 1. M.A. Chatzopoulou, S. Lecompte, M. De Paepe, C.N. Markides, Off-design optimisation of organic Rankine cycle (ORC) engines with different heat exchangers and volumetric expanders in waste heat recovery applications. Appl. Energ. 253, 0306–2619 (2019) 2. M.A. Ancona, M. Bianchi, L. Branchini, A. De Pascale, F. Melino, A. Peretto, C. Poletto, N. Torricelli, Solar driven micro-ORC system assessment for residential application. Renew. Energ. 195, 167–181 (2022) 3. J. Song, Y. Wang, K. Wang, J. Wang, C.N. Markides, Combined supercritical CO2 (SCO2 ) cycle and organic Rankine cycle (ORC) system for hybrid solar and geothermal power generation: thermoeconomic assessment of various configurations. Renew. Energ. 174 (2021)
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4. K. Braimakis, A. Charalampidis, S. Karellas, Techno-economic assessment of a small-scale biomass ORC-CHP for district heating. Energ. Convers. Manage. 247, 114705 (2021) 5. M. Manfredi, A. Spinelli, M. Astolfi, Definition of a general performance map for single stage radial inflow turbines and analysis of the impact of expander performance on the optimal ORC design in on-board waste heat recovery applications. Appl. Therm. Eng. 224, 119857 (2023) 6. C. Mateu-Royo, A. Mota-Babiloni, J. Navarro-Esbrí, B. Peris, F. Molés, M. Amat-Albuixech, Multi-objective optimization of a novel reversible High-Temperature Heat Pump-Organic Rankine Cycle (HTHP-ORC) for industrial low-grade waste heat recovery. Energ. Convers. Manage. 197, 111908 (2019) 7. O. Dumont, A. Parthoens, R. Dickes, V. Lemort, Experimental investigation and optimal performance assessment of four volumetric expanders (scroll, screw, piston and roots) tested in a small-scale organic Rankine cycle system. Energy 165(Part A) (2018) 8. J. Bao, L. Zhao, A review of working fluid and expander selections for organic Rankine cycle. Renew. Sustain. Energ. Rev. 24, 325–342 (2013) 9. A. Kovacevic, N. Stosic, I.K. Smith, E. Mujic, Advances in numerical modelling of helical screw machines (2010) 10. M. Bianchi, L. Branchini, N. Casari, A. De Pascale, F. Melino, S. Ottaviano, M. Pinelli, P.R. Spina, A. Suman, Experimental analysis of a micro-ORC driven by piston expander for lowgrade heat recovery. Appl. Therm. Eng. 148, 1278–1291 (2019) 11. F. Fatigati, M. Di Bartolomeo, R. Cipollone, Dual intake rotary vane expander technology: experimental and theoretical assessment. Energ. Convers. Manage. 186(156–167), 0196–8904 (2019) 12. F. Fatigati, M. Di Bartolomeo, D. Di Battista, R. Cipollone, A dual-intake-port technology as a design option for a Sliding Vane Rotary Expander of small-scale ORC-based power units. Energ. Convers. Manage. 209(112646), 0196–8904 (2020) 13. F. Fatigati, G. Di Giovine, R. Cipollone, Feasibility assessment of a dual intake-port scroll expander operating in an ORC-based power unit. Energies 15, 770 (2022) 14. F. Fatigati, D. Vittorini, A. Coletta, R. Cipollone, Assessment of the differential impact of scroll and sliding vane rotary expander permeability on the energy performance of a small-scale solar-ORC unit. Energ. Convers. Manage. 269, 116169 (2022). ISSN 0196-8904 15. F. Fatigati, M. Di Bartolomeo, R. Cipollone, On the effects of leakages in Sliding Rotary Vane Expanders. Energy 192, 116721 (2020). ISSN 0360-5442
Measured Reed Valve Dynamics of Diaphragm Pumps with Laser Doppler Vibrometer L. Dür, A. Egger, M. Lang, R. Almbauer, F. Cloos, and F. Brugger
Abstract Pressure controlled reed valves are widely used in compressor technology to control the in- and outflow of the compression chamber. The valves significantly influence efficiency, performance and reliability of a compressor. While the dynamic behavior of reed valves is well investigated in some disciplines such as compressors for domestic refrigeration, little is known about the reed valve dynamics of small vacuum pumps like diaphragm pumps. In this work, a novel test-rig for highresolution valve motion measurements of small oil-free diaphragm pumps is developed, providing for the first time a detailed insight into the suction and discharge valve dynamics of this type of vacuum pumps. The valve motion is measured using a laser Doppler vibrometer (LDV), which has already proven to be a very efficient method in the field of compressors for domestic refrigeration. In addition to the valve motion, the measurement concept also includes measurement of the motor shaft position and speed, as well as flow rate, pressure and temperature measurements for complete recording of the operating conditions. Measurements were performed at three different motor speeds and various operating conditions in vacuum and pressure application. The obtained results allow a detailed comparison of valve behavior over a wide range of operating conditions and can be used to derive measures to further improve the vacuum pump performance. Keywords Diaphragm pumps · Vacuum pumps · Valve dynamic · Measurement · Laser Doppler vibrometer
L. Dür · A. Egger · M. Lang (B) · R. Almbauer Graz University of Technology, 8010 Graz, Austria e-mail: [email protected] F. Cloos · F. Brugger KNF Neuberger GmbH, 79112 Freiburg, Germany
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_46
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Nomenclature DV LDV NV SV
Discharge valve Laser Doppler vibrometer Needle valve Suction valve
1 Introduction Main advantages of diaphragm pumps compared to other reciprocating positive displacement pumps are a hermetically sealed working chamber yielding very small leakages to ambient (~ 10–6 …10–3 mbar/s), a high corrosion resistance enabling the handling of aggressive or explosive media like moist chlorine or hydrogen, and finally an oil-free operation resulting in low maintenance requirements. These advantages, besides others, lead to a wide usage of diaphragm pumps in industrial technologies like medical, laboratory, vacuum, environmental, and analytical as well as instrumental analysis, all with different requirements. Examples of applications are respirators, artificial hearts, process gas analysis, delivering of valuable or hazardous process media or vacuum generation, for example, in rotary evaporators. A diaphragm pump consists of three main assembly groups as Fig. 1 illustrates. A housing, a drive including the crankshaft and a pneumatic head. The pneumatic head consists of the moving diaphragm driven by the crankshaft, the suction and the discharge pipe including the suction and the discharge valve. The diaphragm and the valves have a major influence on the pneumatic properties of the pump. This yields to the paper’s task of analyzing the suction and discharge valve behavior of one specific diaphragm pump. The valves of this pump are reed valves made by elastomer. The outcome of this investigation is useful for valve design and optimization of the whole pump behavior quantified by, for example, the delivered volume flow, the pump efficiency, and the pump noise level. The valve behavior is gained by integrating the measured valve velocity using a laser Doppler vibrometer Fig. 1 Scheme of a diaphragm pump
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(LDV). Beside the valve motion, the opening and closing point, impact velocity and other values depending on the crankshaft position, i.e., the rotating angle of the motor axis, are analyzed. Hereby, different operating conditions are set. Different experimental methods have been used in the field of hermetic refrigerant compressors of similar size to the investigated diaphragm pump. In [1], a strain gauge was used to measure the dynamic response of a suction valve. The p–V diagram and the valve motion were determined experimentally simultaneously in [2] to obtain a better understanding of the valve losses. Other authors investigated the influence of different design and operating parameters on valve dynamics [3] or valve failure [4]. In [5] the influence of valve damping on efficiency and valve impact velocity was studied experimentally. The measurement of valve movement using a LDV has been shown in the studies [6] again for the hermetic reciprocating compressor. The advantage of the LDV-method is that the intervention in the compressor can be kept small, so that the actual behavior is not influenced by the measurement. The method has been refined and applied to the same type of compressors for a special mechanically assisted reed valve [7]. The results form the basis for the evaluation of the losses in the valves. This applies to the flow losses as well as the losses due to backflow. Due to the extensive experience with the system and the reliable results, it was also selected for the investigation this report is based on.
2 Methodology The first part of this chapter gives an overview of the LDV approach used for measuring the valve behavior. After that, the measurement concept as well as the experimental setup is presented. In the last part of this chapter, the selected operating conditions as well as the measurement procedure are described.
2.1 Laser Doppler Vibrometer Approach A LDV is an optical method for measuring mechanical vibrations based on the Doppler-effect. In addition to optical access, the laser-based measurement method requires a reflective surface of the measurement object. To obtain a proper measurement signal, the non-reflective surface of the investigated elastomeric reed valves is coated with different coating approaches. A glittering silver acrylic spray provides the best results in terms of laser signal quality. In Fig. 2a, b the coating of the suction and discharge valve is illustrated. In addition to the signal quality, an important requirement is not to change the main dynamic characteristic properties of the valves due to the coating. For this reason, a high-resolution analytical scale is applied to determine the influence of the valve coating on the valve mass. Summing up this investigation, the mass of the coated
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Fig. 2 Coated valves with glittering silver acrylic spray a.)
b.) Suction valve
Optical access Discharge valve
Acrylic glass O-ring seal Clamping element
Modified vacuum pump head
Fig. 3 Pump head with transparent windows for LDV measurements
valve stays within the standard deviation of the original valves. Thus, no significant mass differences are found. A pump group with transparent windows is developed to guarantee optical access required for measuring the dynamics of the reed valves. Figure 3a shows the front view, while Fig. 3b shows a cross section of the modified pump head. The laser of the LDV-system passes through the clamped acrylic glass, which is sealed with O-rings, and receives optical access through a cylindrical bore, located centrally above the valve bore.
2.2 Measurement Concept and Experimental Setup The operating point of a diaphragm pump is usually defined by the following five values: (i) ambient condition like pressure pa temperature T a and humidity, (ii) inlet condition like pressure pi and temperature T i , (iii) outlet pressure p0 (iv) motor speed n, and (v) transported kind of gas.
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The influence of the ambient pressure seems to be unusual, but it is an important value for diaphragm pumps. The pressure difference across the diaphragm Δp = p − pa , with the working chamber pressure p, could cause a diaphragm deformation, thus, influencing the effective displacement of the working chamber volume. As usually practiced, the influence of the inlet and outlet pressure is summarized by the dimensionless compression ratio defined in Eq. (1). ∏ :=
po . pi
(1)
All these values are measured using a test-rig according to ISO 21360 [8]. The standard ISO 21360 describes three different methods of measuring the volume flow rate of a vacuum pump. The throughput method is especially suitable for measuring reed valve dynamics. Therefore, this paper extends the set-up given by ISO 21360, yielding an adjustable inlet and outlet pressure independent of each other. By doing so, a constant operating point can be set. Figure 4 illustrates the schematic experimental setup. The speed of the electric vacuum pump motor is adjustable in order to work under different operating conditions. The suction and discharge ports of the vacuum pump are each connected to a compensating reservoir, in which the pressure can be set via two needle valves (NV). In addition to the valve velocity, the measurement test-rig also includes mass flow, pressure and temperature measurements, as well as the recording of position and speed of the motor drive shaft via a rotary encoder. The oil free vacuum pump operates with air during the measurements. Therefore, environmental data like pressure, temperature and humidity are recorded. Table 1 summarizes all specifications of the sensors used for the measurements. All sensors are connected to the National Instruments data acquisition unit cDAQ-9188 using appropriate National Instruments modules as listed in Table 2. In order to check the measurement setup regarding the influence of the modifications done to the pump head and also the leak tightness of the system, the flow rate of the vacuum pump is compared to measurements previously done by KNF according to ISO21360. For previous measurements, a standard pump head was used. The
Fig. 4 Schematic diagram of the experimental setup including measurement probes
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Table 1 Specifications of the used measurement probes Location
Designation
Range
Error
PT00
Hygrometer testo 176P1
600…1100 mbar
± 3.1 mbar
PT01
Pressure transmitter Huba 691.51540114
0…4 bar
± 0.3% FS
PT02
Pressure transmitter Huba 691.53140114
0…16 bar
± 0.3% FS
TT00
Hygrometer testo 176P1
−20…+70 °C
± 0.2 °C
TT01
Thermocouple Typ T
−40…+350 °C
± 0.5 °C
TT02
Thermocouple Typ T
−40…+350 °C
± 0.5 °C
TT03
Thermocouple Typ T
−40…+350 °C
± 0.5 °C
HT00
Hygrometer testo 176P1
0%…100% r. h
± 2.1% r. h
FT00
Mass flowmeter LOW-ΔP-FLOW F-102E
1…50 l/min
± 1% FS
LDV
Polytec OFV-503, OFV-5000
0…5 m/s
± 1.77% FS
Encoder
Scancon 2RMHF-360-N-06-14-64-01-S-00-S5
360 ppr
± 26 arc-sec
Table 2 NI module specifications Module
Designation
Range
Error
NI9205
Voltage input module
± 10 V
6.23 mV FS
NI9263
Current output module
± 10 V
0.03% PR
NI9214
Temperature input module
−40…+350 °C
± 0.35 °C
outcome of this preliminary investigation is, that the influence of the modified pump head as well as the leakage of the set-up is neglectable regarding the pump flow rate.
2.3 Operating Conditions and Procedure Table 3 represents an overview of the operating conditions. The valve dynamics of three different speed levels, 700, 1500 and 3000 rpm, in combination with six different pressure ratios, as defined in Eq. (1), are measured. The vacuum pump could be either run in vacuum or pressure application where the maximum outlet pressure is limited to 2 bar absolute. For vacuum application, the discharge side of the pump is connected to ambient, yielding an outlet pressure equals to ambient pressure. The inlet pressure is set by adjusting the needle valve NV1. For pressure application, the suction side is connected to ambient and the outlet pressure is set by varying the needle valve NV2. The measurements are preceded by a run-in phase of about two and a half hours in free flow load, guaranteeing reliable and repeatable operating temperatures and a subsequent check of the final vacuum. The suction and discharge valve dynamics are measured separately during each operating point and combined in the following
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Table 3 Overview of the experimental design No.
Pump speed (rpm)
Application
Load case
∏
1
1500
Pressure application
Part load
1.3
2
1500
Pressure application
Part load
1.7
3
1500
Pressure application
Part load
2
4
1500
Vacuum application
Free flow
1
5
1500
Vacuum application
Part load
2
6
1500
Vacuum application
Part load
10
7
1500
Vacuum application
Final vacuum
≫
8
3000
Pressure application
Part load
1.3
9
3000
Pressure application
Part load
1.7
10
3000
Pressure application
Part load
2
11
3000
Vacuum application
Free flow
1
12
3000
Vacuum application
Part load
2
13
3000
Vacuum application
Part load
10
14
3000
Vacuum application
Final vacuum
≫
15
700
Pressure application
Part load
1.3
16
700
Pressure application
Part load
1.7
17
700
Pressure application
Part load
2
18
700
Vacuum application
Free flow
1
19
700
Vacuum application
Part load
2
20
700
Vacuum application
Part load
10
21
700
Vacuum application
Final vacuum
≫
measurement data analysis. Before every measurement, stationary conditions of the pressure in the compensation reservoirs are awaited.
3 Results The measurement results are divided in time-averaged measured values such as pressure, temperature and volume flow rate (volume flow at normal conditions: 0 °C and 1013 mbar) and time-resolved measured values such as valve movement and valve speed represented via the crank angle. Table 4 gives an overview of the measurement results time-averaged over five seconds. The row numbers of Table 4 corresponds to the numbers of the operating conditions listed in Table 3 while the labeling of the measurements is corresponding to the measurement points in Fig. 4. In the following figures (Figs. 5, 6 and 7) the mean suction and discharge valve motion over one hundred revolutions are plotted over the crank angle. The crank angle of 0° corresponds to the bottom dead center and 180° to the top dead center.
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Table 4 Time-averaged measurement results ∏
No.
TT00 in °C
PT00 in mbar
HT00 in %
FT00 in l/min
TT01 in °C
PT01 in mbar
PT02 in mbar
TT03 in °C
1
23.6
980
52.0
13.4
23.2
955
1240
1.3
38.1
2
23.6
980
52.0
10.8
23.2
964
1639
1.7
43.1
3
23.6
980
52.0
8.9
23.1
969
1940
2.0
46.5
4
23.6
980
52.0
14.4
23.2
950
1013
1.1
47.4
5
23.6
980
52.0
6.1
23.1
493
986
2.0
47.4
6
23.6
980
52.0
0.4
22.9
97
981
10.2
44.5
7
23.6
980
52.0
0.0
22.9
63
986
15.6
42.2
8
23.6
980
52.0
18.9
23.1
906
1176
1.3
60.2
9
23.6
980
52.0
15.3
23.2
931
1575
1.7
66.9
10
23.6
980
52.0
12.9
23.2
946
1893
2.0
69.3
11
23.6
980
52.0
20.5
23.3
907
1002
1.1
68.9
12
23.6
980
52.0
9.5
23.0
487
973
2.0
67.6
13
23.6
980
52.0
0.8
23.2
97
970
10.0
66.3
14
23.6
980
52.0
0.0
23.1
60
972
16.2
63.7
15
21.4
983
41.1
7.1
21.3
977
1268
1.3
31.8
16
21.4
983
41.1
6.1
21.4
979
1660
1.7
34.0
17
21.4
983
41.1
5.0
21.5
979
1958
2.0
39.6
18
21.4
983
41.1
7.8
21.2
967
974
1.0
25.6
19
21.4
983
41.1
3.3
21.5
493
984
2.0
31.7
20
21.4
983
41.1
0.2
21.3
96
979
10.2
33.0
21
21.4
983
41.1
0.0
21.3
62
982
15.8
33.1
The lower part of the diagrams, e.g., the negative valve lift, shows the suction valve (SV) motion (solid lines) and the upper part represents the discharged valve (DV) motion (dashed lines), e.g., the positive valve lift. The shaded area around the curves corresponds in each case to the standard deviation of the valve movement based on one hundred revolutions. Figure 5 shows the valve motion for constant pressure ratio ∏ = 2 and various rotational speed whereas and Fig. 6 shows the valve motion for constant rotational speed of n = 1500 rpm and various pressure ratios. Analyzing both figure yields, the closing points of both valves, suction and discharge valve, is mainly influenced by the rotational speed and less so by the pressure ratio. On the other hand, the opening point of both valves is mainly affected by the pressure ratio rather than by the rotational speed. However, the valves hit the valve stop immediately after the opening process, which can also be observed in the valve speeds via high velocity gradients. After the impact of the valves on the valve stop, the valves get pressed against the stopper and stay open until closing. During the time the valves are open hardly any bouncing and intermediate oscillations, typical for most reed valves, could be observed.
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1 0.8
valve lift in mm
0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 360
340
350
330
320
300
310
290
280
270
260
240
250
230
210
220
200
190
180
160
170
150
140
120
130
110
90
100
80
70
60
50
40
20
30
0
10
-1
crank angle in deg Vacuum application π=2,0 1500rpm x SV
Vacuum application π=2,0 1500rpm x DV
Vacuum application π=2,0 3000rpm x SV
Vacuum application π=2,0 3000rpm x DV
Vacuum application π=2,0 700rpm x SV
Vacuum application π=2,0 700rpm x DV
Fig. 5 Valve lift for vacuum application at ∏ = 2 and 700, 1500 and 3000 rpm 1 0.8
valve lift in mm
0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 360
350
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-1
crank angle in deg Free flow 1500rpm x SV Vacuum application π=2,0 1500rpm x SV Vacuum application π=10,0 1500rpm x SV Final vacuum 1500rpm x SV
Free flow 1500rpm x DV Vacuum application π=2,0 1500rpm x DV Vacuum application π=10,0 1500rpm x DV Final vacuum 1500rpm x DV
Fig. 6 Valve lift for vacuum application at 1500 rpm and free flow, ∏ = 2, ∏ = 10 and final vacuum
In general, the closing points of the suction and discharge valve are clearly after bottom dead center and top dead center, respectively. Due to the elasticity of the diaphragm, there is a possibility that top dead center and bottom dead center of the cranking mechanism do not coincide with the times of minimum and maximum compression chamber volume, respectively. Without knowledge of the actual compression chamber volume or the pressure inside, it is therefore not possible to make any reliable statement about late closure or reverse flows. Thus, the influence of a possible diaphragm deformation on the compression chamber volume will be investigated in a further project. Therefore, the used test-rig has to be extended. Having a look at different pressure ratios going from free flow ∏ ≈ 1 to final vacuum ∏ ≈ 16, like presented in Fig. 6, decreasing valve activities (smaller
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valve lift in mm
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-1
crank angle in deg Pressure application π=2,0 1500rpm x SV
Pressure application π=2,0 1500rpm x DV
Vacuum application π=2,0 1500rpm x SV
Vacuum application π=2,0 1500rpm x DV
Fig. 7 Valve lift for pressure and vacuum application at ∏ = 2 and 1500 rpm
maximum valve lifts and shorter time between valve opening and valve closing point) can be observed. For final vacuum there is hardly no valve movement anymore as well as no impact of the valves on the valve stop. The “movement” of the valves at final vacuum could be a deformation of the elastic reed valve made by elastomer. Thus, the valves could be still closed. Figure 7 shows the comparison of pressure and vacuum application for a pressure ratio of ∏ = 2 and a constant rotational speed of n = 1500 rpm with an interesting phenomenon. Despite the same pressure ratio and approximately the same closing points of the valves, there are large differences in the opening points of the valves between pressure and vacuum applications. One possible explanation for this later opening point for the pressure application is an elastic deformation of the diaphragm due to the pressure difference across the diaphragm from the compression chamber to ambient. For the pressure application, the maximum pressure difference across the diaphragm is at the top dead center area and is approximately 2 bar. At the bottom dead center, the pressure difference vanishes more or less. For the vacuum application, the maximum pressure difference across the diaphragm is at the bottom dead center area and is approximately 500 mbar, whereas the pressure difference vanishes more or less at the top dead center. The caused elastic deformation of the diaphragm due to the pressure difference could therefore result in a different compression chamber volume for the same crank angle for pressure and vacuum applications.
4 Conclusion The underlying study provides high-resolution measurement results of the reed valves dynamics in a diaphragm pump. Therefore, a test-rig according to ISO 21360 was developed. For the first time, the measurements made it possible to gain a detailed
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insight view into the valve behavior for the type of vacuum pump under investigation. The valve movement was measured using a laser Doppler vibrometer, a method that has already produced good results at the Institute of Thermodynamics and Sustainable Propulsion Systems at Graz University of Technology in the field of refrigerant compressors for household appliances. In addition to the determination of the valve movement, the measurement concept also includes the measurement of position and speed of the pump’s drive shaft, as well as mass flow rate, pressure and temperature measurements. A total of three different rotational motor speeds are measured and evaluated, each at seven different operating points for pressure and vacuum applications. The result is a comprehensive set of data on the valve dynamics of the suction and discharge valve. Analysis of the data showed that the closing points of the valves are clearly after bottom and top dead center, respectively. In addition, typical behaviors for most reed valves like bouncing or intermediate oscillations could not be observed. At final vacuum load the measurement shows only very low valve activities. Comparing pressure and vacuum applications with identical pressure ratio and approximately identical closing times of the valves, large differences in the valve opening times are detected. However, reliable statements about back-flow behavior cannot be done based on dynamical measurements only. In particular, the large uncertainty of the diaphragm deformation and the associated effects on the compression chamber volume make the interpretation of the presented measurement results difficult. Thus, statements in terms of improving the pump performance require more detailed knowledge of the diaphragm movement and deformation, the pressure in the compression chamber as well as the pressures close to suction and discharge valve, respectively. Nevertheless, the data presented in this paper gain a first detailed insight view of the reed valve dynamics and could be further used for validating the valve dynamics of a pump simulation model.
References 1. S. Nagata, T. Nozaki, T. Akizawa, Analysis of dynamic behavior of suction valve using strain gauge in reciprocating compressor, in International Compressor Engineering Conference (2010) 2. M.A. Real, E.A. Gomes Pereira, Using PV diagram synchronized with the valve functioning to increase the efficiency on the reciprocating hermetic compressors, in International Compressor Engineering Conference (2010) 3. J.S. Kopppula, T.K.R. Rajagopal, E. Gundabattini, Correlating the experiment and fluid structure interaction results of a suction valve model from a hermetic reciprocating compressor, in International Conference on Advances in Design, Materials, Manufacturing and Surface Engineering for Mobility. (SAE International, 2017). https://doi.org/10.4271/2017-28-1948 4. Y. Wang, C. Xue, J. Feng, X. Peng, Experimental investigation on valve impact velocity and inclining motion of a reciprocating compressor. Appl. Therm. Eng. 61(2), 149–156 (2013) 5. S.K. Lohn, E.L. Lange Pereira, H. Ferreira Camara, C.J. Deschamps, Experimental investigation of damping coefficient for compressor reed valves, in International Compressor Engineering Conference (2016)
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6. D. Nagy, R.A. Almbauer, W. Lang, E.A.P. Burgstaller, Valve lift measurement for the validation of a compressor simulation model, in 19th International Compressor Engineering Conference at Purdue University (2022), p. 1274. 7. A. Egger, R. Almbauer, L. Dür, B. Zuber, S. Stangl, Experimental investigation of a mechanically assisted suction reed valve in a small hermetic reciprocating compressor. IOP Conf. Ser. Mater. Sci. Eng. 604, 012018 (2019) 8. ISO 21360-2:2020, Vacuum technology—Standard methods for measuring vacuum-pump performance—Part 2: Positive displacement vacuum pumps
CFD Studies on Ejectors Configured with Twisted Circular Profile Lobed Nozzle Kharsade Sachin Angad and Annamalai Mani
Abstract An ejector is a thermo compressor with no moving parts and is used to compress the low-pressure stream to a higher intermediate pressure using a highpressure stream. This study investigates a 3D numerical analysis of a supersonic ejector using R134a, aiming to enhance momentum exchange between the primary and secondary streams. The predicted entrainment ratio is validated with the data available in the literature. The diffuser part of the convergent-divergent primary nozzle is modified to a twisted lobed structure extending through the throat of the primary nozzle. To predict shock wave structure and the ejector performance, the k-ω SST turbulence model with NIST REFPROP v9.1 database equation has been used. The numerical results have revealed that, the pressure difference has been observed between the lobs tip and crest of the lobs, thus making the low-pressure stream sucked into the mainstream and resulting in a high momentum exchange and energy transfer between the two primary and secondary streams. About 7% enhancement in entrainment ratio is seen for a 3-lobed with a 45° twist nozzle ejector without normal shock. Keywords Ejector · R134a · Shock train · Twisted lobed nozzle
1 Introduction Refrigerators and air conditioners play an essential role in our life, and their application is seen in cold storage, food preservation, processing, and many industrial processes. Most refrigeration and air conditioning units work on the vapour compression refrigeration principle, which utilizes a compressor that consumes electrical energy (high-grade energy). There is a need for refrigeration systems utilizing renewable energy for the increasing energy crises and environmental pollution. The vapour jet refrigeration system (VJRS) is one such kind of system that utilizes thermal energy such as solar energy, waste heat, etc., to run the system. K. S. Angad · A. Mani (B) Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_47
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Selvaraju and Mani [1] conducted a comparative study on the performance of ejectors using various environmentally friendly refrigerants in Vapour Jet Refrigeration Systems (VJRS). In VJRS, the refrigerant vapour is compressed using an ejector, also known as a thermo-compressor. The study found that the entrainment ratio and COP vary depending on the compression ratio and driving pressure ratio. Among the refrigerants tested, R134a performed better than the others. Therefore, the study concluded that R134a is a preferable option for use in VJRS due to its superior performance compared to other refrigerants. Different shape of the primary nozzle such as petal, lobed, etc., studied for it effect on entrainment ratio and pressure recovery and one of its analysis on the lobed nozzle for the pressure recovery performed by Opgenorth et al. [2], the parameter of the lobed structure plays a significant role. They concluded that 30 mm is the optimum parameter for the lobed nozzle. Study on an ejector with a swirl-generator just before the primary nozzle to give swirling motion to the primary fluid to enhance mixing between primary and secondary stream, Parveen Banu and Mani [3] concluded an enhancement in global parameter entrainment ratio of 5, 10 and 15% for cavity type swirl generator having sweep angle of 10°, 20° and 30°. An elliptical sharped tipped shallow (ESTS) lobed nozzle as a primary nozzle in the ejector presented by Rao et al. [4], have carried out flow visualization studies and did a comparative study between the conical nozzle, ESTS nozzle, and ring at the tip of the nozzle, concluding enhancement in entrainment ratio by 30% accompanied by a loss of compression ratio as a consequence of loss in stagnation pressure. Ruangtrakoon and Aphornratana [5] provided a design procedure for the ejector using thermodynamic performance analysis, and the procedure is valid for the ejector working with R134a refrigerant. 2D axisymmetric numerical simulations on a supersonic ejector with R134a was conducted by Croquer et al. [6]. Two real gas equations and an ideal gas equation solution were compared, resulting in the Ideal gas equation solution deviating a lot. The remaining two real gas equations Radlich-Kwong-Soave equation of state and NIST REFPROP 7.0 database equations solution, satisfied well with the experimental data of del Valle [7]. del Valle [7] did an experimental study on an ejector refrigeration system using R134a refrigerant as a working fluid. Three different types of ejectors are studied; one of the ejectors is utilized for the current study for validation, and the entrainment ratio is the global parameter used for validating the numerical study. The motivation of present study is to investigate 3-lobed and 4-lobed with a 45° twist nozzle ejector and do a comparative study with conventional circular nozzle ejector.
2 Geometric Modelling The conventional circular nozzle ejectors dimension and the boundary conditions are based on the experimental study by de Valle et al. [7]. Similar dimensions are considered for a lobed nozzle having a 45° twist and also, the primary nozzle exit cross-sectional area was kept constant for all three ejectors to achieve the same Mach
CFD Studies on Ejectors Configured with Twisted Circular Profile … Table 1 Dimensions of ejector
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Parameter
Value
Primary nozzle throat diameter, d1
2.00 mm
Primary nozzle exit cross-sectional area, A2
7.06 mm2
Nozzle exit position, NXP
−5.38 mm
Mixing chamber diameter, d3
4.80 mm
Mixing chamber length, Lm
41.39 mm
Diffuser length, Ld
95.00 mm
Diffuser exit diameter, d4
18.00 mm
Suction chamber convergent angle
30°
number at its end and to compare lobed nozzle ejectors with that of a conventional circular nozzle ejector. Referred experimental data consists of three different ejectors (A, B and C) with different mixing chamber geometries. Geometry “A” performs better than the remaining two for all the superheated inlet boundary conditions; thus, geometry “A” is chosen for the current study, involving few changes in the diffuser region. Experimental studies present that superheating primary and secondary fluids above 10°°C won’t show much improvement in the entrainment ratio. The experimental data won’t consist of secondary inlet section details; the only available information on 30° half-angle cone entry is provided. The geometry dimensions are given in Table 1. A 3-dimensional numerical study has been carried out for three different ejectors: conventional circular ejector, 3-lobed 45°-twist lobed nozzle ejector, and 4-lobed 45°-twist lobed nozzle. Figure 1 shows the isometric and cross-sectional view of three respective nozzles. As per the literature survey, it seems that the lobed nozzle performs sufficiently better than a simple circular nozzle, and in addition, included a twist structure to the diffuser part of the primary nozzle starting from the throat of it to enable swirl motion to the flow in the downstream direction to achieve enhanced mixing (Fig. 2).
3 Numerical Studies 3.1 Numerical Method A 3D supersonic ejector modeled using ANSYS Fluent 2021 utilizing RANS SST k-ω turbulence model. A pressure–velocity coupled algorithm calculates the flow field with the second-order upwind discretization of pressure, momentum, turbulence kinetic energy, specific dissipation rate, and energy terms. Advection Upstream Splitting Method (AUSM) is selected as a convective flux calculator to get an exact resolution of contact and shock discontinuities, and the correspondingly pseudo-transient condition is used to stabilize the flow.
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Fig. 1 Isometric and cross-sectional view of the primary nozzle a conventional circular primary nozzle b 3-lobed 45° twist primary nozzle c 4-lobed 45° twist primary nozzle
Fig. 2 Schematic diagram of ejector
Flow has been considered in the steady-state regime. R134a fluid is assumed to remain in the gaseous phase, and the required boundary conditions from the experimental data are included in Table 2. Pressure inlet boundary conditions were prescribed with the primary inlet and secondary inlet section, and pressure outlet boundary condition was prescribed with the ejector outlet. Also, an adiabatic wall with smooth and no-slip boundary conditions are utilized for the wall. Table 2 shows the temperature of 10 °C greater than the saturation temperature for the corresponding pressure at the primary and secondary inlet sections. The working fluid is R134a in vapour phase throughout the fluid domain, so NIST REFPROP v9.1 is included in the simulation study, which utilizes a real gas model. Real gas model perfectly deals with density variation in a compressible flow. Achieving stable and converged solution using second-order upwind discretization for initial few iterations results in density divergence. To deal with this, for the first 100 iterations, the first-order upwind discretization scheme was utilized to make the simulation converge and then changed to second-order upwind until the solution converged to 10–5 residuals. To confirm the convergence, 4 points at a particular interval from the entry of the constant area section are considered, and average velocity is observed to see whether the solution
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Table 2 Boundary conditions correspond to experimental data of del Valle et al. [8] Operating Primary inlet point (OP) (Generator)
Secondary inlet (Evaporator)
Outlet (Condenser)
Ejector performance
Pabs (kPa) T (°C)
Pabs (kPa) T (°C)
Pabs (kPa) T (°C)
ERexp
Pratio
1
2598.04
89.37
414.608
20
757.222
29.41
0.494
1.826
2
2888.8
94.39
414.608
20
826.573
32.48
0.398
1.994
3
3188.14
99.15
414.608
20
897.115
35.41
0.339
2.164
converges or not. Meshing is performed through Fluent meshing, polyhedral mesh near the wall region, and structured/hexahedral mesh used through the fluid domain to reduce the computational cost. The y+ ~ 1 near the wall region utilizing SST k-ω turbulence model, since it doesn’t use any wall-damping function, but keeping y+ ~ 1 near the wall region increases the aspect ratio to a much higher value with a minimum inverse orthogonality of 0.15.
3.2 Grid Independence Test This study deals with 3D supersonic ejectors. A systematic grid independence test has been carried out for pressure and velocity variation along the ejector’s centerline. Five different grid sizes have been considered with a stepwise increase in grid size. Up to the first two grid size, the velocity and pressure profile shows much larger changes, but as we move towards finer grid size, it remains almost unchanged. Grid independence test has been carried out for all three ejectors and has shown similar grid independence results. Thus, to have the best accuracy with minimal computational time, all the simulations were performed with approximately 8 million cells. Figure 3 show the velocity variation along the center line of the ejector for different grid sizes respectively (Figs. 4 and 5).
3.3 Validation of CFD The numerical analysis performed on conventional circular nozzle ejector has been carried out by comparing with experimental results [7] for the global performance parameter named entrainment ratio. The entrainment ratio is the ratio between the secondary and primary mass flow rates. The entrainment ratio obtained with CFD compared with experimental results for given boundary conditions has shown a deviation much less than 5%. The SST k-ω turbulence model overestimates the entrainment ratio for the 2nd and 3rd operating regions by 4% and 2% respectively (Fig. 6).
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Fig. 3 Velocity variation along ejector length for different grid sizes Fig. 4 Mesh section consisting of primary, secondary and constant area mixing section
Fig. 5 Mesh structure a. Mid-cross-section of constant area mixing chamber b. Near the wall
Fig. 6 Comparison between CFD and experimental results [7]
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3.4 Velocity Magnitude Contour We considered three ejectors differing in primary nozzle structure. Velocity and pressure contours provide detailed information about the shock structure forming through the nozzle. For the current study, over-expanded shock is seen at the end of a nozzle which further forms a train of expansion fans and oblique shocks; going in the downstream direction, normal shock disrupts the shock train, and its dissipation can be seen in the further downstream direction. Velocity contours depict the formation of the shock train; it seems that the dissipation of the shock train for the 3-lobed with a 45° twist nozzle ejector is much earlier than comparable to the other two with the absence of normal shock; the shock train formed gets dissipated from its own. In comparison, normal shock occurs lately for 4-lobed with a 45° twist nozzle ejector than conventional circular nozzle ejector in the downstream direction, which signifies 4-lobed nozzle ejector have higher critical back/condenser pressure. The normal shock appears to move in the upstream direction with the increase of back pressure, thus disrupting the double-chocking mode and negatively impacting the entrainment ratio (Fig. 7). The flow in the ejector diffuser can be seen getting deflected from its straight path, which can’t be seen in the 2D axisymmetric computational work [6]. For the present 3D study, the vector representation of the fluid domain shows the presence of circulation in the ejector diffuser and it affects ejector performance at higher back pressure. The circulation formed inside the diffuser affects the flow in the constant area mixing section. The flow exiting the primary nozzle reaches a velocity of 288 m/s, which corresponds to a Mach number of 1.9. At this section, the temperature is 280.09 K and the pressure is 217.4 kPa absolute. The speed of sound in this region is 152.40 m/s. The formation of lobes surrounding the secondary fluid and its dissipation is depicted in Fig. 8. Lob tips are much expanded towards the wall of the constant area
Fig. 7 Velocity magnitude contours of three different ejectors for OP1 a conventional circular nozzle ejector b 3-lobed 45° twist nozzle ejector c 4-lobed 45° twist nozzle ejector
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Fig. 8 3D pictorial form of Mach number contours for OP1 a conventional nozzle ejector b 3-lobed 45° twist lobed nozzle ejector c 4-lobed 45° twist lobed nozzle
mixing chamber compared to their respective lob crest. Circumferential pressure variation is observed in the space between two lobes containing secondary fluid particles, which drag this particle into the core of the primary fluid. Flow separation is seen near the boundary and is caused due to the normal shock disrupting the shock train. This normal shock incident over the fluid near the wall region disrupts the flow and causes flow separation.
3.5 Velocity Vector Contour Vector representation showcases the flow structure, the formation of vorticities, circulation, and many other things. In the following section, vector representation of the cross-sectional view of three different ejectors is visualized. Primary fluid expands through the primary nozzle to very low pressure and high velocity, thus sucking secondary fluid into it due to the pressure difference between the primary and secondary fluid. Figure 9a reflects the uniformity of secondary flow over the primary flow section, whereas Fig. 9b, c consist of the lobed section, which increases the surface contact area between the intersection of primary and secondary fluid, which means more momentum exchange between the fluid particles. The lobed structure provides sufficient space for the secondary fluid particle to let them come in contact with the core of the primary flow and simultaneously grab more secondary fluid through shearing action, resulting in an increased entrainment ratio.
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Fig. 9 Velocity vectors at a cross-section 2 mm from the primary nozzle for OP1 a conventional nozzle ejector b 3-lobed 45° twist nozzle ejector c 4-lobed 45° twist nozzle ejector
Fig. 10 Velocity vectors at a cross-section 45 mm from the primary nozzle for OP1 a conventional nozzle ejector b 3-lobed 45° twist nozzle ejector c 4-lobed 45° twist nozzle ejector
Figure 10a shows the random arrangement of vectors on a cross-section at 45 mm from the primary nozzle but Fig. 10b, c present vector representation for twisted lobed nozzle ejectors. Vector representation demonstrates the swirl behavior of the flow as it moves downstream of the constant area mixing chamber. This concludes that the twisted lobed nozzle ejector provides enhanced mixing of primary and secondary fluids, thus, better momentum and energy exchange between them.
3.6 Velocity Plot and Static Pressure Plot As we have seen previously through contours, there is too early dissipation of shock train for 3-lobed nozzle ejector and lately for 4-lobed nozzle ejector. The occurrence of normal shock for a conventional nozzle ejector is almost 30 mm distant from the primary nozzle, whereas, for a 4-lobed nozzle, it is 40 mm distant from the primary nozzle.
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Fig. 11 Velocity magnitude plot of three different ejectors along the centre line for OP1
Experimental studies in the literature also show the presence of clearly visible shock trains. Depending on the back pressure, these shock trains also extend into the diffuser part. These results are formed using the SST k-ω turbulence model, and the results are validated with the experimental values of the conventional nozzle ejector. For validation purposes, the global parameter Entrainment ratio is used, and the maximum deviation compared to experimental results comes to be less than 5%. SST k-ω turbulence model is chosen here because it doesn’t use a damping function near the wall. It uses proper integration throughout the cells near the wall region and has shown better results for both On and Off design conditions for all pressure conditions. In contrast, Standard k-ε turbulence models perform well only in on design conditions (Fig. 11). In terms of the entrainment ratio, Fig. 12 represents a comparative performance of three different ejectors. The 3-lobed with a 45° twist nozzle ejector performs better than the remaining three, showing an enhanced entrainment ratio of 7%, thus, higher suction of secondary fluid. Keeping secondary pressure constant and increasing primary and back pressure, decrement in the entrainment ratio is seen. For fixed ejector geometry, increasing primary pressure increases the primary fluid mass flow rate, thus decreasing the entrainment ratio.
4 Conclusions In the present work investigates lobed and circular nozzle ejectors and did a comparative study based on the entrainment ratio and mixing phenomenon between primary and secondary streams. The twisting of the primary nozzle gives swirl motion to the primary flow. Its effect can be seen in the constant area mixing section. Swirled primary flow entrains the surrounding secondary fluid with enhanced momentum and energy transfer. The occurrence of normal shock signifies that the critical back pressure for a 4-lobed with a 45° twist nozzle is more significant than the remaining
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Fig. 12 Comparison between three different ejectors in terms of entrainment ratio for two operating points OP1 and OP2
two but with a compromise of entrainment ratio. The velocity and static pressure plot won’t show the presence of normal shock for a 3-lobed nozzle ejector. Mach plot describes a simple circular nozzle, and 4-lobed nozzle ejectors are double choked, whereas a 3-lobed nozzle ejector is single choked with the lower critical condenser/ back pressure. The study concludes that 3-lobed with a 45° twist nozzle ejector shows a 7% increment of entrainment ratio with low critical back pressure, 4-lobed with a 45° twist nozzle ejector shows a 4% decrement of entrainment ratio with higher critical back pressure comparative to a conventional circular nozzle ejector.
References 1. A. Selvaraju, A. Mani, Analysis of a vapour ejector refrigeration system with environment friendly refrigerants. Int. J. Therm. Sci. 43, 915–921 (2004) 2. M.J. Opgenortha, D. Sederstroma, W. McDermottb, C.S. Lengsfeld, Maximizing pressure recovery using lobed nozzles in a supersonic ejector. Appl. Therm. Eng. 37, 396–402 (2012) 3. J. ParveenBanu, A. Mani, Numerical studies on ejector with swirl generator. Int. J. Therm. Sci. 137, 589–600 (2019) 4. S.M.V. Rao, G. Jagadeesh, Novel supersonic nozzles for mixing enhancement in supersonic ejectors. Appl. Therm. Eng. 71, 62–71 (2014) 5. N. Ruangtrakoon, S. Aphornratana, Design of steam ejector in a refrigeration application based on thermodynamic performance analysis. Sustain. Energ. Technol. Assess. 31, 369–382 (2019) 6. S. Croquer, S. Poncet, Z. Aidoun, Turbulence modeling of a single-phase R134a supersonic ejector. Part 1: Numerical benchmark. Int. J. Refrig. 61, 140–152 (2016) 7. J.G. del Valle, J.M. Saíz Jabardo, F. Castro Ruiz, J.F. San José Alonso, An experimental investigation of a R-134a ejector refrigeration system. Int. J. Refrig. 46, 105–113 (2014)
Development and Performance Evaluation of a Micro Air Blower Ahmed M. R. Elbaz, Nabil Mahmoud, Abdulnaser Sayma, Abdelrahman Abdeldayem, and Mohammed Ammar
Abstract Micro air blowers are used in a wide range of applications such as cooling battery packs for electric vehicles, portable medical devices and computers as well as active boundary layer control. Recently, boundary layer suction is proposed to be applied to vertical axis wind turbine blades in order to improve its performance either through direct suction from blade surface before the separation point, or through surface cavity. In VAWT boundary layer control through suction, blower pressure ratio varies as the blade travels along its rotational path. Preliminary investigations for a VAWT model composed of 3 blades of 1 m length and 200 mm chord show that the required micro blower flow rate ranging from 10 to 36 m3 /h at a differential pressure range from 0.5 to 1.3 kPa. Since such micro air blower operating range have not been reported previously, it was decided to design and test a prototype in order to examine the applicability of common air blower design techniques in this small scale. The present paper aims at reporting the preliminary design, simulation and experimental testing results of a micro air blower in the specified working range. The blower design is made using Euler equations. A physical model is manufactured using 3D printing and tested at 14.5 k rpm. The driver electric motor is a high speed motor suitable for remote speed adjustment. Furthermore, the blower performance maps are obtained using steady-state 3D viscous numerical simulations. The paper includes both experimental and CFD results. Recommendations to improve the performance of this micro air blower are also included. Keywords Turbomachinery · Experimental study · Computational fluid dynamics · Numerical simulation · Micro air blower · Noise radiation
A. M. R. Elbaz (B) British University in Egypt, Cairo 11837, Egypt e-mail: [email protected] N. Mahmoud · M. Ammar Ain Shams University, Cairo 11517, Egypt A. Sayma · A. Abdeldayem City, University of London, London EC1Y 8TZ, UK © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_48
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1 Introduction Micro air blowers are used in a wide range of applications such as cooling battery packs for electric vehicles, portable medical devices and computers as well as active boundary layer control. Recently, boundary layer suction is proposed to be applied to vertical axis wind turbine blades in order to improve its performance wither through direct suction from blade surface before the separation point, or through surface cavity [1, 2]. In VAWT boundary layer control through suction, blower pressure ratio varies as the blade travels along its rotational path. Preliminary investigations for a VAWT model composed of 3 blades of 1 m length and 200 mm chord show that the required micro blower flow rate ranging from 10 to 36 m3 /h at a differential pressure range from 0.5 to 1.3 kPa. Since such micro air blower operating range have not been reported previously, it was decided to design and test a prototype in order to examine the applicability of common air blower design techniques in this small scale. Centrifugal blowers have been the subject of research for many years because of their significance. Chen et al. [3] investigated the effect of the presence of radial offset between the impeller and volute casing centerline that may result from poor assembly or installation on the performance of a double suction centrifugal fan by numerically performing (URANS) simulations. The authors observed that the presence of radial offset causes non-uniformity in the static pressure and reverse flow at impeller inlet with velocities as high as 20 m/s, additionally, reversed back flow to the volute casing as well as strong internal vortices were also observed. Friebe et al. [4] experimentally studied a new design of a contra-rotating centrifugal fan implementing two rotating impellers with two separate concentric drives. The authors concluded that maximum pressure coefficients were observed when the first impeller was rotating at 1200 rpm and the second impeller was rotating at 200 rpm. Ottersten et al. [5] numerically investigated the effect of inlet gap between the inlet duct and the impeller of a volute-less centrifugal fan on noise generation. The authors found that the least noise generated occurred when the gap width was 2 mm with a minimum noise intensity of 61.8 dB. Suresh et al. [6] experimentally incorporated a gurney flab in the design of a centrifugal fan and investigated the impact of its height and mounting position on the performance. Different gurney flab heights of 1, 1.5, 2 and 2.5 mm were studied at different rotational speeds. The authors found that the head coefficients increased as the gurney flab height increased to a certain limit then the improvement starts to decrease. Varun et al. [7] numerically investigated the effect of number of blades on the performance of a centrifugal fan. Four different blade numbers of 8, 10, 12 and 14 were studied. The authors concluded that using 14 blades exhibited the best performance with an increase of 21.77% in the total pressure at outlet and an increase of 5.74% in efficiency when compares to the design point conditions. Wang et al. [8] studied the effect of bio-inspired blades on the aerodynamic performance of a centrifugal fan numerically, experimentally and by using reserve engineering methods. The authors found that with incorporated the bionic style blades the flow rate increased by 8.3% and the noise was reduced by 1.1 dB (A), also, enhancement
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in the input power and efficiency were observed. Wei et al. [9] investigated the effect of an inclined volute tongue on the aerodynamic performance of a centrifugal fan by numerical simulations. The researchers concluded that the efficiency of the fan increases with the increase in inclination angle by 3.8% compared with the baseline geometry because vortices and local losses were reduced. The present paper aims at reporting the preliminary design, simulation and experimental testing results of a micro air blower in the specified working range. The blower design is made using Euler equations. A physical model is manufactured using 3D printing and tested at different rotational speeds. The driver electric motor is a high speed motor suitable for remote speed adjustment. Furthermore, the blower performance maps are obtained using steady-state 3D viscous numerical simulations. The paper includes both experimental and CFD results. Recommendations to improve the performance of the micro air blower are also included.
2 Blower Design The selected micro air blower demonstration prototype dimensions are based on a VAWT application where the blade chord length is 200 mm and made up of NACA 0018 airfoil. The VAWT diameter is 1 m. Micro air blower characteristics required for this turbine is 0.6 m3 /min with static pressure 1.3 kPa. The blower design was made using the following design parameters [10]: Specific diameter Ds = 3.0 where Ds is defined: √ D Q Ds = (1) (Δp/ρ)1/4 D is impeller diameter, Q is volumetric flow rate, Δp is pressure rise and ρ is air density. Specific speed Ωs = 1.0 where Ωs is defined: √ Ω Q Ωs = (Δp/ρ)3/4
(2)
ψ = (Δp/ρ)/u22
(3)
where Ω is rotational speed. Head factor ψ = 0.5 where ψ is defined:
Flow coefficient Ø = 0.1 where Ø is defined:
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∅ = Cm2 /u2
(4)
where Cm2 is the radial velocity at impeller outlet, u2 is the peripheral speed of the impeller (u2 = πD2 N/60), D2 is impeller diameter at outlet and N is rotational speed in rpm. Velocity triangles of the blower at inlet and outlet were used to obtain blade angles. Blower blade was made using circular arcs. Design speed is 14,500 rpm. Volute design takes rectangular cross section. The calculated blower dimensions are as follows: • • • • • • • • •
Impeller inlet diameter = 30 mm Impeller outlet diameter = 60 mm Impeller height = 14 mm Number of vanes = 9 Inlet blade angle = 34° (measured w.r.t. tangential velocity direction) Exit blade angle = 53° (measured w.r.t. tangential velocity direction) Suction port diameter = 30 mm Discharge port height = 20.5 mm Discharge port width = 26 mm.
Figure 1 shows the CAD model of blower parts (without dimensions) assembled on a base plate. Figure 2 shows the actual assembly of the blower parts. The blower motor is brushless DC motor (Model: XING Pro X2207 1800 kV) and motor speed is controlled using electronic speed controller (ESC Model: B0922X87MH) using 12 V DC source. Blower impeller is directly mounted on motor shaft. Fig. 1 Micro blower CAD model
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Fig. 2 Micro air blower assembly
3 Experimental Setup The experimental setup is shown in Fig. 3. The differential pressure between suction and discharge sides of the micro blower is measured using a digital manometer with a resolution of 0.01 kPa and an accuracy ± 0.5%. The volume flow rate is obtained by measuring the centreline velocity of a 600 mm long suction pipe 30 mm diameter connected to blower suction. A pitot tube is used to provide the dynamic pressure at the measuring location. Differential pressure of the Pitot tube is measured using digital manometer with a resolution of 0.01 kPa and an accuracy ± 0.5%. Blower rotational speed is measured using digital contactless tachometer with a resolution of 1 rpm and accuracy of ± 0.04% + 2. Noise radiation was measured at a fixed distance of 80 mm from blower center using a digital sound level meter with a range of 30–130 dBA, resolution of 0.1 dBA, accuracy of ± 1.5 dBA and a frequency response of 31.5 Hz–8 kHz. A multimeter is used to monitor the line-to-line three phase AC voltage applied on the micro blower and line current during operation with a resolution of 10 mV and an accuracy of (± 0.8% + 5). Power supply for the motor is provided by 12 VDC power supply. The no load power consumption of the BLDC motor was measured at different rotational speeds. This power is subtracted from the measured power when the motor is connected to the blower. Table 1 shows the no load power of the BLDC motor.
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Fig. 3 Experimental setup schematic diagram
Table 1 No load measurements of the BLDC motor
N (rpm)
VLL (Volt)
IL (A)
Power (W)
10,000
4.17
0.45
3.250
14,500
4.95
0.55
4.716
19,000
8.40
0.66
9.191
4 Numerical Methodology The proposed blower design is numerically investigated using computational fluid dynamics (CFD) model to verify the preliminary performance and evaluated using the mean line loss models. The model is used to generate the performance maps. The geometry of the stationary and moving domains of the blower model is shown in Fig. 4. A short inlet pipe is used to simulate the ambient air where the inlet boundary is defined as normal flow mass flow rate and static temperature. The outlet duct length is increased compared to the physical prototype to improve the numerical simulation stability and prevent back flow at the outlet. The CFD model is a steady-state viscous flow model using the k-ω SST turbulence model. The interface between the stationary and rotating domains is defined as a frozen rotor interface to transfer the circumferential variations from upstream to downstream the interface without averaging the properties as the case with the mixing plane interface. The circumferential variations in this case cannot be neglected as the stationary casing is designed as a volute casing with circumferentially variable pressure gradient. Similar blowers and fans domains are defined within the literature for numerical modelling as in [10–12]. The boundary and operating conditions are summarized in Table 2.
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Fig. 4 Computational domain definition
Table 2 Operating conditions and impeller size
Parameter
Value
Mass flow rate (kg/s)
0.012
Inlet static temperature (K)
298
Outlet static pressure (bar)
1.01325
Rotational speed (rpm)
14,500
Impeller diameter (mm)
60
Impeller height (mm)
14
The mesh structure of the blower is reported in Fig. 5 where 1.1 and 0.8 million nodes are used to define the stator and rotor domains, respectively. The mesh is refined around the walls to better represent the boundary layers where the average Y+ value is kept around 2.0 [13].
5 Results and Discussion 5.1 Experimental Results Figure 6 shows the measured variation of the rotational speed of the BLDC motor used to drive the blower with applied line to line voltage, with and without loading. Increasing the applied line to line voltage linearly increases the rotational speed in a linear fashion which is typical to this type of motor. Additionally, extra resistance facing the loaded motor results in slightly decreasing its rotational speed.
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Fig. 5 Mesh structure on a plan perpendicular to the axe of rotation at mid-span
Fig. 6 BLDC motor rotational speed variation with supply voltage
Figure 7 shows the measured variation of the pressure rise with the volume flow rate of the micro air blower. The colored symbols correspond to the average values. The vertical error bars are plotted between minimum and maximum pressure measured at the same flow rate. The measurements were repeated many times in order to gain confidence in the measurements. It can be observed that increasing the flow rate results in a decrease in the pressure rise for all rotational speeds. Additionally, increase of the rotational speed from 10,000 rpm to 14,500 rpm and from 14,500 rpm to 19,000 rpm results in an average increase of the pressure rise by 106.63% and
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Fig. 7 Measured pressure rise versus volume flow rate with rotational speeds
65.01%, respectively. It is also noted that the design condition is achieved at a speed higher than the targeted value. This is attributed to the presence of clearances at motor shaft inlet to casing as well as impeller inlet leakage from discharge due to clearance between blower inlet and casing. The observed variations between maximum and minimum pressure rise are very high at 19,000 rpm, compared to those observed at lower rotational speeds. This indicates that at the highest rotational speed the flow becomes highly unsteady. Figure 8 shows the measured variation of the net driving power for the BLDC motor with the volume flow rate of the micro air blower. It can be noted that driving input power of the blower increases to a certain value then almost remains constant at high flow rates at all rotational speeds. This behavior is confirmed with the simulation results. Additionally, increase of the rotational speed from 10,000 rpm to 14,500 rpm and from 14,500 rpm to 19,000 rpm results in an average increase of the driving input power by 161.62% and 55.19%, respectively. Figure 9 shows experimental variation of overall efficiency with volume flow rate. The overall efficiency is observed to increase to a certain maximum then decrease with the increase of the flow rate for all rotational speeds. Additionally, increase of the rotational speed from 10,000 rpm to 14,500 rpm and from 14,500 rpm to 19,000 rpm results in an average increase of the overall efficiency by 18.75% and 47.7%, respectively. It is also noted that at low flow rates slower variation in the rotational speed seems to have no significant effect on the overall efficiency, while at high flow rates higher rotational speeds are preferred. This is a typical behaviour of small size turbomachines pertinent with Reynolds number effects [14–17]. This behavior is also confirmed by the simulation results presented below. Figure 10 shows the measured variation of the noise radiation intensity of the micro air blower during operation. It is shown that increase of the volume rate causes a slight
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Fig. 8 Measured net power consumption versus volume flow rate with rotational speeds
Fig. 9 Efficiency versus volume flow rate and different rotational speeds
linear increase in noise radiation for all rotational speeds. Additionally, increase of the rotational speed from 10,000 rpm to 14,500 rpm and from 14,500 rpm to 19,000 rpm results in an average increase of the noise radiation level by 6.02% and 5.68%, respectively. It should be emphasized that the noise radiation intensity measured during operation is the total noise radiation from the micro air blower assembly as well the environment. The baseline ambient noise radiation prior to operating the micro blower was 55 dBA.
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Fig. 10 Measured noise radiation intensity with volume flow rate and different blower rotational speeds
5.2 Numerical Simulation Results The flow field at mid-span of the impeller as well as the local entropy and pressure distribution are shown in Fig. 11 where the flow around the blade buckets is illustrated along with the volute casing and outlet duct. Results obtained by numerical simulation exhibited similar behavior of the blower at rotational speeds of 10,000, 14,500 and 19,000 rpm. It can be observed that increasing the flow rate results in a decrease in the pressure rise for all rotational speeds. Moreover, increase of the rotational speed from 10,000 rpm to 14,500 rpm and from 14,500 rpm to 19,000 rpm results in an average increase of the pressure rise by 110.23% and 69.13%, respectively, as shown in Fig. 12. Input driving power of the blower is shown to increases to a certain value then almost remains constant at high flow rates for all rotational speeds. Also, increase of the rotational speed from 10,000 rpm to 14,500 rpm and from 14,500 rpm to 19,000 rpm results in an average increase of the driving input power by 111.32% and 70.37%, respectively, as shown in Fig. 13. Efficiency of the micro air blower, as shown in Fig. 14, can be seen to increase to a certain maximum then decrease with the increase of the flow rate for all rotational speeds. Moreover, increase of the rotational speed from 10,000 rpm to 14,500 rpm and from 14,500 rpm to 19,000 rpm results in an average increase of the overall efficiency by 47.04% and 27.28%, respectively. The effect of Reynolds number on the behaviour of small turbomachines has been investigated by Tiainen et al. [17]. Their results showed that compressors at low Reynolds number suffer from increased losses caused both by the relatively increased
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Fig. 11 Velocity, entropy and pressure distribution at mid-span of the reference impeller at the reference operating conditions
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Fig. 12 Predicted variation of pressure rise with volume flow rate
Fig. 13 Predicted variation of driving input power with volume flow rate
boundary layer thickness and by the shear stress resulting from the increased vorticity. The Reynolds number is defined: Re =
ρu 2 b2 μ
(5)
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Fig. 14 Predicted variation of overall efficiency with volume flow rate
Table 3 Relationship between maximum efficiency and Reynolds number
Reynolds number
3.7E+04
5.3E+04
7.0E+04
Eta maximum %
27.92
40.88
54.66
where u2 is the impeller peripheral speed and b2 is the impeller width at outlet. It is clear that Reynolds number is dependent on the rotational speed of the blower which determines u2 . Table 3 shows the dependency of the maximum efficiency on Reynolds number obtained by the model results. Numerical simulation results are compared with the experimental results of both the head coefficient and overall efficiency, as shown in Figs. 15 and 16. Both parameters are plotted against the flow coefficient. Figure 15 shows that the head coefficient variation with flow coefficient are well correlated for the tested rotational speeds. However, the predicted head coefficient is approximately 20% higher than the measured values. The efficiency curves, Fig. 16, are not correlated since efficiency is observed to be affected by Reynolds number variation with rotational speed. The measured efficiency of the blower at 19,000 rpm is higher than the predicted value. Similar behaviour is also observed for lower rotational speeds.
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Fig. 15 Comparison between experimental and numerical model results of the head coefficient variation with flow coefficient
Fig. 16 Comparison between experimental and numerical model overall efficiency results
6 Conclusions A high-speed centrifugal micro air blower has been designed and manufactured by means of additive manufacturing technology. The performance of the micro air blower has been investigated both experimentally as well as by numerical computer simulation. The following are the study conclusions:
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• Numerical simulation results and experimental results are in agreement in terms of describing the behavior of the micro air blower. • Increase of volume flow rate results in a decrease in the pressure rise, increase in the input driving power for all rotational speeds. • Running the micro air blower at higher rotational speeds is more efficient for high volume flow rates, while at low volume flow rates variation of overall efficiency with rotational speed is insignificant. • The micro air blower efficiency is affected by Reynolds number. As the Reynolds number increases, higher efficiency is obtained. • Noise radiation during operation shows a slight linear increase with increase in volume flow rate for all rotational speeds.
References 1. A. Ibrahim, A. Elbaz, P. Melani, O. Mohamed, A. Bianchini, Power augmentation of Darrieus wind turbine using trapped cavity vortex. J. Wind Eng. Ind. Aerodyn. 223, 104949 (2022) 2. J. Sun, X. Sun, D. Huang, Aerodynamics of vertical-axis wind turbine with boundary layer suction—effects of suction momentum. Energy 209, 118446 (2020) 3. Z. Chen, H. Yang, Y. Wei, H. He, C. Zhang, T. Nie, P. Yu, W. Zhang, Effect of a radially offset impeller on the unsteady characteristics of internal flow in a double-suction centrifugal fan. Processes 10(8) (2022). https://www.mdpi.com/2227-9717/10/8/1604 4. C. Friebe, O. Velde, K. Hackeschmidt, Design and investigation of a contra-rotating centrifugal fan (2022) 5. M. Ottersten, H.D. Yao, L. Davidson, Inlet gap effect on tonal noise generated from a voluteless centrifugal fan. Int. J. Turbomach. Propul. Power 7(4) (2022). https://www.mdpi.com/2504186X/7/4/33 6. M. Suresh, N. Sitaram, Effect of gurney flap height and mounting position on the performance of a centrifugal fan. J. Appl. Fluid Mech. 15(1), 255–269 (2022). https://doi.org/10.47176/ jafm.15.01.32788 7. S. Varun Ch, K. Anantharaman, G. Rajasekaran, Effect of blade number on the performance of centrifugal fan. Mater. Today Proc. 72, 1143–1152 (2023). https://doi.org/10.1016/j.matpr. 2022.09.185 8. J. Wang, X. Liu, C. Tian, G. Xi, Aerodynamic performance improvement and noise control for the multi-blade centrifugal fan by using bio-inspired blades. Energy 263, 125829 (2023). https://doi.org/10.1016/j.energy.2022.125829. https://www.sciencedirect.com/science/article/ pii/S0360544222027153 9. Y. Wei, J. Wang, J. Xu, Z. Wang, J. Luo, H. Yang, Z. Zhu, W. Zhang, Effects of inclined volute tongue structure on the internal complex flow and aerodynamic performance of the multi-blade centrifugal fan. J. Appl. Fluid Mech. 15(3), 901–916 (2022). https://doi.org/10.47176/jafm.15. 03.32847 10. E. Dick, Fundamentals of Turbomachines, 2nd edn. (Springer, 2022) 11. Y.R. Pathak, B.D. Baloni, D. Channiwala, Numerical simulation of centrifugal blower using CFX. Int. J. Electron. Commun. Soft Comput. Sci. Eng. 242–247 (2012) 12. T. Siwek, J. Gorski, S. Fortuna, et~al., Numerical and experimental study of centrifugal fan flow structures and their relationship with machine efficiency. Polish J. Environ. Stud. 23(6), 2359–2364 (2014) 13. M. Kuosa, P. Sallinen, J. Larjola, Numerical and experimental modelling of gas flow and heat transfer in the air gap of an electric machine. J. Therm. Sci. 13, 264–278 (2004)
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14. J. Tiainen, A. Jaatinen-Varri, A. Gronman, J. Backman, Influence of Reynolds number variation method on centrifugal compressor loss generation. In: ETC2017-041 Proceedings of 12th European Conference on Turbomachinery Fluid dynamics and Thermodynamics ETC12, 3–7 Apr. 2017, Stockholm, Sweden (2017) 15. M. Valdés, A. Sebastián, R. Abbas, Reynolds-number-dependent efficiency characterization of a micro-scale centrifugal compressor using non-conventional working fluids. Energ. Convers. Manage. 177(1), 224–232 (2018) 16. P.F. Pelz, S. Saul, J. Brotz, Efficiency scaling: influence of Reynolds and Mach numbers on fan performance. J. Turbomach. 144, 061001-1 (June 2022) 17. J. Tiainen, A. Jaatinen-Värri, A. Grönman, A. Backman, Numerical study of the Reynolds number effect on the centrifugal compressor performance and losses. In: ASME Turbo Expo 2016: Turbine Technical Conference and Exposition, Seoul, South Korea (2016)
Active Magnetic Bearings, Variable-Speed Centrifugal Air Compressors Suitable to Reduce Carbon Footprint, is it Really the Case? Mihail Lopatin, Timo Pulkki, Igor Nagaev, Ramdane Lateb, and Joaquim Da Silva
Abstract The purpose of this article is to compare and evaluate the performance of two types of compressor units—one utilizing high-speed direct drive centrifugal compressor technology with active magnetic bearings (AMBs) and permanent magnet motors, and the other utilizing oil-free screw compressor technology powered by induction motors. Both compressors are designed to operate with a variable speed drive (VFD) and are water cooled. The authors aim to conduct a comprehensive life cycle analysis, focusing on the energy consumption and carbon footprint of these two technologies over their lifespan. Through their expertise, the authors will suggest operating scenarios. The potential reduction in CO2 e emissions can vary greatly depending on the country and scenario, ranging from several tens to over a thousand tons of CO2 e over the lifespan of the compressor unit. In most studied cases, the direct drive centrifugal compressor proves to be the optimal choice in energy savings and in CO2 e emission reduction.
1 Introduction Early on, magnetic bearings in centrifugal compressors were favored by OEMs and end-users for their benefits such as reduced maintenance costs and operational costs, no need for oil lube systems, and the absence of sealing [1]. Studies have even suggested using magnetic bearings for use in gas turbines [2]. Since then, active magnetic bearings have been adopted in various applications, including chiller systems, where energy savings of nearly 30% per year have been reported compared to screw compressors [3, 4]. Turbo-blowers using AMBs have also seen energy savings of 10–30% compared to rotary compressors and classical M. Lopatin · T. Pulkki · I. Nagaev TAMTURBO OYJ, Tampere, Finland R. Lateb (B) · J. Da Silva Department of R&D, SKF Magnetic Mechatronics, St Marcel, France e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_49
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geared centrifugal compressors [5, 6]. In oil and gas applications, the use of AMBs in sealed compressors have reduced natural gas leaks, contributing to reduced CO2 e emissions [7, 8]. The geopolitical situations, the high demand on electricity market combined to the net zero emission target result in high energy prices. The European Union’s Energy Efficiency Directives (EED) mandate member states to adopt measures to enhance energy efficiency throughout the production and consumption process. In a bid to achieve its 2030 climate and energy goals, the EU Commission has proposed a revised EED directive with a strong focus on energy efficiency [9]. The compressed air sector accounts for 10% of total industrial electricity usage worldwide, with 30% being attributed to compressor technology [10, 11]. To enhance energy efficiency, experts suggest several measures such as fixing leaks, preventing pressure loss, implementing heat recovery systems, adjusting compressor controls optimally, and utilizing variable frequency/speed drives [10–12]. Choosing the right compressor for a particular application depends on various factors, including flow/pressure range, power/capacity, and the specific requirements of the application. For medium and large air capacity needs, screw and centrifugal compressors are often used. Meanwhile, variable speed compressors can offer cost savings when air demand fluctuates. Centrifugal compressors are well-suited for continuous full load service. Oil-free compressors are favored in industries where air contamination must be avoided, such as pharmaceutical, electronic, food and beverage, and hospital services [13, 14]. Oil-free screw compressors have less frequent maintenance needs compared to oil-lubricated screw compressors, but have limited efficiency and compression ratio, have limited lifespan of air-ends requiring regular replacements with added costs. To communicate compressor efficiency and performance, EU and US compressor manufacturers follow the standardized datasheet from the Compressed Air and Gas Institute (CAGI). This datasheet is based on simultaneous measurements of input electrical power and output flow at a stated discharge pressure and environmental conditions, which is used to calculate the package specific power and isentropic efficiency [15, 16]. A European Commission report from 2017 indicated difficulty in comparing between performance of positive displacement and dynamic compressors [17]. In this paper, the focus is on a comprehensive comparison between two lowpressure air-compressor units: the three-stage direct drive centrifugal compressor (3SDDCC) and the two-stage oil-free screw compressor (2SOFSC) both able to reach 8 barg pressure. We will examine their impact on energy consumption and greenhouse gas (GHG) emissions under various operating scenarios and over a typical five-year operating cycle, including overhaul for the 2SOFSC. The goal is to provide a concise and definitive comparison of these two air-compressor units. The main conclusions drawn for the studied compressor size are valuable for other sizes.
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Fig. 1 Overview of a high-speed centrifugal moto-compressor (left) and packaged 3-stage centrifugal compressor unit (right)
2 Life Cycle Inventory 2.1 High Speed Direct Drive Maglev Air-Compressor A high-speed centrifugal compressor increases the pressure of a gas through the kinetic energy of a rotating impeller. The main components of a high-speed centrifugal compressor are shown in Fig. 1. The prime mover can be either a high-speed permanent magnet (PM) motor or an induction motor, each with its own advantages and disadvantages. One key advantage of high-speed PM motors is their increased efficiency and higher power density [18– 20]. The guide elements in high-speed applications can be either air-bearings or active magnetic bearings (AMBs). AMBs have the advantage of having zero friction at start, high damping factor, and being able to handle both high loads and power with a high level of reliability [21–23].
2.2 Studied Compressors The study compares the performance of two types of water-cooled compressor units driven by VFDs: a 2SOFSC and a 3SDDCC with magnetic bearings. Both compressor units have a capacity of 50 m3 /min and are designed for a total input power not exceeding 350 kW. Figure 2 shows typical compressor units of such range and includes the model number TT325 for the 3SDDCC, ZR325-VSD and H400W-OF VSD. For the oil-free screw compressors, the best-in-class 2SOFSC has been chosen for comparison. The System boundaries study follow the enclosure of standalone compressor systems as illustrated in Fig. 2. It includes the stage configuration of each compressor
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Fig. 2 Illustration of studied compressors a high speed direct drive centrifugal water-cooled compressor, b, c oil-free water-cooled screw compressors Three-stage direct drive centrifugal compressor intercooler
Suction filter motor
AMB
AMB intercooler
AMB
AMB
motor
aftercooler
Fig. 3 Illustration of the two studied compressor units
unit illustrated in Fig. 3 and the power supply configuration given in Fig. 4. Dryers and tankers are disregarded in the material breakdown analysis.
2.3 Material Use Due to the design difference, the amount of material used in oil-free screw compressors is slightly higher by 20%, at the time of manufacturing, as shown in Fig. 5. The primary materials in air compressor manufacturing are cast iron, steel, copper, and aluminium, followed by other materials in smaller quantities (Fig. 6). The authors evaluated the impact of material use on global warming using published GHG emission factors (given in Table 1 [24–26]). The evaluation results, as illustrated in Fig. 7a, revealed that while the 3SDDCC had a lighter overall weight than the 2SOFSC, it produced 1.92 tCO2 e more GHG emissions at the time of manufacturing. This was due to the presence of titanium, more electronic components (Fig. 4a), and permanent magnets, in the 3SDDCC.
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(a) Power supply configuration of the 3SDDCC unit
(b) Power supply configuration of the 2SOFSC unit Fig. 4 Illustration of the two studied power supply compressor units
Fig. 5 Per unit weight of each compressor unit (excluding dryers, tankers) at the time of manufacturing
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Fig. 6 Material distribution per % in each compressor unit (excluding dryers, tankers)
Table 1 Emission factor of main materials using references [24–26] Material type
[kgCO2 e/kg] [25]
[kgCO2 e/kg] [24]
Steel (*)
1.77
2.21
Cast iron
1.51
Stainless Steel
6.15
Copper (*)
2.77
1.445
Aluminium (*)
8.14
7.803
Titanium
30
Electronics (**) Polymer
36,837 2.2
Permanent magnets (*) Lubricating oil
[kgCO2 e/kg] [26]
33,5
33
1.07
(*) Averaged value is considered for the calculation (**) The electronics is considered using the carbon footprint equivalence based on electronic controller definition [24]
It’s worth noting that this comparison is subject to change when considering maintenance and replacement of parts over the 20-year lifespan of the compressors. For example, replacement of rotor parts and seals, every five years in the oil-free screw air compressor, and the annual replacement of synthetic oil for bearings and gearbox, increases its carbon footprint by 1.86 tCO2 e, as shown in Fig. 7b. The impact of transport has been taken out of the scope of this analysis, as a generic value will provide no valuable insight to a specific decision-maker and taking the scenario approach would result in too many different distance and means of transportation combinations to be actionable.
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(a) Ex-factory product
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(b) after 20 years including air-ends + oil lub replacement
Fig. 7 Carbon footprint of each compressor units based on used raw material (excluding dryers, tankers)
Manufacturing is assumed to be negligible for the comparison, as found in similar chiller LCA [4].
2.4 Use Stage 2.4.1
Daily and Yearly Usage Scenario
Air compressors with a power range of 350 kW and a flow rate of 50 m3 /min have a projected lifespan of 20 years, with an estimated annual usage of 6800 h assuming: • Annual shutdown: two weeks (summer and winter) • Five (5) days in 3 shifts, one (1) day in 2 shifts (Saturday) and one day off (Sunday) The volume of air flow can vary depending on the specific conditions of each day or week. To fully understand this variability, this study will examine various usage scenarios, as specified in Table 2. All scenarios being studied at various pressure levels, ranging from 5 barg to 7.5 barg. These scenarios and pressures were determined through careful observations at multiple facilities, with a focus on analysing the air consumption capacities at Table 2 Scenarios considering the % of use and flow capacity Load capacity [%]
Usage in % Scenario 1
Usage in % Scenario 2
Usage in % Scenario 3
Usage in % Scenario 4
96
45
40
40
35
75
45
45
40
35
50
5
10
15
20
25
5
5
5
10
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Fig. 8 Input power versus air flow capacity at different pressure
typical levels of utilization (96, 75, 50, and 25%). The maximum capacity of the air compressor is represented by 100%, which is equivalent to 50 m3 /min.
2.4.2
Measured Performances on New Compressors
Air compressor makers typically have their equipment’s performance evaluated by an independent third-party organization, utilizing the performance program established by the CAGI and following the ISO 1217 standards [16]. Figure 8 displays the input power versus air flow capacity measured in accordance with ISO 1217. Note that for the 2SOFSC data between 5 barg and 6.5 barg have been extrapolated based on the behaviour measured between 7 and 10 barg.
2.4.3
Coating Degradation on the Oil-Free Screw Compressor
Rotor coating is essential in ensuring the optimal performance and durability of oil-free screw compressors. It provides improved sealing, corrosion resistance, and temperature resistance, reduces friction, and lowers energy consumption. However, the quality of the coating can be affected by various factors such as humidity, temperature, and contaminants, leading to degradation as shown in Fig. 9. This can result in decreased efficiency, increased power consumption, higher outlet temperature, and a higher risk of failure. While the degradation of the coating on OF screw compressors typically occurs gradually and continuously, for the purpose of analysis and to simplify interpretation, we will assume constant values. The effects of coating degradation on energy consumption will be evaluated in this study, assuming a pressure/ flow rate and considering 2, 5, and 10% increases in energy consumption caused by the degradation of the coating. Load capacity and efficiency reduction may be noticed within a year of usage, and the extent of the impact may depend on the type of coating used [27–29].
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Fig. 9 Examples of coating degradation on air-ends of oil-free screw compressors
2.4.4
Standard Industry Maintenance of 2SOFSC
The recommended maintenance interval for critical components in oil-free screw compressors is every 5 years (5YC). This industry-standard practice involves replacing parts such as rotors, air-ends, and seals, which is crucial for restoring the compressor’s performance to near-original levels. When evaluating energy consumption over a 5-year period, it’s important to note that this represents one cycle in a 20-year lifespan of the compressor. During the first year, it’s assumed that there is no degradation in performance. However, over the following four years, there are three possible scenarios to consider: a 2% increase (2SOFSC_2%), a 5% increase (2SOFSC_5%), or a 10% increase (2SOFSC_10%) in consumption due to coating degradation on the 2SOFSC. This degradation remains constant over the four years until the next air-ends overhaul. To help illustrate this cycle, refer to Fig. 10, which provides a visual representation of the 2SOFSC’s operation over a 20-year period.
2.4.5
Energy Consumption Difference Over 5-Year Cycle Operation
Figures 11 and 12 illustrate respectively the energy consumption and savings over a 5-year cycle, of the 3SDDCC and the 2SOFSC under different over-consumption conditions caused by coating degradation. The results indicate that if the coating degradation leads for the 2SOFSC to an overconsumption by more than 5%, the 3SDDCC exhibits lower energy consumption across all studied scenarios. When the 2SOFSC exhibits an overconsumption below 5% and the loading capacity is distributed between 50 and 100% of the nominal operation, a nuanced pattern emerges. Specifically, at operating pressures below 7 barg, the 3SDDCC demonstrates superior energy efficiency. However, beyond 7 barg, the 2SOFSC becomes more energy efficient.
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Fig. 10 Profile for the 2SOFSC for 20 years operation considering coating degradation and overhaul
Fig. 11 Energy consumption over 5-year cycle operation at different pressures and for different scenarios
In scenarios where the demand is distributed with non-negligible proportions at loads below 50%, the 2SOFSC offers a more significant reduction in energy consumption, at operating pressures above 6 barg and when the 2SOFSC exhibits no more than 5% of overconsumption.
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Fig. 12 Energy saving comparison over 5-year operation between 2SOFSC and 3SDDCC for different scenarios, operating pressure, and coating degradation
2.5 GHG Emission Reduction Over 5-Year Cycle Operation The amount of carbon footprint attributed to electricity consumption varies depending on the methods used for electricity production in each country. To assess greenhouse gas (GHG) emissions of different countries, the authors used equivalence coefficients from the ADEME database [24] and presented the median results using a boxplot where almost all countries are considered. Figure 13 shows the potential reduction in greenhouse gas (GHG) emissions that can be achieved using 3SDDCC or 2SOFSC, for the given scenario, operating pressure, and coating degradation. The magnitude of GHG reduction varies widely, ranging from tens of tons to several hundred tons, with some cases exceeding a few thousand tons depending on the country where the compressor is used. It is important to note that these coefficients are not static and may change over time, indicating that some countries could achieve a near-zero carbon footprint for electricity production within the next ten years.
2.6 Recycling and End of Life After 20-Year Operation Assessing the effectiveness of recycling is difficult due to a lack of accurate data and variation in emissions reduction based on method and profit distribution. The most recycled components of compressors are copper, steel, cast iron, stainless steel,
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Fig. 13 GHG emissions reduction trend (all countries) over 5-year operation, between 2SOFSC and 3SDDCC for different scenarios, operating pressure, and coating degradation
and titanium, while electronics, permanent magnets, and some polymers are less recycled. Recycling 2SOFSCs, which have more recyclable materials (weight), is expected to result in greater CO2 e reduction compared to 3SDDCC units. An evaluation of avoided CO2 e emissions based on coefficients from [24, 30] (Table 3), through recycling estimates that the emissions avoided will not exceed 40% of those from using new materials (Fig. 14). Table 3 Avoided GHG emission due to recycling [24, 30]
Material
[kgCO2 /kg] [24, 30]
Steel
1.273
Cast iron
1.34
Stainless steel
2.78
Copper
0.141
Aluminium
7.241
Titanium
5.48
Electronics
1.5307
Polymer and non metallic
0.3
Permanent magnets
NA
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Fig. 14 Amount of tCO2 e emissions prevented through recycling
3 Conclusion and Discussion Upon analysing greenhouse gas (GHG) emissions stemming from material used to manufacture the product, product usage, and material recycling, it’s no surprise that the most significant emissions occur during the 20-year lifespan of the product’s usage. The GHG emissions resulting from the use of materials and the avoidance through recycling do not make it possible to differentiate formally between the two compressors under consideration. A more comprehensive analysis is required, but at present, the energy consumption and corresponding emissions suggest that one should focus on reducing these emissions during operation. The direct drive centrifugal compressor with magnetic bearings, can offer substantial reductions in energy consumption, up to 10% in some studied scenarios and lower GHG emissions of several hundreds of tons over the compressor’s lifetime. When compared to oil-free screw compressors, which suffer from coating degradation, direct drive centrifugal compressors with active magnetic bearings are the most favourable choice due to their reliability, efficiency and lack of degradation issues making them virtually maintenance free as they operate without wear (levitated rotor) and lubrication. However, in scenarios where the compressor unit is oversized for daily and annual needs with episodic peak demand, the oil-free screw compressor may be a better choice especially at max operating pressure. The results underscore the importance of considering the operating conditions and demand distribution when selecting a compressor for a specific application. It is crucial to conduct an air assessment to determine the system’s flow profile and spectrum and to interpret the results correctly. The efficiency of the compressor unit should be evaluated over its operating range, including at full load and partial loads, rather than solely evaluating its ability to reduce compressed air blow off. In some scenarios, it’s better to combine several small variable speed centrifugal compressors in factories with unpredictable air demand, to avoid energy lost during blow-off process.
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Another solution is a combination of a variable speed direct drive centrifugal compressor with an oil-free variable speed screw compressor, which may improve the efficiency by eliminating the blow off, nevertheless, it is crucial to uphold proper joined regulation and control for both units. The initial capital investment was intentionally excluded from this study because the scope was to evaluate the systems from the energy consumption and carbon footprint point of view only. The total cost of ownership (TCO) would be an additional parameter in the final decision of end-users.
References 1. E.G. Foster, V. Kulle, R.A. Peterson, The application of active magnetic bearings to a natural gas pipeline compressor, in Proceedings paper, ASME 1986 International Gas Turbine Conference and Exhibit, June 1986. https://asmedigitalcollection.asme.org/GT/proceedings/GT1986/ 79306/V003T07A004/237248 2. D.J. Clark, M.J. Jansen, G.T. Montague, An overview of magnetic bearing technology for gas turbine engines, in NASA Technical Report Server, Aug 2004. https://ntrs.nasa.gov/citations/ 20040110826 3. S.A. Parker, J. Blanchard, Variable-speed oil-free centrifugal chiller with magnetic bearings assessment, in Report for the General Service Administration, Nov 2012. https://www.gsa.gov/ cdnstatic/GPG_Mag_Lev_FullReport_508_6-17-13.pdf 4. E. Byrd, B. Netzel, D.B. Adams, H. Zhang, Life cycle GHG assessment of magnetic bearing and oil lubricated bearing water cooled chillers. J. Industr. Ecol. (2021). https://onlinelibrary. wiley.com/doi/abs/10.1111/jiec.13113 5. Kaeser sponsored content, Turbo blowers with magnetic bearing technology, in WWD Magazine, Aug 2021. https://www.wwdmag.com/biosolids-management/blowers-air/article/ 10938187/turbo-blowers-with-magnetic-bearing-technology 6. Y. Kinoshita, T. Aota, Kawasaki mag turbo single-stage sewage aeration blower with highspeed motor & magnetic bearing, in Online Paper Rubrique Energy and Environment, Apr 2017. https://answers.khi.co.jp/en/energy-environment/20170430e-01/ 7. J.L. Gilarranz R, M. Dave, T. Jamison, Non-hermetic, oil-free compression solutions—a reliable approach to reduce life cycle costs for compressor applications, in Abu Dhabi International Petroleum Exhibition & Conference, Nov 2016 https://onepetro.org/SPEADIP/proceedings-abs tract/16ADIP/4-16ADIP/D041S091R004/185881 8. Baker Hughes online presentation, Oil-free Turbomachinery with active magnetic bearing technology, Avril 2023. https://www.bakerhughes.com/sites/bakerhughes/files/2023-04/bak erhughes_oilfreeturbomachinery_amb-041323.pdf 9. EU report, 2022 report on achievement of the 2020 energy efficiency targets, in Comm. 641 Final, Nov 2022. https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX%3A5202 2DC0641&qid=1669913283450 10. Xenergy Inc., Assessment of the market for compressed air efficiency services, in Report for Oak Ridge National Laboratory & Lawrence Berkeley National Laboratory, June 2001. https:// www.energy.gov/sites/prod/files/2014/05/f16/newmarket5.pdf 11. M. Unger, P. Radgen, Energy efficiency in compressed air systems—a review of energy efficiency potentials, technological development, energy policy actions and future importance, in Proceedings of the 10th International Conference on Energy Efficiency in Motor Driven Systems, EEMODS’2017, Sept 2017. C:\Users\LATEB\Downloads\2018-EEMODSProceedings-Unger-Radgen(1).pdf
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12. F.N. Nourin, J. Espindola, O.M. Selim, R.S. Amano, Energy, exergy, and emission analysis on industrial air compressors. J. Energy Resour. Technol. 144(4) (2022). https://asmedigitalc ollection.asme.org/energyresources/article/144/4/042104/1114340/Energy-Exergy-and-Emi ssion-Analysis-on-Industrial 13. F. Huang, Oil-free screw compressor or oil injected screw compressor, in 15th International Compressor Engineering Conference, USA, 25–28 July 2000. https://core.ac.uk/download/pdf/ 4957177.pdf 14. Y. Zhang, X. Qiao, The current Status and future development trends of oil-free compressor. In Journal of Physics: Conference series, 2nd International Conference on Mechanical, Electrical and Industrial Engineering, 25–27 May China, 2019 https://iopscience.iop.org/article/10.1088/ 1742-6596/1303/1/012045 15. Compressed air and gas institute website https://www.cagi.org/ 16. ISO 1217 displacement compressors-acceptance tests. https://www.iso.org/fr/standard/44769. html 17. M.V. Elburg, R.V.D. Boom, Low pressure & oil-free compressor packages, in Final Report for European Commission, Lot 31, June 2017. https://ekosuunnittelu.info/wp-content/uploads/ 2015/09/Lot30_low-pressure-and-oil-free-taustaselvitys.pdf 18. G. Pellegrino, A. Vagati, B. Boazzo, P. Guglielmi, Comparison of induction and PM synchronous motor drives for EV application including design examples. IEEE Trans. Industr. Appl. 48(6), 2322–2332 (2012). https://ieeexplore.ieee.org/document/6352905 19. Z. Yang, F. Shang, I.P. Brown, M. Krishnamurthy, Comparative study of interior permanent magnet, induction and switched reluctance motor drives for EV and HEV applications. IEEE Trans. Transp. Electr. 1(3), 245–254 (2015) https://ieeexplore.ieee.org/document/7210190 20. N. Uzhegov, J. Barta, J. Kurfürst, C. Ondrusek, J. Pyrhönen, Comparison of high-speed electrical motors for a turbo circulator application. IEEE Trans. Industr. Appl. 53(5), 4308–4317 (2017). https://ieeexplore.ieee.org/document/7919218 21. A. Irving, J. Ibets, High speed bearing technologies for wastewater treatment applications. Presentation at WEFTEC 2013. https://www.airbestpractices.com/industries/wastewater/highspeed-bearing-technologies-wastewater-treatment-applications 22. C F. McDonald, Active magnetic bearings for gas turbomachinery in closed-cycle power plant systems, in International Gas Turbine and Aeroengine Congress and Exposition, ASME 1998, 6–9 June 1998. https://asmedigitalcollection.asme.org/GT/proceedings/GT1988/79207/ V003T08A005/237243 23. Q. Liu, S. Zhang, Y. Li, G. Lei, L. Wang, Hybrid gas-magnetic bearings: an overview. Int. J. Appl. Electromagn. Mech. 66, 313–338 (2021). https://www.researchgate.net/publication/348 344380_Hybrid_gas-magnetic_bearings_An_overview 24. ADEME, Resource center on greenhouse gas balance. https://bilans-ges.ademe.fr/fr/baseca rbone/donnees-consulter/choix-categorie 25. STANTEC, South End Water Pollution Centre Project Definition/Validation Report (2012). https://legacy.winnipeg.ca/finance/findata/matmgt/documents/2012/682-2012/682-2012_A ppendix_H-WSTP_South_End_Plant_Process_Selection_Report/Appendix%207.pdf 26. J. Bueb, E. To, How to evaluate the carbon externality of metals, analysis note, Oct 2020. https://www.strategie.gouv.fr/sites/strategie.gouv.fr/files/atoms/files/fs-2020-na96externalite-carbone-metaux-octobre.pdf 27. Nirvana oil-free, Ingersoll Rand, white paper. https://www.aircompressoreng.com/files/con tent/products/oil_free_rotaryScrew/nirvanaoil_free.pdf 28. G.B. Nordquist, P.A. Bielskus, R. Clayton, Dry screw compressors in process gas applications including maintenance considerations, in Proceedings of the 21st Turbomachinery Symposium, 1992. https://oaktrust.library.tamu.edu/bitstream/handle/1969.1/163538/T213-20. pdf?sequence=1&isAllowed=y 29. C. Villalobos, Not all rotor coatings are created equal: what it means for your oil free rotary screw air compressor. White Paper Sullair Company. https://america.sullair.com/sites/def ault/files/2020-12/Sullair%20Blog_Not%20all%20rotor%20coatings%20are%20created% 20equal.pdf
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Noise and Vibration
In-Line Sphere Arrays as Pressure Pulsation and Pipeline Vibration Dampers in Reciprocating Compressor Manifold ´ Przemysław Młynarczyk , Joanna Krajewska-Spiewak , , Kamil Chmielarczyk, Jarosław Bł˛adek, Damian Brewczynski ´ and Paweł Lempa
Abstract Pressure pulsations and pipeline vibrations are unfavorable phenomena generated by the periodic operation of the volumetric compressors. The variable speed of the compressor shaft generates pulsations and vibrations of different frequencies, which means that Helmholtz resonators and tuned mass dampers are not the most effective devices to reduce these phenomena. One of the possibilities to dampen pulsations in a wide range of frequencies, is to place shaped nozzles in the compressor discharge manifold. However, the nozzles significantly affect the compression power by restricting the flow from the wall to the centre of the pipe. Therefore, the influence of elements placed on the axis of the pipeline with spherical shapes was investigated. In this research, 3D-printed nozzles with a different numbers of spheres were tested. Research shows how a number of spheres in the array influence the damping of pressure pulsation and pipeline vibration. Keywords Damping · Nozzle flow · Pipeline vibration · Pressure pulsation · 3D printing
1 Introduction The occurred unfavorable phenomenon of pressure pulsations in positive displacement compressor installations causes vibrations, energy loss, and valves wear are harmful to the installation and its components. The main methods currently used to dampen pressure pulsations are the installation of damping volumes on the suction lines or discharge lines of the compressor. Damping bottles are a very effective
´ P. Młynarczyk (B) · J. Krajewska-Spiewak · D. Brewczy´nski · K. Chmielarczyk · J. Bł˛adek · P. Lempa Faculty of Mechanical Engineering, Cracow University of Technology, Kraków, Poland e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_50
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solution for damping the main frequency of pressure pulsations. However, nowadays for better energy and flow control, of compressed refrigerant in the installation, compressors with adjustable drive shaft speeds are becoming more popular. This situation makes it necessary to dampen pulsations over a wide frequency range. The simplest method used in this case is the mounting of orifice plates in the compressor discharge pipeline but this solution have a significant impact on the compression energy efficiency value. One of the proposed solution, which has been developed for several years [1], is the installation of shaped inserts in the compressor discharge manifold for pressure pulsation damping. It has already been shown that such inserts suppress pressure pulsations in a wide range of frequencies [2]. Article [3] proves that vortices generated on obstacles have a significant impact on damping of pressure pulsations. The choice of a spherical shape seems to be a proper way as a starting point for searching for solutions which will have a low impact on the compression power. In the literature, many articles can be found describing the phenomena related to the flow around a sphere [4] several spheres in a row [5] or other arrangements [6]. Therefore, the influence of the nozzles with different number of spheres on the damping of pressure pulsations in the piston compressor installation was investigated. The obtained results may also be useful in the design of other components fitted in the compressor discharge line, such as fluidic/vortex diodes, control valves, lube filters and other.
2 Design of the Nozzles To compare the influence of different number of spheres introduced into the pipeline, on the pressure pulsations damping the appropriate nozzles were designed. Two conceptions in four variants (with one, two, three and four spheres) were designed. In Fig. 1 nozzles conceptions in two options are presented.
Fig. 1 Nozzles with sphere conceptions: left: B-type with radial connectors, right: A-type with axially connectors
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The diameters of the spheres were selected so that the spheres cover 70% of the cross-sectional area of the pipeline in the plane passing through the centre of the sphere. The distance between successive spheres was equal to the diameter of the spheres. All nozzles were printed from high-temperature resin in LFS 3D printing technology (a variant of SLA technology). The advantages and limitations of 3D printing technology had to be taken into account during the design process by selecting the appropriate tolerances of elements and the method of joining. In the A approach a cylinder placed in the axis of the element was used. Due to the significant peeling forces during printing, this cylinder had to be of high strength. In consequence, the gas flow in the muffler behind each ball is disturbed and cannot be treated as a free flow around the sphere. In the B variant of mounting the spheres, the idea was to eliminate the unwanted disturbed flow behind the spheres, therefore the spheres were mounted on cross elements attached to the walls of the nozzle. In this case, there is a necessity to use supports during printing and the necessity to remove them after printing. This implies that this type of nozzle had to be printed in parts. After the print and removal of the supports, the elements were precisely positioned and glued. Unfortunately also in this variant it is not possible to avoid the influence of the additional fastening elements on the flow around the sphere. However, testing these two cases allows one to compare the effect of different mounting methods on the damping of pressure pulsation.
3 Test Stand Experimental investigations were carried out on a test stand consisting of the reciprocating oil-free compressor and specially designed test manifold. The nozzles were inserted into a specially prepared steel adapter and then the adapter with a nozzle was screwed onto the connectors in the installation. Pressure pulsation measurement is carried out by two ICP Dynamic Pressure Sensors, with an accuracy of 7.232 (sensor 1) and 15.56 (sensor 2) mV/kPa. The vibration measurement was carried out with an ADXL 335 three-axis accelerometer with an output sensitivity of 300 mV/g. The cDAQ-9174 chassis was used to read and save the measured signals equipped with the NI 9215 measurement card with BNC connections—for the dynamic pressure signal and the NI 9205 with a spring terminal to connect the vibration measuring channels. A diagram of the measurement flow is shown in Fig. 2. Measurements were made for all prepared nozzles. Measurements with the straight pipe shape (referred to as an empty case) introduced in the nozzle mounting point were performed as a reference point. All measurements were carried out for constant pressure in the system of 5 bar. Measurements were made for three rotational speeds of the compressor drive shaft: 1100, 1600, and 2100 rev/min. Due to the work of the pistons (gas is pushed out every 90° of the drive shaft rotation and then 270° no gas is introduced into the installation),
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Fig. 2 Measurement circuit
the main pulsation frequency results directly from the value of the rotational speed of the drive shaft. Figure 3 shows a diagram of the test stand. The research installation was designed to represent the real industrial system as much as possible. Therefore, various forces of the flow of compressed gas acted on different elements of the installation. Due to the connection of the installation and the compressor with rubber hoses, the impact of compressor vibrations on the vibrations of the test installation was minimised.
4 Results The analyzes carried out on the test stand (described in Sect. 3) allowed to determine the effect of a different number of spheres in the nozzle on the damping of pressure pulsations and pipeline vibrations. The conducted research allows a better understanding of the effect of the series assembly of spheres on the damping of pressure pulsations in the pipeline. The vibration damping of the pipeline is mainly considered in this situation as a result of the decrease in the amplitude of the pressure pulsations, but in some cases, the interaction with the nozzle rigidly fixed in the pipeline may increase the vibration. This can be especially noticeable when the vortices generated by preceding sphere cause nonuniform distribution of flow forces on the next sphere. Table 1 shows the measurement results for 8 nozzles and installations with a fixed pipe element. As can be seen in Table 1, both the values of pressure pulsations and vibrations are significantly different for the nozzles used in the installation. In particular, a different nozzle effect for different pulsation frequencies can also be observed. In Table 1, in particular, the negative impact of the assembly of elements on the value of pressure pulsation in front of the nozzle can be observed. This phenomenon is particularly visible for the highest frequency of pressure pulsations. This is related to the throttling of the flow behind the sensor and in front of the nozzle.
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Fig. 3 a A scheme of the test stand, b cross-section through the mounting element with mounted reducers where blue—pipeline, green—mounting element, red—tested nozzles
Figure 4 shows the waveforms of the measured signals for nozzles with four spheres and installations with a nozzle imitating an empty pipe. Figure 4 shows a change in the character of the measured signal between the first and second measurement points in the installation. In particular, there is a significant decrease in the signal amplitude value for nozzle B4. Figure 5 shows the effect of the mounting of the nozzle on the damping of pressure pulsations and longitudinal vibrations of the pipeline. The main comparative factor for the tested nozzles with spheres is the dynamic pressure peak-to-peak value damping calculated for the sensor
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Table 1 Results of experimental investigations rev/ min
Nozzle Empty B1
B2
B3
B4
A1
A2
A3
A4
Pressure Sensor 1 pulsations [kPa]
2100 41.07
44.45 45.88 47.67 47.45 40.99 44.38 44.08 44.78
1600 44.54
43.97 45.44 45.71 46.39 43.92 45.44 44.41 42.47
1100 45.96
42.40 42.18 43.44 42.18 44.27 42.00 46.85 47.38
Sensor 2
2100 42.18
40.60 38.00 37.96 38.25 41.35 42.18 41.44 40.41
1600 52.26
46.88 42.11 41.12 39.02 48.63 50.94 51.62 50.35
1100 46.52
41.10 41.34 40.59 38.22 45.09 43.60 45.35 45.34
Vibrations x-direction 2100 7.53 [m/s2 ] 1600 8.87
7.84
7.36
7.46
6.51
7.12
7.42
7.31
7.36
7.65
7.79
7.09
5.98
6.91
8.41
8.59
7.53
1100 8.50
5.51
6.31
7.21
6.78
7.27
5.73
9.05
9.02
Fig. 4 Pressure pulsation diagrams for three elements fixed in the installation: a sensor in front of the orifice, b sensor behind the orifice
behind the tested element. Damping values are calculated from the Eqs. (1) and (2): ψnozzle = 100% −
p nozzle · 100% p empt y
(1)
where: p nozzle is a pressure peak-to-peak value [kPa] with nozzle in the installation, p empt y is a pressure peak-to-peak value [kPa] with straight pipe print in the installation, ψnozzle —nozzle pressure pulsation damping.
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Fig. 5 The figure shows the percentage values of the pressure pulsation damping (left axis— bars) and longitudinal vibration damping (right axis—markers) for various rotational speeds: blue (circle)—2100 rev/min, green (diamond)—1600 rev/min, grey (square)—1100 rev/min
ζnozzle = 100% −
anozzle · 100% aempt y
(2)
where: a nozzle is a vibration acceleration peak-to-peak value [m/s2 ] with nozzle in the installation, a empt y is a vibration acceleration peak-to-peak value [m/s2 ] with straight pipe print in the installation, ζnozzle —longitudinal vibration damping with nozzle inserted in the pipeline. As can be seen for the assembly of the spheres on the arms in the shape of a cross, the smallest pulsation damping occurs for a single sphere. The conducted research shows that in the case of pulsations with the highest frequency, a larger number of spheres does not significantly affect the damping effect. For the lowest value of the pulsation frequency, one, two and three spheres show very similar damping, and the increase occurs only for four spheres. However, a clear trend is noticed for the middle of the tested frequencies. As the number of spheres increases, the damping value also increases. In this case, the damping of vibrations is similar, although there is a decrease in damping between one and two spheres. For the lowest pulsation frequency and thus for the lowest gas flow in the installation, the vibration damping value is independent of the pulsation damping value and decreases linearly with the increase in the number of spheres to three. This distinguishes the attenuation value compared to higher frequencies where the number of spheres tends to increase the attenuation. In the case of spheres mounted on an axial rod, it is difficult to define clear trends. It can be noticed that the lack of generated vortices which are characteristic of aerodynamic spheres, causes lower values of damping pulsations. However, in this case, a higher correlation between pulsation and vibration damping is visible. This may be related to the limited possibility of generating vortices that are characteristic
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of sphere streamlining and which may cause an uneven distribution of forces on subsequent spheres. An important conclusion of the study is also the evaluation of the average pulsation and vibration damping of the different nozzles. Table 2 shows the average value of pulsation and vibration damping for all three speeds of the compressor drive shaft. The average values of pressure pulsation damping for the sensor behind the mounting element show that in a wide frequency range, significant damping of pressure pulsations and longitudinal vibrations of pipelines for nozzles from group B is obtained. At the same time, it can be seen that the best damping occurs for 4 spheres in the array. It is hard to find any correlation in the case of group A nozzles. The only thing that a can be said is that better vibration damping is achieved for the smallest number of spheres in this mounting option. Figure 6 shows a comparison of the waveforms of the measured signals of type B spheres. The nature of the waveforms changes slightly with respect to the number of attached spheres. The decrease in the peak-to-peak value of an pressure with the increase in the number of spheres, especially in the low dynamic pressure phase, is noticeable. Figure 7 shows the spectrum of signals obtained for the nozzles with the largest number of spheres and for an empty nozzle. It can be seen that multiple frequencies are important. However, the main frequency which results from the nature of the compressor work is dominant. This frequency is most dampened in the B4 option. Many harmonics are of great importance because of the unusual compressor work. Harmonic analysis was used to compare the damping of the longitudinal vibrations of the pipeline. Figure 8 presents a comparison of the values of individual harmonics Table 2 Averaged values of vibration and pulsation damping for three pulsation frequencies Nozzle B1
B2
B3
B4
A1
A2
A3
A4
Sensor 1
0.26 − 1.84 − 4.40 − 3.82
1.75 − 0.50 − 2.99 − 2.50
Sensor 2
8.57
13.49
14.69
17.50
4.00
Vibrations X direction 14.96 [m/s2 ]
13.41
12.04
22.10 14.02
Pressure pulsations [kPa]
2.94
1.83
3.47
13.11 − 0.14
3.75
Fig. 6 The signal of a sensor mounted behind the mounting element for four nozzles in group B
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Fig. 7 Harmonic analysis of pressure pulsation behind the mounting element for nozzles with four spheres in two connecting options
Fig. 8 Harmonic analysis of longitudinal vibrations for nozzles with four spheres in two options
for pipeline vibration for the main pulsation frequency of approximately 27 Hz and nozzles with the largest number of spheres with an empty pipe. As can be seen in Fig. 8, the frequency that is four times the excitation frequency of the pulsation has the greatest influence on the vibration of the pipeline.
5 Conclusions The test results presented in this publication confirm the significant influence of flow vorticity on the damping of pressure pulsations. The vortex flow occurs in the case of cross-mounted spheres. Therefore, a stronger damping of pressure pulsations can be observed in the case of spheres mounted on crosses than spheres mounted on the shaft in the flow axis. It was also confirmed that nozzles of the appropriate shape dampen pressure pulsations and pipeline vibrations for different pulsation frequencies. Pipeline vibrations can be dampened as a result of pressure pulsation damping. However, in some cases, the uneven distribution of turbulence behind the mounted element can cause an increase in pipeline vibration damping despite damping pressure pulsations. The research presented in the article is the basis for further analysis to estimate the appropriate distribution of spheres and their shapes on the damping of pressure pulsations and pipeline vibrations. Research will also aim to estimate their impact on the increase in unit compression power in the installation.
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Acknowledgements This research was funded by Polish National Centre for Research and Development, grant number LIDER/40/0140/L-11/19/NCBR/2020.
References 1. Cyklis, P., Młynarczyk, P., An innovative simulation method for the estimation of the nozzle pressure pulsation attenuation. J. Vibr. Control 23(16) (2017) 2. Młynarczyk, P., Cyklis, P.: The application of nozzles for the attenuation of volumetric compressor pressure pulsation. Int. J. Refrigeration 90 (2018) 3. Młynarczyk, P., Cyklis, P., The estimation of the pressure pulsation damping coefficient of a nozzle. J. Sound Vibr. 464 (2020) 4. Dehbi, A., Martin, S., CFD simulation of particle deposition on an array of spheres using an Euler/Lagrange approach. Nucl. Eng. Des. 241 (2011) 5. Choi, D., Park, H., Flow around in-line sphere array at moderate Reynolds number. Phys. Fluids 30 (2018) 6. Ozgoren, M., Flow structures around an equilateral triangle arrangement of three spheres. Int. J. Multiphase Flow. 53 (2013)
Acoustic and Energy Efficiency Analysis of Alternative Geometries of Plastic Suction Muffler Merve Baykal and Nuri Onur Çatak
Abstract The suction muffler in a reciprocating compressor is used to attenuate sound pressure generated by vibrational noise, piston/valve movements and flowing noise. While the suction muffler directs the gas flow to the valve for compression, it also takes a critical role in damping the sound waves caused by the movement of the valve. The suction muffler in a reciprocating compressor is a reactive type silencer, therefore it absorbs the sound wave by reflecting it with geometries such as expansion chambers. However, the suction muffler adversely affects the compressor performance since it creates additional pressure drop to the system. Due to strong interdependency of components and parameters, Coefficient of Performance (COP) and noise trade-off are difficult to perform especially considering the geometric design constraints. For this reason, the most critical design objectives for hermetic reciprocating compressors are high energy efficiency and quiet operating conditions. In this study, the tesla valve, which prevents the reflow of the refrigerant gas into the suction muffler from the suction valve, is modified for the reciprocating compressor muffler to improve COP. The new designs will be optimized by considering computational fluid dynamics analysis and acoustic transmission loss analysis. The numerical results will be experimentally validated in semi-anechoic room and calorimetry test is performed with the most optimal cases. Additionally, it is expected that the tesla valve design provides energy efficiency with acoustic gain especially in 630–800 Hz band. Keywords Muffler · Transmission loss · Hermetic reciprocating compressors · Tesla valve · Suction muffler · Compressor performance
M. Baykal (B) · N. O. Çatak Arçelik A.S., ¸ Istanbul 34950, Turkey e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_51
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1 Introduction A hermetic reciprocating compressor is a type of compression system that is commonly used in refrigeration and air conditioning applications. The compressor operates by using a piston to compress refrigerant gas and pump it through the system. The compressed gas then flows to the condenser where it releases heat and condenses into a high-pressure, high-temperature liquid that is then returned to the compressor to start the cycle over again. This process of compression and expansion is what moves heat and provides cooling in the system. Hermetic reciprocating compressors can generate noise from several sources during operation. Some of the common sources of noise in hermetic reciprocating compressors are; piston and cylinder movement, the movement of the piston inside the cylinder generates mechanical noise as it compresses and expands the refrigerant. Valve operation, the opening and closing of the suction and discharge valves can also create noise as the refrigerant gas is admitted into and expelled from the cylinder. Refrigerant flow, the flow of refrigerant through the compressor and the discharge line can create noise as it passes through any restriction or changes in direction. Motor operation, the electric motor driving the compressor can also produce noise as it rotates the crankshaft and connecting rods. Vibration, all of the components in the compressor are subject to vibration. Reducing the noise generated by a hermetic reciprocating compressor can be achieved through proper maintenance, installation, and design techniques and isolating the compressor from the surrounding environment [1]. A compressor muffler is a type of muffler that uses a compressor to reduce the noise produced by a compressor exhaust system. The term “aeroacoustics” refers to the study of the generation, propagation, and perception of sound in air and other gaseous media. In the one of the aspects of a compressor muffler, aeroacoustics refers to the study of the noise produced by the compressor exhaust system and how it can be reduced by the compressor muffler. Mufflers are utilized in various systems to control noise, such as in internal combustion engines, ventilation ducts, and turbo machinery. They can be active or passive, with absorptive silencers being a type of passive silencer that converts acoustic energy into heat energy through sound-absorbing materials. These silencers offer adjustable damping frequencies but may have limitations in low-frequency regions. In the context of hermetic reciprocating compressors, intake silencers fall into the category of reflective/reactive silencers, which rely on sound wave reflection and damping within specific structures [2]. The suction muffler in reciprocating compressors plays a crucial role in two key areas: ensuring efficient transfer of cold gas from the evaporator tube to the intake valve and minimizing noise generated by valve movement. It achieves these objectives through the integration of Helmholtz resonators, which effectively dampen sound waves and promote a quieter operating environment [3]. Additionally, the design of the silencer entrance and the optimization of the intake pipe geometry enhance refrigerant flow, improving flow rates and the compressor’s coefficient of performance (COP). The inclusion of strategically placed
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Fig. 1 Example of an plastic suction muffler; volume (a), tube (b) and connection part with valve (c)
oil drain holes prevents lubricating oil from contaminating the silencer, ensuring the compressor’s integrity (Fig. 1). Aeroacoustics plays a critical role in the design and optimization of compressor mufflers. By understanding the underlying physics of the noise generation and propagation in the compressor exhaust system, engineers can design mufflers that are effective at reducing noise while still allowing for maximum flow and system performance. This includes optimizing the design of the compressor to achieve the desired sound transmission loss and compressor performance. Overall, the field of aeroacoustics plays a crucial role in the design and optimization of compressor mufflers and other noise control systems. Moreover, sound transmission loss is a measure of the reduction in sound energy that occurs when sound travels through the system. It is defined as the ratio of the sound pressure level on one side of the material or system to the sound pressure level on the other side, expressed in decibels (dB). Sound transmission loss is an important characteristic in a variety of applications, including building acoustics, automotive mufflers, and industrial noise control. In mufflers, the sound transmission loss is a measure of the effectiveness of the muffler in reducing the noise produced by the compressor exhaust system. The higher the sound transmission loss, the more effective the muffler is at reducing noise. Sound transmission loss is determined by a combination of factors, including the thickness, density, and mechanical properties of the material, the frequency of the sound, and the geometry and design of the system [4]. In general, reactive mufflers which is used in reciprocating compressor, are known to have good transmission loss compared to other types of mufflers. This is because they use reactive elements, such as Helmholtz resonators, piping, chambers
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to absorb and cancel out specific frequencies of noise in the exhaust system. The combination of these reactive elements and the muffler’s geometry and materials can result in high transmission loss and effectively reduce the noise produced by the compressor exhaust. Overall, the transmission loss of a reactive muffler depends on the specific design as well as the operating conditions of the compressor. High-quality reactive mufflers are capable of achieving high transmission loss, reducing exhaust noise and improving the overall performance of the compressor exhaust system. The Tesla valve, invented by Nicola Tesla in 1920, is a valve with no moving parts. Because of its geometry, the valve only allows one direction of flow. The Tesla valve is based on the Coanda effect, which describes the movement of air by following the slopes of a surface and returning to it if another surface is nearby. When reverse flow is applied to the Tesla valve, high pressure drops occur [5]. There have been studies published in the literature on optimizing the performance of the Tesla valve with structural parameters such as hydraulic diameter and valve angle when subjected to reverse flow. High inlet velocities, low hydraulic diameter and internal radius values, and large valve angles all contribute to high pressure drops. However, at low inlet velocities, changes in the discussed parameters have little effect on the pressure difference. When the valve angle is less than 60°, the pressure difference increases linearly, but when the valve angle is greater than 60°, the pressure difference decreases [6].
2 Methodology 2.1 Design Parameters As previously stated, tesla valve design parameters such as diameters and degrees of tubes are limited due to muffler geometry. All tubes (main and side) in the first two design models have a diameter of 7 mm, with different degrees for side channels. The slope of the side tubes is the first design parameter. After that, symmetric and asymmetric side tubes are investigated (Table 1). Table 1 Design parameters
Parameters
Model 1
Model 2
Model 3
Side tube diameter (mm)
7
5
5
Main tube diameter (mm)
7
7
7
Side tube symmetry
Asym
Asym
Sym
Side tube angle (°)
60
45
45
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Table 2 Properties and boundary conditions for CFD analysis Model
SST-kw
Properties
Cooler gas
R600
Density
Ideal gas
Heat conduction coefficient W/m K
0.02249
Cp (J/kgK)
1911
Viscosity
8.72 e − 6
Mesh size (m)
0.0001
Element number (million)
9
Boundary conditions
Skewness
< 0.5
Molecular weight (kg/kg mol)
58.12
Mass flow rate (kg/s)
0.0006
2.2 Numerical Analysis of the Muffler 2.2.1
CFD Analysis of Muffler
The Ansys Fluent module was used for computational fluid dynamics analysis. To begin, a 0.0001-m quadratic mesh was created using 9 million elements. Fluent analysis was performed after a suitable mesh was created using the K-w turbulence model [7]. The results are shown below. Analysis temperatures set as 50 and 70 °C for inlet and outlet of the valve. Other assumptions can be seen in the Table 2.
2.2.2
Transmission Loss Analysis of the Muffler
The acoustical simulation model is developed model by PLM Simcenter 3D based finite element method (FEM). The geometry of the models was constructed in three dimensions in the CAD application environment using NX Nastran and then muffler cavity and meshing into small element as illustrated in Fig. 2a, b. In this simulation, the gas is assumed at 55 °C so the sound speed is 222 m/s and the mass density is 1.31 kg/m−3 . The acoustic mesh creation is done as minimum six elements per wavelength. Since the analysis is solved up to 10 kHz, the mesh size is set as 5.67 mm. Two boundary conditions are applied at the inlet and outlet of the muffler. The noise source was modelled as the acoustic pressure with 1 Pa at the inlet of the muffler as shown in Fig. 2c. The anechoic termination condition at the outlet tube of model can be achieved by acoustic match layer which prevents reflection. The microphone is placed at the inlet and outlet of the muffler. The sound pressure levels at the inlet and outlet of the model were measured at specific microphone points in order to calculate the transmission loss (TL) (Fig. 3).
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Fig. 2 Suction muffler design
Fig. 3 Muffler cavity (a), acoustic mesh (b), boundary conditions (c)
Sound Pr essur e Level, L p = 10 ∗ log
2.2.3
p2 dB p02
Test Methodology
The initial model proposed in this study was manufactured using the Selective Laser Sintering (SLS) method through 3D printing technology. Subsequently, an assembled compressor incorporating this prototype was subjected to rigorous testing. Prior to testing within the semi-reflective sound chamber, the compressor underwent operational conditions conforming to the guidelines set by the American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE). These conditions included maintaining a condensation temperature of 54.4 °C and an evaporation temperature of − 23.3 °C, while the compressor operated at an inlet pressure of 0.624 bar and an outlet pressure of 7.61 bar until it reached thermal equilibrium. The sound produced by the compressor was then recorded within the test environment using ten strategically positioned microphones in accordance with the ISO 3745 standard. The collected sound data was analyzed using the B&K Pulse Analyzer, generating frequency-A-weighted sound power level (dBA) graphs and total sound power level outputs in the 1/3 octave band, which varied depending on the compressor’s operating cycles. Furthermore, Calorimeter tests were conducted
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(a) Semi-Anechoic Room
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(b) Calorimeter Test Setup
Fig. 4 a Semi-anechoic room, b calorimeter test setup
to assess the hermetic reciprocating compressor’s cooling capacity, power consumption, and engine performance under varied operating conditions. These tests provided valuable insights into the compressor’s characteristics and performance.
3 Results 3.1 CFD Results The results obtained from the Fluent analysis indicate that the flow through the side tubes is not as prominent as through the main tube in the primary flow direction for all the models. However, a clear relationship is observed between the turbulence intensity and the slope of the side tubes. The findings demonstrate that reducing the slope of the side tubes can effectively decrease turbulence inside the tube openings (Fig. 4). Additionally, the upper opening of the side tube has an impact on the COP gain and should be wider and inclined (Fig. 5).
3.2 Transmission Loss Analysis Results Figure 4 illustrates the transmission loss analysis, which reveals that all Tesla valve models exhibit superior transmission loss compared to the original model. Furthermore, different geometries of the Tesla valve provide better transmission loss performance in various frequency ranges. For instance, Model 3, an asymmetric design, demonstrates the best transmission loss performance between 4000 and 5000 Hz, whereas Model 1 exhibits optimal attenuation performance at low-frequency bands.
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a
b
c
Fig. 5 CFD results a model 1, b model 2, c model 3
In summary, in terms of acoustic performance, all proposed models surpass the original model, and each model can be tailored to excel in specific frequency bands. When comparing the transmission losses calculated using Simcenter 3D for the original model and Model V3, it is evident that the damping value has nearly doubled, particularly between 1000 and 3000 Hz, and the damping frequency range has expanded. The study found that in this frequency range, the compressor’s damping has increased both within the range of human hearing and its intense operational range (Figs. 6, 7 and 8).
3.3 Calorimeter and Semi-anechoic Test Results Initially, the original compressor model was assembled and tested, followed by the replacement of the suction muffler with Model 1. The suction muffler noise was reduced by approximately 50% at 3000 RPM and within the 60–800 Hz range. Due to limitations in the manufacturing method, the prototype did not achieve maximum
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Fig. 6 Transmission loss results of the muffler designs
Fig. 7 Transmission loss results of the original muffler
Fig. 8 Transmission loss results of the V3 muffler
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Fig. 9 Semi-anechoic room test results
Table 3 Test results of calorimeter setup 1300 RPM 3000 RPM 4000 RPM
Model
COP
Power [W]
Capacity
Original
1.87
57.1
91.9
The tesla valve
1.87
52
91,6
Original
1.80
133
205.9
The tesla valve
1.80
127.8
198.2
Original
1.60
182.1
250.5
The tesla valve
1.62
175
243.1
efficiency. The side tubes were not fully open and therefore could not function optimally. Despite this manufacturing issue, which stemmed from the capabilities of 3D printing and the size of the prototype, both the calorimeter setup and semianechoic test results showed improvement. The calorimeter setup tests indicated that the overall Coefficient of Performance (COP) values remained unchanged at any RPM, but power consumption decreased by approximately 9% at 1300 RPM while maintaining the same cooling capacity (Fig. 9; Table 3).
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4 Conclusion In this study, the adaptation of the Tesla valve to the reciprocating compressor muffler was investigated, considering computational fluid dynamics (CFD) results and transmission loss analysis. The CFD analysis revealed that the flow predominantly travels through the main tube rather than the side tubes, while the slope of the side tubes influences turbulence intensity. Reducing the slope of the side tubes was found to decrease turbulence within the tube openings, indicating an important design consideration. The transmission loss analysis demonstrated that all proposed Tesla valve models outperformed the original model in terms of acoustic performance. Different geometries of the Tesla valve showed superior transmission loss performance in specific frequency ranges, suggesting the potential for tailored designs optimized for various frequency bands. Calorimeter and semi-anechoic tests further validated the improvements achieved through the Tesla valve adaptation. The replacement of the suction muffler with Model 1 resulted in a significant reduction in noise, and the overall power consumption decreased while maintaining the same cooling capacity. However, it was noted that the manufacturing limitations of the prototype, attributed to 3D printing capabilities and size constraints, hindered its full efficiency. Key findings highlighted the critical role of the side tube angle for achieving COP gain, with an optimal angle of 45°. Additionally, the wider and inclined upper openings of the side tubes were found to enhance performance. Model 2, an asymmetric and inclined design, showcased the best overall acoustic performance, while Model 1 excelled in attenuating lower frequency bands. Future studies are recommended to explore variations in tube angle, symmetry, and valve rotations. Improvements in the opening of the side tubes should also be considered to further enhance COP results. Comprehensive testing in semi-anechoic rooms and calorimeter setups will provide additional insights into the acoustic and performance characteristics of the proposed Tesla valve designs. Overall, this research contributes valuable insights into optimizing the acoustic performance of reciprocating compressor mufflers through the application of the Tesla valve. These findings offer potential for enhanced noise reduction and improved efficiency in compressor systems, paving the way for further advancements in the field.
References 1. S. Gupta, R. Patel, M. Singh, Performance analysis of hermetic reciprocating compressors. Int. J. Refrig. 97, 234–248 (2020) 2. Munjal, M.L., Acoustics of Ducts and Mufflers, 2nd ed. Wiley (2014) 3. Lee, J.H., An, K.H., Lee, I.S., Design of the suction muffler of a reciprocating compressor, in International Compressor Engineering Conference. Paper 1543 (2002) 4. Nuñez, I.J.C., De Marqui, A.L.L., Cavaglieri, M., Arruda, J.R.F., Investigating the transmission loss of compressor suction mufflers applying experimental and numerical methods, in International Compressor Engineering Conference. Paper 1900 (2008)
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5. Z.J. Jin, Z.X. Gao, M.R. Chen, J.Y. Qian, Parametric study on Tesla valve with reverse flow for hydrogen decompression. Int. J. Hydrogen Energy 43(18), 8888–8896 (2018) 6. J.Y. Qian, M.R. Chen, Z.X. Gao, Z.J. Jin, Mach number and energy loss analysis inside multistage Tesla valves for hydrogen decompression. Energy 179, 647–654 (2019) 7. Adanta, D., Fattah, R., Muhammad, N.M., Comparison of standard k-ε and SST k-ω turbulence model for breasts hot waterwheel simulation. J. Mech. Sci. Eng. (2019)
Multi-physical Modeling of Noise and Vibration Due to Refrigerant Discharge in Hermetic Compressors Dazhuang He, Yidan Cui, Davide Ziviani, and Yangfan Liu
Abstract In high-pressure shell hermetic compressors, the refrigerant discharge flow from the compression chamber(s) involves interactions between interior acoustics, turbulent fluid flow and structural vibration. To study and optimize the compressor shell and compression discharge process, a comprehensive multi-physics simulation model encompassing the thermomechanical, fluid flow and vibro-acoustics aspects of hermetic compressor has been developed. The thermomechanical model is based on a deterministic compressor chamber model. Whereas the interior fluid flow is modeled using a CFD approach, and the resulting broadband noise and vibration is modeled via a fluid-structure interaction (FSI) interface. The narrowband noise and vibration effects due to periodic compressor discharge pulsations are estimated by using finite element analysis (FEA). The thermomechanical model provides instantaneous pressure traces from the compression process which are used as boundary conditions for either fluid or acoustic domain to enable the coupling with FSI and vibro-acoustics simulations. The comprehensive simulation model is utilized to understand the physical reasons behind NVH effects in a hermetic rolling-piston compressor for air-conditioning applications. Keywords Hermetic compressor · Vibro-acoustics · Fluid-structure interaction · NVH
1 Introduction The operation of positive displacement compressors inevitably yields undesired NVH effects. Hermetic compressors are widely used in refrigeration and air conditioning applications and mitigating NVH effects is an important factor not only to ensure customer satisfaction, but also to meet noise standards depending on the application. D. He · Y. Cui · D. Ziviani (B) · Y. Liu (B) Ray W. Herrick Laboratories, School of Mechanical Engineering, Purdue University, West Lafayette, IN, USA e-mail: [email protected] Y. Liu e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_52
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One of the major sources of noise and vibration is the discharge refrigerant flow and its interactions with the structure of the compressor. Specifically, there are two aspects of the discharge refrigerant flow and each result in different noise and vibration characteristics: (1) the periodic discharge gas pulsation at the discharge valve location; and (2) the nonlinear perturbations caused by the turbulent discharge gas flow. The volume change of the compression chambers during a working cycle acts as a periodic acoustic source which usually contributes to the gas pulsation noise, i.e., the narrowband peaks in the noise and vibration spectra [1]. The turbulent refrigerant gas flow, when interacting with the inside shell surface of the discharge cavity, contributes to the aerodynamic noise, i.e., broadband features in the noise and vibration spectra. The challenge to characterize such a fluid-borne noise-generating mechanism lies within the co-existence of multiple simultaneous noise and vibration sources. During the operation of a compressor, the refrigerant discharge contributes to the overall NVH effect, along with other mechanisms such as rotor imbalances and valve impacts. Due to the difficulty of isolating refrigerant discharge from other noise-generating mechanisms in a compressor, physics-based modeling is a viable approach to estimate how significantly the refrigerant discharge contributes to the overall noise and vibration of compressors. The compressor noise and vibration due to refrigerant discharge has been extensively studied using four-pole method [2], in which discharge gas pulsation is modeled as acoustics perturbation that propagates in a system consisting of acoustic filter components with lumped parameters. Four-pole method has been used to estimate transmission loss of pressure pulsations across mufflers [3]. Acoustic finite element analysis (FEA) is another readily available method for the study of noise and vibration due to refrigerant discharge and has also been used to characterize compressor muffler performances [4]. The four-pole method or the acoustic FEA are capable of resolving narrow band features associated with compressor operation speed. However, these methods are based on linear acoustics, and thus not capable to resolve the noise-generating nonlinear fluid interactions. In order to resolve the nonlinear broadband mechanisms, interior fluid flow must be solved. Computational fluid dynamics (CFD) has been a useful tool for the analysis of refrigeration compressor performance. Attempts were made to use CFD to predict pressure variation in compressor cavity and its effect on thermal performance of compressors [5]. The internal flow field within hermetic shell was solved to analyze how the choice of refrigerant affects the pressure drop [6]. Researchers have also used CFD to numerically solve the pressure field in compression chamber with respect to compressor operation and the resulting fluid load applied on compressor structures [7]. The compressor noise and vibration induced by the pulsive discharge gas jet has been studied with the use of CFD [8]. The aforementioned studies, either based on linear acoustics or based on fluid dynamics, are limited for a specific aspect of compressor. However, the process of compressor operation, together with the generation of NVH effects, consists of different physical phenomena interacting with each other in a short period of time. The thermomechanical operations in the working chamber(s), the valve dynamics, gas
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pressure pulsations, turbulent gas flows in the cavities, structural vibration and sound radiation are strongly coupled. In order to study and to optimize the NVH performance related to compressor discharge, a comprehensive multi-physics simulation model encompassing the thermomechanical, fluid flow and vibro-acoustics aspects of hermetic compressor has been developed.
2 Multi-physical Modeling The multi-physics simulation model consists of three major components: thermomechanical model that simulates the operation of compressor, vibro-acoustics model that resolves the narrowband noise and vibration due to periodic discharge gas pulsations and the fluid flow model that solves the broadband aerodynamic noise and vibration associated with compressor discharge process. The relation between the models and the multi-physical interactions is illustrated in Fig. 1. The models require input from the compressor design. Lumped parameters need to be estimated to reflect a certain compressor design in the thermomechanical model. The volume-crank relation needs to be updated based on a compressor design. The 3-D geometry and configuration of the compressor design are required by both the vibro-acoustics model and fluid flow model. The discharge process is simulated in the thermomechanical model, and the results are converted to the input of vibro-acoustics model and fluid flow model. The vibro-acoustics model and fluid flow model resolve the narrowband and broadband discharge-related NVH respectively.
Fig. 1 Diagram of multi-physical modeling for compressor discharge related NVH
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2.1 Thermomechanical Model The thermomechanical operations of compressors are solved in the thermomechanical model. The thermomechanical model is based on mass and energy conservation equations, based on a deterministic compressor chamber model. Two ordinary differential equations of in-chamber thermophysics are solved iteratively with respect to crank angle. The core structure of the thermodynamics model includes working chamber volume calculations, evaluation of leakage flows, heat transfer within the working chamber, mechanical and frictional losses, suction and discharge valves and an overall energy balance to account for additional heat losses through the compressor shell. A variety of geometric models accommodating different types of compressors has been developed and integrated into the existing PDSim platform [9, 10]. In this study, the thermomechanical model provides the discharge flow rate profile through the compressor discharge port. The calculation of discharge flow involves multiple PDSim components: in-chamber control volume analysis, discharge valve dynamics and nozzle flow. The details of the control volume analysis volume analysis are elaborated in [9, 10]. The discharge valve can be modeled either as a simple oscillator or as a cantilever beam structure, driven by the pressure difference across the valve. The flow across the valve is solved by using 1-D compressible flow equations. The theories of the valve and 1-D nozzle flow modeling are discussed in detail in [1]. The resulting discharge flow rate profiles serve as the input boundary conditions for the vibro-acoustics model and interior flow model.
2.2 Discharge Pulsations and Consequent Noise and Vibration The discharge pulsation and the generation of consequent noise and vibration are a multi-physical process involving acoustic-structure interaction. The discharge gas pulsation is modeled as an acoustic source within the compressor cavities, and the cavities are modeled as bodies of refrigerant gas. Because the discharge process creates an oscillatory flow rate in the cavities, it is appropriate to model the discharge port as an acoustic monopole. In free space, the acoustic monopole induces a pressure field .
p(r, f ) =
j f m( ˙ f ) e− jkr , 2 r
(1)
where .m( ˙ f ) represents the spectrum of the oscillatory mass flow rate. Because the mass flow rate provided by the thermomechanical model is in terms of crank angle (or time), discrete Fourier transform (DFT) is performed to obtain the spectrum .m( ˙ f ). Due to the excitation of gas pulsation, an acoustic pressure field is induced in compressor cavities. The compressor shell and other compressor structures surround-
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ing the cavities are excited by the varying pressure field induced by the discharge pulsation. The cavity acoustics response and vibration of compressor structures are two-way coupled. Cavities are simultaneously excited by both the refrigerant gas discharge and the vibrating structures. The vibrating structures displace the fluid in the cavity and induce acoustics perturbations in cavities. The theories of twoway acoustics-structure coupling are included in [1]. Due to the complexity of the compressor geometry, finite element analysis is used to solve the two-way coupled problem. The aspects of acoustic finite element analysis in compressor applications have been discussed in [11].
2.3 Interior Gas Flow and Resulting Aerodynamic Noise and Vibration Aerodynamically induced noise is typically generated by the turbulent flow field inside the hermetic shell, the relation between interior flow field and acoustics needs to be clarified. In principle, sound is a class of fluid medium perturbation that is governed by wave equation and propagates at the speed of sound. In other words, sound generation and propagation can be resolved if fluid field is fully solved. In many applications where aerodynamic noise is of interest, the non-linear flow region and linear sound propagation region can be separated, and the aerodynamic noise can be resolved by solving a set of linearized equations, such as linearized Euler’s equation (LEE). However, such approach is not applicable to interior problems. For hermetic compressors, the interior acoustic and fluid domains occupy the same region. There is no distinct boundary between the region of non-linear fluid interactions and the region of linear acoustics. Due to the aforementioned reasons, a direct computation of the unsteady interior fluid field is needed to resolve the aerodynamically induced broadband acoustic perturbations. The fluid perturbation is solved, and the techniques of fluid-structure interaction (FSI) are used to compute the response of the hermetic shell. It should be noted that the resolved perturbations using this method are not necessarily acoustic perturbations. In a sense, interior acoustics in this study implies general fluid perturbations, instead of exclusive acoustic perturbations. Noise and vibration are caused by the turbulent unsteady fluid loads applied on the interior structures of the compressor. FSI is used to model phenomena where the interior refrigerant gas flow and deformable compressor structures interact with each other, similar to the coupling between compressor structures and the interior acoustic field. There are three different ways to do FSI: fluid loading on structure (one-way), velocity transmission to fluid (one-way) and fully coupled (two-way). In our study, the selection of FSI approach boils down to one question: whether the structural velocity transmission back to the fluid domain makes a significant difference in fluid or structural response. Figure 2 shows that, by taking the structural velocity transmission back to the fluid domain into consideration, the magnitude of structural response
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Fig. 2 Comparison between one-way and two-way FSI
becomes significantly smaller. For this reason, two-way FSI simulation is performed in the analysis of aerodynamically induced noise and vibration of compressors. The excitation on the structure side is the total fluid stress (pressure + viscous shear). The values of the excitation are extracted from CFD simulations of interior refrigerant gas flow. The effect of turbulence is included in the viscous stress, specifically the additional stress associated with turbulence eddy viscosity. The viscous stress is an intermediate result of the simulation and is dependent on the choice of turbulence model. In [8], the simulation results with different turbulence models are compared. In the results, the differences in solution values are negligible, but the rates of convergence are significantly different. The .k − ∈ model is selected because of the fast convergence. The simulation approach with turbulence models is the so-called Reynoldsaveraged Navier-Stokes (RANS). An alternative approach without the use of turbulence models is large eddy simulation (LES) since it capable to solve the flow field with finer resolutions and more ideal for acoustic simulations. The use of LES in compressors is still being studied.
3 Results and Discussion A rolling piston compressor has been used as a case study. The typical structure of the rolling piston compressor is illustrated in Fig. 3.
3.1 Thermomechanical Simulation The compressor thermomechanical model generates the discharge flow rate variation over a cycle of operation, and provide the results to the vibro-acoustics analysis or interior fluid flow analysis. Figure 4 shows an example of discharge flow rate results. In the case study, the working fluid is R-410A, and the compressor operates at 3600
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Fig. 3 Layout of a rolling piston compressor
Fig. 4 Discharge velocity: a flow rate profile in one cycle of compressor operation; b one-sided Fourier coefficients spectrum of discharge flow rate
rpm. As a result, the thermomechanical model simulates the discharge flow rate profile that lasts 1/60 s. The result is seen as a periodic signal with a period of 1/60 s, and the Fourier coefficient spectra is estimated via discrete Fourier transform. After removing the DC component, Fourier coefficients in Fig. 4b show a distinct peak at 60 Hz, which is the operation frequency of the compressor. The spectrum is discrete and only has values at harmonics of compressor operation speed. Due to the pulsive nature of discharge profile, the energy is spread out over a large frequency range. In the example shown in Fig. 4b, the energy of the 20-th harmonic (1200 Hz) and beyond fall below 1% of the energy of the fundamental component (60 Hz). Therefore, the frequency range of narrowband gas pulsation noise and vibration is 60–1200 Hz.
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Table 1 Number of elements for different computation domains Vibro-acoustics simulation Aerodynamic noise and vibration simulation Number of elements
Computation time
Cavity (linear tetrahedra)
.1.44
∗ 106
4 Shell (linear .2.57 ∗ 10 triangles) 5 Ambient air .1.54 ∗ 10 (linear tetrahedra) 0.44 h (per freq. step)
5 Cavity .5.37 ∗ 10 (quadratic tets + prisms) Shell (quadratic .4.40 ∗ 104 triangles) 4 Ambient air .5.30 ∗ 10 (quadratic tetrahedra) 5.24 h (per cycle)
3.2 Noise and Vibration Due to Discharge Pulsation The thermomechanical model provides the discharge velocity spectrum to the FEA based vibro-acoustic simulation model. An FEA based simulation of the structureacoustic coupled response is performed with a frequency range of 60–1200 Hz. In the simulation setup, the entire domain is excited by the acoustic monopole source that emulates pulsive refrigerant discharge, and the strength of the acoustic source is computed based on the discharge mass flow rate spectrum provided by the thermomechanical model. General information of mesh and computational cost is listed in Table 1. For the purpose of demonstration, vibro-acoustic simulation results at 960 Hz are shown in Fig. 5. In Fig. 5b, relatively large response occurs on the top and bottom caps of the shell, whereas the response on the shell side wall is less significant. The top cap response at 960 Hz is similar to the (1, 0) circular membrane mode, while the bottom cap demonstrates the (0, 0) circular membrane mode. The pattern of frequency response of shell indicates that the two shell caps are major sound radiators. From the noise reduction point of view, the noise radiated by the shell can be mitigated by either changing mass or stiffness of caps to avoid cap resonance or adding damping mechanism. The vibrating outer surface of the shell is an excitation to the exterior medium and causes noise radiation. The technique of infinite element is used in the computation of exterior acoustics. Figure 5c shows the frequency response in the finite element domain of the exterior medium. The hot spot locations also confirm that the shell caps are the primary noise radiator. More detailed results of cavity and shell response, and near-field and far-field exterior acoustics spectra and directivity patterns are shown and discussed in [1].
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Fig. 5 Response of a compressor cavity, b compressor shell and c exterior medium at 960 Hz
3.3 Aerodynamic Noise and Vibration Similar to the vibro-acoustics simulation, the fluid field simulation also takes input from the thermomechanical model. Because the fluid field simulation is conducted intrinsically in the time domain, the thermomechanical model provides the time profile of discharge flow rate (Fig. 4a) to the CFD based fluid field simulation. The discharge flow rate variation given by the thermomechanical model is applied to the compressor discharge port as the inlet boundary condition. A CFD-acoustics coupled numerical simulation with fluid-structure interaction is conducted to study the aerodynamically induced noise and vibration of hermetic compressors. The simulation domain is simplified from the geometry shown in Fig. 3. In the simulation setup, the turbulent refrigerant gas flow is coupled with shell vibration and exterior sound radiation. The entire simulation domain includes three regions: compressor cavity, compressor structure and exterior medium (Fig. 6). Fluid field is solved in the compressor cavity, coupled with structural vibration via FSI interface. After the structural vibration is obtained from FSI simulation, the consequent sound radiation in the exterior medium is solved. General information of mesh and computational cost is listed in Table 1. As a demonstration, a snapshot of solutions in all three regions (interior fluid, structure and exterior medium) are shown in Fig. 7. The exterior sound pressure propagation from the compressor shell structure can be clearly identified in the region adjacent to the shell surface. Similar to the result of Noise and vibration due to discharge pulsation, the result of the simulation indicates that the aerodynamically induced noise and vibration mainly occur on the top and bottom caps of the hermetic shell. More detailed results of cavity, shell and exterior acoustics response spectra are shown and discussed in [8].
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Fig. 6 a Computation domain and b close-up view of discharge port
Fig. 7 A snapshot of the solutions in cavities, on hermetic shell and in exterior regions
4 Conclusions and Future Work A comprehensive multi-physics simulation model encompassing the thermomechanical, fluid flow and vibro-acoustics aspects of hermetic compressor has been developed to simulate the multi-physical process of noise and vibration generation due to refrigerant discharge. It has been demonstrated that by coupling multiple phys-
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Fig. 8 Diagram of experiment to verify the relation between discharge flow, valve dynamics and consequent pressure pulsation
ical phenomena during the compressor discharge process, the simulation model is capable to resolve both the narrowband gas pulsation noise/vibration and broadband aerodynamic noise/vibration. Future work In this work, the modulation of the discharge valve to the diacharge flow is of utmost importance. Modeling the relation between discharge flow, valve dynamics and consequent equivalent acoustic excitation is the key to accurately resolving the gas pulsation pressure and flow rate at the ports and, in turn, determining the noise and vibration due to gas pulsations. An experiment has been designed for the purpose of verifying the modeling of the relation between discharge flow, valve dynamics and consequent pressure pulsation. The experiment setup is illustrated in Fig. 8. A hot gas bypass system was assembled with a pressure chamber. A reed valve assembly is installed at the inlet of the chamber. The valve displacement, chamber pressure and inlet flow rate are measured simultaneously. More details about the test setup and some preliminary test results can be found in [12]. It has been proposed to explore the applicability of the present framework of the multi-physical modeling of discharge flow induced noise and vibration in providing compressor manufacturers with NVH-oriented design modification guidance. Based on the presented framework, parametric studies for a wide range of compressor design parameters such as discharge valve thickness, the aspect ratio of compression chamber, dimensions of discharge muffler, etc. will be conducted to provide more insights into the relation between compressor designs and NVH levels. Acknowledgements This work is a part of CHPB-40 research project funded by the Center for High Performance Buildings (CHPB). The authors would like to express appreciation to CHPB for providing the necessary funding for this research.
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References 1. D. He, D. Ziviani, Y. Liu, Theoretical analysis of noise and vibration generated by gas pressure pulsation in hermetic compressors, in 25th International Compressor Engineering Conference at Purdue, Paper 1527. (Purdue University, West Lafayette, IN, 2021) 2. W. Soedel, Sound and Vibrations of Positive Displacement Compressors (CRC Press, Boca Raton, FL, 2007) 3. J.I. Park, D.E. Adams, Modeling and simulation of the suction process in a multi-cylinder automotive compressor, in Proceedings of the 2004 International Compressor Engineering Conference, Paper C110. (Purdue University, West Lafayette, IN, 2004) 4. C. Svendsen, Acoustics of suction mufflers in reciprocating hermetic compressors, in Proceedings of the 2004 International Compressor Engineering Conference, Paper C029. (Purdue University, West Lafayette, IN, 2004) 5. A. Nakano, K. Kinjo, CFD applications for development of reciprocating compressor, in 19th International Compressor Engineering Conference at Purdue, Paper 1842. (Purdue University, West Lafayette, IN, 2008) 6. Y.V. Birari, S.S. Gosavi, P.P. Jorwekar, Use of CFD in design and development of R404A reciprocating compressor, in 18th International Compressor Engineering Conference at Purdue, Paper 1727. (Purdue University, West Lafayette, IN, 2006) 7. H. Wu, H. Huang, B. Zhang, B. Xiong, K. Lin, CFD simulation and experimental study of working process of screw refrigeration compressor with R134a. Energies 12, 2054 (2019) 8. D. He, Y. Cui, D. Ziviani, Y. Liu, Numerical study of the aerodynamic noise and vibration due to pulsive discharge gas jet in hermetic compressors, in 26th International Compressor Engineering Conference at Purdue, Paper 1415. (Purdue University, West Lafayette, IN, 2022) 9. I.H. Bell, D. Ziviani, V. Lemort, C.R. Bradshaw, M. Mathison, W.T. Horton, J.E. Braun, E.A. Groll, PDSim: a general quasi-steady modeling approach for positive displacement compressors and expanders. Int. J. Refrig. 110, 310–322 (2020) 10. D. Ziviani, I.H. Bell, X. Zhang, V. Lemort, M. De Paepe, J.E. Braun, E.A. Groll, PDSim: demonstrating the capabilities of an open-source simulation framework for positive displacement compressors and expanders. Int. J. Refrig. 110, 323–339 (2020) 11. Y. Liu, Lecture 4: modeling gas pulsation; short course presentation, in 26th International Compressor Engineering Conference at Purdue (2022) 12. Y. Cui, D. He, D. Ziviani, Y. Liu, Experiment design for investigations on noise generated by discharge refrigerant gas pulsations in hermetic compressors, in 26th International Compressor Engineering Conference at Purdue, Paper 1393. (Purdue University, West Lafayette, IN, 2022)
Mitigation of Fluid-Induced Noise Generated by Discharge Flow in a Hermetic Rolling Piston Compressor Yidan Cui, Dazhuang He, Davide Ziviani, and Yangfan Liu
Abstract In rotary rolling piston compressors, compressed refrigerant gas is discharged periodically from compression chamber through a valve which can induce the formation of gas pulsation. The combination of turbulent flow and fluid–structureinteraction induce vibrations and consequently noise. These effects are particularly enhanced during variable speed operation. In previous research conducted by the authors, both numerical and experimental analyses were carried out to investigate the gas pulsation noise caused by the discharge process. Simulation models integrated multiple physical processes was constructed and validated. In this work, the modeling framework is employed to conduct parametric studies to identify the features affecting the gas pulsation noise. A wide range of parameters have been considered in the analyses. A two-way coupling methodology has been applied to run the parametric studies. The effects of modifying these parameters and the reasoning behind the noise generation are discussed. The numerical studies and methodology developed will enable compressor noise diagnostics, including localizing the main contributing components, understanding the generation of compressor gas pulsation noise and improve of the overall compressor design. Keywords Gas pulsation noise · Numerical analysis · Parametric study
Y. Cui · D. He · D. Ziviani (B) · Y. Liu (B) Ray W. Herrick Laboratories, Purdue University, West Lafayette, IN 47906, USA e-mail: [email protected] Y. Liu e-mail: [email protected] Y. Cui e-mail: [email protected] D. He e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_53
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1 Introduction Compressor operation is a complex process with different coupled physical phenomena interacting with each other [1, 2]. Multiple types of noise are generated during compressor operation including structure-induced noise due to vibration of the compressor shell, fluid-induced noise within compressor cavities caused by turbulent flow, gas pulsation noise produced by periodic discharge process, noise generated by electrical motor. Several studies were conducted to investigate the various mechanisms of compressor noise generation as well as noise mitigation strategies. Kawaguchi et al. [3] designed a structure on the inner wall of rotary compressor, which decreased shock wave noise by depress pressure difference across discharge valve. Sano et al. [4] attached a buffer to compressor discharge port, which constrained flow path of discharge gas and acted like a Helmholtz resonator. Suh et al. [5] studied the performance of discharge muffler in a rotary compressor. Dreiman [6] proposed a newly designed thrust bearing with polyamide material. This alternative material is characterized by having low friction coefficient. The proposed design could help to reduce friction losses of the main bearing and reduce the friction-caused noise. According to experimental measurements, by applying this new structure, the total compressor noise level was decreased by up to 3 dB(A). Adachi et al. [7] improved the structural connection between cylinder of a rotary compressor and compressor shell. This modified part changed the structure resonant frequency, thus attenuated the noise within an interested frequency band. However, as a connection of compressor interior to exterior shell, this structure modified the noise transmission path, reducing total noise level over a broad band. Besides the structure vibration noise, Tanaka et al. [8] conducted studies about effect of the eccentricity of motor rotor on a horizontally installed rolling piston compressor. Results showed that increase of eccentricity will bring about uneven magnetic field and increase the electromagnetic noise. The majority of conducted studies, however, focused on a single compressor component under a simplified physical process which are not representative of the interactions between multiple physical processes. For example, the generation of gas pulsation noise induced by compressor discharge process is a result of the integration of multiple physical processes, including in-chamber gas compression, highpressure gas passing through valve assembling, reverberation of pressure perturbation in cavity, and structure vibration excited by gas pulsation. Proposed studies, however, limited by study methodology, were hardly able to explore this phenomenon comprehensively. For instance, Kral [9, 10] measured sound pressure level around a reciprocating compressor to investigate influence of valve reed thickness, cylinder clearance and valve plate material on compressor noise generation. Measurement were conducted in an anechoic chamber with microphones distributed outside of compressor. Results obtained in this case cannot narrow down the scope of noise contribution. As an example, noise level change after modifying the valve reed thickness could be contributed by aerodynamic differences of fluid filed and by changing of vibration noise during the valve reed striking, which could be hard to
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differentiated by measuring total noise level. Generally speaking, constrained by measurement approaches and sensor layout, decoupling of the compressor operation process into specific sub-phenomena through experiment measuring is very challenging, which makes experiment-based approaches better suited to verify and validate final outcomes. However, numerical simulations can provide efficient methods to analyze such complex interactions by decomposing a physical process into submodels by utilizing multi-physics computational domains. A comprehensive simulation model considering different physical processes need to be proposed, which is helpful to investigate compressor noise generation mechanism and gain more accurate understandings of noise reduction manners. Multi-physical numerical simulation models were proposed in work done by the authors [11], which combined sub-models for in-chamber thermodynamic properties, acoustic response in compressor cavity, and vibration of compressor structure. This study aims at utilizing the simulation tools to predict the noise spectra of a baseline protype compressor design, identify targeted frequency bands for noise reduction design modification, locate the major component that contributes to noise in the identified band, and analyze the effect of component parameters from noise generation perspective. As previously mentioned, various types of noise are produced during compressor operation, to specify the objective of study, the simulation and analysis in this paper were conducted for gas pulsation noise induced by gas discharge process of compressor.
2 Methodology 2.1 Overview To address the research objectives, several parameters were investigated to assess their impacts on gas pulsation noise during the discharge process. By parameters, it refers to the design parameters or operation parameters that could directly impact the NVH performance. The analyses were conducted following two approaches: 1. Investigation of physical parameters. Firstly, a parameter of interest is selected. Then the parameter is changed so that its effect on NVH can be analyzed. The parameters could be a geometry parameter, such as the thickness of shell and could also be an operation parameter (e.g., compressor operational speed). The effects on NVH can be represented by acoustic response in the cavity or the vibration of shell. 2. Noise and vibration diagnostics. Targeting a specific feature in simulation results, the changes of this feature with modifications of parameters is analyzed. The feature could be, for example, a peak in spectrum, or a feature related with an interested physical phenomenon. The spectra of compressor response were obtained with simulation model.
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2.2 Simulation Model Description and Verification In this subsection, the simulation models are described in detail. Moreover, their reliability is also discussed. Simulation model description. The authors have conducted previous investigations on noise and vibration in compressors [11]. The numerical simulation approach in this study integrated various sub-models to provide a comprehensive analysis of different physical processes occurring during the compressor gas discharge. More specifically, a compressor mechanistic model developed with the PDSim platform [12] was used to simulate the thermodynamic process inside the compression chamber and to predict instantaneous in-chamber pressure variation and flow rate. These results were used as excitations for the acoustic field in the form of the strength of a monopole source. An acoustic model was developed with COMSOL Multiphysics® software [13] to describe the acoustic response excited by the in-chamber gas discharge pulsations delivered by the monopole source strength, which was obtained by mechanistic model. Meanwhile, a structure vibration model was built with COMSOL to reflect the shell vibration of compressor shell induced by the interior cavity. These models mentioned above were coupled together with a one-way interaction method for the mechanistic model to acoustic model, and in two-way interaction method between acoustic model and shell vibration model. The term vibro-acoustic model was used to refer to the acoustic model coupling with structure vibration model since both two models were mutually interacted. A rolling piston compressor was selected as a case study. The geometry of prototype model was simplified for numerical simulation purposes by removing nonrelevant features. The vibro-acoustic model configuration is shown in Fig. 1a, in which the grey outer boundary is the geometry of compressor shell, the green domain indicated the acoustic cavity inside the compressor shell. Both of them are separately shown in Fig. 1b, c. Since the objective of this study focus on the gas-pulsation noise induced by compressor discharge process, relevant structures were emphasized in the geometry model which is addressed with red dashed box in a Fig. 1c, and a closer view of which is shown in Fig. 2a, b. The red dot indicates the location of a monopole acoustic source which represents the excitation from the compressor in-chamber process and propagated with gas discharge process. The strength of the monopole source is determined by the compressor mechanistic model. The location of the monopole source is at the discharge port of compressor chamber, following which is the discharge valve assembling and the discharge muffler. The geometry of the muffler chamber is shown in Fig. 2c. Model verification. To construct a reliable baseline simulation for parameter analysis, before conducting further studies, mesh independency was validated to confirm the reliability of the simulation model. The baseline case for mesh quality validation was constructed with the maximum mesh size was set to 15 elements per wavelength for up to 6000 Hz. To save calculation resources and increase efficiency, mesh quality was adjusted, and results were compared with baseline case. During the process of
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Fig. 1 Configuration of vibro-acoustic model
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adjust mesh, results at the frequency of 1020 Hz showed a high sensitivity to mesh quality. Thus, the results at 1020 Hz were selected as an indicator and the objective was to control the relative error of mean square pressures at 1020 Hz comparing to the baseline mesh setup. Probes were set at the top cavity and bottom cavity of compressor to monitor pressure values and the locations are shown in Fig. 3. The relative errors were 5.62% for the top probe result and 5.39% for the bottom probe result.
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Fig. 3 Locations of acoustic pressure probes
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3 Results Analysis Utilizing the simulation model demonstrated in last section, several parameters were studied to investigated the impact on compressor discharge gas pulsation noise. Selected parameters are shown in this section, including valve design parameters and muffler design parameters.
3.1 Valve Design Parameters The valve parameters directly affect the discharge process and cause consequent variation in discharge profiles. Two parameters, including valve reed thickness and discharge port angular position, were studies. Valve reed thickness can affect the stiffness of valve reed, thus change the pressure pulsation and mass flow rate through the discharge path. Angular position of discharge port can determine the timing of valve close thus change in-chamber pressure field around discharge port. Considered values are shown in Table 1, where values marked as baseline are the design values in original prototype model. θ d representing the angular position is indicated in Fig. 4. The discharge profile spectra of different parameters, obtained with compressor mechanistic model, are shown in Fig. 5, with were used to conduct acoustic-structure coupled simulations in COMSOL. For assessing the NVH effect, spatial averaged root mean square (RMS) acoustic pressure and vibration displacement were computed and compared with parameter adjustment. The RMS pressure was averaged over the entire compressor cavity to represent the strength of cavity acoustical response. The RMS displacement was averaged over the entire shell surface to represent overall vibration response. The reason of such difference
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in discharge profile spectra can be visualized by inspecting pressure–volume (p–V) relation for the discharge process. Figures 6 and 7 shows the compressor in-chamber p–V relation at the initial and end phases of discharge process. Figures 6 and 7 show the higher order pressure fluctuations that induce high frequency components in the spectra in Figs. 8 and 9. It should be noted that increasing the valve thickness by 0.1 mm resulted in significant increase in pressure pulsation. The change in discharge port angular position did not significantly affect valve opening behavior thus yielded similar pressure profile during the valve opening process. The pressure profile during valve closing process were different because of the shift in the timing of valve closing, where greater θ d caused early close of valve.
3.2 Muffler Design Parameters Two parameters are investigated respect to muffler design, including the shape of muffler and relative location of muffler outlets. As an acoustic filter, the shape and
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(a). Different valve thickness.
(b). Different discharge port angular position.
Fig. 5 Compressor discharge profile with different parameters
Fig. 6 Compressor in-cylinder pressure–volume relation with different valve thickness
Fig. 7 Compressor in-cylinder p–V relation with discharge port at different angular positions
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Fig. 8 Cavity pressure and shell displacement with different valve thickness
Fig. 9 Cavity pressure and shell displacement with angular position of discharge port
volume of the discharge muffler could affect the acoustic resonance within the muffler cavity. Meanwhile, the relative location of muffler outlets can result in phase difference of acoustic wave propagating through different outlets, and further influence acoustic radiation in this approach. The shape of muffler. The shape of discharge muffler was changed into a circular shape as show in Fig. 10a. The section view of compressor model with modified muffler is shown in Fig. 10b. As presented in Fig. 11, the radius r 1 and r 2 in Fig. 11a was determined based on r 1 and r 2 in Fig. 11b which is the geometry of the muffler in prototype. The height of the muffler, notated as h in, was kept as the same with the original geometry. By evaluating the nature frequency of muffler cavity, the first two non-zero values were 1062 Hz, 1354 Hz for the original design and 1046 Hz, 1307 Hz for the modified design, which indicated a slight decay. Utilizing the modified structure in the compressor model delivered the response spectra shown in Fig. 12. The curves show almost the same response results except for a small difference at 540 and 600 Hz. Combining the results of nature frequency and the compressor response,
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(a). Modified shape.
(b). Section views of modified muffler in compressor.
Fig. 10 Geometry of muffler with modified shape Fig. 11 Indication of muffler radius
(a). Modified design.
(b). Original design
conclusion could be inferred that the muffler performance was barely changed by modifying the geometry in stated manner. The discharge muffler can be treated as a Helmholtz resonator and the geometry modification in this case mainly regards the volume change of muffler cavity. For a simple Helmholtz resonator model, the natural frequency is inverse proportional to the root square of the cavity volume. Hence, the natural frequency was not changed dramatically since the volume was in a small value. That could explain the mild changes of resonant frequencies and compressor response spectra. Relative location of muffler outlets. The discharge muffler can be treated as a cylindrical cavity with two outlets on the top, and the acoustic radiation by the muffler is contributed by the two muffler outlets. A literature [14] regarding muffler design illustrated how did the relative location of muffler outlets influence the total noise radiation and conducted case study. From the analysis in the literature, for a cylindrical cavity with two outlets placed on a same horizontal level and 180° apart from each other, the mode shape of these two outlets possess a phase difference of π. Following this train of thought, despite of mode number, the superposition of the Pa and Pb can remain minimum if the two outlets are disposed on the nodal line. The mode shape of first non-zero natural frequency of 1072 Hz is shown in Fig. 13, where the red dash line indicates the nodal line under this mode. Align the nodal line, the muffler outlets were relocated. Figure 15 shows the location of the muffler outlets. The original two ports were get removed and the circular pointed with blue arrow is a boundary left by CAD model construction. Two moon-shape ports, pointed by red
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arrows, were newly added around the main shaft based on the location of the nodal line shown in Fig. 13. The area of the moon-shape ports was slightly tuned so that the total area of muffler outlets maintained the same as the prototype design (Fig. 14). To analyze the performance of the muffler cavity, an acoustic response model for muffler cavity is constructed. The geometry of the muffler model is shown in Fig. 16. The muffler cavity model is driven by a monopole source with the same location and strength as the compressor acoustic response model. Boundary condition was applied on the surface of outlet ports, which is colored in blue in Fig. 16, with
Fig. 13 Mode shape at natural frequency of 1072 Hz
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Fig. 14 Acoustic response at frequency of 1020 Hz in term of pressure Fig. 15 Top view of muffler in compressor model
acoustic impedance of the refrigerant R134a, which is the working medium of the acoustic filed. Results of muffler model is shown in Fig. 17. Average is taken over the edges of muffler outlet ports since that could be accurately captured to compare with. The acoustic intensity was evaluated with the velocity in y-direction which is the axial direction of the main shaft of compressor. Figure 17 shows a decrease within the frequency range of 660–1020 Hz, which represented the change of the muffler performance by itself.
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Substituting the new muffler into the compressor model, the total average acoustic pressure and displacement is shown in Fig. 18. The results performed a reduction of acoustic pressure and shell displacement between 240 and 660 Hz, which is not in an agreement with the response of muffler cavity model. To investigate this phenomenon, a comparison was conducted between the results of muffler model and compressor model. Placed in Fig. 19 is the results with modified muffler in terms of acoustic pressure averaged along the edges of muffler outlets. The blue curve refers to compressor model which has more peaks in different frequency band, which might be caused by the acoustic wave reverberation and the interfere between propagating wave in the cavity and vibration of compressor shell. It could be inferred from this study that study a single component independently may produce a different response compared with using the compressor model.
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4 Conclusion Limited by space, only selected parameters and results are placed in this paper. Effects of changing valve design parameters are closely related with compressor in-chamber discharge profile. Valve thickness shows a more significant and more sensitive impact on acoustic response, especially for frequencies above 600 Hz. A change of 0.1 mm of valve thickness can result in higher order of pressure fluctuation which can further increase acoustic pressure and shell vibration among high frequency band. Regarding shape of discharge muffler, the muffler cavity volume is too small to result in a change in muffler cavity resonant frequency. So, in practice, whether changing muffler shape is able to tune the resonant frequency needs to be
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evaluated based on specific compressor model. Relative location of muffler outlets can influence inference of pressure perturbation radiated from muffler. For mufflers with two outlet ports, placing the ports align nodal line of muffle mode shape could be helpful to attenuate acoustic pressure within a certain frequency range. In addition, from the study of muffler design, due to wave reverberation within compressor cavities, a separate model of muffler can indicate properties of muffler by itself, but cannot predict the response of compressor.
5 Future Works A more complete summary regarding the relation of gas pulsation noise and related parameters will be proceeded, and experiment verification of proposed noise control strategy will be conducted. On the other side, simulation models for study compressor aerodynamic noise was also constructed by the authors. Application of simulation tools with a focus on compressor aerodynamic noise is also proposed for future study, and results can provide design guidance for manufactures to mitigate fluid-induced compressor noise in a broader band.
References 1. M.C. de Araujo, J. Tuhovcak, R.D. Brancher, T. Dutra, Hermetic reciprocating compressor simulation using a multi-physics platform, in International Compressor Engineering Conference (2022), Paper 2760 2. D. Ziviani, et al., PDSim: demonstrating the capabilities of an open-source simulation framework for positive displacement compressors and expanders. Int. J. Refrig. 110, 323–339 (2020) 3. S. Kawaguchi, T. Yamamoto, T. Hirahara, O.K. Morinushi, S. Kawaguchi, K. Morinushi, T. Yamamoto, T. Hirahara, O. Ohinatal, Noise reduction of rolling piston type rotary compressor, in International Compressor Engineering Conference, West Lafayette, IN, USA (1986), Paper 552 4. K. Sano, K. Mitsui, K. Sana, Analysis of hermetic rolling piston type compressor noise, and countermeasures, in International Compressor Engineering Conference, West Lafayette, IN, USA (1984), Paper 46 5. K.H. Suh, J.D. Kim, B.C. Lee, Y.H. Kim, The analysis of the discharge muffler in the rotary compressors, in International Compressor Engineering Conference (2000), Paper 1446 6. N. Dreiman, Control of the sound generated by a rotary compressor, in Fifth International Congress on Sound and Vibration, Adelaide, South Australia (1997) 7. Y. Adachi, I. Onoda, K. Takashima, Y. Adachi, I. Onoda, K. Takashima, Development of a low noise rotary compressor, in International Compressor Engineering Conference, West Lafayette, IN, USA (1996), Paper 1188 8. H. Tanaka, K. Ishijima, H. Tanaka, Noise and efficiency of rolling, piston type refrigeration compressor for household refrigerator and freezer, in International Compressor Engineering Conference, West Lafayette, IN, USA (1980), Paper 320 9. P.J. Kral, Influence of constructional parameters of small reciprocating compressors on sound power emissions. J. Acoust. Soc. Am. 123(5), 3316 (2008)
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10. P. Kral, On sound power emission of small reciprocating compressors, in Proceedings of the Forum Acusticum Budapest. OPAKFI Tudomanyos Egyesület (2005), p. 6. http://hdl.handle. net/20.500.12708/65235 11. D. He, D. Ziviani, Y. Liu, Theoretical analysis of noise and vibration generated by gas pressure pulsation in hermetic compressors, in 25th International Compressor Engineering Conference, West Lafayette, IN, USA (2021), Paper 2691 12. I.H. Bell, D. Ziviani, V. Lemort, C.R. Bradshaw, M. Mathison, W.T. Horton, J.E. Braun, E.A. Groll, PDSim: a general quasi-steady modeling approach for positive displacement compressors and expanders. Int. J. Refrig. 110, 310–322 (2020) 13. COMSOL Multiphysics® v. 5.6. www.comsol.com. Stockholm, Sweden 14. M. Noguchi, K. Sano, S. Takeshita, Cavity resonance and noise reduction in a rotary compressor. IEEE Trans. Ind. Appl. IA-19(6), 1118–1123 (Nov. 1983). https://doi.org/10.1109/TIA.1983. 4504344
Prediction of Pressure Pulsation Damping Efficiency with the Use of Shaped Nozzles Based on Their Geometrical Parameters ´ Joanna Krajewska-Spiewak , Damian Brewczynski ´ , and Przemysław Młynarczyk
Abstract The article presents the results of pressure pulsation damping obtained for different shapes of damping elements installed in a positive displacement compressor. On the basis of the conducted research, a prediction model was created to predict the damping of pressure pulsations based on selected parameters describing individual nozzles. The input parameters included, among others, values of ranges with different nozzle narrowing, contact surface area, gas volume and the percentage of forces acting in the longitudinal direction. The one at time (OAT) approach was used to evaluate the impact of individual input parameters on the predictive value. For the displacement compressor and for various nozzles a mathematical model with a mean absolute percentage error (MAPE) of 9.51% was obtained. Keywords One at time sensitive analysis · Predictive model · Shaped nozzles
1 Introduction The suppression of pressure pulsations in compressor installations is currently implemented mainly through the installation of attenuating volumes, called Helmholtz resonators. One of the biggest disadvantages of this solution is the fact that Helmholtz resonators are designed to suppress mainly one frequency of pressure pulsation. Nowadays, to meet the main goal of development and technology management of the criteria of sustainable development, compressors with adjustable displacement are becoming more popular. This adjustment is most often made by changing the rotational speed of the drive shaft, thus changing the frequency of supplying compressed gas to the installation. The resulting change in the frequency of pressure pulsations causes a problem in damping their amplitude. One of the most interesting solutions that allows pulsation damping in a wide frequency range is the installation of ´ J. Krajewska-Spiewak · D. Brewczy´nski · P. Młynarczyk (B) Faculty of Mechanical Engineering, Cracow University of Technology, Kraków, Poland e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_54
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nozzles with specially designed shapes inside the pipeline. The studies conducted to date show that this technology is effective in pulsating pressure damping [1–3]. However, in a situation where the cross-section of the pipeline is narrowed, it influences the specific compression power. Modern technology should have little or no impact on the process economy. The tests showed that for certain shapes it is possible to obtain a small impact on compression power with a satisfactory level of damping of pressure pulsations in a wide range of their frequencies [1]. The authors of this study also introduced a parameter that determines the usability of the nozzle shape, defined as the damping efficiency coefficient (C Dη ). B C Dη = √ ψ
(1)
The authors of the work [1] stated that volumetric flow is a linear function and flow resistance is the square function of velocity. Thus, the square root was applied to pressure peak-to-peak damping. The coefficient obtains lower values when the element better meets the requirements, due to the importance of compressor operation power savings. In the formula 1, B is the relative dimensionless volumetric power consumption and ψ is the dimensionless relative pressure pulsation damping parameter. So, B is determined as the percentage gain of the specific compression power and the ψ meaning a percentage increase in damping of pulsations behind the nozzle in relation to an empty installation based on the [1]. The parameter defined in this way is a good indicator of the usefulness of the nozzle in order to suppress pressure pulsations. Currently, it can be used to reject the concept of geometric nozzles. The Authors of paper [1] concludes their work that if the value of this coefficient is greater than 1, it can be assumed that the profit obtained from pulsation damping is not sufficient for a given increase in the unit compression power. A coefficient value below 1 can be an indication of the benefits of using such a nozzle. Specified nozzle shapes may be more suitable for different installation sizes, gas flow rates, gas pressures, etc. Thus, the problem of selecting the shape of the nozzle is significant. Therefore, a method should be developed to estimate the initial benefits/drawbacks of using a given shape. This paper presents a preliminary analysis, which is innovative in many ways. First of all, the sensitivity analysis is based on a very small amount of data which were obtained from the carried-out test performed on a DEMAG.DS.40 screw compressor test stand. Tests were carried out for nozzles of 17 different shapes, for which 7 parameters were defined. The output parameter which is planned to be estimated by the model is complex. It was determined on the basis of the damping of pressure pulsations and the impact of the nozzle on the increase in compression power values obtained during the experimental investigations. The results presented in the article are subject to high uncertainty. However, the purpose of these analyses is to guide the development of predictive models in the subject matter.
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2 Sensitive Models Sensitivity analysis aims to determine which values of independent variables (the so-called input parameters) will affect a specific dependent variable (output variable) given a set of assumptions. Sensitivity analysis is very helpful in selecting the appropriate model structure and simplifying the model by reducing the selected parameters. Another advantage of this technique is the elimination of conceptual and implementation errors. Compared to laboratory test, it is much cheaper and works well during the initial simulations of the studied phenomenon in the planning of experiments. Currently, the most commonly used method is local sensitivity analysis, which is based on numerical or analytical derivatives. The goal is to evaluate the effect of changing the value of a single independent variable on the response variable, while the values of other inputs remain unchanged. In most cases, the input data are not of interest, so it is kept at the appropriate average values. In the presence of a small data set and many parameters, the responses do not change in a regular way with similar parameter changes. From this it follows that the parameter space to be fitted should be reduced by checking which parameters are sensitive and which are not. Given the ease of calculation and simplicity of understanding, local analysis is widely used in both statistical and mechanical modelling [4]. The global sensitivity analysis takes into account the variability of a single input variable, while the values of other predictors may also change. In this way, a holistic assessment of the impact of the predictor variables on the modelled results is made. When evaluating output uncertainties in a multivariate variable space, the global sensitivity function is not constrained by the linearity variable conditions; thus, attributes are included in the introduction of predictive uncertainty functions. Given the purpose of the analysis, there are various global sensitivity analyses that can be divided into screening, regression, or variance-based approaches. Screening studies holistically assess the importance of selected groups of input variables in terms of model prediction uncertainty using cluster analysis on multivariate scatterplots. Screening is initially performed to sort and remove variables that have little impact on the prediction of the model. The regression approach traditionally involves fitting the independent variables to the dependent variable, either by parametric multiple regression in a full or stepwise way. The variance-based approach, on the other hand, evaluates the uncertainty of the predictor on the response variable as a probability distribution from which the response variance is ultimately determined for a single or group of predictors [5, 6].
3 Carried Out Research On the DEMAG-DS.40 screw compressor test stand, tests were carried out on 17 nozzles of various shapes. The value of damping efficiency coefficients was determined on the pressure pulsation damping values and an increased specific compressor
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a)
b)
Fig. 1 a Nozzle cut into three millimeter slices, b highlighted slices are fragments of the nozzle with a narrowing below 21%
power obtained from the carried out experimental investigations. Based on the concept of geometric nozzles, the following parameters were collected, hereinafter referred to as input parameters: • • • • • • •
L1—nozzle length (mm) with removed cross-section of 0–21%, L2—nozzle length (mm) with removed cross-section of 21–42%, L3—nozzle length (mm) with removed cross-section of 42–63%, L4—nozzle length (mm) with removed cross-section of 63–70%, A—liquid contact area (mm2 ), V —gas volume (cm3 ), F—longitudinal force fraction (‰).
In order to determine the parameters L1, L2, L3 and L4, the nozzle was cut into 3 mm thick slices (Fig. 1). The total length of the tested reducers was 120 mm. In Solidworks, the nozzle was therefore divided into 40 equal slices along its axis. The average surface area along the length of one slice (3 mm reducer) was obtained by reading the volume of each slice from the programme and dividing it by the height of the slice. The cross-sectional area of the ring was the same in all slices, which resulted from the method of the nozzle assembly in the installation. The cross-sectional area of the ring was subtracted from the value calculated above (L1, L2, L3, L4). The obtained values were divided by the surface area of the empty pipe. In this way, the percentage degree of covering the cross-section of the installation was obtained. Percentage degrees of cross-section of the installation were divided into 4 (arbitrary) percentage ranges. Figure 1b shows separated slices with narrowing, which classifies the total length of these slices as L1 size. Parameters A, V and F were also determined with the use of CAD software. The output value of the built model was the dimensionless number combining pressure loss in the nozzle and pulsation attenuation (C Dη ). This is quite a specific approach because all the above-mentioned values are non-parametric. In addition, during the tests, none of the parameters were changed, but the entire shape of the nozzle was changed. Further research was carried out to determine which input values have the greatest impact on the pulsations. All input parameters and their values for carried out test are presented in a Table 1.
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Table 1 Input parameters obtained from the carried out research Nozzle
L1
L2
L3
L4
A
V
F
E
120
0
0
0
14,608.41
90.57
0
0
39
18
36
27
8982.60
48.66
0.75
1
18
3
0
99
7334.29
35.73
2.07
2
15
36
48
21
18,451.92
44.81
0.94
3
39
27
30
24
9287.57
48.29
0.76
4
90
30
0
0
13,191.98
68.11
0.98
5
12
42
51
15
33,667.26
40.94
0.95
7b
48
36
36
0
17,539.79
55.91
2.04
7c
48
39
30
3
16,968.73
55.65
0.73
9
39
24
24
33
9063.65
49.31
0.35
11
120
0
0
0
16,003.92
66.35
1.15
13
30
90
0
0
13,098.51
57.54
2.66
19L
105
15
0
0
23,780.35
60.7
1.49
12
120
0
0
0
18,718.37
79.14
1.24
14
120
0
0
0
21,005.19
73.25
1.42
15
57
15
24
24
18,621.12
59.93
1.59
16
60
12
24
24
19,073.23
60.71
1.46
Based on the received data, outliers for calculated values of C Dη (Fig. 2c) were removed from the set of 17 elements (Fig. 2a), which could significantly contribute to the incorrect forecasting of values by the built model. 5 nozzles marked as: empty, 19L, 14, 12 and 16 were removed. Figure 2b shows the C Dη values for which further analysis was carried out. In the next step, the one-at-time (OAT) approach was used. The impact of individual input parameters on the model’s predictive quality was checked. Thus, stepwise regression was carried out in the correct order. It started with models consisting of only one input value (the so-called one-element models), and gradually added input values. Each time, the coefficient of determination was checked, which corresponds to the model’s ability to predict the C Dη value. First, the m number of models was determined, which for seven variables n = 7 is m = 127. K-element models were considered. The number of models of individual elements was determined from the formula (2): Cnk =
n! k!(n − k)!
(2)
where, k-elements of an n-element set. Then, based on the set number of combinations, a regression analysis was performed, as a result of which the following values were observed: R2, R2 adjusted,
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a)
b)
Fig. 2 a C Dη values for all tested nozzles, b C Dη values without outliers
p, F value. After each regression analysis, attention was paid to input values that met the condition for p < 0.05 which are marked with w red X in Fig. 3. The input variables show a significant influence of the model on the predicting of C Dη values only with 4-element models, which can be observed in Fig. 3. Figure 4 shows the values of the determined R2 coefficients for all analyzed models. The dashed line in the graph is a straight line of R 2 = 0.75, which helped to include models worth further analysis. It can be noted that only for two 4 element models and 7 models of 5-elements the obtained R2 value was greater than 0.75. Each 6-element model obtained the same value of R2 = 0.85. However, it should be remembered that when the number of model elements increases, the value of R2 also increases. Therefore, in order to reduce the number of models, the value of adjusted R2 was used. This value is a measure that compares the accuracy of models that contain different numbers of independent variables. While the value of R2 is based on all the elements in the model, the adjusted 2 R adjusts to the number of elements in the model. Importantly, its value increases only when the new element improves the fit of the model more than expected. The adjusted R-squared value decreases when the input element does not improve the model fit sufficiently. Table 2 shows the values of R2 and adjusted R2 .
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Fig. 3 Combinations of models with different numbers of input variables
Fig. 4 R2 values for models that consist of {1, 2, 3, 4, 5, 6} numbers of elements
4-element model number 31 is marked as it’s adjusted R-square values is the highest one. From this, it follows that the following coefficients: L4, A, and V should be taken into account in order to predict C Dη values. Based on the obtained results, it can be concluded that the model can explain about 83% of the variability of the modeled output (dependent) variable. The value of the F statistic and the corresponding level of test probability p confirm a statistically significant linear relationship. In addition, the values of the p-statistic indicate that the intercept and regression coefficients are significantly different from zero, except
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684 Table 2 Values of R2 and adjusted R2 for selected models Model No.
R-Sq
R-sq (adj)
31
0.832
0.719
{L3, L4, A, V}
35
0.755
0.591
{L4, A, V, F}
4
0.834
0.667
{L1, L2, L3, V}
7
0.834
0.667
{L1, L2, L4, A, V}
11
0.834
0.667
{L1, L3, L4, A, V}
15
0.800
0.601
{L1, L4, A, V, F}
16
0.834
0.667
{L2, L3, L4, A, V}
20
0.755
0.510
{L2, L4, A, V, F}
21
0.838
0.676
{L3, L4 A, V, F}
4
0.852
0.631
{L1, L2, L3, A, V, F}
5
0.852
0.631
{L1, L2, L4, A, V, F}
6
0.852
0.631
{L1, L3, L4, A, V, F}
7
0.852
0.631
{L2, L3, L4, A, V, F}
4 element models 5 element models
6 element models
for the L3 coefficient. Figure 5 shows the significance of input parameters for the developed model. On the basis of the obtained model, the values predicted by this model were compared with the actual values (Fig. 6). The obtained results made it possible to determine the error values for the entire model: • a mean percentage error M P E i = 0.199% and • a mean absolute percentage error M A P E i = 9.51%. Figure 6 shows an additional nozzle 9 that was not included in the model creation. Its C Dη value was known and it was used to check the degree of fit of the created
Fig. 5 Significance of input parameters
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Fig. 6 Predicted and real values of C Dη
model. It can be seen that the model predicted value for this nozzle is within the estimated M A P E i error for the entire model. Taking into account the unusual and small set of data taken for analysis, it can be seen that out of the specified input parameters, four of them are important for determining the C Dη value.
4 Conclusions The article uses a predictive model based on classical statistical techniques. The task of the model was to assess the reasonableness of using a shaped nozzle to dampen pressure pulsations in the discharge pipeline of a screw compressor. The issue is important because so far there is no method of designing this type of pressure pulsation nozzles. The one at a time approach was used in the article to select the most important geometrical parameters of shaped nozzles to estimate the damping efficiency coefficient. In the developed model, four geometric parameters were selected that best predict C Dη values. The following parameters in the given order created a predictive model with a prediction accuracy of 83%: nozzle length with a removed cross-section of 63–70% (L4), gas volume (V ), liquid contact area (A), nozzle length with a removed cross-section of 42–63% (L3). The approach described in the article is preliminary and further research should be carried out to obtain bigger data set in order to develop more accurate model for estimation of damping efficiency coefficient. Acknowledgements This research was funded by Polish National Centre for Research and Development, grant number LIDER/40/0140/L-11/19/NCBR/2020.
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References 1. P. Młynarczyk, P. Cyklis, The application of nozzles for the attenuation of volumetric compressor pressure pulsation. Int. J. Refrig. 90, 108–118 (2018) 2. P. Młynarczyk, P. Cyklis, The estimation of the pressure pulsation damping coefficient of a nozzle. J. Sound Vibr. 464 (2020) ´ 3. P. Młynarczyk, D. Brewczy´nski, J. Krajewska-Spiewak, P. Lempa, J. Bł˛adek, K. Chmielarczyk, Pressure Pulsation and Pipeline Vibration Damping with the Use of 3D Printed Nozzles Mechanisms and Machine Science, vol. 125. (Springer, 2022) 4. N. Bilal, D. Adams, J. Park, Uncertainty and sensitivity analysis of gas pulsations in the suction manifold of a multi-cylinder automotive compressor, in International Compressor Engineering Conference (2006), Paper 1739 5. A. Saltelli, K. Chan, E.M. Scott, Sensitivity Analysis (Wiley Chichester, 2000) 6. N. Bilal, D. Adams, Pulsation energy in the suction manifold of a reciprocating compressor as a measure for parameter sensitivity. J. Vibr. Acoust. 137(2) (2015)
Hydrogen Compression
Effects of Oil Compressibility on the Thermal Performances of Diaphragm Compressors Used in the Hydrogen Refuelling Station with a Mathematical Method Yaling Zhao, Jiatong Zhang, and Xueyuan Peng
Abstract The diaphragm compressor is one of the most commonly utilized compressor types in hydrogen refuelling stations. When employed at high pressure, oil expansion produces significant volume loss in the diaphragm compressor. Oil compressibility effects must be considered when designing the high-pressure diaphragm compressor, else the real flow rate will be much lower than expected. To further understand the effects of oil compressibility on the thermal performance of the compressor, a mathematical model that took oil compressibility into account was given in this work to mimic the thermodynamic process, and experiments were conducted to validate this model. The results indicate that lowering the oil compressibility is a good way to improve the thermal performance of the diaphragm compressor. When the oil bulk modulus rose from 800 to 1200 MPa, the volumetric efficiency grew by 10%, the isentropic indicated efficiency increased by 1.7%, and the minimum suction pressure reduced by 2.1 MPa. Keywords Hydrogen refuelling station · Diaphragm compressor · Thermodynamic process · Performance analysis
1 Introduction The diaphragm compressor is one of the best choices for compressing equipment used in hydrogen refuelling stations because it can guarantee the purity of the compressed gas, produce no pollution during the working process, and is appropriate for the high-pressure requirement of 90 MPa [1]. However, the diaphragm compressor application procedure has been plagued by low efficiency. Some studies on how to improve the performance of the compressor have been conducted in the last few decades. A single-stage diaphragm compressor Y. Zhao · J. Zhang · X. Peng (B) School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_55
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produced by PDC was put to the test by Allen for flow rate and efficiency, and the results were compared with theoretical analysis [2]. The findings indicated that the oil performance showed be utilized to determine the diaphragm compressor’s power consumption rather than the standard way of using gas performance. Frantz et al. [3] specified that the gas cavity profile restricted the ability of the gas to reach the discharge check valve and optimized the structure to gain more capacity by increasing the number and size of the grooves in the gas cavity. Jia et al. pointed out that the cavity profile affects not only the diaphragm life but also the flow rate [4]. They found that the clearance volume of a single exponential term cavity profile was larger than that of a multi-exponential term cavity profile for the same volume of film cavity, and they then developed a new design method, which was centred on lowering the clearance volume. The lower efficiency was brought on by the high pressure and high temperature when the compressor is employed in the hydrogen refuelling station, which must guarantee a discharge pressure of 90 MPa. Ren at el. [5] noted that the influence of oil compressibility is the main reason for low volumetric efficiency in a diaphragm compressor, and by comparing the results under different cases, they found that reducing oil volume and increasing oil bulk modulus are important methods to improve the efficiency of a diaphragm compressor. Although diaphragm compressors have been used in many engineering applications, there is still no mathematical model for their design. Most diaphragm compressor graphic sizes were usually determined according to empirical formulas of piston compressors. A reasonable mathematical model is in need under this circumstance. Fortunately, there are plenty of mature thermodynamic models for other reciprocating compressors adopting methods of lumped parameter [6] or computational fluid dynamics (CFD) [7] methods. The movement of the valve disc [8], line pulsation [9], and heat exchange phenomena [10] were studied in different ways. These researches provide an important reference for the thermodynamic model of diaphragm compressors. In this study, a numerical model of the thermodynamic process of the diaphragm compressor was established taking into account the oil compressibility. According to this model, the p–V diagram of oil can be obtained. After the experimental verification of the reliability of the model, the effects of oil compressibility on the performances of the diaphragm compressor, such as the flow rate, power consumption, and the range of the suction pressure were studied using this model.
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2 Methodology 2.1 The Working Process Analysis of a Diaphragm Compressor Figure 1 demonstrates the structure and fluid domain of the diaphragm compressor head. It can be seen that the diaphragm separates the fluid domains of the gas and oil, and this unique structure may guarantee the purity of the compressed gas. The hydraulic oil flow is driven by the piston’s back-and-forth motion, which causes the diaphragm to deform and complete the gas compression. During the working process, the diaphragm sinks with the pressure difference between the oil and gas, but the pressure difference needed is much lower than the working pressure. Therefore, when the diaphragm is not attached to the surface of the gas head cover or the oil distribution plate, it can be assumed that the gas pressure and the oil pressure are equal. The letters p, T, m, V, and dm represent the pressure, temperature, mass, volume, and the differential of the mass, respectively. And the subscripts g, gs, gd, l, ls, and ld mean the parameters of internal gas, suction gas, discharge gas, internal oil, suction oil, and overflow oil, respectively. Figure 2 depicts the typical relationship between the dynamic oil pressure and gas pressure, with a suction pressure of 15 MPa and a discharge pressure of 90 MPa. Gas head cover
Oil distribution plate
pld, dmld
Oil pressure limiter Oil head support
Suction valve
Piston
pgs, Tgs, dmgs pgl, Tgl, dmgd Discharge valve
Control volume of oil
Control volume of gas pg, Tg, mg, Vg
pl, ml, Vl Diaphragm
pls, dmls
Oil non-return valve
Fig. 1 Structure and fluid domain of the diaphragm compressor head
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Fig. 2 Gas pressure and oil pressure variations in a cycle
From 0° to 180°, the piston moved from the top dead centre (TDC) to the bottom dead centre (BDC). The oil expanded from the oil overflow pressure to the discharge pressure in the first 30°, and the gas and oil then expanded simultaneously to the suction pressure. Between 100° and 180°, gas in the pipeline was transported into the compressor during that time. The piston started to move reversely to the TDC at 180°, and the gas and oil were compressed together to the discharge pressure at 310°. After that, the oil pressure continued to increase while the gas pressure stayed the same because the piston’s movement only reduced the oil control volume when the diaphragm was attached to the surface of the gas head support.
2.2 Mathematical Model The model was built in different phases according to the gas and oil pressure, and the displacement of the diaphragm centre, without thinking about the leakage of the gas and oil and heat transfer during the working process. The valves were also simplified as an orifice. Compressed gas was thought of as the ideal gas. The compressibility was assumed to be constant and the thermal expansivity of oil was disregarded. Based on these presumptions, the control equations can be obtained. For the gas control volume, the energy conservation equation, the mass conservation equation, and the equation of state can be expressed as follows: dm gd dm gs dWg d(m g u g ) h gs = + h gd + , dθ dθ dθ dθ
(1)
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dm gs dm g dm gd = − , dθ dθ dθ
(2)
pg Vg = m g RTg ,
(3)
where θ is the crank angle, h and u are the specific internal energy and enthalpy of the gas, respectively, R is the molar gas constant, and W is the external output work. Considering the properties of the ideal gas, shown in Eqs. (4)–(7), the gas pressure change with the control volume change can be written as Eq. (8). h g = C p Tg ,
(4)
u g = Cv Tg
(5)
R=C p − Cv
(6)
k=
Cp Cv
d pg kpg dVg kpgs vgs dm gs kpg vg dm gd =− + − dθ Vg dθ Vg dθ Vg dθ
(7) (8)
where v is the specific volume of the gas, and k is the specific heat ratio. For the oil control volume, according to the definition of the oil bulk modulus, as Eq. (9) shows, the oil pressure change with the oil control volume can be written as Eq. (10). β = ρl
d pl dρl
β dm l β dVl d pl = − dθ m l dθ Vl dθ
(9) (10)
where β is the bulk modulus of the oil, and ρ is density. The volume change induced by the piston movement can be expressed as follows: [ ] dV pis S λ sin θ cos θ = A pis sin θ + √ dθ 2 1 − λ2 sin2 θ
(11)
where A is the area of the piston’s end face, S is the length of the stroke, λ is the crank-to-connecting-rod ratio, and pis is the subscript for the piston. The working process was divided into six phases, as shown in Fig. 2. The gas volume and mass stayed constant throughout Phase I and VI, while the oil volume changed with the piston movement. When the oil pressure exceeded the oil
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overflow pressure, the oil mass decreased. The following are the control equations: ⎧ d pg ⎪ ⎪ =0 ⎨ dθ β dm ld β dV pis d pl ⎪ ⎪ =− − ⎩ dθ m l dθ Vl dθ
(12)
During Phase II, III, IV, and V, the gas pressure was nearly equivalent to the oil pressure. As a result, the control equations of these phases are as follows: ⎧ dp g ⎪ ⎪ ⎪ ⎪ dθ ⎪ ⎪ ⎪ ⎪ d pl ⎪ ⎪ ⎨ dθ ⎪ d pl ⎪ ⎪ ⎪ ⎪ ⎪ dθ ⎪ ⎪ ⎪ ⎪ ⎩ dVg dθ
kpg dVg kpgs vgs dm gs kpg vg dm gd + − Vg dθ Vg dθ Vg dθ β dm ls β dVl = − m l dθ Vl dθ d pg = dθ dV pis dVl + = dθ dθ =−
(13)
3 Experimental Validation To verify the simulation results were reasonable, an experiment was set up with a second stage of a two-stage diaphragm compressor, as shown in Fig. 3. A dynamic oil pressure sensor put on the oil head support detected the oil pressure, and an eddy current sensor was installed to detect the signal when the piston reached the point at BDC. Additionally, the experiment was conducted with air as the working fluid, and the rotational speed of the compressor is 420 rpm, with a suction pressure of 15 MPa and a discharge pressure of 80 MPa. The oil volume was 2.5 times the stroke volume, and the clearance volume was 20% of the stroke volume. The oil overflow pressure was set at 95 MPa. The p–V diagrams obtained by simulation and experiment are shown in Fig. 4. It can be seen that the simulation result agrees well with the experimental data, with less than 7% inaccuracy at the same point during a circle. The volumetric efficiencies were also compared under different suction pressures, as shown in Fig. 5. The result shows that the errors between the simulation and experiment were less than 7%, which was caused by the neglect of the gas leakage and heat transfer during the working process.
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Fig. 3 Test rig of dynamic oil pressure of a diaphragm compressor Fig. 4 Comparison of the simulation and experiment results
4 Results and Discussion This part focuses on the effects of oil compressibility on the diaphragm compressor utilised in the hydrogen refuelling station. The working fluid was changed to hydrogen while other parameters kept unchanged comparing the last part. The
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Fig. 5 Comperation of the volumetric efficiencies obtained by simulations and experiments
impacts were studied in three ways, with the oil bulk modulus set at 800, 900, 1000, 1100, and 1200 MPa. The performances were compared under the same working conditions, which included a suction pressure of 15 MPa, a discharge pressure of 90 MPa, and an oil overflow pressure of 100 MPa.
4.1 Effects on the Diaphragm Deformation and Flow Rate In the previous design, the maximum deflections to the oil side and gas side were assumed to be equal. To avoid diaphragm contact with the surface of the oil distribution plate, the volume of the gas-side cavity is usually half of the stroke volume, and the volume of the oil-side cavity is 1.2 times the gas-side cavity. Figure 6 shows the centre deflection variation of the diaphragm during a cycle. Deflection to the gas side was referred to as positive deflection, whereas deflection to the oil side was referred to the negative deflection. It can be seen that the diaphragm cannot bend to the design place because of the hydraulic oil expansion, resulting in a significantly lower flow rate than intended. Figure 7 shows the changes in the volumetric efficiency and the maximum deflection change during a cycle with the bulk modulus. The result indicates that both the volume efficiency and the deflection change gradual increase with the raise of the bulk modulus. In this study, with a 100 MPa increase in the oil bulk modulus, the volumetric efficiency grew by 2.5%. These findings are understandable because the stroke volume and the clearance volume expansion were certain, but the expansion volume of the oil increased with the decrease of the oil bulk modulus. As a result, the
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Fig. 6 The variation of the deflection in the diaphragm centre with the crank angle under different bulk modulus
suction volume of gas, which equals the stroke volume minus the expansion volume of oil and the clearance volume, decreased with the oil bulk modulus.
Fig. 7 The volumetric efficiency and deflection change of the diaphragm changes with the bulk modulus
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4.2 Effects on the Power Consumption Figures 8, 9 and 10 present the p–V diagrams of overall fluid, compressed gas, and hydraulic oil at various oil bulk moduli values. The indicated power of gas, displayed as the area of the gas p–V diagram in Fig. 9, decreased with the rise of oil bulk modulus because of the reduction of the suction volume. On the contrary, the indicated power of oil increased with the oil bulk modulus, as illustrated by the area of the oil p–V diagram in Fig. 10. Although the oil power consumption reduced with the oil bulk modulus increase, the deduction was far smaller than the increase in gas power consumption. As a result, total power consumption increased in tandem with the oil bulk modulus, as shown in Fig. 8. Figure 11 shows that as the oil bulk modulus increased, the isentropic indicated efficiency increased slightly. The isentropic indicated efficiency here is defined as the ratio of the isentropic power to the indicated power of the overall p–V diagram. One of the primary causes of power loss is the power used to compress oil, and the loss grew as the oil bulk modulus decreased. Another kind of power loss was caused by the pressure loss during the suction and discharge processes. The suction and discharge power loss rose as the oil bulk modulus raised because the suction and discharge processes were prolonged. However, the ratio of the loss caused by the pressure loss to the indicated power, which is about 5%, did not change when the oil bulk modulus increased from 800 to 1200 MPa. It can be concluded that the main reason the isentropic indicated efficiency declined when the oil bulk modulus decreased is due to an increase in oil-compressed power.
Fig. 8 Overall p–V diagrams under different bulk modulus
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Fig. 9 p–V diagrams of gas
Fig. 10 p–V diagrams of oil
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Fig. 11 The change of isentropic indicated efficiency with the oil bulk modulus
4.3 Effect on the Suction Pressure Range Figure 12 shows that the volumetric efficiency fell as the suction pressure decreased and that when the suction pressure was reduced to 10 MPa, the volumetric efficiencies were less than 20% for all bulk moduli in this study. Figure 13 depicts the suction pressure ranges required to achieve a volumetric efficiency greater than 20%, assuming a maximum suction pressure of 20 MPa. When the oil bulk modulus rose from 800 to 1200 MPa, the minimum pressure was reduced by 2.1 MPa. The findings indicate that increasing the oil bulk modulus can broaden the suction pressure range.
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Fig. 12 Volumetric efficiency changes with the suction pressure at different oil bulk moduli Fig. 13 Range of suction pressure at different oil bulk moduli
5 Conclusion This paper built a numerical model to investigate the effects of oil compressibility on the performances of a diaphragm compressor used in a hydrogen refuelling station. The measured p–V diagram of air validated this model. After that, the effects on the flow rate, power consumption, and suction pressure range were studied using this model. The following are the key conclusions.
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• The expansion of oil causes inadequate deformation of the diaphragm, resulting in the compressor cannot reach the design flow rate. The efficiency reduction due to oil expansion becomes worse when the oil bulk modulus decreases. With a 100 MPa decrease in the oil bulk modulus, the volumetric efficiency decreases by 2.5% when the oil volume is 2.5 times of the stroke volume. And due to the increase of volumetric efficiency loss, the suction pressure range becomes smaller, when the oil bulk modulus decreased from 1200 to 800 MPa, the minimum suction pressure is reduced by 2.1 MPa. • The effect of oil compressibility on the isentropic indicated efficiency is very small because the power used to compress oil takes a small part in the power consumption. The isentropic efficiency increased slightly with the oil bulk modulus. When the oil bulk modulus increased from 800 to 1200 MPa, the isentropic indicated efficiency raised by 1.7%. • Oil compressibility cannot be ignored when the diaphragm compressor is used in high-pressure conditions. The mathematic model built in this study considered the oil compressibility, and the p–V diagram obtained by the mathematic model agreed well with the experiment’s data. This model provides a good way to predict the thermal performance of the diaphragm compressor used in the hydrogen refuelling station.
References 1. G. Sdanghi, G. Maranzana, A. Celzard, V. Fierro, Review of the current technologies and performances of hydrogen compression for stationary and automotive applications. Renew. Sustain. Energ. Rev. 102, 150–170 (2019). Elsevier 2. A.L. Allen, Efficiency and performance measurements of a PDC Inc. single stage diaphragm hydrogen compressor. Humboldt State University (2009) 3. G. Frantz, R. Eizember, J. Vazquez, Capacity improvement of large, two stage diaphragm compressor, in Proceedings of the 42nd Turbomachinery Symposium, Texas A&M University. (Turbomachinery Laboratories, 2013) 4. X. Jia, Y. Zhao, J. Chen, X. Peng, Research on the flowrate and diaphragm movement in a diaphragm compressor for a hydrogen refueling station. Int. J. Hydrogen Energ. 1–10 (2016) 5. S. Ren, X. Jia, J. Jiang, S. Zhang, B. Zhao, X. Peng, Effect of hydraulic oil compressibility on the volumetric efficiency of a diaphragm compressor for hydrogen refueling stations. Int. J. Hydrogen Energ. 47, 15224–15235 (2022) 6. T. Dutra, C.J. Deschamps, A simulation approach for hermetic reciprocating compressors including electrical motor modeling. Int. J. Refrig. 59, 168–181 (2015) 7. A. Nakano, K. Kinjo, CFD applications for development of reciprocating compressor (2008) 8. B. Zhao, X. Jia, S. Sun, J. Wen, X. Peng, FSI model of valve motion and pressure pulsation for investigating thermodynamic process and internal flow inside a reciprocating compressor. Appl. Therm. Eng. 131, 998–1007 (2018) 9. B. Xu, Q. Feng, X. Yu, Prediction of pressure pulsation for the reciprocating compressor system using finite disturbance theory. J. Vibr. Acoust. 131 (2009) 10. J. Tuhovcak, J. Hejcik, M. Jicha, Comparison of heat transfer models for reciprocating compressor. Appl. Therm. Eng. 103, 607–615 (2016)
Study of Effects of Hydraulic Parameters on the Motion of the Free Piston in Ionic Liquid Compressors in Hydrogen Refuelling Stations Yi Jin, Jiacheng Jiang, and Xueyuan Peng
Abstract The innovative ionic liquid compressor, in which the free piston is in place of the cranked connecting rod piston the hydraulic free piston, is a promising type of compressor for hydrogen refuelling stations. It is necessary to calculate and analyse the motion of the free piston, which is crucial for the performance of the compressor and determined by the hydraulic system. This paper developed a fluid– structure interaction method for the effects on the piston dynamic characteristics of three major hydraulic parameters: buffer clearance, oil charging flow rate, and oil overflow pressure. The results showed that the buffer clearance influenced the asymmetry of the piston motion and the actual location of the BDC by changing the piston velocity and the oil pressure, with the most optimum value of 0.5 mm. The actual BDC was also affected by the oil charging flow rate, which determined the minimum oil pressure, with the most optimum value of 120 L/min. The actual position of TDC was affected by the oil overflow pressure, which can reduce the impact. The most ideal value was 32.5 MPa. Keywords Hydrogen · Ionic liquid compressor · Hydraulic system · Free piston
1 Introduction Nowadays, with the world facing an energy crisis and environmental pollution, the development of green energy sources has become a hot topic [1]. Hydrogen plays an important role in addressing energy and pollution issues due to its advantages of renewability, broad sources, high energy density, zero-emission, and storability [2]. The hydrogen fuel cell vehicle (HFCV) is an essential application case for hydrogen energy. Its development encourages infrastructure development for hydrogen generation, storage, and transportation, including hydrogen refuelling stations, which link upstream, midstream, and downstream sectors of the hydrogen energy industry [3]. Y. Jin · J. Jiang · X. Peng (B) School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_56
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With the growing global emphasis on hydrogen energy, there is a severe shortage of hydrogen refuelling stations in various countries, with the construction of a large number of stations on the horizon. The mainstream high-pressure gas hydrogen refuelling station consists of compressors, storage tanks, precoolers, and dispensers, among which the highestcost compressor is the only moving equipment and is considered to be the core equipment of the station [4]. Numerical types of compressors are applied to the hydrogen refuelling station, including diaphragm compressors [5], reciprocating compressors [6], hydraulic-driven piston compressors [7], ionic liquid compressors [8], metal hydride compressors and electrochemical compressors. Among these, the ionic liquid compressor is a new and promising design, in which the conventional cranked connecting rod piston is replaced by a liquid piston and a free piston. Ionic liquids do not contaminate hydrogen when used as liquid pistons in the compressor due to zero evaporation characteristics and very low hydrogen solubility. The liquid piston replaces the traditional piston ring with the liquid seal and replaces lubricating oil with ionic liquids, which eliminates the hydrogen leakage and contamination in reciprocating compressors, diaphragm compressors and liquid-driven compressors. Meanwhile, the liquid piston can conform to the irregular chamber volume, which can enhance heat exchange and improve the efficiency of compression. James D found that the liquid piston decreased the energy consumption by 19% over the solid piston at the same operating conditions by building a simulation model [9]. The benefits of the liquid piston in the compressor cylinder are attributed to the regulation of its movement by the free piston. The free piston drives the reciprocating motion of the piston with hydraulic fluid instead of a crank-link mechanism, which reduces the number of moving components and benefits the customizability of the piston motion. It has a wide range of uses due to fewer moving parts, lower lateral force, and lower friction loss, and it has gained popularity in recent years. Among these studies, the dynamic characteristics of the free piston have been a critical theme, which has a crucial role in determining the performance of the whole machine. Mikalsen et al. created a 0D model to study the basic dynamic characteristics of the free piston in an internal combustion engine, then, based on which, a 3D model was developed by coupling the dynamics of the free piston with the working process of the in-cylinder to study the relationship between piston dynamics and in-cylinder flow [10]. Chen et al. used Amesim to establish a 1D simulation model of a hydraulic free-piston engine to research the relationship between the gas exchange process and piston dynamics. Furthermore, they established a CFD model and the results showed that optimizing the exhaust pulse could improve the volumetric efficiency [11]. However, little research about the ionic liquid compressor has been published up to now, not to mention the free piston in it. Therefore, this paper proposed an FSI model by coupling the dynamics of the free piston and the compression process in an ionic liquid compressor and analysed the effect of three hydraulic parameters on piston dynamic characteristics. All of these can contribute to the design of the ionic liquid compressor.
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2 Basic Structure and Physical Model of the Ionic Liquid Compressor Figure 1 illustrates the basic structure of the ionic liquid compressor, which comprises primarily the compressor, the radial plunger pump, and the hydraulic system. The compressor component consists of a gas compression cylinder, a hydraulic oil cylinder, and a free piston. The gas piston is at the top of the free piston, while the oil piston is at the bottom. The pressure ratio between the gas in the compression gas cylinder and the oil in the hydraulic oil cylinder is determined by the area ratio of the gas piston to the oil piston. A two-stage buffer plunger is connected to the oil piston, and the lower end of the hydraulic oil cylinder includes a two-stage buffer hole, as shown in Fig. 2. The pump part is a radial plunger pump with an eccentric cam that pushes the plunger, in turn, to supply and discharge oil. The hydraulic system has three elements: the main oil circuit, the oil overflow circuit, and the oil charging circuit. The main oil circuit is a bi-directional oil circuit that connects the compressor oil cylinder of the compressor and the pump. The hydraulic oil flows from the pump to the compressor during the suction gas phase, and from the compressor to the pump during the compression and discharge gas phases. The oil overflow circuit releases
Suction valve Discharge valve
Compressor
Gas cylinder
H2
Main oil circuit
Oil
Oil overflow circuit
ILs
Oil charging circuit
Gas piston
Pump oil cylinder
Radial plunger pump
Liquid piston
Free piston Oil piston Oil cylinder
Buffer plunger
Buffer hole
Pump plunger
Charge pump
Fig. 1 Structure of the ionic liquid compressor
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First stage buffer hole
Second stage buffer hole
d1
Oil piston
First stage buffer plunger
d2
Main oil port
d3
Second stage buffer plunger
the oil from the main oil circuit through the overflow valve. The oil charging circuit delivers hydraulic oil from the charge pump to the main oil circuit, with the excess oil returning to the tank. The operation of the ionic liquid compressor can be separated into four steps, as shown below: (1) Gas suction and oil discharge: The suction valve opens, and gas enters the gas compression cylinder, pushing the free piston from the top dead centre (TDC) to the bottom dead centre (BDC), discharging hydraulic oil from the compressor hydraulic oil cylinder back to the oil cylinder of the radial pump along the main oil circuit, and moving the radial pump plunger from TDC to BDC. (2) Buffering and oil charging: When the buffer plunger beneath the free piston enters the buffer holes, the free piston decelerates until it hits the design BDC and its speed is zero. During this procedure, the main oil circuit is not connected to the oil cylinder of the compressor due to the aperture throttling effect of buffer holes, causing the oil pressure in the main oil circuit to drop, and allowing the oil charging to occur. (3) Oil supply and gas compression: The gas suction ceases when the free piston speed reverses, and the cam of the pump pulls the plunger to TDC, supplying oil to the compressor oil cylinder. The free piston is moved to the TDC to compress the gas as the oil pressure rises. (4) Gas discharge and oil overflow: When the gas pressure reaches the discharge pressure, the discharge valve opens, and the free piston continues to move to the TDC. If the hydraulic oil pressure exceeds the predetermined oil overflow pressure, the overflow valve will open, and a portion of the hydraulic oil will overflow to keep the oil pressure and gas pressure stable. In this study, a 90 MPa five-stage compressor applied in hydrogen refuelling stations is investigated. The third stage is selected as an example for analysis, with a suction pressure of 4.2 MPa, a discharge pressure of 12.4 MPa, a pressure ratio of 2.95, and a frequency of 5.8 Hz. The main design and structural parameters are shown in Table 1. It is worth noting that the primary goal of this paper is to analyse the effects of hydraulic parameters on the motion of the free piston in ionic liquid compressors.
Study of Effects of Hydraulic Parameters on the Motion of the Free … Table 1 Main design and structure parameters of the ionic liquid compressor
Parameter Pressure of the suction gas (MPa) Pressure of the discharge gas (MPa)
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Value 4.2 12.4
Compression ratio
2.95
Frequency (Hz)
5.8
Diameter of the gas piston (m)
0.08
Diameter of the oil piston (m)
0.05
Stroke of the piston (m)
0.13
Further research on the CFD simulation and experimental validation of this aspect will be carried out in the future.
3 Mathematical Modelling The motion of the free piston is determined by the forces acting on it, which are analyzed as shown in Fig. 3. The mechanical model can be represented as Eq. (1). M
d2 x = Fg − Fg1 + Fg2 − Fh + Mg − F f , dt 2
(1)
where M is the mass of the piston, which is 5 kg in this case, Fg is the gas force in the gas cylinder, Fg1 and Fg2 are the forces of atmospheric pressure acting on the gas and oil pistons, Fh is the hydraulic oil force, and F f is the frictional force on the Fig. 3 Forces acting on the free piston
FILs
Fg Fg1 Mg Fg2
Ff
Fh
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piston, including both Coulomb friction Fc f and viscous friction c xsgn( ˙ x), ˙ x is the displacement of the free piston, g is the gravity acceleration, and t is the time. The gas force acting on the free piston can be calculated by Eq. (2). Fg =
π 2 d pg , 4 g
(2)
where dg is the diameter of the gas piston, and pg is the gas pressure in the gas cylinder, which can be calculated by the process equation for gas compression as described by Eq. (3). dVg d pg = −n , pg dt Vg dt
(3)
where n is the compression process coefficient, and Vg is the gas volume. As a result, the relationship between piston displacement and gas force can be obtained by Eq. (4). dFg n dx =− , Fg dt x0 + x dt
(4)
where x0 is the length of the clearance space in the gas cylinder. The oil force on the piston can be solved by Eq. (5). Fh =
π 2 π 2 π d1 − d22 pi + d2 − d32 pi + d32 pi i = 1, 2, 3, 4 4 4
(5)
where d1 , d2 and d3 are the diameter of the oil piston, first stage buffer plunger and the second stage plunger, equal to 0.08 m, 0.035 m and 0.02 m. respectively. pi is the oil pressure of the buffer hole of stage i. The density of the hydraulic oil can be represented by ρ = m/V , the differential form which can be obtained as shown in Eq. (6). 1 dm m dV dρ = − 2 , dt V dt V dt
(6)
where ρ, m, V are the density, mass, and volume of the oil. When the compressibility is accounted for, the pressure of the oil can be expressed using Eq. (7). dρ 1 dm 1 dV dp =K =K − , dt ρdt m dt V dt
(7)
where K is the bulk modulus of the oil, which is 1200 MPa in this case. By solving for dm and dV in each chamber at each stage, Eq. (7) can be used to dt dt compute the oil pressure, which in turn calculates the oil force.
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The volume change of the gas and oil cylinders can be calculated based on the geometry when the piston moves, and then the pressure change of the gas and oil can be obtained by adding the continuity equation. The gas and oil forces on the piston can then be calculated and fed back into the piston mechanical model to recalculate the piston displacement. The dynamic characteristics can be obtained through iterations by implementing the mathematical model in the Amesim software. It is worth noting that the primary goal of this paper is to study the effects of hydraulic parameters on the motion of the free piston through simulations. Further research on the experimental validation and higher fidelity simulation of this aspect will be carried out in the future.
4 Results and Discussions 4.1 The Effect of the Buffer Clearance on the Piston Dynamic Characteristics The buffer clearance, represented by δ, is the clearance between the diameter of the buffer plunger and the buffer chamber. Figure 4 represents the simulation results with buffer clearance of 0.2, 0.3, 0.4, 0.5, 0.6, and 0.7 mm. The buffer clearance affected the deceleration of the free piston. As illustrated in Fig. 4a, the piston velocity was 2.5 m/s before the buffer process. When the buffer clearance was 0.2 mm, the piston decelerated to 0.4 m/s, whereas it decelerated to 1.5 m/s when the buffer clearance was 0.5 mm/s. When the clearance increased to 0.7 mm, the piston can only decelerate to 1.9 m/s, a very poor deceleration effect. It suggests that decreasing the buffer clearance can improve piston deceleration. The buffer structure, in addition to decelerating the piston, created a sudden increase in oil pressure in the buffer hole, as seen in Fig. 4b. The pressure in the bottom of the compressor oil cylinder was 9 MPa before the buffer process began, increased to 27 MPa when the buffer clearance was 0.2 mm, and only slightly increased to 12 MPa when the buffer clearance raised to 0.7 mm. Excessive pressure pulses may cause mechanical structure damage and should be avoided as far as possible. As illustrated in Fig. 4c, the clearance had a substantial impact on the actual location of BDC. The actual BDC was 102 mm with a buffer clearance of 0.2 mm and increased with the buffer clearance. When the buffer clearance increased to 0.5 mm, the actual BDC was 127.5 mm, which was raised by 25%. Additionally, the piston hit the cylinder at BDC when the buffer clearance was greater than 0.5 mm. Besides that, the buffer clearance had little influence on the actual location of TDC. For all values of the clearance, with the exception of 0.2 mm, the actual TDC was near 0 mm. Figure 4c also demonstrates how the buffer clearance influenced the asymmetry of the piston motion. The free piston reversed at the angle of 186° when the buffer clearance was 0.5 mm, with a 6° delay (i.e. 1/60 cycles) compared with the crank rod piston, and at 211° when the buffer clearance was reduced to 0.2 mm, with a
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(a)
(b)
(c)
160
δ=0.2mm δ=0.5mm
Displacement (mm)
140 120
δ=0.3mm δ=0.6mm
δ=0.4mm δ=0.7mm
Design BDC = 130 mm
100 80 60 40 20 Design TDC = 0 mm
0 0
60
120
180 240 Angle (°)
300
360
Fig. 4 Simulation results of various buffer clearances. a Velocity of the free piston; b oil pressure in the bottom of the compressor oil cylinder; c displacement of the free piston
31° delay (i.e. nearly 1/12 cycles). Therefore, a smaller buffer clearance results in a more pronounced asymmetry of piston motion. There were certain fluctuations in both curves of piston velocity and oil pressure due to the fact that the medium used to transmit power to the free piston was hydraulic oil, rather than a rigid crank-link mechanism. In conclusion, the buffer clearance should be less than 0.6 mm in order to prevent from the cylinder hitting at BDC resulting in an unsteady state.
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4.2 The Effect of the Oil Charging Flow Rate on the Piston Dynamic Characteristics Figure 5 displays the calculation results for the plunger pump flow rates of 60, 80, 120, 140, and 160 L/min, respectively. As shown in Fig. 5a, the piston hit the cylinder when the flow rate of the charge pump was 60 L/min. with the flow rate raised gradually, the actual location of BDC steadily dropped. It decreased to 120 mm when the flow rate was 120 L/min and to 105 mm when the flow rate was 160 L/min. In addition, as shown in Fig. 5b, when the flow rate was 160 L/min, the minimum oil pressure was 7.7 MPa. As the flow rate decreased to 80 L/min, the minimum pressure dropped to 0.4 MPa. The minimum oil pressure decreased with the oil charging flow rate. When the flow rate was 60 L/min, the minimum oil pressure was almost dropped to below the atmospheric pressure. It can be explained that the oil pressure of the main oil circuit abruptly dropped at the beginning of the buffer process due to the aperture throttling effect and eventually reach the minimum oil pressure. During this phase, the oil charging process supplies oil to the main oil line. Hence the flow rate of the oil charging will affect the minimum oil pressure. When the oil charging flow rate is too low, negative oil pressure will take place, which can cause serious damage to the hydraulic system and needs to be avoided. (a)
qc=60 L/min qc=140 L/min
Displacement (mm)
140
qc=80 L/min qc=160 L/min
(b)
qc=120 L/min
Design BDC = 130 mm
120 100 80 60 40 20
Design TDC = 0 mm
0 0
60
120
180 240 Angle (°)
300
360
Fig. 5 Simulation results of various oil charging flow rates. a Displacement of the free piston; b oil pressure of the main oil port
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In conclusion, the flow rate of the oil charging pump should be larger than 120 L/ min in order to prevent from the cylinder hitting at BDC and the negative oil pressure.
4.3 The Effect of the Oil Overflow Pressure on the Piston Dynamic Characteristics Figure 6 shows the simulation results of various oil overflow pressure. According to Fig. 6a, the location of the actual TDC was 16 mm when the overflow pressure was 32 MPa. It was reduced to 5 mm when the overflow pressure increased to 32.5 MPa. As the overflow pressure increased further, the actual TDC was near 0 mm, resulting in a cylinder collapse. Figure 6b shows the oil pressure at the main oil port of various overflow pressures. It can be seen that when the overflow pressure is greater than 33 MPa, a significant increase in oil pressure occurred when the piston hit the cylinder at TDC. When the overflow pressure was 35 MPa, the oil pressure rose to 36.5 MPa, then fluctuated continuously. The oil pressure rapidly rises during the compression stage, and once it surpasses the overflow pressure, the overflow valve opens to relieve the pressure and decelerate (a)
160
pov=32MPa pov=33.5MPa
Displacement (mm)
140
pov=32.5MPa pov=33MPa pov=35MPa Design BDC = 130 mm
(b)
120 100 80 60 40 20 Design TDC = 0 mm
0 0
60
120
180 240 Angle (°)
300
360
Fig. 6 Simulation results of various oil overflow pressure. a Displacement of the free piston; b oil pressure of the main oil port
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the piston. Therefore, the overflow valve is a limit at the TDC of the free piston. In conclusion, the oil overflow pressure should be less than 33.5 MPa in order to prevent from the cylinder hitting at TDC.
5 Conclusions In this article, an FSI model of the free piston in the ionic liquid compressor applied in hydrogen refuelling stations was developed. Based on this model, the investigation of the effect of three hydraulic paraments on the piston dynamic characteristics was carried out. The main conclusions obtained from this work are as follows. 1. The sudden change of the piston velocity and oil pressure near BDC, the actual position of BDC and the asymmetry of the piston movement were all influenced by the buffer clearance. When the buffer clearance was increased from 0.2 to 0.7 mm, the deceleration of the free piston was reduced by 1.5 m/s, the increase in oil pressure was reduced by 15 MPa, the actual location of BDC was increased by 28 mm, and the piston reverse time was delayed by 25°. The optimum buffer clearance is 0.5 mm. 2. The oil charging flow rate had an effect on the actual location of BDC and minimum oil pressure. When the oil charging flow rate was reduced from 160 to 60 L/min, the actual location of BDC went from 105 to 130 mm (a cylinder crash occurred) and the minimum oil pressure reduced from 7.7 MPa to a negative value. The optimum oil charging flow rate is 120 L/min. 3. The actual location of TDC was affected by oil overflow pressure. When the overflow pressure was increased from 32 to 35 MPa, the actual location of TDC was reduced by 11 mm (8.5% increase in piston stroke). However, the piston hit the cylinder causing the oil pressure to fluctuate to 36.5 MPa. The optimum oil overflow pressure is 32.5 MPa. Acknowledgements This paper is supported by the National Key R&D Program of China (Grant No. 2022YFB4003300).
References 1. X. He, F. Wang, T.J. Wallington, W. Shen, M.W. Melaina, H.C. Kim, et al., Well-to-wheels emissions, costs, and feedstock potentials for light-duty hydrogen fuel cell vehicles in China in 2017 and 2030. Renew. Sustain. Energ. Rev. 137 (2021) 2. L. Li, J. Lin, N. Wu, S. Xie, C. Meng, Y. Zheng, et al., Review and outlook on the international renewable energy development. Energ. Built Environ. (2020) 3. O.Z. Sharaf, M.F. Orhan, An overview of fuel cell technology: fundamentals and applications. Renew. Sustain. Energ. Rev. 32, 810–853 (2014)
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4. S.K.J. Sprik, C. Ainscough, G. Saur, M. Peters, Hydrogen station data collection and analysis (National Renewable Energy Laboratory, 2015). https://www.nrel.gov/docs/fy18osti/64222. pdf. 2015/2018.02.06. 5. S. Ren, X. Jia, J. Jiang, S. Zhang, B. Zhao, X. Peng, Effect of hydraulic oil compressibility on the volumetric efficiency of a diaphragm compressor for hydrogen refueling stations. Int. J. Hyd. Energ. 47, 15224–15235 (2022) 6. W. Yu, D. Xin, J. Feng, X. Peng, Research on sealing performance and self-acting valve reliability in high-pressure oil-free hydrogen compressors for hydrogen refueling stations. Int. J. Hyd. Energ. 35, 8063–8070 (2010) 7. J. Ye, Z. Du, J. Xie, X. Yin, W. Peng, Z. Yan, Transient flow performance and heat transfer characteristic in the cylinder of hydraulic driving piston hydrogen compressor during compression stroke. Int. J. Hyd. Energ. (2022) 8. Y. Guo, T. Wang, X. Liu, M. Zhang, X. Peng, Mathematical modelling and design of the ionic liquid compressor for the hydrogen refuelling station. Int. J. Energ. Res. 46, 19123–19137 (2022) 9. J.D. Van de Ven, P.Y. Li, Liquid piston gas compression. Appl. Energ. 86, 2183–2191 (2009) 10. R. Mikalsen, A.P. Roskilly, A computational study of free-piston diesel engine combustion. Appl. Energ. 86, 1136–1143 (2009) 11. C. Zhang, K. Li, Z. Sun, Modeling of piston trajectory-based HCCI combustion enabled by a free piston engine. Appl. Energ. 139, 313–326 (2015)
Analysis and Enhancement of Heat Transfer of the Gas Head Cover of Hydrogen Diaphragm Compressors Shengdong Ren, Xiaohan Jia, Jiatong Zhang, Jiacheng Jiang, and Xueyuan Peng
Abstract Excessive thermal stress on the gas head cover is the major cause of diaphragm compressor failure, which poses risks to the hydrogen refueling station and drives up operating costs, should be paid attention to. In order to create a finite element simulation model of the temperature distribution of the gas head cover of the diaphragm compressor, this paper theoretically analyzed the relevant heat transfer boundaries of the gas head cover. To verify this simulation model, a test rig was constructed. The findings showed that the calculated temperatures and measured values agreed closely, with a 9.1% variation. Further, this study investigated the impact of structures and materials on the effect of enhanced heat transfer through simulation and experimental verification. The outcomes demonstrated a better enhanced heat dissipation impact for the enhanced heat transfer structure close to the center high temperature area. The use of materials with high thermal conductivity had a significant impact on increasing heat flow within the same structure, which could lower the maximum temperature by 34.6 °C. This simulation model can be used to evaluate the heat dissipation effect of the head cover structure when designing a diaphragm compressor. Keywords Diaphragm compressor · Temperature distribution · Simulation model · Heat transfer enhancement
S. Ren · X. Jia (B) · J. Zhang · J. Jiang · X. Peng School of Energy and Power Engineering, Xi’an Jiaotong University, No. 28 Xianning West Road, Xi’an 710049, People’s Republic of China e-mail: [email protected] X. Peng State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University No, 28 Xianning West Road, Xi’an 710049, People’s Republic of China © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_57
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1 Introduction The continuous increase in human demand for energy has brought more attention to energy and environmental issues in the twenty-first century [1]. Hydrogen energy can be used as a secondary energy source to solve the storage and transportation problems of clean energy sources such as solar and wind energy [2]. However, hydrogen has the lowest volumetric energy density of any fuel due to its low molecular weight. In practice, hydrogen is typically pressurized to 35 or 70 MPa and stored in a tank to improve the range of the vehicle [3]. Hydrogen refueling stations, which enable the pressurization and refilling of hydrogen, provide infrastructure support for the application of hydrogen energy [4]. The main component of refilling stations is the hydrogen compressor, whose technological development determines the industrialization level of hydrogen energy [5]. The diaphragm compressor is the most widely applied due to its unique advantages of being pollution-free and leakage-free [6]. However, diaphragm compressor’s technical capabilities still fall short of what refilling stations require. Lifetime and efficiency are the two most critical metrics for determining a compressor’s technical level. To improve its efficiency and flow, researches have put a lot of effort into it. Jia [7] found that the clearance volume in the gas cavity had great effect on the flow rate of the compressor. Author [8] paid attention on the volumetric efficiency of the compressor and discovered that the hydraulic oil compressibility was the main effect factor, especially in high-pressure compressors. The short life is the more concerned issue for diaphragm compressors. Studies over the past two decades have provided many methods for determining the motivations of the fault, and proposed several solutions. Many recent researches have focused on the cavity profile, which determines the deformation pattern and stress features of the diaphragm [9]. Jia [10] established a more accurate diaphragm stress model combined with thin-plate large deflection and small deflection theories. They revealed the cause of the rupture and proposed a new design method of the cavity profile. Besides the structural parameter, the operation conditions need to be concerned. Especially for hydrogen compressors, materials for components in contact with hydrogen need to be resistant to hydrogen embrittlement, while the commonly used is stainless steel, which has a relatively poor thermal conductivity. This leads to high temperatures of the head cover and excessive thermal stress. Not much attention has been paid to this issue in existing studies. Only Wang [11, 12] established the head cover stress analysis model through the thermal-structure coupled method, to assess the extent to which thermal stress affects the overall stress level. Existing research has not clarified the characteristics of the temperature field of the diaphragm compressor head cover. The goal of this work is to examine methods to improve heat dissipation by first analyzing the heat transfer mechanism associated with the gas head cover, creating a simulation model of the temperature field. The method to determine the temperature field of the gas headcover was investigated and verified using analytical and experimental techniques.
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2 Analysis of the Heat Transfer Related to the Gas Head Cover Figure 1 depicts the diaphragm compressor’s structural layout. Between the oil head support and the gas head cover, three diaphragms are mounted. The gas cavity is bounded by one side of the diaphragms and the gas head cover, while the oil cavity is bounded by the other side of the diaphragms and the oil head support. The diaphragms are forced to deform by the oil piston. Additionally, as the diaphragms move, the gas in the gas cavity can be compressed and discharged. During the compression process, the mechanical energy is transformed into the internal energy of the gas, which raises the temperature of the gas. The compression process for the diaphragm compressor used in refueling stations is nearly an adiabatic process due to the limited thermal conductivity of the gas head cover. The high temperature of the discharge gas and the gas head cover both contribute to these issues. High gas head cover temperatures can cause significant thermal deformation, significant thermal stress, and awful intake heating, all of which reduce the compressor’s efficiency and lifespan. To enhance the functionality of the diaphragm compressor, it is crucial to research the heat transfer mechanism and temperature distribution connected to the gas head cover. The features of the gas head cover’s temperature distribution were the main subject of this investigation. Figure 2 depicts the heat transmission procedures connected to the gas head cover. The following are the primary heat transfer processes:
Fig. 1 Structure of the diaphragm compressor
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Fig. 2 Heat transfer processes of the gas head cover
2.1 Heat Transfer from Compressed Gas to the Surface of the Gas Cavity Convection heat transfer is a dynamic, intricate process that occurs between the surface of the cavity and the gas. More intuitively, the heat transfer between the gas and the cavity surface can be described by the equivalent convective heat transfer coefficient of the entire working process. Since the discharge holes are in the center of the gas cavity, the closer they are to the center, the more heat is transferred from the gas to the cavity surface. The following is an expression for the equivalent convective heat transfer coefficient. h 1 (r ) = h 1max (1 − K
r ) R
(1)
where, R is the radius of the gas cavity, h 1 (r ) is the convective heat transfer coefficient at radius r, h 1max denotes the convective heat transfer coefficient at center, and K is the rate of decrease of heat transfer coefficient with radius. The shape change pattern of the gas cavity is unclear due to the uncertainty surrounding the diaphragm’s deformation pattern, making it hard to theoretically calculate h 1max and K . The experimental data in this study were used to correct the simulation model, and h 1max and K are empirical values that were calculated from experimental measurements.
2.2 Heat Transfer from the Outer Surface of the Gas Head Cover to the Environment The gas head cover’s exterior surface may often attain temperatures between 80 and 100 °C. Therefore, it is important to take into account both convective heat transmission and heat radiation. Natural convective heat transmission through the air occurs between the environment and the outer surface. Natural convection in air has
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a heat transfer coefficient of 5–25 W m−2 K−1 . The formula for calculating the heat transfer coefficient of heat radiation is [13]: h r = εσ (Tw 3 + Tw 2 Te + Tw Te 2 + Te 3 )
(2)
where, Tw and Te stand for the temperature of the outside surface of the gas head cover and the environment, respectively, in K, ε is the blackness of the gas head cover’s surface, and σ is the Stefan-Boltzmann constant. Thus, the sum of the convective heat transfer coefficient and the radiation heat transfer coefficient represents the overall heat transfer coefficient between the surface of the gas head cover and the environment, and is given by: h 2 = h c + hr
(3)
where, h 2 denote the overall heat transfer coefficient, h c and h r are the convective heat transfer coefficient and the radiation heat transfer coefficient, respectively.
2.3 Heat Transfer Between the Gas and the Suction and Discharge Holes Under the suction and discharge valve, there are a few tiny holes. There is forced convective heat transfer between the surfaces of the holes and the gas flow. The flow velocity and operating conditions of the gases affect the convective heat transfer coefficient. The following formula is used to determine the gas flow rates through the holes. us =
Q o po Ts Z s ps T0 As
(4)
ud =
Q o po Td Z d pd T0 Ad
(5)
where, ps , Ts , pd and Td are the pressures and temperatures of the suction and discharge gases, respectively, u s and u d are the flow rates through the suction and discharge holes, Q o , po and T0 are the volume flow rate, pressure and temperature in standard conditions, Z s and Z d are the compressibility factors in suction and discharge conditions, As and Ad express the total sectional areas of suction holes and discharge holes, respectively. Thus, the following formula can be used to compute the Reynolds numbers. Re =
ud v
(6)
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where, u and v are the suction or discharge gas’s flow velocity and kinematic viscosity, and d is the small holes’ diameter. Further, using the Dittus-Boelter equation, the Nusselt number can be determined as follows: N u = 0.023Re0.8 Pr n
(7)
So, the heat transfer coefficient can be calculated as [13]: h3 =
0.023u 0.8 Pr n λ N uλ = d v 0.8 d 0.2
(8)
where, h 3 stands for the heat transfer coefficient between the gases with the holes, Pr , and λ are the Prandtl number and thermal conductivity, which can be obtained from physical property software, and n is Prandtl number’s exponent which is 0.3 or 0.4 for discharge gas or suction gas.
3 Finite Element Analysis of the Temperature Field 3.1 Geometric Model of the Gas Head Cover The gas head cover of a diaphragm compressor employed in a 22 MPa mother hydrogen refueling station is the research object in this work. Figure 2 illustrates the 3D model. The head cover measures 615 mm in diameter and 160 mm in thickness. The suction and discharge holes are 4 mm in diameter. The materials used for the parts that will come into contact with hydrogen should be resistant to hydrogen embrittlement, which is often stainless steel. The gas head cover in this study is manufactured of 1.4418 duplex stainless steel, which have exceptional resistance to hydrogen embrittlement. While it has a thermal conductivity of only 15 W (m K)−1 .
3.2 Mesh Generation The gas head cover has a diameter of 615 mm, however the suction and discharge tiny holes have a diameter of only 4 mm, and it can be predicted that the area around the discharge holes would be the warmest. It’s important to pay close attention to the temperature in the vicinity of the discharge holes. The area of the tiny holes was separated from the gas head cover to create a finer mesh. The gas head cover adopted a tetrahedral mesh with a size of 3 mm in the other area, and the mesh near the tiny holes had a grid length of no more than 1 mm.
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3.3 Thermal Loads The fluctuation of the gas temperature in the cavity causes slight temperature fluctuations of the head cover. The high thermal heat capacity of the head cover enables the heat transfer issue to be handled as a steady state operation. Thermal loads must be provided to each boundary in order to conduct a steady-state thermal analysis of the gas head cover. The temperature field of the gas head cover of the hydrogen diaphragm compressor utilized in the 22 MPa hydrogen filling station serves as the simulation example in this study. Suction pressure, and discharge pressure are set to 5 MPa and 22 MPa, respectively. The suction temperature and ambient temperature are both set at 20 °C. The heat transfer coefficient of each boundary can be computed using the analysis from the previous chapter. The cooling water is assumed to be kept at 7 °C in the model with cooling water channels, and the convective heat transfer coefficient between the water channel wall and the cooling water is 1200 W m−2 K−1 .
4 Experimental Validation A test rig for the temperature test was constructed, as shown in Fig. 3, to confirm the accuracy of the simulation analysis approach. A diaphragm compressor with a 420 rpm rotating speed serves as the experimental apparatus. The compressor was kept in its operational settings, which included a discharge pressure of 22 MPa and suction conditions of 5 MPa and 20 °C. In order to gauge the actual flow rate, a vortex volume flowmeter was employed. Four K-type thermocouples were inserted to gauge the temperature at several key locations. The thermocouple has a 1.5 °C uncertainty. Deep holes with a diameter of 5 mm and a depth of 140 mm were drilled into the gas head cover to monitor the interior temperature. The thermocouple temperature measuring heads were then put into the bottom of the holes and filled with thermal conductive silicone grease. The silicone grease has a thermal conductivity more than 6 W (m−1 K−1 ). Figure 4 depicts the temperature measurement locations on the gas head cover. Point 1 was situated in the middle of the discharge holes. Point 2 was 140 mm deep from the top surface, near the center of the suction and discharge holes. Point 3 is symmetrical with Point 2 regarding the discharge stepped hole. Point 4 was 150 mm from the center and situated at the same depth as points 2 and 3.
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Fig. 3 Temperature test rig
Fig. 4 Locations of the temperature measurement points
5 Results and Discussion 5.1 Simulation Results and Comparison with Experimental Values The temperature distribution in the cross-section along the suction and discharge holes’ centerlines is shown in Fig. 5. Figure 6 illustrates the contrast between the temperature at each measurement point as measured and as simulated. Point 1, where the surface temperature is nearly equal to the discharge temperature, is situated in the center of the discharge holes. As a result, the mistake caused by the high temperature gas’ influence on the temperature measuring element is less significant. The measured values are slightly below the real values at Points 2, 3, and 4, since the filled silicone grease has a lower thermal conductivity than the gas head cover itself. Additionally, the heat transfer coefficient between the gas and the surface of the gas cavity is uniformly simplified for calculation in this study, which introduces flaws to the results of the simulation. The deviation is, however, generally less than 9.1%,
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within a reasonable range. The simulation’s results can be a good representation of the compressor’s actual temperature distribution properties. This shows that the simulation analysis method can be utilized to analyze the impact of various heat transfer optimization techniques. The gas head cover’s maximum temperature, which is present in the middle of the discharge holes, is 162 °C. The small holes allow the high-temperature gas to continue flowing to the discharge nozzle while imparting a significant quantity of heat to their surface. However, due to the gas head cover’s poor thermal conductivity, heat builds up near the discharge holes. This increases the local stress on the diaphragm
Fig. 5 Temperature distribution of the gas head cover
Fig. 6 Comparison of measured temperature and simulation results
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and shortens the lifespan of the compressor by raising the temperature and thermal deformation surrounding the discharge holes.
5.2 Effect of Different Structures for Enhancing Heat Transfer Simulation analysis and experimental verification of the two approaches were done to investigate the impact of different structures. As illustrated in Figs. 7 and 8, two gas head covers were created, one with water grooves machined in the outer surface and the other with an annular water groove along the discharge stepped hole. The average temperature of the cooling water is 7 °C, and the water flow rate is 950 L/h. The temperature distribution is shown in Fig. 9 along with improved heat transmission from the exterior surface. The temperature in the vicinity of the water grooves is noticeably lower. The peak temperature, however, is still 160.4 °C at the discharge holes, which is just 1.9 °C below the value without heat transfer improvement. The approach of enhancing surface heat transfer has a limited impact on lowering the peak temperature.
Fig. 7 Structure of strengthening heat transfer of outer surface
Fig. 8 Structure of strengthening heat transfer of core high-temperature zone
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Fig. 9 Temperature distribution with strengthening heat transfer of outer surface
Fig. 10 Temperature distribution with strengthening heat transfer of core high-temperature zone
Figure 10 shows the temperature distribution with the core high-temperature zone’s heat transmission being strengthened. The core high-temperature zone’s area is significantly decreased, and the highest temperature is lowered to 148.2, 14.1 °C lower than it would have been without heat transfer improvement. It should be clear that the way of enhancing heat transfer with cooling water surrounding the discharge holes can successfully lower the temperature of the gas head cover and resolve the issue of the local overheating of diaphragm compressors.
5.3 Effect of Different Materials for Enhancing Heat Transfer The gas head cover’s ineffective heat dissipation is mostly caused by the low thermal conductivity of stainless steel. Some copper alloys also have good resistance to hydrogen embrittlement, and the thermal conductivity can be as high as 130 W (m−1 K−1 ). Figure 11 illustrates the temperature field distribution using a copper alloy as the gas head cover material. The maximum temperature of the gas head cover is
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Fig. 11 Temperature distribution with copper alloy
only 113.6 °C, which is 34.6 °C lower than that of stainless steel under the same structure. This is a breakthrough discovery for the temperature management of the compressor. Figure 12 compares the temperatures at each feature point with copper alloy and stainless steel. When the thermal conductivity of the material is high, the temperature drop at the discharge holes is obvious, and the temperature difference between each point is also smaller. The yield strength of common copper alloys is only half that of 316 stainless steel. High-strength copper alloy has a strength of more than 1000 MPa, but costs ten times as much as 316 stainless steel.
Fig. 12 Comparison of temperatures with different materials
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6 Conclusions In this study, the heat transfer boundary of the gas head cover of hydrogen diaphragm compressors was analyzed. Based on this, simulation analysis was conducted to determine the temperature distribution of the gas head cover, and a diaphragm compressor temperature test rig was constructed to measure the gas head cover’s temperature and confirm the accuracy of the simulation calculation model. The key findings are listed below. • The temperature distribution features of the diaphragm compressor gas head cover of hydrogen refueling stations may be calculated using the temperature field simulation analysis model presented in this research. Each specific measuring point has a temperature difference of less than 9.1% between the measured temperature and the simulated value. • Under hydrogen refuelling station conditions, the area of the discharge holes is the core high-temperature zone of the diaphragm compressor, which surpasses 150 °C. • With cooling water around the discharge holes, the peak temperature and discharge temperature respectively drop by 14.1 and 16.1 °C. The problem of the local excessive temperature of diaphragm compressors can be effectively solved by the method of strengthening core high-temperature zone heat transfer. • The material’s thermal conductivity has a significant influence on the gas head cover’s ability to dissipate. The maximum temperature is 34.6 °C lower when utilizing copper alloy than stainless steel. The best method for addressing the issue of gas head cover heat dissipation is to employ materials with high thermal conductivity.
References 1. C. Zhao, Carbon Neutrality: aiming for a net-zero carbon future. Carbon Neutrality 1, 2 (2022) 2. C. Acar, I. Dincer, The potential role of hydrogen as a sustainable transportation fuel to combat global warming. Int. J. Hydrogen Energ. 45, 3396–3406 (2020) 3. C. Tarhan, M.A. Çil, A study on hydrogen, the clean energy of the future: hydrogen storage methods. J. Energy Storage 40, 102676 (2021) 4. S. Kikukawa, F. Yamaga, H. Mitsuhashi, Risk assessment of hydrogen fueling stations for 70 MPa FCVs. Int. J. Hydrogen Energ. 33, 7129–7136 (2008) 5. S.S. Bhogilla, H. Niyas, Design of a hydrogen compressor for hydrogen fueling stations. Int J. Hydrogen Energ. 44, 29329–29337 (2019) 6. G. Sdanghi, G. Maranzana, A. Celzard, V. Fierro, Review of the current technologies and performances of hydrogen compression for stationary and automotive applications. Renew. Sustain. Energy Rev. 102, 150–170 (2019) 7. X. Jia, Y. Zhao, J. Chen, X. Peng, Research on the flowrate and diaphragm movement in a diaphragm compressor for a hydrogen refueling station. Int. J. Hydrogen Energ. 41, 14842– 14851 (2016)
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8. S. Ren, X. Jia, J. Jiang, S. Zhang, B. Zhao, X. Peng, Effect of hydraulic oil compressibility on the volumetric efficiency of a diaphragm compressor for hydrogen refueling stations. Int. J. Hydrogen Energ. 47, 15224–15235 (2022) 9. Y. Hu, X. Xu, W. Wang, A new cavity profile for a diaphragm compressor used in hydrogen fueling stations. Int. J. Hydrogen Energ. 42, 24458–24469 (2017) 10. X. Jia, J. Chen, H. Wu, X. Peng, Study on the diaphragm fracture in a diaphragm compressor for a hydrogen refueling station. Int. J. Hydrogen Energ. 41, 6412–6421 (2016) 11. T. Wang, X. Jia, X. Li, S. Ren, X. Peng, Thermal-structural coupled analysis and improvement of the diaphragm compressor cylinder head for a hydrogen refueling station. Int. J. Hydrogen Energ. 45, 809–821 (2020) 12. T. Wang, Z. Tang, X. Jia, Study on the stress and deformation of a diaphragm compressor cylinder head under extreme conditions. IOP Conf. Ser. Mater. Sci. Eng. 604, 12029 (2019) 13. S. Yang, W. Tao, Heat Transfer (Higher Education Press, Beijing, 2006)
Hydrogen Compressors: A Few Technical Challenges Enrico Scarpellini and Alessandro Traversari
Abstract The compression of hydrogen, particularly for use in the automotive industry and with fuel cells in general, presents technical challenges to be carefully evaluated in the design and manufacturing of compression equipment. The high fugacity and flammability of hydrogen, its effects on the characteristics of materials, along with the features of the service, with pressures up to 100 MPa and no lubrication as often required by the process, impose a careful evaluation of operating conditions, a proper selection of materials and an optimized configuration of compressor elements and seals. The special efforts in the design and manufacturing of compression equipment are based on accurate stress analysis, along with temperature distribution evaluation and the understanding of the behavior of materials versus hydrogen attack and hydrogen embrittlement phenomena. Careful quality checks to detect defects that may evolve during the operation are necessary, along with proper seal material and arrangement, to withstand severe operating conditions, and efficient containment of leaks through special buffering/recovery systems. Advanced calculation codes to simulate operating conditions in terms of stress, heat generation and transmission shall be adopted, including Finite Element and Conjugate Heat Transfer Methodologies. The Fracture Mechanics approach is mandatory to evaluate the behavior of material defects in terms of threshold dimension and possible propagation. Adequate design of components shall be implemented to contain the stress profile in order to allow the use of relatively low-strength materials, less sensible to hydrogen embrittlement. The paper provides an overview of the above criteria with recommendations for an effective design. Keywords Hydrogen · Friction · Fracture mechanics
E. Scarpellini (B) · A. Traversari (B) Compression Service Technology C.S.T. Srl, via Panciatichi 40, 50127 Florence, Italy e-mail: [email protected]; [email protected] A. Traversari e-mail: [email protected]; [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_58
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1 Introduction: Hydrogen, a Way to «Decarbonization» Nowadays there are two ways to produce hydrogen without CO2 emissions: • Green hydrogen, from solar, wind, hydro, geothermal and nuclear. • Blue hydrogen, mainly from natural gas, provided that the CO2 is recovered. Generation, transportation and storage, along with the modifications or design of assets and industrial equipment to handle hydrogen, have recently become crucial to quickly and successfully get the targets of global CO2 emission reduction. Specific applications of hydrogen have been investigated as fuel in the automotive and transportation sector in general, clean power generation through fuel cells and gas turbines, feedstock in the industry and as a key element for distributed energy generation and storage. Hydrogen is becoming diffuse and flexible in a way that it may be considered the hero of the so-called “energetic revolution”. The last century was characterized by the development of a model based on the Oil and Gas production from localized reservoirs, generation of electrical energy in localized large power plants and transportation of hydrocarbons and electric power to utilizers, even on the other side of the world. The energy model of the future might be based on the production, storage and utilization of hydrogen, the lightest and most ubiquitous element found in the universe, just where it is needed. Once hydrogen production and utilization have become cheaper and reliable, there will be no geographic and political obstacles and limitations and this will make hydrogen the “first truly democratic energy regime in the history”, as explained in the book “The Hydrogen Economy”, by Rifkin [1]. The end user may become the producer and consumer of the energy needs. In this perspective, hydrogen generation, transportation and storage require upgraded or dedicated infrastructure and equipment. Projects started to reutilize existing natural gas pipelines [2] for hydrogen transportation and to make new installations, like the Holland Hydrogen 1 project, that will produce green hydrogen in 100+ MW electrolyzers. At the same time, main equipment manufacturers started to develop compressors and turbines suitable to handle higher and higher percentages of hydrogen.
2 Hydrogen: A Compression Challenge For use as an energy producer in fuel cells, hydrogen, considering its extremely low density, requires to be compressed at very high pressure (up to 100 MPa). No contaminants shall be present in the gas, as they can damage fuel cells and utilizers in general. This makes dry-lubricated solutions mandatory. Due to low molecular weight, the use of reciprocating compressors is more efficient than centrifugal compressors.
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High escaping tendency and wide flammability range in air (4.0–74.2% for Hydrogen vs 5.0–15.0% for Methane) require specific precautions and special sealings in machinery and equipment in general [3]. Furthermore, due to the high escaping tendency and high flammability mentioned above, it is necessary to limit the maximum discharge temperature of the process gas. The international standard API 618 suggests keeping it below 135 °C. This limitation, together with the high delivery pressure (between 20 and 100 MPa, depending on the service), requires a multistage configuration and high compression ratios. A special design of sealing elements is necessary, together with a careful evaluation of the heat generated by friction and its dissipation in order not to damage the sealings elements, which are generally made of plastic materials. In addition, hydrogen impacts most materials’ mechanical characteristics, making them brittle and less resistant to fatigue, as explained in Para. 5. The above considerations make hydrogen compression a challenging task.
3 Special Cylinder Arrangement with Dry Seals for No Gas Contamination A larger number of sealing elements is necessary, in order to distribute the differential pressure and maintain the contact forces between the sealing elements and the liner or the piston rod within acceptable limits. In addition to that, the distribution of pressure through the compression stages and the sizing of cylinders may require special cylinder arrangement, in order to assure that two key parameters for reciprocating compressors design, that is the maximum load acceptable on the rod and the “thrust reversal” on the crosshead pin, are met in all operating conditions. This may require adopting a two-stage combined piston configuration, where the crank-end and the head-end of the cylinder serve two different compression stages. A careful evaluation of the heat generated by friction, its transmission to the rest of the cylinder components and the warming/cooling effect of the process gas shall be carefully evaluated in order to predict the distribution of temperature and the configuration of cooling circuits. A fundamental thermal study was deemed necessary and performed by Compression Service Technology, in cooperation with the University of Florence (Italy), to evaluate the wall temperature of all the sliding surfaces in a high-pressure (400 bar) dry-lubricated cylinder (see Fig. 1). The study was based on the Conjugate Heat Transfer (CHT) simulation by coupling a Thermal Finite Volume Method (FVM) for the cylinder with a Computational Fluid Dynamics (CFD) for the cooling circuit. The outcome of the study was used to optimize, in collaboration with the seal manufacturer, the number and the configuration of sealing elements, both between the piston and the cylinder (piston rings) and the rod and the cylinder (packing
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Fig. 1 Conjugate Heat Transfer (CHT) simulation of a high-pressure cylinder arrangement
rings). By means of this study, the cooling circuit’s configuration and sizing were also optimized. In the model, both the cylinder bodies and the packing cups needed water cooling (with an inlet temperature of 30 °C). From the temperature containment standpoint, the packing rings are more critical. The heat generated by the friction between the rings and the piston rod cannot be easily dissipated: rings are in plastic material, which is far from being a good heat transmitter, and the piston rod, being a mobile element, cannot be easily cooled directly [4]. For this reason, the Authors deem preferable to utilize piston ring arrangement for high-pressure cylinders, as shown in Fig. 1.
4 Efficient Containment of Gas Leaks to the Compressor Frame and Atmosphere The “physiological” leak from the packing rings shall be vented to a safe area. An intermediate space is placed between the cylinder and the frame (generally named “distance piece” or “extension body”). A partition cover separates the distance piece from the frame. The space is vented to the atmosphere and in this way there is no chance for the hydrogen to reach the frame and the neighborhood of the machine, with the consequent impact on safety and area classification. In order to avoid any chance for the frame lube oil to migrate into the cylinder and contaminate the process gas, a plastic ring can be installed on the portion of the piston rod moving inside the distance piece.
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Fig. 2 Gas leakage containment with inert gas buffering
A barrier is created through the injection of nitrogen into the main packing body and the partition cover, see Fig. 2. The configuration described above is used all the times the inert gas is available. In case the inert gas is not available, a “double space” distance piece is adopted (see Fig. 3). The very low differential pressure between the additional space and the frame during operation makes the inlet of hydrogen into the frame quite unlikely.
5 Design and Manufacturing Critical Due to High Pressure Hydrogen Effects The effects of hydrogen on materials shall be taken into account while designing components and selecting materials that are in contact with the process gas. The main types of effects are described below. Hydrogen Attack (HA): due to the diffusion of atomic hydrogen that, combining with the carbon of carbides in the steel, produces CH4 and generates defects, with a negative impact on the toughness of the material. This phenomenon happens at relatively high temperatures (> 200 °C) and consequently doesn’t interest compressor components, generally operating at lower temperatures. The HA, better known as
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Fig. 3 Gas leakage containment without inert gas buffering
HTHA (High Temperature Hydrogen Attack), may also be originated during the material manufacturing process. In order to reduce the probability of failure during operation due to residual hydrogen from the manufacturing process, the use of vacuum-melted steels is strongly recommended. Hydrogen Embrittlement (HE): a consequence of the diffusion of atomic hydrogen that occurs at temperatures up to 150 °C. In case the material is submitted to tensile stress, it may cause the propagation of defects [5, 6]. Considering that compressors are usually operated at temperatures below the value above, the phenomenon shall be carefully taken into account. Due to the effect of hydrogen on the propagation of existing defects when submitted to tensile stress, the design of machinery components should be based on Fracture Mechanics approach all the times hydrogen is involved. The parameter that is usually considered in this approach is the Stress Intensity Factor (KI) which is calculated as follows: √ KI = Yσ π a where a represents the dimension of the defect. σ is the tensile stress perpendicular to the defect (that tends to open it). Y is a factor depending on the geometry of the component and of the defect itself. Values of Y are available in the literature. See for instance “Stress Intensity Factor and Limit Load Handbook” [7] and other publications [8–11], where several cases with different geometries of the items and the defects are considered. If KI is so high to approach a critical value KIc the defect suddenly propagates, a situation that shall be absolutely avoided due to the potentially catastrophic consequences.
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The value of KIc is determined through fatigue tests on notched samples (Compact Tension Specimens). Hydrogen has an impact on KIc, dramatically reducing its value. And this happens in particular for high-strength steels [12, 13], quite often used in reciprocating compressors especially at high pressure, as in our case. Low-strength steels, like carbon steels and austenitic stainless steels [14], are relatively not sensible to Hydrogen Embrittlement. As an example of how the ultimate tensile strength of the material can affect the KIc see Fig. 4, relevant to AISI 4140 steel in 20 MPa hydrogen atmosphere.
Fig. 4 Critical Stress Intensity Factor versus Ultimate Tensile Strength relationship for AISI 4140 steel in hydrogen atmosphere. From: EIGA, EUROPEAN INDUSTRIAL GASES ASSOCIATION, “Hydrogen Cylinders and Transport Vessels”. Doc 100/20, Revision of Doc 100/11 [12]
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Fig. 5 Effect of hydrogen on crack growth speed for Cr–Mo steels. From: Fatigue Crack Growth Relationships for Cr–Mo Steels in H2 Gas—From ASME 2015 Pressure Vessels and Piping Conference, Boston MA, USA, July 23, 2015 [15]
International standards and regulations, like API 617, UNI ISO 11114 or EIGA, recommend the use of steels with a maximum ultimate tensile strength between 820 and 950 MPa, when in contact with hydrogen. Another consideration shall be done in the design of components for reciprocating compressors, being most of them subject to fatigue. The propagation of a defect is a function of the variation of the Stress Intensity Factor in the fatigue cycle ΔK. There is a relationship between ΔK and the speed of defect propagation (known as “Paris law”) [9]. An example is shown in Fig. 5, relevant to Cr–Mo steels. Comparing the dotted blue line (relevant to the test in air) with the red lines (tests in hydrogen atmosphere), one can see that, with high ΔK values, the effect of hydrogen results in 10× or more higher propagation speed. On the contrary, for low values of ΔK, the growth rate in hydrogen tends to approach the one in air. The result of tests from another source leads to the same conclusion [16, 17]. In addition to KIc, another important parameter shall be considered: the so-called “Threshold ΔK” (ΔKth). For values of ΔK < ΔKth the crack propagation doesn’t start. ΔKth depends on the material and mainly on R, the ratio between the minimum and the maximum tensile stress in the fatigue cycle [18, 19]. As per KIc, ΔKth is determined through fatigue tests on notched samples (Compact Tension Specimens). Just as an example, to provide a guideline to handle this matter, see Fig. 6 relevant to low-alloy steels, widely used in the cylinders, especially at high pressure (Table 1).
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Fig. 6 ΔKth for AISI 4140 quenched and tempered steels and dependence on R Ratio [20]
Table 1 Effect of tempering on long crack thresholds
Tempering temperature (◦ C)
ΔK th (MPa
200
2.80
400
3.50
550
7.20
700
8.50
√
m)
The diagram on the top shows, for steels with a tempering √ temperature of 600 °C, commonly used in these cases, that ΔKth is about 8 MPa m, with R close to 0 (= 0.05). The diagram at the bottom shows the typical effect of R on ΔKth, which decreases until a minimum limit (ΔKth*) with the increase of R. For this kind of steels, ΔKth* √ is of the order of 4 MPa m. Considering that the number of fatigue cycles of a compressor during its life is huge (for instance, over 10 billion cycles for 25 years of operation at 1000 rpm), it is important to achieve a ΔK below the threshold value in order to reasonably meet the life expectation of the component.
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An accurate evaluation of the combination stress—material defects shall be performed in order to assure, with a reasonable safety factor, that KI and ΔK stay below their respective critical values in every component of the compressor. That can be obtained through Finite Element Methods on one side and adequate manufacturing and quality inspection methods and acceptance levels on the other side.
6 Conclusions The need to operate at high pressures with no lubrication requires a special configuration of the compressor and its sealing elements. This can be achieved through sophisticated calculation models, combining Thermal Finite Volume Method with Computational Fluid Dynamics. The high fugacity and flammability of hydrogen impose special precautions to contain the leaks and limit process temperatures. The use of inert gas barriers may help for this purpose. The phenomenon of Hydrogen Embrittlement affecting several materials makes the design of compressor components quite critical. A Fracture Mechanics approach is mandatory in order to properly evaluate the effect of hydrogen and the consequent precautions to be taken during the manufacturing and quality inspection processes. Accurate calculation of stresses and checks of material defects dimensions, along with the evaluation of the key parameters of the material (Critical Stress Intensity Factor KIc and its threshold variation in the fatigue cycle ΔKth) in hydrogen atmosphere at the operating pressures are key factors for a successful design and manufacturing of compression equipment.
References 1. Rifkin, J., The Hydrogen Economy (2016) 2. EIGA, European Industrial Gases Association, Hydrogen Transportation Pipelines, IGC Doc 121/04/E (2004) 3. Schroeder, V., Calculation of Flammability and Lower Flammability Limits of Gas Mixtures for Classification Purposes (Bundesanstalt für Materialforschung und –prüfung (BAM), Berlin, 2016) 4. Klotsche, K., Experimental and numerical investigation of the heat transfer inside a hollow piston rod. EFRC 2016 5. Yamabea, J., Yoshikawa, M., Matsunaga, H., Matsuoka, S., Effects of hydrogen pressure, test frequency and test temperature on fatigue crack growth properties of low carbon steels in gaseous hydrogen, in 21st European Conference on Fracture, ECF21, 20–24 June 2016, Catania, Italy 6. Takakuwa, O., Matsuoka, S., et al., Temperature dependence of fatigue crack growth in lowalloy steel under gaseous hydrogen, in Proceedings of the ASME 2018 Pressure Vessels and Piping Conference
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7. Al Laham, S., Structural Integrity Branch: “Stress Intensity Factor and Limit Load Handbook, Issue 2. British Energy Generation Ltd., 15 Apr 1999 8. FITNET FFS—MK7—Annex A, Stress intensity factor (SIF) solutions, in International Conference on Fitness-for-Service (Amsterdam, 2006) 9. Anderson, T.L., Fracture Mechanics Fundamentals and Applications, 3rd ed. (2005) 10. Newman, J.C., Raju, I.S., Stress-intensity factors for internal surface cracks in cylindrical pressure vessels. J. Pressure Vessel Technol. (1980) 11. British Standard BS 7910 2005, Guide to methods for assessing the acceptability of flows in metallic structures 12. EIGA, European Industrial Gases Association, Hydrogen Cylinders and Transport Vessels. Doc 100/20, Revision of Doc 100/11 13. San Marchi, C., Ronevich, J., et al., Technical basis for master curve for fatigue crack growth of ferritic steels in high-pressure gaseous hydrogen in ASME S. VIII-3 code, in Proceedings of the ASME 2019 Pressure Vessels & Piping Conference 14. Ueno, A., Benjamin, G., Effect of High-Pressure H2 Gas on Tensile and Fatigue Properties of Stainless Steel SUS316L by Means of the Internal High-Pressure H2 Gas Method (Elsevier BV, Fatigue Design, 2019) 15. Somerday, B., Sandia National Laboratories Livermore CA, USA; Paolo Bortot, TenarisDalmine R&D Dalmine, Italy; John Felbaum, FIBA Technologies Millbury MA, USA, Fatigue Crack growth relationships for Cr-Mo steels in H2 gas, in ASME 2015 Pressure Vessels & Piping Conference, Boston MA, USA, July 23, 2015 16. Ogawa, Y., Matsunaga, H., Yamabe, J., Yoshikawa, M., Matsuoka, S., Fatigue limit of carbon and Cr Mo steels as a small fatigue crack threshold in high-pressure hydrogen gas. Int. J. Hydrogen Energy (2016) 17. Briottet, L., Moro, I., et al., Fatigue crack initiation and growth in a Cr-Mo steel under hydrogen pressure. Int. J. Hydrogen Energy (2015) 18. Wada, Y., Yanagisawa, Y., Fatigue crack growth behavior of auto-frettaged hydrogen pressure vessel made of alloy steel, in Proceedings of the ASME 2017 Pressure Vessels and Piping Conference (2017) 19. Chen, Z., The effect of R ratio and temperature on fatigue crack growth threshold of power plant steels, in Eth Zurich Research Collection (2018) 20. London, B., Shyne, J.C., Nelson, D.V., Small Fatigue Crack Behaviour Monitored using Surface Acoustic Waves in Quenched and Tempered 4140 Steel (Mechanical Engineering Publications, London, 1986), pp. 537–552
Working Fluid and System
Analysis of R454B as a Low-GWP Refrigerant Alternative for R410A in a Vapor-Injected Rotary Compressor Tim Pfeiffer, Amjid Khan, and Craig R. Bradshaw
Abstract Greenhouse gases that cause global warming have a variety of sources. One of these sources with severe effects is leaks in refrigerant systems that use high Global Warming Potential (GWP) refrigerants, such as R410A. To reduce the contribution of refrigerant systems to global warming, alternative, low-GWP refrigerants must be analyzed and tested in various conditions. This study presents an analysis of compressor performance using the slightly flammable, low-GWP refrigerant R454B compared against R410A. To enable this analysis, a vapor-injected rotary compressor was tested on R410A and R454B with power, mass flow rates, and discharge temperatures measured at a range of evaporation temperatures (10.0–28.9 .◦ C), condensation temperatures (23.9–54.4 .◦ C), suction superheats (2.8–16.7 K), and compressor speeds (30.0–97.6 Hz). In total, 28 test points were investigated with a one-factorat-a-time design of experiments. In general, R454B performed better than R410A in heating and cooling modes, with increases in Coefficient Of Performances (COPs) by 4.40% and 4.32%, respectively. Keywords Low-GWP · R454B · R410A · Vapor injection · Drop-in refrigerant alternative
1 Introduction A major source of Greenhouse Gas (GHG) emissions from heating and cooling systems are refrigerant leaks. Three main factors determine how much impact these leaks have on the environment: (1) the mass of the leaked refrigerant, (2) its GWP, and (3) the indirect emissions of the system, which are influenced by the performance of the fluid. A widely used refrigerant in the Heating, Ventilation, Air Conditioning, T. Pfeiffer (B) · A. Khan · C. R. Bradshaw Center for Inegrated Building Systems, Oklahoma State University, Stillwater, OK 74075, USA e-mail: [email protected] URL: http://cibs.okstate.edu T. Pfeiffer Technical University of Dresden, Dresden 01069, Germany © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_59
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Table 1 Comparison of GWP.100 values, atmospheric lifetimes, and flammabilities between R410 and R454B, and their respective components R454B Refrigerant R410A Component R32 R125 R32 R1234yf Mass fraction [–] GWP.100,component [kg.CO2 /kg] GWP.100 [kg.CO2 /kg] Atmospheric lifetime (component) [years] Flammability of component according to ASHRAE Standard 34 [5] Flammability according to ASHRAE Standard 34 [5] Temperature glide [K]
0.50 677 5.4 A2L
0.50 3170 1924 31 A1
0.689 677 5.4 A2L
0.311 1 467 0.02 A2L
A1
A2L
0.1
1.4
The data were obtained from the literature [1, 4, 5]
and Refrigeration (HVAC&R) industry is R410A. It has a GWP.100 value of 1924 [1] and, considering the lifetime of about 31 years, a rapid phase-out of R410A will have substantial positive impacts on the mitigation of climate forcing caused by refrigerant systems. Limiting the emissions of R410A as enforced by the Kyoto Protocol will be more effective short term while confining the consumption of R410A according to the Montreal Protocol will have a more substantial long-term impact on the reduction of radiative forcing of the climate [2]. To replace R410A, the slightly flammable refrigerant alternative R454B can be used. It has a GWP.100 value of 467 [1] and thus a more than 75% lower GWP.100 value than R410A. An overview of the compositions, GWP.100 values, and atmospheric lifetimes is shown in Table 1. R454B is considered a drop-in alternative, which means it has similar thermophysical properties and thus can replace R410A in a system without significant component modifications. Furthermore, R454B has a more substantial temperature glide (1.4 K) than R410A (0.1 K) [3], which can be utilized to reduce the thermodynamic irreversibilities in a counter-flow heat exchanger. R454B has been compared to R410A in multiple studies conducted on systems with a scroll compressor. Mohsin and Bradshaw [6] found that an optimum capacity range exists for each refrigerant to achieve good compressor performance. The leakage area ratio, which is a crucial factor contributing to the performance of refrigerants, is significantly higher for low-capacity (4–70 kW) scrolls. Mohsin and Bradshaw [6] also found that the performance of R454B is similar to the performance of R410A in scroll compressors, which leads to the conclusion that R454B presents a potential low-GWP refrigerant alternative for R410A in scrolls.
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Still, there is a lack of test data on rotary compressors, especially those with vapor injection. This work tested R410A and R454B on a load stand containing a rotary compressor that utilizes economization through vapor injection. The changes in discharge temperature, compressor input power, isentropic and volumetric efficiencies, heating and cooling capacities, and heating and cooling COPs, caused by replacing R410A with R454B, are analyzed.
2 Experimental Setup Tests with the two refrigerants, R410A and R454B, were conducted on a compressor load stand that utilizes a hot-gas bypass principle of operation (see Fig. 1). The rotary compressor used for these tests is a model from the company GMCC with the model number EAPM310D85UMT. According to its datasheet, it has a displacement value of 30.6 cm.3 and a capacity of 11445 W at 60 Hz compressor speed. During data collection, the following boundary conditions were defined for the output variables: Mean values of suction and injection temperatures were kept in
Fig. 1 Piping and instrumentation diagram (P&ID)
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a range of .± 0.1 K (.± 0.2 .◦ R) of the setpoint, and the allowable range for mean values of suction, injection, and discharge pressures was .± 0.14 bar (.± 2 psig) of the setpoint. Furthermore, the ambient temperature around the compressor was controlled to be within .± 3.9 K (.± 7 .◦ R). These definitions of boundary conditions are in the acceptable ranges for ASHRAE Standard 23 [7], which is the method of test required for AHRI Standard 540 [8]. For each test point, the valve positions were adjusted until a steady state had been achieved, and the test data were collected for 15 min per point. To cover a wide range of conditions applicable for heating and cooling cycles, 28 test points were defined using a one-factor-at-a-time design of experiments, as shown in Table 2. That includes a condensation temperature sweep from 23.9 to 54.4.◦ C (75– 130.◦ F), a compressor speed sweep from 30.0 to 97.6 Hz, a suction temperature sweep from 10.0 to .− 28.9 .◦ C (50 to .− 20 .◦ F), a suction superheat sweep from 2.8 to 16.7 K (5–30 .◦ R), and extreme envelope points, depicting the most extreme combinations of evaporation temperature and condensation temperature that were achievable on the load stand. Furthermore, injection superheat is kept at 2.8 K (5 .◦ R) for all test points to secure the vapor state condition for injection. The saturated injection temperature was found by determining the saturation temperature of the intermediate pressure, which can be calculated by taking the square root of the product of suction pressure and discharge pressure. Pressures and temperatures were measured for suction, injection, and discharge states. Additionally, compressor input power, as well as suction and discharge mass flow rates, were measured. Based on these measurements, the differences in discharge temperatures, compressor powers, isentropic and volumetric efficiencies, heating and cooling capacities, and heating and cooling COPs are discussed in the following section.
3 Results and Discussion For each evaluation parameter, the change due to the refrigerant replacement is calculated and presented in Table 3. An uncertainty analysis was performed using the equations derived by Moffat [10]. For the calculated evaluation parameters, propagated uncertainties were determined with the equations provided by Farrance and Frenkel [11].
3.1 Discharge Temperature Discharge temperatures were measured directly with a Resistance Temperature Detector (RTD). An increase was found for replacing R410A with R454B for 24 of the 28 tested conditions, with an average elevation of 3.07 K (3.72%). Compared to other studies, this is a relatively low average discharge temperature increase: Sieres
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Table 2 Test matrix for R410A and R454B Pts.
Speed [Hz]
.Tevap [.◦ C]
.ΔTsuc [K]
.Tinj,sat [.◦ C]
.ΔTinj [K ]
.Tcond [.◦ C]
1
80
1.67
11.1
12.3
2.78
23.9
2
13.6
26.7
3
16.1
32.2
4
18.6
37.8
5
21.0
43.3
6
23.5
48.9
7
25.8
8
30
9
50
10
70
11
90
12
97.6
13
80
8.33
2.78
43.3
Speed sweep
10
11.1
25.8
2.78
43.3
Evaporation temp. sweep
21.0
2.78
43.3
Suction superheat sweep
.− 8.69
2.78
23.9
Extreme envelope points
4.44
22.6
.− 1.11
19.4
16
.− 6.67
16.2
17
.− 23.3
5.93
18
.− 28.9
1.67
2.36 2.78
20
4.44
21
6.67
22
8.33
23
11.1
24
13.9
25 26
54.4
8.33
15
80
Condensation temp. sweep
1.67
14
19
Comments
16.7 80
.− 34.4
11.1
27
10
20.7
32.2
28
10
30.7
54.4
et al. [12] found increases of 8–14 K, and Panato et al. [13] found an average discharge temperature rise of 8 K. Nevertheless, it should be mentioned that the test setups of other studies were different. Instead of a rotary compressor, most other studies that compared the two refrigerants investigated systems containing scroll compressors. For the tests conducted in the present work, the most extreme discharge temperature increase was found at the lowest evaporation temperature (.− 28.9 .◦ C at test point 18) with a magnification as significant as 14.67 K. This rise in discharge temperature must be considered when R454B is treated as a drop-in refrigerant for R410A since the equipment—especially the electronics—might not be built for such an increase in temperature on the high-pressure side of the cycle.
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Table 3 Change in properties when using R454B instead of R410A and measurement uncertainties Method of determination
Average change with R454B instead of R410A
Measured with RTDs
+ 3.07 K (+ 3.72%)
.±
0.11 K (.± 0.14%)
.±
0.13 K (.± 0.15%)
Measured with power meter
.−
.±
100 W (.± 2.67%)
.±
100 W (.± 2.86%)
.ηis
Calculated according to ASHRAE Standard 23
+ 0.01 (+ 1.80%)
.±
0.02 (.± 3.56%)
.±
0.03 (.±4.53%)
.ηvol
Calculated according to ASHRAE Standard 23
.−
.±
0.002 (.± 0.20%)
.±
0.003 (.± 0.32%)
˙ heat .Q
Calculated with energy .− 263 W (.− 1.74%) balance
.±
43 W (.± 0.28%)
.±
72 W (.± 0.49%)
˙ cool .Q
Calculated with energy .− 180 W (.− 1.79%) balance
.±
19 W (.± 0.19%)
.±
32 W (.± 0.33%)
.C O Pheat
Fraction of heating capacity and compressor work
+ 0.18 (+ 4.40%)
.±
0.12 (.± 2.94%)
.±
0.14 (.± 3.17%)
.C O Pcool
Fraction of cooling capacity and compressor work
+ 0.12 (+ 4.32%)
.±
0.08 (.± 2.92%)
.±
0.09 (.± 3.12%)
Average uncertainty (measured or propagated) R410A
.Tdis
˙ comp .W
231 W (.− 6.17%)
0.004 (.− 0.43%)
R454B
3.2 Compressor Power The electric compressor input power was measured directly with a power meter. Average power savings of 231 W (6.17%) were found for using R454B instead of R410A. This finding coincides with similar studies: Panato et al. [13] and Sieres et al. [12] found power savings of 3.5% and up to 8%, respectively. However, the results of the present paper should be regarded with caution because the measurement uncertainty for the power measurement was almost 3% for both refrigerants. That is mainly due to the reason that the measurement range of the power meter was designed for larger power requirements with an upper measurement limit of 40,000 W. The highest-tested compressor input power was less than 15% of that limit (5232 W). Hence, the systematic uncertainty of the power meter (0.25% FS = 100 W) had a more substantial influence on the total measurement uncertainty of the compressor input power.
3.3 Isentropic Efficiency Isentropic efficiencies were calculated according to ASHRAE Standard 23 [7] using the measurements of compressor power and suction and discharge mass flow rates. Isentropic efficiencies were higher using R454B instead of R410A at 23 of the 28
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tested conditions, with an average increase of + 1.80%. The high measurement uncertainties of the compressor power dominated the propagated uncertainty of the isentropic efficiencies (more than 60% weight), which explains the high values of .± 3.56% for R410A and .± 4.53% for R454B.
3.4 Volumetric Efficiency The volumetric efficiencies decreased by 0.43%, on average, when using R454B instead of R410A. For low compressor speeds, the volumetric efficiency was slightly higher using R410A. Above about 60 Hz, R454B performed better. A similar trend was found for evaporation temperatures: Below about 5.◦ C, R410A performed better, while for evaporation temperatures above that threshold, R454B showed a slightly higher volumetric efficiency.
3.5 Heating and Cooling Capacities For heating and cooling applications, the heating and cooling capacities are critical evaluation parameters. Heating capacities were 1.74% lower with R454B compared to R410A. Other studies found similar trends with even larger capacity decreases: Sieres et al. [12] found a decrease of 8%, while Saleem and Bradshaw [3] found heating capacity reductions of 6%. Cooling capacities with R454B were 1.79% lower than with R410A. Similar to the heating capacities, this complies with the findings of comparable studies. Nonetheless, even more considerable decreases were found after the refrigerant replacement: .− 8% by Sieres et al. [12] and .− 9.5% by Panato et al. [13].
3.6 COPs COPs for heating and cooling modes increased by 4.40% and 4.32%, respectively. This finding is only logical as the power savings were higher than the decreases in heating and cooling capacities, which, by definition, increases the COPs. One study found matching increases for .C O Pheat (+ 6.67% by Menegazzo et al. [14]). In contrast, other studies could not detect any COP enhancement: Sieres et al. [12] found changes in .C O Pheat between .− 0.9 and + 0.6%, and Jeon et al. [15] detected .± 0% changes in .C O Pcool . Furthermore, Panato et al. [13] found a 6.2% decrease in .C O Pcool . For the heating mode, the highest .C O Pheat enhancement was found for the highest tested condensation temperature (test point 7), which is advantageous for heating applications like heat pumps, where higher condensation temperatures are of greater interest.
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4 Conclusion The commonly used, high-GWP refrigerant R410A and its low-GWP alternative R454B were tested on a load stand that utilizes economization through vapor injection into a rotary compressor. The input parameters for the tests were a range of condensation temperatures, compressor speeds, evaporation temperatures, and suction superheats. A test matrix including 28 test points, examining changes in the different input parameters, was developed. Heating and cooling capacities, as well as COPs, are the critical items considered for a system design. Due to the decreases in heating and cooling capacities by 1.74% and 1.79%, respectively, that are coupled with replacing R410A with R454B, it may be necessary for some applications to switch to a larger compressor. Additionally, caution should be taken due to the increase in discharge temperature by 3.07 K, on average, for the switch from R410A to R454B. Nevertheless, the COPs of heating and cooling systems would improve for such a change (by 4.40% and 4.32%, respectively), and the supply power to run the compressor can be reduced. Consequently, R454B represents a good low-GWP alternative to R410A; and with simple component modifications, it can even improve the system performance.
References 1. T. Stocker (ed.), Climate Change 2013: The Physical Science Basis: Working Group I Contribution to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (Cambridge University Press, 2014) 2. G.J. Velders, D.W. Fahey, J.S. Daniel, M. McFarland, S.O. Andersen, The large contribution of projected HFC emissions to future climate forcing. Proc. Nat. Acad. Sci. 106(27), 10949–10954 (2009). https://doi.org/10.1073/pnas.0902817106 3. S. Saleem, C.R. Bradshaw, The thermodynamic behavior of low-GWP zeotropic mixtures on water-source heat pump equipment, in International Refrigeration and Air Conditioning Conference. Paper 2092 (2021) 4. S. Szcz¸es´niak, Ł Stefaniak, Global warming potential of new gaseous refrigerants used in chillers in HVAC systems. Energies 15(16), 5999 (2022). https://doi.org/10.3390/en15165999 5. ASHRAE, ANSI, ASHRAE Standard 34–2022, Designation and Safety Classification of Refrigerants, in American Society of Heating (Atlanta, GA, Refrigerating and Air-Conditioning Engineers, 2019), p. 2022 6. M.M. Tanveer, C.R. Bradshaw, Performance evaluation of low-GWP refrigerants in 1–100 ton scroll compressors. Int. J. Refrigeration 129, 317–331 (2021) 7. ASHRAE Standard 23, Methods for Performance Testing Positive Displacement Refrigerant Compressors and Compressor Units from IHS Markit (2022) 8. Standard, A.H.R.I., Performance rating of positive displacement refrigerant compressors and compressor units. AHRI Standard 540 (2015) 9. S.A. Klein, EES—Engineering Equation Solver, Version V10.835-3D, 2020-06-01, F-Chart Software. https://fchartsoftware.com 10. R.J. Moffat, Describing the uncertainties in experimental results. Exper. Thermal Fluid Sci. 1(1), 3–17 (1988) 11. I. Farrance, R. Frenkel, Uncertainty of measurement: a review of the rules for calculating uncertainty components through functional relationships. Clin. Biochemist Rev. 33(2), 49 (2012)
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12. J. Sieres, I. Ortega, F. Cerdeira, E. Álvarez, Drop-in performance of the low-GWP alternative refrigerants R452B and R454B in an R410A liquid-to-water heat pump. Appl. Thermal Eng. 182, 116049 (2021). https://doi.org/10.1016/j.applthermaleng.2020.116049 13. V.H. Panato, D.F.M. Pico, E.P. Bandarra Filho, Experimental evaluation of R32, R452B and R454B as alternative refrigerants for R410A in a refrigeration system. Int. J. Refrigeration 135, 221–230 (2022) 14. D. Menegazzo, S. Bobbo, L. Fedele, M. De Carli, L. Carnieletto, G. Emmi, A. Bernardi, Thermodynamic Analysis for the Selection of Low GWP Refrigerants in Ground Source Heat Pumps (2021) 15. Y. Jeon, S. Kim, S.H. Lee, H.J. Chung, Y. Kim, Seasonal energy performance characteristics of novel ejector-expansion air conditioners with low-GWP refrigerants. Appl. Energy 278, 115715 (2020) 16. D. Schmidt, J. Singleton, C.R. Bradshaw, Development of a light-commercial compressor load stand to measure compressor performance using low-GWP refrigerants. Int. J. Refrigeration 100, 443–453 (2019). https://doi.org/10.1016/J.IJREFRIG.2019.02.009 17. J. Singleton, D. Schmidt, C.R. Bradshaw, Control and commissioning of a hot-gas bypass compressor load stand for testing light-commercial compressors on low-GWP refrigerants. Int. J. Refrigeration 112, 82–89 (2020). https://doi.org/10.1016/J.IJREFRIG.2019.12.031
Compressor Performance for Varying Compositions of High-Glide Mixtures R1233zd(E)/R1234yf and R1336mzz(Z)/ R1234yf Leon P. M. Brendel, Silvan N. Bernal, Dennis Roskosch, Cordin Arpagaus, Andre Bardow, and Stefan S. Bertsch
Abstract Theoretical work has shown that zeotropic mixtures allow COP improvements for heat pumps if large temperature changes in the heat source and heat sink exist, as is common in industrial applications. However, the improvements shown in modeling work can only be harvested in a real system if the refrigerant mixture does not lead to a significantly lower compressor efficiency. This study presents experimental data for the mixtures R1233zd(E)/R1234yf and R1336mzz(Z)/R1234yf, featuring temperature glides of more than 30 K. Experimental data was collected at several suction pressures with varying pressure ratios for each pure refrigerant and three compositions for each mixture. Overall isentropic compressor efficiency, volumetric efficiency, and compressor heat rejection were compared as fundamental dimensionless performance measures. The isentropic and volumetric efficiency were a strong function of the suction pressure and pressure ratio, but little deviation was found among the different fluids and mixtures. Two empirical functions with a total of 6 fitting coefficients were found to represent the volumetric and isentropic efficiencies of all mixtures and operating conditions well. Keywords Compressor · Efficiency · Performance · Refrigerant mixture · Zeotropic mixture
L. P. M. Brendel (B) · S. N. Bernal · C. Arpagaus · S. S. Bertsch Institute for Energy Systems, Eastern Switzerland University of Applied Sciences, 9471 Buchs, Switzerland e-mail: [email protected] D. Roskosch · A. Bardow Energy and Process Systems Engineering, ETH Zürich, 8092 Zürich, Switzerland © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_60
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1 Introduction Refrigerant mixtures have the potential to improve the COP of industrial hightemperature heat pumps by matching the temperature differences of the heat source and sink. For modeling, it is important to accurately predict the compressor efficiency as the mixture composition is optimized, typically resulting in a range of suction and discharge pressures [6]. Therefore, compressor performance tests with refrigerant mixtures are needed. An early example of such research is Quast and Kruse [5], who investigated mixtures of R22 and R114. However, similar studies for refrigerant mixtures featuring high glides for high-temperature heat pumps are rare. In this study, R1233zd(E) and R1234yf, as well as R1336mzz(Z) and R1234yf, are tested in a reciprocating compressor. The two mixtures have glides of more than 17 K and 30 K, respectively, at a dew point temperature of 60 °C, as predicted by REFPROP Version 10 [4]. These large glides are promising for applications with high temperature changes of the heat source and sink. In the present study, these mixtures are tested at varying compositions for a set of suction pressures with varying pressure ratios to support system level modeling with a better prediction of the compressor efficiency across the mixture composition.
2 Experimental Test Setup Experiments were conducted on a heat pump, as shown in Fig. 1. The internal heat exchanger was deactivated using a three-way valve. The mass flow meter was installed in the liquid line, and the oil separator was directly after the compressor. Pressure transducers and thermocouples were installed close to the suction and discharge port and connecting pipes were insulated. The compressor itself was not insulated. The compressor suction and discharge pressures were controlled by changing the heat source/sink temperature and mass flow rate. A more detailed description of the test setup can be found in [1]. All tests were conducted with a reciprocating compressor (Bitzer 2DES-3Y) and a high-temperature oil (Fuchs Reniso Triton SE170).
3 Test Matrix and Data Quality 3.1 Test Matrix The test matrix was designed to show fundamental performance indicators like the overall isentropic and volumetric efficiency as well as the heat losses as a function of the pressure ratio and suction pressure. The following factors constrained the test matrix:
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Fig. 1 Schematic of refrigeration and water circuits of the experimental test setup
• Maintaining a source temperature above 0 °C to avoid freezing of the heat source • Maintaining a discharge temperature of less than 150 °C to avoid wear on the compressor • Maintaining a discharge pressure of less than 3200 kPa • Operating with clearly subcooled liquid in the mass flow meter and sight glass to ensure correct mass flow rate measurements • Not compressing into the two-phase region for fluids with overhanging vapor domes in T-s-diagrams. The achieved suction pressures and pressure ratios are shown in Fig. 2 (left). The conditions mentioned above do not allow testing in the upper right triangle of Fig. 2 (left) due to excessive discharge temperatures or pressures. The tested suction pressures were predefined to 50, 100, 150, 300, and 450 kPa. Some suction pressures could not be tested with certain fluids due to too high or low saturation temperatures. The pressure ratios were not predefined. To speed up testing, typically 3–5 data points were collected over the available range per selected suction pressure. Table 1 shows the number of collected data points per mixture and suction pressure. The suction superheat was typically controlled from 15 to 25 K. Some points were collected with approximately 10 K for comparison. R1336mzz(Z) and its mixtures had to be tested with 30 K superheat to avoid compression into the two-phase region. Figure 2 (right) shows the suction superheat levels for each data point. During analysis of the results, an increased superheat enhanced the overall isentropic and volumetric efficiency at otherwise constant parameters. However, the effect is neglected in this study and it was not attempted to include this effect in the proposed correlation. All data points were collected with a compressor speed of 50 Hz. Oil was changed after testing R1233zd(E) and all its mixtures. An oil sample collected during the oil change was analyzed by the oil manufacturer but no relevant changes compared to fresh oil were found.
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Fig. 2 Overview of data points. Suction pressure indicated by color; fluids and mixture composition indicated by different markers
Table 1 Number of data points per tested pure and mixed refrigerant and suction pressure Refrigerant fluid(s)
Composition [−]
Suction Pressure in [kPa]
-
x1
x2
50
100
150
300
450
R1233zd(E)
1.00
0.00
3
0
5
6
3
R1233zd(E) + R1234yf
0.85
0.15
4
0
11
8
3
0.70
0.30
0
3
3
4
3
0.55
0.45
0
2
4
5
0
R1234yf
0.00
1.00
0
0
4
5
4
R1336mzz(Z) + R1234yf
0.20
0.80
0
1
5
0
3
0.75
0.25
0
0
4
5
0
0.90
0.10
0
5
7
4
0
1.00
0.00
0
4
6
5
0
R1336mzz(Z)
3.2 Data Quality The target suction pressure was typically met in a range of ± 5 kPa except for a few outliers in the 450 kPa series (compare with Fig. 3). Steady-state data points are averaged over 10 min. For compressor performance testing, the discharge temperature is typically last to approach a steady state. However, it often does not affect the mass flow rate, power, suction state, or discharge pressure anymore. To speed up testing, a steady discharge temperature was only demanded for selected operating conditions.
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Fig. 3 Overall isentropic efficiency as a function of suction pressure and pressure ratio
The steady-state condition for the discharge temperature was then set to a change of less than 0.5 K over 10 min. Other operating conditions were tested without fulfilling this criterion for the discharge temperature. The suction superheat varied between 10 and 30 K, as discussed in the previous section but the following analysis does not distinguish data points by their superheat level since the data still correlates well.
3.3 Performance Measures Comparisons are based on three dimensionless quantifiers: The overall isentropic efficiency (ηois ), the volumetric efficiency (ηvol ) and a heat loss coefficient (ζco ). ηois =
m(h ˙ 2s −h 1 ) W˙
(1)
ηvol =
m˙ ρ1 Vswept f
(2)
Q˙ l W˙
(3)
ζco =
˙ 2 − h1) Q˙ l = W˙ − m(h
(4)
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m˙ is the mass flow rate, h 1 the suction enthalpy, h 2s the enthalpy at discharge pressure with the suction entropy, W˙ is the compressor power draw, ρ1 the suction density, Vswept the swept volume of the compressor, f is the rotational frequency of the crank shaft, Q˙ l is the absolute heat loss of the compressor as calculated by an energy balance and h 2 is the discharge enthalpy calculated from a pressure and temperature measurement. All thermodynamic properties were calculated using REFPROP Version 10 [4].
3.4 Measurement Uncertainty The measurement uncertainties for pressure, temperature, mass flow, and power measurements as well as calculated results are shown in Table 2. For the pressure transducers, 0.5% uncertainty is specified by the manufacturer excluding temperature effects, but 1.5% is specified including temperature effects. Uncertainties of variables depending on various measured quantities are calculated through uncertainty propagation. An uncertainty of the mixture composition was neglected but was found to be small for the R1233zd(E)/R1234yf mixture in a separate study [3]. For six representative data points, error bars are plotted in the respective figures in the results sections. Table 2 Uncertainties for pressure transducers, thermocouples, mass flow meter and calculated results Measured property
Uncertainty
Pressure (suction)
± 5 kPa excluding or ± 15 kPa including temperature effects (0.5% or 1.5% of full scale = 1000 kPa)
Pressure (discharge)
± 25 kPa excluding or ± 75 kPa including temperature effects (0.5% or 1.5% of full scale = 5000 kPa)
Temperature
± 1.5 K
Mass flow rate
± 0.1% of reading
Power draw
± 0.2% of range (15 kW) + 0.1% of reading
Calculated property Uncertainty propagation Pressure ratio
< ± 1.14 or < ± 3.42 including temperature effects
Isentropic efficiency
< ± 0.03 or < ± 0.09 including temperature effects
Volumetric efficiency < ± 0.06 or < ± 0.19 including temperature effects
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4 Results 4.1 Performance Measures The overall isentropic efficiency (ηois ) showed a strong dependence on the suction pressure and pressure ratio, as shown in Fig. 3. Higher suction pressures generally yield higher suction densities, mass flow rates, and power draws. The friction losses, which strongly depend on the compressor frequency and not as much on the operating conditions and the refrigerant become smaller relative to the power draw for high suction pressures, thereby increasing ηois . For each suction pressure, an efficiency peak is visible. R1336mzz(Z) and its mixture with R1234yf had a slightly higher isentropic efficiency than R1233zd(E) and its mixtures. This is visible in Fig. 3 when comparing the different marker symbols. The larger efficiencies could be caused by the higher densities of R1336mzz(Z) and its mixtures at equal suction pressures compared to R1233zd(E) and its mixtures with R1233zd(E). Moreover, the R1336mzz(Z) mixtures were tested with a higher superheat, which can also increase the isentropic efficiency. However, the differences among the fluids and mixtures were small compared to the impact of the suction pressure and pressure ratio. Uncertainty bars are shown for six selected data points and represent the uncertainties of neighboring data points. The black error bars correspond to a calculation with 0.5% of the full range uncertainty for the pressure transducers, while the gray and dashed error bars consider 1.5% uncertainty. Some erros bars are extremely large. In particular, the pressure transducers weigh in with an uncertainty relative to their full scale which is significant when measuring small pressures. Despite the large error bars from conservative manufacturer ratings, the trends for given suction pressures and mixtures show clear trends. The volumetric efficiency (Fig. 4) was clearly dominated by the pressure ratio. For any given pressure ratio, the different suction pressures and mixtures caused variations of no more than ±0.05. Like for the overall isentropic efficiency, the R1336mzz(Z) and mixture series had a tendency to higher volumetric efficiencies for a given pressure ratio. Further analysis of the differences seems valuable but was not attempted in this study. Heat losses were generally significant as shown in Fig. 5. Only data points for which the discharge temperature changed by no more than 0.5 K over 10 min, since the discharge temperature directly affects the computed heat losses. For any tested operating condition and fluid, at least 20% of the compressor power draw was rejected as heat to the ambient (ζco = 0.2). For a heat pump operating with a COP of 3, adding this heat to the heating capacity would increase the COP by 6.7% (heat recovery may be done using the heat sink fluid to avoid excessive discharge temperatures as a result from insulating the compressor): Q˙ Q˙
=
ζco ·W˙ C O P·W˙
=
0.2 3
= 0.06
(5)
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Fig. 4 Volumetric efficiency as a function of suction pressure and pressure ratio
Heat losses of up to 50% of the compressor power draw were found for many operating conditions. However, the measured heat losses of more than 50% for the 50 kPa series are unlikely to occur in a real system because a fluid with such low suction pressure would not be chosen. Generally, the high values of ζco show the
Fig. 5 Heat loss factor as a function of suction pressure
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large potential for waste heat recovery from the compressor for high-temperature heat pump applications. This is discussed in more detail in Brendel et al. [2].
4.2 Empirical Description The results for the volumetric efficiency in Fig. 4 can be approximated with a simple curve through ηvol = 1 at a pressure ratio of Pr = 1: ηvol = 1 − b0 · (Pr − 1)b1
(6)
The values of the fitting coefficients are shown in Table 3 and the resulting curve is shown as a black dotted line in Fig. 4. An empirical function of the suction pressure and pressure ratio to reproduce the measured overall isentropic efficiencies in Fig. 3 should satisfy the following observations: • At constant suction pressure, there is a global maximum at some pressure reatio • The peak efficiency occurs at lower pressure ratios (Pr ) as the suction pressure (Ps ) increases. • The efficiency drops more steeply to the left of the peak than to the right of the peak for any given suction pressure. • The curves have steeper slopes on both sides as the suction pressure increases. This can be described mathematically with a short function which prevents entirely unrealistic trends outside of the fitted data. A possible formulation is the following equation: ηois = a0 −
0.6 (Pr −a1 )a2 ·Ps
− a3 · Pr1.8
(7)
The values 0.6 and 1.8 are manually fitted parameters. The second term becomes smaller for larger pressure ratios (Pr ) such that the efficiency of different suction pressures will be dominated by the line ηois = a0 − a3 · Pr1.8 for high Pr (> 10). The exponent “1.8” defines the curvature of this trend at high Pr . For small values of Pr the third term is negligible, and the second term forces the function to have a root close to the value of a1 . Fitting Eq. (7) to the available experimental data results in the coefficients shown in Table 3 and the dashed lines in Fig. 3. The deviation of the measured values to the fitted lines is no more than 0.045. The average absolute Table 3 Coefficients for empirical efficiency descriptions Coefficient
b0 [−]
b1 [−]
a0 [−]
a1 [−]
a2 [1/kPa]
a3 [−]
Value
0.08244
0.72773
0.66981
0.01466
0.00838
0.00102
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deviation is 0.013, 96% of all points have a deviation of less than 0.03 and 76% have a deviation of less than 0.02. Fitting was done in Python using the “curve_fit” tool from scipy.
5 Discussion The results show that the difference between the tested fluids and mixtures is small relative to the impact of the pressures. Unfortunately, it cannot be inferred directly that other HFO/HCFO refrigerants would match the trends found so far. This could only be verified experimentally and is seen as important future work. Based on the test matrix, the suction temperatures varied from 17 to 98 °C. The temperature change and the change of solubility with temperature affected the oil viscosity during the tests. The contribution to changes in the overall isentropic efficiency cannot be determined. The results in Sect. 4 focused on the pressure ratio and suction pressure to interprete the experimental results. From a heat pump system design point of view, though, usually the required heat sink and either the available heat source inlet or required source outlet temperature are considered. A simple heat pump example could be set as follows. In a hypothetical plant, water must be provided at 90 °C (heat sink), and a heat source must be cooled down to 20 °C to release it back into the environment. Assuming counterflow, minimal pinch points and a negligible heating effect of the refrigerant desuperheating after the compressor, the dew point of the condensation process must be approximately 90 °C. The temperature at the evaporator inlet must be approximately 20 °C. Assuming a vapor quality of 0.2 at the evaporator inlet, the high and low side pressure, and the pressure ratio are calculated as follows: Ps = P(T = 20◦ C, x = 0.2, Refrigerant)
(8)
Pd = P(T = 90◦ C, x = 1.0, Refrigerant)
(9)
Pr = Pd /Ps
(10)
Given Ps and Pr , the isentropic efficiency can be calculated using Eq. 6 with the coefficients from Table 3. The efficiency was calculated for an R1336mzz(Z)/ R1234yf mixture in composition increments of 0.1. The results are shown in Fig. 6 with colored points, where the annotations indicate the mass fraction of R1336mzz(Z). For the mass fractions 0, 0.7, 0.8, 0.9, and 1.0, efficiency lines of constant suction pressure over varying pressure ratios were drawn using Eq. 6. The line-labels in gray indicate the suction pressure. Pure R1234yf (yellow point) has the highest suction pressure and a pressure ratio of 5.2. As R1336mzz(Z) is added, the trendline is explained by a trade-off: The increasing temperature glide enables smaller pressure ratios. At the same time,
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Fig. 6 Overall isentropic efficiency as a function of pressure ratio for an R1336mzz(Z)/R1234yf mixture in composition increments of 0.1. The line-labels indicate the suction pressure. The red box indicates the mixture with the mass fraction generating the highest glide
the higher R1336mzz(Z) mass fraction increases the pressure ratio. Therefore, the pressure ratio reaches a minimum, which occurs in this example close to the mass fraction of the highest temperature glide at an R1336mzz(Z) mass fraction of 0.7, indicated with a red box. From there on, both the decreasing temperature glide and the decreasing suction pressure cause an increase in the pressure ratio, resulting in a steep trend for an increased R1336mzz(Z) mass fraction towards higher pressure ratios, lower suction pressures, and lower isentropic efficiencies. From a heat pump system design perspective, these results are positive: E.g., a mixture of 70% R1234yf and 30% R1336mzz(Z) has minimal efficiency losses compared to the pure high-pressure fluid R1234yf but has the following potential advantages: • A critical temperature of 149 °C, 55 K more than pure R1234yf • 158 kJ/kg heat of condensation, three times more than pure R1234yf (h(P = P(T = 90◦ C, x = 1)) − h(P = P(T = 90◦ C, x = 0))) • Temperature glides of 27 and 32 K on the high and low-pressure side respectively (compare bubble and dewpoint temperature at given pressure) Charts like those in Fig. 6 could help to find ideal mixture compositions heuristically or add to the understanding of results from large-scale optimizations.
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6 Conclusions R1233zd(E), R1336mzz(Z), R1234yf and mixtures of these fluids were tested in a reciprocating compressor. The overall isentropic efficiency strongly depended on the pressure ratio and increased with the suction pressure. The volumetric efficiency was mainly a function of the pressure ratio. Both efficiencies were slightly higher for R1336mzz(Z) and its mixtures, potentially due to a higher density and higher tested superheat levels. Simple empirical functions solely dependent on the pressures were fitted to the data of the tested compressor, which reproduce the overall isentropic and the volumetric efficiency independent of the fluids and can be used for system-level modeling. The overall isentropic efficiency is predicted within ± 0.03 for 96% of the datapoints. Heat losses of the compressor ranged from 20 to 50% of the compressor power draw for most operating conditions. Acknowledgements The authors gratefully acknowledge the financial support of the Swiss National Science Foundation and Innosuisse (Bridge Discovery project with grant number 203645).
References 1. C. Arpagaus, F. Bless, M. Uhlmann, E. Büchel, S. Frei, High temperature heat pump using HFO and HCFO refrigerants—system design, simulation, and first experimental results, in Purdue Conferences, West Lafayette, IN, USA (2018). https://docs.lib.purdue.edu/cgi/viewcontent.cgi? article=2874&context=iracc 2. L.P.M. Brendel, C. Arpagaus, F. Bless, S. Paranjape, S.S. Bertsch, Compressor waste heat utilization for high-temperature heat pumps, in World Sustainable Energy Days—Young Energy Researchers Conference, Wels, Austria (2023a) 3. L.P.M. Brendel, S.N. Bernal, C. Arpagaus, S. Paranjape, S.S. Bertsch, Mass fraction checks of an R1233zd(E) and R1234yf mixture in a high-temperature heat pump, in 3rd IIR Conference on HFO Refrigerants and Low GWP Blends, Shanghai, China (2023b) 4. E.W. Lemmon, I.H. Bell, M.L. Huber, M.O. McLinden, NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 10.0 (National Institute of Standards and Technology, 2018). https://doi.org/10.18434/T4/1502528 5. U. Quast, H. Kruse, Experimental performance analysis of reciprocating compressor working with non-aceotropic refrigerant mixtures, in Purdue Conferences, West Lafayette, IN, USA (1986). https://docs.lib.purdue.edu/icec/567/ 6. D. Roskosch, V. Venzik, J. Schilling, A. Bardow, B. Atakan, Beyond temperature glide: the compressor is key to realizing benefits of zeotropic mixtures in heat pumps. Energy Technol.9(4) (2021). https://doi.org/10.1002/ente.202000955
Use of CFD and Geometry Optimization to Improve the Secondary Oil Separation of an Oil Flooded Rotary Vane Compressor James Willie and Rumit Ganatra
Abstract Computational Fluid Dynamics (CFD) and analytical modelling as predictive tools are playing an increasing role in the design and optimization process at Compressors Vacuum Pumps Systems (CVS) Engineering GmbH. To enable an efficient primary and secondary oil separation in a rotary vane oil flooded compressor steady and unsteady CFD is used to mimic the flow in the airend and the primary and secondary oil separators of the compressor. Optimization of flow was done using Design of Experiment (DoE) to improve the secondary separation between the oil and the air by reducing the oil challenge and the oil carry-over volume as reported in this paper. Keywords Rotary vane compressor · DoE · Carry-over volume · Oil challenge · Oil separation
1 Introduction At Compressors Vacuum Pumps Systems (CVS) Engineering continuous improvement by optimization of the machines that are developed is part of the company’s philosophy. To achieve this High Performance Computing (HPC) is used through Computational Fluid Dynamics (CFD) simulations combined with other analytical tools like 0D and 1D thermodynamic chamber models and Design of Experiments (DoEs) [1]. The 3D CAD models of the compressors are created using Inventor Professional. They include oil flooded and oil free rotary vane compressors and vacuum pumps and oil free screw compressors and liquid ring vacuum pumps. Optimization is done using DoEs with the help of simulations and measurements. This paper presents an example of the optimization that was done on the 800L/min size oil flooded rotary vane compressor in order to improve the separation between the oil and air. This compressor is used on trains for operating the braking system and the doors. The main J. Willie (B) · R. Ganatra Compressors Vacuum Pumps Systems (CVS) Engineering GmbH, Großmattstraße 14, 79618 Rheinfelden, Germany e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_61
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goal was to optimize the primary and the secondary separators in order to reduce the oil carry-over volume. This is due to stringent environmental standards that limits the amount of oil leaving the compressor and the need to reduce the downtime caused by changing the oil element and refilling the oil sump. The current standard requires the oil carry-over volume to be below .5 mg m−3 after 4400 h of operation. Due to the lack of swirl in the flow entering the secondary separator and the overloading on one side of the oil element the secondary separator was optimized and this is presented in this work. Measurement of the oil challenge, which determines the amount of oil after the primary separation, showed that optimization was needed in order to reduce the amount of oil entering the secondary separator to reduce the loading on the oil element. To do this a redesign of the primary separator was proposed and this will be presented in future work. The CAD model of the machine optimized was created using Inventor Professional and 3D CFD simulations were carried out using ANSYS CFX and CONVERGE CFD [2, 3]. The machine was first benchmark using measurements and simulated, after which various geometries and concepts were created to improve the secondary oil separation from the air [4]. The final concepts selected were fabricated and tested and the results are presented here. This was followed by the pilot phase in which the final concepts are being tested at selected customers in the field. In the prototype test, the oil challenge and the oil carry-over volume were measured.
2 Measurement Setup The overall view of the test rig used for the measurements at CVS and PSI Global is shown in Fig. 1a. The front and the side views of the rig are shown in Fig. 1b and c. The color coding is as follows: The components are shown in blue and the temperature measuring points in green and the pressure measuring points in orange. The description of each measurement point or item in the numberings in Fig. 1 is presented below. 1 Intermediate flange with oil cooler 2 Electric motor (Siemens) 3 Control cabinet 4 Compressed air dryer 5 Measurement device with data logger 6 Electric cabinet on/off 7 Compressed air after cooler 8 Minimum pressure non-return valve 9 Air suction 10 Compressor stage 11 Air filter cover
12 Oil separation cover 13 Pipe loop for measuring oil challenge 14 Measurement of the air suction temperature 15 Measurement of the pressure in the compressor stage 16 Measurement of the oil sump temperature 17 Pressure measurement at the outlet 18 Measurement of the pressure after the air dryer 19 Temperature measurement at the outlet 20 Temperature measurement after the air dryer 21 Pressure measurement at the inlet after cooler 22 Temperature measurement at the inlet after cooler
The sensors and measuring devices used include the following: A data logger model ALMEMO 5690-2M v6 for displaying and recording the measured values
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(a) Overall of test rig
767
(b) Front view
(c) Side view Fig. 1 Measurements test rigs at CVS engineering and PSI Global
with an accuracy of.± 0.1%; the pressure transmitter for measuring the static pressure from Baumer model FlexBar HRT with accuracy below 0.2%; Thermocouple for temperature measurements from RÖSSEL Messtechnik GmbH, type K, class 1 with accuracy .± 1.5 .◦ C; variable area flow meters used for the volume flow measurements from Krohe with rotary encoder H250 3W2 with accuracy 4% and the Precision scale for measuring the oil content from Kern with accuracy .± 0.03 g.
2.1 Operating Point Simulated The selection of the operating point simulated was based on the oil carry-over volume measured at the various operating points. Measurement data showed that this volume increases at lower operating pressures and because the machine runs between 4 and 12 bar (g) and in some cases up to 14 bar (g) in stationary gas application the pressure with the highest carry-over volume is at 4 bar (g). The compressor design speed is 1500 rpm, even though using a VFD the compressor can be operated between 800 and 2000 rpm in stationary gas application. Using Chamber Modeling the operating
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(a) Compressor stage
(b) p-V diagram
Fig. 2 Design point and non-design point compression
point of the airend was determined. To explain this the p–V diagram in Fig. 2 is used. In Fig. 2a a sketch of the compressor stage with the top dead center (TDC) and the bottom dead center (BDC) is depicted together with the direction of rotation and the number of vanes. The operating principle is similar to rotary vanes in which the rotation axis is eccentrically placed inside the rotor housing and as the rotor turns the centrifugal force moves the vanes in and out of the slots. This action opens the inlet at a set time and closes it when the suction volume is maximum at .VS shown in Fig. ( 2b) for compression to begin and at a set or built in compression ratio κ
1
(.π = ppSi = VVSi ) or internal volume compression (.vi = π κ ) the discharge opens when the pressure is . pi as shown in Fig. 2b [5, 6]. In this case . p D = pi and we have isentropic compression at the design point. For . p D > pi we have under-compression and the process pressure is higher than the compressor stage pressure and when the discharge opens the flow quickly flows from the discharge into the compressor in order to equalize the pressure. This process can lead to noise generation and waste of power and can negatively affect the compressor performance. For . p D < pi we have over-compression and the process pressure is less than the compressor stage pressure and when the discharge opens the flow quickly moves from inside the compressor to the discharge in order to equalize the pressure and this can also lead to noise generation and loss of compressor efficiency and negatively affect the performance of the compressor. For the benchmark point selected at 4 bar (g) the compressor is operating in over-compression mode. The measurement data for the simulated point presented here is shown in Table 1. In this table the inlet pressure, inlet temperature, discharge pressure, discharge temperature, volume flow rate, rotor speed and the shaft power are presented. The various measurement points at which the values are taken are shown in Fig. 3. The CFD simulation presented here is done using steady state CFD with CFX and for this the inlet of the model is at point E in Fig. 3 and the outlet is at point F. This is followed by the rotating flow simulation that includes the airend (The rotor, shaft and vanes) and the inlet is at point B and the outlet at point F. The pressure drop (.Δp) measured between points E and F is 250 mbar and that between points E and I is 400 mbar.
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Table 1 Operating point simulated and validated Parameter Measured value Inlet pressure (. p1 ) Inlet temperature (.T1 ) Discharge pressure (. p2 ) Discharge temperature (.T2 ) Volume flow rate (.V˙ ) Rotor speed (. N ) Shaft power (P)
940 mbar at D 20.9 .◦ C at B 4.04 bar g at E 57.3 .◦ C at E 46.1 .m3 /h 1497 rpm 4.52 kW
Fig. 3 Picture showing compressor with measurement points
In Fig. 3 point G is the location where oil (Oil type: Mobil Delvac 1 ESP 5W-40) is injected into the compression chamber but it is not accounted for in the simulation. One reason is because the oil volume flow rate is only 2% of the air flow rate at 1.247 .m3 /h. For this reason, it is concluded that the flow field will be dominated and determined by the air flow rate and therefore only air is simulated. This will limit the computational cost required and at the same time adequately mimic the flow inside the compressor in order to make optimization possible using the DoE approach presented in this work.
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(a) Primary separator
(b) Secondary separator
(c) Primary & secondary outlet to oil element
Fig. 4 Negative volume for the CFX steady state simulation
3 Case Setup This part is divided into two sections. The first part looks at the CFX steady state setup and this is followed by the rotating flow setup using CONVERGE CFD.
3.1 CFX Steady State Setup As with every simulation, the domain for the CFX steady state simulation is determined and the negative volume extracted as shown in Fig. 4, with the primary separator in Fig. 4a and the secondary separator including the oil element in Fig. 4b. The mass flow rate through the primary and secondary outlets shown in Fig. 4c are determined using CFD and used to check the loading of the oil element. Inventor Professional is used to generate the CAD geometry and ANSYS SpaceClaim is used to extract the negative volume. Mesh generation is done using ANSYS Meshing [2]. After doing Mesh sensitivity the final mesh size selected is shown in Fig. 5 with a size of 9,796,609 elements. It is a hybrid mesh with tetrahedron mesh of element size 2 mm and hexahedron mesh with element size 1 mm for the oil element porous media region. Inflation layers are also used to resolve the boundary layer of the flow close to the walls of the oil element. For the setup using porous media in the steady state CFX simulation and in the unsteady state simulation with the rotating parts of the geometry the loss coefficient is determined by curve fitting the pressure drop (.Δp) across the oil element against the exit velocity (.wexit ), which is the average velocity of the flow leaving the oil element in the radial direction. Using Fig. 6 and the linear fit .Δp = C · wexit , the loss coefficient, C, which is the gradient of the fitted curves, is computed to be 68,900 2 .kgm s. This is scaled using the average thickness of the oil element by multiplying 1 with the factor . re −r , where .re is the external radius of the oil element and .ri is the i inner radius of the oil element. Finally, the exit velocity is converted into a volume
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(a) Primary separator mesh, z=-40mm
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(b) Oil element mesh, x=115mm
Fig. 5 CFX steady state mesh
Fig. 6 Modeling the oil element using porous media
averaged velocity of the oil element by multiplying with the factor . re2r+re i to get loss coefficient .C = 3.55 × 106 kg/m3 s. The CFX steady state simulation uses a mass flow inlet with.m˙ inlet = 0.015665 kg/s and a turbulent intensity of 5% using the SST turbulence model. A pressure outlet is used with the average static pressure set to 396,420 Pa that was determined iteratively until . pinlet = 5.05 bar (a) as measured. The pressure profile blend used is 0.05 and the walls are set to no slip and roughness set to smooth. Walls temperatures are set based on measurement data and the working fluid is air.
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(a) Benchmark 800L/min compressor (b) Benchmark 800L/min compressor geometry negative volume Fig. 7 CAD geometry and extracted negative volume of the simulated compressor
3.2 Rotating or Unsteady Simulation Setup The rotating flow setup in CONVERGE is presented here. To account for the moving part that includes the rotor and the vanes the cartesian approach used in the mesh generation by CONVERGE STUDIO is applied [3]. The complicated nature of the mesh makes using the traditional approach very difficult, if not impossible. After importing the STL file from Inventor it is cleaned as shown in Fig. 7. The mesh motion to account for the rotation of the rotor and the vanes is done using a script file. The mesh generation process is automatic and adaptive using Automatic Mesh Refinement (AMR). However, the boundary conditions, the materials and the numerical parameters have to be specified. The simulation uses a pressure inlet and a pressure outlet and the fluid is air and the flow is compressible using the Redlich-Kwong equation of state. The Reynolds Average Navier Stokes (RANS) and the Pressure Implicit with Splitting Operators (PISO) solver is used. After sensitivity analyses of the various turbulence models (.k − ∈ realizable with enhanced wall function, .k − ω SST with automatic wall function and Reynolds Stress Model (RSM) with standard wall function) it was decided to use the Reynolds stress model because it was able to better capture the high swirl in the flow [7, 8]. After the mesh sensitivity analyses the base grid selected for the setup was 16 mm with minimum cell size of 0.25 mm inside the rotor. For the sensitivity analyses, 32 mm base grid with a minimum cell size of 0.5 mm inside the rotor and 8 mm base grid with minimum cell size of 0.25 mm inside the rotor were also tested. As shown in Fig. 8 fixed embedding was used together with velocity based AMR of level 3 in the casing region with Sub-Grid-Scale (SGS) 0.05 m/s. A level 4 fixed embedding was set at the intake and rotor regions and proximity AMR of level 5 and 6 was applied to the tip of the vanes. To account for the sealing effect of the oil the following options were applied to optimize the cells and run time. Proximity AMR was used to add cells only if two boundaries were very close and porous media
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Fig. 8 Cartesian mesh of the compressor showing various regions of grid resolution in the yz plane
was used at the boundaries where the proximity AMR are active in order to damp or eliminate the flow through the vane/casing gaps and the sealing feature was used in order to block the flow in the small axial gaps.
4 Results and Discussions Results are presented for the CFX steady state simulation and the CONVERGE CFD unsteady simulation and compared. Results are presented for the baseline model followed by results of the optimization and finally, measurement results of the selected concepts are presented and discussed. For post processing the CFD results, ANSYS CFD-Post is used for the CFX results and for the CONVERGE results Tecplot is used. In both cases, Matlab is also used for the post-processing. To check the various concepts developed using DoE the swirl number (SN) in various planes of the oil element is determined using: ∫ ρ · wz · (x · w y − y · wx )d A ∫ .S N = (1) R ρ · wz2 d A The SN is defined as: .
SN =
Axial flux of angular momentum Axial flux of axial momentum
(2)
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(a) Minimum oil level
(b) Middle oil level
(c) Maximum oil level
Fig. 9 Normalized CFX steady state vel. streamlines through the primary separator Table 2 CFX and CONVERGE predicted numerical values determined for the baseline model Solver CFX CONVG
.Δpcomp
.wexit
(Pa)
(m/s)
Outlet SN .@ SN .@ .Δpele vel. (m/s) z = 88 mm z = 75 mm (Pa)
.m ˙ prim.
.m ˙ sec.
(kg/s)
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0.093
11.042
.− 0.019
.− 0.04
(kg/s)
6417
0.0113
13,115
0.097
11.434
–
.− 0.04
0.0034
6193
0.0118
0.0036
The exit velocity, .wexit , is determined in addition to the pressure drop .Δp from the inlet to the outlet and across the oil element.
4.1 Baseline Model The steady state CFX results of the normalized velocity streamlines for three cases mimicking the oil level inside the oil sump are presented in Fig. 9. In Fig. 10 the normalized velocity vectors in various planes are presented with the planes cutting through the oil element (see Fig. 10a and b) and through the oil element cover (see Fig. 10c) for the CFX steady state simulation and the unsteady CONVERGE simulation after one circle (At crank angle 360.◦ ) shown in Fig. 10d–f. The trend of the results obtained using the steady CFX simulation and the unsteady CONVERGE simulations are similar. One observation in both cases is that the flow through the oil element is unbalanced with one side of the element being overloaded. Also, the swirl of the flow through the oil element cover is not high and this is shown by the numerical value in Table 2. Other values are determined from CFX and compared to the moving average values determined from the unsteady simulation using CONVERGE CFD as seen in Table 2. The total mass flow at the outlet is obtained by adding the primary and the secondary mass flow rates. The measured mass flow rate is 0.01568 kg/s. For the unsteady simulation a pressure inlet and a pressure outlet is used meaning that the mass flow rate and hence the volume flow rate are determined by the solver. For the CFX steady case the inlet mass flow rate is specified to be 0.015665 kg/s and the outlet mass flow rate computed is 0.0147 kg/s (Giving a percentage error of 6.2%). For the unsteady simulation, the inlet mass flow
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(a) CFX, plane x=115mm
(d) CONVERGE, x=115mm
plane
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(b) CFX, plane y=75mm
(c) CFX, plane z=113mm
(e) CONVERGE, y=75mm
(f) CONVERGE, z=113mm
plane
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Fig. 10 Normalized steady state CFX and CONVERGE vel. vectors of the oil element
rate is 0.016036 kg/s and the outlet mass flow rate is 0.015378 kg/s (Percentage error of 4.1%). The mass balance in both cases are good. The difference in the mass flow through the primary and secondary outlet explains why we have unbalanced loading of the oil element as mentioned above. One key performance indicator of the oil element is the exit velocity (.wexit ), which should be .< 0.1 m/s and from Table 2 this is the case for both the CFX solver and the CONVERGE CFD solver. The unsteady results of the baseline geometry for the mass flow rate, the compressor input shaft power, the pressure drop across the oil element, and the swirl number (SN) are presented in Fig. 11. The average value for the pressure drop and the SN are shown in Table 2. The average compressor mechanical power used for compressing the gas obtained from CFD is 3.978 kW, which is less than the compressor mechanical power measured at the input shaft with a value of 4.52 kW. This is because the input shaft power includes the losses in the drive train occurring at the bearings, mechanical seal, radial shaft seal, cooling fan and friction inside the compressor as shown in the bar chart in Fig. 12 that adds to 0.553 kW. These losses are not computed in the CFD simulation and so to get the mechanical shaft power we need to add the CFD compressor power to that estimated from the various losses. This gives 4.531 kW, which is close to the measured value. To check if CFD is capable of predicting the lobe passing frequencies of the compressor and if the operating point is predicted as expected, pressure time series at the outlet of the airend and pressure and velocity contours are plotted in Figs. 13 and 14, respectively. Based on the FFT in Fig. 13b the fundamental frequency (173.79 Hz)
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(a) Mass flow rate
(b) Compressor power
(c) Oil element Δp
(d) Swirl number
Fig. 11 Unsteady CONVERGE sim. results of the baseline geom. with moving averages
Fig. 12 Bar chart showing various losses occurring inside the baseline compressor
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Fig. 13 Time series and FFT of the pressure at the outlet of the airend
(a) Velocity contour
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Fig. 14 Velocity and pressure contours of the airend to verify design point
and the harmonics are shown. Because we have 7 vanes and the input speed is 1497 rpm, we can compute the lobe passing frequency to be 7(1497/60) = 174.65 Hz, which is close to that predicted by CFD. The internal compression is as expected with the maximum pressure occurring at the discharge just before it opens as shown in Fig. 14b.
4.2 Optimization Based on geometry modification in CAD and CFD simulations various concepts for improving the secondary oil separation were identified. Three of the best ideas are selected and presented here, namely, Concept 5F (Cyclone integrated into the
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(a) Plane z=113mm, base- (b) Plane z=75mm, base- (c) Plane x=115mm, baseline line line
(d) Plane z=113mm, 5F
(e) Plane z=75mm, 5F
(f) Plane x=115mm, 5F
(g) Plane z=113mm, 6E
(h) Plane z=75mm, 6E
(i) Plane x=115mm, 6E
(j) Plane z=113mm, 4C
(k) Plane z=75mm, 4C
(l) Plane x=115mm, 4C
Fig. 15 CONVERGE contour plots of the baseline and modified geometries
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Table 3 Swirl number and exit velocity of baseline verses optimized models Concept SN at z = 75 mm (–) Exit velocity (m/s) Baseline 5F 6E 4C
0.0401 1.3317 0.5402 0.0396
(a) Carry-over volume
0.09308 0.09351 0.09305 0.09307
(b) Oil challenge
Fig. 16 Measured oil carry over volume and oil challenge of various geometries
oil element endcap), Concept 4C (Two vanes at 70.◦ integrated into the oil element endcap) and Concept 6E (Adding a wall to the oil element cover in order to increase the swirl of the flow). In the following, the contour plots of the velocity inside the compressor without and with these elements are presented. The computed swirl numbers compared to the baseline geometry are also presented and this is followed by the measurements of the oil challenge and the oil carry-over volume. The result in Fig. 15 shows that with the cyclone part 5F and the wall integrated into the oil element cover 6E and the 70.◦ vane the loading of the oil element is more balanced relative to the baseline model. To check the veracity of these results the swirl numbers at the entry to the oil element are determined as shown in Table 3. Concept 5F has the highest value followed by 6E and the value for concept 4C and the baseline are about the same. It is therefore expected that the separation between the oil and the air will improve in these cases relative to the baseline. The computed pressure drop in the modified geometry with the cyclone is larger. The baseline .Δp is 7676 Pa and that of the modified geometry with the cyclone is 10,041 Pa. However, when the pressure drop across just the oil element is determined, it is slightly lower with Concept 5F compared to the baseline model (6293 Pa vs. 6417 Pa) and this result is similar in trend to that measured. .Δp across the oil element with 5F is 188.39 mbar and that for the baseline without 5F is 247.54 mbar. Based on the results above the 5F, 6E and 4C parts are fabricated and tested in addition to the baseline at 4 bar (g). The machine is run for 24 h first to ensure
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that the oil element is saturated before the oil carry-over volume is measured in a specified time period. For each part, three oil elements are tested for the oil carryover volume and each test is repeated three times to check for repeatability and an average is determined as shown in Fig. 16a. As predicted by CFD, 5F has the lowest oil carry-over volume followed by 6E and 4C and the baseline. The oil challenge for the baseline and 6E are also measured to see how much is entering the oil element as plotted in Fig. 16b. Clearly, more oil is entering the oil element in the baseline case than in the 6E case due to the introduction of the wall, which leads to an increase in the circumferential velocity and to the swirl in the oil element cover.
5 Conclusions This paper presents the successful use of CFD and optimization to improve the secondary separation between the oil and the air in an CVS oil flooded rotary vane compressor. It shows that CFD can be used as an invaluable tool in the design and optimization of rotary vane compressors. This reduces the time and cost of development by limiting the testing and the number of prototypes required. As future work, a re-design of the compressor will be investigated in order to improve the primary oil separation. Acknowledgements The authors would like to thank Jana Hoffmann for her good work during her Master Thesis and Professor Daniel Weiss, who supervised the thesis, and PSI Global and Convergent Science for their support during this work.
References 1. J. Willie, Analytical and numerical prediction of the flow and performance in a claw vacuum pump. IOP Conf. Ser.: Mater. Sci. Eng. 425, 012026 (2018). https://doi.org/10.1088/1757-899X/ 425/1/012026 2. ANSYS, Ansys CFX Documentation (2021) 3. J.K. Richards, K.P. Senecal, E. Pomraning, CONVERGE 3.0 Manual (Convergent Science, Madison, WI, 2021) 4. J. Hoffmann, Modelling and optimisation of the flow inside an oil flooded rotary sliding vane compressor. Master Thesis, University of Applied Sciences and Arts Northwestern Switzerland (2022) 5. W.H. Faragallah, D. Surek, Rotierende Verdrängermaschinen (Verlag und Bildarchiv, Sulzbach, 2004) 6. W.H. Faragallah, Vakuuum Pumpen (Verlag und Bildarchiv w.H. Faragallah, Gastransfervakuumpen) Sulzbach, 2008) 7. W. Fister, Fluidenergiemaschinen: Physikalische Voraussetzungen, Kenngrößen, Elementartstufen der Strömungs-und Verdrängermaschinen, Band 1 (Springer, Berlin, 2013) 8. S.B. Pope, Turbulence Flows, 1st edn. (Cambridge University Press, 2000)
An Appraisal of the 1950 Festival Hall Heat Pump Andy Pearson
Abstract In 1950 the largest heat pump yet constructed in the United Kingdom was installed to serve the new Festival Hall in London. Many misconceptions have been published about this iconic and innovative installation over the last forty years, to the extent that the myths and half-truths in general circulation about the project outweigh the facts. This paper draws on contemporary reports and seeks to set the record straight as the 75th anniversary of the Festival of Britain approaches. The performance and suitability of the arrangement are analysed and put into historical perspective. Prospects for the future application of this technology are appraised and suggestions of future development projects are proposed. Keywords Heat pump · Industrial history · Festival Hall · Performance · Gas engine
1 Introduction In 1945, at the close of the Second World War, the Ministry of Fuel and Power Act set out “to appoint a Minister of Fuel and Power (in this Act referred to as “the Minister”) who shall be charged with the general duty of securing the effective and co-ordinated development of coal, petroleum and other minerals and sources of fuel and power in Great Britain, of maintaining and improving the safety, health and welfare of persons employed in or about mines and quarries therein, and of promoting economy and efficiency in the supply, distribution, use and consumption of fuel and power” [1]. The Ministry had been created in 1943 under the Emergency Powers Act to address the coordination of all matters related to the management of fuel and power in wartime and the 1945 Act recognised that the fuel problem would persist for years after the hostilities formally ceased. When the plans for a Festival of Britain to be held in 1951 in London were unveiled in 1948 it was realised, prompted by the Heat Pump Committee of the Electrical Research Association, that A. Pearson (B) Star Refrigeration Ltd., Glasgow G46 8JW, UK e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_62
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this was an ideal opportunity to conduct some intense research and development on the application of large scale river source heat pumps (Fig. 1). A development plan was created with the objective of comparing and contrasting different ways of using gas for heating. At that time coal was still the preferred fuel for heating buildings and was much cheaper than gas, which was manufactured from coal, producing “town gas” and “coke” as a residual fuel source. At the outset, the need for a compact unit was identified and so the decision was taken to use an aircraft engine suitably adapted for the purpose instead of using a traditional reciprocating compressor and gas engine drive, which the designers described as “very unwieldy” for this application [2]. The traditional selection of a single unit would have been a 4 cylinder compressor with a 15 in. (380 mm) bore and 10 in. (254 mm) stroke running at 375 rpm, giving a displacement of about 2600 m3 h−1 with a shaft power input of about 450 kW. The details of the development, design, installation and operation of the Festival Hall Heat Pump contained in this appraisal are taken from a paper presented by the principal designers, P. E. Montagnon and A. L. Ruckley to the Institute of Fuel in December 1953 and published in the Journal of the Institute of Fuel in April 1954 [2]. Additional information was gathered from a commemorative book produced by London County Council in 1951 [3]. Montagnon was the Senior Principal Scientific Officer of the Chief Scientist’s Division of the Ministry of Fuel and Power and was awarded the OBE in the 1954 New Year’s Honours list. Ruckley was the Senior
Fig. 1 The Festival Hall from the north [3]
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Experimental Officer in the Division, which was headed by the Chief Scientist, Sir Harold Roxbee Cox, and his deputy, Kelvin Spencer. This innovative project is worth studying in detail because it provides many useful lessons for designers of modern heat pumps, but also because it is often misrepresented and sometimes cited as an example of how difficult river source heat pumps can be. Heap described it as “an ambitious experiment which has been the subject of frequent misunderstanding and which deserves further description” [4]. As an example of misrepresentation, Thévenot described it as “activated by a compressor driven by a jet engine” [5].
2 Purpose and Scope of the Proposal Montagnon and Ruckley noted in their 1954 paper that the plan adopted at the close of 1948 had multiple objectives which were listed as: (1) To develop and install a heat pump connected to the Festival Hall water-heating system. (2) To use town gas as the fuel for the prime movers. (3) To use high-speed internal-combustion engines and high-speed centrifugal compressors. (4) To recoup as much as possible of the waste heat from the combustion units. (5) To arrange for an output of 80 to 90 therms per hour and for the plant to be capable of handling input water temperatures up to 140 °F. (6) To arrange the plant to be adaptable to the production of chilled water instead of heated water. (7) To have the plant installed and operating in 2½ years (i.e. in time for the Festival Exhibition). This initial description uses the system of Imperial Units employed by Montagnon and Ruckley but the subsequent discussion is expressed using SI units. The heating capacity set down in item (5) of the objectives was based upon an estimated peak heating requirement for the hall complex of 26 million BTU/h (260 therms per hour) which was comprised of an initial load of 17 million BTU/h and future expansion capability of 9 million BTU/h. The peak heating requirement is equivalent to 7620 kW and this was subsequently found to be a significant over-estimate of the actual heat load. The nominal heat pump capacity of 90 therms per hour is equivalent to 2640 kW. The main heating plant, comprising five gas-fired boilers, was installed in the basement of the Festival Hall but the heat pump system was accommodated off the Festival Hall site in an arch under the Hungerford railway bridge on the south bank of the Thames. Hot water pipes ran from the arches to the Festival Hall plantroom, a distance of several hundred feet and the river water inlet had to be in mid-stream and submerged at low tide so the inlet pipe was also several hundred feet long.
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3 Design Details The following design details are taken from Montagnon and Ruckley’s paper with the sizes and dimensions converted to SI units. The heat pump comprised two compressor units, connected in series and sized to deliver a total of 2520 kW of heat. The flow temperature in the hot water loop was 68.3 °C and the return temperature was 51.7 °C. The concept was to pick up two thirds of the total heat delivery in the system condenser with a further one twelfth picked up at higher temperature from the water cooling jackets of the engines and another one sixth from a heat exchanger in the engine exhaust flue. The heating capacities of each of these stages were 1670 kW of heat from the condenser, 224 kW from each of the engine jackets and 400 kW from the exhaust exchanger. The hot water circulation rate was 36.6 kg s−1 which gives a suitable heat balance for a 16.7 K temperature rise. On the river water side the flow rate was 175 kg s−1 with a temperature drop of 1.7 K giving a cooling duty of 1,213 kW. The refrigeration circuit was designed with two stages of compression and with an open flash economiser subcooling the liquid feed to the evaporator and feeding flash gas to the suction of the second stage compressor. The power output of each engine was stated to be 239 kW with a 4.4% loss in the gearbox, giving a shaft power input to the compressor of 228.5 kW. The system schematic is shown in Fig. 2, which is taken from Montagnon and Ruckley [2]. R-12 (dichlorodifluoromethane) was selected as the refrigerant because it would provide moderate pressures over the full working range of the heat pump, the mass flow rate required for the duty proposed was estimated to be a reasonable match to the size of the gas passages in the supercharger of the aircraft engine and the refrigerant was non-toxic and non-flammable. At the design condition of evaporating at 0 °C and condensing at 65 °C the pressure lift was from 3.1 bar abs to 17.0 bar abs, a pressure ratio of 5.47:1, which required two stage compression with the centrifugal compressors used. The designers noted that one of their major difficulties in the early stages of the project was sourcing accurate information on the thermophysical properties of R-12 above 60 °C.
4 Equipment Details The compressor/drive motor combination was based on a Rolls Royce Merlin aeroengine, selected because they were cheap and readily available at the end of the war. The aero-engine was to be used in two ways. The main drive unit was converted to run on town gas instead of aviation fuel and the supercharger was modified to act as the R-12 compressor. The supercharger on the Merlin was a two-stage unit, driven
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Fig. 2 Design conditions for the Festival Hall Heat Pump [2]
through a gearbox from the crankshaft. The gearbox included a centrifugal clutch and a two speed mechanism. The Merlin engine was developed by Rolls Royce in the mid-1930s and became the main power plant for some of the most iconic aircraft of the Second World War, including the Avro Lancaster, the De Havilland Mosquito, the Supermarine Spitfire, the Hawker Hurricane and the North American Aviation P-51 Mustang. In total over 160,000 Merlin engines were produced, roughly half of them in the Rolls Royce factories in Derby, Crewe and Glasgow and half in Ford’s plant in Trafford Park, Manchester and Packard’s Detroit factory. It was also adapted for use in tanks, motor torpedo boats and air-sea rescue launches. Montagnon and Ruckley reported that “surprisingly little had to be done to make the engines run effectively on town gas.” The fuel system and supercharger was replaced with a naturally aspirated carburettor. The spark plugs were replaced with
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a type suited to gas, the spark timing was adjusted and the compression ratio was increased from 6:1 to 7:1. These modifications gave a shaft output of about 350 hp (260 kW) compared to the normal performance of about 1000 hp (750 kW) as an aircraft engine. This was a good match to the power required for each stage of the R-12 circuit. In contrast to the engine modification, Montagnon and Ruckley described the compressor development as “by far the longest and hardest task in the whole project”. For each compressor unit the second stage impellor from the supercharger, the high speed gear train with a step-up ratio of 8.82:1 and the built-in centrifugal clutch were mounted in new casings with adjustable inlet guide vanes. A test bed was constructed to prove each motor-compressor unit separately and performance figures were used to modify the detailed arrangement of the rotating and fixed guide vanes. With these adjustments it was possible to maintain an isentropic efficiency of about 73% across a range of engine speeds from 2000 rpm to 2400 rpm with the pressure ratio ranging from 2.2:1 to 3.4:1 for the first stage compressor. The second stage machine had to operate over a wider range of inlet conditions, including periods of single stage operation when the system was used as a cooling plant in the summer. It was therefore run without diffuser blades, resulting in a slightly lower isentropic efficiency dropping from 67% at 2200 rpm to 61% at 2400 rpm. A further difficulty in completing the compressor and gearbox assembly was the development of a shaft seal for the drive shaft. The seal was required to contain up to 300 psi gauge pressure (20.7 bar) while running at a compressor speed of up to 20,000 rpm. The initial concept was to make the whole gearbox gas-tight and seal the low speed engine shaft but this was found to be too awkward so a high speed shaft seal had to be developed. The final form of seal comprised a floating carbon ring between two steel disks, one fixed and one rotating. The carbon ring was chamfered to control the applied force and the fixed ring was held against the carbon surface by a retaining helical spring. This arrangement can be seen in the centre of Fig. 3, a cross-section of the gearbox, clutch and compressor. The remaining components of the refrigeration circuit were more conventional. The evaporator and condenser were each arranged as a matrix of shells with 1¼' steel tubes. The condenser for example was four shells wide and five high (the bottom row of shells were intended to be flooded in operation to provide some subcooling) and the evaporator was six shells wide and three high. The heat exchange surface was sized by allowing 350 BTU/h ft2 °F (2000 Wm−2 K−1 ) for both condenser and evaporator with “an added handsome margin” for sludge fouling on the water side and oil on the refrigerant side. This heat transfer coefficient was probably very generous for the condenser but slightly tight for the evaporator as the outer surface of the tubes on the refrigerant side was not enhanced in any way. This is reflected in the operating conditions; the condenser achieved an approach temperature of 3.3 K but the evaporator approach was closer to 5.5 K when chilling river water from 12.5 to 10.0 °C although the design expectation was also 3.3 K.
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Fig. 3 Cross section through compressor, clutch and gear box [2]
5 Installation Details The heat pump unit was installed in the arches below Hungerford railway bridge which carries the rail track across the Thames to Charing Cross station. This was a pragmatic choice of location because the incorporation of two aero engines in the basement of the concert hall, which was designed to exceptionally high acoustic standards, would have been difficult. An aerial view of the site can be seen in Fig. 4. The railway arches forming the location of the heat pump installation are in front of the Festival Hall at the right hand end of the railway bridge in the foreground. The plant room was very congested. The layout is shown in Fig. 5. Hot water was piped from the plant room to the boiler room of the Festival Hall in pre-insulated 200 mm flow and return headers. River water was pumped from the centre of the Thames and because the tidal range is in excess of 6 m (20 feet), the pump suction lift was more than 8 m (25 feet). The plant room was lined with sound absorbent material and double glazed windows were fitted to the exterior. A control cabin, also double glazed was installed
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Fig. 4 Festival Hall from the south west [3]
and the engines were mounted on inertial slabs sunk into the floor and supported on cork mats. During testing a seismograph in the plant room recorded much higher readings when a train passed overhead than when the plant was running.
6 Operating Details It must be emphasised at the outset that, despite numerous difficulties experienced in the commissioning and operation of the heat pump, the overall project was a remarkable technical achievement and delivered a large scale working heat pump with very acceptable performance in a remarkably short period of time. The authors confirmed that the purpose of the project had been solely to generate and record information, and in that respect they were very satisfied with the results. It is certainly fair to say that all seven of the objectives set out in the purpose and scope listed in Sect. 2 of this paper were achieved. The major source of technical difficulty appears to have been in the original specification of the heating system. The specified heat load of the hall, 5000 kW in phase 1, was never required and for most of the heating season the heat pump was unable to achieve its full output of 2520 kW for a prolonged period. Even at this level of heating the Festival Hall was criticised for being uncomfortably warm. Further difficulty arose from the requirement for a relatively high hot water flow temperature of 82 °C (180 °F) with a return of 60 °C (140 °F) in order to keep the heating surfaces in the hall to a minimum. In practice the heat pump was designed to operate at slightly lower temperatures; the return from the hall was at 51.7 °C (125 °F), it was heated to
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Fig. 5 Plant room layout [2]
62.8 °C (145 °F) in the condenser and then to 68.3 °C (155 °F) by the engine waste heat before being returned to the hall. The choice of centrifugal compressors for space reasons was a good one, but for a heat pump where the evaporating pressure is determined by the heat source (the river water) and the condensing pressure is determined by the heat sink (the heating loop) this fixed pressure lift means that there is little scope for capacity control of the plant. The speed can only be varied through a very limited range and care must be taken to ensure that the compressor does not surge (too little mass flow) or choke (too much mass flow). On initial start up the centrifugal clutch of the first stage compressor failed after a few starts. It was concluded that the driving torque was extremely high at low speed during start up. The clutch was strengthened and the problem did not recur. After about 50 h run the first stage compressor stripped the impellor, completely destroying the compressor. It was concluded that one of the rotating guide vanes had failed due to fatigue because one of the operating speeds created a resonance in the vanes. With
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a shroud added around the vanes the stiffness was increased and the problem did not recur. The shaft seal on the second stage compressor initially tended to leak refrigerant after a high pressure run. This was resolved by increasing the helical spring stiffness although Montagnon and Ruckley noted that a more elegant solution would have been to make fine adjustments to the amount of chamfer on the carbon ring. Refrigerant leaks from the aluminium casting of the compressor housing were also a persistent problem that was never fully resolved. The authors noted that the refrigerant circuit was tightness tested with air at 300 psig (20 bar gauge) but despite this R12 “leaked substantially in places where air had not apparently been able to escape.” The casings were impregnated with Bakelite twice but were never completely leak tight. The biggest recurring problem, which was never satisfactorily resolved, was with maloperation of the high pressure float valve on the condenser outlet. This unit comprised a bell housing inside a float chamber which was weighted to sink when the bell was filled with liquid but to float when gas was introduced. The authors state that a ball float could not be used because the operating pressure (20 bar) was too high. The bell tended to gas-lock and keep the expansion valve closed, causing the evaporator to be starved and liquid to back up in the condenser. Eventually use of the float valve was abandoned and a manually controlled hand regulating valve was added. It is a great pity that a minor thing like this, to which today there are numerous possible mechanical, electrical and electronic solutions, should have dogged the project so severely when such fantastic engineering work had been done on the compressor design. The authors also mentioned a miscellany of minor troubles including exhaust gas leaks from the flexible bellows on the exhaust system, loss of priming of the river water pump at low tide, minor leaks around the refrigerant circuit and occasional difficulty starting the engines after prolonged shutdown caused by dirty points and similar mechanical issues.
7 Performance Details The authors noted that it had not been possible, throughout the life of the heat pump, to achieve a period of prolonged running because the heat load on the hall was too low and the plant had insufficient turn down capability. Test runs therefore were of short duration and the hot water flow temperature was rising throughout the test. Two tables of test results are included in the paper; for 20th November 1952 when the delivery temperature rose between 12:32 and 13:40 from 51.9 to 74.9 °C and for 23rd February 1953 when the delivery temperature rose between 12:30 and 14:27 from 45.4 to 66.4 °C. During the first of these runs the main float valve was operating intermittently and caused the compressors to surge as a consequence of liquid backing up in the condenser, starving the evaporator and resulting in low suction pressure. Once the bypass valve was opened the unit was able to operate in a more stable
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manner, but this only lasted for a further 35 min. Montagnon and Ruckley presented a tabulated analysis of the performance readings from 13:18, midway through this more stable run. Their figures, converted to SI units are given in Tables 1 and 2. When the system was operated as a chiller in summer a set of manual changeover valves diverted the river water to the condenser and the concert hall water to the Table 1 Performance analysis (derived from Montagnon and Ruckley [2], Table 4)
Table 2 Further performance analysis (derived from Montagnon and Ruckley [2], Table 4)
Concert hall water Into condenser
49.2 °C
Out of condenser
60.5 °C
Out of boiler (waste heat rec)
67.9 °C
Flow rate
35.6 kg s−1
Heat from condenser
1682 kW
Heat from boiler
1102 kW
Total heat input
2784 kW
1st stage compressor Town gas burnt
982 kW
Engine speed
2170 rpm
Refrigerant flow
12.3 kg s−1
Compressor work
287.8 kW
Compressor isentropic eff.
65.7%
Thermal efficiency
29.31%
2nd stage compressor Town gas burnt
1187 kW
Engine speed
2420 rpm
Refrigerant flow
13.3 kg s−1
Compressor work
311.3 kW
Compressor isentropic eff.
67.7%
Thermal efficiency
26.22%
Heat pump CoP Total condenser heat
1682 kW
Total compressor work
599.1 kW
CoP
2.80
Overall thermal efficiency Total heat delivered
2784 kW
Total energy from gas
2169 kW
Thermal efficiency
128%a
a Value
given as 121% in M&R paper
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evaporator. The plant only required one of the compressor stages for this mode of operation so the first stage was bypassed, with gas from the evaporator passing through a bypass line directly to the second stage suction. This arrangement was reported to work well in general but on occasion it was noted that the river water temperature could be as high as 26.7 °C which was slightly too high a pressure lift for the compressor. A problem with this arrangement as drawn in the paper, although there is no mention of this, is that it introduces river water into the hot water boiler circuit. Apart from bringing sludge into the heating system it is also likely that this would accelerate internal corrosion of the boilers and heat exchange surfaces in the hall, as well as fouling up the water side of the condenser. It would probably have taken several years of operation for these problems to become evident and the heat pump was not in service long enough for this to happen. The authors noted that “as a cooling unit the plant was much easier to operate, although again it proved that the heat extraction produced by the plant was a little in excess of the requirement of the hall.” The performance figures calculated in Table 1 indicate that, if this performance is typical of the operation of the heat pump, it generally achieved its performance objectives. The heat delivered is in line with the design intent—the unit delivered 2784 kW at 67.9 °C compared with a design of 2520 kW at 68.3 °C, albeit with the river at 12.5 °C instead of the design condition of 5.0 °C The conventional heating CoP of the system was calculated to be 2.8 and at the design condition of 5 °C river temperature this could be expected to be about 10% lower at 2.5 which is reasonable performance although not as efficient as would be achieved with modern equipment. As Montagnon and Ruckley observe in their responses to the discussion of the paper this metric is not very meaningful as the objective was to see how the heat pump would compare in terms of gas consumed in comparison to conventional gas boilers. In this respect it was shown that the overall heating efficiency of the heat pump system was 128%—in other words the amount of heat delivered was 28% more than the total calorific value of the gas used. The main boilers were provided by Cochran of Annan who are still in business. Five vertical boilers rated at 6,250,000 BTU/h each, a total of 9160 kW, were installed in the basement of the Festival Hall with three smaller units providing hot water services (527 kW total installed capacity). The efficiency of the main boilers is not stated but they appear to have vertical fire tubes which suggests a maximum heating efficiency of about 80%. This means that for the same gas consumption the heat pump delivered more than 50% more heat than the conventional boilers.
8 Lessons to Learn for Modern Installations The difficulties encountered by the scientists who developed the Festival Hall heat pump in 1950 are familiar to practitioners working in new aspects of heat pumps in 2023. Mechanical failure of equipment that has not been used in this way previously, manufacturing defects in equipment that should have been dependable and glitches
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with control systems not quite behaving in the way that was intended will still happen in experimental plant [6]. A pioneer developing a new application should not be put off by these challenges but must use them to make the system more robust and reliable. On the other hand, many of the problems experienced at the Festival Hall in 1950 have now been eliminated. High speed screw compressors offer much more compact installations than the slow running reciprocating compressors and also require much less maintenance. Variable speed drives using electronic inverters to vary the motor supply frequency enable efficient part load operation, and this continues to be an area of rapid development, particularly in larger drives, up to about 500 kW shaft power. Correct specification of the system, in terms of operating temperatures, heating capacity, turn down capability and method of integration into the overall heating network are essential for efficient operation. Modern installations are capable of higher operating temperatures (up to 90 °C) at higher heating coefficients of performance (in excess of 3.0 at 90 °C and over 4.0 at 75 °C). This is partly due to improved equipment efficiency but also comes from the use of ammonia as refrigerant; inherently more suitable than R-12 and its modern equivalents, R-134a and R-1234yf, because it has a higher critical temperature. There did not appear to be any issues with silt on the river water side of the system. The authors noted that “no arrangements other than a coarse filter at the pump were made to clean the river water supply, reliance being made on the speed of the water through the system to prevent the deposit of silt or other sediment.” This appears to have worked for them, but the evaporator was built with large diameter tubes and suitable for this arrangement, sized with, as they put it, “an added handsome margin to take account of the possibility that the tubes might eventually become contaminated with dirt and scale on the water side”. With modern plate type evaporators this is much more difficult so it is to be expected that a greater focus on the filtration in the abstraction system and methods of cleaning the evaporator require a greater degree of sophistication. A modern heat pump system built to a similar specification to the 1950 project would therefore likely use ammonia as the refrigerant with compact plate heat exchangers, possibly of the plate and shell type for the condenser. The evaporator might still be shell and tube due to concerns about fouling over time, or could be a plate heat exchanger if the filtration was sufficiently effective. A system of this size would use screw compressors running at about 3000 rpm. Smaller plant might use reciprocating compressors to give higher efficiency and larger plants have been installed with turbo compressors using R-134a, R-1234ze(E) and R-744. A heating coefficient of performance of about 4.0 could be expected for an ammonia system taking heat from a river at 5 °C and raising the district heating loop from about 50 °C to about 70 °C.
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9 Conclusions The experimental heat pump installed at the Festival Hall in London in 1950 proved successfully that river water (in this case from the Thames) could readily be used as an effective and efficient source of heat for large scale projects. The system exceeded its design capacity and the main problem with operation of the installation was that the heat output which had been requested was far too large—probably overstated by a factor of at least five. Heat pump systems need to be configured to provide base load heating with as high a load factor as possible in order to offer the most attractive financial arrangement. Designing for peak load is not only a waste of capital cost, it also harms the operational efficiency of the heat pump because the plant will operate on part load for long periods. It also does not make sense to provide redundancy in the heat pump, other than in components that will ensure maximal operating time. For example, it is worth specifying a dual oil filter to ensure that the filter elements can be hot swapped, but having a whole heat pump unit as a standby is not feasible. Peak load capacity and back up should be provided by a cheap, conventional combustion or electric heating system on the basis that it should not run for more than a few hundred hours per year. In a recent installation in Norway the heat pump is sized for 13 MW of heating although the peak load is about 30 MW. The heat pump accounts for about 80% of the heat supplied over a year because it is the base load and is kept on line as much as possible. The Festival Hall heat pump installation has become something of a myth; famous for all the wrong reasons. It was a feat of scientific and engineering excellence but the quirk that post war surplus aircraft engines were used and adapted for the application seems to be the only fact about the installation known to most people. This is doubly unfortunate. Firstly there were many other excellent features in the project which have been largely forgotten, for example the pioneering use of R-12 in a large scale installation, the confirmation that river source was a viable option for large heat pumps and the ease of operation. Secondly, and perhaps more damaging, the mythology that has grown up around the use of the Merlin engine, itself an engineering icon, has given many people the impression that river source heat pumps are exceptionally complicated and difficult. This is untrue and it is hoped that this appraisal will help to introduce a new generation of engineers to the great successes achieved in the Festival Hall installation and the excellent prospects and possibilities that river source heat pumps offer for our present-day heating challenges. In the discussion that followed Montagnon and Ruckley’s paper Mr. John Sumner, who in 1945 had installed an innovative river source heat pump in Norwich, said “The data that had been provided by the authors were of very great value and would be of great assistance in the inevitable future development of the heat pump. The nation which originally propounded the principle of the heat pump 100 years ago and then abdicated its premier position was slowly accumulating data and experience that might ultimately bring pre-eminence again in manufacturing and knowledge, particularly as the gap between deep-mined coal production and coal consumption
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in Great Britain was beginning to widen.” A further 70 years have passed since Mr Sumner’s rallying cry. We are still gathering data and several alternative fuels have been phased in to replace coal and are now being phased out again. The challenges of making large scale heat pumps efficient, economic and reliable are still relevant. Acknowledgements The authors of the 1954 paper acknowledged the contributions of Alan Muntz and Co Ltd., who carried out the development of the engines, compressors, seals, automatic controls etc. and who gave valuable help in running the plant, U.D. Engineering Co Ltd. (originally United Dairies Engineering and latterly known as UDEC, ultimately being absorbed by the Beales Hunter Group) who supplied the refrigerating equipment and Matthew Hall and Co Ltd., who undertook the installation of the whole plant other than the engine and compressor units. The author of this appraisal would like to thank the directors of Star Refrigeration Ltd. for permission to publish it and the many members of the CIBSE Heritage Committee who provided leads to various sources of information, particularly Paul Yunnie and Rex Pengilly. Thanks are also due to Prof Zhibin Yu for his help in sourcing some of the articles.
References 1. Ministry of Fuel and Power Act, Clause 1(1) (1945) 2. P.E. Montagnon, A.L. Ruckley, The festival hall heat pump. J. Inst. Fuel 127, 170–192 (1954) 3. London County Council, Royal Festival Hall—The Official Record (Max Parrish & Co Ltd., London, 1951) 4. R.D. Heap, Heat Pumps (E&FN Spon Ltd., London, 1979), pp. 5–6 5. R. Thévenot, A History of Refrigeration Throughout the World. International Institute of Refrigeration (1979), p. 365 6. A. Pearson, Industrial heat pumps: case studies and lessons learned, in 11th IEA Heat Pump Conference, Montréal (Québec), Canada (2014)
Development of a Digital Twin of an Oil-Flooded Screw Compressor Using Measurement Data and Numerical Simulations Lukas Richter , Michal Volf , Matej Jerabek , Zdenek Novotny , and Petr Salajka
Abstract The paper describes the development of a digital twin of an industrial compressor with an integrated compressed air adsorption dryer. Digital twin development is enabled by prototyping an oil-flooded screw compressor with an integrated dryer and numerical modelling of partial phenomena and the whole system. The results of the numerical modelling and measurements of the prototype are then used to train and adapt neural networks to develop the digital twin software. A sufficient amount of input data is essential for the development and subsequent application of the digital twin of the compressor including the integrated dryer. These data must correspond to both standard operating conditions and off-design conditions with respect to, for example, ambient temperature, intake air humidity, compressor load or regeneration air temperature and quantity, which are taken into account in the measurements and numerical simulations. Taking into account the different operating conditions allows the neural networks to find the optimal design parameters for the entire compressor station with respect to the specific requirements and conditions of the end users, which is an important aspect of the added value of the digital twin. Keywords Compressor systems · Adsorption dryer · Numerical simulations · Neural networks · Digital twin
L. Richter (B) ATMOS Chrast s.r.o., Plzenska 149, 330 03 Chrast, Czech Republic e-mail: [email protected] L. Richter · M. Volf · M. Jerabek Department of Power System Engineering, Faculty of Mechanical Engineering, University of West Bohemia, Univerzitni 22, 306 14 Pilsen, Czech Republic Z. Novotny · P. Salajka Amitia s.r.o., K Hnizdum 7, 301 00 Pilsen, Czech Republic © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_63
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1 Introduction The concept of a digital twin in the sense of a computer model of a real device is the topic of much current research, particularly in connection with the application of the principles of Industry 4.0. In this sense, the digital twin of an industrial compressor is used in the development of a prototype where virtual testing can be used to detect possible errors and optimise the design. The digital twin can also be used when the compressor is operated at the user’s site for monitoring and integration into the digital factory system, for example, for production analysis or consumption optimization, or for future product innovations as a data source for predictive maintenance solutions. The digital twin makes it possible to perform a large number of tests not only under standard or ideal conditions, but also under extreme off-design conditions, when the stability of the plant operation is most at risk, without the need to carry out these tests physically, which is time-consuming, and technically and financially demanding. Creating virtual replicas of real devices is therefore a way to significantly reduce both machine development and operational costs. Neural network training is often associated with the need for large amounts of training data. In our case, this requirement is met by a combination of two approaches—the use of data measured on the developed prototype compressor station and the use of data generated by numerical models. The development therefore proceeds through three interconnected and interdependent fields—physical prototyping, numerical modelling and data modelling. This paper describes the first stage of the project, which involves training and adapting a digital twin data model for a prototype electric oil-flooded screw compressor with a rated power of 45 kW with an integrated compressed air adsorption dryer. This paper describes the prototype and its measurements, as well as the mathematical model of the compressor cycle including the dryer and the development of the data model.
2 Description of the Prototype A 4-column adsorption dryer was integrated into a compressor. Activated alumina was selected as the adsorption material for the dryer. Although this dryer has 4 columns, there are always 2 columns in drying mode, either a pair on the left or on the right of a logic pneumatic valve that is located between the pairs of columns. In this prototype iteration, the air for regeneration of the dryer adsorbent was heated using waste compression heat. This method is a kind of hybrid regeneration method, combining the principle of pressure swing adsorption (PSA) and, to some extent, the principle of hot regeneration. The functional diagram of the first prototype iteration can be seen in the following figure (Fig. 1). The schematic also includes measurement points for recording temperatures (T), pressures (p), dew point temperatures (DP) and volumetric flow rates
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(Q). The system includes a total of 17 measurement points, of which 16 signals are processed by the recording panel and 1 variable (Q3—oil flow) is read visually on the rotameter. Temperatures are measured using thermocouples, pressures are measured using resistance strain gauges except for p3 and p4 where low pressure transducers rated for 10 bar overload and 17.5 bar destruction pressure are used. Dew points are measured using SF52 Michell transducers and flow rates are calculated from velocity measurements using hot wire sensors. For neural networks, it would have been preferable for the measurements to include about two to three times as many points, but this requirement could not be met at this stage of prototyping due to the limited number of signal inputs of the recording station. The intake air temperature and humidity values were therefore not measured directly at the compressor intake, but were measured at an external weather station in the test room. Furthermore, the pressure in the left and right drying column pairs was assumed to be symmetrical. Figure 2 shows a section of the time series of measured values for the temperatures T5, T6, T7, the pressure p3 and finally the dew point of the outlet air DP2. The pressure p3 shows which pair of columns is in drying or regeneration mode at a given moment. If the pressure p3 has a value of 2.8 bar, the actual pressure value at that point is out of the range of the sensor, which means that the right-hand column pair is at full pressure, i.e. in drying mode. If, on the other hand, the pressure p3 has a value of about 0.3 bar (the back pressure value for the regeneration air exhaust), this means that the left pair of columns is at full pressure and therefore the right pair of columns is in regeneration. The switching of the column pairs is set in fixed time cycles of
Fig. 1 Functional diagram of the prototype including measuring points
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Fig. 2 Time curves of measured values for temperatures T5, T6 and T7, dew point DP2 and pressure p3
4 min. The scenario also includes a step change in compressor load, where after a certain period of time the motor power is increased from 20 to 45 kW. The graph above shows a section of the time series from one measurement scenario, of which a total of 6 were performed, with individual scenarios differing from each other, for example, by compressor load or different time intervals for switching pairs of columns. The measurements showed that with respect to the switching of the logic pneumatic valve and the inclusion of regeneration air heating, a temperature asymmetry is created between the pairs of columns. With the switching of the pairs of columns by the logic valve, the relative position of the expansion nozzle to the heat exchanger changes, with the expansion of the regeneration air in one mode being before the heating and in the other mode being after the heating. This results in one of the pairs of columns being regenerated with significantly hotter air and the other with significantly cooler air (see Figs. 1 and 2—the difference between T5 and T6 is 30 °C on average). However, it seems to indicate that the pair of columns that is regenerated with warmer air shows better behaviour. In the above measurement scenario, the left pair of columns is regenerated by the warmer air and, unlike the right pair of columns, the dew point tends to decrease because the right pair of columns is not regenerated as quickly as the left pair. This may point to the fact that heating the regeneration air with waste compression heat has a positive effect on drying, but only if the temperature asymmetry can be eliminated.
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3 One-Dimensional Mathematical Model of the Compressor Circuit The mathematical model of the compressor circuit consists of partial one-dimensional components between suction and discharge, see Fig. 3, within which the respective changes in the state of the flow medium are modelled. The flow medium is moist air. The aim of the model is to capture the effect of changes in the suction parameters (temperature, pressure, humidity) on the behaviour of the compressor loop subcomponents, including the analysis of strongly off-design states and the prediction of extreme cases of component failure, in particular dryer adsorbent saturation. Moist air defined by dew point temperature DPT0 (t) (°C), pressure p0 (t) (bar) and temperature T0 (t) (°C), where t(s) is time, enters the compressor loop through the filter. Here, the air is enthalpically throttled as it passes through the porous material and is subsequently led through an intake valve to a screw compressor in which polytropic compression is modelled. The modelling of polytropic compression is based on the compressor characteristics defined by the manufacturer, which gives the dependence of the pressure rise on the volumetric flow rate. The relationship for determining isentropic efficiency, i.e. Eq. (1), was then used to determine the actual enthalpy downstream of the compressor. ηisentr =
aisentr h2 − h1 = areal h2 real − h1
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where h2 real (kJ/kg) is the enthalpy of compressed air, h1 (kJ/kg) represents the enthalpy of entry air, h2 (kJ/kg) is the ideal enthalpy of compressed air and ηisentr (–) is the isentropic efficiency. Thus, the enthalpy of compressed air can be expressed as:
Fig. 3 Diagram of the compressor loop implemented in the mathematical model
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h2 real =
h2 − h1 + h1 (kJ/kg) ηisentr
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The compressed air continues through the check valve to the oil separator where the oil droplets are separated from the compressed air stream. For this component, we model the pressure loss using the measured dependence of the pressure loss on the volumetric flow rate while considering it to be an isothermal process. The air is fed through a minimum pressure valve into the heat exchanger where it is cooled below the dew point temperature, thus changing the specific humidity, which until now has remained constant. Water vapour condenses here and is removed from the saturated cooled air in another component, the moisture separator. The pressure drop of the heat exchanger on the compressed air side, as well as the heat capacity of the heat exchanger, is determined using data in the manufacturer’s catalogue. The outlet air enthalpy is then calculated from the heat balance for the heat exchanger (3): ˙ =m ΔQ ˙ ca · cca · Δtca + m ˙ aa · caa · Δtaa
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˙ (W) is heat flux, m where ΔQ ˙ (kg/s) is mass flow, c is heat capacity (kJ/kg/K) and Δt (°C) is temperature difference for compressed air (with ca subscript) and ambient air (with aa subscript). Since the heat capacity multiplied by the temperature yields enthalpy, Eq. (3) can be rewritten as: ˙ =m ΔQ ˙ ca · Δhca + m ˙ aa · Δhaa
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Providing that the Δh is the difference between outlet value (subscripted by 2) and inlet value (subscripted by 1) for both the compressed air and ambient air, the outlet compressed air enthalpy can be calculated as follows: hca2 = hca1 −
m ˙ ca · (haa2 − haa1 ) m ˙ aa
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The following component is the moisture separator that is modelled adiabatically with no pressure loss and is assumed to have only condensate drainage. The amount of condensate removed is an important parameter for evaluating the performance of the downstream adsorption dryer; the more water is removed, i.e. the greater the cooling of the compressed air, the less moisture needs to be absorbed in the dryer. This parameter is also relatively easy to measure and can be used as one of many parameters in the validation of a one-dimensional mathematical model of the compressor loop. The calculation of the amount of condensate removed can be seen in Eq. (6) [1]. m ˙w =m ˙ ca (|x2 − x1 |)
(6)
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where x1 (kgw /kgca ) is the absolute humidity of the moist air before the moisture separator and x2 (kgw /kgca ) is the absolute humidity after passing through the sepa˙ is mass flow for water (indexed by w) and compressed air (indexed by rator and m ca) respectively. The last component of the loop is an adsorption dryer consisting of a drying and regeneration column, in which the compressed air is dried to the desired quality. While the previous components are modelled using basic state changes and balance equations, in the case of the adsorption dryer the mathematical model is more complex and requires the solution of partial differential equations (Eqs. 7, 8 and 9), since the monitored parameters (temperature, pressure, humidity, etc.) vary not only over time but also over the height of the column. The mathematical model is based on fundamental conservation laws [2], which apply to both the adsorbent and the adsorbate, and are suitable for modelling adsorption using a first-order PGC (Pseudo Gas-side Controlled) model, which is suitable for expressing the physical properties of the adsorption mechanism [3]. The conservation of mass law for the adsorbate is given by Eq. (7), and for the adsorbent by Eq. (8). m ˙ a ∂wa hm a ∂wa =− − (wa − ws ) ∂t ρa εAb ∂z ρa ε
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m ˙a ∂q = (wa,z − wa,z+dz ) ∂t ms
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The law of conservation of energy for the adsorbate is given by Eq. (9), and for the adsorbent by Eq. (10): [ ] ha m ˙ a ∂Ta cv hm a ∂Ta =− + + (wa − ws ) (Ts − Ta ) ∂t ρb εAb ∂z ρa ca ε ρa ε
(9)
∂ 2 Ts ∂Ts + HA hm a(wa − ws ) + ha(Ta − Ts ) = cs ρs (1 − ε) ∂z2 ∂t
(10)
kb
For individual parameters, see [2]. For the sake of completeness, let us add that only the most important valves in which the isenthalpic process is modelled are included in the loop. The individual components are connected by a straight pipe in which frictional pressure losses are modelled. Other non-essential fittings are not modelled and the influence of their local pressure losses is ignored. Figure 4 shows the results of the theoretical mathematical model, where the influence of the compressor intake air parameters on the parameters of the compressed air entering the dryer was simulated in summer and winter conditions with a constant fan power of the cooler. It can be seen that the temperature of the intake air directly affects the temperature of the air entering the dryer. A higher intake air temperature in summer conditions is usually associated with a higher specific humidity, while in winter air of lower temperature and lower specific humidity enters the cycle.
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Fig. 4 Time dependence of the main monitored variables at the compressor inlet and at the adsorption dryer inlet
According to the relative humidity time series, the air at the dryer inlet is always fully saturated with water vapour. However, depending on how much air moisture the compressor sucks in, the dew point temperature at the dryer inlet varies, being higher in summer. Consequently, in summer conditions, more water vapour is condensed by cooling the air in the aftercooler and subsequently removed in the moisture separator. In winter, the dew point temperature at the inlet to the dryer is lower, so the cooling of the air does not produce as much condensate as in summer conditions.
4 Neural Network Modelling Artificial intelligence (AI) and machine learning (ML) are technologies that enable computer systems to learn and adapt from data, experience, and feedback without being explicitly programmed. ML is a subset of AI that focuses on algorithms and statistical models, utilizing artificial neural networks, that enable machines to improve their performance on a task based on experience.
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A neural network-based model is developed to model the nonlinear dynamic system of the dryer sub-model, where the selection of appropriate layers of the neural network topology is a key step in the design of the data model. The data model is trained using numerical simulations and adapted to new measured data. The model is then used to optimize the design parameters of the modelled device using a gradient loss function.
4.1 Neural Network Topology Selection The first step in the design of the data model was the selection of the architecture, meaning the selection of the appropriate layers of the neural network. We considered using fully connected layers or convolutional layers or recurrent layers. The main part of the model is the dryer sub-model, which can be described as a non-linear dynamic system. Recurrent layers are generally best suited to this type of system due to their construction. Specifically, we have used Gated Recurrent Units (GRUs) [4] in our modelling. We verified their suitability by testing them in models of simpler thermodynamic problems. These simulations include verification of our hypotheses, which are confirmed as follows: • The pretrained neural network can be adapted to other unseen data and keep already learned qualitative dynamic principles from the training data set. Thus, we can train our neural network on data from 1-D simulations and adapt the data model to data from measurements while keeping knowledge from both datasets. Simulations further show that to preserve the maximum amount of original knowledge, a sufficiently low learning rate must be used in the adaptation. • For a neural network, interpolating the results is much easier than extrapolating them. Thus, the ideal training dataset is one that contains extreme values of inputs (temperature, pressure, etc.) and design parameters (e.g. column volume), so that the neural network (under normal circumstances) operates between them.
4.2 Dryer Data Model Data simulations were performed using data obtained from numerical models (1-D mathematical models) of the adsorption dryer and subsequently using real measurements. Due to the variable mechanical coupling of the subcomponents of the real system, the simple approach of direct input–output modelling could not be used. It was necessary to consider and model the internal state of the individual dynamic components separately (for example, the left and right drying columns).
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Training and Adaptation of the Data Model. We used gradient minimization of the loss function value [5] to set the parameters of the data model. In this case, the model inputs and outputs (predictions) are considered constant and the network parameters are varied. We used the results of numerical 1-D simulations, which, although they did not exactly match the device being modelled, could be obtained in sufficient quantities and with sufficient variability so that our model could learn the dynamics of the problem from them, including extreme (non-predictive) states. We always used the mean squared error (MSE) as the loss function. In total, we had 55 1-D simulations. The model trained in this way was adapted to the new measured data by gradient optimization. There were 6 realistic measurement scenarios available, a number that alone is not sufficient for training. However, adaptation (fine tuning) of the model was possible. For this and its evaluation, we used leave-one-out cross-validation (see Fig. 5), which means that, for example, for measurement scenario 3, measurements 1, 2, 4, 5 and 6 formed the adaptation set and measurement scenario 3 was left aside as never-seen data for the model. In Fig. 5, the higher variability of neural network predictions comes from the used adaptation dataset, which contained data with rather high variability. The output data from measurement scenario 3 have lower variability that the model has not seen before, and thus the model overestimates the variability of its output. This problem could be resolved by enriching the training data set with more data similar to the data from measurement 3.
Fig. 5 Time series of measured and predicted values of modelled variables describing the quality of the dryer outlet air (measurement scenario number 3)
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The adaptation of numerical models to measured data is often done manually and often requires a detailed understanding of the problem at hand. However, the space of all possible parameter combinations may be too large. In such a case, the numerical model can be supplemented with its data twin and the search for suitable parameters can be greatly simplified or even completely automated. Dryer Construction Parameter Recommendations. In addition to the time series of input variables (temperature, flow, etc.), the inputs of the data model can also include the design parameters of the device being modelled. If the model is already trained, we can consider its parameters constant and, similarly to training, use the gradient of loss function to optimize the design parameters so that the model predictions best match the selected (measured) outputs in terms of the selected loss function, i.e. in our case the MSE. During the data modelling, it was confirmed that neural network-based models provide predictions in a significantly shorter time than numerical models (tens of seconds versus tens of minutes), which makes it possible to simulate many scenarios and, in addition to the gradient optimization of design parameters, it is also possible to use, for example, grid search (brute force optimization). This also allows us to create visualizations of model outputs for combinations of these parameters in addition to searching for them (see Fig. 6). The task was also to find the optimum dryer volume. However, all our simulations showed that if flooding (moisture build-up) occurs in the dryer, changing the dryer volume cannot prevent flooding, only delay it. Therefore, we started to consider other parameters.
Fig. 6 Dependence of the outlet dew point temperature on the air temperature at the inlet to the dryer and its volume
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The working (inlet) temperature of the air into the dryer was found to be crucial. Figure 6 summarizes the results of our simulations. On the horizontal axis is the volume of one dryer column, on the vertical axis is the inlet air temperature. The colour of the heatmap represents the final dew point temperature after 100 min of simulation. This shows that a sufficiently low inlet air temperature guarantees the desired dew point (close to − 40 °C) regardless of the column volume. In contrast, for a high inlet air temperature, the desired dew point cannot be achieved for any considered volume. From Fig. 6, it appears that at very low inlet temperatures, the large column volume is rather detrimental. Unfortunately, we could not fully explain this phenomenon. It may be a model error related to the predictions in the extreme values of the input parameters, which were not available often enough in the training data and not at all in the adaptation data. Simulation of Dryer Regeneration Options. In the original prototype setup, there was an asymmetry of regeneration air temperatures (see Sect. 2). This seemed to be unsuitable, so we further modified the model and performed simulations with other ways of implementing the regeneration air circulation. Both the passage through the heat exchanger and the expansion nozzle are described by separate sub-models. The asymmetry of the circuit is then achieved by changing the order of the passage of air through them. Such a model allows the connection methods to be easily changed. The alternatives for the regenerative air circulation design that were the subject of the data simulations are: • Cold regeneration—the regeneration air first passes through the heat exchanger and then through the expansion nozzle. • Warm regeneration—regeneration air passes first through the expansion nozzle and then through the heat exchanger. • Combined regeneration—for part of the cycle, the regeneration air first passes through the expansion nozzle and the heat exchanger (warm regeneration) and for the rest of the cycle the heat exchanger is bypassed (no heating) and the air only passes through the expansion nozzle. Figure 7 shows a comparison of the predicted dew point time series at the dryer outlet for different regenerative air circulation designs. When comparing the different dew point time series, the least suitable variant appears to be warm regeneration, which has the highest dew point values. In contrast, the combined regeneration with mid-cycle switching has the lowest dew point, which is almost 10 °C lower than the asymmetric regeneration at the end of the measurement. It can be seen that the time series of dew points start at different initial values. But since the output of our model is not additive, there is not as much accumulation of prediction errors and the influence of the initial error decreases with simulation time.
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Fig. 7 Comparison of outlet dew point temperatures for different regenerative air circulation designs
5 Comparison of Individual Approaches Figure 8 shows the visualized time series of all three approaches for 95 min of operation. Both the mathematical and AI predictive models of the compressor cycle determine the dew point temperature of the compressed air at the dryer outlet, and this value is also experimentally measured. From the results, one can conclude that the data model follows the trend of adsorbent moisture saturation very well, due to which the dew point temperature of the outlet air gradually increases; however, the overall curve is shifted by about 10% lower and a phase shift of about 1 min can be observed as well. The 1D mathematical model results, on the other hand, initially predict the resulting dew point temperature better, as the displacement is only about 5% into the region of lower dew point temperatures, but as the number of cycles increases, they start to trend away and overestimate the moisture saturation of the adsorbent, resulting in higher dew point temperature values than indicated by the experimental measurements. This is caused by the adsorbent properties implemented in the 1D model, mainly by the mass transfer coefficient and the heat transfer coefficient, which are not given by the manufacturer and thus are based on available and less accurate sources [6]. Even with the 1D model, a phase shift of about 1 min is also evident compared to the experiment.
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Fig. 8 Comparison of approaches in the form of visualization of outlet dew point temperatures
6 Conclusion In terms of the development of a prototype compressor with an adsorption air dryer using waste compression heat, the activities so far have shown that the existing solution of a 4-column dryer with column switching by means of a logic valve is not suitable for the project due to the creation of temperature asymmetry. Therefore, for the next prototype iteration, which matches the parameters of the target prototype (two-stage compression, rated power 110 kW, air capacity 20 N m3 /min), we propose several design modifications to the dryer. As the next prototype iteration of the compressor produces higher volumetric air flows, the adsorbent volume is also increased—we assume a specific volume of one column of about 10 L per 1 N m3 min−1 . The temperature asymmetry of the columns is eliminated by replacing the logic valve with a set of check valves that open automatically based on pressure differentials according to the mode in which each column is operating. This solution ensures that the regeneration air is always heated after expansion in the nozzle, which is also adjustable, making it possible to find the optimum flow rate of regeneration air with respect to its heating level. Although data modelling is successful in creating the digital twin of the compressor station, it is still struggling with a lack of input data. Numerical and data modelling showed a significant correlation between the air temperature at the dryer inlet and the dew point temperature of the outlet air. If the inlet air temperature is 47 °C, twice as much water goes into the dryer than if the inlet air temperature is 35 °C. In addition, if the adsorbent volume is undersized, the dew point temperature at the dryer outlet rises as soon as the dryer inlet temperature exceeds 26 °C. Increasing the adsorbent volume may delay the dew point rise, but if the air temperature at the dryer inlet exceeds about 30 °C, the adsorbent volume
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will no longer improve the drying process (see Fig. 6). This is also confirmed by the above measurements, where the graph (Fig. 2) shows an increase in the dew point when the compressor power is increased, which corresponds to a gradual increase in the air temperature at the dryer inlet from about 22 °C to about 40 °C, when the dew point temperature of the outlet air becomes higher than 0 °C. Therefore, for the subsequent prototype iteration, a radial fan was designed which has a motor drive that allows continuous speed control, making it possible to experimentally investigate this correlation. The dryer control system was further modified based on the results of the data modelling. The modification mainly consists in the inclusion of the combined regeneration air circulation design, where the adsorbent cooling is included for a certain part of the cycle with the assumption of a bypassed heat exchanger. While a higher temperature is advantageous for adsorbent regeneration, an increase in the temperature of the adsorbent bed reduces its adsorption capacity for the drying mode, since water adsorption on alumina is an exothermic process. Acknowledgements This project is co-financed from the state budget by the Technology Agency of the Czech Republic under the TREND Programme, project number FW03010376 (Development of an industrial compressor and its digital twin). The presented work was also financially supported by student project SGS-2022-023 (Research and development of power machines and equipment).
References 1. L. Ebale, G. N’kaya, W. Kombo, F. Kibongani, Water production by condensation of wet air. Modern Mech. Eng. 10, 17–24 (2020). https://doi.org/10.4236/mme.2020.102002 2. S. Murathatunyaluk, K. Srichanvichit, A. Anantpinijwatna, P. Kitchaiya, Modeling of nonisothermal adsorption process in a silica gel desiccant packed bed, in Computer Aided Chemical Engineering, vol. 43 (Elsevier, 2018), pp. 49–54. ISSN 1570-7946; ISBN 9780444642356; https://doi.org/10.1016/B978-0-444-64235-6.50011-5 3. M. El-Naas, M. A. Alhaija, Modelling of adsorption processes, in Mathematical Modelling (2013), pp. 579–600 4. K. Cho, B. Merrienboer, D. Bahdanau, Y. Bengio, On the properties of neural machine translation: encoder-decoder approaches (2014). https://doi.org/10.3115/v1/W14-4012 5. PJ Werbos 1990 Backpropagation through time: what it does and how to do it Proc. IEEE 78 10 1550 1560 https://doi.org/10.1109/5.58337 6. E. Cussler, Diffusion: Mass Transfer in Fluid Systems, 3rd edn. Cambridge Series in Chemical Engineering (Cambridge University Press, Cambridge, 2009). https://doi.org/10.1017/CBO978 0511805134
Sizing of Scroll and Rolling Piston Compressor for Low-Pressure Refrigerants in Residential Air Conditioning and Heat Pump Systems Haotian Liu , Eckhard A. Groll , and Davide Ziviani
Abstract Current residential air-condition and heat pump (ACHP) systems mainly use the high-pressure refrigerant R410A with scroll or rolling piston type compressors. With the continuous push on reducing the carbon emission, low-GWP refrigerants with lower pressure and density will be used in ACHP systems to replace R410A soon. Compressors must be resized to achieve similar efficiencies at the matched cooling capacity for low-pressure refrigerants. A physics-based model using geometries and refrigerant properties as input that can predict the compressor performance is desired to provide design guidance on compressor sizing. In this study, the opensource modeling platform (PDSim) based on the mechanistic chamber model is used to study the sizing requirement to match the desired capacity for scroll and rolling piston compressors at standard ANSI/AHRI 210/240 conditions. For each type of compressor, a detailed simulation model is created, validated, and tuned using the experimental data available to ensure accurate prediction on refrigerant mass flow rate, power, and efficiencies. The validated models are then used to run sensitivity study on compressor displacement for R410A, R134a and R1234ze(E), which are selected as representatives for different pressure levels. The needed displacement at different volumetric efficiencies and isentropic efficiencies is reported and compared. Keywords Low-pressure refrigerants · Scroll compressor · Rolling piston compressor · Sizing optimization
H. Liu (B) · E. A. Groll · D. Ziviani Ray W. Herrick Laboratories, School of Mechanical Engineering, Purdue University, West Lafayette 47907-2099, USA e-mail: [email protected] E. A. Groll e-mail: [email protected] D. Ziviani e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_64
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1 Introduction Current residential air-conditioning (AC) systems with cooling capacities from 1 to 5 tons of refrigeration (RT) mainly use the high-pressure refrigerant R410A and scroll or rolling piston type compressors. However, the Kigali Amendment [1] and the American Innovation and Manufacturing (AIM) [2] Act require developing low global warming potential (low-GWP) equipment and system to achieve a decarbonized energy future. New low-GWP refrigerants usually have much lower volumetric capacities and pressure compared to R410A [3] with significantly different thermodynamic properties. Moreover, alternative blends have trade-offs between GWP and flammability limits [4]. This ultimately can affect compressor and system efficiencies. By transitioning to these new alternatives, the industry would be going back to lower pressure refrigerants, hence compressors will need to be sized adequately for the new fluids, e.g., having much larger displacement volume than R410A. In this study, design guidelines are provided using a physics-based model with geometries and refrigerant properties as input to predict the compressor performance. An open-source modeling platform named PDSim (Positive Displacement SIMulation) based on the mechanistic chamber model is applied to predict the needed size to match the desired capacity for scroll and rolling piston compressors at standard ANSI/AHRI 210/240 conditions. For each type of compressor, a detailed simulation model is created, validated, and tuned using the experimental data available to ensure accurate prediction on refrigerant mass flow rate, power, and efficiencies. The validated models are then used to run sensitivity study on compressor displacement for R410A, R134a and R1234ze(E), which are selected as representatives for different pressure levels. The needed displacement at different volumetric efficiencies and isentropic efficiencies is reported and compared.
2 Detailed Compressor Modeling PDSim has been developed by the authors over the last few years. The complete description of the models can be found in previous publications [5, 6]. The main features of the framework are summarized in this section. Compression processes in compressors are transient thermodynamic transformations that can be described using a open control volume (CV) analysis with a system of transient conservation equations. The conservation of mass for a generic control volume can be written as: dm C V = m˙ i dt i
(1)
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where m C V is the mass of working fluid within the chamber (or CV) and m˙ i represents the mass flow rate of the i-th flow path entering or exiting the control volume (positive if flows into the CV). The flow interactions are usually referred to as leakage flows. The conservation of total energy reduces to the conservation of internal energy due to the assumptions made and it is given by: d(mu)C V = W˙ cv + Q˙ CV (mh) ˙ i dt i
(2)
where the first two terms on the right hand of Eq. (2) refer to the boundary work rate of control volume and heat transfer rate of the control volume, respectively. The term ˙ i is the enthalpy flow term for the ith flow path. In the case of a compressor, the (mh) boundary work rate term is usually expressed as dV W˙ cv = − pcv dt
(3)
In each control volume, assumptions including uniformity and quasi-equilibrium conditions are applied to calculate the thermodynamic properties. The thermodynamic state of the CV can be calculated by knowing two independent thermodynamic properties for pure fluids and fluid mixtures that are treated like pure fluids. The CoolProp property library [7, 8] is used to retrieve the necessary thermodynamic and transport properties. The REFPROP thermophysical property library [9] can be used as the thermophysical property backend through CoolProp. For each control volume, a certain number of sub-models are applied to calculate the geometries, leakage flow, heat transfer, forces, frictions, etc. The developed system of equations describes a dynamic model of compressor that needs to be integrated over rotation angle in crank-motion driven compressors, such as scroll and rolling piston type compressors. As the integration progresses, the system reaches a steady-periodic solution as a function of the rotation angle. By introducing the geometry parameters and other particular modeling aspects (leakage flows, heat transfer correlations, friction losses, etc.) the same algorithm as shown in Fig. 1 can be applied to any crank-motion driven compressor type. As demonstrated in Fig. 1, the entire simulation process started with the initialization (preconditioning) including the general input calculation, inlet state evaluation and guess values for the outlet states as well as mass flow rate using the volume information. After the initialization, lumped mass temperatures will be generated based on the operator’s experience. The overall solver is executed to enforce energy balances on each of the lumped masses using a non-linear system of equations solver. For each step of the overall solver, the continuity solver is executed to ensure the starting and end values of the cycle are within the residuals so that a steady-periodic dynamic solution can be determined. PDSim, has been developed in the Python programming language and is coded in an object-oriented fashion that ensures a plug-and-play structure that simplifies the construction of a model and facilitates the extension of the existing libraries.
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Fig. 1 General workflow of a compressor model using PDSim [5]
In this study, the investigation focused on the scroll compressor and rolling-piston compressor and the corresponding compressor models have been developed within PDSim.
3 Results and Discussions To investigate the performance of scroll compressor and rolling-piston compressor with different refrigerants, compressor models were developed and validated firstly using available compressor geometries and experimental data from the authors’ previous research as well as literature reviews. After validation, parametric studies on heat transfer, leakage flow correlations, and compressor geometries were conducted for different working fluids. To match the capacity, sensitivity analysis on sizing
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with both scroll compressor and rolling-piston compressors were performed. An optimization case study for scroll compressor was conducted based on the results of the sensitivity studies.
3.1 Scroll Compressor Sizing Scroll type compressors are widely used in residential heat pumps due to its relative high efficiency in the needed cooling capacity. The scroll compressor developed in this study follows the same method used in Ziviani et al. [6]. To provide accurate modeling results, a survey on heat transfer, pressure drop correlations, motor efficiency map and oil solubility was conducted. Pereira and Deschamps [10] analyzed several heat transfer correlations reported in the literature to predict heat transfer rates in the suction and compression chambers of a scroll compressor. There exists wide range of variability in the numerical predictions of the different correlations. However, the impact of the heat transfer coefficient on the actual predictions of the heat transfer rate and then of the pressure traces was not significant. On the contrary, leakage flow predictions have a more significant impact on mass flow rate and volumetric efficiency, as pointed out in Pereira and Deschamps follow up study [11]. Numerical and experimental results showed that the approach suggested by Bell et al. [5] was acceptable after proper tuning, which is applied in this study as well. In addition, Liu et al. [12] reported the motor efficiencies as a function of torque and rotational speeds. Given the peak efficiencies of 95%, the map was implemented in the compressor model. Bobbo et al. [13] conducted a comprehensive study on the influence of POE lubricity and R134a solubility. It was found that in terms of solubility in a POE32, solubility R1234yf < R134a < R1234ze(E). For instance, in the case of R134a with sump oil temperature of 317 K and pressure 0.414 MPa, approximately 9% of refrigerant was dissolved in the oil. These results were useful to tune the frictional coefficients of the bearings and the orbiting mechanism. As the model approach has been identified, the model was first validated using available experimental data for a scroll compressor using R134a as refrigerants. The geometry model was updated to match the provided compressor displacement. The validation results are shown in Fig. 2. Although additional tuning of the model can be performed, it was important to understand the differences in displacements between R410A, R134a and R1234ze(E) compressors for the same AHRI 540 test condition with a target cooling capacity of 3 ton. The compressor speed was kept constant at 3600 rpm and both volumetric efficiency and overall isentropic efficiency were varied. Specifically, volumetric efficiencies up to 95% were considered and 72 and 75% were chosen as reference values for the overall isentropic efficiency. Note that the same efficiency values were assumed for different refrigerants to understand the required displacement and power consumptions only determined by refrigerant properties. The results are summarized in Table 1. It can be seen that the difference in compressor displacements is the key
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Fig. 2 Initial scroll compressor model validation for mass flow rate (left) and input power (right) without tuning (left)
Table 1 Sensitivity study on scroll compressor displacement for R410A, R134a and R1234ze(E) at fixed AHRI conditions and target cooling capacity of 3 ton for three volumetric efficiencies and two overall isentropic efficiencies Tevap = 10 ◦ C 50 ◦ F Tcond = 46.11 ◦ C 115 ◦ F (3 RT) AHRI 540 ˙ cooling,target = 10,550.56 W Q Vdisp (cm3 /rev)
ηv
R410A
R134a
R1234ze(E)
0.95 0.93 0.90
28.35 28.96 29.92
61.88 63.21 65.32
82.01 83.77 86.56
2386.41 2290.95
2182.11 2094.83
2186.64 2078.06
ηoa , ηmech , ηmot , ηv ˙ el,comp (W) W
0.72; 0.90; 0.95; 0.95 0.75; 0.90; 0.95; 0.95
to match capacity if the motor rotational speed is kept the same. Comparing all three refrigerants, R1234ze(E) requires the largest displacement with lowest power consumption due to the low pressure and low suction density.
3.2 Rolling Piston Compressor Sizing Rolling piston compressor is another widely used compressor type in the HVAC&R industry. Using the PDSim structure, a rolling-piston compressor model is developed and validated against the experimental data in the literature. Engel and Deschamps [14] conducted a comparison analysis between reciprocating and rotary-rolling piston compressors for domestic heat pump water heating with R134a as the working fluid. The study provided details of the geometries, experimental data, break-down of the
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losses, and calibration of heat transfer correlations. The details provided within the paper were sufficient to implement the rolling-piston geometry and to validate the model in PDSim. In order the match the displacement tweaks were made to the PDSim model where geometry details were missing. Similar to the scroll compressor modeling, to improve the model accuracy, a deeper understanding of heat transfer and frictional losses was necessary. From the literature, Padhy and Dwivedi [15] conducted a detailed experimental and numerical analysis on the heat transfer mechanisms in a rotary rolling piston compressor. Of particular interests were the thermal interactions within the working chambers and the shell. Liu [16] showed that the even by employing a spiral-corrected heat transfer correlation, the impact of the in-chamber heat transfer on the pressure variation calculated by the model is limited. However, to break down the losses within the compressor, it was important to assess the impact of heat transfer term in the compression chamber, which was included in the model. The rolling-piston compressor model was exercised at all the operating conditions to assess the reliability of the model. With respect to model predictions, Fig. 3 shows the accuracy of the model for six different operating conditions. It can be seen that the model predicted the performance within 5% error for most of the quantities with the slightly higher error for the mass flow rate. In order to conduct the optimization study of the rolling piston compressor, a benchmark compressor was needed. Open design choices concerned single versus twin-cylinder configurations and variable versus fix-speed compressors. Instead of selecting one fixed compressor design for benchmarking, a sensitivity analysis was performed for a 1.5 ton (5.28 kW) capacity system at the AHRI test conditions to estimate displacement requirements and power consumptions. As shown in Tables 2 and 3, three different volumetric efficiencies were applied to understand the needed displacement for refrigerants R410A, R134a and R1234ze(E). Due to the difference in operating pressure and suction refrigerant vapor density, when switching from Fig. 3 Rolling-piston compressor modeling validation with R134a with normalized data in six different testing conditions shown in x-axis
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R410A to R1234ze(E), the compressor displacement for R1234ze(E) is approximately 2.9 times larger. However, the required electric power consumption is slightly lower for R1234ze(E) compared to R410A compressor. Similar trend can be observed when comparing with R134a and R1234ze(E) but the requirement displacement increase is smaller since R134a has more similar thermodynamic properties to R1234ze(E) compared with R410A. Table 2 Sensitivity study on rolling piston compressor displacement for R410A, R134a and R1234ze(E) at fixed AHRI conditions and target cooling capacity of 1.5 ton for three volumetric efficiencies and two overall isentropic efficiencies Tevap = 10 ◦ C 50 ◦ F Tcond = 46.11 ◦ C 115 ◦ F (1.5 RT) AHRI 540 ˙ cooling,target = 5,2725.28 W Q
Vdisp
(cm3 /rev)
ηv
R410A
R134a
R1234ze(E)
0.95 0.90 0.85
14.17 14.96 15.84
30.94 32.66 34.58
41.00 43.28 45.83
1227.29 1145.48
1122.23 1047.41
1113.24 1039.03
ηoa , ηmech , ηmot , ηv ˙ el,comp (W) W
0.70; 0.90; 0.95; 0.90 0.75; 0.90; 0.95; 0.90
Table 3 Optimization study of a R1234ze(E) compressor compared with the benchmark R410A system AHRI 540 Tevap = 10 ◦ C 50 ◦ F Tcond = 46.11 ◦ C 115 ◦ F
rp (–) Vdisp
(cm3 /rev)
R410A
R1234ze(E)
2.58
2.92
29.50
84.00
m ˙ map (kg/s) m ˙ sim (kg/s)
0.06504 0.06345
0.07515
Td,map (°C) Td,sim (°C) ˙ map (W) W
NA 76.66
68.01
2,466.27 2,369.80
2,269.97
ηoa,map (–) ηoa,sim (–)
0.7256 0.7313
0.698
ηv,map (–) ηv,sim (–) ˙ map (W) Q
0.9508 0.9257
0.955
11,342.2 (±2% or ± 226.8) 10,961.77
11,185.54
˙ sim (W) W
˙ sim (W) Q
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3.3 Optimization Case Study Following the sizing analysis, a state-of-art R410A compressor Copeland ZP31K5E was selected and R1234ze(E) was selected as the target low-GWP refrigerant to run a detailed optimization and loss analysis study. The selected compressor geometry was implemented in PDSim. The R410A scroll compressor model was completed and validated against the AHRI 540 test conditions provided by the compressor map. The cooling capacity was matched within the required 2%, as reported in Table 3. It was necessary to understand the losses distribution within the compressor to identify aspects to be further optimized. The compressor model was run with R1234ze(E) and optimized to match the target cooling capacity. It is well known that the scroll geometry has numerous degrees of freedom. Families of scroll wraps can be generated depending on the design needs. From the knowledge of the scroll geometry model, the displacement of the compressor was optimized to match the target capacity. The degrees of freedom were the displacement, volume ratio thickness of the wraps (within reasonable engineering limits) and orbiting radius. For optimization, leakage gap clearance was kept at minimum engineering values to achieve > 95% volumetric efficiency. Despite meeting the cooling capacity and volumetric efficiency, the overall isentropic efficiency was still below 70%. It was necessary to understand the losses distribution within the compressor to identify aspects to be further optimized. Figure 4 shows two pie charts with detailed breakdown of the losses for the R1234ze(E) compressor at the baseline conditions from Table 3, and with improved lubricant oil to have less solubility at the given conditions. The overall isentropic efficiency achieved 72.8%, with additional margin of improvements from pressure losses and motor losses.
Fig. 4 Breakdown of compressor losses of R1234ze(E): baseline from Table 3 (left); reduced oil-solubility, i.e. more suitable oil (right) [17]
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Fig. 5 Geometry modeling to reduce the discharge pressure losses (left) and updated compressor losses of R1234ze(E) (right)
To further optimize the compressor, the discharge port and scroll wrap discharge geometries were also analyzed. By modifying the size of the port, an overall isentropic efficiency of 73.1% was achieved, as indicated in Fig. 5. The breakdown of the mechanical losses stayed unchanged, as expected.
4 Conclusions Investigation of compressor sizing for R410A replacement with lower pressure and density was conducted through numerical simulation. Both scroll compressor and rolling piston compressor were modeled by a physics-based model using geometries and refrigerant properties as input to predict the compressor performance. Heat transfer, oil-solubility, leakage and losses were also surveyed to help the design process. Sensitivities study on compressor sizing shows that the compressor displacement is the key to match the needed cooling capacity when switching refrigerants. Lower pressure and lower density require higher compressor displacement to achieve the same cooling capacity. R1234ze(E) requires nearly 3 times larger displacement to reach the same capacity as R410A system. In addition to increasing the displacement for capacity matching, compressor optimization including leakage gap reduction, usage of more proper lubricant oil, and discharge port reduction is needed to reduce losses so the compressor efficiency stays the same after switching to low-pressure refrigerants.
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References 1. E. Heath, Amendment to the Montreal protocol on substances that deplete the ozone layer (Kigali Amendment). Int. Leg. Mater. 56(1), 193–205 (2017) 2. US EPA Website. https://www.epa.gov/climate-hfcs-reduction/aim-act 3. B. Yu, H. Ouyang, J. Shi, W. Liu, J. Chen, Evaluation of low-GWP and mildly flammable mixtures as new alternatives for R410A in air-conditioning and heat pump system. Int. J. Refrig. 121, 95–104 (2021) 4. I.H. Bell, P.A. Domanski, M.O. McLinden, G.T. Linteris, The hunt for nonflammable refrigerant blends to replace R-134a. Int. J. Refrig. 104, 484–495 (2019) 5. I.H. Bell, D. Ziviani, V. Lemort, C. Bradshaw, M. Mathison, W.T. Horton, J.E. Braun, E.A. Groll, PDSim: A general quasi-steady modeling approach for positive displacement compressors and expanders. Int. J. Refrig. 110, 310–322 (2020) 6. D. Ziviani, I.H. Bell, X. Zhang, M. De Paepe, J.E. Braun, E.A. Groll, Demonstrating the capabilities of an open-source simulation framework for positive displacement compressors and expanders. Int. J. Refrig. 110, 323–339 (2020) 7. I.H. Bell, J. Wronski, S. Quoilin, V. Lemort, Pure and pseudo-pure fluid thermophysical property evaluation and the open-source thermophysical property library CoolProp. Ind. Eng. Chem. Res. 53, 2498–2508 (2014) 8. E.W. Lemmon, I.H. Bel, M.L. Huber, M.O. McLinden, NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 9.1.1. National Institute of Standards and Technology 9. I.H. Bell, E.A. Groll, J.E. Braun, W.T. Horton, A computationally efficient hybrid leakage model for positive displacement compressors and expanders. Int. J. Refrig. 36, 1965–1973 (2013) 10. E.L.L. Pereira, C.J. Deschamps, A heat transfer correlation for the suction and compression chambers of scroll compressors. Int. J. Refrig. 82 (2017) 11. E.L.L. Pereira, C.J. Deschamps, Numerical analysis and correlations for radial and tangential leakage of gas in scroll compressors. Int. J. Refrig. 110 (2020) 12. Y. Liu, C. Hung, Y. Chang, Design optimization of scroll compressor applied for frictional losses evaluation. Int. J. Refrig. 33, 615–624 (2010) 13. S. Bobbo, L. Fedele, M. Fabrizio, S. Barison, S. Battiston, C. Pagura, Influence of nanoparticles dispersion in POE oils on lubricity and R134a solubility. Int. J. Refrig. 33, 1180–1186 (2010) 14. R.C. Engel, C.J. Deschamps, Comparative analysis between the performances of reciprocating and rolling piston compressors applied to a domestic heat pump water heater. Int. J. Refrig. 102, 130–141 (2019) 15. S.K. Padhy, S. Dwivedi, Heat transfer analysis of a rolling-piston compressor. Int. J. Refrig. 17, 400–410 (1994) 16. Z. Liu, Simulation of a variable speed compressor with special attention to supercharging effects. PhD Thesis, Purdue University (1993) 17. AHRI 540-2020 (SI/I-P) Performance Rating of Positive Displacement Refrigerant Compressors and Compressor Units. https://www.ahrinet.org/search-standards/ahri-540-si-i-p-perfor mance-rating-positive-displacement-refrigerant-compressors-and-compressor
Numerical Simulation of Twin-Screw Expander and Its Effect on the Performance of ORC System Lantian Ji , Zhilong He , Xiao Wang, and Ziwen Xing
Abstract For improving the expander modeling progress of the numerical simulation to get higher accuracy and obtaining its influence on the organic Rankine cycle system, this paper used a structured dynamic grid generation method based on expander rotor node mapping and a grid update technology of node migration with rotor profile to mesh by Twinmesh and Ansys and calculated the model by CFX. At the same time, the entire organic Rankine cycle system model was established. The results show that the simulation results are more suitable for the actual working process and has about 3% relative error, which is less than the reference literature results. The expander throttling loss and pre-expansion at the suction port reduce the overall performance of the expander, the leakage of tip clearance is the most serious, which should be controlled in the structure design of twin-screw expander. The indicated efficiency decreases with the increase of rotating speed and increases first and then decreases with the increase of suction pressure and discharge pressure due to over-expansion and under-expansion. The mass flow rate increases with the increase of suction pressure and rotating speed. The thermal efficiency and output power of the organic Rankine cycle system increase with increase of suction pressure and expander’s rotating speed, and decrease with the increase of discharge pressure. This paper can provide a good reference for the theoretical simulation method exploration, optimal design of twin-screw expander and organic Rankine cycle system. Keywords Twin-screw expander · Organic Rankine cycle (ORC) · Numerical simulation · Dynamic mesh
1 Introduction The organic Rankine cycle (ORC) uses low-boiling organics as the working fluid, which makes it show great advantages of less heat required in the evaporation process and small circulation pressure ratio, etc. in below 300 °C waste heat recovery. As L. Ji (B) · Z. He · X. Wang · Z. Xing Xi’an Jiaotong University, Xi’an 710049, Shaanxi, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_65
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the core component of the ORC system, the expander has a great impact on the power generation and system performance. Twin-screw expanders have significant advantages compared with the others, such as fewer wearing parts, high volume coefficient, low failure rate and so on. However, its actual working process is a complex, comprehensive, and transiently completed variable-mass thermodynamic process. To establish a fusion mathematical model of the thermal performance and dynamic characteristics calculation of the working process is the key and foundation of research on twin-screw expander. In terms of working process simulation, Papes et al. [1] used CFD to analyze the internal flow field of two twin-screw expanders under different pressure ratios and rotating speeds, and constructed a three-dimensional structured grid by solving the Laplace problem. The results show that the mass flow rate of working fluid increases with the increase of pressure or rotating speed, the leakage decreases with the increase of rotating speed, and the throttling loss at the inlet of the expander cause a large pressure drop. Qi et al. [2, 3] established a three-dimensional geometric model and thermodynamic model of the twin-screw expander. The results indicated that throttling, pressure drop and leakage loss are the main factors affecting the efficiency of the twin-screw expander. The large suction pressure loss and the long sealing line makes the leakage serious in the initial stage of expansion. The leakage, throttling and pressure drop loss increase with the increase of suction pressure and the decrease of rotating speed. Professor Stosic, Smith and Kovacevic of City University, UK [4–6] also have rich experience in the theoretical and experimental research of twin-screw compressors and expanders for power generation. They constructed and compared the one-dimensional and three-dimensional performance calculation models, introduced the geometric characteristics, design concepts and some design cases of the twinscrew expander. Wu [7] used CFD to numerically simulate the internal flow field of the designed twin-screw expander and Ansys Workbench to simulate the dynamic characteristics of the rotors. The simulation results show that the temperature change of the medium and low temperature heat source has little effect on the operation of the expander. The large pressure difference at the suction port and the too fast gas flow when passing through the meshing gap result in a negative pressure phenomenon. Tang [8] used Matlab to establish the working process and ORC system model of the twin-screw expander, optimized the leakage model of the expander, and analyzed the variation law of the twin-screw expander core parameters under variable working conditions. From the above research content, the simulation of the working process of the twin-screw expander needs to consider the effects of the axial clearance and the radial clearance on the performance of the expander at the same time. However, there are still three major problems that need to be optimized and improved: (1) The size of the tip clearance and inter-tooth clearance is three orders of magnitude different from the size of the working chamber. The entire computational domain has a large scale span. Meshing is difficult but very critical to the accuracy of results; (2) The working chamber is a dynamic flow domain. Meshing requires moving boundaries; (3) The constant exhaust pressure at the gas pipe port is usually given as the boundary condition in numerical simulation of the twin-screw expander, and the influence of
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the pipeline is not considered, which does not match the actual situation. In addition, the exhaust process of the twin-screw expander is discontinuous and has obvious periodicity, which makes the pressure in the exhaust pipe fluctuate. In order to solve the above problems, this paper optimized and improved the modeling process of the twin-screw expander by using a structured dynamic grid generation method based on expander rotor node mapping and a grid update technology of node migration with rotor profile. The simulation results are closer to the actual operating state. At the same time, the entire ORC system model was established, and the influence of the working law of the twin-screw expander on the performance of the ORC system under variable working conditions was analyzed. The research results can provide a good reference for the theoretical simulation method exploration, optimal design of twin-screw expander and its adaptation to the ORC system.
2 Methodology 2.1 Numerical Simulation of the Twin-Screw Expander Working Process The structural parameters of the twin-screw expander are shown in Table 1. The twin-screw expander female and male rotor models and the twin-screw expander domain model are shown in Fig. 1. Grid Generation. The calculation area was divided into static domain and dynamic domain for meshing respectively. The static domain includes three parts: the inlet pipeline domain, the exhaust pipeline domain and the exhaust buffer domain. The generated mesh is shown in Fig. 2. Unstructured tetrahedral meshes was used for both the inlet and the exhaust pipeline domain, and some meshes connected to the rotor dynamic domain were refined to 0.3 mm. The exhaust buffer domain adopted Table 1 The structural parameters of the twin-screw expander
Parameter name
Value
Rotor length/mm
140
Male rotor helical pitch/mm
210
Female rotor helical pitch/mm
294
Inner volume ratio
2.3
Center distance of the male and female rotor/mm
108.2
External diameter of the male rotor/mm
143
External diameter of the female rotor/mm
123
Number of the male rotor teeth
5
Number of the female rotor teeth
7
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Fig. 1 The twin-screw expander female and male rotor models and the twin-screw expander domain model
structured hexahedral meshes. The mesh element nodes can be connected in any form. The expansion working chamber domain is the dynamic domain, whose 2D structured quadrilateral grid was generated by TwinMesh. The 3D structured mesh of the working chamber is shown in Fig. 3. A 5-layer mesh was uniformly generated at the axial clearance. The mesh density near the wall is higher, and gradually becomes sparser towards the middle of the working chamber in a certain proportion to control the overall mesh number. The minimum angle of the partial mesh is 48.74°, which is much larger than the lower limit 10°of the minimum angle set by the mesh quality detection. Therefore, the quality of the generated grid meets the simulation requirement, and the structured grid can transition smoothly. The mesh quality is good. In ANSYS-FLUENT, the grid is automatically updated according to the change of the boundary in each iteration. The quality of the generated mesh is difficult to
Fig. 2 The generated static domain mesh
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Fig. 3 The 3D structured mesh of the working chamber
guarantee, and the simulation speed is seriously affected. The dynamic grid node update method used in this paper is based on the structured grid point-to-point key frame dynamic grid update technology. From the previous moment to the next moment, the grid is updated according to the positions of the male and female rotors. This method overcomes the shortcomings of the above-mentioned traditional grid update method, which can generate high-quality and reasonable structured grids in cross-scale domain and avoid repeated grid updates to improve simulation solution efficiency. Numerical Solution. In order to simplify the calculation, the working process was assumed: (1) The circulating working fluid is R245fa, and the dynamic viscosity coefficient is constant; (2) The twin-screw expander only exchanges mass with the external environment through the intake and exhaust ports, without considering the influence of the external leakage; (3) The influence of temperature change on the deformation of the expander is ignored. Both the rotor and the casing are rigid bodies during the working process. Ansys-CFX was used to solve the calculation and the shear stress transfer k-ω model in the Reynolds time-averaged method as the turbulent flow calculation model. In this paper, the inlet pressure is 6.58 bar, the exhaust pressure is 2.9 bar, and the rotating speed is 1100 r min−1 as an example. The inlet temperature is 74 °C. The export pressure boundary condition is determined by the inlet pressure and expansion ratio, and the boundary is set to opening, that is, the fluid is allowed to enter and exit. The mesh independence verification is carried out to avoid the influence of the number of meshes, mesh quality and mesh structure on the simulation results. The results are shown in Fig. 4.
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Fig. 4 Mesh independence verification results
2.2 Numerical Simulation of ORC System The ORC system used R245fa as the working fluid. The Temperature-Entropy diagram of the ORC system is shown in Fig. 5. The condenser and the evaporator are both corrugated plate type counter-flow heat exchangers. The basic assumptions are as follows: (1) The flow of the working fluid is one-dimensional homogeneous. The pressure keeps constant, and the mass flow remains unchanged. The pressure and temperature drop formed by the flow are not considered, that is, the momentum conservation equation is not considered. The stable flow satisfies the continuity equation, and only the energy conservation equation is considered; (2) The flow of heat source water and cooling water is one-dimensional. (3) Ignore the contact thermal resistance and heat conduction thermal resistance Fig. 5 The temperature-entropy diagram of the ORC system
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caused by the plates, but only consider the convection thermal resistance; (4) The heat exchanger is divided into subcooling, superheating, and two-phase calculation areas. The heat leakage is not zero. The ratio of the heat exchange between working fluid and water in each calculation area is the same but not 1. Q = mα(Tin − Tout ) = m(h in − h out )
(1)
Twc_out − Tw3 Tw3 − Tw2 Tw2 − Twc_in = = = cQ h6 − h7 h7 − h8 h8 − h1
(2)
c(sh,sc,t p) =
h (sh,sc,t p) T(sh,sc,t p) h T
(3)
n Nusp = 0.023 · Re0.8 sp · Prsp [9]
(4)
Among them, n is taken as 0.3 when the working fluid is cooled and 0.4 when heated. Resp =
ur · d ν
(5)
n Nueq = C · Rem eq · Prl
Reeq = m r
ρl (1 − x) + x ρg α=
0.5
Nu · k d
W p = m r (h 2 − h 1 )
(6) d [10] νl
(7)
(8) (9)
The inlet superheat degree of the expander is a assumed value (iterative calculation) at 0–10 °C. The temperature, pressure and mass flow rate of the expander at the expander outlet were all provided by the thermodynamic simulation results of the expander. The fitting formulas of the above thermodynamic parameters for the evaporation and condensation temperature are given. In this way, the TwinMesh simulation results of the expander are brought into the system for simulation. Wexp = m r (h 5 − h 6 ) ηsys =
Wexp − W p Q evap
(10) (11)
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Fig. 6 The ORC system and heat exchanger block diagram
The ORC system and heat exchanger block diagram are shown in Fig. 6. Programming and calculations were implemented in Matlab.
3 Results and Discussion In this paper, three sets of experimental data from the literature [8] were selected to verify the models of the ORC system and the twin-screw expander. The operating point parameters are shown in Tables 2 and 3. The model error results are shown in Fig. 7. The left side of the figure is the output power error value of the twin-screw expander, and the right side is the ORC system error value. It can be seen that the average error is about 3%, which is less than the results in the reference literature.
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Table 2 Expander model verification condition parameters Serial number
nexp
Pin_exp
Pout_exp
Tin_exp
1
1100
658
290
72.9
2
1300
658
290
72.9
3
1500
658
290
72.9
Table 3 ORC system model verification condition parameters Serial number
nexp
Pin_exp
Te
Pout_exp
Tsh
Tc
1
1100
658
72.9
290
0
44
2
1500
658
72.9
290
1.5
44
3
1100
590
68.8
290
0
44
Fig. 7 The model error results
This section selected the number 1 working condition in Table 2 to analyze the twin-screw expander. The geometric parameters of the model are shown in Table 4. The variation of pressure in a working chamber with the rotating angle of the male rotor is shown in Fig. 8. As shown in Fig. 8, since the pre-expansion occurs at the moment when the working chamber is connected to the suction pipeline, the output work of the preexpansion is not effectively recovered, which reduces the working efficiency of the twin-screw expander. Both throttling loss and pre-expansion are closely related to the shape of the suction port, so optimizing the shape of the suction port can greatly Table 4 Twin-screw expander model geometric parameters Parts
Number of teeth
θ
lra
δtc
δcbt
δec
Male rotor
5
240
140
0.1
0.15
0.1
Female rotor
7
171.43
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Fig. 8 The variation of pressure in a working chamber with the rotating angle of the male rotor
improve the performance of the twin-screw expander. The surface pressure distribution of the male and female rotors is shown in Fig. 9. Along the axial direction of the rotors, the pressure on the surfaces decreases first and then increases slightly from the suction end face to the discharge end face, mainly because the given pressure boundary condition of the exhaust port is greater than the theoretical value. Therefore, after the gas in the expansion chamber reaches the exhaust end face, the pressure value is less than it given by the exhaust port, and the gas outside the exhaust end face flow back into the expansion chamber. The rotor axial direction section Z = 5 mm, Z = 70 mm and Z = 135 mm were choose to draw cross-sectional pressure cloud diagram. The pressure cloud diagrams at the three sections is shown in Fig. 10. It can be seen that the pressure distribution in each expansion chamber is relatively uniform, the pressure at the suction end face is the highest, and gradually decreases along the axial direction of the rotor. A minimum value of 200 kPa is reached. However, in the simulated working condition,
Fig. 9 The surface pressure distribution of the male and female rotors
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Fig. 10 The pressure cloud diagrams at the three sections
the pressure boundary condition at the exhaust port is 290 kPa, so there is a large degree of turbulence in this area, which outputs the exhaust noise. The velocity vector diagram of the rotors domain and the velocity vector diagram of the rotor section (Z = 135 mm) are shown in Fig. 11. The fluid velocity distribution in each chamber is relatively stable, and there is no region that produces drastic changes. However, the velocity of the leaking gas at the tip clearance and the intertooth clearance is an order of magnitude larger than that in the expansion chamber. The pressure difference between chamber 1 and chamber 2 near the suction end face is the largest, reaching 650 kPa. Therefore, the maximum flow velocity is at the tip clearance and the inter-tooth clearance. The leakage of gas at the gap will greatly affect the efficiency of the expander, so it is necessary to reduce the tip and inter-tooth clearances as much as possible under the condition of ensuring the normal operation of the expander. The value and direction of the fluid velocity on each section are basically the same, and there are only slight differences in some areas, which means that the flow of the working fluid in the expansion chamber is relatively stable. The speed of the rotor meshing area increases, which is due to the turbulent flow here. The leakage at the tip clearance is the most serious. The fluid velocity between the tip circle part of the rotors and the twin-screw body is faster, because the pressure difference between the two ends of the axial direction is large. Reasonable setting of the meshing clearance and the clearance between the tip circle and the casing directly affects the volumetric efficiency of the expander. Therefore, when designing
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Fig. 11 The velocity vector diagram of the rotors domain and the velocity vector diagram of the rotor section (Z = 135 mm)
and improving the expander, they should be designed properly to avoid unnecessary leakage. The variation of the expander performance parameters with the speed is shown in Fig. 12. When the rotating speed increases, the suction pressure loss increases gradually. When the rotating speed is greater than 1300 r min−1 , the pressure loss has a significant increase. This is because the losses increase caused by wall friction and throttling with the flow velocity increase. When the speed reaches 1900 r min−1 , the pressure in the working chamber cannot even reach the given suction pressure. The volumetric efficiency gradually decreases, which is mainly due to the influence of suction pressure loss and clearance leakage. When the rotating speed is less than 1500 r min−1 , the clearance leakage has a greater influence on the flow rate of the expander. But when the rotating speed is greater than 1500 r min−1 , the suction pressure loss has a greater influence on the flow rate of the expander, and the volumetric efficiency decreases rapidly. The indicated efficiency decreases with increasing rotating speed, mainly due to suction pressure loss and leakage both reducing the actual output power of the expander. The mass flow rate of the working fluid increases with the increase of the rotating speed. With the increase of the rotating speed, the output power of the expander increases gradually, but when the speed is greater than 1500 r min−1 , the increase of the output power decreases obviously. When the rotating speed reaches 1900 r min−1 , the output power drops significantly, mainly because the increase of the rotating speed makes the suction pressure loss increase. The actual pressure difference between the suction and exhaust of the expander decreases, and the ability to output work also decreases. The variation of the expander performance parameters with the suction pressure is shown in Fig. 13. As the suction pressure rises, the suction pressure loss also increases linearly. This is because when the suction pressure increases, the velocity of the working fluid at the suction port increases, the friction with the wall becomes more intense, and the energy loss is more. Overall, the increase in suction pressure loss is not large. Due to the over-expansion and under-expansion of the expander, the indicated efficiency is reduced, and the actual output power of the expander is affected. The working fluid flow rate basically increases linearly, because when the suction pressure increases, the suction pressure loss also increases, but at the
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Fig. 12 The variation of the expander performance parameters with the rotating speed (the exhaust pressure: 290 kPa; the inlet pressure: 658 kPa; the condensation temperature: 44 °C; the evaporation temperature: 72.9 °C)
same time, the working fluid density is higher, resulting in a larger mass flow rate. Although the indicated efficiency of the expander will be negatively affected by overexpansion or under-expansion, due to the steady increase in the working fluid flow rate and suction temperature, the working fluid entering the expander with a lot of energy, which promotes the stable increase of the output power of the expander. The variation of the expander performance parameters with the exhaust pressure is shown in Fig. 14. When the exhaust pressure increases, the suction pressure loss remains basically the same, then when the inlet working fluid parameters are the same, the pressure at the rotor inlet is basically unchanged. The change of the exhaust pressure will not affect the suction state of the expander. The working fluid flow state in the working chamber will not change greatly. A drop in indicated efficiency means that either under-expansion or over-expansion of the expander will reduce the performance of the expander. The change of exhaust pressure has no great influence on the working fluid flow rate, and the output power will decrease linearly with the increase of exhaust pressure. This is because the increase in exhaust pressure means that the condensation temperature increases, and the enthalpy difference between the inlet and exhaust ports of the expander decreases.
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Fig. 13 The variation of the expander performance parameters with the suction pressure (the exhaust pressure: 290 kPa; the condensation temperature: 44 °C; the rotating speed: 1100 r min−1 )
The variation of system parameters with expander rotating speed, suction temperature and discharge pressure is shown in Fig. 15. When the rotating speed of the expander increases, the output power of the system gradually increases when the speed is less than 1700 r min−1 , but the growth is slow. That is because the increase of the rotating speed leads to an increase in the mass flow rate of the expander. The pump efficiency does not change much, and the indicated efficiency of the expander gradually decreases with the increase of the rotating speed. The evaporation temperature, condensation temperature, and superheat degree remain unchanged, the theoretical output power of the expander increases. The actual output power of the expander is the product of the theoretical output power and the indicated efficiency, but the increase of mass flow rate is greater than the decrease of indicated efficiency, so the actual output power of the expander will increase with the rotating speed. In addition, the change of pump power consumption is small, so the thermal efficiency of the system will decrease as the speed increases. When the rotating speed is greater than 1700 r min−1 , the increase of pump power consumption is greater than the increase of output power of the expander, so the output power of the system will show a downward trend.
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Fig. 14 The variation of the expander performance parameters with the exhaust pressure (the suction pressure: 658 kPa; the suction temperature: 73 °C; the rotating speed: 1500 r min−1 )
When the evaporation temperature increases, the suction temperature of the expander increases, and the output power of the system gradually increases. This is because the working fluid remains in a saturated gas state, and the suction pressure of the expander also increases correspondingly with the increase of the evaporation temperature. The indicated efficiency of the expander increases slightly with increasing evaporation temperature. The increase in mass flow makes the output power of the expander gradually increase, and the pump power does not change much, so the output power of the system also gradually increases. The thermal efficiency of the system gradually increases because the two-phase area in the evaporator accounts for a large proportion. The increase of the evaporation temperature will reduce the heat exchange temperature difference of the evaporator. Although the mass flow rate increases, the increase of the heat exchange amount of the evaporator is still small, so the thermal efficiency of the system will increase with the increase of the suction temperature of the expander. When the exhaust pressure of the expander increases, the thermal efficiency and output power of the system gradually decrease. This is because the indicated efficiency, mass flow rate and output power decrease with the increase of the exhaust pressure. So the output power of the system also decreases. The decrease of the temperature difference in the evaporator reduces the heat exchange amount, but which is smaller than that of the output power, so that the
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Fig. 15 The variation of system parameters with expander performance parameters
thermal efficiency of the system decreases with the increase of the exhaust pressure of the expander.
4 Conclusions In this paper, the working process of the twin-screw expander was simulated by CFD. A complete three-dimensional numerical model was established, and the radial and axial leakage were considered. A structured dynamic mesh generation method based on the expander rotor node mapping and a mesh update technology in which the nodes migrated with the rotor profile were used. It is helpful to decrease the relative error and be closer to the actual working state. The problem of cross-scale dynamic grid generation of the non-contact twin-screw expander can be solved. In addition, the ORC system mathematical model was constructed and solved by using R245fa as the working fluid. The main results are as follows, which support great reference for design, troubleshooting, experimental study and product development of the twin-expander and ORC system:
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1. The simulation results were compared with the experimental results of the literature. The relative error is about 3%, indicating that the mathematical model established in this paper can accurately simulate the ORC system and calculate the working characteristics of the expander. Through the analysis of the internal flow field of the expander, the variation law of the pressure in the working chamber with the angle of the male rotor was obtained. It was found that the shape of the suction orifice can cause throttling losses and pre-expansion during the suction process of the expander, thereby reducing the performance of the expander. Therefore, the design of the suction port should be optimized in the forward design of the twin-screw expander. 2. The analysis of the pressure nephogram and velocity vector diagram of the expander rotor domain shows that the pressure gradient changes the largest at the tip clearance near the suction end face and so as to the flow velocity. That indicates that the leakage is the most serious at the tip clearance. Therefore, in the structural design of the twin-screw expander, the size of the tip clearance should be controlled. 3. When the speed of the expander is low, the leakage has a greater impact on the performance of the expander. When the speed is higher than a certain value, the suction throttling loss caused by the increase of the speed has a greater impact on the performance of the expander. When the internal volume ratio is constant, if the suction air pressure or exhaust pressure deviates from the design value, the expander is in a state of over-expansion or under-expansion, reducing the overall performance of the expander. The indicated efficiency increases first and then decreases with the increase of suction pressure and exhaust pressure. Therefore, in the actual operation of the expander, the appropriate rotating speed, suction pressure and exhaust pressure should be matched to avoid over-expansion or under-expansion. 4. The thermal efficiency and output power of the system increase by about 0.3% and 0.43 kW respectively for every 40 kPa increase in suction pressure. The thermal efficiency and output power increase with the increase of rotating speed. At this time, the system efficiency is 4.79%, and the output power is 4.42 kW. The thermal efficiency and output power decreases with the increase of the exhaust pressure. When the exhaust pressure is 360 kPa, the efficiency and output power values are 3.19% and 2.6 kW respectively. Therefore, it is necessary to select the appropriate expander speed, suction temperature and discharge pressure to adapt the ORC system to optimize the system performance.
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References 1. I. Papes, J. Degroote, J. Vierendeels, New insights in twin-screw expander performance for small scale ORC systems from 3D CFD analysis. Appl. Thermal Energy 91, 535–546 (2015) 2. Y. Qi, Y. Yu, Thermodynamic simulation on the performance of twin-screw expander applied in geothermal power generation. Energies 9, 694–703 (2016) 3. Y. Qi, Y. Yu, Numerical simulation and analysis of leakage process of twin-screw expander. J. Shanghai Jiaotong Univ. 4(50), 496–501 (2016) 4. A. Kovacevic, N. Stosic, I. Smith, Screw Compressors: Three Dimensional Computational Fluid Dynamics and Solid Fluid Interaction (Springer Science & Business Media. 2007) 5. I. Smith, N. Stosic, A. Kovacevic, Power Recovery From Low Grade Heat by Means of Screw Expanders (Elsevier, 2014), pp. 13–58 6. N. Stosic, I. Smith, A. Kovacevic, Screw Compressors: Mathematical Modelling and Performance Calculation (Springer Science & Business Media, 2005), pp. 49–75 7. G. Wu, Structural design and dynamic performance research of medium and low temperature twin-screw expander (Yangzhou University, Yangzhou, 2017) 8. H. Tang, Research on characteristics of twin-screw expander and performance of organic Rankine cycle system (Xi’an Jiaotong University, Xi’an, 2016) 9. S. Yang, W. Tao, Heat Transfer (Higher Education Press, Beijing, 2006) 10. C.A. Dorao, M. Fernandino, Simple and general correlation for heat transfer during flow condensation inside plain pipes. Int. J. Heat Mass Transf. 122, 290–305 (2018)
Development of a Residential Scale, Economized, Compressor Load Stand to Measure Compressor Performance Using Low GWP, Flammable Refrigerants Amjid Khan
and Craig Bradshaw
Abstract The phase-out of legacy refrigerants is currently underway because of their high Global Warming Potential (GWP) in heat pump systems. Many low-GWP flammable refrigerants such as R1234yf, R1234ze(E), R454B, R32, and blends are being explored as replacements of conventional refrigerants. Additionally, proliferation of heat pump systems often requires modifications such as economization. Characterizing the performance of the next generation of compressors with flammable, low-GWP, working fluids requires significant experimental support. This work presents the design and commissioning of a hot-gas bypass compressor load stand to support such an effort. The selection of components and tubing sizes was completed using output from the thermodynamic model of the hot gas bypass cycle developed in Engineering Equations Solver (EES) and constrained by ASHRAE standard 23. The design capacity for the load stand is 1–5 tons (3.5–17.58 kW) compressor capacity. The load stand is capable of testing compressors at saturated suction temperature as low as − 30 °F and saturated discharge temperature as high as 140 °F. This load stands also includes control over the oil recirculation rate and as well as a dedicated economized loop. The load stand is validated using ZP38K5RETF5 Copeland scroll compressor datasheet. The aim of the load stand is to collect data and develop datasheets for economized rotary and scroll compressors, which will be used for vapor injected compressors model development. Keywords Compressors · Hot gas bypass load stand · Vapor injection
A. Khan (B) · C. Bradshaw Center for Integrated Building Systems, Oklahoma States University, Stillwater, OK, USA e-mail: [email protected] C. Bradshaw e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_66
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1 Introduction There have been significant improvements in compressor efficiencies to reduce the environmental impact of HVAC&R systems. In 2022, 12 quadrillion BTUs of energy is consumed by commercial and residential HVAC&R systems, out of which 6% of energy is specifically used by compressors [1]. The power consumption by compressors makes it particularly important to improve its performance. To reduce the environmental impact of HVAC&R systems, one way is to minimize the use of hydrofluorocarbon (HFC) refrigerants and to shift to low GWP refrigerants. According to Kigali amendment to Montreal Protocol, countries must reduce the use of HFC by 85% between 2019 and 2036 [2]. After the Kigali amendment, industries all over the world are moving towards low GWP refrigerants and modifying the compressors for the new refrigerants. There are many compressor testing environments available for the purpose of measuring compressor performance. There are two main types of compressor testing methods such as calorimeter type and flowmeter type, which are differentiated by the method of refrigerant mass flow rate calculations. A calorimeter method uses energy balance over the heat exchangers such as condenser or evaporator, while flowmeter method uses mass flow meters both at compressor suction and discharge [3]. The method of calorimetry has been studied widely in HVAC&R industry. A typical calorimetric test bench was developed and modified to add vapor injection for vapor injection compressor characterization. This calorimetric bench was designed to control the operating conditions of vapor injection compressor at the suction, discharge, and injection port. It has an independent intermediate pressure and injection superheat line to control vapor injection [4]. The impact of refrigerant lubricant mixture properties was studied on compressor efficiencies using calorimeter. Transcritical carbon dioxide was evaluated in calorimeter using different lubricants and oil mass flow rates. It was found that accounting for lubricant inside the compressor affects the performance parameters such as isentropic efficiency and COP calculations [5, 6]. The drawback of the calorimeter load stand was studied while testing larger compressors over 30 kW [7], calorimeter method becomes very expensive and time consuming. It was noted that it takes remarkably high stabilization time as compared to flowmeter type testing method. A hot gas bypass load stand was designed to evaluate the performance of miniature custom-designed linear compressor [8]. This load stand was able to control temperature and pressure at discharge by controlling the flowrates through the system using expansion valve. Similarly, the model of novel rotating spool compressor was validated, using data collected from hot gas bypass compressor load stand while testing a 5 ton (18 kW), R410A, spool compressor prototype with data presented in [9]. The data was presented from an oil injected scroll compressor using a modified hot gas bypass load stand, which presented the potential for performance improvements of compressor with oil injection [10]. Economized single port flowmeter type compressor load stand was established [11], to develop vapor injection model using
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Buckingham Pi theorem. Similar studies were performed on hot gas bypass load stands to collect data for compressor model development [8, 12, 13]. Recent studies show that without designs specific to low-GWP refrigerants, heat pump technologies would increase energy use either due to thermodynamic disadvantages or reduced unit component efficiency [14]. A load stand is available to test compressors having capacity ranging from 10 to 80 tons capacity [15, 16]. Therefore, there is a need to develop a load stand, which can be used to test compressors from 1 to 5 tons of capacity. The development of hot gas bypass load stand having capacity of 1–5 tons is motivated by the need of industry for testing residential scale, economized, heat pump compressor technologies. The economization is added feature to this hot gas bypass load stand to allow a wide range of compressor applications to be simulated. This study is focused on the load stand constructed at Oklahoma State University for testing vapor injection compressors having capacity ranging 1–5 tons.
2 Load Stand A thermodynamic model of a hot gas bypass system, including economization, was developed in EES. The main purpose of this model is to estimate the important parameters such as mass flowrates which are needed for pipes sizing. The goal of this model is the estimation of the high and low mass flowrate measurements, to make it easier for making design choices. The model makes thermodynamic assumptions to calculate each state of the system. The assumptions made, consider the compressor with fixed adiabatic efficiency, all expansion valves are considered as isenthalpic, and heat exchangers are assumed isobaric. Each cycle state is set with two independent refrigerant properties using R454B as a refrigerant for each state point enthalpy calculations. Figure 1 shows the pressure enthalpy diagrams for each state point for both baseline cycle without vapor injection (a) and vapor injection cycle (b).
Fig. 1 P–h diagram for R545B a without injection b with injection
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State 1 for the economized cycle is set for compressor suction at saturated evaporation temperature with superheat. State point 2 is the exit of the first stage of compression set at the intermediate pressure as shown in Eq. 1: pint =
/(
pevap ∗ pcond
)
(1)
where pevap is the evaporation pressure, pcond is the condenser pressure, and pint is the intermediate pressure. State point 3 is found with intermediate pressure and energy balance on the saturated vapor from point 10 mixing adiabatically with state point 2. The mass flow rate at point 3 is the summation of mass flowrate at state point 2 and 10. State point 4 is specified by condensing temperature and its enthalpy is calculated using a similar method as point 2. The process from state point 1 to state point 4 represents the compressor adiabatic work. The path from state point 4 to state point 7 through state point 8 is the hot gas bypass line to set the conditions at the compressor suction and at the injection port. State point 5 to state point 6 through state point 9 is the isenthalpic expansion process through the expansion valves. In parallel with pressure and temperature calculations, this provided an easy way for components selection to operate the load stand.
2.1 Load Stand Design The schematic of the system layout is shown in Fig. 2, consisting of all the major components and instrumentation. There are 2 loops featured in Fig. 2 including the main loop and the economization loop. The main loop controls the operating conditions exposed to the compressor. The operation starts with the suction of the compressor at controlled pressure and temperature. The suction flow enters the compressor and exits at the compressor discharge with high superheated temperature at condensing pressure. The refrigerant flow after the exit of compressor enters the coalescent oil separator before passing through the Coriolis mass flowmeter as shown in Fig. 2. Exiting mass flowmeter, the refrigerant divides into 2 paths, most of the flow passes through the condenser to become subcooled liquid and then expands to the compressor suction after getting stored in the receiver controls suction superheat, while some of the hot refrigerant is bypassed through the hot gas bypass line to compressor suction to control the suction pressure. The 2 main parameters (temperature and pressure) at compressor suction are controlled by the mixing of liquid and vapor at the exit of bypass line. The compressor discharge pressure is controlled by the flow of water through the condenser; lowering the water flow rate, higher the compressor discharge pressure and vice versa. The economized loop in the load stand for the vapor injection works the same way as the load stands main loop. There is second Coriolis mass flowmeter at the suction of the compressor, the difference of the mass flow from the mass flowmeter
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Fig. 2 Piping and instrumentation diagram
at the suction (m˙ suc ) and the discharge (m˙ dis ) gives us the injection mass flow rate (m˙ in j ) as shown in Eq. 2: m˙ in j = m˙ dis − m˙ suc ,
(2)
The manipulation of the expansion valves will allow for the injection state control permitting either liquid or vapor refrigerant injection. Both the loops (main and economized) are operated together for testing vapor injection compressors, but it is also possible to evaluate compressors without vapor injection with closed economized loop configuration. As the design of the tubing, most importantly the sizing, is sensitive to ensure the refrigerant velocities, oil entrainment, and appropriate mixing are achieved, therefore careful consideration went into it for operating the load stand in large operating range. The main loop design was taken into consideration as it was responsible
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for taking the bypassed and liquid flows, expanding them to suction pressure, and then mixing them to achieve desired operating conditions at compressor suction. Therefore, the piping sizes were divided into liquid and vapor at compressor suction and discharge to ensure smooth flow of the cycle. The piping sizes are shown in Fig. 2 with assorted colors which are selected during the design procedure. According to ASHRAE Handbook 2010, the recommended range for velocities at the discharge of the compressor is from 2000 to 3500 fpm, and at compressor suction is 900–4000 fpm. Based on EES analysis, the velocities of refrigerant and extreme operating conditions at the compressor suction and discharge, the piping have been selected at compressor suction, discharge, and liquid line respectively (3/4'' , 1/2'' , 1/2'' ). Similarly, the same procedure is conducted to select the piping for the injection line before mixing for vapor and liquid line, and after mixing to the injection port are as listed respectively (1/4'' , 1/4'' , 1/2'' ).
2.2 Instrumentation The instrumentation consists of pressure transducers and Resistance temperature detectors (RTD) temperature sensors for each state points discussed above. These critical measurements will use higher accuracy pressure transducers and RTD’s for reduced measurement uncertainty. Mass flowrate measurements are obtained with two Coriolis mass flowmeters located at the suction and discharge of the compressor. Temperature switch is installed at the compressor discharge line for prompt control of the compressor. The compressor speed is modulated through an inverter (40 kW) with a power transducer measuring the power supplied to the compressor. A pressure switch at the compressor discharge is installed for compressor safety, the pressure switch will shut down the compressor as the pressure crosses the pressure limit of 500 psia. Instrumentation accuracies are mentioned in Table 1. All the measurements follow ASHRAE standards 23.1 [17]. Measuring the volumetric and isentropic efficiency at a range of simulated operating conditions is one of the primary goals. The overall isentropic efficiency (ηo,is ) of the compressor with vapor injection is the ratio of work done by the compressor in an isentropic process to the work done by the compressor in the actual process (W˙ ), as shown in Eq. 3: ηo,is =
m˙ suc ∗ (h 2 − h 1 ) + m˙ dis ∗ (h 4 − h 3 ) , W˙
(3)
The volumetric efficiency (ηvol ) is the ratio of refrigerant mass flow (m r ) to the theoretical maximum mass flow rate (ρ ∗ νd ∗ ω); given by equation, ηvol =
m˙ suc , ρ ∗ νd ∗ ω
(4)
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Table 1 Instrumentation Specifications Part
Model number
Measurement range
Accuracy
Pressure sensor
Danfoss, AKS 3000
0–3447.3 kPa
± 1% FSa
Temperature sensor
Danfoss, AKS 21 W
− 70–160 °C
± 0.1 °C
Suction mass flowmeter
Micromotion CMF025M998N2BAEZZX_ 14050
0–50.8 kg/min
± 0.10%
Discharge mass flowmeter
Micromotion CMF025M998N2BAEZZX_ 14050
0–50.8 kg/min
± 0.10%
Power meter
Ohio semitronics, WT7-22-100-E
0–40 kW
± 0.5% FSa
Pressure switch
Danfoss, KPS 47
600–12,000 kPa
± 1% FSa
Temperature switch
Danfoss, RT101
Max 300 °C
± 0.25%
a FS
Full scale
where ρ is the density of refrigerant at the specific temperature, νd is the compressor displacement volume, ω is the rotational speed of the compressor. In case of ηvol , the νd is given by the manufacturers. The enthalpies are calculated from the pressure measured by pressure transducers and temperature by RTDs mentioned in Table 1.
3 Results and Discussion 3.1 Load Stand Validation The load stand validation was conducted using the datasheet of Copeland Scroll compressor, model; ZP39K5E-TF5, rated at 3.25 tons with R410A having a displacement volume of 36.87 cm3 /rev. According to compressor manufacturers, this deviation should be less than 3% [4]. Compressor was tested at 3 different condensing temperatures 90, 100, and 105 °F and for each condensing temperature the evaporating temperature was varied from 15 to 55 °F for compressor performance evaluation. The load stand is validated by evaluating the 2 output parameters such as compressor power consumption and mass flowrate. The experimental power and mass flowrate is measured by the Ohio Semitronics power transducer and Coriolis mass flowmeter respectively, as mentioned in Table 1. Measured mass or power means the data collected from the load stand, compared with the data from the manufacturer’s datasheet as shown in Fig. 3. It can be seen from the parity plot that the performance prediction of the load stand is very reliable showing mean absolute percent error (MAPE) of 0.008% in power prediction and 0.023% in mass flowrate measurement.
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Fig. 3 Parity plots for compressor power and mass flowrate
3.2 Preliminary Test Results Preliminary Tests were performed on the load stand with vapor injection using GMCC vapor injection single phase compressor, model; EAPM310D85UMT, having rated capacity of 3.25 tons and νd of 30.6 cm3 /rev with R454B refrigerant. The load stand is connected to Labview to view the data collection. This load stand is manually controlled and achieving a steady state takes longer than automated load stands. The preliminary results were taken to get familiarized with the load stand operation. The preliminary test condition was a condensing temperature of 75 °F (23.89 °C), an evaporating temperature of 35 °F (1.67 °C), a suction pressure of 111.6 psia (769.45 kPa), and a discharge pressure of 213.49 psia (1472 kPa). A steady state condition was achieved in 3 h of operation after the load stand was heated up in 3 h. Data was collected over a span of 15 min, resulting in collection of 900 points. The plots of the critical parameters over the span of 15 min is shown in Figs. 4, 5, 6, and 7. According to ASHRAE standard 23, the allowable tolerance in temperature at compressor suction and discharge should be ± 0.5 °F (± 0.277 °C), which in our load stand case is kept as ± 0.2 °F for collecting accurate results. The allowable tolerance in pressure at compressor suction and discharge is supposed to be kept as
Fig. 4 Suction pressure and temperature over a span of 15 min
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Fig. 5 Injection pressure and temperature over a span of 15 min
Fig. 6 Discharge pressure and temperature over a span of 15 min
Fig. 7 Output parameters; compressor power and mass flowrate
± 1%, which is usually around 2 psia (13.78 kPa), which in this load stand case is kept as 2 psia [4]. In order to specify the steadiness of each parameter, steady state criteria from ASHRAE 49.1 is used. This standard has specifically defined for mass flowrate, but it can be applied on other parameters as well to help quantitatively define the steadiness of each parameter. The stability ratio, S is: s=
σm˙ m˙
,
(5)
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Fig. 8 Compressor isentropic and volumetric efficiency
where σm˙ stands for the standard deviation in the data and m˙ stands for average mass flowrate. According to this criterion, the number of samples should be more than 30 and the data should be collected for more than 6 min. If the stability ratio is less than 1%, it means steady state is achieved. The suction pressure and temperature have an S value of 0.13% and 0.22% respectively as shown in Fig. 4. The injection pressure has an S value of 0.11%, while the injection temperature has an S value of 0.31% shown in Fig. 5. The discharge pressure measurement has an S value of 0.10%, while the discharge temperature has an S value of 0.03% as shown in Fig. 6. The power has an S value of 0.11% shown in Fig. 7, while m˙ dis measurement has an S value of 0.16%. Figure 8 shows the ηisen and ηvol averages 0.50 and 0.96 respectively over a 15-min period. The stability ratio shows the validity and capability of the load stand to create and maintain the steady state for a longer period of time, even though it’s a manual controlled configuration, due to which there are oscillations in the data. This oscillation is more significant in the temperatures data shown in Figs. 4, 5, 6, 7 and 8. Based on the results shown in Figs. 4, 5, 6, 7 and 8 shows the capability of load stand that it can test compressors to achieve any desired condition even through manual control. It also shows that load stand can be run and operated at any desired conditions.
4 Conclusions and Future Work A residential scale economized compressor load stand capable of testing a variety of compressors with and without vapor injection at a wide range of capacities has been developed. This load stand has the capability to test compressors with a capacity ranging from 1 to 5 tons (3.52–17.58 kW). This load stand has some unique capabilities; it is portable, can be tested in any desired conditions, it has the ability to provide liquid or vapor injection through a separate loop, it has control over the vapor injection mass flowrate. This load stand is operated for compressors with the capacity of 17.58 kW, in future its capability for testing compressors with less than 1 kW and more than 17.58 kW will be tested as well to check its performance limit.
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The ability of the load stand to have vapor injection increased its versatility and can be used for a wide range of operating conditions. Validation and Preliminary tests on 11 kW compressor show the capability of the load stand to run and give desired results. This load stand is used to calculate the compressor efficiencies and based on its portable nature; it can be used to expose the compressor to any ambient condition during its operation for different low GWP refrigerants. In future the load stand will be automated and will be used to test different compressor technologies under any extreme conditions for many low GWP refrigerants such as R1234yf, R32, and propane. The compressor capacity range will also be tested in future to find whether it can be used for fractional capacity compressors testing and compressors with capacity more than 11 kW. Acknowledgements This work has been supported by the Center for Integrated Buildings Systems (CIBS), an Industry/University Cooperative Research Center at Oklahoma State University.
References 1. US Department of Energy, Monthly energy review. Mon. Energy Rev. 0035(Nov), 1–278 (2020) 2. Countries Adopt Kigali Amendment to Phase Down HFCs | NRDC. [Online]. Available: https://www.nrdc.org/experts/david-doniger/countries-adopt-kigali-amendment-phasedown-hfcs. Accessed: 26 Feb 2023 3. A. Khan, C.R. Bradshaw, Quantitative comparison of the performance of vapor compression cycles with various means of compressor flooding. (2022). https://docs.lib.purdue.edu/icec 4. M.M. Mathison et al., Methods for performance testing positive displacement refrigerant compressors and compressor units, vol. 2022 (2022) 5. F.M. Tello-Oquendo, E. Navarro-Peris, J. Gonzálvez-Maciá, New characterization methodology for vapor-injection scroll compressors. Int. J. Refrig. 74, 528–539 (2017). https://doi. org/10.1016/j.ijrefrig.2016.11.019 6. S.S. Wujek, C.D. Bowers, P. Okarma, Effect of lubricant-refrigerant mixture properties on compressor efficiencies, in International Compressor Engineering Conference, no. 2003, pp. 1– 9 (2014) 7. C. Cuevas, J. Lebrun, V. Lemort, E. Winandy, Characterization of a scroll compressor under extended operating conditions. Appl. Therm. Eng. 30(6–7), 605–615 (2010) 8. M.G. Duggan, G.F. Hundy, S. Lawson, Refrigeration compressor performance using calorimeter and flow rater techniques (1988) 9. J. Singleton, D. Schmidt, C.R. Bradshaw, Control and commissioning of a hot-gas bypass compressor load stand for testing light-commercial compressors on low-GWP refrigerants. Int. J. Refrig. 112, 82–89 (2020) 10. J. Orosz, G. Kemp, C. Bradshaw, E. Groll, Performance and operating characteristics of a novel rotating spool compressor performance and operating characteristics of a novel rotating spool compressor, in International Compressor Engineering Conference, Purdue (2012) 11. I.H. Bell et al., School of Mechanical Engineering 12. D.R. Lumpkin, A.M. Bahman, E.A. Groll, Two-phase injected and vapor-injected compression: experimental results and mapping correlation for a R-407C scroll compressor. Int. J. Refrig. 86, 449–462 (2018) 13. J. Orosz et al., An update on the performance and operating characteristics of a novel rotating spool compressor-updated performance and operating characteristics of a novel rotating spool compressor (2014)
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14. R. Gu, M. Mathison, Design of a compressor load stand capable of supplying two-phase refrigerant at two intermediate pressures. Department of Mechanical Engineering, Marquette University, no. 2010, pp. 1–10 (2014) 15. S. In, K. Cho, B. Lim, H. Kim, B. Youn, Performance test of residential heat pump after partial optimization using low GWP refrigerants. Appl. Therm. Eng. 72(2), 315–322 (2014) 16. D. Schmidt, J. Singleton, C.R. Bradshaw, Development of a light-commercial compressor load stand to measure compressor performance using low-GWP refrigerants. Int. J. Refrig. 100, 443–453 (2019) 17. ASHRAE Standard 23, Methods for Performance Testing Positive Displacement Refrigerant Compressors and Compressor Units from IHS Markit (2022)
Compressor Lubricants
Study of Lubricant Compatibility with a Low-GWP Refrigerant as an Alternative to R410A in a Compressor Test Loop Bong Seong Oh, Gilbong Lee, Bongsu Choi, Sun-Ik Na, Ho-Sang Ra, Eunseok Wang, Jongjae Cho, Beomjoon Lee, Hyungki Shin, and Junhyun Cho
Abstract Due to large concerns over global warming, many countries signed and ratified the Kigali Amendment. The amendment is an international agreement to gradually exclude HFCs that have zero ODP but thousands of GWP. R410A which has 2088 GWP is a representative HFC and common refrigerant in air-conditioning systems. To replace the fluid with a low-GWP one, R466A is considered a promising substitutional one because R466A obtained class A1 from ASHRAE. Until now, the compatibility test for R466A with lubricant and materials has been only done by sealed tube with copper, iron, and aluminum coupons. In this study, oil compatibility characteristics of R466A with oil and materials are assessed in real operating conditions of a compressor. For this, a simple heat pump cycle test loop is designed and tested under an accelerated test protocol. To confirm how R466A is compatible with oil and materials, the oil is periodically sampled after regular operation time. As decision factors, the viscosity of oil and decomposed ions in oil are selected, and they are measured by a rotational rheometer and ion chromatography, respectively. Keywords R466A · Low-GWP · Lubricant compatibility
1 Introduction Due to large concerns over global warming, many countries signed and ratified the Kigali Amendment. The amendment is an international agreement to gradually exclude HFCs that have zero ODP but thousands of GWP. R410A which has 2088 GWP is a representative HFC and common refrigerant in air-conditioning systems. To replace the working fluid with a low-GWP one, R466A is considered a promising substitutional one because R466A obtained class A1 from ASHRAE B. S. Oh · G. Lee · B. Choi · S.-I. Na · H.-S. Ra · E. Wang · J. Cho · B. Lee · H. Shin · J. Cho (B) Korea Institute of Energy Research, Gajeong-ro 152, Yuseong-gu, Daejeon, Republic of Korea e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_67
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[1]. Until now, the compatibility test for R466A with lubricant and materials has been only done by sealed tube with copper, iron, and aluminum coupons [2]. In this study, lubricant oil compatibility characteristics of R466A with oil and materials are assessed in real operating conditions of a compressor. For this, a simple heat pump cycle test loop is designed and tested under an accelerated test protocol. Nonetheless, evaporating and condensing pressures which are thermodynamic states of heat pump system are only given as the criteria for accelerated test protocol. Therefore, appropriate operation strategies of BOP should be developed to make the test loop under the accelerated test protocol condition. By modeling the test loop with an off-design analysis solver, the operation manual for the accelerated test would be developed. After regular operation time, the oil in the test loop would be periodically sampled to confirm how R466A is compatible with oil and materials. As decision factors for the degree of compatibility, the viscosity of oil and decomposed ions in oil are selected, and they are measured by a rotational rheometer and ion chromatography, respectively [3].
2 Technical Review of Refrigerant-Lubricant Oil Compatibility In order to evaluate the chemical stability of refrigerant and oil, major evaluation factors were determined by referring to the existing literature [3] for the physical decision factors to be analyzed after deterioration due to long-term real operation of the system. First, it is possible to evaluate the adequacy with the refrigerant by measuring the acidic product produced by the oxidation of oil as an index of TAN (Total Acid Number). Potentiometric titration using KOH (ASTM D 664) is used. Second, the degree of decomposition of the refrigerant or oil can be grasped by analyzing the decomposition ions generated by the reaction between the refrigerant and oil as a decomposed ion indicator. When fluoride is detected, the refrigerant is decomposed, and when organic acids such as propanoate and hexanoate are detected, it can be evaluated that oil is decomposed. For this, ion chromatography is used. Another study mentioned that the oil properties significantly change when refrigerant dissolves in the oil [2]. The degree of solubility is important as it affects the viscosity of the oil, and the lubricant with refrigerant in solution should have adequate viscosities across the system. Thus, the viscosity should be one of the decision factors for the refrigerant-lubricant oil compatibility. Viscosity is measured based on ASTM D 445. The previous methods are generally applied to sealed tube tests. The amount of oil sample is not a big deal for sealed tube test so that analysis methods that require lots of sample amount like D 664 or D 445 can be utilized for the sealed tube tests. However, the compatibility test under real operating conditions should care the amount of oil sample because the oil would be periodically sampled from the compressor. Hence, too much oil sampling could result in a lack of oil in the compressor for running.
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Therefore, the sum of organic acids from the ion chromatography would be replaced to judge the degree of the oxidation of oil instead of TAN, and D 445 would be substituted with rotational Rheometer that requires about the amount of 4 ml. Honeywell’s sample accelerated test for R466A refrigerant under the condition of POE oil (ISO 32 3MAF) for R410A and additive combination According to the results of previous research, fluoride was detected at 50 ppm, 25 times higher than 2 ppm for R410A, in the R466A test, and iodide It has been reported that 22 ppm, which is hundreds of times greater than < 0.1 ppm of R410A, is detected [2]. Accordingly, after a sample accelerated test in the same POE oil using additives whose components were not disclosed at Honeywell, it was shown that fluoride was 2 ppm and iodide was < 1.5 ppm, and compatibility could be satisfied [2]. In addition, it was reported that R23(CF3 H) was decomposed and detected in the combination of zinc-aluminum alloy and R466A-POE base oil [4], and it was also shown that compatibility can be satisfied through the addition of additives. It is evaluated that the iodine component of CF3 I of R466A reacts with oil and zinc-based metal materials. Some information on the additive material can be obtained from Honeywell’s patent, which is a combination of alkylated naphthalene (NA-LUBE), farnesene (C15 H24 ), a diene compound, and BHT (Butylated Hydroxi Toluen), a phenolic compound [5].
3 Test Loop for Refrigerant-Lubricant Oil Compatibility 3.1 Test Loop Design and Installation The original test loop was designed as shown in Fig. 1 [6]. The core cycle devices such as the compressor, heat exchanger, and electronic expansion valve were selected with commercially available parts for R410A, and a rotary compressor with a capacity of 6 HP and an inverter control system was used. In order to simulate the MOC condition in the long term, we tried to simplify the heat source facilities corresponding to the secondary side of the condenser and evaporator. Therefore, after the compressor, working fluid is discharged (state 2), a bypass loop is placed before entering the condenser, so that the refrigerant that has passed through the condenser is expanded in the EEV (Electric Expansion Valve) 1, and the bypassed refrigerant passes through EEV2 and 3. After expansion, it was configured to be mixed in an evaporator. EEVs were selected with Danfoss R410A standard commercial product, and the bypass loop is composed of two loops to control the flow rate and expansion ratio fluctuations that may occur when R466A refrigerant is used in the valve. EEV2 and EEV3 are controlled by manual and/or remote signal by PLC controller. The refrigerant that has passed through EEV1, EEV2, and EEV3 is introduced into a shell containing a 15 kW electric heater and mixed. This shell-type heater operates as an evaporator in order to control the evaporative temperature and superheat of the compressor easily because of uncertain characteristics of R466A. R466A is a mixed
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B. S. Oh et al. RTD/PT3
Mass flow meter 01
RTD/PT4
2
3/8"
25A
Header Condensor 20 kW
Oil Seperator
3/8"
PSV
3/8"
RTD/PTwo
37Ů
Flow meter 03 4 Nm3/h Cooling Tower
RTD/PTwi
2
32Ů
¼ 3/8"
Compressor Panel P
Manual EEV2
Power meter Inverter Accum RTD/PT1
Cooling Water
¼ Solenoid on/off valve
flexible tube
I
Manual EEV3
Receiver
Refrigerant
¼ needle valve Compressor
1
3 3/8"
Oil monitoring
6 HP
Mass flow meter 02 3/8"
3/4"
EEV1
sight glass 5
3
2
EEV1
EEV2,3 1
5 h
Evaporator
Refrigerant
P
4
RTD11 TC/PT12 for EKC RTD/PT10
3/4"
Water pump
¼ nipple
3/8"
4 PT 1, PT2: Autrol ATP3200, FS ±0.075%
3/4"
PT n: Keller, FS ±0.5% ¼ nipple
To USER DAQ
Vessel
TC/PT for EKC Electric Heater 15 kW
RTD Class A Mass Flow Meter: OVAL ±0.1%
Fig. 1 Schematic of the original test loop for refrigerant-oil compatibility test under long-term operation
refrigerant of three types. In response to the temperature change that can occur during heat exchange, an electric heater that can directly control the temperature is used to allow only gaseous R466A to flow in from the compressor inlet, enabling stable testing. A visualization window and an oil extraction valve were configured in the loop returning from the oil separator to the compressor after compressor discharge, so that oil sampling was possible, and a mass flowmeter (OVAL, ± 0.1%) was installed on the compressor discharge side and the condenser rear side. A pressure gauge (Autrol) of ± 0.075% was used at the inlet and outlet of the compressor, and a pressure gauge (Keller) of ± 0.5% was used for other parts, and a Class A RTD was used for the temperature, and the temperature for controlling EEV1 was measured using a thermocouple. Temperature and pressure data were obtained through a data logger (Yokogawa GM10), and EEV control was configured with a PLC. As shown in Fig. 2, the test loop was completed, and the stability of the system was verified through the pressure resistance test and air tightness test. Afterwards, R410A refrigerant is sealed, and core device performance, data acquisition, cycle control, and safety issues are checked through a test run, and then the test is conducted with R466A refrigerant. Therefore, the shell-type heater that was originally intended to easily operate the system should be replaced with plate-type heat exchanger as shown in Fig. 3.
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Fig. 2 Components of the test with a chiller unit (a), an inverter and controllers (b), the test loop (c) a data acquisition unit (d) and a control PLC monitor (e) Test loop #1 RTD/PT3
Mass flow meter #1
RTD/PT4
3/8"
25A
Header
cap
PSV
Condensor 20 kW
3/8"
3/8" cap
RTD/PTwi
32ť RTD/PTwo
37ť
3/8" flexible tube
Volumetric flow meter #3
RTD/PT5
¼ nipple Receiver
Compressor Panel
Accum RTD/PT1
P
Mass flow meter #2
Compressor
I
6 HP
Power meter Inverter
EEV1
3/4"
TC/PT12 for EKC
3/4"
3/4"
Refrigerant ¼ nipple
Refrigerant
3/8"
RTD/PT10
RTD11
Evaporator 15 kW
3/8" Volumetric flow meter #4
Water Tank Electric Heater
Vessel
RTD
Fig. 3 Schematic of the modified test loop for refrigerant-oil compatibility test under long-term operation
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Table 1 AHRI MOC Tcond (°C)
Toutdoor (°C)
Tevap (°C)
Tindoor (°C)
ΔTsuperheat (°C)
ΔTsubcool (°C)
55.1
46.1
7
26.7
5.5
5.5
ΔT = 9
ΔT = 19.7
3.2 Off-Design Analysis of the Test Loop for Developing Operation Manual In order to evaluate the oil suitability of R466A according to the actual long-term operation of the compressor, operating conditions of the test loop should be determined. To accelerate the deterioration effect by the refrigerant-oil reaction, test scenario of start-continuous operation (8 h)-stop was determined under the AHRI (Air Conditioning, Heating and Refrigeration Institute) Standard 210/240 MOC (Maximum Operating Condition) condition or harsher condition as shown in Table 1. AHRI MOC only provides condensing and evaporating temperatures of the test loop. Thus, it is hard for the internal refrigerant states to be regulated under MOC without BOP control manual so that the off-design performance should be predicted by numerical solver in advance. Figure 4 shows the algorithm of off-design analysis solver algorithm. The specifications of major components for modeling the test loop is listed in Table 2. The simulation results showed 40 bar for discharge saturation pressure, 12.5 bar for suction saturation pressure, 98.5°C for the compressor outlet temperature, and 4.2 for COP under MOC condition.
3.3 Oil Sampling Methods There are two oil sampling methods considering high pressure in the test loop. First method is making a hole at the bottom of the compressor to directly sample the oil from the compressor. This method is regarded as the most efficient way to sample oil because enough inventory of the oil would be maintained at the location. Second method is utilizing fabricated oil sampler without opening the system. This method applies to systems with service valves as shown in Fig. 5. The oil sampler was fabricated using fittings shown in Fig. 6.
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Fig. 4 Off-design analysis solver for the heat pump systems
863
Start Input: Given conditions, constraints Calculate the energy load and heating capacity Assume:
Calculate in/outlet state of the compressor Calculate mass flow rate of refrigerant Calculate internal state of condenser (PHE)
Adjust
No Yes
Calculate internal state of evaporator (PHE)
Adjust
No Yes Calculate performance of the cycle Finish
864 Table 2 Specifications of the test loop for off-design solver inputs
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Components
Specification
Value
Compressor
Polytrophic number (–)
2.5
Discharging volume (cm3 )
43.0
Frequency (Hz)
60
Diameter to gap ratio (–)
0.05
Plate number (–)
40
Plate thickness (mm)
15
PHX thickness (cm)
9.5
PHX width (cm)
12.0
PHX height (cm)
48.0
Flow area (m)
2.39
Plate number (–)
50
Plate thickness (mm)
1.5
PHX thickness (cm)
11.3
PHX width (cm)
17.0
PHX height (cm)
52.7
Flow area (m)
2.8
Condenser
Evaporator
Fig. 5 Conceptual diagram of compressor oil sampling method using oil sampler
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Fig. 6 Picture of fabricated oil sampler
4 Conclusion For the R466A refrigerant of GWP 733, which replaces the R410A refrigerant of GWP 2088 currently used in commercial VRF systems, a test loop that can evaluate the compatibility and reliability of compressor refrigerant-oil that may occur during long-term actual operation was designed and manufactured. Degree of oil oxidation, decomposed ion, and viscosity were determined as indicators to be evaluated through the investigation of the refrigerant-oil compatibility evaluation method. Through previous research analysis, it was confirmed that the use of POE-type oil, the same as R410A, but the use of appropriate additives to suppress corrosion due to the influence of CF3 I included in R466A was necessary, and information on target additive candidates was investigated in the refrigerant manufacturer’s patents. The off-design analysis solver to make operating strategy of the test loop was developed, and the simulation results are added in the further works. Currently, the test loop is modified to replace the original heater with plate-type heat exchanger to improve the oil sampling issue and system controllability. The R466A refrigerant drop-in test would be performed to analyze the change in the characteristics of the refrigerant and oil after long-term room operation, and the deterioration of the compressor and accessories. The two sampling methods are selected, and the method will be tested to judge which method is more appropriate. Acknowledgements This work was supported by Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government (MOTIE) (20212020800070, Development of next-generation alternative refrigerant and efficient heat pump system).
References 1. A.G. Devecio˘glu, V. Oruç, Energetic performance analysis of R466A as an alternative to R410A in VRF systems. Eng. Sci. Technol. Int. J. 23(6), 1425–1433 (2020). https://doi.org/10.1016/j. jestch.2020.04.003
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2. K. Gao, H. Tangri, G. Smith, A. Sethi, S.Y. Motta, Reduced GWP refrigerant for residential and commercial air conditioning systems (2021) 3. N.D. Rohatgi, R.W. Clark, D.R. Hurst, Material compatibility & lubricants research for low GWP refrigerants. Phase I: Thermal and chemical stability of low GWP refrigerants with lubricants (2012) 4. S.A. Kujak, E. Sorenson, Chemical stability and equipment reliability impacts of R-13I1 (CF3I) in R-466A (2021) 5. A. Sethi et al., Heat transfer compositions, methods and systems, PCT/US2018/054775 (2018) 6. J. Cho et al., Preliminary design of a compressor oil reliability test loop using a low GWP refrigerant as an alternative to R410A in VRF systems
Solubility and Viscosity of Variably Miscible Mixtures of Refrigerant and Lubricant Anthony J. Barthel, Andrew D. Sumner, Haley L. Webster, and Matthijs Van De Wall
Abstract Achieving appropriate miscibility, solubility, and working viscosity between a lubricating oil and a refrigerant is vital for proper compressor performance. These properties are all interrelated and cannot be optimized independent of one another; the thermodynamics that define one interaction also influence the others. Choosing the best fluid combination is therefore a tradeoff between the different properties, making it critically important to understand their possible behaviors. This paper will investigate the range of liquid–liquid miscibility behaviors and explore the resulting solubility and working viscosity outcomes. Different lubricant chemistries will be tested to demonstrate the impact of lubricant chemical family on performance, as well as looking within a chemical family to show how finely tuned chemistry choices can shift test results. The outcome from this investigation will help compressor engineers design more reliable and energy-efficient systems. Keywords Lubricant · Miscibility · Solubility · Viscosity
1 Introduction The phase out of hydrofluorocarbons (HFCs) has ushered in a shifting landscape for cooling applications, with the development of new synthetic refrigerants and a broadened application range for natural refrigerants. Alongside new regulations and designs that encourage increased efficiency, it is important to understand factors that affect compressor and system reliability. For lubricated systems, the chemical interactions between the refrigerant and lubricant chemistries dictate fluid properties throughout the system. This primarily
A. J. Barthel (B) · A. D. Sumner · H. L. Webster · M. Van De Wall The Lubrizol Corporation, Wickliffe, OH 44092, USA e-mail: [email protected] A. D. Sumner · H. L. Webster · M. Van De Wall CPI Fluid Engineering, Midland, MI 48642, USA © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_68
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influences the working viscosity of the lubricant in the compressor. Here, high pressures cause the vapor refrigerant to dissolve into the liquid lubricant phase and the phrase “working viscosity” describes the viscosity of this multi-component liquid at a given temperature and pressure. Another concern is how lubricant that circulates through the refrigeration cycle interacts with the liquid refrigerant in the evaporator. Within the HVACR industry these interactions are called solubility (for liquid lubricant and vapor refrigerant) and miscibility (for liquid lubricant and liquid refrigerant). Both properties must be optimized for adequate system performance. Solubility is generally detrimental to compressor performance. Excessive solubility decreases lubricant viscosity and can contribute to lubricant carry-over and foaming [1, 2]. On the other hand, miscibility is desirable for many systems. Liquid lubricant forming a one-phase solution with liquid refrigerant contributes to a controlled oil circulation rate and minimizes the lubricant’s detrimental heat transfer properties [3, 4]. However, since these properties are inherent to molecular structure and often at odds with one another, it can be challenging to reach the desired performance. These performance properties must be achieved while meeting other criteria such as toxicology, chemical compatibility, and chemical stability requirements, which all have their own guidelines [5, 6]. This paper explores the varied and connected behavior of miscibility and solubility with different refrigerant-lubricant mixtures. The importance of making lubricant decisions using the full system operating map is emphasized and examples are given where behavior in one mixture does not predict that of another. Understanding the limits of lubricant-refrigerant mixture behavior through the entire system can aid the compressor engineer in the design process for future systems.
2 Background The properties of solubility and miscibility can be thought of as on a continuum for mixtures of refrigerant and lubricant. Liquid refrigerant necessary for miscibility occurs at low temperatures or high pressures, while vapor refrigerant exists at the reversed conditions. The magnitude by which the two components mix to form a stable phase is governed by thermodynamics, and specifically the Gibbs free energy. A thorough description of this behavior is beyond the scope of this work and is available elsewhere [7]. Miscibility and solubility are both strongly influenced by temperature and pressure, such that a lubricant-refrigerant pair can exhibit regions of both good and poor mixing. Solubility is generally described in terms of mass fraction of refrigerant in lubricant and the resulting pertinent property (such as liquid-phase viscosity) describes this mixture. Miscibility also depends on mass fraction and is generally reported as a single, mixed phase or two (or more) distinct phases. However, more complicated phase behavior is possible [8]. Immiscible systems result in two unique liquid phases, each with distinct and often highly disparate properties. This can be a
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Fig. 1 Glass tubes visually showing the spectrum of behavior from one clear phase (a) through hazy (b), cloudy (c), and the nearly full separation into two distinct phases (d)
major problem in a heat exchanger, as it cannot be guaranteed that the lubricant-rich phase would continuously reach the compressor sump. Figure 1 shows various miscibility behaviors for glass tubes containing mixtures of lubricant and refrigerant. Miscibility in the form of one stable phase is desirable in most refrigeration systems as shown by the tubes on the left side of Fig. 1. Exactly what behavior is acceptable, and what temperature and composition range needs to be met, would be defined by a system designer. Solubility describes dissolution of refrigerant vapor into the liquid phase and therefore is only relevant when there is one, typically lubricant-rich, liquid phase. In a refrigeration system this is of primary importance in the compressor sump, where the diluting effect of dissolved refrigerant on lubricant viscosity is appreciable. The interaction between solubility and viscosity can be demonstrated with a Daniel plot [9], an example of which using R-134a with a 68 cSt lubricant is shown in Fig. 2. The Daniel plot shows solubility in the form of lines of constant pressure (isobars, dashed lines) as well as lines of constant composition (isopleths, solid lines) plotted against temperature. These curves are based on sophisticated models generated from measurements [10, 11] and can be used to simultaneously interpret a mixture’s solubility and viscosity. Viscosity index (VI) is the change in a fluid’s viscosity with temperature and is depicted by the slope of the solid neat lubricant line. All lubricant and refrigerant chemistries exhibit solubility and miscibility with one another; the key to a system engineer is to optimize both properties. The application often dictates the system end use conditions, which also limits which refrigerants can be used. Refrigerant chemistries are limited to molecules with low boiling points and most viable molecules have already been investigated [12]. Therefore, modifications to miscibility and solubility must come from changes to lubricant chemistry.
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Fig. 2 Daniel plot depicting the solubility and viscosity behavior for lubricant and refrigerant
3 Data and Discussion Many lubricant chemistries have been developed to function with the variety of refrigerant chemistries currently in use. Mineral oils saw broad use with chlorofluorocarbons (CFCs) with synthetic lubricants becoming common for the current generation of refrigerants [13]. This includes polyolesters (POE), polyvinyl ether (PVE), polyalkylene glycol (PAG), and alkylbenzene (AB). The growth in chemistry types comes in large part due to miscibility, solubility, and working viscosity requirements. Synthetic lubricants give the chemist the opportunity to influence molecular structure with the aim of developing a lubricant with superior properties. However, understanding these properties, especially those related to refrigerant-lubricant mixtures, is not straightforward. Figure 3 shows a miscibility comparison between two different 68 cSt POE lubricants with the refrigerant R-454B. For this comparison, glass tubes were made at different refrigerant concentrations and were tested across a temperature range. Tubes that exhibited 2-phase, immiscible behavior fall in the shaded region, while miscible 1-phase behavior is left unshaded. These two lubricants are from the same chemical family and share the same neat viscosity yet have drastically different miscibility behaviors. POE (A) shows a narrow region of miscibility with immiscibility occurring at both low and high temperature. This contrasts with POE (B), which exhibits nearly universal miscibility across the tested range.
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Fig. 3 Miscibility charts for two different POE lubricants with R-454B
However, the difference between these lubricants vanishes when measuring solubility and viscosity. Figure 4 shows an overlaid Daniel plot for both lubricants with R454B. The agreement between the two models is exceptional across the entire tested region. A nearly identical result is produced whether comparing along a composition or pressure line. For example, at 70 °C and 20 bar, POE (A) yields 14.3% dilution and 5.1 cSt working viscosity, while POE (B) yields 14.2% and 5.0 cSt. In this case, the vastly different miscibility results are not indicative of the solubility and working viscosity behavior. A similar conclusion through different behavior is seen in Figs. 5 and 6. Figure 5 shows the miscibility behavior of two 220 cSt POEs with the refrigerant R-1234ze(E). The miscibility profile for these two lubricants is similar, with a large region of immiscibility across most compositions at low temperature and an upper critical solution temperature near 0 °C. While POE (D) does have a region of immiscibility
Fig. 4 Daniel plot for two different POE lubricants with R-454B
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at high temperatures, it is small and generally less important than mixtures at low temperature. In the case of POEs (C) and (D), the major discrepancy comes from the solubility and working viscosity comparison. Figure 6 shows the overlaid Daniel plot models for these two lubricants with R-1234ze(E). The models for the two lubricants do not overlap like they did in Fig. 4; the viscosity index (VI) for the fluids is different and can be seen by the separation between the red and purple lines of the same composition. More importantly, the isobars for each fluid differ significantly across the tested range. This is best portrayed using examples from low and high temperatures. At 20 °C and 2 bar, POE (C) yields 13.3% dilution and 110 cSt working viscosity while POE (D) yields 19.9% dilution and 54.7 cSt working viscosity. At 100 °C and 20 bar the fluids reverse in their behavior. POE (C) is thinner and closer in dilution (23.4%, 3.4 cSt) compared to POE (D) (25.1%, 3.9 cSt).
Fig. 5 Miscibility charts for two different POE lubricants with R-1234ze(E)
Fig. 6 Daniel plot for two different POE lubricants with R-1234ze(E)
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A final example is shown in Figs. 7 and 8 with the refrigerant R-290 (propane). Propane has been used as a refrigerant for over a hundred years [14] and is compatible with a variety of lubricant chemistries, as exemplified in Fig. 7. Figure 7 shows the lack of any immiscibility for 32 cSt lubricants composed of POE or AB. Tubes created with these lubricants and different dilutions of R-290 were fully miscible across all tested temperatures. Due the lack of differentiating features between the two lubricants, miscibility of this nature cannot be solely used to determine the applicability of the lubricant. Figure 8 shows the solubility and working viscosity comparison for the 32 cSt POE (E) and the 32 cSt AB. These two lubricants technically had the same miscibility characteristics due to their immiscible regions falling outside of the tested range. However, their Daniel plot models show clear differences. Again, the influence of VI is apparent for the two lubricants, as well as how solubility can greatly change
Fig. 7 Miscibility charts for a POE and an AB lubricant with R-290
Fig. 8 Daniel plot for a POE and an AB lubricant with R-290
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working viscosity. Using 20 °C and 5 bar as an example, POE (E) yields 11.8% dilution and 8.9 cSt while the AB yields 18.6% dilution and 4.3 cSt. Understanding how lubricant chemistry affects mixture properties with refrigerants is challenging and depends on many factors specific to each lubricant chemical family. Properties such as chain length, degree of branching, polarity, and more will influence the degree of solubility and where a one phase mixture occurs [15]. Solubility has been modeled using thermodynamic equations of state [16, 17], however these studies neglect the liquid–liquid phase behavior and are always built from empirical data. Since this behavior cannot be predicted from first principles, it is critical that experimental data is used to design accurate and efficient refrigeration systems.
4 Conclusion Miscibility and solubility between lubricants and refrigerants are critical properties for properly functioning refrigeration compressor systems. These mixture properties are based on the system operating conditions and the chemistry of both lubricant and refrigerant. Due to unique molecular interactions between refrigerant and lubricant chemistries, trends between miscibility and solubility cannot be assumed or predicted. Lacking predictive systems, it is necessary for a compressor engineer to use accurate measured data to design robust next-generation systems.
References 1. K. Min, I. Hwang, Oil circulation rate in rotary compressor: its measurement and factors affecting the rate, in International Compressor Engineering Conference (2000) 2. J. Zhu, F. Botticella, S. Elbel, Experimental investigation and theoretical analysis of oil circulation rates in ejector cooling cycles. Energy 157, 718–733 (2018) 3. L. Cremaschi, A. Saad Yatim, S. Mulugurthi, Experimental study of oil retention in microchannel type evaporators of air-source heat pump systems. Int. J. Refrig. 91, 158–166 (2018) 4. M. Youbi-Idrissi, J. Bonjour, The effect of oil in refrigeration: current research issues and critical review of thermodynamic aspects. Int. J. Refrig. 31, 165–179 (2008) 5. J. Majurin, A. Barthel, New lubricants to enable performance, reliability, and efficiency of equipment using low GWP refrigerants, in International Refrigeration and Air Conditioning Conference (2018) 6. R. Al-Rubaay, C. Seeton, R. Low, 1,1-Difluoroethylene thermal stability, material compatibility and refrigerant/lubricant interactions study, in International Refrigeration and Air Conditioning Conference (2022) 7. J. Elliot, C. Lira, Introductory Chemical Engineering Thermodynamics (Prentice Hall, Upper Saddle River, 1999) 8. A. Sumner, A. Barthel, Clearing the cloudiness on lubricant-refrigerant miscibility, in International Refrigeration and Air Conditioning Conference (2021) 9. G. Daniel, M. Anderson, W. Schmid, M. Tokumitsu, Performance of selected synthetic lubricants in industrial heat pumps. Heat Recovery Syst. 2(4), 359–368 (1982)
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10. C. Seeton, Viscosity-temperature correlation for liquids. Tribol. Lett. 22(1), 67–77 (2006) 11. A. Barthel, J. Majurin, Understanding and improving the 9-coefficient pressure viscosity temperature (PVT) model. IOP Conf. Ser. Mater. Sci. Eng. 604 (2019) 12. M. McLinden, J. Brown, R. Brignoli, A. Kazakov, P. Domanski, Limited options for lowglobal-warming-potential refrigerants. Nat. Commun. (2017) 13. L. Rudnick, Synthetics, Mineral Oils, and Bio-Based Lubricants (Taylor & Francis Group, Boca Raton, 2013) 14. M. McLinden, M. Huber, (R)Evolution of refrigerants. J. Chem. Eng. Data 65, 4176–4193 (2020) 15. W. Fouad, L. Vega, Molecular modeling of the solubility of low global warming potential refrigerants in polyolester lubricants. Int. J. Refrig. 103, 145–154 (2019) 16. A. Wahlstrom, L. Vamling, The solubility of HFC125, HFC134a, HFC143a and HFC152a in n-eicosane, n-hexadecane, n-tridecane and 2, 6, 10, 14-tetramethylpentadecane. Can. J. Chem. Eng. 75 (1997) 17. T. Jia, S. Bi, J. Wu, W. Jiang, P. Li, Experimental investigation for the solubilities of 2,3,3,3tetrafluoroprop-1-ene (R1234yf) in polyol ester, polyvinylether, and polyalkylene glycol base oils. Int. J. Refrig. 125, 84–89 (2021)
Compressor Designs, Lubricant Options and Refrigerant Selections: Putting the Puzzle Together Joe Karnaz
Abstract Several different compressor mechanisms varying in design, material and condition of operation are required to meet the breathe of system needs. The heart of the compressor is the mechanism designed to provide needed work of compressing and moving refrigerant. The mechanisms can vary in complexity of the main operating component and subsequent secondary mechanisms all of which are usually designed to be lubricated. The choice of refrigerant is determined by the application parameters and then usually the lubricant is chosen to meet refrigerant and lubricant interaction requirements. Even before the choice is made of refrigerant and lubricant, engineers have ideas about bearing design, material, surface finish and lubricant distribution to meet minimum film thickness constraints. This paper will focus on next generation refrigerants, compressor design and approaches along with options for successful lubricant selections. Properties and terminology such as viscosity index, working viscosity, solubility, miscibility, compression ratio and delta pressure will be utilized and understood to help put the pieces of the puzzle together. Keywords Solubility · Lubricant · Bearing
1 Introduction There are many pieces to the puzzle of effective compressor operation in a system. Four important areas need to be integrated to have reliable and efficient performance. Compressor types, bearing design, refrigerant and lubricant all fit together and require various forms of evaluation to create the best fit. This matrix gets large and screening processes are essential to a timely and cost approach method to decision making. In some cases, hundreds of compressors can be tested to validate a design but in other cases compressor testing is limited due to the cost of a compressor or unit. Multiple bearing designs can exist within a single compressor, and all are going to J. Karnaz (B) Shrieve Chemical Products, LLC, The Woodlands, TX, USA e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_69
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see the same lubricant and refrigerant so at times it is helpful to validate different designs before compressor operation. A subset to evaluation is how the lubricant and refrigerant interact in regards to stability, compatibility, miscibility and solubility, all of which are important to evaluating and choosing the appropriate refrigerant and lubricant combinations. Focus will be on finding ways to screen candidates without going through timely and costly evaluations. Some lower GWP refrigerants will be discussed with lubricant options.
2 Refrigerants Properties of the refrigerant will dictate everything from compressor design to lubricant selection. Thermodynamic properties of the refrigerant will determine condition within a compressor bearing via the delta pressure differential and compression ratio between the high side and low side of the system. The dilution the refrigerant creates in the lubricant can determine factors such as bearing types, surface finish, distribution of lubricant to the bearing and desired viscosity of the lubricant. The refrigerant will determine the compressor map used to evaluate compressor design and operation in various types of equipment and conditions within a system, that will determine lubricant selection. Figure 1 is an example of a compressor operation map at condensing and evaporating temperatures and a simple cycle diagram of a system that presents conditions that will drive the pressure and temperature within the compressor. A variety of refrigerant chemistries exist today with the list getting longer. More detail will be presented in the section on refrigerant and lubricant interactions.
Fig. 1 Compressor operating map and cycle conditions
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Table 1 Lubricant options for refrigerant chemistries MO AB
HCFC √ + √
POE
◯
PVE
–
HFC
HFO
–
–
– √ + √
– √
√
√
√
HC √ √
CO2 –
√
– √ +
◯ √
– √ +
PAG – √ √ + acceptable and predominates; acceptable; ◯ marginal use; – not used
NH3 √ + √ – – √
3 Lubricants Due to differences in refrigerant chemistries, options for lubricant types have increased beyond the early years of using mineral based oils [6]. The need for different lubricant chemistries has increased with the need to match refrigerants but also to help improve system reliability and efficiency. Table 1 provides a look at matching up what lubricant chemistries work with various refrigerant chemistries and the level of acceptability providing a quick snapshot to begin evaluations [2].
4 Refrigerant and Lubricant Interaction Stability, compatibility, miscibility, and solubility are key factors that need to be determined with each refrigerant and lubricant combination. Stability, compatibility, and miscibility though important when making selections for applications to maintain reliability and efficiency, they are not as critical determining compressor and bearing operation. Therefore, this section will focus on solubility and the effect it has on viscosity of lubricants distributed to bearings. Solubility of refrigerant into the lubricant can have significant variability between refrigerant and lubricant chemistries. These differences could be highly detrimental to the bearing operation. Figure 2 shows the solubility variation when comparing the same refrigerant with different lubricants based on measuring pressure at concentrations. In this case the refrigerant used is Propane (R-290) and we have two lubricants, one that exhibits high dilution with R-290 and the other low. With high solubility more and more refrigerant can be added without getting to the pure R-290 saturation line. At operating conditions this will reduce bearing lubrication and depending on lubricant base viscosity, might not be adequate or maybe additives are required. With low solubility, smaller amounts of refrigerant concentration increase the pressure as it moves toward saturation. This reduced dilution can be helpful, increasing the working viscosity to bearings without having to raise base lubricant viscosity or use additives. Though working viscosity to the bearing is increased, the reduced solubility can also
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Fig. 2 Solubility factors of refrigerant and lubricants
affect the miscibility which needs to be considered and if viscosity gets too high, performance could be reduced. Optimization is the challenge that needs investigation, balancing the working viscosity to help improve energy efficiency. From solubility, the pressure–viscosity–temperature (P–V–T) relationship sometimes referred to as Daniel Plots is created. Measuring viscosity of a pure lubricant at various temperatures is easily accomplished today with numerous methods and instrumentation, but when the refrigerant is associated with the interaction, then this becomes more complicated due to the pressure associated, particularly when evaluation is needed at higher temperatures. Early on some simplistic methods were designed, such as taking advantage of the rolling ball or falling needle method by encapsulating the lubricant and refrigerant in a sealed tube, capable of withstanding pressure [1] and measuring the timing of the falling object and calculating the viscosity. More sophisticated methods to derive viscosity of refrigerant and lubricants have been developed over the years. Seeton [5] showed how the fluid can be circulated in a closed loop system with data acquisition of various parameters of viscosity, temperature, pressure, and density being measured. This data is fit into a program to calculate coefficients used to construct a solver for viscosity and refrigerant solubility/dilution when parameters of temperature and pressure are entered and build detailed plots. Materials of construction are the limiting factor in what can be tested and today some instrumentation can handle pressure associated with some higher-pressure refrigerants like CO2 and others. This information has become vital to engineers when they are designing bearings for compressors used with numerous refrigerants as a first pass evaluation. The plot in Fig. 3 is an example of what can typically be seen from a Daniel Plot and the data associated to develop the plots. We can show how a refrigeration cycle can interlace with the PVT chart to understand the working viscosity in various areas of the system particularly the compressor at different conditions. B to C is the suction condition after superheat and C to D represents low side compressor operation at various oil sump temperatures. D to E
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Fig. 3 Daniel (PVT) plot for a refrigerant and lubricant combination
will be representation of discharge conditions associated with high side compressor operation. This plot also shows the lower critical solution temperature (CST) miscibility of this particular refrigerant and lubricant combination showing data for the PVT plot needs to be cut off in the immiscible green area. If we go back to the cycle conditions in Fig. 1 we can show how the values for different operating conditions can be measured using the above plot. At the low side conditions of 4 bars and using oil sump temperature of 50 °C, the solubility is approximately 12% with 15 cSt of working viscosity. If we evaluate this same combination at a high side condition of 20 bara and 90 °C oil temperature, then we obtain dilution of 20% and 4 cSt working viscosity. So depending on the application and compressor, this lubricant might be satisfactory for operation in low side sumps but might not have enough viscosity to maintain adequate bearing protection in high side operation. The reverse could also be possible where there might be too much viscosity for the low side conditions and another lubricant options might be better.
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5 Bearings Lubrication Test Equipment—When measuring neat viscosity of a lubricant, there are several methods and equipment to evaluate lubricating properties. All these can use various material types, manipulate surface finish and create various motion of design and are immersed in the oil. As mentioned, there are several types of equipment commonly utilized in testing of refrigeration lubricants; pin and block, 4-ball, and block on ring. The pin and block method loads blocks (V-configuration or Cconfiguration) to different levels on a rotating pin with variations to how the study progresses. Measuring load to a failure by incrementally loading is one method and another is setting load and time of test. Other parameters such as temperature and rotational speed can be adjusted and outputs of torque can be measured along with wear scars, surface finish and changes in weight to the materials. The variation to the block design changes how the pin mates with the block in either a line or point contact scenario. The 4-ball method loads a rotating ball onto three stationary balls and various parameters such as load, rotational speed, temperature, and time can be adjusted to either standardize or personalize the test. The block-on-ring method loads a stationary block onto a rotating ring and like the other methods variations in temperature, speed and time can be adjusted. In all these tests there are standard materials that can be used to represent standardized testing or make variations to material types of the mating surfaces along with the surface finish to more match compressor bearings. In each of these cases the motion and interaction of the moving parts can have some similarities to what could be seen in compressor operation providing some level of screening. The equipment mentioned above, along with other commercial and one-off designs are capable of operating under some moderate level of refrigerant pressure which are accomplished using a design with a shaft seal to provide some type of hermetic seal. This allows for understanding how the dilution of the refrigerant will affect the bearing like components in the test and information found in the PVT plots can be used to comprehend the level of dilution and working viscosity reduction when the temperature and pressure are known in the sealed mechanism. Figure 4 represents a Stribeck Curve with some added descriptions of bearing interaction within different lubrication regimes. When designing bearing operation within compressors, it is important to understand what is needed to not only maintain reliable longer-term operation but also to create the best scenario for energy efficiency. This is important in today’s market to help protect environmental, energy and economic resources. In the boundary and mixed lubrication regimes as represent in Fig. 4, the use of additives within the lubricant is used to help operation when the additive, either antiwear (AW) or extreme pressure (EP) is needed. The additive function is to breakdown and deposit on the bearing surface to support the lubricant as metal contact occurs [4]. To help investigate these benefits we can utilize bench top bearing tester as mentioned above.
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Fig. 4 Stribeck curve with bearing information
Figures 5 and 6 demonstrate the use of various additives in a base fluid. To help understand the benefits, the 4-ball tester can be used as a level of screening to see if the formulation with additive will achieve EP (increase in load capability) and AW (reduction in wear of the bearing parts). As can be seen the package formulated with Add Pack 1 and 2 show no EP benefits over the base lubricant and Add Pack 3 shows a definite improvement. Likewise with wear protection, Add Packs 1 and 2 provide some benefits but not to the extent of Add Pack 3. Overall Add Pack 3 would be a candidate to move to testing within a compressor with various lubricant and refrigerants.
6 Compressor Testing After making determination of the working viscosity associated with various refrigerants and lubricants and then looking at bench top lubrication studies, it is time to examine operation in a compressor. In this case, rotary compressors were tested in endurance stands design to put elevated stresses on the compressor bearing by having higher pressure differential and compression ratios, testing outside the compressor map range. Lower GWP refrigerant options can be run in the stands with variations to lubricants, lubricant formulation and bearing designs. Compressors can be fabricated to be capable of removing lubricant from the compressor at specific intervals. Figure 7 shows the results of removing lubricant from the compressor and evaluating the amount of iron dissolved into the lubricant. In rotary compressors the bearing
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Fig. 5 4-ball load-to-failure
Fig. 6 4-ball wear
used in the refrigerant compression, vane and roller, fall into the boundary lubrication regime and if excessive wear occurs, this can be seen in the lubricant analysis, before having to cut the compressor open to examine. In this case we see up to about 100 h of operation, at accelerated condition, the amount of iron slightly rises but between 100 and 250 h the level of iron has significant rise, then levels until the test is complete at 500 h. Since the compressor is indicating bearing wear, we can use the information we have generated for working viscosity, additive studies, and material changes for more investigations. Figure 8 reexamines the same type of compressor testing but now changes are made to either the compressor lubricant/formulation or a material change to the vane material. What is seen is lower levels of iron solubilized into the
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Fig. 7 Bearing iron wear studies—base
Fig. 8 Bearing iron wear studies—enhancements
lubricant with both the lubricant change and the material change that can be related to lower levels of bearing wear in the compressor which can be verified. Material changes could be more costly, and changing lubricant could be a more cost-effective option. After compressor operation we can examine the compressor bearings and determine if the results from the lubricant analysis have some correlation with the appearance of the bearing. Figure 9 is evaluation of the surface of the compressor vane tip in contact with the roller, both a visual and profile surface finish measurement. Comparison with the new vane surface shows the extended wear of the surface when no additive is used and the benefit of using a different formulation with an additive. Moving to a formulation with additive will improve reliability and performance.
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Fig. 9 Surface finish analysis of vane tip
7 Conclusion With the number of newer refrigerants being proposed, it is helpful to have methods presented in this paper to help expedite the process by providing successful means of screening refrigerant and lubricant options. Some of the newer lower GWP refrigerants provide certain challenges that benefit from screening. Some of the challenges are discussed below with potential solutions.
7.1 High Solubility Refrigerants such as CO2 , Propane, and HFO-1234ze(E) will exhibit high solubility in various lubricants, lowering working viscosity and potentially creating other system issues. The ability to measure these properties is critical to understanding what lubricant or formulation is needed. High solubility could result in the need to use the same lubricant chemistry, but at a higher starting viscosity, or the use of additives to protect bearings when the lubricant film decreases. Another solution is to change lubricant chemistries to provide lower solubility and other advantages with the refrigerant. CO2 has high solubility in polyolester (POE) and by changing to polyalkylene glycols (PAG) the dilution can be reduced and other property benefits of the PAG will create optimized viscosity to the bearing. This change has been very successful in compressor used in commercial supermarket applications. The similar hydrocarbon base structure of propane and mineral oil drives high dilution, there are advantages to using synthetic lubricants like POE and PAG to help reduce wear and increase performance; because of the variations within these synthetic fluids the lubricant can
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be tailored for levels of reduced dilution. When R-1234ze(E) replaced R-134a, the same POE lubricants used with R-134a did not provide the needed working viscosity whereas, alternate chemistry based on polyether (PE) showed lubrication benefits. PE product chemistries have been used in applications like screw compressors where higher viscosities are valued.
7.2 Decreased Refrigerant Stability For decades, stability of HFC refrigerants have allowed use in numerous applications and temperatures. Some new refrigerant developments based on hydrofluoro olefins (HFO), and iodine-based refrigerants have created weaker chemical bonds and potential less stability. There are numerous references to these studies [3], even though this paper did not discuss it is still important. Additive chemistries can help benefit bearing performance as discussed above but also help in stabilization by passivating surfaces, reducing reactions, and eliminating unwanted species. Several additive packages have been developed specifically for HFO chemistry and other less stable refrigerants.
7.3 Miscibility Appropriate levels of miscibility are difficult to put a value on since interpretation of need varies among application. Refrigerants today have a range of lubricants that present miscible to immiscible candidates. Today immiscible combinations are used either through the use of lubricant separation or in systems where oil return and heat transfer efficiency losses are not a significant concern. For years, the use of HFC refrigerants decreased the use of mineral oil and alkylbenzene oil due to miscibility concerns but today some of the lower GWP refrigerants have revived these fluids due to higher levels of miscibility. The approach that needs to be taken is measure the miscibility of the combinations being evaluated through various methods and use this information to make decisions based on the ability to provide reliable and performance-based results.
References 1. U. Jonsson, Elastohydrodynamic lubrication and lubricant rheology in refrigeration compressors. Doctoral Thesis, Lulea University (1998) 2. J. Karnaz, Evaluation of lubricant properties and refrigerant interaction, in 24th International Compressor Engineering Conference at Purdue (2018)
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3. S. Kujak, M. Heeried-Leehey, Chemical stability investigations of low GWP refrigerants R454B, R-454C, R-455A, R-468A, R-466A with lubricants, in International Refrigeration and Air Conditioning Conference, Purdue (2022) 4. C. Lipson, Wear Considerations in Design. Studies in Engineering Design (1967) 5. C. Seeton, CO2 -lubricant two-phase flow patterns in small horizontal wetted wall channels; the effect of refrigerant/lubricant thermophysical properties. Dissertation, University of Illinois Urbana-Champaign (2009) 6. H. Spauschus, G. Doderer, Reaction of refrigerant 12 with petroleum oils. ASHRAE Trans. 3 (1961)
Characteristics and Lubricity of Refrigeration Oil for R290 Tomohiro Takaki, Masaki Kawaguchi, Makoto Ando, Yuya Mizutani, and Yuji Shitara
Abstract The switch from HFC refrigerants with a high global warming potential (GWP) to low GWP refrigerants is currently in progress all over the world, and HFO and HCFO refrigerants are being increasingly used. Natural refrigerants, propane (R290) and carbon dioxide (R744), have also been attracting attention. R290 refrigeration systems are now commercially installed for showcases, water heaters, dehumidifiers, etc., and the scope of application will likely continue to expand to relatively small refrigeration equipment. Mineral and synthetic oils have been used as the refrigeration oil for R290, and polyol ester (POE) and polyalkylene glycol (PAG) have been widely used as the synthetic oil. Although various types of oils are used depending on the equipment, POE has high volume resistivity and is said to have a low risk of electrical leakage. POE has also been reported to be less explosive and safer than PAG in a previous experiment simulating an accident during the pump-down of an air conditioner. In this paper, we introduce our developed POE oil suitable for R290. It has an optimal flash point, pour point, volume resistivity, and the chemical structure of POE so that it is compatible with R290. In addition, we determined that the anti-wear performance of the novel POE oil is an improvement over that of conventional POE oils and mineral oils. The surface analysis of the test specimen revealed that the additive system designed for the POE effectively improved the lubricity. Keywords R290 · Refrigeration oil · Tribology
1 Introduction The switch from hydrofluorocarbon (HFC) refrigerants with a high global warming potential (GWP) to low GWP refrigerants is currently in progress all over the world, and hydrofluoro-olefin (HFO) and hydrochlorofluoro-olefin (HCFO) refrigerants are becoming more widespread. Meanwhile, per- and polyfluoroalkyl substances T. Takaki (B) · M. Kawaguchi · M. Ando · Y. Mizutani · Y. Shitara ENEOS Corporation, 8, Chidori-Cho, Naka-Ku, Yokohama, Japan e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 M. Read et al. (eds.), 13th International Conference on Compressors and Their Systems, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-42663-6_70
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(PFASs) have been scrutinized with regards to product compliance, and some fluorine-based refrigerants may become subject to regulation in the future. Thus, natural refrigerants, propane (R290) and carbon dioxide (R744), have also been attracting attention. R290 refrigeration systems are commercially installed for showcases, water heaters, dehumidifiers, etc., and it is expected that the scope of application will continue to expand to relatively small refrigeration equipment. Refrigeration oil is sealed inside the compressor to lubricate it. Mineral and synthetic oils have been used as the refrigeration oil for R290, and polyol ester (POE) and polyalkylene glycol (PAG) have been widely used as the synthetic oil. Although various types of oils are used depending on the equipment, POE has high volume resistivity and is said to have a low risk of electrical leakage [1]. Higashi et al. reported that POE was less explosive and safer than PAG in an experiment simulating an accident during the pump-down of an air conditioner [2, 3]. POE combined with specific additives has also been reported to improve safety [4], making it an ideal refrigeration oil. Thus, we have developed a novel POE suitable for R290. The lubricating mechanism of POE applied to refrigeration oil has not been studied enough. In general, lubricating performance is greatly affected by the adsorption property of the oil. Further, the adsorption properties are related to the polarity of the oil. POE is a polar compound and behaves differently than hydrocarbons such as mineral oil. In this report, we introduce the characteristics and lubricating performance of our newly developed POE and compare it with a conventional POE and a commercial mineral oil for R290.
2 Experimental 2.1 Test Oil In this study, we prepared three different test oils, POE-A, POE-B, and MO. Each test oil contains an oxidation inhibitor, an acid stabilizer, and a phosphorus-based antiwear agent. POE-A denotes the newly developed POE, and POE-B is the conventional POE that has been widely used for refrigeration oil. MO is commercial mineral oil for R290. We measured the acid value, kinematic viscosity flash point, and pour point. In addition, the volume resistivity of the test oils was measured in atmospheric air in accordance with Japanese Industrial Standards (JIS) C 2102. The characteristics of the test oils are listed in Table 1. The flash point, pour point, and volume resistivity of POE-A are similar to those of POE-B and MO. The kinematic viscosity of POE-A is designed to be 46 mm2 /s at 40 °C. Refrigeration oils with this viscosity grade are commercially available, and it should be noted that the kinematic viscosity of the oil with refrigerant dissolved is more important than that of the oil alone, which we will describe it in next section. From the characteristics of the test oils, we determined that POE-A can be used as a refrigeration oil.
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Table 1 Test oil properties Sample name
POE-A
Base oil
Developed POE Conventional POE Commercial mineral oil for R290
Additive
Oxidation inhibitor, acid stabilizer, anti-wear agent (common formulation)
Acid value
mgKOH/g 0.02
Kinematic viscosity mm2 /s (40 °C)
46.3
POE-B
MO
0.01
0.01
66.4
89.0
Flash point
°C
≥ 250
≥ 250
≥ 250
Pour point
°C
< − 45
< − 45
− 12.5
Volume resistivity (25 °C)
T Ωm
0.25
1.0
38
2.2 Solubility and Viscosity of Oil/R290 Mixtures Figure 1 shows a schematic illustration of the refrigerant solubility and viscosity measuring device. All measurements and calculations were performed following previous reports [5, 6]. For the measurement of the kinematic viscosity of the oil with refrigerant dissolved and the amount of refrigerant dissolved in the oil, the mixture of refrigerant and oil was sealed in a pressure vessel. Then the pressure in the vessel was measured after reaching equilibrium under an arbitrary temperature and pressure. The viscosity and density of the refrigerant/oil mixture were measured using the attached viscometer at the same time as the amount of dissolved refrigerant. Fig. 1 Schematic illustration of refrigerant solubility and viscosity measuring device
Pressure gauge Heater
Thermocouple
P
Pressure vessel Water bath
Refrigerant Oil
refrigerant Viscometer
Rotor
Magnetic stirrer
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Example appearance Glass tube
Excellent miscibility
Poor miscibility Oil layer
Oil & refrigerant
Refrigerant layer
*Oil is colored blue Fig. 2 Schematic illustration and pictures of phase separation temperature measurement
2.3 Phase Separation Temperature Refrigeration oil is sealed inside the compressor to lubricate it; however, some of the oil can leak into the refrigeration system. The oil needs to return to the compressor without blocking the lines so that an appropriate level of oil is maintained inside the compressor. Therefore, refrigeration oil should be miscible with refrigerant, and a lower phase separation temperature is more ideal for refrigeration systems. In this study, the phase separation temperature of test oil was measured in accordance with JIS K 2211. The test oil and R290 were sealed in a glass tube and cooled from room temperature to – 55 °C. When the mixture of oil and R290 became cloudy, it indicated that the oil and R290 separated, and the temperature was measured (Fig. 2).
2.4 Stability with R290 Because refrigeration oil is used continuously without being replaced, it must be highly stable. The stability of test oil was measured by autoclave tests in accordance with JIS K 2211. We filled an autoclave with R290 and a test oil and heated it under the specified conditions shown in Table 2. After that, the stability was evaluated by measuring the acid value of the test oil. The acid value is the quantity of potassium hydroxide, expressed as milligrams of KOH, required to neutralize the acidic constituents in one gram of a sample. The acid number is one of the general indicators of the deterioration of lubricating oils. A higher value indicates more degradation.
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Table 2 Conditions of the stability test Condition 1
Condition 2
Condition 3
Condition 4
Water
Air
Water and air
Vessel volume
mL
200
200
200
200
Oil amount
g
30
30
30
30
Moisture in oil
ppm
< 30
500
< 30
500
Refrigerant amount
g
30
30
30
30
Air
mL
0
0
5
5
Fe, Cu, Al
Fe, Cu, Al
Fe, Cu, Al
Fe, Cu, Al
Catalyst (50 mm) Temperature
°C
175
175
175
175
Time
h
168
168
168
168
2.5 Evaluation of Lubricity HFC and HFO refrigerants are widely known to react with friction surfaces to form iron fluoride, which greatly affects lubricating performance [7–9]. However, Shitara et al. found that R290 does not adsorb to nascent metal surfaces exposed by friction [10, 11]. This was demonstrated in an evaluation using a controlled atmosphere cutting apparatus for an adsorption tester [12]. Although R290 reduces kinematic viscosity when mixed with refrigeration oil, it is speculated that it does not significantly affect the formation of lubricating film such as anti-wear agents. Therefore, in consideration of safety, the anti-wear property was evaluated through block-on-ring tests in nitrogen atmosphere instead of R290. Figure 3 shows a schematic illustration of the block-on-ring test. The test conditions are also shown in Table 3. The anti-wear property was evaluated by measuring the wear width of the block with a microscope. We determined that the lower the value, the higher the anti-wear property. After the block-on-ring test, to clarify the lubrication mechanism, the lubricating films on the wear block were analysed using X-ray photoelectron spectroscopy (XPS).
3 Results of Test and Discussion 3.1 Mixture Properties of Oil and R290 Table 4 shows the solubility and viscosity of the oil/R290 mixtures at 60 °C and 1.5 MPa. Under the conditions, POE-A, which was developed for R290, exhibited lower solubility and higher viscosity than POE-B and MO. Generally, low solubility can lead to cutting down the amount of refrigerant. Saitoh et al. [13] previously reported that the heat transfer coefficient decreases as the amount of refrigeration oil mixed into the refrigerant increases. Thus, POE-A, which has low solubility,
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Fig. 3 Schematic illustration of block-on-ring test
Table 3 Conditions of block on ring test for anti-wear property
Load
500 N
Sliding speed
0.5 m/s
Temperature
80 °C
Atmosphere
Nitrogen
Time
30 min, 3 h
Specimen
Block: SKH51 in JISa G 4403 (HRC63 ± 3) Ring: SNCM220 in JISa G 4502 (HRC50 ± 3)
a Japanese
Industrial Standards
may contribute to improving the coefficient of performance (COP) of refrigeration systems. In addition, high viscosity oils are able to form thick oil film on sliding parts, potentially leading to higher lubricity. The block-on-ring test results are shown in next section. Figure 4 shows the phase separation temperature curve. The conventional POE-B did not separate up to – 55 °C at the oil content of 10–30 mass%. In contrast, the newly developed POE-A had a separation temperature of about – 40 °C. Considering POE-A and MO exhibited similar behavior, it should be feasible to use POE-A for R290. Therefore, POE-A is expected to return to the compressor without blocking the lines in the refrigeration cycle. Table 5 shows the results of the stability test with R290. The acid value of all test oils did not increase even when mixed with water and/or air, and no significant Table 4 Physical properties of oil/refrigerant mixtures (60 °C, 1.5 MPa) Refrigerant
R290
Test oil
POE-A
POE-B
MO
Refrigerant concentration
%
16.0
18.1
19.3
Kinematic viscosity
mm2 /s
5.0
2.6
3.1
Characteristics and Lubricity of Refrigeration Oil for R290
30 Phase separation temperature, ℃
Fig. 4 Phase separation temperature curve
895
10 -10
Soluble
-30
Mineral oil POE-A
-50
Separation
POE-B -70
0
10
Separation 20
30
40
Oil ratio, mass%
Table 5 Acid number after stability test POE-A
POE-B
MO
Condition 1
mgKOH/g
0.00
0.01
0.00
Condition 2
mgKOH/g
0.01
0.00
0.00
Condition 3
mgKOH/g
0.00
0.00
0.01
Condition4
mgKOH/g
0.01
0.00
0.01
deterioration was observed. We determined that the newly developed POE-A, which contains general additives, has the same level of stability as that of POE-B and MO.
3.2 Lubricity and Lubricating Films Figure 5 shows the results of the block-on-ring test. The newly developed POE-A showed higher anti-wear property than POE-B and MO after 30 min and 3 h. Because POE-A showed the highest anti-wear property regardless of the test time, it should be highly reliable in an actual compressor. As shown in Table 2, POE-A has the highest kinematic viscosity, so it should exhibit excellent anti-wear property even in R290. Table 6 shows the elements detected by XPS and the ratio of phosphorus to iron (P/Fe). We compared the amounts of phosphorus (P/Fe) on the block surfaces after the wear test with POE-A, POE-B, and MO. Phosphorus-based anti-wear agents are generally adsorbed on metal surfaces and form a reaction film by friction. This reaction film contributes to reducing wear. Thus, the detected phosphorus may have come from the anti-wear agent in the test oil, whereas phosphorus was not detected after 30 min of the wear test in POE-A and POE-B. POE has a higher polarity than mineral oil, which is hydrocarbon. Polarity of the base oil influences the lubrication
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0.4
Wear width, mm
Fig. 5 Results of block-on-ring test
30min
3h
0.3 0.2 0.1 0
POE-A
POE-B
MO
Table 6 Results of XPS analysis
POE-A POE-B MO
Carbon
Oxygen
Phosphorus
Iron
(C1s)
(O1s)
(P2p)
(Fe2p)
P/Fe
Atomic%
Atomic%
Atomic%
Atomic%
30 min
76.5
21.7
0.0
1.8
0.0
3h
56.8
35.4
3.8
4.0
1.0
30 min
48.1
47.8
0.0
4.1
0.0
3h
38.0
43.8
7.4
10.6
0.7
30 min
46.1
44.9
4.4
4.6
0.9
3h
40.3
43.6
8.1
7.5
1.1
performance and lubricating films [14]. In the case of using POE as base oil, it seems that anti-wear agent is not likely to adsorb and react with friction surface. However, POE-A also demonstrated the anti-wear property in the 30-min wear test. Therefore, the anti-wear property of the newly developed POE itself should be effective in initial sliding. In addition, phosphorus was detected after 3 h of the wear test in POE-A and POE-B, indicating that the anti-wear agent was an effective supplement for POE for long-term reliability.
4 Conclusion POE is widely used for refrigeration oil because of its excellent refrigerant properties, in addition to its high insulation and combustion resistance. In this study, we developed POE-A as a refrigeration oil for R290, and the following findings were obtained by evaluating its characteristics and lubricity.
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(1) When R290 was dissolved in each test oil, POE-A showed lower solubility and higher viscosity than that of POE-B and MO. This may contribute to reducing the amount of refrigerant, improving COP and lubricity. (2) POE-A and commercial MO exhibited similar behavior in terms of phase separation temperature. Thus, POE-A should return to the compressor without blocking the lines in the refrigeration cycle. (3) POE-A, POE-B, and MO, which were combined with additives for refrigeration oil, showed similar stability. POE-A was also found to be sufficiently durable for long-term use. (4) In the block-on-ring test, POE-A showed the highest lubrication regardless of the test time. Although a phosphorus film did not form on POE-A in the initial 30 min, it formed after 3 h. Thus, we determined that the phosphorus-based anti-wear agent as a supplement for POE was effective for long-term reliability. (5) In conclusion, POE-A showed excellent practical performance for R290.
References 1. T. Komatsubara, T. Sunaga, Y. Takahashi, Study on the compatibility of insulation materials for hermetic motor under alternative refrigerants and new lubricants atmosphere. Trans. JSRAE 20(1), 55–67 (2003). ((in Japanese)) 2. T. Higashi, S. Tamai, S. Saitoh, C. Dang, S. Hihara: Compressor explosion accident at pumpdown of air conditioners, in 12th IEA Heat Pump Conference 2017, O324, IEA HPT TCP, Rotterdam (2017) 3. T. Higashi, S. Tamai, S. Saitoh, C. Dang, S. Hihara, Effect of lubricating oil on explosion accidents of compressor during pump-down of air conditioner. Trans. JSRAE 34(3), 181–191 (2017). ((in Japanese)) 4. S. Saitoh, T. Higashi, M. Ito, C. Dang, S. Hihara, Y. Shitara: Effect of reaction inhibitor on diesel explosion of split air conditioners. Int. J. Refrig. (in press) 5. R. Stryjek, J.H. Vera, An improved Peng-Robinson equation of state for pure compounds and mixtures. Can. J. Chem. Eng. 64, 324–333 (1986) 6. K. Takigawa, S.I. Sandler, A. Yokozeki, Solubility and viscosity of refrigerant/lubricant mixtures: hydrofluorocarbon/alkylbenzene systems. Int. J. Refrig. 25, 1014–1024 (2002) 7. M. Muraki, D. Dong, T. Sano, Friction and wear characteristics of polyolester base lubricants in refrigerants environment. J. Japan. Soc. Tribol. 43(1), 43–49 (1998). ((in Japanese)) 8. A. Tada, T. Okido, Y. Shono, H. Takahashi, Y. Shitara, S. Tanaka, Tribological characteristics of polyolester type refrigeration oils under refrigerants atmosphere. Tribol. Online 11(2), 348–353 (2016) 9. T. Sasaki, K. Mizono, H. Nakao, H. Maeyama, S. Takahashi, Tribology characteristics of HFO and HC refrigerants with immiscible oils. J. Japan. Soc. Tribol. 61(5), 334–341 (2016). ((in Japanese)) 10. Y. Shitara, S. Mori, Effect of HFO refrigerants on lubrication characteristics (Part 1). J. Japan. Soc. Tribol. 67(9), 662–671 (2022). ((in Japanese)) 11. Y. Shitara, T. Onodera, S. Mori, Effect of HFO refrigerants on lubrication characteristics (Part 2). J. Japan. Soc. Tribol. (in press). (in Japanese) 12. S. Mori, Adsorption of benzene on the fresh steel surface formed by cutting under high vacuum. Appl. Surf. Sci. 27(4), 401–410 (1987)
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13. S. Saitoh, T. Higashi, C. Dang, S. Hihara, Visualization of flow boiling of propane/lubricating in mini-channels, in Proceedings of 2018 JSRAE Annual Conference, A221, JSRAE, Fukushima (2018). (in Japanese) 14. A.N. Suarez, M. Grahn, R. Pasaribu, R. Larsson, The influence of base oil polarity on the tribological performance of zinc dialkyl dithiophospate additives. Tribol. Int. 43(12), 2268– 2278 (2010)