Advances in Building Services Engineering: Studies, Researches and Applications [1st ed. 2021] 3030647803, 9783030647803

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Ioan Sarbu

Advances in Building Services Engineering Studies, Researches and Applications

Advances in Building Services Engineering

Ioan Sarbu

Advances in Building Services Engineering Studies, Researches and Applications

123

Ioan Sarbu Department of Civil and Building Services Engineering Polytechnic University of Timişoara Timisoara, Romania

ISBN 978-3-030-64780-3 ISBN 978-3-030-64781-0 https://doi.org/10.1007/978-3-030-64781-0

(eBook)

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 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

Nothing remarkable in the world has been achieved without passion Galileo Galilei (1564–1642)

This book is dedicated to my grandchildren, Andrei, Ella and Ava

Preface

Building services ensure the obligatory needs of man (heat/cold, water, light, etc.) and constitute the link in the architecture/construction/installation triad, which is the basis for the construction of a building, regardless of type, size, shape and destination. The construction facilities have been made and used since ancient times, depending on the importance and evolution of the buildings, by ad hoc personnel trained in solving the obligatory needs (water supply, sewerage, heating/cooling, ventilation and air conditioning, lighting, etc.). Today, the building services have known a development that includes a diversification on specialised fields: production of equipment, research, design, execution and operation. The heating, ventilating and air-conditioning (HVAC) system makes up approximately 50% of a building’s energy consumption. Achieving ambitious targets for reducing fossil fuel consumption as primary energy and related CO2 emissions and meeting Kyoto Protocol targets, improving energy efficiency, integrating renewable energy sources and using high-performance HVAC and refrigeration (HVAC&R) equipments in the existing building stock have been addressed in recent decades. It is also known that the world energy consumption for water distribution is about 7% of the global energy. Additionally, it is estimated that 2–3% of the worldwide electricity consumption is used for pumping in water distribution systems (WDSs). Given the importance and spread of WDSs, since the last century, there have been intense concerns to improve their calculation, implementation and operation methods. This reference book is a comprehensive and consistent overview, systematised in a unitary and clear manner, of the author’s original theoretical, experimental and numerical studies bringing together multiple strands of research in building services engineering domain with diverse subjects, guided by two important features such as energy savings and reduction of the pollutant emissions especially in recent decades. It is based on the numerous articles written alone or in collaboration and published in various indexed journals and proceedings of international conferences along with others book chapters published by prestigious international publishers such as Elsevier, Springer, and Nova Science Publishers. The publication of such a ix

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book is a novelty in the literature. It is unique with respect to its complex contents, the experimental case studies at lab scale, numerical examples and text presentation style. Technical, economic and energy saving aspects related to design, modelling, optimisation and operation of diverse building services systems is explored. The book being rigorous includes for this purpose numerous theoretical studies, numerical and optimisation models, experiments and applications in this field. This book gives an emphasis to: indoor environment quality (IEQ) assurance; energy analysis, modelling and optimisation of heating systems; improving the energy performance of refrigeration and air-conditioning systems; valorising solar energy and geothermal heat pumps for heating/cooling of buildings; analysis of thermal energy storage (TES) technologies; hydraulic simulation and optimisation of WDSs; improving the energy-efficiency of water pumping; designing local and for small localities wastewater treatment plants; numerical modelling of heat transfer and application of computerised calculation. The topics are presented in the logical and pedagogical order. Each of the chapter sections involves learning aims, section summaries, numerical examples and solutions to support the theory presented and extensive bibliography. This book is structured as eleven chapters with an accessible style. Chapter 1 summarises a short description of the author’s significant contributions to making relatively recent advances on various topics corresponding to several research directions in the field of building services engineering. Chapter 2 approaches several aspects of assessing the IEQ and human performance in buildings with different destinations. Thus, a computation and testing model of thermal comfort in buildings based on predicted mean vote (PMV)— predicted percent dissatisfied (PPD) indices, a computational model for indoor air quality (IAQ) numerical simulation, as well as a methodology to determine the outside air flow rate and to verify the IAQ in rooms are developed. Additionally, the thermal comfort is assessed based on the PMV−PPD indices using subjective and experimental measurements in two air-conditioned classrooms at a university, where the air-exchange rate is assured by natural ventilation. To estimate academic performance depending on air temperature, classroom air relative humidity and CO2 concentration in three simple Gaussian correlations are developed using twelve data sets containing the concentrated and distributive attention tests for students. Finally, a simulation model in the Transient System Simulation (TRNSYS) program of the PMV−PPD indices and heating/cooling energy demand for an amphitheatre with natural ventilation is developed. Chapter 3 provides an extensive survey on the modelling and optimisation of district heating systems (DHSs) focused on the heat distribution network, an energy analysis of unbalanced central heating systems, as well as a comprehensive discussion about pump control in heating stations, analysing the energy efficiency of flow control methods. For this purpose, the major components of a DHS have been described and discussed, and their modelling has briefly reviewed including numerical simulation models for heat sources, end-users and especially, the distribution network. The main deterministic and heuristic optimisation techniques are briefly explained. A comparative energy analysis is performed on the hot water flow

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rate adjustment using throttling control valves and variable-speed drives in a district heating plant constructed in Romania. To correlate the pumped flow rate with the heat demand and to ensure the necessary pressure using minimum energy, an automatic device has been designed. Additionally, the performance of a fluid temperature control system using self-adjustable cables and the main plastic materials used for the manufacturing of tubes for heat distribution in buildings are presented, and a comparative analysis of the physical, mechanical, geometric and hydraulic characteristics of the tubes produced both from classical metallic materials and from different plastic materials is performed. Chapter 4 discusses the vapour compression-based refrigeration systems and describes the operation principle and theoretical thermodynamic cycle of them, the types of refrigeration compressors, the ecological refrigerants and some recovery possibilities of the thermal energy produced by refrigeration systems. Additionally, a computational model for optimal design of refrigeration insulations on flat and cylindrical surfaces and another for refrigeration columns for soil freezing operating with gaseous refrigerant, as well as an experimental study on the frost self-protection of cooling towers on an air-conditioned stand using a vapour compression-based refrigeration system are presented. Finally, an investigation of the energy efficiency of conventional air-conditioning systems in office buildings is included. For this application, an air-water mist cooled system for the air-cooled chiller is proposed. The results of the experiments showed that the most efficient ventilation and air-conditioning system for office buildings consists of an air handling unit and fan-coil units with an air-water mist cooled chiller and a cooled water temperature of 8 °C. Chapter 5 presents a detailed theoretical study, numerical modelling and some applications for solar heating and cooling systems focused on active and combi systems. Important informations on simulating solar heating systems are discussed and the TRNSYS program is also briefly described. Additionally, a detailed review of different solar thermal-driven refrigeration and cooling systems including sorption technology (open or closed systems) and thermo-mechanical technology (ejector system) is also provided. The study refers to a comparison of various solar thermal cooling systems, and to some useful suggestions of these systems. A comprehensive survey of solar thermoelectric (TE) cooling systems is also provided. Finally, the possibility of solar TE cooling technologies application in “nearly-zero” energy buildings is briefly discussed and some future research directions are included. Chapter 6 presents the operation principle of a heat pump (HP) and the necessity for using HPs in the heating/cooling systems of buildings, discusses the vapour compression-based HP systems and describes the thermodynamic cycle and the calculation, as well as operation regimes of a vapour compression HP with electro-compressor. The calculation of greenhouse gas emissions of HPs and energy and economic performance criteria that allow for implementing an HP in a heating/cooling system is considered. A detailed theoretical study and experimental investigations on ground-source HP (GSHP) technology concentrating on ground-coupled heat pump (GCHP) systems are also included. Additionally, an

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analytical model for evaluation of the ground thermal conductivity and the borehole thermal resistance using a thermal response test is developed and the Earth Energy Designer (EED) simulation program is used to calculate the fluid temperature for a case study of the ground heat exchanger. An experimental study is performed to test the energy efficiency of the radiator or radiant floor heating system for an office room connected to a GCHP. Experimental measurements are also used to test the performance of a reversible vertical GCHP system at different operating modes. Finally, two simulation models of thermal energy consumption in heating/cooling and domestic hot water operation were developed using TRNSYS software. Chapter 7 is focused on the analysis of TES technologies that provides a way of valorising solar heat and reducing the energy demand of buildings. The principles of several energy storage methods and calculation of storage capacities are described. Sensible heat storage (SHS) technologies, including the use of water, underground and packed-bed are briefly reviewed. Latent-heat storage (LHS) systems associated with phase-change materials (PCMs) and thermo-chemical storage, as well as cool thermal energy storage are also discussed. Finally, an abridged version of the comprehensive review published on the development of LHS systems focused on heat transfer and enhancement techniques employed in PCMs to effectively charge and discharge latent heat energy, and the formulation of the phase change problem are provided. Chapter 8 presents a detailed theoretical study on hydraulic simulation and optimal design and energy-efficiency optimisation of WDSs focused on looped distribution systems in steady-state and transient conditions, including the development of new, high-performance models for hydraulic analysis of looped networks using variational formulations, original models for optimising design and choosing their optimal route using deterministic methods such as linear, non-linear and dynamic programming, as well as proposing solutions to optimise the energy-efficiency of these systems (zoning procedures, potential elements). Additionally, an overview of the multi-objective optimisation of water distribution networks is also included. Chapter 9 presents two plants proposed for local wastewater treatment: (1) an autonomous sewage treatment plant (STP) for wastewater from buildings and transport vehicles and (2) a small plant for wastewater treatment from isolated buildings or of wastewater from industrial enterprises with their own low-capacity purification stations and a pilot STP designed for small or very small localities (up to 500 inhabitants) such as villages, communes, hotels and camps, located inside the STP in Timisoara, Romania. Chapter 10 develops a general analytical model that solves in a unitary manner the complex problems of hydraulic computation for open channels with steady-state uniform flow and can be easily programmed and implemented on microcomputers and proposes a new calculation model for sizing vertical sewer columns inside buildings. Chapter 11 presents two numerical simulation models based on finite or boundary elements of conductive thermal fields generated or induced into solid body in steady-state and performs a study of the velocity and temperature fields due

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to laminar forced heat convection in a concentric annular tube with constant heat flux boundary conditions using dual reciprocity method. Additionally, a numerical simulation model of change in time along the pipe of ice layer formed inside outdoor pressurised pipes, under non-stationary atmospheric regime is described. Generous permissions have been provided by many publishers for the use of their figures, drawings and tables to make this book more complete and useful. This book has a comprehensive coverage, introductory work, adequate depth of study, and good-structured numerical examples and case studies. It provides a useful source of information and basis for extended research for all those involved in the field, whether as a graduate student, M.Sc. student and also Ph.D. student, academic, scientific researcher, industrialist, consultant, other specialist or government agency with responsibility in this area. This book was completed in the year of celebrating the centenary of the author’s university, who is convinced that the way in which the book is designed will increase interest in research, design and operation of building services systems and thanks all those who supported him in the realisation of this work. Timisoara, Romania

Prof. Emeritus Ioan Sarbu

Contents

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Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Generalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Assurance of Indoor Environmental Quality . . . . . . . . . . . . . 1.3 Modelling, Optimisation and Modernisation of Heating Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Efficient Refrigeration and Air-Conditioning Systems . . . . . . 1.5 Solar Heating and Cooling Systems . . . . . . . . . . . . . . . . . . . 1.6 Ground-Sources Heat Pumps for Sustainable Heating and Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7 Thermal Energy Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.8 Analysis and Optimisation of Water Transmission and Distribution Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.9 Efficient Wastewater Treatment Plants . . . . . . . . . . . . . . . . . 1.10 Hydraulic Calculation of Open Channels and Sewer Columns in Buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.11 Numerical Modelling of Heat Transfer . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Assurance of Indoor Environment Quality in Buildings . . . . 2.1 Generalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Comfort and Indoor Air Quality Assessment in Closed Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Preliminary Considerations . . . . . . . . . . . . . . . . 2.2.2 Fundamental Components of the Comfort . . . . . 2.2.3 Prediction of Thermal Comfort . . . . . . . . . . . . . 2.2.4 Thermal Comfort Criteria for Design of Heating Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.5 The Relationship Between Thermal Environment and Human Performance . . . . . . . . . . . . . . . . . . 2.2.6 Evaluation of Olfactory Comfort . . . . . . . . . . . .

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2.2.7 2.2.8

Indoor Air Quality Simulation Model . . . . . . . . . . . Computation of Outside Air Flow Rate and Air Quality Control . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.9 Influence of CO2 on Human Performance and Productivity . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.10 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Experimental and Numerical Research to Assess IEQ and Schoolwork Performance in University Classrooms . . . . 2.3.1 Preliminary Considerations . . . . . . . . . . . . . . . . . . . 2.3.2 Description of Building and Classrooms . . . . . . . . . 2.3.3 Evaluation of Thermal Comfort in the Amphitheatre by Subjective and Experimental Measurements . . . . 2.3.4 Prediction of Student Schoolwork Performance Depending on the IEQ Parameters . . . . . . . . . . . . . . 2.3.5 Simulation of PMV-PPD Indices and Heating/ Cooling Energy Demand Using Software TRNSYS . 2.3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Modelling, Optimisation and Modernisation of Heating Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Generalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Modelling and Optimisation Techniques for District Heating Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Preliminary Considerations . . . . . . . . . . . . . . . . 3.2.2 Study Objectives and Methodology . . . . . . . . . . 3.2.3 Configuration of a District Heating System . . . . 3.2.4 Modelling of Distribution Networks . . . . . . . . . 3.2.5 Optimisation Techniques . . . . . . . . . . . . . . . . . . 3.2.6 Optimisation of Distribution Networks . . . . . . . . 3.2.7 Example of Single-Objective Optimisation . . . . . 3.2.8 Overview of the Optimisation Models in the Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.9 Conclusions and Directions for Future Research . 3.3 Energy Analysis of Unbalanced Central Heating Systems 3.3.1 Preliminary Considerations . . . . . . . . . . . . . . . . 3.3.2 Indoor Temperature . . . . . . . . . . . . . . . . . . . . . 3.3.3 Heat Losses and Energy Consumption . . . . . . . . 3.3.4 Building Elements Influence . . . . . . . . . . . . . . . 3.3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Energy Saving Potential for Pumping Water in District Heating Plants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Preliminary Considerations . . . . . . . . . . . . . . . . 3.4.2 Thermal Load of the Heating Plant . . . . . . . . . .

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3.4.3 3.4.4

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Solutions for Reducing the Pumping Energy . . . . . . Throttling Control Valve Versus Variable-Speed Drive—Case Studies . . . . . . . . . . . . . . . . . . . . . . . . 3.4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Heat Distribution Systems in Buildings . . . . . . . . . . . . . . . . 3.5.1 Preliminary Considerations . . . . . . . . . . . . . . . . . . . 3.5.2 Radiator Heating System . . . . . . . . . . . . . . . . . . . . 3.5.3 Radiant Heating Systems . . . . . . . . . . . . . . . . . . . . 3.5.4 Efficiency of Heating Systems . . . . . . . . . . . . . . . . . 3.5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Fluids Temperature Regulation Using Self-adjustable Cables . 3.6.1 Preliminary Considerations . . . . . . . . . . . . . . . . . . . 3.6.2 System Description . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.3 Structure of Heating Cable . . . . . . . . . . . . . . . . . . . 3.6.4 Operating Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.5 Technical Characteristics and Utilisations of Self-adjustable Cable . . . . . . . . . . . . . . . . . . . . . 3.6.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Comparative Characterisation of Plastic Tubes . . . . . . . . . . . 3.7.1 Preliminary Considerations . . . . . . . . . . . . . . . . . . . 3.7.2 Classification of Plastics . . . . . . . . . . . . . . . . . . . . . 3.7.3 Plastics Used for the Production of Tubes in Building Services . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7.4 Comparative Analysis of the Plastic Tubes Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Efficient Refrigeration and Air-Conditioning Systems . . . . . 4.1 Generalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Vapour Compression-Based Refrigeration Systems . . . . 4.2.1 Preliminary Considerations . . . . . . . . . . . . . . . 4.2.2 Operation Principle and Thermodynamic Cycle 4.2.3 Energy Efficiency and CO2 Emission . . . . . . . . 4.3 Types of Compressors . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Preliminary Considerations . . . . . . . . . . . . . . . 4.3.2 Reciprocating Compressors . . . . . . . . . . . . . . . 4.3.3 Rotary Screw Compressors . . . . . . . . . . . . . . . 4.3.4 Centrifugal Compressors . . . . . . . . . . . . . . . . . 4.3.5 Scroll Compressors . . . . . . . . . . . . . . . . . . . . . 4.4 Substitution Strategy of Non-ecological Refrigerants . . . 4.4.1 Preliminary Considerations . . . . . . . . . . . . . . . 4.4.2 Environmental Impact of Refrigerants . . . . . . . 4.4.3 Influence of Refrigerants on Process Efficiency

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4.4.4 4.4.5

4.5 4.6

4.7 4.8

4.9 4.10

4.11 4.12

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Strategy Concerning Non-ecological Refrigerants . . . Environmental Impact Analysis of Possible Substitute for R22 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Using Recovered Thermal Energy from Refrigerating Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.1 Preliminary Considerations . . . . . . . . . . . . . . . . . . . 4.6.2 Hot Water Production . . . . . . . . . . . . . . . . . . . . . . . 4.6.3 Heating the Ground Under Cooled Spaces . . . . . . . . 4.6.4 Defrosting the Air-Cooled Surfaces . . . . . . . . . . . . . 4.6.5 Heat Recovery by a Heat Pump . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optimal Design of Refrigeration Insulations . . . . . . . . . . . . . 4.8.1 Preliminary Considerations . . . . . . . . . . . . . . . . . . . 4.8.2 Types of Insulation for Refrigeration Applications . . 4.8.3 Optimisation Model . . . . . . . . . . . . . . . . . . . . . . . . 4.8.4 Numerical Application . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermal Calculation of Refrigeration Columns for Soil Freezing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.10.1 Preliminary Considerations . . . . . . . . . . . . . . . . . . . 4.10.2 Mathematical Model . . . . . . . . . . . . . . . . . . . . . . . . 4.10.3 Numerical Application . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental Study on the Frost Self-protection of Cooling Towers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.12.1 Preliminary Considerations . . . . . . . . . . . . . . . . . . . 4.12.2 Theoretical Aspects on the Cooling Towers and Their Frost Self-protection . . . . . . . . . . . . . . . . . . . . . . . . 4.12.3 Description of the Experimental Stand and Measuring Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.12.4 Experimental Investigation . . . . . . . . . . . . . . . . . . . 4.12.5 Processing and Interpretation of the Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental and Numerical Investigations of the Energy Efficiency of Conventional Air-Conditioning Systems . . . . . . 4.14.1 Preliminary Considerations . . . . . . . . . . . . . . . . . . . 4.14.2 Description of the Experimental Office Room . . . . . 4.14.3 Description of the Experimental VAC System . . . . . 4.14.4 Measuring Apparatus . . . . . . . . . . . . . . . . . . . . . . . 4.14.5 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . 4.14.6 Optimal Control of Energy Consumption . . . . . . . . .

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4.14.7 Assessment of Thermal Comfort . . . . . . . . . . . . . . . 4.14.8 Numerical Simulation of Energy Consumption and Thermal Comfort Using TRNSYS Software . . . 4.14.9 Influence of Design Indoor Air Parameters on Energy Consumption of Heating and Air Conditioning . . . . 4.15 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

6

Solar Heating and Cooling Systems . . . . . . . . . . . . . . . . . . . 5.1 Generalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Solar Water and Space Heating Systems . . . . . . . . . . . . 5.2.1 Preliminary Considerations . . . . . . . . . . . . . . . . 5.2.2 Solar Water Heating Systems . . . . . . . . . . . . . . 5.2.3 Solar Space Heating Systems . . . . . . . . . . . . . . 5.2.4 Solar Combisystems . . . . . . . . . . . . . . . . . . . . . 5.2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Solar Thermal Cooling Systems . . . . . . . . . . . . . . . . . . . 5.3.1 Preliminary Considerations . . . . . . . . . . . . . . . . 5.3.2 Solar Sorption Cooling Systems . . . . . . . . . . . . 5.3.3 Solar Thermo-Mechanical Cooling Systems . . . . 5.3.4 Hybrid Cooling and Heating Systems . . . . . . . . 5.3.5 Comparison of Various Solar Thermal Cooling Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Solar Thermo-Electric Cooling Systems . . . . . . . . . . . . . 5.4.1 Preliminary Considerations . . . . . . . . . . . . . . . . 5.4.2 General Description of a Solar Thermo-Electric Cooling System . . . . . . . . . . . . . . . . . . . . . . . . 5.4.3 Development of Thermo-Electric Materials . . . . 5.4.4 Thermo-Electric Cooler . . . . . . . . . . . . . . . . . . . 5.4.5 Characteristics and Performance of the Coolers . 5.4.6 Thermo-Electric Cooling Modelling . . . . . . . . . . 5.4.7 Optimisation of the TE Cooling System Design . 5.4.8 Thermo-Electric Cooling Applications . . . . . . . . 5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . 308 . . 312 . . 316 . . 320 . . 322

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329 329 331 331 332 340 346 353 354 354 357 391 397

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401 402 403 403

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405 407 410 412 420 422 423 434 435

Heat Pumps for Sustainable Heating and Cooling . . . . . . . . . . . 6.1 Generalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Energy-Economic Analysis of Building Heating and Cooling by Heat Pump Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Preliminary Considerations . . . . . . . . . . . . . . . . . . . 6.2.2 Classification and Operation Principle of an HP . . . . 6.2.3 Thermodynamic Cycle of a Vapour Compression-Based HP . . . . . . . . . . . . . . . . . . . . .

. . 447 . . 448 . . 450 . . 450 . . 450 . . 451

xx

Contents

6.3

6.4

6.5

6.6

6.2.4 6.2.5 6.2.6 6.2.7 6.2.8 General 6.3.1 6.3.2 6.3.3 6.3.4 6.3.5 6.3.6 6.3.7

Operation Regimes of an HP . . . . . . . . . . . . . . . . . Performances and CO2 Emission of HP . . . . . . . . . . Energy-Economic Analysis of Different Systems . . . Examples of HP Utilisation . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Review of Ground Source Heat Pump Systems . . . . Preliminary Considerations . . . . . . . . . . . . . . . . . . . Operation Principle of an HP . . . . . . . . . . . . . . . . . Description of HP Types . . . . . . . . . . . . . . . . . . . . Ground Source Heat Pump Systems . . . . . . . . . . . . Environmental Performances . . . . . . . . . . . . . . . . . . Hybrid GCHP Systems . . . . . . . . . . . . . . . . . . . . . . Better Energy Efficiency with Combined Heating and Cooling by HPs . . . . . . . . . . . . . . . . . . . . . . . . 6.3.8 Energy, Economic and Environmental Performances of a Closed-Loop GCHP System . . . . . . . . . . . . . . . 6.3.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simulation of Ground Thermo-Physical Capacity for a Vertical Closed-Loop GCHP System . . . . . . . . . . . . . . . . . . . . . . . . 6.4.1 Preliminary Considerations . . . . . . . . . . . . . . . . . . . 6.4.2 Ground Thermal Response Test . . . . . . . . . . . . . . . 6.4.3 Use of EED Simulation Program: Case Study for a BHE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Performance Analysis of Different Heating Systems Connected to a GCHP for an Office Room . . . . . . . . . . . . . . . . . . . . . . 6.5.1 Preliminary Considerations . . . . . . . . . . . . . . . . . . . 6.5.2 Description of Office Room . . . . . . . . . . . . . . . . . . 6.5.3 Experimental Facilities . . . . . . . . . . . . . . . . . . . . . . 6.5.4 Borehole Heat Exchanger . . . . . . . . . . . . . . . . . . . . 6.5.5 Heat Pump Unit . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.6 GCHP Data Acquisition System . . . . . . . . . . . . . . . 6.5.7 Heating Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.8 Measuring Apparatus . . . . . . . . . . . . . . . . . . . . . . . 6.5.9 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . 6.5.10 Thermal Comfort Assessment . . . . . . . . . . . . . . . . . 6.5.11 Numerical Simulation of Useful Thermal Energy and System COP Using TRNSYS Software . . . . . . . 6.5.12 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Performance of an Experimental Vertical GCHP System for Heating, Cooling and DHW Operation . . . . . . . . . . . . . . 6.6.1 Preliminary Considerations . . . . . . . . . . . . . . . . . . . 6.6.2 Description of Experimental Laboratory . . . . . . . . . .

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454 456 462 470 476 476 476 477 478 483 495 496

. . 498 . . 501 . . 505 . . 505 . . 505 . . 506 . . 510 . . 514 . . . . . . . . . . .

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515 515 516 517 518 518 519 519 520 521 524

. . 526 . . 529 . . 530 . . 530 . . 530

Contents

xxi

6.6.3 6.6.4 6.6.5 6.6.6

Description of the Experimental System . . . . . . Measuring Apparatus . . . . . . . . . . . . . . . . . . . . Laboratory Experiment Results . . . . . . . . . . . . . Numerical Simulation of Useful Thermal Energy Using TRNSYS Software . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . 531 . . . . . 536 . . . . . 536

. . . . . 548 6.6.7 . . . . . 552 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553

7

8

Thermal Energy Storage . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Generalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 An Overview of Thermal Energy Storage . . . . . . . . . 7.2.1 Classification and Characteristics of Storage Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.2 Sensible Heat Storage . . . . . . . . . . . . . . . . . 7.2.3 Latent Heat Storage . . . . . . . . . . . . . . . . . . 7.2.4 Chemical Energy Storage . . . . . . . . . . . . . . 7.2.5 Cool Thermal Energy Storage . . . . . . . . . . . 7.2.6 Conclusions and Future Trends . . . . . . . . . . 7.3 Heat Transfer Analysis in TES Using LHS Systems and PCMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.1 Preliminary Considerations . . . . . . . . . . . . . 7.3.2 Latent Heat Thermal Energy Storage . . . . . . 7.3.3 Heat Transfer Analysis . . . . . . . . . . . . . . . . 7.3.4 Conclusions and Future Research Directions References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . 559 . . . . . . . . 559 . . . . . . . . 561 . . . . . .

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561 563 569 575 576 578

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579 579 580 604 619 620

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629 629 631 631 633 635 636 640 647

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648 648 649 651 654 654

Hydraulic Simulation and Optimisation of Water Transmission and Distribution Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Generalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Nodal Analysis of Urban Water Distribution Networks . . . . . 8.2.1 Preliminary Considerations . . . . . . . . . . . . . . . . . . . 8.2.2 Steady State Network Equations . . . . . . . . . . . . . . . 8.2.3 Principle of the Nodal Method . . . . . . . . . . . . . . . . 8.2.4 Nodal Analysis Models . . . . . . . . . . . . . . . . . . . . . . 8.2.5 Numerical Examples . . . . . . . . . . . . . . . . . . . . . . . . 8.2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Hydraulic Analysis of Looped Networks Using Variational Formulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.1 Preliminary Considerations . . . . . . . . . . . . . . . . . . . 8.3.2 Basis of Hydraulic Analysis . . . . . . . . . . . . . . . . . . 8.3.3 Variational Formulation of the Problem . . . . . . . . . . 8.3.4 Numerical Application . . . . . . . . . . . . . . . . . . . . . . 8.3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xxii

Contents

8.4

8.5

8.6

8.7

8.8

8.9

Solving Flow-Constrained Networks . . . . . . . . . . . . . . . . 8.4.1 Preliminary Considerations . . . . . . . . . . . . . . . . . 8.4.2 Mathematical Model Formulation . . . . . . . . . . . . 8.4.3 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . 8.4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . Determination of Neutral Point in Looped Network Pipes with Variable Discharge on Route . . . . . . . . . . . . . . . . . . 8.5.1 Preliminary Considerations . . . . . . . . . . . . . . . . . 8.5.2 Mathematical Model . . . . . . . . . . . . . . . . . . . . . . 8.5.3 Numerical Application . . . . . . . . . . . . . . . . . . . . 8.5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hydraulic Analysis of a Recycled Technological Water Supply Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.6.1 Preliminary Considerations . . . . . . . . . . . . . . . . . 8.6.2 Mathematical Model . . . . . . . . . . . . . . . . . . . . . . 8.6.3 Computer Program OPREATER . . . . . . . . . . . . . 8.6.4 Numerical Application . . . . . . . . . . . . . . . . . . . . 8.6.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . Path Optimisation of Water Transmission and Distribution Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.7.1 Preliminary Considerations . . . . . . . . . . . . . . . . . 8.7.2 Path Optimisation Models for Water Adduction Mains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.7.3 Path Optimisation Model for Water Branched Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.7.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optimisation of Pressurised Water Adduction Mains . . . . . 8.8.1 Preliminary Considerations . . . . . . . . . . . . . . . . . 8.8.2 Specific Cost Indices . . . . . . . . . . . . . . . . . . . . . 8.8.3 Flow Equation . . . . . . . . . . . . . . . . . . . . . . . . . . 8.8.4 Optimisation Model . . . . . . . . . . . . . . . . . . . . . . 8.8.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optimisation Models of Looped Urban Water Supply Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.9.1 Preliminary Considerations . . . . . . . . . . . . . . . . . 8.9.2 Steady State Network Equations . . . . . . . . . . . . . 8.9.3 Objective Function and Optimisation Criteria . . . . 8.9.4 Optimisation Methodology . . . . . . . . . . . . . . . . . 8.9.5 Computational Model of Optimal Discharges . . . . 8.9.6 Non-linear Optimisation Model . . . . . . . . . . . . . . 8.9.7 Linear Optimisation Model . . . . . . . . . . . . . . . . . 8.9.8 Numerical Application . . . . . . . . . . . . . . . . . . . . 8.9.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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656 656 657 661 663

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663 663 664 667 667

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669 669 670 674 674 678

. . . . 678 . . . . 678 . . . . 679 . . . . . . . .

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687 692 693 693 694 695 695 698

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699 699 702 703 705 705 708 713 718 725

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xxiii

8.10 Multi-objective Optimisation of Water Distribution Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.10.1 Preliminary Considerations . . . . . . . . . . . . . . . . . . . 8.10.2 Methods and Techniques of Optimisation . . . . . . . . 8.10.3 Objective of Optimisation . . . . . . . . . . . . . . . . . . . . 8.10.4 Decision Variables and Constraints . . . . . . . . . . . . . 8.10.5 Overview of the Multi-objective Optimisation Models in Literature . . . . . . . . . . . . . . . . . . . . . . . . 8.10.6 Examples of WDN Design Optimisation . . . . . . . . . 8.10.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.11 Numerical Simulation of Unsteady Flow in Water Distribution Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.11.1 Preliminary Considerations . . . . . . . . . . . . . . . . . . . 8.11.2 Overview of Transient Evaluation . . . . . . . . . . . . . . 8.11.3 Considerations on Pipe System Design . . . . . . . . . . 8.11.4 Transient Analysis in Pipe Networks . . . . . . . . . . . . 8.11.5 Optimisation of Pipe Networks . . . . . . . . . . . . . . . . 8.11.6 Numerical Example . . . . . . . . . . . . . . . . . . . . . . . . 8.11.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.12 Optimisation of Water Distribution System Energy Efficiency Using Potential Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.12.1 Preliminary Considerations . . . . . . . . . . . . . . . . . . . 8.12.2 Improving Energy Efficiency of Water Pumping . . . 8.12.3 Energy Optimisation Methodology . . . . . . . . . . . . . 8.12.4 Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.12.5 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . 8.12.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Sewage Treatment Plants . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 Generalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Local Plants and Efficient Procedures for Wastewater Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.1 Preliminary Considerations . . . . . . . . . . . . . . 9.2.2 Autonomous Sewage Treatment Plant . . . . . . 9.2.3 Small Sewage Treatment Plant . . . . . . . . . . . 9.2.4 The Cavitation Air Flotation System . . . . . . . 9.2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 9.3 Designing a Pilot Sewage Treatment Plant for Small Localities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.1 Preliminary Considerations . . . . . . . . . . . . . . 9.3.2 Parameters for Wastewater Treatment Design . 9.3.3 Description of Pilot STP . . . . . . . . . . . . . . . .

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726 726 727 728 731

. . 732 . . 735 . . 745 . . . . . . . .

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746 746 747 749 750 756 761 763

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763 763 765 772 778 782 785 786

. . . . . . . 799 . . . . . . . 799 . . . . . .

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800 800 801 803 806 809

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809 809 809 811

xxiv

Contents

9.3.4 Designing the Components of Pilot STP . . . . . . . . . . . 812 9.3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 815 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 815 10 Hydraulic Calculation of Open Channels and Sewer Columns in Buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1 Generalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 General Analytical Model for Hydraulic Computation of Open Channels with Steady State Uniform Flow . . . . . . . . . . . . . . 10.2.1 Preliminary Considerations . . . . . . . . . . . . . . . . . . . 10.2.2 Simple Channels . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.3 Compound Channels . . . . . . . . . . . . . . . . . . . . . . . 10.2.4 Numerical Applications . . . . . . . . . . . . . . . . . . . . . 10.2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3 A New Calculation Model for Design of Sewer Columns in Buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1 Preliminary Considerations . . . . . . . . . . . . . . . . . . . 10.3.2 Flow Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.3 Computational Model . . . . . . . . . . . . . . . . . . . . . . . 10.3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Numerical Modelling of Heat Transfer . . . . . . . . . . . . . . . . . . . . 11.1 Generalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Numerical Simulation of 2D Steady State Heat Conduction Using Finite and Boundary Element Methods . . . . . . . . . . . . 11.2.1 Preliminary Considerations . . . . . . . . . . . . . . . . . . . 11.2.2 Analytical Model of Heat Conduction . . . . . . . . . . . 11.2.3 Numerical Model with Finite Elements . . . . . . . . . . 11.2.4 Numerical Model with Boundary Elements . . . . . . . 11.2.5 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Numerical Simulation of the Laminar Forced Convective Heat Transfer Between Two Concentric Cylinders . . . . . . . . . . . . 11.3.1 Preliminary Considerations . . . . . . . . . . . . . . . . . . . 11.3.2 Physical Problem and Its Mathematical Formulation . 11.3.3 Numerical Model . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3.4 Simulation Results and Discussion . . . . . . . . . . . . . 11.3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4 Numerical Simulation of Water Freezing in Outdoor Pressurised Pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4.1 Preliminary Considerations . . . . . . . . . . . . . . . . . . . 11.4.2 Elements of Thermal Energy . . . . . . . . . . . . . . . . . . 11.4.3 Thermal Balance . . . . . . . . . . . . . . . . . . . . . . . . . .

. . 817 . . 817 . . . . . .

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818 818 819 827 830 831

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832 832 832 835 837 838

. . 839 . . 839 . . . . . . .

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840 840 841 843 850 853 860

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861 861 862 863 869 873

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876 876 878 880

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11.4.4 11.4.5 11.4.6 References . .

xxv

Mathematical/Numerical Model . . . . . . . . . . . . . . . . . . 881 Numerical Applications and Results . . . . . . . . . . . . . . 886 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 888 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 889

About the Author

Ioan Sarbu is a professor emeritus and doctoral degree advisor of the Department of Civil and Building Services Engineering at the Polytechnic University of Timisoara (UPT), Romania. He obtained a diploma in civil engineering from the “Traian Vuia” Polytechnic Institute of Timisoara in 1975 and a Ph.D. degree in civil engineering from the Timisoara Technical University in 1993. Starting in 1975, he worked as an engineer and designer with Water Resources Management Company in Timisoara. He became an assistant professor with the university in 1978, ultimately dedicating over 40 years to his alma mater. Additionally, he is a European engineer (Eur. Eng.), as designated by the European Federation of National Engineering Associations (Brussels) in 2001, and since 2004 was entrusted as a doctoral degree advisor in the civil engineering and building services branch coordinating up to 20 Ph.D. students, almost 50 M.Sc. students, and more than 200 graduate students. In 2019 he was awarded by the UPT the honorary title of “Professor emeritus” and became a Laureate of the “Henri Coanda” award of the Romanian Academy for 2017. He was Head of the Building Services Department within the UPT for almost 20 years, until his retirement in 2017, and between 2001 and 2017 he was also Head of the National Building Equipment Laboratory in Timisoara, of the 1st degree. His main research interests are related to refrigeration systems, heat pumps, and solar energy conversion and storage. He is also active in the field of thermal xxvii

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comfort and environmental quality, energy efficiency and energy savings, water and heat distribution systems, and numerical simulations and optimisations in building services. He is involved in preparation of regulations and standards related to energy and environment. Additionally, he is a member of the American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE), International Association for Hydro-Environment Engineering and Research (IAHR), Romanian Association of Building Services Engineers (RABSE), Romanian General Association of Engineers (RGAE), and Society for Computer Aided Engineering (SCAE). He is a noted expert in integrating thermal applications, building urban water and heat distribution systems, computer utility, and integrating wastewater treatment into design. He has also been certified as an energy auditor of buildings since 2003, the same year he coordinated an international academic research project with the Global Gnomon Company in Madrid. He was an expert reviewer on the National Board of Scientific Research for Higher Education (Bucharest), vice president of the National Board of Certified Energetically Auditors Buildings (Bucharest), a member of the National Council for Validation of University Titles, Diplomas and Certificates, and a member of the Technical Council for Civil Engineering from Ministry of Regional Development and Public Administration. He is serving several journals like Science Bulletin of Polytechnic University, Romanian Journal of Civil Engineering, and Energies (https://www.mdpi.com/ journal/energies/sectioneditors/energy_buildings) as an editorial board member, a guest editor at Energies open access journal, and a reviewer in over 20 international journals with high impact factor such as Journal of Thermal Science and Technology, Energy Conversion and Management, Applied Thermal Engineering, International Journal of Refrigeration, International Journal of Sustainable Energy, Energy and Buildings, Energy Efficiency, Applied Energy, Building and Environment, Energy, Entropy, Thermal Science, Energies, Journal of Renewable and Sustainable Energy, International Journal of Heat and Mass Transfer, Journal of Hydraulic Research, and Journal of Water Supply: Research and Technology.

About the Author

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He has published about 390 scientific papers in his research domains, 39 books and 10 book chapters in prestigious publishers in the country (Technique, Romanian Academy) and abroad (Elsevier, Springer, Nova Science Publishers), more than 150 articles in Clarivate Analytics/Web of Science (WOS) and other international databases indexed journals, and about 60 articles in proceedings of international conferences. He is also the author of 6 patent certificates, 15 innovations and up to 30 computer programs. His current h-index is 14 (Clarivate Analytics WOS), 15 (Scopus), 18 (ResearchGate) and 21 (Scholar Google) as of November 2020. His international recognition is evidenced by the high number of citations of his published works, well over 4300 (1000 in Clarivate Analytics/WOS), by the listing in different Who's Who publications (e.g., Who’s Who in the World, Who’s Who in Science and Engineering, and Who’s Who in America) and other biographical dictionaries (e.g., Cambridge Blue Book of Foremost International Engineers, Dictionary of International Biography, Encyclopedia of Romanian personalities, etc.), as well as by the various distinctions, awards, diplomas and medals received during his career: (1) Distinctions: “Distinguished Assistant Professor”— Ministry of Education, Bucharest (1986), “Decoration for significant achievements in engineering”—International Biographical Centre (IBC), Cambridge, UK (2015), “Cultural merit for outstanding achievement in scientific research”—IBC Cambridge (2016); (2) Awards: “AGIR 1997 Award”—RGAE (1997), “Albert Einstein Award of Excellence”—American Biographical Institute (ABI), North Carolina, USA (2010), “World Congress of Arts, Sciences and Communications Lifetime Achievement Award”— IBC Cambridge (2013), Award of “Distinguished Service to Engineering”—IBC Cambridge (2016), “Henri Coandă Award”—Romanian Academy (2019) for the book “Solar Heating and Cooling Systems: Fundamentals, experiments and applications” published by Elsevier, Oxford, UK in 2017, which is present in the libraries of over 300 top

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universities in the world (http://www.worldcat.org/ oclc/976029539) and indexed in Clarivate Analytics/WOS. (3) Diplomas/Plaques: “Man of the Year in Science”— ABI North Carolina (2008), “Hall of Fame for Distinguished Accomplishments in Science and Education”—ABI North Carolina (2009), “International Educator of the Year”—IBC Cambridge (2009), “Top 100 Engineers”—IBC Cambridge (2012), “Diploma of excellence”— RGAE (2016); (4) Medals: “Gold Medal for Romania”—ABI North Carolina (2007), “Order of Scientific and Technical Merit”—ABI North Carolina (2008) “Medal for Scientific Achievements”—IBC Cambridge (2014). In recognition of outstanding contributions to his profession, Prof. Sarbu has been featured on the Marquis Who’s Who Lifetime Achievers website. Other information can be found on the website: https:// www.ct.upt.ro/studenti/cursuri/sarbu/index.htm.

Chapter 1

Introduction

Abstract This chapter summarises a short description of the author’s significant contributions to making relatively recent advances on various topics corresponding to several research directions in the field of building services engineering.

1.1 Generalities In the context of sustainable development, energy is one of the most prominent resources that concern the contemporary world. Carbon dioxide (CO2 ) is one of the most important greenhouse gases (GHGs), and the most dominant source of CO2 contributing to the rise in atmospheric concentration is the combustion of fossil fuels. Moreover, despite the commitment of many countries to reach an early peak in emissions related to fossil fuel consumption, in 2018, the energy-related CO2 emissions reached the highest annual increase since 2013 (+1.9%) according to the International Energy Agency. Economy, population and per capita energy consumption have increased the demand for energy during the last several decades. Statistical data has indicated that buildings account for approximately 40% of energy end-use in the European Union (EU) (Fig. 1.1), of which more than 50% is electricity. According to the United Nations Environment Programme, 60% of the global electrical energy is consumed by residential, commercial and office buildings, with an increasing trend over time. Buildings offer the greatest and most cost-effective potential for energy savings. Building services refers to the equipment and systems that contribute to controlling the internal environment to make it safe and comfortable to occupy. Typically the building services installation is worth 30–60% of the total value of a project. Studies have also shown that saving energy is the most cost-effective method for reducing GHG emissions. Furthermore, higher energy efficiencies will contribute to worldwide sustainability. When deciding on both energy performance and comfort when designing a new building, the information provided by the Rankey diagram [1] is usually used to analyse the energy balance of the building. In this diagram the energy fluxes are represented by arrows, and the arrows thickness is proportional to the corresponding © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 I. Sarbu, Advances in Building Services Engineering, https://doi.org/10.1007/978-3-030-64781-0_1

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1 Introduction

Fig. 1.1 Primary energy consumption in EU

energy flux. With the Rankey diagram, the building is represented by a single space and there are no heat fluxes between rooms, thermal bridges and different types of windows and doors or solar heating systems (active or passive). For example, Figure 1.2 shows the energy balance diagram of a usual building, for the cold season and temperate continental climate. The energy flux introduced into the building (1) comes from a fossil fuel (liquid, gas), being used for heating and for the preparation of domestic hot water (DHW) and food. The energy flux (2) represents the electrical power related to the building, Fig. 1.2 Rankey diagram

1.1 Generalities

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of which one part (19) can be used for the exterior lighting of the building, and the other part for the indoor consumers. The ratio of energy fluxes (1) and (2) depends largely on the energy source used to prepare food and DHW. Also, the energy flux (3) enters the building from the environment, representing the solar inputs. Combustion of the fuel results in energy losses, which, for simplicity, are included in the chimney losses (4). As the chimney passes through rooms in the building, some of these losses (18) are recovered by conduction. Of particular importance in reducing energy losses when burning fuel is the regulation and automation of burners, but especially the use of condensing boilers. The installation systems consume electricity (12) to supply the pumps, fans and the operation of the automation device. Part of the energy losses from pumps and fans is used to heat the thermal agent or air, and another part reaches the environment. The heat flux given off by the distribution pipes of the heating system (15) represents energy loss, if it reaches an unheated space, or useful energy, if these pipes pass through heated spaces. Of the heat flux consumed for the production of DHW and food (13), one part reaches the users of the building, and another part (16) reaches directly into the external environment through the internal sewerage system of the building, respectively through the air intake hoods mounted on top of cooking machines. It should be noted that from these heat losses energy can be recovered by recuperative heat exchangers or heat pumps. Inside the building there are interior heat sources such as lighting (11) and occupants (17), which represent the internal heat input of the building. Part of the heat flux required to heat the building is lost by conduction through the ceiling (6), walls (7), glazed surfaces (8) and floor directly on the ground or above the basement (9), in proportion to the surface and heat transfer coefficient of these construction elements. Also, the heat loss through the ventilation system (5) depends on the number of hourly air exchanges of the building, which can be significantly reduced if the fresh air is preheated in buffer spaces or by means of recuperative heat exchangers. In the case of other meteorological situations (climate, temperature), the structure of the energy balance of the building remains unchanged and only the ratios between the thermal fluxes change. Romania had to reach the objectives imposed by the EU to attain nearly zero energy buildings (NZEBs) by year 2020, which means that the share of renewable in the total gross of Romania’s energy consumption should be 20%, the CO2 emissions and the final energy consumption must decrease by 20%, and all the new buildings must be passive. Some renewable energy sources (RES) options are available for NZEBs, being implemented due to the mandatory RES share of 20% of EU energy consumption in 2020. RES to be applied in NZEBs include photovoltaic (PV)/thermal, solar/geothermal hybrid systems for heating, solar thermo-electric, and solar powered sorption systems for cooling. Moreover, when including RES in buildings, both thermal energy storage and advanced control become of extreme importance to achieve adequate performance and energy savings. Generating electricity with solar PV panels is also a viable solution in all regions of Romania for both independent PV systems and for the realisation of photoelectric power plants connected to the national energy system.

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1 Introduction

To realise the ambitious goals for reducing the consumption of fossil fuel as primary energy and the related CO2 emissions, and to reach the targets of the Kyoto Protocol, improved energy efficiency, integration of RES, and the use of heating, ventilation, air-conditioning and refrigeration (HVAC&R) equipments with high performance in the existing building stock must be addressed in the near future. Nevertheless, strict saving policies may contrast with users’ comfort. That is why smart and innovative HVAC systems are needed, which compensates for energy costs and ambient comfort of users. The use of intelligent management systems inside buildings can improve the control and management of HVAC, DHW system, lighting, fire safety, and other “energy-hungry” devices and also facilitate the integration of RES. It is also known that energy and water resources are fundamental to human existence, and are regularly subject to economic, technological, demographic and social pressures. Water, sanitary and wastewater services represent a substantial proportion of the cost of construction, averaging 10% of the capital costs of building and with continuing costs in operation and maintenance. The world energy consumption for water distribution is about 7% of the global energy. Additionally, it is estimated that 2–3% of the worldwide electricity consumption is used for pumping in water distribution systems (WDSs). Given the importance and spread of WDSs, since the last century, there have been intense concerns to improve their calculation, implementation and operation methods. Modern computers have provided the ability to process calculation to a higher level, and have enabled new formulations and requirements for the design and operation of WDSs. The author’s significant contributions to making relatively recent advances on various topics corresponding to the multiple fields of building services engineering are set out below.

1.2 Assurance of Indoor Environmental Quality Potential benefits of a newer building in regard to the indoor environment that might improve productivity include upgraded technology, increased natural day lighting, better indoor air quality and increased thermal comfort. Occupants spend 80–90% of their time inside buildings; and thus, the indoor environmental quality (IEQ) plays a vital role on occupants’ health, satisfaction and working productivity. The IEQ is characterised, for example, by thermal comfort and indoor air quality (IAQ) variables (e.g., CO2 and volatile organic compound (VOCs) concentration). In this regard, it is a tough mission to maintain the satisfied IEQ while reducing energy consumption in buildings. Sarbu and Sebarchievici [2] performed an olfactory comfort analysis in buildings starting from a general description of the comfort fundamental components (thermal, olfactory, acoustic and visual comfort) and find that visual comfort is also related to the thermal environment, which affects performance and productivity. The parameters of indoor air, temperature, level of acoustic pressure, lighting level together with the age of occupants, gender, level of education and the activity

1.2 Assurance of Indoor Environmental Quality

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contribute to their comfort [4]. The European standard EN 7730 ISO [4] aims at using the predicted mean vote (PMV) and predicted per cent of dissatisfied (PPD) indices to evaluate the thermal comfort in buildings. Sarbu and Sebarchievici [5] approached the numerical prediction of thermal comfort in closed spaces on the basis of PMV-PPD model, and its testing to asymmetric or non-uniform thermal radiation, as well as the IAQ simulation and control. Additionally, the thermal comfort criteria for design of heating systems, the relationship between thermal environment and human performance, as well as the influence of CO2 on human performance and productivity were presented. The relation between the window height, U-value, outdoor air temperature and air velocity were able to ensure local thermal comfort was also reported. The energy consumption of buildings is closely related to how they are exploited. The values set for the calculation of the IEQ indices must lead to efficient energy consumption, efficient ventilation and air conditioning. The IAQ is very important for the health of population, the more so in case of students who spend most of their time in classrooms, amphitheatres and libraries. In addition to adverse respiratory and somatic symptoms, poor IAQ can have a direct and indirect impact on occupant performance of cognitive-based tasks. Thermal comfort since has been related to productivity, well-being and energy conservation in schools, has gained importance in recent years. In this context, an experimental and numerical research to assess IEQ and schoolwork performance in university classrooms was performed by Sarbu and Pacurar [6, 7]. The primary aim of this study was to assess thermal comfort based on the PMV and PPD indices using subjective and experimental measurements in two airconditioned classrooms at Polytechnic University of Timisoara, Romania, where the air-exchange rate was assured by natural ventilation. The secondary aim of this research was to develop a prediction model of the academic performance during the cooling season. Application of this model indicates that the indoor environmental conditions can strongly affect student performance. Additionally, a simulation model on the Transient System Simulation (TRNSYS) program of the PMV-PPD indices and heating/cooling energy demand for an amphitheatre with natural ventilation is also proposed.

1.3 Modelling, Optimisation and Modernisation of Heating Systems District heating systems (DHSs) are also envisioned as one of the most practical and sustainable engineering solutions to meet the heating demand of the consumers and to reduce GHG emissions. A DHS provide thermal energy to a range of consumers [8]. Hence, an adequate sizing of the key elements involved in the energy supply system and their management are critical. The heat distribution network, pumps and valves are essential components of a DHS as they ensure hydraulic operating conditions are met for the energy distribution process.

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1 Introduction

The main goal of a central heating system design is to obtain appropriate thermal comfort minimising the investment and operational costs. This scope could be theoretically realised with the available modern control techniques. However practice has shown that, if the preconditions are not fulfilled, the correct operation of the heating system could not be assured even by the most sophisticated control equipment. Therefore, the control elements could not fulfil their function if the hot water flow rate differs from the designed value and the thermal comfort is not realised unless with higher energy consumption. The operation of unbalanced central heating systems was studied in [9], where the thermal comfort and the energy consumption were analysed. In this purpose some computation models were developed. Sarbu et al. [10, 11] provided an extensive survey on the modelling and optimisation of DHSs focused on the heat distribution network, including some recommendations for future developments. Authors conclude that researchers generally take the approach of DHS optimisations under steady state conditions using deterministic approaches, such as linear programming (LP), integer linear programming (ILP), non-linear programming (NLP), integer non-linear programming (INLP), and dynamic programming (DP), which generally don’t guarantee a global optimal solution. Thus, Sarbu and Brata [12] conceived an optimisation model to design new and partially extended hot water branched district heating (DH) networks in steady state conditions based on total annual cost (capital and energy cost) as the objective function, and solved it according to the LP method, using the Simplex algorithm. This model provides an optimal distribution of standardised diameters along the length of each pipe, together with the length of the pipe segments corresponding to these diameters. However, recent research shows that researchers tend to use metaheuristic optimisation techniques such as simulated annealing (SA), particle swarm optimisation (PSO) and ant colony optimisation (ACO) [13]. To distribute the heat in buildings, a hydronic system (radiant panels and hot water radiators) or a central forced-air system can be used. In central heating systems, the hot water supply temperature can have different values. In the recent past, the most used value in Romania, as well as in other EU countries, was 90 °C with a 20 °C temperature drop, but currently, the supply temperature is typically lower than 90 °C. One way to obtain higher efficiency of the heating systems is to use reduced temperature [14]. In addition, it is possible to use RESs with higher efficiency as solar energy and heat pumps (HPs). The energy and energy efficiency of central heating systems is higher at reduced hot water temperatures [15], but based on [16], it has to be stated that this is valid only for totally balanced systems. After the introduction of plastic piping, the application of water-based radiant heating with pipes embedded in room surfaces (i.e., floors, walls and ceilings) has significantly increased worldwide. Due to the large surfaces needed for heat transfer, these systems work with low water temperatures for heating. Sarbu and Sebarchievici [17] performed a study that addressed many different topics related to energy saving in central heating systems with reduced supply temperature and radiant panel heating (floors, walls, ceilings). They investigated the performance of these different types of low-temperature heating system using numerical modelling, simulation tools and also site measurements. This study showed that floor-ceiling heating works better than

1.3 Modelling, Optimisation and Modernisation of Heating Systems

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other low-temperature heating systems regarding providing better thermal comfort, lower energy consumption, lower CO2 emission and lower operating cost. Additionally, Sarbu et al. [18] provided a study that briefly describes the heat distribution systems in buildings, focusing on the radiant panels (floor, wall, ceiling, and floorceiling). Main objective of this study is the performance investigation of different types of low-temperature heating systems with different methods. Additionally, a comparative analysis of the energy, environmental, and economic performances of floor, wall, ceiling, and floor-ceiling heating using numerical simulation with TRNSYS software is performed. All heating systems (heaters, warm-air or panels) do have the aim to assure in buildings the best thermal comfort. The influence of heating systems on IEQ was studied in [19], where an analysis of the temperature distribution (in air, on warm or cold surfaces, etc.) and of the air streams velocity is performed, according to the type of the used heating system. It is defined, as well, the efficiency of heating systems for more degrees of thermal comfort and energy consumption. A computation model for the design of water-radiator heat distribution networks in buildings with circulation of water by pumping was developed by Sarbu and Popina [20]. Based on this model, it has been elaborated a computer program for IBM-PC compatible systems that offers the possibility of an operative and precise calculus as well as the efficient solving of design problems. The advantages to use the proposed program are showed through a numerical application. Hydraulic balancing of heating systems in buildings is necessary, on the one hand, to provide a sufficient amount of heat to consumers and, on the other hand, to reduce energy losses in the system. Circulation pumps, fittings and pipes must be provided in such a way that, even in variable operating conditions, a proper distribution of the heat carrier is ensured and the noise levels allowed in the installation are not exceeded. These requirements can be met with the help of thermostatic valves, control valves, flow and differential pressure regulators, as well as variable speed pumps addressed in detail in [21, 22]. The development of modern technologies in chemical industry has allowed the production of plastic tubes, corresponding from point of view of material quality and duration of use, with superior performances to classical materials. In [23] a comparative study of the physical, mechanical, geometric and hydraulic characteristics of the tubes produced both from classical metallic materials and from different plastic materials used for building services was developed. The specific consumption of energy embedded in these tubes, as the use possibilities for them are also analysed. To prevent the water cooling in the pipes of DHW supply system at low consumption or if water is stationary, could be used some modern regulation systems for water temperature. Also, radiant floor heating systems can use such systems. Sarbu and Valea [24] presented the performance of a fluid temperature control system using self-adjustable cables. For this purpose, they provided some elements about structure and operating mode of heating cable, and some data about technical and performance characteristics of various heating cable types with different practical uses.

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1.4 Efficient Refrigeration and Air-Conditioning Systems Refrigeration systems typically operate in the range of −5 °C (for Freon systems) to as low as −45 °C (for ammonia systems). Vapour compression-based refrigeration systems involve a cycle of evaporation, compression, condensation and expansion. Refrigeration systems, HPs, and air-conditioner (A/C) equipment use compressors to move heat in refrigerant cycle. The main types of compressors are: reciprocating compressor (piston compressor), rotary screw compressor, centrifugal compressor and scroll compressor (spiral compressor) [25, 26]. These refrigerating systems can use a variety of refrigerants. The use of high global warming potential (GWP) refrigerants causes abnormal climate changes and an increase in average atmospheric temperature, accelerating the global warming effect [27]. Therefore, the recent legislative actions, such as the EU F-Gas regulations [28] and the Montreal Protocol Kigali Amendment [29], are proposed to limit the production and use of high-GWP refrigerants, the alternative refrigerants have attracted more and more attentions [30]. Sarbu [31] performed a study on the recent development of possible substitutes for non-ecological refrigerants employed in HVAC&R equipment based on thermodynamic, physical and environmental properties, and total equivalent warming impact (TEWI) analysis. There are two main ways for the utilisation of alternative refrigerants. One is the synthetic refrigerants advocated by the United States, such as R1234yf and R1234ze. The other is the natural working fluids that European countries, China, and Japan advocate, such as ammonia—NH3 (R717), water (R718), propane (R290), isobutene (R600a), ethylene (R1270), and CO2 (R744). However, the synthetic refrigerants are difficult to be promoted globally due to the high costs and uncertain environmental factors [31]. Natural working fluids have the advantages of low cost, 0 ozone depletion potential (ODP), low GWP, etc., and they are considered to be long-term replacements for hydro-chlorofluorocarbons (HCFCs) and hydro-fluorocarbons (HFCs) [25, 32]. A theoretical study on some recovery possibilities of the heat produced by refrigeration systems based on vapour compression or vapour absorption, of a great importance in actual economic and energy conditions, was performed in [33]. The numerical results obtained allow concluding a lot of important opportunities for design. The role of insulation of a refrigerating system is to reduce heat flux to cooled spaces or to cold devices and pipes in which the refrigerant temperature below ambient temperature (free air, soil or neighbouring rooms). Therefore, refrigeration insulation is commonly used to reduce energy consumption of refrigerating systems and equipments [34]. Sarbu et al. [35] developed a computational model of the optimal thickness of these insulations, with a high level of generality. This model uses multiple dynamic optimisation criteria simple or compound, which better reflects the economic and energy complex aspects, present and future. The method of freezing the soil by artificial cold has received a wide extension, having a wide field of application to urban- and hydro-technical constructions (water capture and pumping stations, drilled wells, underground mains, dams, etc.) along

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with the extractive industry. Sarbu and Kalmar [36] developed a mathematical model for thermal calculation of a vertical soil freezing column operating with gaseous refrigerant, taking into account the variation of the refrigerant temperature with depth. Sarbu and Borza [37] conducted an experimental research on the self-protection system to frost of cooling towers using an acclimatised stand. They followed the parameters that influence the forming of ice-curtains on the air access section into the cooling tower and proposed an analytic relationship for calculating the aerodynamic resistance of the self-protection system. The main purpose of most buildings and installed ventilating and air-conditioning (VAC) systems is to provide an acceptable environment that does not impair the health and performance of the occupants. Relatively recent studies have demonstrated that air-conditioning (AC) systems represent between 10 and 60% of the total energy consumption of office buildings [38]. Conventional AC systems, such as variable air volume (VAV), constant air volume (CAV) and fan-coil units (FCUs) air-conditioning systems, supply cool air to spaces to remove thermal loads. These systems need a refrigeration plant (chiller) to produce cold water and a complex pipe network to distribute the cold water to the air conditioned spaces. Air-cooled chiller systems are commonly used in office buildings because of their flexibility. The operation of chillers usually takes up the highest proportion of the total electricity consumption of buildings. One of the main innovative contributions of a study performed by Sarbu and Adam [39, 40] consists in the achievement and implementation of an air–water mist cooled system for the air-cooled chillers of different VAC systems that has a significant effect on the energy performance improvement of these systems. The experimental measurements were used to develop a mathematical model to minimise the power consumption by optimal control, depending only on non-controlled parameters (solar radiation intensity and outdoor air temperature) and to validate a TRNSYS simulation model for energy consumption of a VAC system.

1.5 Solar Heating and Cooling Systems The renewable energy refers to energy that is produced from natural resources that have the characteristics of inexhaustibility over time and natural renewability. RES include wind, solar, geothermal, biomass and hydro energies. Romania has a very good potential mix of solar energy, hydropower, biomass and geothermal energy [41]. Romania is pursuing RES in three different directions [42]: • Electricity. The renewable energies used to produce electricity are wind, hydropower, solar PV and biomass; • Heating/cooling. The renewable energies most suited for heating and cooling are: biomass, geothermal and solar resources;

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1 Introduction

Fig. 1.3 Structure of the primary energy

• Transportation. Biofuels for transport are obtained by processing the rape, corn, sunflower and soybean crops. It is obvious that, in the medium term, RESs can not be seen as a total alternative to conventional sources, but it is certain that, due to their advantages, they must be used complementarily with fossil fuels and nuclear energy. The structure of the primary energy demand in 2000 and of the one estimated for 2030 are presented in Fig. 1.3. Solar energy offers a clean, climate-friendly, very abundant and inexhaustible energy resource to mankind, relatively well-spread over the globe. Its availability is greater in warm and sunny countries, those countries that will experience most of the world’s population and economic growth over the next decades. Solar energy is the most advantageous RES. It collects and converts the abundant energy of the sun into available energy. The largest solar contribution to world energy needs is currently through solar heat technologies. The potential for solar water heating is considerable. Solar energy can provide a significant contribution to space heating demand of residential and commercial buildings, both directly and through HPs [42]. Direct solar cooling offers additional options but may face tough competition from standard cooling systems run by solar electricity. • Solar heating systems are a type of renewable energy technology that has been increasingly used in the past decade across Europe to provide heating, AC and DHW for buildings. These systems have enabled the use of low-temperature terminal units, such as radiators and radiant systems. A description of main types of solar space and water heating systems, concentrating on classifications, system components and operation principles is provided in [43, 44]. It is also focused on active and combisystems. Additionally some examples of DHW systems and combisystems application are presented.

1.5 Solar Heating and Cooling Systems

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• Solar cooling systems are a viable solution to reducing the carbon footprint of air conditioning in buildings. A detailed review of different solar refrigeration and cooling methods was provided by Sarbu and Sebarchievici [45]. They presented theoretical basis and practical applications for cooling systems within various working fluids assisted by solar energy. Thermally powered refrigeration technologies are classified into two categories: sorption technology (open systems or closed systems) and thermo-mechanical technology (ejector system). Solid and liquid desiccant cycle represents the open system. Absorption and adsorption technologies represent the closed system. The adsorption cooling typically needs lower heat source temperatures than the absorption cooling. The ejector system represents the thermo-mechanical cooling, and has a higher thermal coefficient of performance (COP) but require a higher heat source temperature than other systems. In [46] was performed a compressive overview of the solar closed sorption refrigeration systems, which utilise working pairs (fluids). This research show that solarpowered closed sorption refrigeration technologies can be attractive alternatives not only to serve the needs for air-conditioning, refrigeration, ice making, thermal energy storage or hybrid heating and cooling purposes but also to meet the demands for energy conservation and environmental protection. The rejected heat at the condenser still presents an important heat potential especially for activating a sorption chiller. A sorption chiller can use either a solid solution (adsorption chiller) or liquid solution (absorption chiller). The use of absorption chiller systems powered by solar thermal collectors is increasing. As reported by Sarbu and Sebarchievici [46], the COP and cooling capacity of an absorption chiller are greater than the adsorption technology. Basically, the single effect COP of the absorption chiller ranges from 0.5 to 0.73 for an operating temperature comprised between 60 °C and 110 °C. A comprehensive review of solar thermoelectric (TE) cooling systems was provided by Sarbu and Dorca [47], which presents the details referring to TE cooling parameters and formulations of the performance indicators and focuses on the development of TE cooling systems in recent decade with particular attention on advances in materials and modelling and design approaches. This study can be used by engineers working on theory, design and/or application of TE cooling systems.

1.6 Ground-Sources Heat Pumps for Sustainable Heating and Cooling Shallow geothermal energy (SGE) is an environmentally friendly, renewable and sustainable energy source and has become increasingly important in European energy policy and strategy. The ground-source heat pump (GSHP) can be the most common and wide application of SGE. The GSHP technology, which takes heat extraction or rejection from ground through borehole heat exchanger (BHE) with help of so-called

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closed-loop systems, is a safe and stable source for space heating (low temperature hydronic systems, warm-air or convective systems with fan-coil units) and for water heating (DHW, swimming pools or hot water for processes) with a minimum ecological impact. Sarbu and Sebarchievici [48] provided a detailed literature review of the GSHP systems, and their recent advances. The operation principle and energy efficiency of a HP are defined, and a detailed description of the surface water (SWHP), groundwater (GWHP), and ground-coupled (GCHP) heat pumps are performed. Additionally, the most typical simulation and ground thermal response test models for the vertical ground heat exchangers currently available are summarised including the heat transfer processes outside and inside the boreholes. Some information about the possibility to obtain the better energy efficiency with combined heating and cooling by GCHP is also presented. Generally, it is recommended the GSHPs to serve both for heating and cooling applications. This can be performed with either a reversible (heating–cooling) or a double effect system [25]. It contributes to reduction of CO2 and dust emissions in Europe and beyond. In recent years, many GSHP systems have been developed and installed because of their environmentally friendly performance and high efficiency. The efficiency of HP systems depends on the efficiency of the unit itself and the thermal energy needs of the building in which it is used. Studies on vertical closed-loop GCHPs can result in a range of 30–70% reduction of annual electricity consumption compared with the air-to-air HP systems [48]. Sarbu et al. [49] presented the economic, energy and environmental performance criteria which show the opportunity to implement a HP in a heating/cooling system. A computational model of annual energy consumption for an air-to-water HP based on the degree-day method and the bin method implemented in a computer program was developed. Additionally, from a case study a comparative economical analysis of heating solutions for a building was performed and the energy and economic advantages of building heating solution with a water-to-water HP was reported. Sarbu and Sebarchievici [50, 51] discussed vapour compression-based HP systems, briefly describing the thermodynamic cycle calculations, as well as the COP and CO2 emissions of a HP with an electro-compressor and compared different heating systems in terms of energy consumption, thermal comfort and environmental impact. They performed an experimental study to test the energy efficiency of the radiator or radiant floor heating system for an office room connected to a GCHP. Additionally, dynamic building energy simulation software was used to analyse the savings achievable on building energy use while taking into account different variables. Two numerical simulation models of useful thermal energy and the system COP in heating mode are developed using TRNSYS software. Sebarchievici and Sarbu [52, 53] conceived an energy-operational optimisation device for a GCHP system involving insertion of a buffer tank between the heat pump unit and fan coil units and consumer supply using quantitative adjustment with a variable speed circulating pump. Then, the experimental measurements were used to test the performance of the GCHP system in different operating modes. In addition, using TRNSYS software, two simulation models of thermal energy consumption in heating, cooling and DHW operation were developed.

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Sarbu et al. [54] presented a working methodology and developed an analytical model for evaluation of the thermal conductivity and the borehole thermal resistance using a thermal response test (TRT). Additionally, they used the Earth Energy Designer (EED) simulation program developed on the basis of the line-source model to calculate the fluid temperature for a case study of the ground heat exchanger (GHG) according to the monthly heating and cooling loads and the borehole thermal resistance. Analysing the time evolution of the fluid temperatures in the ground for the peak loads reveals that these values are approximately constant, meaning that the heat source (ground) is fully regenerated and thus the GCHP will maintain high performance in operation. Other aspects of TRT were included in [55], which concerns the assurance of vaporisation thermal power for vertical closed-loop GCHP systems.

1.7 Thermal Energy Storage Due to humanity’s huge scale of thermal energy consumption, any improvements in thermal energy management practices can significantly benefit the society. One key function in thermal energy management is thermal energy storage (TES). TES is a technology that stocks thermal energy by heating or cooling a storage medium so that the stored energy can be used at a later time for heating and cooling applications and power generation. Sarbu and Sebarchievici [56, 57] focused on TES technologies that provide a way of valorising solar heat and reducing the energy demand of buildings. The principles of several energy storage methods and calculation of storage capacities were described. Sensible-heat storage technologies, including water tank, underground and packed-bed storage methods were briefly reviewed. Additionally, latent-heat storage (LHS) systems associated with phase-change materials (PCMs) for use in solar heating/cooling of buildings, solar water heating, HP systems and concentrating solar power plants as well as thermo-chemical storage were discussed. Sarbu and Dorca [58] provide a comprehensive survey on the development of latent heat storage systems focused on heat transfer and enhancement techniques employed in PCMs to effectively charge and discharge latent heat energy, and the formulation of the phase change problem. PCMs have been widely used in the fields of TES units, heating and cooling systems, and thermal management due to their high phase change enthalpy, wide and stable phase change temperature, and low cost [59]. Nevertheless, one of the major drawbacks in PCMs is the low thermal conductivity, which reduces the heat transfer rate and limits their further potential applications [42]. To improve the TES performance of PCMs, numerous strategies have been designed to improve the thermal conductivity. One of the most popular strategies is adding highly conductive fillers, which can be categorised in terms of the dimension, i.e., nanoparticles (zero dimension), nano-shee (two-dimension), short or long fibbers (one dimension) and three-dimensional (3D) porous structure materials (expanded graphite (EG), carbon foam, and metal foam). Among these fillers, EG appears to be more efficient in improving the thermal conductivity without increasing the specific

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gravity due to the high melting point, high surface area, high thermal conductivity, and lightweight, which is of the most frequently used thermal conductivity enhancements in TES applications [58].

1.8 Analysis and Optimisation of Water Transmission and Distribution Systems The worldwide water supply represents a significant portion of the global energy consumption. The distribution network is an essential part of all urban water supply systems. Distribution system costs within any water supply scheme may be equal to or greater than 60% of the entire cost of the project [60]. Formulation of appropriate mathematical models, which allow the determination of flow rate and pressure distribution in looped networks with non-standard components is essential both for accurate and efficient resolution of design stage, and network analysis in different operating conditions (normal or emergency state). Using sufficient number of simulations can determine the appropriate settings for the piezometric head (heads) of the supply node (nodes) as well as other necessary measures for service pressure to ensure the energy optimisation of the network. For such a purpose, the use of nodal analysis, in which the unknowns are generally the hydraulic heads at the nodes of the network, is efficient. Sarbu [61] developed a generalised classic model for the nodal analysis of complex urban looped systems with non-standard network components and the solvability of new problems, along with the determination of the pressure state in the system. A different approach to solving this problem by using the variational formulation method for the development of some new analysis models based on unconditioned optimisation techniques for both nodal analysis and cyclical analysis is presented by Sarbu and Valea [62]. Additionally, the necessary and sufficient conditions for the solvability of the inverse problem with respect to flow-constraints were discussed by Sarbu [63]. A mathematical model for the determination of water stall point location in the pipes with distributed consumption is also exposed in [64]. A hydraulic analysis model of a recycled technological water supply network and a numerical simulation model of technological water consumption for an enterprise in chemical sector with self-supply system were developed in [65, 66]. The efficient design of a water transmission (adduction) main and a branched network involves several optimisation processes among which an important place is held by their path optimisation. That problem is approached also on the looped network design to determine an independent loop system (the virtual branched network) [67]. In this context, Sarbu and Valea [68] developed two deterministic mathematical models, one for optimisation of water adduction main path, based on techniques of sequential operational calculus (graph-theory and DP) and other which generates all minimal trees of the graph comprising the network nodes where

1.8 Analysis and Optimisation of Water Transmission …

15

consumers are placed and links (pipes) between them, based on graph-theory. Thus, can be determined all optimal solutions, for a given criterion. The reliability of water supply is much greater in the case of looped networks. Such distribution networks are achieved in an increasingly complex structure (looped networks, several supply sources, booster pumps, inner potential elements, etc.). The distribution network requires efficient design and operation, which may be achieved through effective application of optimisation methods. Optimisation, as it applies to WDS design is the process of finding the best, or optimal, solution to the problem under consideration. The most used optimisation methods have included such techniques as LP, NLP, DP, MIP and heuristic algorithms (HAs) such as genetic algorithm (GA), simulated annealing (SA) and others. Two optimisation models coupled with a computational iterative procedure of optimal discharges through pipes [69] are described by Sarbu [70] for the design of new and partially extended water networks supplied by pumping or gravity, which have an increased generality degree and a notable performance. Thus, an improved non-linear optimisation model (NOM) of looped networks supplied by direct pumping is developed in [71], which has the advantage of using not only cost criteria, but also consumed energy, included energy, consumption of scarce resources, operating costs, etc. Additionally, a linear optimisation model (LOM), based on LP technique, allows the determination of an optimal distribution of commercial available diameters between each pair of network nodes and the length of pipe segments corresponding to these diameters which guarantees a high reliability [72]. Sarbu et al. [73] performed a study of the most approached method, models and numerical examples for multi-objective optimisation of water distribution networks (WDNs) design and operation. The main deterministic and heuristic optimisation techniques were synthesised and presented, a single- and multi-objective optimisation problem was generally formulated, and the main optimisation objectives, decision variables and constraints for the design, rehabilitation and operation of WDNs were discussed. Additionally, some deterministic and heuristic multi-objective optimisation models for WDN design/rehabilitation were included and numerically exemplified. The electricity consumption due to the water pumping in distribution systems represents the highest proportion of the energy costs in these systems. An important goal is the absolute reduction of pumping energy, which is possible by dividing the system into zones [74]. Sarbu [75] presented several comparative studies of energy efficiency in WDSs considering distinct configurations of the networks and also considers implementation of the variable-speed pumps. He described in detail four strategies for improving energy efficiency of water pumping: control systems to vary pump speed drive according to water demand, pumped storage tanks, intermediary pumping stations integrated in the network and elevated storage tanks floating on the system. Finally, this study compares the results of the application of four water supply strategies to a real case in Romania. The results indicated high potential operating cost savings.

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The conducted investigation showed the importance of a well-conceived pump operation schedule, avoiding peak hours, and the influence of the system configuration on energy consumption [76]. The operation of water supply networks is a task which commonly requires the utilisation of hydraulic pumps, whose function is to enable the water to be conducted in appropriate amount and pressure to its users. In order to guarantee an ideal pumping pressure, a proportion between 70 and 80% of all the energy consumed in many WDSs is exclusively destined to this purpose. The costs related to the working of the pumps can be reduced by minimising energy consumption. An interesting strategy to fulfil this goal is the utilisation of variable-speed pumps instead of fixed-speed pumps. The operation point of a centrifugal pump (defined by a pair of flow rate and head values) is usually controlled by adjusting itself to the pump’s rotation speed, aiming at the reduction in its energy consumption. In general, the speed control is accomplished with a frequency converter which enables the control of an induction motor’s rotation speed. In hot water systems, the possibility of variation in the pump’s rotation speed by using an inverter enables to adjust the pressures to the instantaneous thermal load. Besides directly influencing efficiency, the speed reduction entails other advantages, such as lower bearing loads, higher degree of reliability, lower maintenance costs and reduced rates of fugitive emissions, discarding the control valve from the pipe [77]. Due to the fact that the change in rotation leads to the slide of the pump’s operating point, causing alterations in the flow rate measures, head, power and efficiency, it becomes necessary to make an estimate of the new efficiency under which the pump will operate in its new characteristics with the maximum accuracy. Therefore, Sarbu and Borza [78] proposed a formula to calculate the efficiency of a variablespeed pump when its operating point is altered, which was appreciated and used by specialists [79–82]. An unsteady flow in pipe networks is usually a transient state from one steady state to another, including to and from resting state. Sarbu and Tokar [83] presented the basic concepts associated with transient flow, discussed the theoretical background of water hammer, and introduced aspects of system design that should be considered during transient analysis. Additionally, several analysis models of transient flows were developed including the transient analysis and design optimisation for pipe networks using GA method. Finally, the versatility of this approach was demonstrated by solving a numerical example.

1.9 Efficient Wastewater Treatment Plants As part of general environmental protection measures, simple, easy-to-maintain and efficient installations are necessary for the treatment of wastewater from isolated buildings, transport vehicles (which cannot be connected to a public sewage network) and industrial enterprises that evacuate great concentrations of oil and fat into the public sewage network.

1.9 Efficient Wastewater Treatment Plants

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Sarbu and Filip [84] proposed two plants designed for local wastewater treatment: an autonomous plant for wastewater treatment from buildings and transport vehicles (trains, mobile homes, and boats) and a small plant for wastewater treatment from isolated buildings (vacation houses, fuel distribution stations and their annexes) or of wastewater from industrial enterprises with their own low-capacity purification stations, based on a invention patent [85]. They also presented an efficient cavitation air flotation system which isolates fats, oils and solid particles from the wastewater of cities and industrial areas in a colloidal suspension. Additionally, Sarbu and Filip [86] designed a pilot sewage treatment plant (STP) located inside the STP in Timisoara, Romania, for small or very small localities (up to 500 inhabitants) such as villages, communes, hotels, and camps, which ensures influent wastewater is discharged at standardised parameters. They presented a brief overview of the parameters for wastewater treatment design and different technologies, followed by a detailed section on each component explaining the specific formulas of the design and applied-treatment processes.

1.10 Hydraulic Calculation of Open Channels and Sewer Columns in Buildings Artificial open channels have been widely used for different purposes because they can be constructed on diverse topographies and soil conditions and also prevent the wasting of water. As a result, it is known that for open channels, modern techniques use both linear cross-sections (trapezoidal, rectangular, and triangular) as well as curved cross-sections (parabolic, semi-elliptic and semi-circular). In addition, taking into-account the construction deficiencies of trapezoidal channels, the industrialisation necessity of the hydro-amelioration and hydro-urban systems, and the hydraulic advantages, compound cross-section channels with flat sides and cylindrical bottom were adopted in engineering practice. Design and operational validation of such cross-sections was and still is an active area of research. Thus, Sarbu and Iosif [87] developed a general analytical model that solves in a unitary manner the complex problems of hydraulic computation for open channels with steady state uniform flow and can be easily programmed and implemented on microcomputers. Starting with some theoretical aspects of optimal hydraulic computation of open channels, the conditions of hydraulically optimal sections were determined for channels with simple curve sections as well as for compound section channels. Sewer columns in buildings take wastewater or conventionally clean water from sanitary objects, industrial containers, terrace receivers, etc., to evacuate it in the external sewerage network, having at the same time the role of ventilating the entire evacuation system. The design of sewer columns in buildings consists in determining the calculation flow rates and their diameters so that, in the given functional and constructive conditions, the evacuation in good conditions of wastewater and meteoric water with rational investment and operation costs is ensured. In the

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current design practice, the diameter of sewer columns for domestic and technological wastewater is chosen only according to the calculation flow rate. Retezan and Sarbu [88] proposed a new computational model for designing the sewer columns, which also takes into account the influence of their height, and for this purpose diagrams and calculation relations were elaborated useful in the design practice.

1.11 Numerical Modelling of Heat Transfer The role of numerical methods is to provide a series of approximate solutions for those cases in which the classical methods of analytical and experimental analysis are inoperative or inefficient. In the last decades, numerical methods have received a special importance and have been enriched with new aspects, due to the appearance and improvement of numerical computers. Numerical modelling of heat transfer has been developed based on three main methods: finite difference method (FDM), finite element method (FEM) and boundary element method (BEM). Sarbu [89] developed two numerical simulation models based on FEM or BEM of conductive thermal fields generated or induced into solid body in steady state. The temperature distribution in some solid bodies and in pipe insulation is analysed using analytical method and FEM or BEM, implemented in two computer programs. The velocity and temperature fields due to laminar forced heat convection in a concentric annular tube with constant heat flux boundary conditions have been also studied [90] using numerical simulations. The dual reciprocity method (DRM) has been used to solve the governing equation, which is expressed in the form of a Poisson equation. A test problem was employed to verify the DRM solutions with different boundary element discretisations and numbers of internal points, and the results of the numerical simulations were discussed and compared with exact analytical solutions. Sarbu and Kalmar [91] developed a mathematical model for numerical simulation of changes in time along the pipe of ice layer formed inside outdoor pressurised pipes, under-non-stationary atmospheric regime and provided some numerical examples. This model can be used for obtaining economical solutions of the problem to protect these pipes from frost. To solve certain research-design problems specific to building services engineering, the author developed a number of computer programs in the FORTRAN programming language, implemented on personal computer (PC) microsystems and grouped in 5 packages [92]: AQUA (Water supply and sewerage installations), SANITGA (Sanitary and gas installations), TERMIC (Heating systems), FRIGO (Refrigeration systems), and CLIVENT (Air conditioning and ventilation systems). It can be concluded that the numerous studies and fundamental and advances researches performed by the author and above mentioned have had significant contributions to the advances in building services engineering, which can be grouped into the following categories:

1.11 Numerical Modelling of Heat Transfer

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• Energy optimisation of buildings by promoting new solutions with highperformance heating systems and modern equipment that simultaneously achieve energy savings and increase comfort and ensure normal air quality in rooms. • Energy analysis, modelling and optimisation of DHSs and low-temperature heat distribution systems in buildings. • Improving the energy performance of refrigeration and air-conditioning systems focusing on vapour compression-based systems with ecological refrigerants, optimal design of the insulation of these systems, and achievement and implementation of an air–water mist cooled system for the air-cooled chillers of different VAC systems • Utilisation of renewable energies such as solar heating and cooling systems for buildings and geothermal heat pumps, especially solar thermal heating systems and solar sorption and thermoelectric cooling systems, respectively GCHPs. • Analysis of TES technologies focused on LHS systems associated with PCMs for use in solar heating/cooling of buildings, solar water heating, and HP systems. • Hydraulic simulation and optimisation of water transmission and distribution systems including the development of new, high-performance models for hydraulic analysis of looped distribution networks using variational formulations, original models for optimising design and choosing their optimal route using deterministic methods such as linear, non-linear and dynamic programming, as well as proposing solutions to optimise the energy efficiency of these systems (zoning procedures, potential elements). • Improving the energy efficiency of pumping in a water or heat distribution system using variable-speed pumps and proposing a formula to calculate the efficiency of a variable speed pump when its operating point is altered. • Designing local and for small localities sewage treatment plants, and developing a generalised model for hydraulic calculation of complex open channels and vertical sewer columns in buildings. • Numerical modelling, simulation and application of computerised calculation, using both classical and modern numerical methods with finite and boundary elements, implemented in original computer programs, as well as the commercial software TRNSYS for transient system simulation. This book is a comprehensive and consistent overview, systematised in a unitary and clear manner, of the author’s original theoretical, experimental and numerical studies bringing together multiple strands of research in building services engineering domain with diverse subjects, guided by two important features such as energy savings and reduction of the pollutant emissions especially in recent decades. It is based on the numerous articles written alone or in collaboration and published in various journals and proceedings of international conferences indexed in Clarivate Analytics/Web of Science or other international databases along with other book chapters published by prestigious international publishers such as Elsevier, Springer and Nova Science Publishers. The book is structured to make it easy to refer to, and is written in an easy to understand manner.

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References 1. Sarbu I, Bura H (2004) Considerations on the energetic balance of a building. Sci Bull Polytech Univ Timisoara 50(2):5–12 2. Sarbu I, Sebarchievici C (2011) Olfactory comfort assurance in buildings. In: Mazzeo N (ed) Chemistry, emission control, radioactive pollution and indoor air quality. InTech, Rijeka, Croatia, pp 407–428 3. Huang YC, Chu CL, Lee SNC, Lan SJ, Hsieh CH, Hsieh YP (2013) Building users’ perceptions of importance of indoor environmental quality in long-term care facilities. Build Environ 67:224–230 4. EN ISO 7730 (2005) Moderate thermal environment—determination of the PMV and PPD indices and specification of the conditions for thermal comfort. International Organisation for Standardisation, Geneva 5. Sarbu I, Sebarchievici C (2013a) Aspects of indoor environmental quality assessment in buildings. Energy Build 60(5):410–419 6. Sarbu I, Pacurar C (2015a) Experimental and numerical research to assess indoor environment quality and schoolwork performance in university classrooms. Build Environ 93(11):141–154 7. Sarbu I, Pacurar C (2015b) Assessment of indoor environment quality and schoolwork performance in university buildings. In: Mills H (ed) Environmental quality and human health. Nova Science Publishers, New York, pp 1–40 8. Laajalehto T, Kuosa M, Makila T, Lampinen M, Lahdelma R (2014) Energy efficiency improvements utilising mass flow control and a ring topology in a district heating network. Appl Therm Eng 69(1–2):86–95 9. Sarbu I (2010) Energetically analysis of unbalanced central heating systems. In: Proceedings of the 5th IASME/WSEAS International Conference on Energy and Environment, pp 112–117. Cambridge, UK 10. Sarbu I, Marza M, Crasmareanu E (2019) A review of modelling and optimisation techniques for district heating systems. Int J Energy Res 43(13):6572–6598 11. Sarbu I, Marza M, Crasmareanu E (2017) Comprehensive review on modelling and optimisation of district heating systems. In: Proceedings of the 17th international multidisciplinary scientific GeoConference SGEM 2017, Section Renewable Energy Sources and Clean Technologies, pp 1314–2704. Albena, Bulgaria, 27 June–6 July 2017 12. Sarbu I, Brata S (1994) Optimal design of district heating networks. In: Proceedings of the 14th Hungarian conference on district heating, pp 112–117. Debrecen, Hungary 13. Sarbu I, Marza M, Crasmareanu E (2020) Optimisation of district heating systems using heuristic methods: a review. In: Proceedings of the Romanian Academy, series a—mathematics, physics, technical sciences, information science 21(4):1–10 14. Andersen N (1999) End users dictate the potential for low temperature district heating. Energy Environ J 4:30–31 15. Sarbu I, Bancea O, Cinca M (2009) Influence of forward temperature on energy consumption in central heating systems. WSEAS Trans Heat Mass Transfer 4(3):45–54 16. Sarbu I, Kalmar F, Cinca M (2007) Thermal building equipments: energy optimisation and modernisation. Polytechnic Publishing House, Timisoara (in Romanian) 17. Sarbu I, Sebarchievici C (2015a) A study of the performances of low-temperature heating systems. Energ Effi 8(3):609–627 18. Sarbu I, Marza M, Crasmareanu E (2017) Performance of radiant heating systems of low-energy buildings. Mater Sci Eng 245:art. 032088 19. Sarbu I (2014a) Influence of heating systems on indoor environmental quality. Appl Mech Mater 510:208–214 20. Sarbu I, Popina O (2004) Design of the interior heating networks. Sci Bull Polytech Univ Timisoara 50(2):25–29 21. Sarbu I (2003a) Regulation devices for heating systems in buildings (I). Installer J 1:4–7 22. Sarbu I (2003b) Regulation devices for heating systems in buildings (II). Installer J 2:23–26

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23. Sarbu I, Valea ES (2010) Comparative characterization of plastic tubes for building installations. Metalurgia Int 15(9):11–18 24. Sarbu I, Valea ES (2014a) Fluids temperature regulation using self-adjustable cables. Adv Mater Res 909:202–207 25. Sarbu I, Sebarchievici C (2016a) Ground-source heat pumps: fundamentals, experiments and applications. Elsevier, Oxford, UK 26. Sarbu I (1999) Rotary screw compressors. Installer J 6:57–60 27. Choudhari CS, Sapali SN (2017) Performance investigation of natural refrigerant R290 as a substitute to R22 in refrigeration systems. Energy Proc 109:346–352 28. Schulz M, Kourkoulas D (2014) Regulation (EU) No 517/2014 of The European parliament and of the council of 16 April 2014 on fluorinated greenhouse gases and repealing regulation (EC) No 842/2006. Official J Eur Union 2014:L150 29. Heath EA (2017) Amendment to the Montreal protocol on substances that deplete the ozone layer (Kigali amendment). Int Legal Mater 56:193–205 30. Raabe G (2019) Molecular simulation studies on refrigerants: past—present—future. Fluid Phase Equilib 485:190–198 31. Sarbu I (2014b) A review on substitution strategy of non-ecological refrigerants from vapour compression-based refrigeration, air-conditioning and heat pump systems. Int J Refrig 46(10):123–141 32. Sarbu I, Valea ES (2014b) Past, present and future perspective of refrigerant in air-conditioning, refrigeration and heat pump applications. WSEAS Trans Heat Mass Transfer 9:27–38 33. Sarbu I, Valea ES, Sebarchievici C (2010) Use of recovered thermal energy from refrigerating systems. Energetica 58(6):301–305 34. ASHRAE (2009) Fundamentals handbook. American Society of Heating, Refrigerating and Air-Conditioning Engineers, Atlanta, GA 35. Sarbu I, Valea ES, Ostafe G (2014) Optimisation of insulation design for refrigerating systems. Appl Mech Mater 510:202–207 36. Sarbu I, Kalmar F (2000) Calculation model of soil freezing columns. In: Proceedings of the 19th national conference on modern science and energy, pp 148–156. Cluj Napoca, 15–17 May 37. Sarbu I, Borza I (1999) Study on the frost self-protection of cooling towers. Period Polyteh Mech Eng 43:37–46 38. Perez-Lombard OJ, Pout, C (2008) A review on buildings energy consumption information. Energy Build 40(3):394–398 39. Sarbu I, Adam M (2014) Experimental and numerical investigations of the energy efficiency of conventional air-conditioning systems in cooling mode and comfort assurance in office buildings. Energy Build 85(12):45–58 40. Sarbu I, Adam M (2016) Investigation of the energy efficiency of conventional air-conditioning systems in office buildings. In: Acosta MJ (ed) Advances in energy research, vol 23. New York. USA, Nova Science Publishers, pp 161–196 41. Muresan A, Attia S (2017) Energy efficiency in the Romanian residential building stock: A literature review. Renew Sustain Energy Rev 74:349–363 42. Sarbu I, Sebarchievici C (2017a) Solar heating and cooling systems: fundamentals, experiments and applications. Elsevier, Oxford, UK 43. Sarbu I, Adam M (2011) Applications of solar energy for domestic hot-water and buildings heating/cooling. Int J Energy 5(2):34–42 44. Sarbu I, Tokar D (2018) Solar water and space heating systems. In: Proceedings of the 18th international multidisciplinary scientific GeoConference SGEM 2018, Section energy sources and clean technologies, pp 635–642. Albena, Bulgaria, 30 June–6 July 2018 45. Sarbu I, Sebarchievici C (2013b) Review of solar refrigeration and cooling systems. Energy Build 67(12):297–308 46. Sarbu I, Sebarchievici C (2015b) General review of solar-powered closed sorption refrigeration systems. Energy Convers Manage 105(11):403–422 47. Sarbu I, Dorca A (2018) A comprehensive review of solar thermoelectric cooling systems. Int J Energy Res 42(2):395–415

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48. Sarbu I, Sebarchievici C (2014) General review of ground-source heat pump systems for heating and cooling of buildings. Energy Build 70(1):441–454 49. Sarbu I, Dan D, Sebarchievici C (2014) Performances of heat pump systems as users of renewable energy for building heating/cooling. WSEAS Trans Heat Mass Transfer 9:51–62 50. Sarbu I, Sebarchievici C. Performance evaluation of radiator and radiant floor heating systems for an office room connected to a ground-coupled heat pump. Energies 2016;9(4),art. 2287:1– 19. 51. Sarbu I, Sebarchievici C (2016b) Using ground-source heat pump systems for heating/cooling of buildings. In: Ismail BI (ed) Advances in geothermal energy. InTech, Rijeka, Croatia, pp 1–36 52. Sebarchievici C, Sarbu I (2015) Performance of an experimental ground-coupled heat pump system for heating, cooling and domestic hot-water operation. Renew Energy 76(4):148–159 53. Sarbu I, Sebarchievici C (2015c) Numerical and experimental analysis of the ground-coupled heat pump systems. In: Acosta MJ (ed) Advances in energy research, vol 22. New York. USA, Nova Science Publishers, pp 75–110 54. Sarbu I, Sebarchievici C, Dorca A (2017) Simulation of ground thermo-physical capacity for a vertical closed-loop ground-coupled heat pump system. In: Proceedings of the 17th international multidisciplinary scientific GeoConference SGEM 2017, pp 557–565. Albena, Bulgaria, 27 June–6 July 2017 55. Sarbu I, Bura H (2010) Vapourisation thermal power assurance for vertical closed-loop ground-coupled heat pump systems. In: Proceedings of the 8th WSEAS international conference on environment, ecosystems and development, advances in biology, bioengineering and environment, pp 125–130. Vouliagmeni, Athens, Greece, 29–30 December 2010 56. Sarbu I, Sebarchievici C (2018) A comprehensive review of thermal energy storage. Sustainability 10(1), art. 191:1–32 57. Sarbu I, Sebarchievici C (2017b) Solar thermal energy storage. In: Acosta MJ (ed) Advances in energy research, vol 27. New York. USA, Nova Science Publishers, pp 63–122 58. Sarbu I, Dorca A (2019) Review of heat transfer analysis in thermal energy storage using heat storage systems and phase change materials. Int J Energy Res 43(1):29–64 59. Qureshi ZA, Ali HM, Khushnood S (2018) Recent advances on thermal conductivity enhancement of phase change materials for energy storage system: a review. Int J Heat Mass Transf 127:838–856 60. Sarbu I, Tokar A (2018) Water distribution systems: numerical modelling and optimisation. Polytechnic Publishing House, Timisoara, Romania 61. Sarbu I (2014c) Nodal analysis of urban water distribution networks. Water Resour Manage 28(10):3159–3175 62. Sarbu I, Valea ES (2011) Analysis of looped water distribution networks using variational formulations. Metalurgia Int 16(1):48–53 63. Sarbu I (1996) General model for the analysis of water distribution networks. In: Proceedings of the national conference on building services and ambient comfort, pp 96–101, 16–18 April 1996 64. Sarbu I, Ostafe G (2014) Determination of neutral point in distribution network pipes with variable discharge on route. Adv Mater Res 909:428–432 65. Sarbu I (2016) Hydraulic analysis of a recycled technological water supply network. J Eng Appl Sci 11(7):4526–4532 66. Sarbu I, Ostafe G, Valea ES (2013) Optimisation of technological water consumption for an industrial enterprise with self-supply system. Lecture Notes Electr Eng 2:843–847 67. Sarbu I (1997) Energetically optimisation of water distribution systems. Romanian Academy Publishing House, Bucharest (in Romanian) 68. Sarbu I, Valea ES (2014) Optimisation of path for water transmission and distribution systems. In: Yang G-C, Ao S-I, Huang X, Castillo O (ed) Transaction on engineering technologies, vol 275. Springer, Heidelberg, Germany 69. Sarbu I (2005) Optimisation of the discharges distribution in water supply networks. Hydrotechnics 50(6):15–19

References

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70. Sarbu I (2020) Optimisation models of looped urban water supply networks. In: Advances in engineering research, vol 36, 95–148. Nova Science Publishers, New York, pp 95–148 71. Sarbu I, Kalmar F (2002) Optimisation of looped water supply networks. Period Polytech Mech Eng 46(1):75–90 72. Sarbu I, Ostafe G (2016) Optimal design of urban water supply pipe networks. Urban Water J 13(5):551–535 73. Sarbu I, Popa-Albu S, Tokar A (2020) Multi-objective optimisation of water distribution networks: an overview. Int J Adv Appl Sci 7(11):74–86 74. Sarbu I (2009) Procedures and solutions for energetically optimization of water distribution systems. Tech Bull Debrecen Univ 1(2):35–42 75. Sarbu I (2016) A study of energy optimisation of urban water distribution systems using potential elements. Water 8(12), art.593:1–19 76. Constantin A, Nitescu CS (2019) Considerations on water supply pumping station operation in the context of sustainable development. Earth Environ Sci 222: art.012002 77. Sarbu I, Valea ES (2015) Energy savings potential for pumping water in district heating stations. Sustainability 7(5):5705–5719 78. Sarbu I, Borza I (1998) Energetic optimization of water pumping in distribution systems. Period Politech Mech Eng 42:141–152 79. Marchi A, Simpson AR, Ertugrul N (2012) Assessing variable speed pump efficiency in water distribution systems. Drink Water Eng Sci 5:47–65 80. de Abreu Costa JN, de Castro MAH, Costa LHM, Barbosa JMC (2018) New formula proposal for the determination of variable speed pumps efficiency. Brazilian J Water Resour 23:1–11 81. Pérez-Sánchez M, López-Jiménez PA, Ramos HM. Modified affinity laws in hydraulic machines towards the best efficiency line. Water Resour Manage 32:829–844 82. Simão M, Ramos HM (2019) Micro axial turbine hill charts: affinity laws, experiments and CFD simulations for different diameters. Energies 12, art.2908:1–16 83. Sarbu I, Tokar A. Numerical simulation of unsteady flow in water supply pipe networks. Annals Faculty Eng Hunedoara Int J Eng 16(3):17–26 84. Sarbu I, Filip A (2015) Efficient plants and procedures for wastewater treatment. J Water Resour Hydraulic Eng 4(3):279–285 85. Sarbu I (1989) Installation for water purification, patent no. RO100299, OSIM Bucharest 86. Sarbu I, Filip A (2017) Designing a pilot sewage treatment plant for small localities. In: Proceedings of the 17th international multidisciplinary scientific GeoConference SGEM 2017, pp 227–283.. Albena, Bulgaria, 27 June – 6 July 2017 87. Sarbu I, Iosif A (2018) A general analytical model for hydraulic computation of open channels with steady state uniform flow. Int J Adv Appl Sci 5(1):1–7 88. Retezan A, Sarbu I (1986) Considerations on the sizing of sewer columns. Constructions 9(10):68–70 89. Sarbu I (2011) Numerical modelling of two dimensional heat transfers in steady state regime. Int J Energy Environ 5(3):435–443 90. Sarbu I, Iosif A (2017) Numerical simulation of the laminar forced convective heat transfer between two concentric cylinders. Computations 5(2), art.593:1–19 91. Sarbu I, Kalmar F (2001) Numerical simulation and prevention of water freezing in outdoor penstocks. J Hydraul Res 39(4):258–270 92. Sarbu I, Kalmar F (2000) Computer aided design of building equipment. Mirton Publishing House, Timisoara (in Romanian)

Chapter 2

Assurance of Indoor Environment Quality in Buildings

Abstract This chapter approaches several aspects of assessing the IEQ and human performance in buildings with different destinations. Thus, a computation and testing model of thermal comfort in buildings based on predicted mean vote (PMV)— predicted percent dissatisfied (PPD) indices, a computational model for indoor air quality (IAQ) numerical simulation, as well as a methodology to determine the outside air flow rate and to verify the IAQ in rooms are developed. Additionally, the thermal comfort is assessed based on the PMV-PPD indices using subjective and experimental measurements in two air-conditioned classrooms at a university, where the air-exchange rate is assured by natural ventilation. To estimate academic performance depending on air temperature, classroom air relative humidity and CO2 concentration in three simple Gaussian correlations are developed using twelve data sets containing the concentrated and distributive attention tests for students. Finally, a simulation model in the Transient System Simulation (TRNSYS) program of the PMV-PPD indices and heating/cooling energy demand for an amphitheatre with natural ventilation is developed.

2.1 Generalities Energy consumption of buildings depends significantly on the criteria used for the indoor environment and building design and operation. Reducing energy consumption in buildings is one of the main current directions of research in building constructions. An important part of household energy consumption is necessary to achieve, in living spaces, indoor microclimate parameters. Therefore, is particularly the important achievement of structural elements, building equipments and operating modes to allow getting both adequate comfort parameters and energy saving. The greatest majority of people carry on 80-90% of their lives inside buildings, which must satisfy the objective and subjective requests linked to vital functions of the occupants. That is why the enclosed spaces must insure the possibility for both physical and intellectual work, as well as for some recreation activities, for rest and sleep under most favourable conditions. The achievement of these conditions

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 I. Sarbu, Advances in Building Services Engineering, https://doi.org/10.1007/978-3-030-64781-0_2

25

26

2 Assurance of Indoor Environment Quality in Buildings

Fig. 2.1 Comfort sensation

depends on very many factors that decisively influence the sensation of comfort perceived, the work capacity and man’s regeneration capacity. The environmental factors that define the indoor environment quality (IEQ) are: thermal comfort, indoor air quality (IAQ) or olfactory comfort, acoustic comfort and visual comfort. The perception and appreciation of basic comfort elements to man are influenced by some psychological factors, but at the same time evolution and man’s psychological equilibrium are closely linked with the environment. So, between psychological and technical comfort is a reciprocal connection. Human psyche depends also on other independent factors like: age, gender, etc., influencing the technical comfort level appreciation. So pleasant sensation may occur as a result of optimum technical and psychological comfort parameters (Fig. 2.1). This chapter approaches several aspects of assessing the IEQ and human performance in buildings with different destinations.

2.2 Comfort and Indoor Air Quality Assessment in Closed Spaces 2.2.1 Preliminary Considerations In existing and future buildings there will be an increasing focus on energy uses and IEQ. Energy consumption of buildings depends significantly on the criteria used for the indoor environment (temperature, ventilation and lighting) and building design and operation. Indoor environment also affects health, productivity and comfort of the occupants. Recent studies have shown that costs of poor indoor environment for the employer, the building owner and for society, as a whole are often considerably higher than the cost of the energy used in the same building [1]. The design of the closed spaces must take into consideration these conditions and present tendencies to reduce the energy consumption that is decisively influencing the optimal or admissible values of comfort parameters. Thus, the inside microclimate of

2.2 Comfort and Indoor Air Quality Assessment in Closed Spaces

27

a building must be the result of a computation of multicriterial optimisation, taking into account technical and psychological comfort and the energy saving. The environmental factors that define the indoor environmental quality are: thermal comfort, IAQ, acoustic comfort, and visual comfort. In accordance with the dissatisfied person percent of the ensured comfort: 10%, 20% and 30%, rooms are classified into three categories: A, B and C. Subjective comfort of persons in a closed space depends on many factors: temperature, humidity and air circulation; smell and respiration; touch and touching; acoustic factors; sight and colours effect; building vibrations; special factors (solar-gain, ionisation); safety factors; economic factors; unpredictable risks. Because of some technical conditions the common influence of these factors can not be analysed, and the adaptation of the human body to a certain environment is a complex process, this one reacting to the common action of more parameters. In general nationally specified criteria for design of heating systems must be used, but in case of no national regulations international standards give values for thermal comfort in informative annexes. The recommended criteria are given for general thermal comfort based on predicted mean vote (PMV)— predicted percent dissatisfied (PPD) model or operative temperature and for local thermal comfort parameters like vertical temperature differences, radiant temperature asymmetry, draft and surface temperatures. Such requirements can be found in existing standard and guidelines. In this section, a comfort analysis and assessment in buildings is performed starting from a general description of the comfort fundamental components (thermal, olfactory, acoustic and visual comfort) [2]. Thus, a computation and testing model of thermal comfort in buildings based on PMV-PPD indices, a computational model for indoor air quality (IAQ) numerical simulation, as well as a methodology to determine the outside air flow rate and to verify the IAQ in rooms, according to the European standard CEN 1752 [3] are developed. Additionally, the thermal comfort criteria for design of heating systems, the relationship between thermal environment and human performance, as well as the influence of carbon dioxide (CO2 ) on human performance and productivity are also discussed [4].

2.2.2 Fundamental Components of the Comfort 2.2.2.1

Thermal Comfort

The subjective sensation of thermal comfort is decisively determined by the following parameters [5]: indoor air temperature (t i ); mean radiant temperature (t mr ) of bordering surfaces; relative humidity of air (ϕi ); partial water vapours pressure (pa ); air velocity (vi ); thermal resistance of clothing (Rcl or Rh ) and their influence on the vaporisation; heat production of human body and human thermoregulation. The first four are physical parameters, and the other two express the capacity of the human

28

2 Assurance of Indoor Environment Quality in Buildings

body to adapt it in order to maintain the thermal equilibrium. The main factors that influence the thermal equilibrium of the human body are: • Heat production of human body, which depends on the activity level, age, sex. • Body heat loss, which depends on clothing and on the other parameters mentioned previously. In general, comfort is gained when body temperatures are held within narrow ranges, skin moisture is low, and the physiological effort of regulation is minimised. Surprisingly, although climates, living conditions and cultures differ widely throughout the world, the temperature that people choose for comfort under similar conditions of clothing, activity, humidity, and air movement has been found to be very similar [6–8]. To evaluate the sensation of thermal comfort we use the thermal sensation scale with seven levels [9]: +3 (hot); +2 (warm); +1 (slightly warm); 0 (neutral); −1 (slightly cool); −2 (cool); −3 (cold).

2.2.2.2

Olfactory Comfort

Comfort and IAQ depend on many factors, including thermal regulation, control of internal and external sources of pollutants, supply of acceptable air, occupant activities and preferences and proper operation and maintenance of building systems. Ventilation and infiltration are only part of the acceptable IAQ and thermal comfort problem. The condition to achieve human body metabolism in a enclosed space is oxygen (O2 ) taking and CO2 releasing. After respiration process air reaches the lungs through upper and lower airways. Upper airways filter the inspired air, while providing to it the proper temperature and humidity. The oxygen is transported from the lungs to tissues through blood that carry back the CO2 . Expired CO2 flow rate is illustrated in Table 2.1. Air composition in living spaces differs from that of the outside air. CO2 concentration in outside air is between 300 and 400 ppm, and in living spaces is about 900 ppm. The maximum admitted limit of CO2 concentration in the inhaled air is 1000 ppm (Pettenkofer’s number). Table 2.2 presents the effect of different CO2 concentrations on human body. Table 2.1 Expired CO2 flow rate Activity

M [W/pers] Inspired air [m3 /h] Expired CO2 [l/h] Consumed O2 [l/h]

Sedentary

–

0.30

12

14

Intellectual

120

0.375

15

18

Physical very easy 150

0.575

23

27

Physical easy

190

0.75

30

35

Physical hard

>270

>0.75

>30

>35

2.2 Comfort and Indoor Air Quality Assessment in Closed Spaces

29

Table 2.2 The effect of CO2 concentration on human body CO2 concentration

Effect

[%]

[ppm]

3

30000

Deep breathing, strong

4

40000

Headaches, pulse, dizziness, psychic emotions

5

50000

After 0.5−1.0 h may cause death

8−10

80000−100000

Sudden death

Air quality is prevailingly determined by people’s sensations to different odorants. Because it is impossible to be measured each of the air contaminants quantitatively and qualitatively (about 8000), Fanger proposed that all these compounds are to be measured by one parameter: the odour. The odours arise in inhabited areas by the release of the human body (ammonia, methan, fatty acids), emanations of the furniture, carpets, paintings and other building materials (formaldehyde), by combustion and heating processes (carbon monoxide, fuel vapour), by exhaust gas polluted air infiltration or air from industrial areas, meal preparation, toilettes areas, mold chemical reactions, mushrooms or any decomposition products. Most of these unpleasant products are made of complex organic substance. Excitation level in confront of some odours is very low. For example, mercaptan odour is perceived starting from a concentration of 0.00000004 mg/l. The olfactory organ’s main feature is adaptation. After a while, due to continuous charging, sensation of smell intensity decreases (Fig. 2.2). A large number of pollutants come a time in the air with tobacco smoke. This affects the eyes, the nose and it is a risk factor for different diseases. Reduce air pollution by tobacco smoke can not be done only by increasing the air exchange rate. Thus, to annihilate the negative feelings created by smoking one cigarette are requested 100 m3 of fresh (outside) air. Fig. 2.2 Time evolution of odour intensity

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2 Assurance of Indoor Environment Quality in Buildings

Fig. 2.3 Variation of CO concentration

Along with tobacco smoke in the air reaches carbon monoxide (CO). Maximum CO concentration permissible values, given by international prescriptions, are 10 mg/m3 for housing spaces and 20 mg/m3 for kitchen and ancillary areas (3 h maximum residence time). Figure 2.3 illustrates the variation of CO concentration depending on smoked cigarettes number and fresh air flow rate introduced into the room. The smoking weighty influences the CO content of expired air, whose values are indicated in Table 2.3 Sometimes IAQ scientists can not successfully resolve complaints about air in offices, schools and other non-industrial environments. Customarily, complaints are attributed to elevated pollutant concentrations; frequently, however, such high concentrations are not found, yet complaints persist. Assuming that the inability to find a difference between air pollutant levels in buildings with registered complaints and those without complaints is due to inadequacies of pre-vailing measurement techniques, Fanger [10] changed the focus from chemical analysis to sensory analysis. He quantified air pollution sources by comparing them with a well-known source: a sedentary person in thermal comfort. A new unit, the olf , was defined as the emission rate of air pollutants (bio-effluents) from a standard person. A decipol (dp) is one olf ventilated at a rate of 10 l/s of unpolluted air. Table 2.3 Average values of CO concentration in expired air

No.

Category

CO concentration [mg/m3 ] Male

Female

1

Nonsmoker

7.1

5.8

2

Former smoker

7.8

6.5

3

Cigar and pipe smoker

9.6

12.0

4

Tobacco smoker

24.3

21.1

2.2 Comfort and Indoor Air Quality Assessment in Closed Spaces Table 2.4 Sensory pollution load from different pollution sources

31

No.

Source

Sensory load

1

Sedentary person (1−1.5 met)

1 olf

2

Person exercising low level (3 met)

4 olf

3

Person exercising medium level (3 met)

10 olf

4

Children, kindergarten (3−6 yrs)

1.2 olf

5

Children, school (4−16 yrs)

1.3 olf

6

Low-polluting building

0.1 olf/m2

7

Non-low polluting building

0.2 olf/m2

Fig. 2.4 PPD as a function of ventilation rate per standard person (i.e., per olf)

The idea behind the olf is to express both human and nonhuman sensory sources in a single unit: equivalent standard persons (i.e., in olfs). A room should therefore be ventilated to handle the total sensory load from persons and building. Table 2.4 shows the sensory loads from different pollution sources used in standard CEN 1752. The sensory load on the air in a space can be determined from Fig. 2.4 by measuring the outside air flow rate and determining the per cent dissatisfied, using an untrained panel with a minimum of 20 impartial persons [11]. The required outside air flow rate depends on the desired percentage of occupant satisfaction. Various factors make odour control an important consideration in ventilation engineering: • Contemporary construction methods result in buildings that allow less air infiltration through the building envelope. • Indoor sources of odours associated with modern building materials, furnishings, and office equipment have increased. • Outdoor air is often polluted. • Energy costs encourage lower ventilation rates at a time when requirements for a relatively odour-free environment are greater than ever.

32

2.2.2.3

2 Assurance of Indoor Environment Quality in Buildings

Acoustic Comfort

Another key element contributing to the overall comfort in an enclosed space is acoustic comfort. The difference between the notions of sound and noise should be made. Thus, the notion of sound has several definitions, depending on the purpose of interpretation. If sound is considered a physical phenomenon, then it represents the elementary vibration of elastic matter which spreads as wave in transport medium. The concept of sound can have the sense of external excitement of creature’s auditory organ, which leads to different reactions from them. Perceptible sound field to human is illustrated in Fig. 2.5. The third sense of the sound concept is aesthetic and understanding effect. From this point of view the sound has a coded form information content, that the brain decodes it and the correct perception of sound crucial influence the human comfort. The main element of relationship between people is speaking and any event that disturbs the understanding it creates uncertainty and with this the discomfort. So there are sound effects, negatively perceived by human, called noises and they are indistinguishable by sound after the first two definitions. The difference between them is made by human through the given interpretation. From researches performed in medical science it is known that the noises act on the autonomic nervous system. Nervous system reflex response is strangling noises capillaries. Increased blood flow resistance does not involve the increase of heart beatings. This leads to a decrease blood flow rate that determines the amount reduction of oxygen transported to cells. Reduced amount of oxygen is manifested by various symptoms such as headaches, migraines, decreased concentration, blurred vision, etc. The negative effect of the arterial system bottleneck is felt especially during sleep when the body functions are reduced to a minimum. If in this state the body is subjected to the effect of noise, then reduce the amount of oxygen that feeds Fig. 2.5 Range of human audibility with normal hearing

2.2 Comfort and Indoor Air Quality Assessment in Closed Spaces

33

Table 2.5 Acceptable interior noise level, according to CEN 1752 Room destination

Noise level [dB (A)]

Room destination

Small offices A

30

B

35

Restaurant rooms

C

40

Large offices A

35

B

40

C

45

A

30

B

35

C

40

Study rooms A

30

B

33

C

35

Conference rooms

Category

Classrooms

Kindergaertens

Deposits

Category

Noise level [dB (A)]

A

35

B

45

C

55

A

30

B

35

C

40

A

30

B

40

C

45

A

40

B

45

C

50

the cells causes lengthening the period of regeneration. It was shown that frequent sleep disturbances lead to nervousness, loss of efficiency, fatigue and nervous system degeneration. Also, intellectual activity done in terms of high noise level the yield is particularly low. Acceptable interior equivalent noise level, according to prescriptions of the European standard CEN 1752, is shown in Table 2.5.

2.2.2.4

Visual Comfort

Human life is closely connected with the visual environment, because the information is collected at a rate of 90% within sight, and activity is also linked to vision in most cases. The visual comfort is conscious state, which occurs due to physiological and psychological actions, expressing satisfaction with the environment. Visual environment in an enclosed space appears if it is illuminated and has two components: (1) the room delimited by opaque or transparent surfaces (passive component); (2) the light that makes the room visible (active component). Human perceives only the light reached in the eyes. Thus, are seen only the surfaces that send light in the observer’s eye. Usually those are opaque surfaces (walls, floors, furniture, etc.). The surfaces that allow natural light (windows, skylights, etc.) have a particular importance because: – glased and opaque surfaces do not create the same visual environment; – usually the visual environment does not coincide with built interior space.

34

2 Assurance of Indoor Environment Quality in Buildings

Fig. 2.6 Relation between lighting level, lighting temperature and visual comfort

In function on the room destination there are requirements for visual environmental characteristics which can be divided as follows: • The information about certain parts of the space has to be accurate. • The visible space must not create discomfort (visual disturbance). Accurate vision means also the right colours perception. They are regarded as suitable if they coincide with the colours seen in natural light, hence the need for natural lighting. For artificial lighting, the source light quality can be differentiated from the point of view of body natural colours reveling. So if the bodies colour lighted with artificial source corresponds to their natural colour when colour rendering is perfect, otherwise the color rendering is more or less good. The visual comfort sensation represents the concordance between lighting and the quality of light, characterised by light colour or its temperature. The color pleasant effect refers to the fact that a less lighting ambient presents visual comfort if is the result of a rich warm colour and a lighted ambient presents visual comfort if is the result of cold light. In terms of colour rendition, the visual comfort can be analysed in the base of Kruithoff charts that presents the variation of lighting E with light temperature T (Fig. 2.6). So, a light source with temperature T * can create different observer sensations depending of lighting value: • For E < E *a , the lighting is perceived as cold. • For E *a < E < E *f , the visual comfort conditions are satisfied. • For E > E *f , the lighting is perceived as artificial (disturbing). For a given value of lighting E ** , created subjective visual sensation depends on light temperature: artificial lighting at T I , visual comfort at T II and cold lighting at T III .

2.2 Comfort and Indoor Air Quality Assessment in Closed Spaces

2.2.2.5

35

Sick Building Syndrome

Concern about the health effects associated with indoor air dates back several hundred years, and has increased dramatically in recent decades. This attention was partially the result of increased reporting by building occupants of complaints about poor health associated with exposure to indoor air. Since then, two types of diseases associated with exposure to indoor air have been identified: sick building syndrome (SBS) and building related illness (BRI). The people with their activity in buildings with large glazed exterior surfaces, equipped with complex building climatisation systems (commercial areas, office buildings, etc.) are affected by SBS. Sick building syndrome describes a number of adverse health symptoms related to occupancy in a “sick” building, including mucosal irritation, fatigue, headache and, occasionally, lower respiratory symptoms and nausea. There is no widespread agreement on an operational definition of SBS. Some authors define it as acute discomfort (e.g., eye, nose, or throat irritation; sore throat; headache; fatigue; skin irritation; mild neurotoxic symptoms; nausea; building odours) that persists for more than two weeks at frequencies significantly greater than 20%. In Figs. 2.7 and 2.8 are presented the main symptoms of the “sick” building for their occupants and also the consequences of these ones. The most common causes of SBS are thermal comfort and inadequate air quality. The increased prelevance of health complaints among office workers is typical of sick building syndrome [12]. The widespread occurrence of these symptoms has prompted the World Health Organisation to classify SBS into several categories [13]: – – – –

sensory irritation in the eyes, nose, or throat; skin irritation; neurotoxic symptoms; odor and taste complaints.

Fig. 2.7 The “sick” building symptoms distribution

36

2 Assurance of Indoor Environment Quality in Buildings

Fig. 2.8 Causes of sick building syndrome

Some investigations have sought to correlate SBS symptoms with reduced neurological and physiological performance. In controlled studies, SBS symptoms can reduce performance in susceptible individuals [14]. Research performed on the basis of questionnaires on a sample of 4000 people (43.1% men and 56.9% women) with their activity in a Frankfurt administrative building revealed the following discomfort factors [15]: indoor climate (65.4%); noises (32.7%); non-corresponding lighting (25.5%); tobacco smoke (24.7%); small work space (23.9%); overtime work hours (12.8%); stress caused by chief (9.7%); competition (7.1%).

2.2.3 Prediction of Thermal Comfort Numerical prediction of thermal comfort in a room is performed by using the PMV– PPD model, and testing is achieved at asymmetric thermal radiation, caused by building elements with a temperature t el lot different from the mean radiant temperature t mr . Radiant asymmetry is the difference in radiant temperatures seen by a small flat element looking in opposite directions. Four calculation methods of radiant temperature asymmetry are available in technical literature [16].

2.2.3.1

Mathematical Model

Taking into account the thermal interaction of the human body with its environment it is possible to write the well-known energy balance equation: M − W = Q i = (C + R + E sk ) + .(Cr es + Er es )

(2.2.1)

2.2 Comfort and Indoor Air Quality Assessment in Closed Spaces

37

where: M is the rate of metabolic heat production; W is the rate of mechanical work accomplished (zero for most of the activities); Qi is the internal heat production; C, R are the convective and radiant heat losses outer surface of a closed body; E sk is the rate of evaporative heat loss from skin; C res is the rate of evaporative heat loss from respiration; E res is the rate of convective heat loss from respiration. All the terms in the basic heat balance equation are expressed per unit body nude surface area. • Convective heat loss (C) is given by Eq. (2.2.2) and radiant heat loss R is expressed in terms of the Stefan–Boltzmann law (2.2.3): C = f cl αc (th − ti )

(2.2.2)

  R = 3.96 · 10−8 f cl (th + 273)4 − (tmr + 273)4

(2.2.3)

where f cl =

Ah AD

(2.2.4)

A D = 0.202 m 0.425 h 0.725

(2.2.5)

in which t i is the indoor air temperature; t h is the mean temperature of the outer surface of the closed body; t mr is the mean radiant temperature; αc is the convective heat transfer coefficient; f cl is the clothing area factor dimensionless; Ah is the actual surface area of the clothed body; AD is the nude body surface area [17]; m is the mass of human body; h is the height of human body. The sensible heat (C + R) is transferred through conduction from the skin surface to the outer clothing surface: C + R = Qs =

t p − th Rh

(2.2.6)

where Rh = 0.155Rcl

(2.2.7)

in which Qs is the sensible heat loss from skin to outer clothing surface; Rh is the thermal resistance of clothing, in (m2 K)/W; Rcl is the thermal resistance of clothing, in clo; t p is the skin temperature expressed by: t p = 35.7 − 0.032(M − W )

(2.2.8)

38

2 Assurance of Indoor Environment Quality in Buildings

• Evaporative heat loss from skin (E sk ) may be computed with the equation:

E sk = E d + Er sw

(2.2.9)

  E d = 0.35 1.92t p − 25.3 − pa

(2.2.10)

Er sw = 0.42(M − W − 58)

(2.2.11)

where

in which E d is the evaporative heat loss by diffusion of water through the skin; E rsw is the evaporative heat loss by regulatory sweating; pa is the water vapour partial pressure in indoor air. • Respiratory heat loss (C res + E res ) is often expressed in terms of sensible C res and latent E res heat losses. The C res and E res can be computed as follows:

Cr es + Er es = 0.0014M(34 − ti ) + 1.73 · 10−5 M(5870 − ps )

(2.2.12)

where ps is the saturated water vapour pressure at the humid operative temperature. The body’s mechanical efficiency is defined by: η=

W M

(2.2.13)

The energy balance Eq. (2.2.1) is under the form: Q ac = M − W − E − (Cr es + Er es ) − (C + R)

(2.2.14)

where Qac is the accumulated heat in body. If Qac = 0, thermal comfort felt by occupants is adequate. When Qac > 0, body temperature rises and the person will have a sense of warmth, and if Qac < 0, body temperature decreases and the person will have a sense of coldness. Writing the energy balance Eq. (2.2.14), for Qac = 0, in the form: M − W − E − (Cr es + Er es ) = Q s = C + R

(2.2.15)

and explaining the terms in it with Eqs. (2.2.2), (2.2.3), (2.2.6), (2.2.9), and (2.2.12), the thermal comfort equation is obtained: M(1 − η) − 0.35[43 − 0.061M(1 − η) − pa ] − 0.42[M(1 − η) − 58]−

2.2 Comfort and Indoor Air Quality Assessment in Closed Spaces

39

35.7 − 0.032M(1 − η) − th = 0.155T Rcl = f cl αc (th − ti ) − 3.96 · 10−8 f cl [(th + 273)4 − (tmr + 273)4 ] (2.2.16)

−0.0014M(34 − ti ) − 0.0023M(44 − pa ) =

Considering some parameters as constant in Eq. (2.2.16), after it is solved and the solutions graphically represented the comfort diagrams are obtained. Substituting the thermal comfort Eq. (2.2.16) into expression of PMV index established by Fanger [18], the predicted mean vote index is obtained, for a certain point of the room:   P M V = 0.352 exp(−0.042M) + 0.032 × {M(1 − η) − 0.35[43 − 0.061M(1 − η) − pa ] − 0.42[M(1 − η) − 58] − 0.0023M(44 − pa ) − 0.0014M(34 − ti ) − f cl αc (th − ti ) − 3.96 · 10−8 f cl [(th + 273)4 − (tmr + 273)4 ]}

(2.2.17)

PMV index has the optimum value equal to zero, but according to the prescriptions of standard EN ISO 7730 [19] it is considered that the domain of thermal comfort corresponds to values between −0.5 and +0.5. The use of PMV index is recommended only for values between +2 and−2. In Fig. 2.9 are represented the values of operative comfort temperature t c (corresponding to index PMV = 0), correlated to thermal resistance of clothing (Rcl and Rh ), metabolic rate iM and metabolic heat production M. In Table 2.6 is illustrated the optimal values of operative temperature t c according to building use, summer and winter, according to European standard CEN 1752. The predicted per cent dissatisfied PPD is function of PMV index as follows:   PPD = 100 − 95 exp −0, 0335P M V 4 − 0, 2179P M V 2

Fig. 2.9 Operative comfort temperature function of clothing and activity

(2.2.18)

40

2 Assurance of Indoor Environment Quality in Buildings

Table 2.6 Optimum values of operative temperature t c iM [met] Pers./m2 floor Room t c [o C] category Summer Winter Summer

Room destination

Rcl [clo]

Small offices

0.5

Large offices

0.5

1.0

1.0

1.2

1.2

0.10

0.07

Winter

A

24.5±0.5 22.0±1.0

B

24.5±1.5 22.0±2.0

C

24.5±2.5 22.0±3.0

A

24.5±0.5 22.0±1.0

B

24.5±1.5 22.0±2.0

C

24.5±2.5 22.0±3.0

Conference rooms

0.5

1.0

1.2

0.50

A B C

24.5±0.5 22.0±1.0 24.5±1.5 22.0±2.0 24.5±2.5 22.0±3.0

Study rooms

0.5

1.0

1.2

1.50

A

24.5±0.5 22.0±1.0

B

24.5±1.5 22.0±2.0

Restaurant rooms

0.5

Classrooms

0.5

Kindergartens 0.5

Deposits

0.5

1.0

1.0

1.0

1.0

1.4

1.2

1.4

1.6

0.70

0.50

0.50

0.15

C

24.5±2.5 22.0±3.0

A

23.5±1.0 20.0±1.0

B

23.5±2.0 20.0±2.0

C

23.5±2.5 20.0±2.5

A

24.5±0.5 22.0±1.0

B

24.5±1.5 22.0±2.0

C

24.5±2.5 22.0±3.0

A

23.5±1.0 20.0±1.0

B

23.5±2.0 20.0±2.0

C

23.5±2.5 20.0±2.5

A

23.0±1.0 19.0±1.5

B

23.0±2.0 19.0±3.0

C

23.0±3.0 19.0±4.0

The optimal value for PPD index is of 5% [9] and may be obtained only using air-conditioning systems, with a high automation degree. A relationship between the radiant temperature asymmetry and the per cent dissatisfied was established (Fig. 2.10). Figure 2.10 shows that people are sensitive, to asymmetry caused by an overhead warm surface than by a vertical cold surface. These data are particularly important when using radiant panels to provide comfort in spaces with large cold surfaces or cold windows. Figure 2.11 illustrates the different correlations between PMV and PPD indices [20] based on the studies of several researchers. While the correlation developed by Fanger indicates, for an index PMV = 0, a percentage of dissatisfaction PPD of 5%, studies conducted by Mayer show that PMV’s position shifted by 0.4 from the initial experiments, resulting in a percentage of people dissatisfied with 16%.

2.2 Comfort and Indoor Air Quality Assessment in Closed Spaces

41

Fig. 2.10 Variation of percent dissatisfied function of radiant temperature asymmetry

Fig. 2.11 Different relationships between PMV and PPD

On the basis of this mathematical model was elaborated computer program COMFORT 1.0 [21], in FORTRAN programming language, which allows both direct computation of PMV and PPD indices in different points of a room, and their comparative analysis. It is also possible to determine the mean radiant temperature in isolated points or in a series of points situated on a straight line.

2.2.3.2

Numerical Application

The room with geometrical dimensions of 4.4 m × 6 m × 2.7 m from Fig. 2.12 is considered. The following data are known: heat transfer coefficient of building components: walls [0.7 W/(m2 K)], ceiling [0.4 W/(m2 K)], windows and doors [2.9 W/(m2 K)]; glass walls surface: 7.5 m2 ; indoor air temperature: 24 °C; thermal power of heater: 1900 W.

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2 Assurance of Indoor Environment Quality in Buildings

Fig. 2.12 Room heated

A comparative study of PMV and PPD indices is performed using the computer program COMFORT 1.0 in several points situated on a straight line (discontinuous), at different distances from the window, function of clothing thermal resistance and metabolic rate. Results of the numerical solution obtained for the following pair of values: 0.33clo–1met, 1clo–1met, 0.5clo–2.8met, are reported in Table 2.7. According to the performed study it was established that PMV index has values closed to zero only for the pair of values 1clo–1met. For any other pair of values Rcl -iM the percent dissatisfied people of the thermal comfort would be greater by 5%.

2.2.4 Thermal Comfort Criteria for Design of Heating Systems 2.2.4.1

Criteria for General Thermal Comfort

For the design of buildings and heating, ventilation and air-conditioning (HVAC) systems the thermal comfort criteria (minimum room temperature in winter and

24.43

24.86

25.34

25.67

25.78

25.70

25.63

25.55

25.37

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

t mr

[o C] PPD [%] 36.28 34.37 30.18 27.45 26.56 27.20 27.77 28.43 29.92

PMV −1.22 −1.18 −1.09 −1.03 −1.01 −1.03 −1.04 −1.05 −1.09

0.33 clo−1 met

1.0

Distance from the window [m]

Table 2.7 Numerical results of COMFORT 1.0 computer program

25.37

25.55

25.63

25.70

25.78

25.67

25.34

24.86

24.43

t mr

[o C]

1 clo−1 met

−0.06

−0.04

−0.03

−0.02

−0.01

−0.02

−0.07

−0.13

−0.18

PMV

5.08

5.03

5.01

5.01

5.00

5.01

5.09

5.38

5.64

PPD [%]

25.37

25.55

25.63

25.70

25.78

25.67

25.34

24.86

24.43

t mr [o C]

−0.55

−0.52

−0.51

−0.50

−0.48

−0.50

−0.56

−0.63

−0.70

PMV

0.5 clo−2.8 met PPD [%]

11.35

10.68

10.41

10.16

9.89

10.26

11.46

13.42

15.39

2.2 Comfort and Indoor Air Quality Assessment in Closed Spaces 43

44

2 Assurance of Indoor Environment Quality in Buildings

maximum room temperature in summer) and required ventilation rates for an acceptable IAQ shall be used as input for heating load. The basis for establishing the criteria is standard EN ISO 7730 and the use of the PMV-PPD indices, as shown in Table 2.8. Based on the specified type of clothing and activity of the occupants it is possible to calculate the corresponding ranges of operative temperature. As an example, thermal design criteria for different types of space with sedentary activity and typical winter clothing are given in Table 2.8. The heat emission system must fulfil the requirement that the difference between the operative temperatures in the warmest position in the space must be inside the chosen temperature range (3-5 K). Especially in a very deep room with a fully glazed façade the difference may be critical. By a simplified design method [22] showed that the maximum operative temperature difference in a room at an outdoor air temperature of −12 °C can be calculated according to the equation: tc2 − tc1 ≤ 0.96 Uw

(2.2.19)

where: t c1 is the operative temperature at the coldest position, in °C; t c2 is the operative temperature at the warmest position, in °C; U w is the average U-value of the facade, in W/(m2 K). For a typical modern standard window (U = 1.5 W/(m2 ·K)) the difference in operative temperature is lower than the criteria, because additional variation in operative temperature will be caused by the control system. If the difference is too large it will be necessary to position a heat emitter at the façade (radiator, floor heating, and convector), change the design of the façade, and choose a higher insulation of the façade. Table 2.8 Examples of recommended categories for design of mechanical heated and cooled buildings Type of building Category or space

Offices and spaces with similar activity (single offices, open-plan offices, conference rooms, auditoriun, cafeteria, restaurants, classrooms); iM = 1.2 met

Thermal comfort indexes

Operative temperature range [°C]

PPD [%]

Winter (Rcl = 1 clo)

PMV [–]

Summer (Rcl = 1 clo)

I

65

3.7 Comparative Characterisation of Plastic Tubes

187

• Flexibility at low temperature is also much better at PE-Xa tube, which allows mounting at the beginning or end of cold season; • Stability in time is given in case of PE-Xa by complete end of controlled reticule process in the moment of exit from production installation; The greatest possible share of retiled structure in tube material is determined regarding life cycle, because is inversely proportional to the probability of cracks appearance in materials under the action of external factors. That is why, PE-Xa tubes are used mainly in pre-insulated systems of pipes for heating and warm water, while PE-Xb tubes are used for floor heating system. • Polybutene (PB) is a thermoplastic synthetic material, partly crystal. But it differs from other polymers especially because they are in different crystal forms, stables or meta-stables. Polybutene has an unusual combination of impact resistance, flexibility and a great tensile and creep strength, abrasion resistance and mechanical stress. It can be mounted both by welding and strings special fittings. This material is used for inside installations of hot and cold water, as well as for heating systems. • Polypropylene (PP) is also a thermoplastic material with partly crystal structure. Are distinguished three types of polypropylene: homo-polymerised (PP-H), mass copolymerised (PP-C) and statistic copolymerised (PP-R). PP-H is composed only by polypropylene, has a low flexibility and is relatively brittle at temperatures below +5 °C. This material is used especially in industry. PP-C is obtained by combining polypropylene molecules with ethylene ones, the last ones being placed by regular intervals between polypropylene molecules. As a result the flexibility is increased but also reduces the thermal stability of the material. PP-R is obtained also by inserting ethylene molecules in polypropylene mass, but at irregular intervals. This disposition of the ethylene particles gives a more uniform distribution of mechanical tension on the tube wall. The PP-R tubes are joined by welding, and chemical resistance of this material makes him useful especially in industry. Polypropylene is a very good material for tubes and connections for inside installations of cold water and sewage. Also, tubes reinforced with aluminium, for taking the dilation effect at temperatures higher than 70 °C, are used for heating installations [256]. • Polyvinyl chloride (PVC) is a plastic material from amorphous thermoplastics group, obtained by polymerisation of vinyl chloride. It is the oldest and most widely spread plastic material, being used in several industrial domains for household products. It is easy to bind, easy to make welded connections and can be modelled with heat repeatedly. Polyvinyl chloride which is not plasticised (PVCU) is used especially for the pipe system of drinking water supply installations and sewerage of domestic water. • Chlorinated polyvinyl chloride (PVC-c) is a thermoplastic amorphous structure material, starting from polyvinyl chloride. Due to addition of stabilisers can cover

188

3 Modelling, Optimisation and Modernisation of Heating Systems

a large using domain such as hot and cold water installations, heating, industrial, solar. The tubes made by this material do not joint by welding, but by binding and are not flexible.

3.7.4 Comparative Analysis of the Plastic Tubes Characteristics 3.7.4.1

Physical Characteristics

The main physical characteristics of plastic materials compared with physical characteristics of metallic materials, used for inside installations, are summarised in Table 3.16. • Density ρ is the mass of the volume unit of the material from which the tube is made. Table 3.16 shows that the density of the “heaviest” plastic, PVC-c, is five times lower than that of steel. • Thermal conductivity λ is the heat flux that passes through the wall of a tube with a length of 1 m at a temperature difference of 1 K between the inner and outer environment of the tube. It is observed that the heat losses through the plastic tube walls are much smaller than in the case of copper or steel tubes. Therefore, the use of plastic tubes leads to the removal of the insulating layer, necessary for metal tubes. • Coefficient of linear expansion α indicates the elongation, in mm, of a 1 m long tube at a temperature increase of 1 K. The length variation of a tube due to the change of the temperature of the transported water is calculated with formula [257]: L = α L t

(3.7.1)

where: L is the tube elongation; L is the tube length; t is the fluid temperature difference. Table 3.16 Main physical characteristics of materials Material

Characteristics ρ (kg/m3 )

λ (W/(m·K))

α (mm/(m·K))

E (MPa)

PER

940

0.41

0.20

PB

930

0.22

0.13

600 350

PP-R

900

0.24

0.18

800

0.08

PVC-c

1550

0.14

Steel

7850

42…53

0.0012

210,000

3500

Copper

8890

407.1

0.018

12,000

3.7 Comparative Characterisation of Plastic Tubes

189

Considering a tube with a length of 10 m, at a temperature difference of 50 K, the values of the tube elongation, in mm, for different materials are presented in Fig. 3.57. Maximum elongations occur in the case of PE and PER tubes, these materials having the highest values of the linear expansion coefficient (Table 3.16). • Modulus of elasticity E characterises the material rigidity. Thus, the more rigid the material, the larger its modulus of elasticity or the more flexible the material, the lower its modulus of elasticity. Table 3.16 shows that the most rigid plastic is PVC-c. Based on the values of the linear expansion coefficient and the modulus of elasticity, the necessary length of the expansion arm is determined, which has the role of taking over the deformations that appear in the tubes. The formula for calculating the length of the expansion arm is [258]: Lb = C

√

D L

(3.7.2)

where: L b is the length of the expansion arm; D is the tube diameter; C is a materialspecific constant, given in Table 3.17.

Fig. 3.57 Values of tube elongation

Table 3.17 Constant C values Material

PE

PER

PB

PP-R

PVC-c

C

27

12

10

30

34

190

3 Modelling, Optimisation and Modernisation of Heating Systems

Fig. 3.58 Arm length expansion for plastics

Considering a plastic tube with a length of 10 m, a diameter of 40 mm, Fig. 3.58 shows the lengths of the expansion arm, in mm, corresponding to a temperature difference of 50 K, for various plastics.

3.7.4.2

Mechanical Characteristics

• Creep resistance is a very important factor in the realisation of plastic installations, which intervenes especially in the technique of assembling and fixing tubes. Creep expansion is the elongation of the material in time, at constant temperature and under constant load. Figure 3.59 shows the elongation of the PER tube over time compared to that of the PB tube, at a tensile stress of 8 MPa and a temperature of 20 °C. • Minimum breaking strength σr is the equivalent stress in the wall of a tube given by the internal pressure, which causes the tube to break through its permanent action. The minimum breaking strength of various plastics, for a life of one year and temperatures between 20 and 100 °C is illustrated in Fig. 3.60. • Behaviour over time at permanent loads (endurance) expresses the relationship between the equivalent stress, temperature and life of the material, which is represented graphically by the regression curves. Figure 3.61 shows the time variation of the equivalent stress for various plastics at a water temperature of 70 °C.

3.7 Comparative Characterisation of Plastic Tubes

191

Fig. 3.59 Creep elongation of the PER and PB tube

Fig. 3.60 Minimum breaking strength for plastics

Table 3.18 gives the values of the equivalent stress for a tube life of 50 years, considering the constant operating temperature of 70 °C and the same safety factor [259] for each type of material. Depending on the equivalent stress, the operating pressure ps can be determined, in MPa, with the formula [251]: ps =

0.1στ δ f (D − δ)

(3.7.3)

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3 Modelling, Optimisation and Modernisation of Heating Systems

Fig. 3.61 Endurance of plastic tubes

Table 3.18 Equivalent stress values σ, in MPa

PER

PB

PP-R

PVC-c

5.3

7.5

3.1

7.5

with: f =

σ σp

(3.7.4)

where: σ is the equivalent stress, in MPa; τ is the life duration, in years; δ is the thickness of tube wall, in mm; D is the tube diameter, in mm; f is the safety coefficient; σp is the equivalent stress for design (maximum admitted), established based on regression curves. Considering a safety coefficient equal with 1.5 and an operation temperature of 70 °C result the values from Table 3.19 for service pressure [251], function of life cycle, for a tube with 40 mm diameter made of various plastic materials and different nominal pressure (service pressure admitted for 50 years lifetime and operation temperature of 20 °C).

3.7 Comparative Characterisation of Plastic Tubes

193

Table 3.19 Service pressure values ps, in MPa Life cycle τ (ani)

Material /(Nominal pressure) PER/(Pn 20)

PB/(Pn 16)

PB/(Pn 25)

PP-R/(Pn 20)

PP-R/(Pn 25)

PVC-c/(Pn 20)

PVC-c/(Pn 25)

25

1.14

1.05

1.64

9.1

1.14

1.09

1.37

30

1.13

1.04

1.62

8.8

1.10

1.05

1.31

50

1.12

1.01

1.58

–

1.00

1.02

1.28

Table 3.20 Geometric and hydraulic characteristics of tubes Characteristic

UM

Material/(Nominal pressure) PER/(Pn 20)

PB/(Pn 16)

PP-R/(Pn 20)

PVC-c/(Pn 25)

Wall thickness

mm

5.5

3.7

6.7

4.5

Inner diameter

mm

29.0

32.6

26.6

31.0

Inner section

mm2

660

834

555

754

Absolute roughness

mm

0.01

0.007

0.007

0.001

Water specific content dm3 /m

0.66

0.83

0.55

0.75

Water velocity for a m/s flow rate G = 2 dm3 /s

3.0

2.4

3.6

2.7

Specific head loss for G = 2 dm3 /s and t = 10 °C

mm/m

332

188

505

241

Specific head loss for G = 2 dm3 /s and t = 60 °C

mm/m

286

158

432

192

3.7.4.3

Geometric and Hydraulic Characteristics

The dependence between the wall thickness and the transported fluid flow rate is presented comparatively for PER, PB, PP-R and PVC-c tubes in Table 3.20. Having a higher strength of the material at the same outer diameter (40 mm), the PB tube has a larger inner diameter, so it allows the transport of a higher fluid flow rate than the PER, PP-R and PVC-c tubes. At the same flow rate PB can be used with a smaller diameter size, thus resulting in a substantial saving in plant investment.

3.7.4.4

Life Cycle

In addition to the temperature and pressure of the fluid, in the exploitation of plastic tubes, other factors such as the diffusion of oxygen, the cuts in the tube wall and the action of ultraviolet radiation have an important influence on their lifespan.

194

3 Modelling, Optimisation and Modernisation of Heating Systems

• Oxygen diffusion. Plastics have an amorphous macromolecular structure, so that the tubes made from them are permeable to gases (especially oxygen) on the entire circumference. This undesirable phenomenon causes corrosion on the metal surfaces of the installation continuously, because the water in installation is permanently enriched with penetrated oxygen. Particles released by water due to corrosion are transported throughout the installation, leading to a decrease in water quality and deposits, and in the case of low velocities negatively affect the operation of the installation. For removal of these phenomena, it can choose one of the following solutions: (a) Use of multilayer tubes impermeable to oxygen. These tubes have a mantle resistant to the diffusion of oxygen through the wall (diffusion barrier), which can be an intermediate layer of aluminum or the outer layer of electrostatically sprayed aluminum or plastic (ethylene vinyl alcohol). The diffusion barrier is attached to the tube to prevent air infiltration between the jacket and tube in case of damage to the jacket. Also, the diffusion barrier must have a coefficient of linear expansion close to that of the tube material, to avoid destroying the adhesion of the jacket to the tube in case of temperature variations in the system. The fittings used for multilayer tubes are made in such a way that the diffusion barrier is not destroyed by joining. (b) Use of chemical substances mixture. By adding certain chemicals (inhibitors) it is possible to reduce or even eliminate the attack of oxygen on the metallic parts of the installation. Inhibitors bind oxygen in water by reacting with it, while being a means of electro-chemical protection of metal surfaces. Substances used as corrosion inhibitors must meet the following requirements: – to have an anodic/cathodic protection action to remove corrosion; – to have high thermal stability, i.e., not to change or lose its properties under the action of temperature variations in the installation; – to be insensitive to bacterial action; – do not modify the characteristics of plastic tubes; – not to pollute the environment; – to be easily detectable in water. To obtain the desired effect, the effective concentration of the inhibitor in the thermal agent must be continuously compared with the prescribed theoretical concentration, the under-dose or insufficient activity of the inhibitor can lead to corrosion in all metal components of the installation (c) Separation of the installation elements involve inserting a heat exchanger between the primary circuit of the boiler and the secondary heating circuit, which does not contain metallic elements or if they contain them they are resistant to corrosion.

3.7 Comparative Characterisation of Plastic Tubes

195

The role of the heat exchanger is to separate the primary circuit, with high temperature and pressure, from the secondary circuit, with low temperature and pressure. This solution applies to low-temperature heating systems, such as radiant floor heating with plastic pipes. • Cuts in the tube wall. The transport, handling and laying of plastic pipes must be made with great care, so that they are not exposed to the appearance of cuts or scratches in the tube wall, because these defects considerably shorten their life. Diffusion barrier of multilayer tubes, placed outside the tube, following scratches or cuts can no longer fulfil its role of preventing the infiltration of oxygen through the tube wall, so that the metallic parts of the installation will be exposed to corrosion. A cut in the wall of a plastic tube decreases its resistance to long-term stress (Fig. 3.62). At the same operating temperature, the maximum working pressure inside the cut-off tube will be lower and the tube becomes unsuitable in relation to the requirements of the installation. For example, cross-linked polyethylene tubes used in radiant floor heating systems are tested at a temperature of 95 °C and an equivalent voltage of 4.6 MPa, corresponding to an operating pressure of 1.1 MPa. The duration of the tests is 170 h. In this case, a cut of up to 20% in the tube wall does not influence the resistance to long-term stresses, because the links between molecules are very good, and when a cut occurs the stresses will be taken over by neighbouring molecules, stress concentrations compensating in this way. • Ultraviolet radiation. Plastics subjected to the action of ultraviolet radiation are exposed to thermal oxidation, which causes breaks in the molecule chain (Fig. 3.63). A factor that decisively influences the decomposition rate is the configuration of the molecule chain, the branches being from this point of view the weak parts of the molecule. Thus, polypropylene compared to polyethylene is much more strongly disposed to the oxidation because in the molecule chain at every second carbon atom there is a branch. Fig. 3.62 Influence of cuts on long time efforts

196

3 Modelling, Optimisation and Modernisation of Heating Systems

Fig. 3.63 Polyethylene thermal oxidation

Molecule decomposition by thermal oxidation is a chain reaction, and if it is not intervened, it does not stop. To achieve the desired lifespan of plastic tubes, phenols are added as stabilisers (antioxidants), which react faster with oxygen than polymers. In order for the duration of operation of the tubes to reach the prescribed duration, the conditions imposed by the manufacturer for each material must be known and strictly observed in all phases of the installation.

3.7.4.5

Reuse of Plastics and Energy Saving

The consumption of crude oil for the production of plastics represents only approximately 6%. In the diagram in Fig. 3.64 are given for comparison the specific consumptions of energy w embedded in the manufacture of tubes, depending on their material and diameter D. From the energy point of view, it results that the lowest specific energy consumption is PB tubes, followed by PVC-c, PER, PP-R and steel tubes, and the copper ones have the highest specific energy embedded. However, based on the general principle of saving primary resources, the possibility of exploiting the residual and energy value of plastic waste and discarded plastic products can not be neglected. The main possibilities for their use are: (1) reuse, respectively manufacture of new products and (2) combustion for the production of heat. In the first case, the plastic waste is returned to the initial state of basic raw material, by different processes (hydrolysis, pyrolysis and regranulation). Recyclable plastics

3.7 Comparative Characterisation of Plastic Tubes

197

Fig. 3.64 Specific energy embedded for manufacturing tubes

Table 3.21 Calorific power Pc , in kJ/kg, for different materials Marsh gas

LPG

Oil fuel

Coal

Wood

PE/PB/PP

PVC/PVC-c

Domestic waste

50,000

45,000

40,000

29,000

16,000

44,000

19,000

8000

are mainly thermoplastics (PE, PB, PP, PVC, PVC-c) Cross-linked polyethylene can not be recycled in the production circuit. In domestic waste incineration plants, plastics can be used for energy by combustion. For example, in Germany, incinerated plastic waste provides an annual amount of heat equivalent to the combustion of 500,000 t of liquid fuel (fuel oil). Table 3.21 shows the calorific power for the main combustible materials compared to that of plastics and domestic waste. If the combustion of polyolefin’s (PE, PB, PP) emissions of toxic or corrosive gases are lower, as their molecular structure does not contain halogens (Cl, Fl) or sulphur (S), the same does not happen with PVC and PVC-c. As plastics are not soluble or degradable, their disposal together with public waste does not imply restrictions from the point of view of environmental protection.

3.7.5 Conclusions With a certain future, also in our country, plastic tubes are gaining ground compared to classic solutions, imposing their superior physical, mechanical and hydraulic characteristics and remarkable performance related to assembly works, very safe and fast.

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3 Modelling, Optimisation and Modernisation of Heating Systems

Additionally, compared with other type of materials, plastics are much efficient from energy point of view, specific consumption of energy for their obtaining being lowest. From the global analysis of the comparative data on the technical characteristics of the plastic tubes used in the inside installations it results that polybutene, closely followed by reticulate (cross-linked) polyethylene, is imposed by superior values of resistance to mechanical stress, high flexibility and low weight, moderate linear expansion, minimal head losses, large transport capacity at the same diameter, joining facilities (welding, special tightening fittings), being at the same time also reusable or energy efficient. The efficiency of plastic tube installation systems is conditioned by a professional design, a good technological coordination and a correct execution. The large number of types of tubes, differentiated by the manufacturing material (copper, steel, PER, PB, PP-R, PVC-c), creates special problems for specialists in the decision-making stage, requiring their differentiation through an overall analysis that also take into account the essential quality requirements.

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182. Bene JG, Selek I, Hos C (2010) Neutral search technique for short-term pump schedule opti-mization. J Water Resourc Plan Manag 136:133–137 183. Decision no 406/2009/EC of the European Parliament and of the Council of 23 April 2009 on the effort of member states to reduce their greenhouse gas emissions to meet the community’s greenhouse gas emission reduction commitments up to (2020) Brussels. European Parliament, Belgium, p 2009 184. Jack DW, Thomas B, Devine G (1991) Pump scheduling and cost optimization. Civil Eng Syst 4:197–206 185. Baiu S (1992) A practical system for applying VSDs to pumping systems. Electricity Today 2:26–31 186. Chase DV, Ormsbee LE (1993) Computer-generated pumping schedules for satisfying operational objectives. J American Water Works Assoc 85(7):54–61 187. Yu G, Powell RS, Sterling MJH (1994) Optimized pump scheduling in water distribution systems. J Optim Theory Appl 83(3):463–488 188. McCormick G, Powell RS (2003) Optimal pump scheduling in water supply systems with maximum demand charges. J Water Resourc Plan Manag 129(3):372–379 189. Rishel JB (2003) Control of variable speed pumps for HVAC water systems. ASHRAE Trans 109(1):380–389 190. Hansen EG (1995) Parallel operation of variable speed pumps in chilled water systems. ASHRAE J 37(10):34–38 191. Bernier MA, Bourret B (1999) Pumping energy and variable frequency drivers. ASHRAE J 41(12):37–40 192. Carlson R (2000) The correct method of calculating energy savings to justify adjustablefrequency drive on pumps. IEEE Trans Ind Appl 36(6):1725–1733 193. Ma Z, Wang S (2009) Energy efficient control of variable speed pumps in complex building central air-conditioning systems. Energy Build 41(2):197–205 194. Suceveanu ID (1988) Adjustment possibilities analysis of technological parameters varying rotational speed of equipments. Energetica 36(4):156–160 195. Georgescu I (1988) Energy savings by driving with variable rotational speed of pumps and fans in automation of technological processes. Energetica 36(3):99–109 196. Sarbu I, Valea ES (2015) Energy savings potential for pumping water in district heating stations. Sustainability 7(5):5705–5719 197. Ilina M (1990) Building heating using classical fuels. Technical Publishing House, Bucharest, Romania (in Romanian) 198. Sarbu I, Borza I (1998) Energetic optimization of water pumping in distribution systems. Periodica Polytechnica, Mech Eng 2(2):141–152 199. Sarbu I (1997) Energetically optimisation of water distribution systems. Romanian Academy Publishing House, Bucharest (in Romanian) 200. Rishel JB (2002) Water pumps and pumping systems. McGraw-Hill, New York USA 201. Hooper W (1999) Advantages of parallel pumping. Plant Eng 31:4–6 202. Volk M (2005) Pump characteristics and applications. Taylor & Francis, Boca Raton 203. Marchi A, Simpson AR, Ertugrul N (2012) Assessing variable speed pump efficiency in water distribution systems. Drinking Water Eng Sci 5:15–21 204. Ulanicki B, Kahler J, Coulbeck B (2008) Modelling the efficiency and power characteristics of a pump group. J Water Resourc Plan Manag 134:88–93 205. Fuchsloch JF, Finley WR, Walter RW (2008) The next generation motor. IEEE Trans Ind Appl 14:37–43 206. Melfi M, Evon S, McElveen R (2009) Induction versus permanent magnet motors. IEEE Trans Ind Appl 15:28–35 207. Stockman K, Dereyne S, Vanhooydonck D, Symens W, Lemmens J, Deprez W (2010) Iso efficiency contour measurement results for variable speed drives. In: Proceedings of the XIX international conference on electrical machines. ICEM, Rome, Italy 208. Allard F, Seppänen O (2008) European actions to improve energy efficiency of buildings. Rehva Journal 45(1):10–20

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209. Andersen N (1999) End users dictate the potential for low temperature district heating. Energy Environ J 4:30–31 210. Zhang Z, Pate B (1987) A semi analytical formulation of heat transfer from structures with embedded tubes. Heat Transf Build Struct 78:17–25 211. Strand K, Pederson O (2002) Modelling radiant systems in an integrated heat balance based energy simulation program. ASHRAE Trans 108:1–9 212. Miriel J, Serres L, Trombe A (2002) Radiant ceiling panel heating-cooling systems: experimental and simulated study of the performances, thermal comfort and energy consumptions. Appl Therm Eng 22(16):1861–1873 213. Laouadi A (2004) Development of a radiant heating and cooling model for building energy simulation software. Build Environ 39:421–431 214. Bojic M, Cvetkovic D, Miletic M, Malesevic J, Boyer H (2012) Energy, cost, and CO2 emission comparison between radiant wall panel systems and radiator systems. Energy Build 54:496–502 215. Sarbu I, Sebarchievici C (2015) A study of the performances of low-temperature heating systems. Energ Effi 8(3):609–627 216. Sarbu I, Marza M, Crasmareanu E (2017) Performance of radiant heating systems of lowenergy buildings. Mater Sci Eng 245:art. 032088 217. BUDERUS, Handbuch fur Heizung-stechnik. Beuth Verlag, Berlin, Germany (1994) 218. Ilina M, Burchiu S (1996) Influence of heating systems on microclimate from living rooms. Installer J 6:24–29 219. Berglund LG, Fobelets A (1987) A subjective human response to low level air currents and asymmetric radiation. ASHRAE Trans 93(1):497–523 220. Sarbu I, Sebarchievici C (2013) Aspects of indoor environmental quality assessment in buildings. Energy Build 60(5):410–419 221. Sarbu I (2010) Energy efficiency of low temperature central heating systems. In: Proceedings of the 4th WSEAS international conference on energy planning, energy saving and, environmental education, Kantaoui, Sousse, Tunisia, pp 30–35 222. Demidovitch B, Maron I (1979) Numerical computation elements. Mir, Moscow, Russia 223. Sarbu I, Popina O (2004) Design of the interior heating networks. Sci Bull Polytech Univ Timisoara 50(2):25–29 224. Sarbu I, Kalmar F (2000) Computer aided design of building equipment. Mirton Publishing House, Timisoara, Romania (in Romanian) 225. Arsenie DA (1983) A formula for calculation of Darcy–Weisbach friction factor. Hydrotechnics 30(12):12–19 226. Sarbu I (2003) Regulation devices for heating systems in buildings. Installer J. 1:4–7 227. Hesaraki A, Holmberg S (2013) Energy performance of low temperature heating systems in five new-built Swedish dwellings: a case study using simulations and on-site measurements. Build Environ 64:85–93 228. ASHRAE handbook: HVAC systems and equipment. American Society of Heating, Refrigerating and Air Conditioning Engineers Atlanta, GA, USA (2016) 229. REHVA, Guidebook no 7: Low temperature heating and high temperature cooling (2007) 230. Kim KW, Olesen BW (2015) Radiant heating and cooling systems. ASHRAE J 57(2 and 3):28–37, 34–42 231. ISO 7730, Moderate thermal environment—determination of the PMV and PPD indices and specification of the conditions for thermal comfort. International Organisation for Standardisation (ISO), Geneva, Switzerland (2005) 232. ISO/TS 13732–2 (2001) Ergonomics of the thermal environment—methods for the assessment of human responses to contact with surface (Part 2): human contact with surfaces at moderate temperature. International Organisation for Standardisation (ISO), Geneva, Switzerland 233. ASHRAE Standard 55 (2010) Thermal environmental conditions for human occupancy. American Society of Heating, Refrigerating and Air-conditioning Engineers, Atlanta, GA, USA

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234. Sarbu I (2014) Influence of heating systems on indoor environmental quality. Appl Mech Mater 510:208–214 235. ISO 11855, Building environment design—design, dimensioning, installation and control of the embedded radiant heating and cooling systems. International Organisation for Standardisation (ISO), Geneva, Switzerland (2012) 236. Roumajon J (1996) Modélisation numerique des émissions thermiques. Chaud, Froid Plomberie 579(4):55–58 237. ASHRAE handbook: Fundamentals. American Society of Heating, Refrigerating and AirConditioning Engineers, Atlanta, GA, USA (2013) 238. ASHRAE handbook: HVAC applications. American Society of Heating, Refrigerating and Air-Conditioning Engineers, Atlanta, GA, USA (2015) 239. Bechthler H, Browne MW, Bansal PK, Kecman V (2001) New approach to dynamic modelling of vapour-compression liquid chillers: artificial neural networks. Appl Therm Eng 21(9):941– 953 240. ANRE, National Authority of Energy Settlement (2012). http://www.anre.ro/energie-electr ica/legislatie/preturi-si-tarife-ee/energia-electrica-2010-2012. Accessed 5 Nov 2014 241. IEE, Intelligent Energy Europe (2013). http://ec.europa.eu/energy/environment. Accessed 5 Nov 2014 242. Sarbu I, Kalmar F, Cinca M (2007) Thermal building equipments: Energy optimisation and modernisation. Polytechnic Publishing House, Timisoara, Romania (in Romanian) 243. Manescu Al, Sandu M, Ianculescu O (1994) Water supply. Teaching and Pedagogical Publishing House, Bucharest (in Romanian) 244. Sarbu I, Kalmar F, Cinca M (2007) Thermal building equipments: energy optimisation and modernisation. Polytechnic Publishing House, Timisoara, Romania (in Romanian) 245. http://www.underflowheating.cables.co.uk. Accessed 15 Feb 2014 246. http://www.electrictraceheating.co.uk. Accessed 15 Feb 2014 247. http://www.incalzireinpardoseala.com.ro. Accessed 15 Feb 2014 248. Sarbu I, Valea ES (2014) Fluids temperature regulation using self-adjustable cables. Adv Mater Res 909:202–207 249. Mateescu T, Profire M, Pop A, Ciascai I (1998) Plastic pipes for urban utility systems. Matrix Rom Publishing House, Bucharest (in Romanian) 250. Sarbu I, Valea ES (2010) Comparative characterisation of plastic tubes for building installations. Metalurgia Int 15(9):11–18 251. Sarbu I, Kalmar F (2002) Energetically optimisation of buildings. Matrix Rom Publishing House, Bucharest (in Romanian) 252. Badea G (1998) Multilayer piping systems and essential quality requirements. In: Proceedings of the national symposium on modern science and energy, Cluj–Napoca, May 1998, p 161 253. Company catalogs for: Thermconcept, Ecoflex, Prandelli, Rehau, and GF (2013) 254. Janson LE (1989) Plastic pipes for water supply and sewage disposal. Neste UPONOR, Stockholm, Sweden 255. Pavel C (2010) Networks of PEX pre-insulated flexible pipes. Installer J 2:12–16 256. EN/12202 Kunststoff - Rohrleituns-systeme für Heiss - und Kaltwasser - Polypropylen, Entwurf Jänner (1996) 257. Sarbu I, Kalmar F (1998) Plastic pipes use for building services. In: Proceedings of the national conference on building services and ambient comfort, vol 1, Timisoara, April 1998, pp 98–108 258. Sarbu I, Kalmar F (1999) Characteristics of plastic tubes. Installer J 2:65–69 259. Sarbu I, Kalmar F (1998) Safety of high density polyethylene pipes. In: Proceedings of the national conference on building services and ambient comfort, vol 1, Timisoara, 15–16 April 1998, pp 420–428

Chapter 4

Efficient Refrigeration and Air-Conditioning Systems

Abstract This chapter discusses the vapour compression-based refrigeration systems and describes the operation principle and theoretical thermodynamic cycle of them, the types of refrigeration compressors, the ecological refrigerants and some recovery possibilities of the thermal energy produced by refrigeration systems. Additionally, a computational model for optimal design of refrigeration insulations on flat and cylindrical surfaces and another for refrigeration columns for soil freezing operating with gaseous refrigerant, as well as an experimental study on the frost selfprotection of cooling towers on an air-conditioned stand using a vapour compressionbased refrigeration system are presented. Finally, an investigation of the energy efficiency of conventional air-conditioning systems in office buildings is included. For this application, an air–water mist cooled system for the air-cooled chiller is proposed. The results of the experiments showed that the most efficient ventilation and air-conditioning system for office buildings consist of an air handling unit and fan coil units with an air–water mist cooled chiller and a cooled water temperature of 8 °C.

4.1 Generalities From the first uses of cold to the production of low temperatures in modern refrigeration systems with automated operation, monitored and controlled by computers, cold science and technology have developed continuously, as new scientific knowledge and technological advances have been discovered and accumulated. The history of the development of the cooling technique and especially of the artificial cooling is related to the preoccupations for the achievement of a comfort and better living conditions. Obtaining artificial cold has, of course, advantages over natural cold, namely: (1) the possibility of cooling bodies to temperatures well below ambient temperature, (2) the continuity of cooling processes and (3) the possibility of obtaining cold in any period of the year, regardless of climatic conditions. The production of artificial cold is a vast and complex field with the most diverse applications in construction, food industry, air conditioning, heat pumps, recovery of secondary energy resources, chemical industry, metallurgy, electrical engineering © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 I. Sarbu, Advances in Building Services Engineering, https://doi.org/10.1007/978-3-030-64781-0_4

209

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and electronics, etc. According to the second principle of thermodynamics, the transfer of heat from a body with a lower temperature to a body with a higher temperature can be achieved only on the basis of external energy consumption in different forms: mechanical, thermal, kinetic, electrical, solar, etc. The systems in which such processes are performed are called heat transformers. If the temperature t of the cold source is lower than the temperature t a of the environment, which plays the role of the hot source (t < t a ), the heat transformer is a refrigeration system. If the cold source is the environment or a thermal waste with your temperature ta > ta , and the hot source has a temperature th > ta , the heat transformer is a heat pump system. The domestic refrigerator is one of the most popular household appliances because of its use in food preservation. Most of these refrigerators are based on vapour-compression technology, and their continuous operation represents a high-energy consumption. The adoption of eco-friendlier cooling solutions is mandatory to mitigate the contemporary environmental challenges and to respect the different regulations on the progressive ban of hydro-fluorocarbons. This chapter discusses the vapour compression-based refrigeration systems and describes the operation principle and theoretical thermodynamic cycle of them, the types of refrigeration compressors, the ecological refrigerants and some recovery possibilities of the thermal energy produced by refrigeration systems. Additionally, a computational model for optimal design of refrigeration insulations on flat and cylindrical surfaces and another for refrigeration columns for soil freezing operating with gaseous refrigerant, as well as an experimental study on the frost self-protection of cooling towers on an air-conditioned stand using a vapour compression-based refrigeration system are presented. Finally, an investigation of the energy efficiency of conventional air-conditioning systems in office buildings is included.

4.2 Vapour Compression-Based Refrigeration Systems 4.2.1 Preliminary Considerations Vapour compression-based refrigeration systems with electro-compressor are widespread in the cold technique due to their high reliability and efficiency in operation. Vapour-compression system consists of compressor, condenser, expansion valve and evaporator, connected with refrigerant pipelines (Fig. 4.1). In these systems, during the operating cycle, the refrigerant changes its state of aggregation twice, in evaporator and condenser. This section discusses vapour compression-based refrigeration systems with electro-compressor and describes the theoretical thermodynamic cycle and their calculation, as well as the operation principle and energy efficiency of these systems [1, 2].

4.2 Vapour Compression-Based Refrigeration Systems

211

Fig. 4.1 Schematic of a single-stage compression refrigeration system

4.2.2 Operation Principle and Thermodynamic Cycle The basic vapour-compression cycle is considered to be one with isentropic compression, with no superheat of vapour and no sub-cooling of liquid (Fig. 4.2). Operational processes are outlined next: 1–2: isentropic compression in the compressor K, which leads to increased pressure and temperature from the values corresponding for evaporation p0 , t 0 to those of the condensation pc , t 2 > t c ; 2–2’: isobar cooling in the condenser C at pressure pc from the temperature t 2 to t 2’ = t c ; 2’–3: isotherm–isobar condensation in the condenser C at pressure pc and temperature t c ; 3–4: isenthalpic lamination in expansion valve EV, leading the refrigerant from 3 state of the liquid at pc , t c in 4 state of wet vapour at p0 , t 0 ; 4–1: isotherm–isobar evaporation in the evaporator E at pressure p0 and temperature t 0 .

Fig. 4.2 Single-stage vapour-compression process in t-s and p-h diagrams

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In a theoretical vapour-compression cycle, the refrigerant enters the compressor at state 1 as saturated vapour and is compressed isentropically to the condensation pressure. The refrigerant temperature increases during this isentropic compression process to well above the temperature of the surrounding medium. The refrigerant then enters the condenser as superheated vapour at state 2 and leaves as saturated liquid at state 3 as a result of heat rejection to the surroundings. The refrigerant temperature at this state is still above the temperature of the surroundings. The saturated liquid refrigerant at state 3 is throttled to the evaporation pressure by passing it through an expansion valve. The refrigerant temperature drops below the temperature of the cold environment during this process. The refrigerant enters the evaporator at state 4 as a low-quality saturated mixture, and it completely evaporates by absorbing heat from the cold environment. The refrigerant then leaves the evaporator as saturated vapour and re-enters the compressor, completing the cycle [3]. The specific compression work w, in kJ/kg, the specific cooling power q0 , in kJ/kg, the specific heat load at condensation qc , in kJ/kg, and the volumetric refrigerating capacity q0v , in kJ/m3 , are calculated for above presented processes as follows: w = h2 − h1

(4.2.1)

q0 = h 1 − h 4 = h 1 − h 3

(4.2.2)

qc = h 2 − h 3

(4.2.3)

q0v =

q0 = q0 ρ1 v1

(4.2.4)

where v1 , ρ1 are the specific volume, in m3 /kg and density, in kg/m3 of the refrigerant to state 1. The required cooling power of system Q0 , in kW, is expressed as: Q 0 = mq0

(4.2.5)

where m is the refrigerant mass flow rate, in kg/s. The power necessary for the isentropic compression Pis , in kW, may be calculated using the equation: Pis = mw

(4.2.6)

The effective power Pef on the compressor shaft is larger and is defined as: Pe f = where ηis is the isentropic efficiency.

Pis ηis

(4.2.7)

4.2 Vapour Compression-Based Refrigeration Systems

213

For the computation of the thermodynamic cycle of a single-stage compression refrigeration system, the computer program CICLU1 was developed in FORTRAN programming language and implemented on IBM-PC micro-systems [1, 4].

4.2.3 Energy Efficiency and CO2 Emission The coefficient of performance (COP) of a refrigeration system is defined as: COP =

h2 − h3 q0 Q0 = = Pel w h2 − h1

(4.2.8)

In addition, energy efficiency ratio (EER), in British thermal unit per Watt-hours (Btu/(Wh)), is defined by equation: EER = 3.412 COP

(4.2.9)

where 3.412 is the transformation factor from Watt to Btu/h. The exergetic efficiency ηex of the cycle is expressed as: ηex = COP

ta − t0 t0

(4.2.10)

where t a is the absolute temperature of the environment, and t 0 is the absolute evaporation temperature. The electricity consumption of a refrigeration system is considered the most important source for greenhouse gas (GHG) emissions [5]. Note that although carbon dioxide (CO2 ) represents the most important GHG, there exist several other compounds that contribute similarly to climate change. Their combined impact is commonly normalised to the specific effect of CO2 , and all emissions are expressed in CO2 equivalents. For the sake of readability, however, the emissions are expressed only in kg CO2 . Thus, the CO2 emissions CCO2 of the refrigeration system during its operation can be evaluated with the following equation: CCO2 = gel E el

(4.2.11)

where gel is the specific CO2 emission factor for electricity. The average European CO2 emission factor for electricity production is 0.486 kg CO2 /kWh and for Romania is 0.547 kg CO2 /kWh [6].

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4 Efficient Refrigeration and Air-Conditioning Systems

4.3 Types of Compressors 4.3.1 Preliminary Considerations A refrigeration compressor is a mechanical device that increases the pressure of a gas (refrigerant vapour) by reducing its volume. Heat pump and air-conditioner equipment use compressors to move heat in refrigerant cycle. The main types of heat pump compressors according to European Heat Pump Association are illustrated in Fig. 4.3. Compressors used in refrigeration systems are often described as being hermetic, open or semi-hermetic. In hermetic and most semi-hermetic compressors, the compressor and motor driving the compressor are integrated, and operate within the pressurised vapour envelope of the system. The motor is designed to operate in, and be cooled by, the refrigerant vapour being compressed. Typically in hermetic and most semi-hermetic compressors, the compressor and motor driving the compressor are integrated, and operate within the refrigerant system. The motor is hermetic and is designed to operate, and be cooled by, the refrigerant being compressed. The disadvantage of hermetic compressors is that the motor drive can not be repaired or maintained, and the entire compressor must be removed if a motor fails.

Fig. 4.3 Types of refrigeration compressors

4.3 Types of Compressors

215

An open compressor has a motor drive which is outside of the refrigeration system, and provides drive to the compressor by means of an input shaft with suitable gland seals. Open compressor motors are typically air-cooled and can be fairly easily exchanged or repaired without degassing of the refrigeration system. The disadvantage of this type of compressor is a failure of the shaft seals, leading to loss of refrigerant. Open motor compressors are generally easier to cool (using ambient air) and therefore tend to be simpler in design and more reliable, especially in high-pressure applications where compressed gas temperatures can be very high. However the use of liquid injection for additional cooling can generally overcome this issue in most hermetic motor compressors. This section presents a detailed description of the refrigeration compressor types (reciprocating, rotary screw, centrifugal and scroll compressors) [2].

4.3.2 Reciprocating Compressors A reciprocating compressor or piston compressor is a positive-displacement compressor that uses pistons driven by a crankshaft to deliver gases at high pressure [7]. The intake gas enters the suction manifold, then flows into the compression cylinder where it gets compressed by a piston driven in a reciprocating motion via a crankshaft, and is then discharged. The reciprocating compressor has the following main characteristic parameters [8]: • theoretical vapour flow rate (displacement) D0 , in m3 /s: D0 =

π d2 1 s N nk 4 60

(4.3.1)

where d is the cylinders’ diameter, in m; N is the number of cylinders; s is the piston path, in m; and nk is the compressor speed, in rev/min. • real volumetric flow rate D, in m3 /s: D = λk D 0 where λk is the volumetric efficiency of compressor

(4.3.2)

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4 Efficient Refrigeration and Air-Conditioning Systems

• vapour mass flow rate m, in kg/s: m=

Q0 D λk = = D0 q0 v1 v1

(4.3.3)

where Q0 is the cooling power, in kW; q0 is the specific heat load at evaporation, in kJ/kg; and v1 is the specific volume of absorbed vapour, in m3 /kg. • thermal power of the compressor Qk , in kW: Q k = λk

q0 D0 v1

(4.3.4)

pd ps

(4.3.5)

• pressure ratio H p : Hp =

where pd is the discharge pressure and ps is the suction pressure. • power consumed by the compressor Pk , in kW: Pk = m w

(4.3.6)

where w is the specific compression work, in kJ/kg, which can be isothermal, adiabatic or polytrophic. • indicated power Pi , in kW: Pi =

Pk Q0 = ηi COPηi

(4.3.7)

where ηi is the indicated efficiency of the compressor (ηi = T 0 /T c ). • electric motor power of the compressor Pe , in kW: Pe =

Q0 ηi ηen COP

(4.3.8)

where ηem is the electromechanical efficiency of the motor-compressor system.

4.3 Types of Compressors

217

4.3.3 Rotary Screw Compressors Rotary screw compressors are also positive-displacement compressors. Two meshing screw-rotors rotate in opposite directions, trapping refrigerant vapour and reducing the volume of the refrigerant along the rotors to the discharge point. • Compressor operation. Rotary screw compressors [9] use two meshing helical screws, known as rotors, to compress the gas. In a dry running rotary screw compressor, timing gears ensure that the male and female rotors maintain precise alignment. In an oil-flooded rotary screw compressor, lubricating oil bridges the space between the rotors, both providing a hydraulic seal and transferring mechanical energy between the driving and driven rotor. Gas enters at the suction side and moves through the threads as the screws rotate (Fig. 4.4a). The meshing rotors force the gas through the compressor (Fig. 4.4b), and the gas exits at the end of the screws (Fig. 4.4c). The effectiveness of this mechanism is dependent on precisely fitting clearances between the helical rotors, and between the rotors and the chamber for sealing of the compression cavities. The pressure ratio H p is defined by: Hp =

pd ps

(4.3.9)

where pd is the discharge pressure and ps is the suction pressure. • Characteristic parameters. The theoretical flow rate D0 , in m3 /min, of the compressor is expressed as follows: D0 =

n k V0 1000

(4.3.10)

where V 0 is the vapour volume transported to a main rotor rotation, in dm3 /rev, and nc is the rotational speed of the main compressor shaft, in rev/min.

Fig. 4.4 Phases of compression process

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4 Efficient Refrigeration and Air-Conditioning Systems

The real volumetric flow rate D of the compressor is smaller than D0 due volumetric losses: D = λk D 0

(4.3.11)

where λk is the volumetric efficiency of the compressor. The power consumed by the compressor Pk , in kW, is given by the equation: Pk =

1 D0 (i 2 − i 1 ) 60 v1

(4.3.12)

where v1 is the specific volume, in m3 /kg, of the refrigerant vapour in the suction state and i1 and i2 are the corresponding enthalpies, in kJ/kg, of the refrigerant for the aspiration and discharge conditions. The final compression temperature t 2 , in °C, for an oil-free compressor can be calculated using the equation: t2 = t1 + t

(4.3.13)

in which: T1 t = λk



pd ps

 χ−1 χ

 −1

(4.3.14)

where t 1 is the suction temperature, in °C; T 1 is the absolute suction temperature, in K; and χ is the isentropic index (approximately 1.4 for air and 1.2 for other gas). The final temperature of the compressed working fluid can reach a maximum value of 250 °C. This temperature corresponds to pressure ratio values of 4.5 and 7 for air and other gases, respectively. In an oil-injected rotary screw compressor, oil is injected into the compression cavities to aid sealing and provide a cooling sink for the gas charge. The final compression temperature of the vapour is lower than 90 °C, and the pressure ratio can be H k ≥ 21. Figure 4.5 shows the characteristic diagram of a screw compressor. The thermal power Qk , in kW, of a compressor in imposed running conditions is given by: Qk =

1 q0 λk D 0 60 v1

where q0 is the specific heat load at evaporation, in kJ/kg. The evaporator cooling power can be determined using the equation:

(4.3.15)

4.3 Types of Compressors

219

Fig. 4.5 Characteristic diagram of a rotary screw compressor

  1 qc Q 0 = mq0 = Q k = Qk 1 + q0 COP

(4.3.16)

where q0 is the specific cooling power of the working fluid, in kJ/kg. The coefficient of performance of the compressor εk is defined as: εk =

Q0 Pk

(4.3.17)

In variable operational conditions, the rotary screw compressor is characterised by a variable absorbed vapour flow rate and compression power achieving variable cooling powers. Figure 4.6a shows the cooling and compression power diagrams

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4 Efficient Refrigeration and Air-Conditioning Systems

Fig. 4.6 Operational characteristics variation of a screw compressor. a cooling and compression power diagrams; b efficiency variation diagram

at different operational conditions for a screw compressor (nk = 3000 rev/min, D0 = 816 m3 /h) operating with R22. Figure 4.6b shows the variation diagram of the efficiency εk . Large capacity heat pumps used in the heating/cooling of manufacturing facilities, office buildings, administrative buildings and hotels are equipped with screw compressors which operate alone or in parallel.

4.3.4 Centrifugal Compressors Centrifugal compressors, sometimes termed radial compressors (Fig. 4.7), are a subclass of dynamic axisymmetric work-absorbing turbo-machinery. The idealised compressive dynamic turbo-machine achieves a pressure rise by adding kinetic energy/velocity to a continuous flow of fluid through the rotor or impeller. This kinetic energy is then converted to an increase in potential energy/static pressure by slowing the flow through a diffuser. The pressure rise in impeller is in most cases almost equal to the rise in the diffuser section.

4.3 Types of Compressors

221

Fig. 4.7 Centrifugal compressor

In the case of where flow simply passes through a straight pipe to enter a centrifugal compressor; the flow is straight, uniform and has no vorticity. As the flow continues to pass into and through the centrifugal impeller, the impeller forces the flow to spin faster and faster. According to a form of Euler’s fluid dynamics equation, known as “pump and turbine equation”, the energy input to the fluid is proportional to the flow’s local spinning velocity multiplied by the local impeller tangential velocity. A simple centrifugal compressor has four components: inlet, impeller/rotor, diffuser and collector [10]. The inlet to a centrifugal compressor is typically a simple pipe. It may include features such as a valve, stationary vanes/airfoils (used to help swirl the flow) and both pressure and temperature instrumentation. All of these additional devices have important uses in the control of the centrifugal compressor. Centrifugal impeller is the key component that makes a compressor centrifugal. The impeller contains rotating set of vanes (or blades) that gradually raises the energy of the working gas. This is identical to an axial compressor with the exception that the gases can reach higher velocities and energy levels through the impeller’s increasing radius. The diffuser is the next key component to the simple centrifugal compressor. Downstream of the impeller in the flow path, it is the diffuser’s responsibility to convert the kinetic energy (high velocity) of the gas into pressure by gradually slowing (diffusing) the gas velocity. Diffusers can be vane less, vanes or an alternating combination. The collector of a centrifugal compressor can take many shapes and forms. When the diffuser discharges into a large empty chamber, the collector may be termed a Plenum. When the diffuser discharges into a device that looks somewhat like a snail shell, bull’s horn or a French horn, the collector is likely to be termed a volute or scroll. A collector’s purpose is to gather the flow from the diffuser discharge annulus and deliver this flow to a downstream pipe.

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4 Efficient Refrigeration and Air-Conditioning Systems

Because of the wide variety of vapour compression-based cycles and the wide variety of refrigerants, centrifugal compressors are used in a wide range of sizes and configurations.

4.3.5 Scroll Compressors A scroll compressor, also called spiral compressor is a device for compressing air or refrigerant (Fig. 4.8). Many residential central heat pump and air-conditioning systems employ a scroll compressor instead of the more traditional rotary and reciprocating compressors. A scroll compressor uses two interleaving scrolls to pump, compress or pressurise fluids such as liquids and gases [11]. The vane geometry may be involutes, Archimedean spiral or hybrid curves. Often, one of the scrolls is fixed, while the other orbits eccentrically without rotating, thereby trapping and pumping or compressing pockets of fluid between the scrolls. The compression process occurs over approximately two to two and one-half rotations of the crankshaft, compared to one rotation for rotary compressors and one-half

Fig. 4.8 Scroll compressor

4.3 Types of Compressors

223

rotation for reciprocating compressors. The scroll discharge and suction processes occur for a full rotation, compared to less than a half-rotation for the reciprocating suction process, and less than a quarter-rotation for the reciprocating discharge process. Reciprocating compressor has multiple cylinders (typically, anywhere from two to six), while scroll compressors only have one compression element. Scroll compressors never have a suction valve, but depending on the application may or may not have a discharge valve. The use of a dynamic discharge valve is more prominent in high-pressure ratio applications, typical of refrigeration. The use of a dynamic discharge valve improves scroll compressor efficiency over a wide range of operating conditions, when the operating pressure ratio is well above the built-in pressure ratio of the compressors. The isentropic efficiency of scroll compressors is slightly higher than that of a typical reciprocating compressor when the compressor is designed to operate near one selected rating point. The scroll compressors are more efficient in this case because they do not have a dynamic discharge valve that introduces additional throttling losses. However, the efficiency of a scroll compressor that does not have a discharge valve begins to decrease as compared to the reciprocating compressor at higher pressure ratio operation. The scroll compression process is nearly 100% volumetrically efficient in pumping the trapped fluid. The suction process creates its own volume, separate from the compression and discharge processes further inside. By comparison, reciprocating compressors leave a small amount of compressed gas in the cylinder, because it is not practical for the piston to touch the head or valve plate. That remnant gas from the last cycle then occupies space intended for suction gas. The reduction in capacity (i.e., volumetric efficiency λk ) depends on the suction and discharge pressures with greater reductions occurring at higher ratios of discharge to suction pressures. Until recently, a powered scroll compressor could only operate at full capacity. Modulation of the capacity was accomplished outside the scroll set. In order to achieve partial loads, engineers would bypass refrigerant from intermediate compression pocket back to suction, vary motor speed or provide multiple compressors and stage them on and off in sequence. Recently, scroll compressors have been manufactured that provide partial load capacity within a single compressor. These compressors change capacity while running. While scroll compressors can also rely on vapour injection to vary the capacity, their vapour injection operation is not as efficient as for the case of reciprocating compressors. This inefficiency is caused by continuously changing volume of the scroll compressor compression pocket during the vapour injection process. As the volume is continuously being changed the pressure within the compression pocket is also continuously changing which adds inefficiency to the vapour injection process. Some of the best compressors with efficiency up to 60% of Carnot’s theoretical limit are produced by Danfoss, Copeland, York, Trane, Embraco and Bristol compressor manufacturers.

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4.4 Substitution Strategy of Non-ecological Refrigerants 4.4.1 Preliminary Considerations Environmental pollution represents a major risk for all life on our planet (men, flora, fauna), because it consists not only of the local noxious effects of different pollutants but also the imbalances produced on a large scale over the entire planet. Environmental protection represents the fundamental condition of the society’s sustainable development and a high priority of national interest that is realised in institutional framework in which the legal norms regulate the development of activities with environmental impact and exerts control on such activities. The purpose of environmental protection is to maintain the ecological balance, to maintain and improve the natural factors, to prevent and control pollution, to promote the development of natural values, to ensure better life and work condition for the present and future generations and it refers to all actions, means and measures undertaken for these purposes. One of the minor components of the atmosphere, the ozone layer, has a special importance in maintaining the ecological balance. Ozone is distributed primarily between the stratosphere (85–90%) and troposphere. Any perturbation of the atmospheric ozone concentration (which varies between 0 ppm and 10 ppm, depending on the regions) has direct and immediate effects upon life. For most of the states the problems of forming and maintaining the earth’s ozone layer, represents a major priority. In this context during the last 30 years, the European Union has adopted a large number of laws and regulations concerning environmental protection to correct the pollution effects, frequently by indirect directives, through imposition of the levels of allowable concentrations by asking for government collaboration, programs and projects for the regulation of industrial activities and productions. The Alliance for Responsible Atmospheric Policy is an industry coalition and leading voice for ozone protection and climate change policies, which maintains a brief summary of the regulations for some countries [12]. Refrigerants are the working fluids in heat pump (HP), air conditioning (A/C) and refrigeration systems. They absorb heat from one area, such as an air-conditioned space, and reject it into another, such as outdoors, usually through evaporation and condensation. Working fluids escaped through leakages from cooling equipment during normal operation (filling or empting) or after accidents (damages) gather in significant quantities at high levels of the atmosphere (stratosphere). In the stratosphere, through catalytically decompounding, pollution from working fluid leakage depletes the ozone layer that normally is filtering the ultraviolet radiation from the sun, which is a threat to living creatures and plants on earth. Stratospheric ozone depletion has been linked to the presence of chlorine and bromine in the stratosphere. In addition, refrigerants contribute to global warming (also called global climate change) because they are gases that exhibit the greenhouse effect when in the atmosphere.

4.4 Substitution Strategy of Non-ecological Refrigerants

225

Concerning the polluting action upon the environment, for atmospheric ozone, as presented through the Montreal Protocol [13] and the subsequent amendments, as well as for the greenhouse effect according to the Kyoto Protocol [14], refrigerants can be classified as follows: • having strong destructive action on the ozone layer and with significant amplification of the greenhouse effect upon the earth (Chlorofluorocarbons-CFCs); • having reduced action on the ozone layer and with moderate amplification of the greenhouse effect (Hydro-chlorofluorocarbons-HCFCs); • being harmless to the ozone layer, with less influence upon the greenhouse effect (Hydro-fluorocarbons-HFCs); • being harmless to the ozone layer, with very less or even no influence upon greenhouse effect (carbon dioxide—CO2 (R744), natural hydrocarbons (HCs) and ammonia—NH3 (R717), respectively). Vapour compression-based systems are generally employed with halogenated refrigerants. The international protocols (Montreal and Kyoto) restrict the use of the halogenated refrigerants in the vapour compression-based systems. As per Montreal Protocol 1987, the use of CFCs was completely stopped in most of the nations. However, HCFCs refrigerants can be used until 2040 in developing nations and developed nations should phase out by 2030 [15]. To meet the global demand in the HP and A/C sector, it is necessary to look for long-term alternatives to satisfy the objectives of international protocols. From the environmental, ecological and health point of view, it is urgent to find some better substitutes for HFC refrigerants. HC and HFC refrigerant mixtures with low-environment impacts are considered as potential alternatives to phase out the existing halogenated refrigerants. This section presents a study on recent development of possible substitutes for non-ecological refrigerants employed in heating, ventilating, air-conditioning and refrigerating (HVAC&R) equipment based on thermodynamic, physical and environmental properties and total equivalent warming impact (TEWI) analysis. This study also contains a good amount of information regarding the environmental pollution produced by the working fluids of the HP, A/C and commercial refrigeration applications and the ecological refrigerant trend. Overall, it is useful for those readers who are interested in current status of alternative refrigerant development related to vapour compression-based systems. Additionally, this study describes the selection of refrigerants adapted to each utilisation based on the thermodynamic, physical and environmental properties, the technological behaviour and the use constraints as the principal aspects of the environmental protection. Finally, a comparative analysis of the TEWI for possible substitutes of refrigerant R22 used in various A/C, refrigeration and HP systems is performed [16, 17].

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4 Efficient Refrigeration and Air-Conditioning Systems

4.4.2 Environmental Impact of Refrigerants The design of the refrigeration equipment depends strongly on the properties of the selected refrigerant. Refrigerant selection involves compromises between conflicting desirable thermo-physical properties. A refrigerant must satisfy many requirements, some of which do not directly relate to its ability to transfer heat. Chemical stability under conditions of use is an essential characteristic. Safety codes may require a non-flammable refrigerant of low toxicity for some applications. The environmental consequences of refrigerant leaks must also be considered. Cost, availability, efficiency and compatibility with compressor lubricants and equipment materials are other concerns. Safety properties of refrigerants considering flammability and toxicity are defined by ASHRAE standard 34 [18]. Toxicity classification of refrigerants is assigned to classes A or B (Table 4.1). Class A signifies refrigerants for which toxicity has not been identified at concentrations less than or equal to 400 ppm by volume, and class B signifies refrigerants with evidence of toxicity at concentrations below 400 ppm by volume. By flammability refrigerants are divided in three classes. Class 1 indicates refrigerants that do not show flame propagation when tested in air (at 101 kPa and 21 °C). Class 2 signifies refrigerants having a lower flammability limit (LFL) of more than 0.10 kg/m3 and a heat of combustion less than 19,000 kJ/kg. Class 3 indicates refrigerants that are highly flammable, as defined by an LFL of less than or equal to 0.10 kg/m3 or a heat of combustion greater than or equal to 19,000 kJ/kg. New flammability class 2L has been added since 2010 denoting refrigerants with burning velocity less than 10 cm/s. Minimising all refrigerant releases from systems is important not only because of environmental impacts but also because charge losses lead to insufficient system charge levels, which in turn results in suboptimal operation and lowered efficiency. The average global temperature is determined by the balance of energy from the sun heating the earth and its atmosphere and of the energy radiated from the earth and the atmosphere into space. Greenhouse gases (GHGs), such as water vapour, as well as small particles trap heat at and near the surface, maintaining the average temperature of the Earth’s surface at a temperature approximately 34 K warmer than would be the case if these gases and particles were not present (greenhouse effect). Global warming is a concern because of an increase in the greenhouse effect from increasing concentrations of GHGs attributed to human activities. Thus, the negative environmental impact of the working fluids, especially the effect of halogenated refrigerants on the environment, can be synthesised by two effects [19]: Table 4.1 Safety classification of refrigerants

Flammability

Safety code Lower toxicity

Higher toxicity

higher flammability

A2

B2

lower flammability

A2L

B2L

no flame propagation

A1

B1

4.4 Substitution Strategy of Non-ecological Refrigerants

227

• depletion of the ozone layer; • contribution to global warming at the planetary level via the greenhouse effect. The measure of a material’s ability to deplete stratospheric ozone is its ozone depletion potential (ODP), a relative value to that of R11, which has an ODP of 1.0. The global warming potential (GWP) of a GHG is an index describing its relative ability to collect radiant energy compared to CO2 , which has a very long atmospheric lifetime. Therefore, refrigerants will be select so that the ozone depletion potential will be zero and with a reduced GWP. The most utilised halogenated refrigerants are the family of chemical compounds derived from the hydrocarbons (HC) (methane and ethane) by substitution of chlorine (Cl) and fluorine (F) atoms for hydrogen (H) (Fig. 4.9), whose toxicity and flammability scale according to the number of Cl and H atoms. The presence of halogenated atoms is responsible for ODP and GWP. Table 4.2 presents the principal characteristics of halogenated refrigerants (pure and mixtures), with the symbol for refrigerant, chemical name and formula, as well as their application domains [16]. During the last century, the halogenated refrigerants have dominated the vapour compression-based systems due to its good thermodynamic and thermo-physical properties. Thermodynamic properties of pure refrigerants are listed in Table 4.3 [20]. But the halogenated refrigerants are having poor environmental properties with respect to ODP and GWP. The second generation of refrigerants, CFCs replaced classic refrigerants in early twentieth century. Refrigerants as CFCs (R12, R11 and R13) have been used since the 1930 s because of their superior safety and performance characteristics. However, their production for use in developed countries has been eliminated because it has been shown that they deplete the ozone layer. The CFCs and HCFCs represented by R22 and mixture R502 dominated the second generation of refrigerants. HCFCs also deplete the ozone layer, but to a much lesser extent than CFCs. HCFCs production for use as refrigerants is scheduled for elimination by 2030 for developed countries and by 2040 for developing countries [15]. The traditional refrigerants (CFCs) were banned by the Montreal Protocol because of their contribution to the disruption of the stratospheric ozone layer. The Kyoto Protocol listed HCFCs as being with large GWPs. With the phasing out of the use of CFCs, chemical substances such as the HCFCs and the HFCs, were proposed and have been used as temporary alternatives. The HFCs do not deplete the ozone layer and have many of the desirable properties of CFCs and HCFCs. They are being widely used as substitute refrigerants for CFCs and HCFCs. The HFC refrigerants have significant benefits regarding safety, stability and low toxicity, being appropriate for large-scale applications. Also, the HC and HFC refrigerant mixtures with low-environment impacts are considered as potential alternatives to phase out the existing halogenated refrigerants. HC-based mixtures are environment-friendly, which can be used as alternatives without modifications in the existing systems. But HC refrigerant mixtures are highly flammable, which limits the usage in large capacity systems [21]. HFC mixtures are

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Fig. 4.9 Chlorofluoro compound derived from methane and ethane

ozone-friendly, but it has significant GWP. HFC mixtures are not miscible with mineral oil, which require synthetic lubricants (such as polyolester). Earlier investigations reported that HFC/HC mixtures are miscible with mineral oil. It is possible to mix HC refrigerants with HFC to replace the existing halogenated refrigerants [22].

C2 H3 ClF2 Chlorodifluoroethane

C2 Cl2 F4 Dichlorotetrafluoroethane

R114

R142b

C2 Cl3 F3 Trichlorotrifluoroethane

R113

CHClF2 Chlorodifluoromethane

CBrF3 Bromotrifluoromethane

R13B1

R22

CClF3 Chlorotrifluoromethane

R13

CHCl2 F Dichlorofluoromethane

CClBrF2 Bromochlorodifluoromethane

R12B1

R21

CCl2 F2 Dichlorodifluoromethane

R12

HCFC

CCl3 F Threechlorofluoromethane

R11

CFC

Chemical formula/Chemical name

Refrigerant

Group

Table 4.2 Application domains of halogenated refrigerants

+10 +80 +20 +10 +10 +60

−20 +10 −20 −50 −20 +10

−40

−80 +15 +50

−60

−100

0 +15

+50

+10 +40

−40 +10 0

+60

0

Evaporation temperature, t 0 (o C)

Air conditioning Heat pumps (continued)

Industrial-, food-, commercial refrigeration, air conditioning

Air conditioning, heat pumps

Air conditioning, Heat pumps

Air conditioning Heat pumps

Mono-, two stage- and in cascade refrigeration systems, for industry

Cascade refrigeration systems

Air conditioning, Heat pumps

Domestic and commercial refrigeration Air conditioning, heat pumps

Air conditioning, heat pumps

Applications

4.4 Substitution Strategy of Non-ecological Refrigerants 229

(R22/R115)

(R125/R134a)

(R32/R125)

(R32/R125/R134a)

(R125/R143a/R134a)

R507

R410A

R407C

R404A

C2 H4 F2 Difluoroethane

R152a

(R12/R152a)

C2 H2 F4 Tetrafluoroethane

R134a

R502

C2 HF5 Pentafluoroethane

R125

R500

CH2 F2 Difluoromethane

R32

Mixtures

CHF3 Threefluoromethane

R23

HFC

Chemical formula/Chemical name

Refrigerant

Group

Table 4.2 (continued)

Cascade refrigeration systems for industry and laboratory

−60 −10 +10 +20 +10 +10 −20 −10 0 0 0

−100 −60 −50 −30 −30 −40 −60 −50 −50 −40 −40

Industrial and commercial refrigeration

Industrial and commercial refrigeration

Industrial and commercial refrigeration

Industrial and commercial refrigeration

Industrial and commercial refrigeration

Household and industrial refrigeration, heat pumps

Industrial and commercial refrigeration, air conditioning

Domestic-, commercial-, industrial refrigeration, air conditioning

Industrial and commercial refrigeration, air conditioning

Industrial and commercial refrigeration

Applications

Evaporation temperature, t 0 (o C)

230 4 Efficient Refrigeration and Air-Conditioning Systems

4.4 Substitution Strategy of Non-ecological Refrigerants

231

Table 4.3 Thermodynamic properties of pure refrigerants Refrigerant

Molecular mass, M [g/mol]

Critical temperature, t cr (°C)

Critical pressure, pcr (MPa)

Boiling point, t 0n (°C)

R11

137.37

198.0

4.41

23.7

R12

120.90

112.0

4.14

−29.8

R22

86.47

96.2

4.99

−41.4

R23

70.01

25.9

4.84

−82.1

R32

52.02

78.2

5.80

−51.7

R41

34.03

44.1

5.90

−78.1

R123

152.93

82.0

3.66

27.8

R124

136.48

122.3

3.62

−12.0

R125

120.02

66.2

3.63

−54.6

R134a

102.03

101.1

4.06

−26.1

R142b

100.49

137.2

4.12

−9.0

R143a

84.04

72.9

3.78

−47.2

R152a

66.05

113.3

4.52

−24.0

R161

48.06

102.2

4.70

−34.8

R170

30.07

90.0

4.87

−88.9

R218

188.02

71.9

2.68

−36.6 −42.2

R290

44.10

96.7

4.25

R600

58.12

152.0

3.80

−0.5

R600a

58.12

134.7

3.64

−11.7 −33.3

R717

17.03

132.3

11.34

R744

44.01

31.1

7.38

−78.4

R1270

42.08

92.4

4.67

−47.7

A second influence of refrigerants upon the environment, as previously mentioned, guided to a new classification of refrigerants according to their contribution to global warming. Comparison of this specific contribution to the greenhouse effect is performed even for R11 (the most noxious even from the point of view of ODP) as well as for CO2 . Halogenated refrigerants is categorised in the undesirable position 3 (14%) between the greenhouse gases, which could be explained by their great absorption capacity of infrared radiation. In the case of HP systems, although supplementary to the direct action to the greenhouse effect because of the refrigerants leakage in atmosphere, it must be considered even the indirect action to global warming by the CO2 quantity released during the production of the drive energy for system is obviously greater than the associated direct action [23]. While the refrigerant quantity increases in the system, the effect of direct action rises. The environmental impact of an HVAC&R system is due to the release of refrigerant and the emission of greenhouse gases for associated energy use. The total

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equivalent warming impact (TEWI) is used as an indicator for environmental impact of the system for its entire lifetime. TEWI is the sum of the direct refrigerant emissions, expressed in terms of CO2 equivalents and the indirect emissions of CO2 from the system’s energy use over its service life. The life cycle climate performance (LCCP) of an HVAC&R system includes TEWI and adds the effects of direct and indirect emissions associated with manufacturing the refrigerant. The analysis of the TEWI index for refrigeration systems operating with different refrigerants (R22, R134a, R404A, R717, R744) indicated that the direct effect generated by CO2 is negligible compared with the other refrigerants [24]. The indirect effect generated by CO2 is significant because of the high-condensation pressures that determine the large amount of energy consumption and in consequence the maximum value of TEWI for CO2 . Environmentally preferred refrigerants have: • • • • • •

low or zero ODP; relatively short atmospheric lifetimes; low GWP; ability to provide good system efficiency; appropriate safety properties; ability to yield a low TEWI or LCCP in system applications.

Table 4.4 lists the environmental properties of refrigerants [16]. Because HFCs do not contain chlorine or bromine, their ODP values are negligible and represented by 0 in this table. NH3 , HCFCs, most HFCs and HFOs have shorter atmospheric lifetimes than CFCs because they are largely destroyed in the lower atmosphere by reaction with OH radicals. A shorter atmospheric lifetime generally results in lower ODP and GWP values. The European Commission [25] has published its firm proposal for changes to EU F-Gas Regulation. These changes aim to substantially reduce the emissions of fluorinated (F) gases over the next 20 years. F-Gases are greenhouse gases, with a GWP several thousand times higher that of CO2 . The largest use of F-Gases in Europe is for HFC refrigerants, and under the new F-Gas regulation, their use will be severely restricted. The two most important proposals are: • a gradually phase-down in EU consumption of HFCs (from 2019 to 2047) to achieve 85% reduction; • a ban on the use of high-GWP refrigerants from 2020. Recently, new HFC refrigerants (named HFOs) with low GWPs are appeared on the market.

4.4.3 Influence of Refrigerants on Process Efficiency The design and efficiency of the refrigeration equipment depends strongly on the selected refrigerant’s properties. Consequently, operational and equipment costs depend on refrigerant choice significantly. The single-stage vapour-compression system with a single component or azeotropic refrigerant has the thermodynamic cycle illustrated in Fig. 4.10.

4.4 Substitution Strategy of Non-ecological Refrigerants

233

Table 4.4 Environmental properties of refrigerants Group

Fluid

ODP

GWP GWP Atmospheric (R11 = 1) (CO2 = lifetime [years] 1)

CFC

R11

1

1

4000

50–60

R12

1

2.1–3.05

10600

102–130

R113

0.8–1.07

1.3

4200

90–110

R114

0.7–1.0

4.15

6900

130–220

R12B1

3–13

−

1300

11–25

R13B1

10–16

1.65

6900

65–110

R21

0.05

0.1

−

0 was recommended in summer and the up bound that PMV < 0 was recommended in winter.

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47. Li D, Groll EA (2005) Transcritical CO2 refrigeration cycle with ejector-expansion device. Int J Refrig 28:766–773 48. Gillaux S (2012) Inside view into the Japanese hat pump market. Rehva Journal 49(5):55–56 49. Goto H, Goto M, Sueyoshi T (2011) Consumer choice on ecologically efficient water heaters: Marketing strategy and policy implications in Japan. Energy Economics 33:195–208 50. Maratou A, Lira JT, Jia H, Masson N (2012) CO2 heat pumps in Europe market dynamics & legislative opportunities. Rehva Journal 49(5):50–52 51. Fatouh M, Kafafy M (2006) Experimental evaluation of a domestic refrigerator working with LPG. Appl Therm Eng 26:1593–1603 52. Didion DA, Bivens DB (1990) Role of refrigerant mixtures as alternatives to CFCs. Int J Refrig 13:163–175 53. Nickl J, Will G, Quack H, Kraus WE (2005) Integration of a three-stage expander into a CO2 refrigeration system. Int J Refrig 28:1219–1224 54. Calm JM, Domanski PA (2004) R22 Replacement status. ASHRAE J 46:29–39 55. Cox N, Mazur V, Colbourne D. The development of azeotropic ammonia refrigerant blends for industrial process applications. In: Proceedings of the International Conference on Ammonia Refrigeration Technology, Ohrid, North Macedonia, 7–9 May; 2009 56. Girip A, Ilie A, Drughean L, Hera D. Environmental impact of some possible substitutes for R22 in refrigeration and heat pump systems. In: Proceedings of the National Conference on the Building Services for Beginning of Three Millennium, Sinaia, Romania, 13–15 November; 2013, pp 195-205 57. AIRACH, Methods of calculating total equivalent warming impact (TEWI). In: Best Practice Guidelines. Melbourne, Australia: Australian Institute of Refrigeration, Air-conditioning and Heating; 2012 58. Eiseman BJ (1949) Effect on elastomers of Freon compounds and other halo-hydrocarbons. Refrigerating Engineering 12:1171 59. Sarbu I, Valea ES, Sebarchievici C (2010) Use of recovered thermal energy from refrigerating systems. Energetica 58(6):301–305 60. Chiriac F (1981) Refrigeration systems. Didactic and Pedagogical Publishing House, Bucharest (in Romanian) 61. Sarbu I. Model and program for the analysis and operational optimisation of vapour compression-based refrigeration systems. In: Proceedings of the National Symposium on Building Services and Ambient Comfort, vol. II, Timisoara, Romania; 1992, pp 120–130 62. Sarbu I. Exergetic analysis of processes in absorption refrigeration systems with hydroammoniacal solution. In: Proceedings of the Technical-Scientific Colloquium on Building Services and Energy Saving, vol. II, Iasi, Romania; 1992, pp 307–313 63. Sarbu I, C. Sebarchievici C. Solar heating and cooling systems: Fundamentals, expe-riments and applications. Oxford, UK: Elsevier; 2017 64. Porneala S (1985) Possibilities for domestic hot water preparation by heat recovery from resorption refrigeration systems. Journal of Chemistry 36(4):331 65. ASHRAE handbook: Refrigeration. Atlanta, GA, USA: American Society of Heating, Refrigerating and Air Conditioning Engineers; 2006 66. Iosifescu C, Gheorghiu C, Porneala S (1970) Considerations on the optimal operating regime of two-stage compression refrigeration systems. Food Industry 21(11):644 67. Niculita P, Ceanga E, Bumbaru S (1983) Automation of industrial refrigeration systems. Technical Publishing House, Bucharest (in Romanian) 68. Radcenco V, Florescu AL, Duica T, Burchiu N, Dimitriu S et al (1985) Heat pump systems. Technical Publishing House, Bucharest (in Romanian) 69. La Remo J (1984) production combinée de chaleur et le froid. Révue Générale du Froid 2:81 70. Drevali IK (1984) Efficiency of the floor heating system using the released heat of the refrigeration unit. Holodilnaia Tehnica 4:17 (in Russian) 71. Storkmann M (2004) Insulating against the low temperatures by flexible insulation materials. Building Equipments Technique 22(5):60–62 72. Malloy JF (1969) Thermal insulation. Van Nostrand Reinhold, New York, USA

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Chapter 5

Solar Heating and Cooling Systems

Abstract This chapter presents a detailed theoretical study, numerical modelling and some applications for solar heating and cooling systems focused on active and combisystems. Important information’s on simulating solar heating systems are discussed and the TRNSYS program is also briefly described. Additionally, a detailed review of different solar thermal-driven refrigeration and cooling systems including sorption technology (open systems or closed systems) and thermo-mechanical technology (ejector system) is also provided. The study refers to a comparison of various solar thermal cooling systems, and to some suggestions for the use of these systems. A comprehensive survey of solar thermo-electric (TE) cooling systems is also provided. Finally, the possibility of solar TE cooling technologies application in “nearly-zero” energy buildings is briefly discussed and some future research directions are included.

5.1 Generalities Energy, similar to water, food and shelter, is an essential need of all human beings in the world. The technological advancement and economic growth of every country depends on the energy consumed [1], and the amount of energy available reflects the quality of life of that country. Fossil fuels are the prominent source for generating utilisable forms of energy [2]. Therefore, fossil fuels are the major contributor to global warming and the greenhouse effect on the ozone. The ever increasing worldwide energy consumption has created an urgent need to find new ways to use the energy resources in a more efficient and rational way. It is estimated that the global energy consumption will increase by 71% from 2003 to 2030 [3, 4]. Currently, heating is responsible for almost 80% of the energy demand in houses and utility buildings, used for space heating and domestic hot water (DHW) gene-ration, whereas the energy demand for cooling is growing yearly. The awareness of global warming has intensified in recent times and has reinvigorated the search for energy sources that are independent of fossil fuels and contribute less to global warming. The European strategy to decrease the energy dependence rests on two objectives: the diversification of the various sources of supply and policies to control consumption. The key to diversification is ecological and renewable © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 I. Sarbu, Advances in Building Services Engineering, https://doi.org/10.1007/978-3-030-64781-0_5

329

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5 Solar Heating and Cooling Systems

energy sources (RES) because they have significant potential to contribute to sustainable development [5]. Because of the desirable environmental and safety aspects it is widely believed that solar energy should be utilised instead of other alternative energy forms, even when the costs involved are slightly higher. The use of surface heating systems is increasing in Europe, but it is still much less than the use of hot water radiators. Also, low-temperature panel heating and cooling systems for residential buildings are increasingly used [6]. Moreover, one solution for addressing worldwide energy demand increase and climate changes will be using renewable energy to providing cooling instead of fossil fuel-consuming air-conditioning (A/C) systems, making solar cooling technologies important for future. Solar energy is currently a subject of great interest, and refrigeration is a particularly attractive application due to the coincidence between the peak of cooling demand and the solar radiation availability. Solar thermal energy is appropriate for both heating and cooling. Key applications for solar technologies are those that require low-temperature heat such as domestic water heating, space heating, pool heating, drying process and certain industrial processes. Depending on the other uses of energy in buildings, DHW production can represent up to 30% of the energy consumed. Solar water heaters represent one of the most profitable applications of solar energy today. For centuries Romanians have been used wind and water to put in force mills, wood and solar energy to heat water and buildings. The type of resources and the energy potential of each are summarised in Table 5.1 [7]. Solar applications can also meet cooling needs, with the advantage that the supply (sunny summer days) and the demand (desire for a cool indoor environment) are well matched. To generate synergy effects in climates with heating and cooling demand combined systems should be used. Different ways could be considered to reduce primary energy consumption due to fossil fuel and equivalent CO2 emissions related to space heating and cooling: • interventions on opaque and transparent building envelope reducing transmittance; Table 5.1 Energy potential of renewable energy sources No.

RES

Annual energy potential

Economic energy equivalent (ktoe)

Application

1

Solar energy: • thermal

60·106 GJ

1,433.0

Thermal energy

• photovoltaic (PV)

1,200 GWh

103.2

Electrical energy

2

Wind energy

23,000 GWh

1,978.0

Electrical energy

3

Hydro-energy

40,000 GWh

3,440.0

Electrical energy

4

Biomass

318·106 GJ

7,594.0

Thermal energy

5

Geothermal energy

7·106 GJ

167.0

Thermal energy

5.1 Generalities

331

• introducing high-efficiency energy conversion systems, such as condensing boiler, cogeneration system, gas engine driven HP and ground-source HP; • introducing renewable energy system based on solar thermal collectors considering different technologies; • solar electric driven system: solar PV collectors interacting with a space heating and cooling system based on an electric heat pump; • solar thermal assisted electric heat pump: thermal energy available from solar collector used to operate an electric heat pump at lower evaporating temperature; • a combination of renewable energy based and high-energy conversion efficiency technologies. If effective support policies are put in place in a wide number of countries during this decade, solar energy in its various forms (i.e., solar heat, solar PV and solar thermal electricity) can make considerable contributions to solving some of the most urgent problems the world now faces: climate change, energy security and universal access to modern energy services. This chapter presents a detailed theoretical study, numerical modelling and some applications for solar heating and cooling systems.

5.2 Solar Water and Space Heating Systems 5.2.1 Preliminary Considerations The concept of low-energy building is based on the reduction of the primary energy demand through a high-insulation level, the use of high-efficiency heating/cooling systems and the integration of RES into the building plant. Each system design aims to increase the solar fraction (SF) value and to reduce the consumed auxiliary energy which is usually selected as fossil fuelled sources. Solar heating systems are a type of renewable energy technology that has been increasingly used in the past decade across Europe to provide heating, A/C and DHW for buildings. These systems have enabled the use of low-temperature terminal units, such as radiators and radiant systems. One of the great things about solar energy is the use both simple and complex strategies to capture it and the utilisation for space and water heating. There are two strategies for capturing the power of the sun: active and passive solar heating. Passive solar systems require little, if any, non-renewable energy to make them function [8]. Every building is passive in the sense that the sun tends to warm it by day, and it loses heat at night. Passive systems incorporate solar collection, storage and distribution into the architectural design of the building. Passive solar heating and lighting design must consider the building envelope and its orientation, the thermal storage mass and window configuration and design.

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Active solar systems use either liquid or air as the collector fluid. Active systems must have a continuous availability of electricity to operate pumps and fans. A complete system includes solar collectors, energy storage devices and pumps or fans for transferring energy to storage or to the load. Active solar energy systems have been combined with heat pumps for water and/or space heating. Freeman et al. [9] presents information on performance and estimated energy saving for solar heat pumps. A solar thermal system consists of a solar collector, a heat exchanger, storage, a backup system and a load. The load can be space heating or hot water. This system may serve for both space heating and DHW production. This section provides a description of main types of solar space and water heating systems, concentrating on classifications, system components and operation principles. It is also focused on active and combisystems. Important information’s on simulating solar heating systems are discussed and the Transient System Simulation (TRNSYS) program is also briefly described. Additionally, some examples of DHW systems and combisystems application are presented [10, 11].

5.2.2 Solar Water Heating Systems Water heating is one of the most basic energy services. The share of energy used to heat the DHW has been increasing significantly as the thermal performance of building envelope has been improving. The heating energy for DHW depends on the use of water, which has decreased significantly during the last few decades. Twenty five years ago the average use was around 200 l/day/pers in residential buildings; now it is 120–140 l/day/pers. The reduction is partly due to water saving faucets, new washing methods and even more importantly, the common use of a shower instead of a bath tub for better personal hygiene. About 40% of the domestic water is used as hot water. It can correspond to 30–40 kWh/m2 of energy use in residential buildings, which is significant (25%) in relation to energy use in the EU buildings that is typically in the range of 100–150 kWh/m2 . The shares are even higher in low energy and nearly zero-energy buildings: approximately 50% in single-family buildings and more than 50% in multifamily buildings. Solar heating of DHW is, in most cases, the most cost-effective use of renewable energy. Water use profiles affect the sizing of the collector, storage tanks and backup heating. An important issue to keep in mind with solar water heating systems is the possibility of low-temperature level (below 55 °C) in the system, which may allow the growth of Legionella bacteria in the plumbing system. A solar water heating system (Fig. 5.1) includes a solar collector that absorbs solar radiation and converts it to heat, which is then absorbed by a heat transfer fluid (HTF) (water, antifreeze or air) that passes through the collector. The HTF is stored or used directly. For the storage water heaters, the required heating rate Qhw , in W, can be computed using equation:

5.2 Solar Water and Space Heating Systems

333

Fig. 5.1 Components of water heating system

Q hw =

G hw ρcp t η

(5.2.1)

where: Ghw is the maximum flow rate of hot water, in m3 /s; ρ is the water density, in kg/m3 ; cp is the specific heat of water, in J/(kg K); t is the temperature rise, in K; η is the heater efficiency. An exact calculation of the heat demand for DHW can be made using international or national norms. The volume of hot water storage tank V ST , in m3 , can be computed using equation: VST = τ

Q hw ρcp t

(5.2.2)

where τ is the heating time of water, in s. The volume of DHW storage tank V ST , in litres, can be expressed as: VST =

2Vdhw Np (tdhw − tcw ) tST − tcw

(5.2.3)

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5 Solar Heating and Cooling Systems

where: V dhw is the specific DHW volume, in litres/pers; N p is the person number; t dhw is the DHW temperature, in °C; t ST is the water temperature in storage tank, in °C; t cw is the cold water temperature, in °C. Portions of the solar energy system are exposed to the weather, so they must be protected from freezing. The system must also be protected from overheating caused by high-insolation levels during periods of low-energy demand.

5.2.2.1

Types of Solar Water Heating Systems

In a solar water heating system, water is heated directly in the collector or indirectly by a HTF that is heated in the collector, passes through a heat exchanger and transfers its heat to the domestic or service water. The heat transfer fluid is transported by either natural or forced circulation. Natural circulation occurs by natural convection (thermo-siphon), whereas forced circulation uses pumps or fans. Except for thermosiphon system which need no control, solar domestic and service water heaters are controlled by differential thermostats. Five types of solar systems are used to heat domestic and service hot water: thermosiphon, direct circulation, indirect circulation, integral collector storage and site built. Recirculation and drain down are two methods used to protect direct solar water heaters from freezing. Drains down systems are direct-circulation water heating systems in which potable water is pumped from storage to the collector array where it is heated. Circulation continues until usable solar heat is no longer available. When a freezing condition is anticipated or a power outage occurs, the system drains automatically by isolating the collector array and exterior piping from the city water pressure and using one or more valves for draining. • Direct and indirect systems. Direct or open-loop systems (Fig. 5.2) circulate potable water through the collectors. They are relatively cheap but can have the following drawbacks: • They offer little or no overheat protection unless they have a heat export pump. • They offer little or no freeze protection, unless the collectors are freeze-tolerant. • Collectors accumulate scale in hard water areas, unless an ion-exchange softener is used. Until the advent of freeze-tolerant solar collectors, they were not considered suitable for cold climates since, in the event of the collector being damaged by a freeze, pressurized water lines will force water to gush from the freeze-damaged collector until the problem is noticed and rectified. Indirect or closed-loop systems (Fig. 5.3) use a heat exchanger that separates the potable water from the HTF that circulates through the collector. The two most common HTFs are water and an antifreeze-water mix that typically uses nontoxic propylene glycol. After being heated in the panels, the HTF travels to the heat exchanger, where its heat is transferred to the potable water. Though slightly more expensive, indirect systems offer freeze protection and typically offer overheat protection as well.

5.2 Solar Water and Space Heating Systems

335

Fig. 5.2 Direct systems a-passive system with tank above collector; b-active system with pump and controller driven by a photovoltaic panel

Fig. 5.3 Indirect DHW heating system

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5 Solar Heating and Cooling Systems

To produce DHW with temperature of 45 °C from cold water at temperature of 10 °C, the absorber plate must reach the temperature of 50–70 °C to transfer efficiently the heat to HTF and DHW. • Passive and active systems. Passive systems (Fig. 5.2a) rely on heat-driven convection or heat pipes to circulate water or heating fluid (heat carrier) in the system. Passive solar water heating systems cost less and have extremely low or no maintenance, but the efficiency of a passive system is significantly lower than that of an active system. Overheating and freezing are major concerns. Active systems (Fig. 5.2b) use one or more pumps to circulate water and/or heating fluid in the system. Though slightly more expensive, active systems offer several advantages: • The storage tank can be situated lower than the collectors, allowing increased freedom in system design and allowing pre-existing storage tanks to be used; • The storage tank can be hidden from view; • The storage tank can be placed in conditioned or semi-conditioned space, reducing heat loss; • Drain back tanks can be used; • Superior efficiency; and • Increased control over the system. Modern active solar water systems have electronic controllers that offer a wide range of functionality, such as the modification of settings that control the system, interaction with a backup electric or gas-driven water heater, calculation and logging of the energy saved by solar water heating system, safety functions, remote access and informative displays, such as temperature readings. The most popular pump controller is a differential controller (DC) that senses temperature differences between water leaving the solar collector and the water in the storage tank near the heat exchanger. In a typical active system, the controller turns the pump on when the water in the collector is approximately 8–10 °C warmer than the water in the tank and it turns the pump off when the temperature difference approaches 3–5 °C. This ensures the water always gains heat from the collector when the pump operates and prevents the pump from cycling on and off too often. Some active solar water heating systems use energy obtained by a small PV panel to power one or more variable speed DC pump(s). To ensure proper performance and longevity of the pump(s), the DC pump and PV panel must be suitably matched. Some PV pumped solar thermal systems are of the antifreeze variety and some use freeze-tolerant solar collectors. The solar collectors will almost always be hot when the pump(s) are operating (i.e., when the sun is bright), and some do not use solar controllers. Sometimes, however, a DC is used to prevent the operation of the pumps when there is sunlight to power the pump but the collectors are still cooler than the water in storage. One advantage of a PV-driven system is that solar hot water can still be collected during a power outage if the sun is shining. An active solar water heating system can be equipped with a bubble pump instead of an electric pump. A bubble pump circulates the HTF between collector and storage tank using solar power, without any external energy source, and is suitable for FPC

5.2 Solar Water and Space Heating Systems

337

Fig. 5.4 Integrated collector storage system

as well as TTC. In a bubble pump system, the closed HTF circuit is under reduced pressure, which causes the liquid to boil at low temperature as it is heated by the sun. The HTF typically arrives at the heat exchanger at 70 °C and returns to the circulating pump at 50 °C. In frost-prone climates the HTF is water-propylene glycol solution, usually in the ratio of 60 to 40%. • Passive direct systems. Integral collector storage (ICS) system (Fig. 5.4) uses a tank that acts as both storage and solar collector. Batch heaters are basically thin rectilinear tanks with a glass side facing the position of the sun at noon. They are simple and less costly than plate and tube collectors, but they sometimes require extra bracing if installed on a roof suffer from significant heat loss at night since the side facing the sun is largely uninsulated, and are only suitable in moderate climates. Convection heat storage (CHS) system is similar to an ICS system, except that the storage tank and collector are physically separated and transfer between the two is driven by convection. CHS systems typically use standard FPCs or ETCs, and the storage tank must be located above the collectors for convection to work properly. The main benefit of a CHS system over an ICS system is that heat loss is largely avoided since (1) the storage tank can be better insulated, and (2) since the panels are located below the storage tank, heat loss in the panels will not cause convection, as the cold water will prefer to stay at the lowest part of the system. • Active indirect systems. Pressurised antifreeze systems use a water-antifreeze (glycol) solution for HTF in order to prevent freeze damage. Though effective at preventing freeze damage, antifreeze systems have many drawbacks: • If the HTF gets too hot (for example, when the homeowner is on vacation,) the glycol degrades into acid. After degradation, the glycol not only fails to provide freeze protection, but also begins to eat away at the solar loop’s components:

338

5 Solar Heating and Cooling Systems

the collectors, the pipes, the pump, etc. Due to the acid and excessive heat, the longevity of parts within the solar loop is greatly reduced. • The water-glycol HTF must be replaced every 3–8 years, depending on the temperatures it has experienced. • Some jurisdictions require double-walled heat exchangers even though propylene glycol is non-toxic. • Even though the HTF contains glycol to prevent freezing, it will still circulate hot water from the storage tank into the collectors at low temperatures (e.g., below 4 °C), causing substantial heat loss. Drain back systems are generally indirect active systems that circulate the HTF (water or water-glycol solution) through the closed collector loop to a heat exchanger, where its heat is transferred to the potable water. Circulation continues until usable energy is no longer available. When the pump stops, HTF drains by gravity to a storage or tank (Fig. 5.5). In a pressurized system, the tank also serves as an expansion tank, so it must have a temperature−and pressure relief valve to protect against excessive pressure. In an unpressurized system, the tank is open and vented to the atmosphere [12]. Fig. 5.5 Operation principle of drain back system

5.2 Solar Water and Space Heating Systems

5.2.2.2

339

Examples of Solar DHW Systems

Technique development in field of solar energy in the last 20–25 years has generated the emergence of a diversified range of DHW solar systems. As an example, three constructive variants used in practice for closed circuit and with heat exchanger solar systems are presented [3]: • The standard variant for a DHW solar system is presented in Fig. 5.6. The solution is the simplest and cheapest system with forced circulation, thus being the most common installation. The circulating pump transports the HTF between solar collector and heat exchanger in the storage tank (coil), when the fluid temperature in solar collector is higher than the DHW temperature in storage tank; • For medium and large plants, two lower-volume storage tanks instead of a large volume one are used, and a three-way valve, driven depending on HTF and tank water temperature (Fig. 5.7) is used to control the water heating in the two storage tanks. This constitutes an advantageous operational solution (variable consumptions). The storage tanks can be both for DHW or one for DHW and another one for heating (preheating) of distribution fluid (heat carrier) in heating system; • Another constructive variant is represented by solar collector use for domestic water heating as well as for heating of swimming pool water by means of a heat exchanger (Fig. 5.8). For each m2 of swimming pool with normal depth are necessary for 0.5–0.7 m2 of solar collector.

Fig. 5.6 Closed circuit with storage tank and heat exchanger system

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Fig. 5.7 Closed circuit with two storage tanks and heat exchanger system

5.2.3 Solar Space Heating Systems Because of the reduction of the world fossil fuel reserves and strict environmental protection standards, one main research direction in the construction field has become the reduction of energy consumption, including materials, technology, and building plans with lower specific energy need, on one hand, and equipment with high performance on the other hand. Thermal energy obtained from the sun with a solar thermal system can be used for space heating. The solar heating systems fall into two principal categories: passive and active. Passive systems may be divided into several categories. In a direct-gain passive system, the solar collector (windows) and storage (e.g., floors, walls) are part of the occupied space and typically have the highest per cent of heating load met by solar. To reduce heat losses, thermal mass should be well-insulated from the outdoor environment or ground [12]. Thermal mass can be defined as a material’s ability to absorb, store, and release heat. When the sun’s rays enter the building in the winter months, the heat energy is absorbed by the materials inside the building that have a high thermal mass. This would include materials that are dense, such as stone, brick and concrete or ceramic tile. These materials absorb and hold onto heat during the period of time that the sun shin on them and then slowly release that heat throughout the nighttimes, keeping the home at a more stable and comfortable temperature. Indirect-gain passive systems use the south-facing wall surface or the roof to absorb solar radiation, which causes a rise in temperature that, in turn, conveys heat into

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Fig. 5.8 Solar system for DHW and swimming pool water heating

the building in several ways. The glazing reduces heat loss from the wall back to the atmosphere and increases the system’s collection efficiency. In another indirectgain passive system, a metal roof/ceiling supports transparent plastic bags filled with water. Movable insulation above these water-filled bags is rolled away during the winter day to allow the sun to warm the stored water. The water then transmits heat indoors by convection and radiation. Active solar space heating systems (Fig. 5.9) use solar energy to heat a HTF (liquid or air) in collector circuit and then transfer the solar heat directly to the interior space or to a storage tank for later use. Liquid systems are more often used when storage is included, and are well suited for radiant heating systems, boilers with hot water radiators and even absorption heat pumps. Thus, the distribution fluid (hot water) that is used by existing heating system (e.g., radiator, radiant floor) is circulated through a heat exchanger in the storage tank. As the hot water passes through the heat exchanger, it is warmed, and then returned to heating system. If the solar system cannot provide adequate space heating, an auxiliary or backup system provides the additional heat. Both liquid and air systems can supplement forced-air systems.

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Fig. 5.9 Active solar space heating system

5.2.3.1

Components and Control of System

Solar space heating systems are designed to provide large quantities of hot water for residential and commercial buildings. A typical system includes several components: • Solar collectors absorb sunlight to collect heat. • Pumps are used in active systems to circulate the HTF through the solar collectors. A controller is used to turn the pump on when the sun is out and off for the rest of the time. Pump size depends on the size of the system and the height the water has to rise. A good pump will last at least 20 years. • Heat exchanger is used in closed-loop systems to transfer the heat from HTF to distribution fluid (hot water) without the liquids mixing. • Storage tank holds the hot water. The tank can be a modified water heater, but it is usually larger and very well-insulated. Systems that use fluids other than water usually heat the water by passing it through a coil of tubing in the tank, which is full of hot fluid. Specialty or custom tanks may be necessary in systems with very large storage requirements. They are usually stainless steel, Fiberglas or high-temperature plastic. Concrete and wood (hot tub) tanks are also options.

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• Monitoring system used by system owners to measure and track system performance. Two types of control schemes are commonly used on solar collectors on buildingscale applications: on-off and proportional. With an on-off controller, a decision is made to turn the circulating pumps on or off depending on whether or not useful output is available from the collectors. With a proportional controller, the pump speed is varied in an attempt to maintain a specified temperature level at the collector outlet. Both strategies have advantages and disadvantages, largely depending on the ultimate use of the collected energy. The most common control scheme requires two temperature sensors, one in the bottom of the storage unit and one on the absorber plate at the exit of a collector (or on the pipe near the plate). Assume the collector has low heat capacity. When HTF is flowing, the collector transducer senses the exit fluid temperature. When the fluid is not flowing, the mean plate temperature t p is measured. A controller receives this temperature and the temperature at the bottom of the storage unit. This storage temperature will be called t s,i; when the pump turns on, the temperature at the bottom of storage will equal the inlet fluid temperature if the connecting pipes are lossless. Whenever the plate temperature at no-flow conditions exceeds t s,i by a specific amount t on , the pump is turned on. When the pump is on and the measured temperature difference falls below a specified amount t off , the controller turns the pump off. Care must be exercised when choosing both t on and t off to avoid having the pump cycle on and off. The turn-off criterion must satisfy the following inequality or the system will be unstable: toff ≤

Ac FR UL ton mcp

(5.2.4)

where: Ac is the solar collector area, in m2 ; F R is the collector heat removal factor; U L is the overall heat loss coefficient, in kW/(m2 K); m is the mass flow rate of fluid, in kg/s; cp is the specific heat of fluid, in kJ/(kg K).

5.2.3.2

Types of Solar Space Heating Systems

There are two basic types of active solar heating systems: those that use hydronic collectors, and those that use air collectors. The collector is the device that is exposed to the sun, and warms air or a fluid for use by the system. • Hydronic (liquid-based) systems. These systems are an extension of solar water heating systems. Hydronic collectors warm a liquid (water or an antifreeze solution) by circulating them through a manifold that is exposed to the sun. Solar liquid collectors are most appropriate for central heating.

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• Air systems. These systems are designed to collect and transfer heat to warm the air circulating in the building. As the name suggests, air collectors similarly pass air through a sun-exposed collector, rather than a liquid. Both hydronic and air systems absorb and collect solar radiation to heat a liquid or air then use the heated liquid or air to transfer heat directly to an interior building space or to a storage system from which the heat can be distributed.

5.2.3.3

Simulating Solar Heating Systems

Some design methods for solar thermal systems are based on short-cut simulations. In these methods, simulations are done using representative days of meteorological data and the results are related to longer term performance. Simulations are numerical experiments and can give the same kinds of thermal performance information as can physical experiments. They are, however, relatively quick and inexpensive and can produce information on effect of design variable changes on system performance by a series of numerical experiments all using exactly the same loads and weather. Once simulations have been verified with experiments, new systems can be designed with confidence using simulation methods. In principle, all of the physical parameters of collectors, storage and other components are the variables that need to be taken into account in the design of solar systems. Some of the programs that have been applied to solar processes have been written specifically for study of solar energy systems. Others were intended for no solar applications but have had models of solar components added to them to make them useful for solar problems. The common thread in them is the ability to solve the combinations of algebraic and differential equations that represent the physical behaviour of the equipment. Over the past two decades hundreds of programs have been written to study energy efficiency, renewable energy and sustainability in buildings. This subsection includes a brief description of TRNSYS program [13], originally developed for study of solar processes and its applications but it is used for simulation of a wider variety of thermal processes. Subroutines are available that represent the components in typical solar energy systems. A list of the components and combinations of components in the TRNSYS library is shown in Table 5.2. Users can readily write their own component subroutines if they are not satisfied with those provided. By a simple language, the components are “connected” together in a manner analogous to piping, ducting and wiring in a physical system. The programmer also supplies values for all of the parameters describing the components to be used. The program does the necessary simultaneous solutions of the algebraic and differential equations which represent the components and organizes the input and output.

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Table 5.2 Components in standard library of TRNSYS • Building loads and structures Energy/(degree-hour) house Roof and attic Detailed zone (transfer function) Overhang and wing wall shading Window Thermal storage wall Attached sunspace Detailed multizone building Lumped-capacitance building • Controller components Differential controller with hysteresis Three-stage room thermostat Iterative feedback controller Proportional-integral-differential (PID) controller (in heating) Microprocessor controller Five-stage room thermostat • Electrical components Shepherd and Hyman battery models Regulators and inverters Photovoltaic (PV) thermal collector Wind energy conversion system (wind turbines) Photovoltaic array Diesel engine generator set (DEGS) DEGS dispatch controller Power conditioning Lead-acid battery (with gassing effects) Alternating current bus bar • Heat exchangers Constant-effectiveness heat exchanger Counter flow heat exchanger Cross-flow Parallel flow Shell and tube Waste heat recovery • HVAC equipment Auxiliary heaters Dual source heat pumps Cooling coils (simplified and detailed models) Conditioning equipment Part-load performance Cooling towers Parallel chillers Auxiliary cooling unit Single-effect hot water-fired absorption chiller Furnace • Hydrogen systems Electrolyser controller Master level controller for stand alone power systems Advanced alkaline electrolyser Compressed gas storage Multistage compressor Fuel cells (PEM and alkaline) • Hydronics Pumps

Tee-piece, flow mixer, flow diverter, tempering valve Pressure relief valve Pipe Duct Fans • Output devices Printer Histogram plotter Simulation summarizer Economics Online plotter • Physical phenomena Solar radiation processor Collector array shading Psychrometrics Hourly weather data generator Refrigerant properties Shading by external objects Effective sky temperature calculation Undisturbed ground temperature profile Convective heat transfer coefficient calculation • Solar collector components Flat-plate solar collector Thermosyphon collector with integral storage Evacuated tube solar collector Performance map solar collector Theoretical flat-plate solar collector Compound parabolic trough (CPC) solar collector • Thermal storage components Stratified fluid storage tank Rock bed thermal storage Algebraic tank (plug flow) • Utility components Data file reader Time-dependent forcing function Quantity integrator Load profile sequencer Periodic integrator Unit conversion routine Calling Excel worksheets Calling Engineering Equation Solver (EES) routines Parameter replacement Formatted file data reader (TRNSYS TMY, TMY2, Energy Plus) Variable-volume tank Detailed fluid storage tank with optional heaters and variable internal time step Input value recall Holiday calculator Utility rate scheduler Calling CONTAM Calling MATLAB Calling COMIS • Weather data reading and processing Standard format files User format files

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Current versions of TRNSYS have, in the executive program, three integration algorithms. The one that is extensively used is the Modified-Euler method. It is essentially a first-order predictor-corrector algorithm using Euler’s method for the predicting step and the trapezoid rule for the correcting step. The advantage of a predictor-corrector integration algorithm for solving simultaneous algebraic and differential equations is that the iterative calculations occurring during a single time step are performed at a constant value of time (this is not the case for the Runge– Kutta algorithms). As a result, the solutions to the algebraic equations of the system converge, by successive substitution, as the iteration required solving the differential equation progresses. Meteorological data, including solar radiation, ambient air temperature and wind speed, influence collector performance, and is needed to calculate system performance over time. All simulations are done with past meteorological data, and it is necessary to select a data set to use in simulations. For studies of process dynamics, data for a few days or weeks may be adequate if they represent the range of conditions of interest. For design purposes it is best to use a full year’s data or a full season’s data if the process is a seasonal one. Data are available for many years for some stations, and it is necessary to select a satisfactory set. The METEONORM program [14] has a database of over 7000 worldwide stations that can generate data on monthly, daily or hourly time scales on surfaces of any orientation. An Hourly Weather Data Generator based upon different algorithms is available in TRNSYS.

5.2.4 Solar Combisystems 5.2.4.1

System Description

High energy consumption in buildings is an important problem for sustainable future and many researchers tried to solve this problem via different heating/cooling systems. A solar combisystem (SCS) is one of these systems which provide both solar spaces heating/cooling as well as hot water from a common array of solar thermal collectors, usually backed up by an auxiliary non-solar heat source [15]. When a geothermal heat pump is used, the combisystem is called geosolar. The experimental studies showed that SCSs are capable of providing energy demand from 10 to 100% depending on the climatic conditions, system components, and system efficiencies [16]. Europe has most well-developed market for different solar thermal applications [17]. Thus, depending on the size of the SCS installed, the annual space heating contribution can range from 10 to 60% or more in ultra-low energy buildings; even up to 100% where a large interseasonal thermal store or concentrating solar thermal heat is used. Table 5.3 summarise the major studies about SCS in the literature. Solar combisystems may range in size from those installed in individual properties to those serving several in a block heating scheme. Those serving large groups of district heating properties tend to be called central solar heating systems.

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Table 5.3 Some studies about SCS in the literature Researchers

Year

Weiss [18]

2003 Scientific book

Investigation topic

Andersen et al. [19]

2004 Thermal performance of SCS Thermal performance of a in different climatic SCS mostly affected by the conditions balance between energy input and consumption (in Denmark)

Kacan and Ulgen [20]

2012

Energy saving ratio is observed between 59 and 89% monthly and annual fractional solar consumption (FSC) value is found as approx. 83%

Asaee et al. [21]

2014

FSC values are determined between 32 and 93% for different locations in Canada

Ellehauge and Shah [22]

2000 Different system design in the 33–50% are used for DHW market and the most common system design is two closed flow-cycles for both DHW and space heating

Drück and Hahne [23]

1998 Thermal performance of combistores

Creating a temperature distribution in storage tank facilitates the output of hot water for different purposes

Kacan [24]

2011 PhD thesis

Energetic and exergetic efficiency results of the system are found by 1-min time intervals and FSC value is ranged between 10 and 100% annually

Hin and Zmeureanu [25] 2014 System optimisation

Results Basic principles of the system

The payback times of (5.8–6.6 years) different system configuration is found to be not acceptable

SCSs can be classified according to two main aspects: (1) by the heat storage category (the way in which water is added to and drawn from the storage tank and its effect on stratification); (2) by the auxiliary heat management category (the way in which auxiliary heaters can be integrated into the system). These categories are described in Tables 5.4 and 5.5. The simplest combisystems, the type A, have no “controlled storage device”. Instead they pump warm water from the solar collectors through radiant floor heating pipes embedded in the concrete floor slab. The floor slab is thickened to provide

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Table 5.4 Heat storage categories Category Description A

No controlled storage device for space heating and cooling

B

Heat management and stratification enhancement by means of multiple tanks and/or by multiple inlet/outlet pipes and/or by three- or four-way valves to control flow through the inlet/outlet pipes

C

Heat management using natural convection in storage tanks and/or between them to maintain stratification to a certain extent

D

Heat management using natural convection in storage tanks and built-in stratification devices

B/D

Heat management by natural convection in storage tanks and built-in stratifies as well as multiple tanks and/or multiple inlet/outlet pipes and/or three- or four-way valves to control flow through the inlet/outlet pipes

Table 5.5 Auxiliary heat management categories Category

Description

M (mixed mode)

The space heating loop is fed from a single store heated by both solar collectors and the auxiliary heater

P (parallel mode)

The space heating loop is fed alternatively by the solar collectors (or a solar water storage tank), or by the auxiliary heater; or there is no hydraulic connection between the solar heat distribution and the auxiliary heat emissions

S (serial mode)

The space heating loop may be fed by the auxiliary heater, or by both the solar collectors (or a solar water storage tank) and the auxiliary heater connected in series on the return line of the space heating loop

thermal mass and so that the heat from the pipes (at the bottom of the slab) is released during the evening. Tools for designing solar combisystems are available, varying from manufacturer’s guidelines to nomograms to different computer simulation software (e.g., CombiSun [26], SHWwin [27]) of varying complexity and accuracy. Figure 5.10 shows one of the many systems for DHW and space heating [12]. In this case, a large, atmospheric pressure storage tank is used, from which water is pumped to the collectors by pump P1 in response to the differential thermostat T1 . Drain back is used to prevent freezing, because the amount of antifreeze required would be prohibitively expensive. DHW is obtained by placing a heat exchanger coil in the tank near the top, where, even if stratification occurs, the hottest water will be found. An auxiliary water heater boosts the temperature of the sun-heated water when required. Thermostat T2 senses the indoor temperature and starts pump P2 when heat is needed. If the water in the storage tank becomes too cool to provide enough heat, the second contact on the thermostat calls for heat from the auxiliary heater. Water-to-air heat pumps, which use sun-heated water from the storage tank as the evaporator energy source, are an alternative auxiliary heat source.

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Fig. 5.10 Schematic of solar system for DHW and space heating

Storage tank sizing is one of the essential problems of system optimization and determines annual solar fraction (the annual solar contribution to the water heating load divided by the total water heating load). In Fig. 5.11 is presented, for two buildings, specific energy requirement qreq of auxiliary heat source, which has the value of

Fig. 5.11 Auxiliary heat requirement for buildings with different thermal insulations

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Fig. 5.12 Sizing factor for combination heating and water heating boilers

80 kWh/(m2 ·year) for the building with heat demand of 100 kWh/(m2 ·year) and the value of 25 kWh/(m2 ·year) for the building with heat demand of 50 kWh/(m2 ·year). When DHW is heated indirectly by a space heating boiler, Fig. 5.12 [12] may be used to determine the additional boiler capacity required to meet the recovery demands of the domestic water heating load. Indirect heaters include immersion coils in boilers as well as heat exchangers with space heating media. Because the boiler capacity must meet not only the water supply requirement but also space heating loads, Fig. 5.12 indicates the reduction of additional heat supply for water heating if the ratio of water heating load to space heating load is low. The factor obtained from Fig. 5.12 is multiplied by the peak water heating load to obtain the additional boiler output capacity required.

5.2.4.2

Examples of Solar Combisystems Application

Solar combisystems can be well used by isolated consumers for DHW production and building heating. An efficient solar thermal system is one that combines solar passive heating with solar active heating and utilise long time storage of collected heat by a buried thermal-insulated storage tank (Fig. 5.13). Collected heat is used in winter for space heating and DHW production. Currently, a large number of installations are based on the use of solar energy in combination with the heat pump. For the most efficient use of solar energy throughout the year, the energy is stored in summer and is consumed during the winter. The heat from the sun is stored in water contained in thermal-insulated storage tanks. The heating and hot water system in a solar house (Fig. 5.14) from Essen, Germany uses solar energy as a heat source through the flat-plate collector (5) [28].

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Fig. 5.13 Solar DHW and heating system for isolated consumers

Fig. 5.14 Solar-assisted water-to-water heat pump for heating and DHW, 1-DHW storage; 2heating water storage; 3-additional electric heater; 4-DHW electric heater; 5-flat solar collector

The hot water from the solar collector circuit heats boiler (1) used for DHW production and boiler (2) used to heat the water for the radiators. When this system is not enough, a heat pump starts to operate using heated water from the solar collector, producing the hot water in condenser C for the heaters. The installation has the possibility to heat water with electric energy when this is not possible with solar energy. Figure 5.15 presents a radiant floor heating system with a heat pump and a vacuum tube solar collector, operating with water temperatures of 20–3 0 °C [28]. A groundwater heat pump with horizontal collectors or vertical loops and solar collectors transfers its heat to a stratified hot water tank. Reheating hot water is performed both by an additional heat pump and directly by an electric heater.

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Fig. 5.15 Radiant floor heating system with heat pump and solar collector

For a family house with a heat demand of approximately 8000 kWh/year, the solar collector can cover approximately 2000 kWh/year. If taking into account the circulation pumps’ power, the electricity consumption of the heat pump reaches 1500 kW/year, and the coefficient of performance (COP) of the heat pump can reach a value of 4. Initially, installation can be realised without the solar collector, leaving the possibility of installing one in the future. Instead, a heat pump for hot water reheating can be mounted with an electric heater. In heating-dominated climates, the single ground-coupled heat pump (GCHP) system may cause a thermal heat depletion of the ground, which progressively decreases the heat pump’s entering fluid temperature. As a result, the system performance becomes less efficient. Similar to the cases of cooling-dominated buildings, the use of a supplemental heat supply device, such as a solar thermal collector, can significantly reduce the ground heat exchanger (GHE) size and the borehole installation cost. Figure 5.16 shows the basic operating principle of the hybrid GCHP system with a solar collector. The idea to couple a solar collector to the coil of pipes buried in the ground, by means of which solar energy can be stored in the ground, was first proposed by Penrod in 1956. Recently, a number of efforts have been made to investigate the performance

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Fig. 5.16 Schematic diagram of a GCHP system with solar collector

and applications of the solar-assisted GCHP systems. Chiasson and Yavuzturk [29] presented a system simulation approach to assess the feasibility of the hybrid GCHP systems with solar thermal collectors in heating-dominated buildings. Yuehong et al. [30] conducted the experimental studies of a solar-ground heat pump system, where the heating mode is alternated between a solar energy-source heat pump and a groundsource heat pump with a vertical double-spiral coil GHE. Ozgener and Hepbasli [31] experimentally investigated the performance characteristics of a solar-assisted GCHP system for greenhouse heating with a vertical GHE. A solar-assisted GCHP heating system with latent heat thermal energy storage (LHTES) was investigated by Zongwei et al. [32]. The hybrid heating system can implement eight different operation models according to the outdoor weather conditions by means of alternative heat source changes among the solar energy, ground heat and the latent heat thermal energy storage tank. Finally, it is claimed that the LHEST can improve the solar fraction of the system, and thus the COP of the heating system can be increased.

5.2.5 Conclusions Solar systems implemented in the building services represent an economic nonpolluting energy source with high-energy performance, resulting considerable economies of fuel consumption. However, when choosing technical solution, the climatic characteristics of area and the building peculiarities, as well as an economic-energy analysis of chosen system is important to keep in consideration.

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The efficiency of solar heating and/or DHW systems with seasonal energy storage can be improved by conceiving mix systems with heat pumps or other forms of energy. Compared to other RES (hydraulic energy, wind energy and geothermal energy), solar energy leads to simple installations with relatively low costs.

5.3 Solar Thermal Cooling Systems 5.3.1 Preliminary Considerations Usual vapour-compression-based cycles are electrically powered, consuming large amounts of high-quality energy, which significantly increases the fossil fuel consumption. The International Institute of Refrigeration in Paris estimated that ~15% of all the electrical energy produced worldwide is employed for A/C and refrigeration processes [33]. In recent years, these sectors have witnessed manifold growth, and have become essential not only for human comfort but also for a variety of applications. Providing cooling by utilising renewable energy such as solar energy is a key solution to the energy and environmental issues. Solar cooling depends primarily on solar energy, either by hot water production through solar collectors or electricity production through photovoltaic (PV) panels. In comparison with conventional electrically driven compression systems, substantial primary energy savings can be expected from solar cooling, thus aiding in conserving energy and preserving the environment. Another advantage of using solar energy is the coincidence of the peak of the cooling demand and the availability of solar radiation. Solar electrical and thermal-powered refrigeration systems can be used to produce cooling [34]. The first is a PV-based solar energy system, in which solar energy is initially converted into electrical energy and then utilised for producing the cooling, similar to conventional methods [35] or by thermoelectric processes [36, 37]. The second one utilises solar thermal energy to power the generator of a sorption cooling system or converts the thermal energy to mechanical energy, which is utilised to produce the cooling effect. Thermal-powered cooling systems are classified into two categories: sorption system (absorption, adsorption and desiccant system) and thermo-mechanical system (ejector system). Table 5.6 shows the stages and options in solar cooling techniques. Figure 5.17 illustrates a schematic diagram of a solar thermal cooling system. The solar collection and storage system consists of a solar collector (SC) connected through pipes to the thermal storage tank (ST). SCs transform solar radiation into heat and transfer that heat to the heat transfer fluid (HTF) in the collector. The fluid is then stored in a thermal ST to be subsequently utilised for various applications. The thermal A/C unit is run by the hot refrigerant coming from the storage tank, and the refrigerant circulates through the entire system.

1. Sensible 2. Latent 3. Thermo-chemical

Solar thermal 1. Flat-plate collector 2. Evacuated tube collector 3. Concentrated collector

Solar PV (electric)

Thermal storage (Hot energy)

Conversion

Table 5.6 Stages and options in solar cooling techniques

Vapour-compression Thermoelectric

1. Absorption (a) Single-effect (b) Half-effect (c) Double-effect (d) Triple-effect 2. Adsorption 3. Desiccant 4. Ejector

Production of cool energy 1. Sensible 2. Latent 3. Thermo-chemical

Thermal storage (Cool energy)

1. Air conditioning (a) Office (b) Building (c) Hotel (d) Laboratory 2. Process industries (a) Dairy (b) Pharmaceutical (c) Chemical 3. Food preservation (a) Vegetables (b) Fruits (c) Meat and Fish

Applications

5.3 Solar Thermal Cooling Systems 355

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Fig. 5.17 Schematic of a solar thermal cooling system

The performance of cooling systems is determined based on energy indicators of these systems. The coefficient of performance (COP) of a cooling system can be calculated as follows: COP =

Eu Ec

(5.3.1)

where E u is the cooling usable energy, in Wh and E c is the consumed energy by system, in Wh. The solar COP is defined through the equation: COPsol =

Ec Es

(5.3.2)

where E c is the usable energy produced by solar collectors, in Wh, and E s is the energy received by solar collectors, in Wh. The overall COP of a solar thermal cooling system (COPsys ) is given by combination of the two COPs in Eqs. (5.3.1) and (5.3.2): COPsys = COPsol × COP =

Eu Es

(5.3.3)

Additionally, energy efficiency ratio (EER), in British thermal unit (Btu) per Watt-hour (Wh), is defined by equation: EER = 3.412 COP

(5.3.4)

where 3.412 is the transformation factor from W in Btu/h. This section provides a detailed review of different solar thermal-driven refrigeration and cooling systems including sorption technology (open systems or closed systems) and thermo-mechanical technology (ejector system) [34, 38, 39]. The topic approached focused on solar closed sorption cooling systems is an abridged version of the article published by Sarbu and Sebarchievici [38] that provides useful information

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updated and more extensive on their principles, development history, applications and recent advances. Additionally, the thermodynamic properties of most common working fluids and the use of ternary mixtures in solar absorption systems are overviewed and some information’s on hybrid cooling and heating systems are included. Finally, the study also refers to a comparison of various solar thermal cooling systems and to some suggestions for the use of these systems.

5.3.2 Solar Sorption Cooling Systems Sorption technology is utilised in thermal cooling techniques. This technology can be classified as either open sorption systems or closed sorption systems [40]. Desiccant cycles represent the open systems. Absorption and adsorption technologies represent closed systems. Sorption refrigeration uses physical or chemical attraction between a pair of substances to produce the refrigeration effect. A sorption system has the unique capability of transforming thermal energy directly into cooling power. Among the pair of substances, the substance with a lower boiling temperature is called the refrigerant (sorbate) and the other is called the sorbent.

5.3.2.1

Desiccant Cooling Systems

Open sorption cooling is more commonly called desiccant cooling because sorbent is used to dehumidify air. Basically, desiccant systems transfer moisture from one air stream to another by using two processes: sorption and desorption (regeneration) processes [34]. Various desiccants are available in liquid or solid phases. Basically all water absorbing sorbents can be used as a desiccant. In the sorption process the desiccant system transfer moisture from the air into a desiccant material by using the difference in the water vapour pressure of the humid air and the desiccant. If the desiccant material is dry and cold, then its surface vapour pressure is lower than that of the moist air, and moisture in the air is attracted and absorbed to the desiccant material. In regeneration process, the captured moisture is released to the airstream by increasing the desiccant temperature. After regeneration, the desiccant material is cooled down by the cold airstream. Then it is ready to absorb the moisture again. When these processes are cycled, the desiccant system can transfer the moisture continuously by changing the desiccant surface vapour pressures, as illustrated in Fig. 5.18 [34]. To drive this cycle, thermal energy is needed during the desorption process. The difference between solid and liquid desiccants is their reaction to moisture. • Liquid desiccant system. Materials typically used in liquid desiccant systems are lithium chloride (LiCl), calcium chloride (CaCl) and lithium bromide (LiBr). In a liquid desiccant cooling system, the liquid desiccant circulates between an

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Fig. 5.18 Process of moisture transfer by desiccant

absorber and a regenerator in the same way as in an absorption system. Main difference is that the equilibrium temperature of a liquid desiccant is determined not by the total pressure but by the partial pressure of water in the humid air to which the solution is exposed to. A typical liquid desiccant system is shown in Fig. 5.19 [41]. In the dehumidifier, a concentrated solution is sprayed at point A over the cooling coil at point B while ambient or return air at point 1 is blown across the stream. The solution absorbs moisture from the air and is simultaneously cooled down by the cooling coil. The results of this process are the cool dry air at point 2 and the

Fig. 5.19 A liquid desiccant cooling system with solar collector

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diluted solution at point C. Eventually an aftercooler cools this air stream further down. In the regenerator, the diluted solution from the dehumidifier is sprayed over the heating coil at point E that is connected to solar collectors and the ambient air at point 4 is blown across the solution stream. Some water is taken away from the diluted solution by the air while the solution is being heated by the heating coil. The resulting concentrated solution is collected at point F and hot humid air is rejected to the ambient at point 5. A recuperative heat exchanger preheats the cool diluted solution from the dehumidifier using the waste heat of the hot concentrated solution from the regenerator, resulting in a higher COP. Since Lof [42] investigated liquid desiccant solar cooling, most of the research on liquid desiccant solar cooling began in the early 1990s. Moreover, the latest developments are focused on liquid sorption applications since the liquid sorption materials have advantages of higher air dehumidification at the same driving temperature, as well as the possibility of high-energy storage by means of hygroscopic solutions. Ameel et al. [43] compared the performance of various absorbents, including LiCl, CaCl and LiBr. They concluded that LiBr outperformed the other absorbents. Gommed and Grossman [44] developed the prototype of the liquid desiccant cooling system assisted by the flat solar collectors using LiCl/H2 O as its working fluid. Through the parametric study, they demonstrated that conditions of the ambient air are the major parameters considerably affecting the dehumidification process in the liquid desiccant system. They reported that the system provided 16 kW of dehumidification capacity with a thermal COP of 0.8. In efforts to reduce a building’s energy consumption, designers have successfully integrated liquid desiccant equipment with standard absorption chillers [45]. In a more general approach, the absorption chiller is modified so that rejected heat from its absorber can be used to help regenerate liquid desiccants. • Solid desiccant system. The solid desiccant system is constructed by placing a thin layer of desiccant material, such as silica gel, on a support structure [40]. Figure 5.20 shows an example of a solar-driven solid desiccant cooling system. The system has two slowly revolving wheels and several other components between the two air streams from and to a conditioned space. The return air from the conditioned space first goes through a direct evaporative cooler and enters the heat exchange wheel with a reduced temperature (A→B). It cools down a segment of the heat exchange wheel which it passes through (B→C). This resulting warm and humid air stream is further heated to an elevated temperature by the solar heat in the heating coil (C→D). The resulting hot and humid air regenerates the desiccant wheel and is rejected to ambient (D→E). On the other side, fresh air from ambient enters the regenerated part of desiccant wheel (1→2). Dry and hot air comes out of the wheel as the result of dehumidification. This air is cooled down by the heat exchange wheel to a certain temperature (2→3). Depending on the temperature level, it is directly supplied to the conditioned space or further cooled in an aftercooler (3→4). If no aftercooler is used, cooling effect is created only by the heat exchange wheel, which was previously cooled by the humid

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Fig. 5.20 A solid desiccant cooling system with solar collector

return air at point B on the other side. Temperature t 3 at point 3 cannot be lower than t B , which in turn is a function of the return air condition at point A. In principle, the COP of an open desiccant system is similar to its closed counterpart. For example, COP of 0.7 was said achievable with a solid desiccant cooling system under “normal” operating conditions [46]. Henning et al. [47] installed a solar-assisted desiccant cooling system with a 20 m2 flat-plate solar collector and a 2 m3 hot water storage tank. They reported that a solar fraction of the cooling between the solar heat and auxiliary heat provided was 76%, with an overall collector efficiency of 54% and a cooling COP of 0.6 during typical summer conditions. In addition, they proposed a combination of a solar-assisted solid desiccant cooling system with a conventional vapour-compression chiller for warm and humid climates, and claimed up to 50% of primary energy savings. A desiccant cooling system is actually a complete system which has ventilation, humidity and temperature control devices in a ductwork. Therefore it is inappropriate to compare a desiccant cooling system with such components as chillers. Desiccant dehumidification offers a more efficient humidity control than the other technologies. When there is a large ventilation or dehumidification demand, solar-driven desiccant dehumidification can be a very good option. • Desiccant based evaporative cooling systems. A well suitable alternative of mechanical vapour-compression system is evaporative cooling system which can be efficiently used for air-conditioning applications with less power requirements i.e., one fourth of the mechanical vapour-compression. It is an energy saving, cost-effective, simple and environment-friendly air-conditioning technique. Many researchers have investigated different types of evaporative coolers such as direct,

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indirect and modified coolers. Evaporative cooling systems are suitable for dry and high-temperature climatic conditions [48]. In the indirect evaporative system the process air stream does not interact directly with the cooling fluid stream rather it is cooled sensibly. The cooling process inside an indirect evaporative cooler is represented on psychrometric chart shown in Fig. 5.21 [49]. The temperature of air is lowered using some type of heat exchange arrangement in which primary air is cooled sensibly using a secondary air stream. The secondary air is cooled using water. In the indirect evaporative cooling system, both dry as well as wet bulb temperature of the air are lowered. The indirect evaporative cooling has an efficiency of 60–70%. The flow arrangement inside the indirect evaporative cooler is shown in Fig. 5.22 [49]. In direct evaporative system moisture is also added to the cooled air stream because process air stream comes in direct contact with the cooling water. The temperature of the process air is lowered because of the high-moisture content in the air so it is an adiabatic process which is only suitable for hot and dry climates and for hot and humid climates indirect evaporative cooler is preferred. In the direct evaporative cooling, dry bulb temperature of the air is lowered and wet bulb temperature remains unchanged. The wet bulb temperature is an important parameter for the performance of direct evaporative cooler. The efficiency of a well-made direct evaporative cooler reaches an efficiency of approximately 85% [50]. Both the schematic and psychrometric process

Fig. 5.21 Cooling process representation of indirect evaporative cooler on psychrometric chart DPT-dew point temperature; WB-wet bulb temperature; DB-dry bulb temperature

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Fig. 5.22 Flow arrangement inside indirect cooler

of the direct evaporative cooler is shown in Fig. 5.23. The ambient air comes in direct contact with the sprayed water which decreases the temperature of the supply air and adds moisture content to it as shown on the psychrometric chart. The process of indirect evaporative cooling needs input energy only for the water pump and fan that is why this system has high coefficient of performance.

Fig. 5.23 The direct evaporative cooler a schematic diagram b and psychrometric process WB-wet bulb temperature; DB-dry bulb temperature

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Fig. 5.24 Schematic of solar evaporative desiccant cooling systems

The evaporative desiccant cooling system consists of a desiccant dehumidifier, a regenerator and a cooling unit. The basic working principle of a solar activated evaporative desiccant cooling system is illustrated in Fig. 5.24 [51]. The air is dehumidified using desiccant dehumidifier and its temperature is lowered using evaporative cooler or some other cooling device. For continuous operation of the system the desiccant dehumidifier is regenerated by using heat energy provided by solar collectors as shown in Fig. 5.24. Some heat recovery units are also utilised to make the system more efficient. In desiccant based evaporative cooling technique, latent and sensible loads are separately removed using desiccant dehumidification system and cooling unit, respectively. The type of cooling units used to reduce the temperature of dehumidified air, mainly defines the type of hybrid desiccant cooling system. The selection of the cooling unit depends on operating conditions, that is, humidity and temperature of the air. The most commonly used cycles for desiccant based evaporative cooling systems are recirculation and ventilation. The schematic of a typical desiccant dehumidification system in conjunction with evaporative cooler shown in Fig. 5.20 is operated on ventilation mode. Some advantages of the desiccant-aided evaporative cooling systems are: • They can be used for hot and humid climates because evaporative cooling alone is not feasible for such conditions. • A lot of energy is saved as compared to vapour-compression system because of no preheating is required.

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Fig. 5.25 Schematic of a solar thermal regeneration system for LDAC

• Environment-friendly system, because of no use of refrigerant that affects the ozone layer. • Separate and better control of sensible and latent loads; the desiccant wheel controlling the latent part and the evaporative cooler controlling the sensible one. • The overall system has low maintenance cost because it operates at almost atmospheric conditions. • Low grade energy such as solar, biomass, etc. can be effectively used to drive the system. • Solar liquid desiccant regeneration methods. Currently, solar desiccant regeneration systems are mostly driven by solar thermal energy. Solar electro-dialysis regeneration is also being investigated as a means of new solar regeneration method. A common type of solar thermal regeneration system for liquid desiccant airconditioner (LDAC) is shown in Fig. 5.25 [52]. Weak desiccant solution flows from the dehumidifier into the solar collector and causes an increase in the temperature. Then, hot but still dilute desiccant solution is discharged to the regenerator and contacts with the air passing upwards. Water molecules in the desiccant solution are absorbed by the air stream and the dilute solution becomes regenerated. The concentration of the desiccant solution is adjusted and strong desiccant solution is obtained as a result of this process. The strong solution is introduced to the dehumidifier from the strong solution storage to carry on the dehumidification cycle. A recent solar method for the liquid desiccant regeneration is being studied. Electro-dialysis (ED) is a technology-based method that ions transport through the selective membranes under the influence of an electrical field [53]. Cation and anion exchange membranes are alternately set in between a cathode and anode within an electro-dialyser. Under the electrical field, the anions and cations inside the electro-dialyser cells move towards the anode and cathode. During this process, the anions and cations pass through anion exchange membranes and cation exchange membranes, respectively. This flow causes a rise in the ions concentration in the concentrate compartments and fall into the dilute compartment. By this way, both the concentrated desiccant solution and pure water can be acquired. A schematic diagram of the PV–ED regeneration method is presented in Fig. 5.26.

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Fig. 5.26 Schematic of the PV–ED regeneration system

In a PV–ED regeneration process, the dilute desiccant solution is drained from the dehumidifier to the regenerator. The PV panels driven regenerator is made of ED stacks formed of a mass of cells located in parallel between two electrodes. As shown in a schematic of an ED regenerator, the cells a, b and e are the concentrate, dilute and electrode rinse cells, respectively. The weak solution is introduced to the dilute cell and regenerated solution to the concentrate cell. After this process, the dilute solution becomes regenerated which is sent to the dehumidifier unit of the LDAC system [54]. In a PV–ED regeneration process, the dilute desiccant solution is drained from the dehumidifier to the regenerator. The PV panels driven regenerator is made of ED stacks formed of a mass of cells located in parallel between two electrodes. As shown in a schematic of an ED regenerator, the cells a, b and e are the concentrate, dilute and electrode rinse cells, respectively. The weak solution is introduced to the dilute cell and regenerated solution to the concentrate cell. After this process, the dilute solution becomes regenerated which is sent to the dehumidifier unit of the LDAC system [54]. New developments of solar-assisted liquid desiccant evaporative cooling system with small capacity will open up new market segments alike solar combisystems.

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Principles of Closed Sorption Systems

In closed sorption technology, there are two basic methods: absorption refrigeration and adsorption refrigeration. Figure 5.27 shows a schematic diagram of a closed sorption system. The component where sorption takes place is denoted as absorber Ab, and the one where desorption takes place is denoted as generator G. The generator receives heat Qg from the solar collector SC to regenerate the sorbent that has absorbed the refrigerant in the absorber. The refrigerant vapour generated in this process condenses in the condenser C, rejecting the condensation heat Qc to the ambient. The regenerated sorbent from the generator is sent back to the absorber, where the sorbent absorbs the refrigerant vapour from the evaporator E, rejecting the sorption heat Qa to ambient. In the evaporator, the liquefied refrigerant from the condenser evaporates, removing the heat Qe from the cooling load. In an adsorption system, each of the adsorbent beds functions alternatively as the generator and absorber due to the difficulty of transporting solid sorbent from one to another. For sorption cooling cycle, Eq. (5.3.1) can be rewritten in Eq. (3.5.5): COP =

Qe Q g + Pel

(5.3.5)

where: COP is the coefficient of performance of the sorption system; Qe is the cooling power of evaporator, in W; Qg is the thermal power consumed by generator, in W; Pel is the electrical power consumed in system, in W. Absorption refers to a sorption process where a liquid or solid sorbent absorbs refrigerant molecules into its interior and changes physically and/or chemically in

Fig. 5.27 Solar closed sorption cooling system

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the process. Adsorption involves a solid sorbent that attracts refrigerant molecules onto its surface by physical or chemical force and does not change its form in the process.

5.3.2.3

Absorption Systems

Absorption refrigeration has been most frequently adopted for solar cooling. It requires very low or no electric input, and, for the same capacity, adsorption systems are larger than absorption systems due to the low specific cooling power of the adsorbent. Absorption is the process by which a substance changes from one state into a different state. These two states create a strong attraction to make a strong solution or mixture. The absorption system is one of the oldest refrigeration technologies. The first evolution of an absorption system began in the 1700s. It was observed that in the presence of H2 SO4 (sulphuric acid), ice can be made by evaporating pure H2 O within an evacuated container. In 1859 Ferdinand Carre designed an installation that used a working fluid pair of ammonia/water (NH3 /H2 O). In 1950, a new system was introduced with a water/lithium bromide (H2 O/LiBr) pairing as working fluids for commercial purposes [55]. The absorption cooling technology consists of a generator, a pump and an absorber that are collectively capable of compressing the refrigerant vapour. The evaporator draws the vapour refrigerant by absorption into the absorber. The extra thermal energy separates the refrigerant vapour from the rich solution. The refrigerant is condensed by rejecting the heat in a condenser, and then the cooled liquid refrigerant is expanded by the evaporator, and the cycle is completed. The refrigerant side of the absorption system essentially works under the same principle as the vapour-compression system. However, the mechanical compressor used in the vapour-compression cycle is replaced by a thermal compressor in the absorption system. The thermal compressor consists of the absorber, the generator, the solution pump and the expansion valve. The attractive feature of the absorption system is that any type of heat source, including solar heat and waste heat, can be utilised in the desorber. NH3 /H2 O and H2 O/LiBr are typical refrigerant/absorbent pairs used in absorption systems. Each working pair has its advantages and disadvantages, as shown in Table 5.7. The NH3 /H2 O systems are often used for refrigeration and in industrial applications, whereas the H2 O/LiBr systems are more suitable for air-conditioning purposes. The operation of the H2 O/LiBr-based absorption system is limited in terms of the evaporating temperature and the absorber temperature due to the freezing of the water and the solidification of the LiBr-rich solution, respectively. The operation of the NH3 /H2 O-based absorption system is not limited in terms of either the evaporation temperature or the absorption temperature. However, ammonia is toxic, and its usage is limited to large capacity systems. The most suitable refrigerant/absorbent working pair alternative to NH3 /H2 O and H2 O/LiBr can be ammonia/lithium nitrate (NH3 /LiNO3 ), lithium chloride/water

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Table 5.7 Comparison between the absorption system with NH3 /H2 O and H2 O/LiBr Working pair

Advantages

Disadvantages

NH3 /H2 O

Evaporative at the temperatures below 0 °C

Toxic and dangerous for health (NH3 )

High COP

The risk of congelation, therefore a device anti-crystallisation is necessary

In need of a column of rectifier Operation at high pressure

H2 O/LiBr

Low operation pressures

Environmental friendly and in-noxious Relatively expensive (LiBr) Large latent heat of vaporisation

(LiCl/H2 O), ammonia/calcium chloride (NH3 /CaCl2 ), ammonia/sodium thiocyanate (NH3 /NaSCN), methanol/TEGDME (tetraethylene glycol dimethyl ether) and trifluoro-ethanol (TFE)/TEGDME. Abdulateef et al. [56] performed a comparative study between the performances of NH3 /H2 O, NH3 /LiNO3 and NH3 /NaSCN mixtures for absorption systems. Their results indicated that NH3 /LiNO3 and NH3 /NaSCN mixtures gives better performance compared to NH3 /H2 O mixture at temperatures below the freezing point of water. However above the freezing point of water NH3 /H2 O has comparatively better performance than the other two. They also stated that NH3 /LiNO3 and NH3 /NaSCN mixtures are simpler in operation because of no requirement of rectifier in their operation. Experimental studies. Although NH3 /H2 O and H2 O/LiBr pairs have been used throughout the world, researchers continue to search for new pairs. In 1994, Erhard and Hahne [57] developed a solar powered absorption refrigeration system with NH3 and SrCl2 as the working pair. The overall COP of the cooling system has been calculated to be 0.49. In 1995, a better overall COP (0.45–0.82) was attained. Moreno-Quintanar et al. [58] analysed the use of a ternary mixture consisting of a binary absorbent solution (LiNO3 H2 O) and a refrigerant (NH3 ) in comparison with the binary working pair NH3 /LiNO3 for producing 8 kg of ice. Compound parabolic concentrators (CPC) were used in the experimental investigation. They reported an increase of 24% in the COP using the ternary mixture compared to the binary mixture. Simulation studies. Pilatowsky et al. [59] analysed the monomethylamine/H2 O working pair for an absorption cooling system powered by flat-plate SCs. Their simulation results indicated that a COP of 0.72 can be reached while operating the system at a generator temperature of 60 °C and producing a cooling effect of 10 °C. Fong et al. [60] optimised a solar thermal cooling system employing LiCl/H2 O mixtures. The optimisation results indicated a reduction in the primary energy consumption of 12.2% for LiCl/H2 O systems. Rivera and Rivera [61] simulated the performance of a solar intermittent adsorption refrigeration chiller with a H2 O/LiBr pair for Mexico. A compound parabolic concentrator with a glass cover is used for powering their system by solar energy. They reported that 11.8 kg of ice could be produced at a COP ranging from 0.15 to 0.40 when operating at a generation temperature of 120 °C. One recent trend in

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the field of solar powered absorption systems is the use of a ternary mixture as the working fluid for such systems. Based on the thermodynamic cycle of operation and solution regeneration, the absorption systems can be divided into three categories: single-, half- and multieffect (double-effect and triple-effect) solar absorption cycles. The single-effect and half-effect chillers require relatively lower hot water temperatures with respect to multi-effect systems [62]. Grossman [63] provided typical performances of the single- and multi-effect absorption systems, as shown in Table 5.8. Typical cooling COPs of the single-effect, double-effect and triple-effect absorption systems are 0.7, 1.2 and 1.7, respectively. As shown in Table 5.8, a flat-plate collector (FPC) can be used for the single-effect cycle. However, the multi-effect absorption cycles require high temperatures above 85°C, which can be delivered by evacuated tube or concentrating-type collectors. According to the collector catalogue [64], a 40%-efficient evacuated tube collector working at 150 °C costs 600–700 e/m2 (gross area). For less expensive collectors working at approximately 90 °C, a single-effect LiBr/H2 O or a NH3 /H2 O absorption system with a COP between 0.6 and 0.8 can be considered [41]. The price of a solar collector varies widely in this temperature range. The price of a 50%-efficient collector at 90 °C ranges between 300 and 600 e/m2 . It must be noted that the SC efficiencies listed above are only indicative, and the actual efficiencies will depend on the ambient air temperature and solar radiation. • Continuous operation systems. The continuous operation systems belong to a specific classification of absorption cooling systems, in which both the generation and absorption processes take place simultaneously. Such systems operate with a cyclic behaviour with a cycle time of less than a day (24 h). The schematic diagram of the continuous operation-based solar powered absorption system is shown in Fig. 5.28. The basic components of a continuous operation absorption refrigeration system are the generator G, absorber Ab, condenser C, evaporator E, expansion valve EV and a solution pump P. The generator is powered by solar collectors SC in the case of a solar powered absorption system. To ensure continuous operation and reliability of the system, a hot water storage tank (ST) is used. Table 5.8 Typical performance of absorption cycles No.

Absorption system

COP (–)

EER (Btu/(Wh))

1 2 3

Heat source temperature (o C)

Type of solar collectors matched

Single-effect

0.7

2.39

85

Double-effect

1.2

4.10

130

Flat-plate/Compound parabolic concentrator

Triple-effect

1.7

5.80

220

Evacuated tube/Concentrating collector

Flat-plate

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Fig. 5.28 Continuous operation-based solar absorption system

In the absorber, the absorbent-rich solution is diluted with the refrigerant. During this process, the absorber is cooled to keep its pressure at a low level. Then, the solution pump increases the pressure of the absorbent/refrigerant mixture to the high-pressure level. The solution pump’s electrical power requirement is much less than that of the compressors in the vapour-compression systems. Since the refrigerant is more volatile than the absorbent, it is separated from the solution when adequate heat is added in the generator (desorber). Along with the basic components, certain heat recovery components are added to the continuous operation absorption system to increase its COP. These heat recovery components are a solution heat exchanger (SHX) and a refrigerant pre-cooler (PC). The performance of the absorption system falls by 3–5% without the PC and the usage of the SHX in the system does not increase the system performance as expected [65]. Also, additional refrigerant rectification equipment such as a rectifier and a dephlegmator is added in the design to rectify the refrigerant vapour in the case of a volatile absorbent. Rectification equipment is added to restrict the volatile absorbent (water) within the generator and absorber, thus preventing it from entering into the evaporator. The rectification equipment is normally constructed in the form of a column and divided into two subsections [66]. Fernandez-Seara et al. [67] used a helical coil rectifier in an absorption refrigeration system and analysed the influence of the heat and mass transfer coefficients on the rectifier performance. The construction of the rectifier plays a very important role in the refrigerant purification process. • Intermittent operation systems. The intermittent operation systems comprise a specific class of absorption refrigeration systems in which the generation and absorption processes do not take place simultaneously but rather follow each other in an intermittent manner. Because of the intermittent nature, it is possible to utilise the NH3 /H2 O vessel to behave as a generator G during the daytime and as an absorber Ab during the night (Fig. 5.29). Such systems operate cyclically

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Fig. 5.29 Intermittent operation-based solar absorption system

with a cycle time of one complete day (24 h). The pressurisation process in the intermittent operation systems is carried out by isochoric heating of the NH3 /H2 O solution in the generator. In this way, electrical energy is not required at all in the operation of intermittent absorption systems. The intermittent solar absorption cooling system has two configurations: the first is a single stage and the second is a two-stage configuration. Here “two stages” distinctly refers to stages of generation, namely, high-pressure generation and low-pressure generation. The overall COP of the two-stage system operating at this temperature is 0.105, which is twice that of a single-stage system operating at 120 °C. Thus, a two-stage system operating at a low generation temperature is better than a single-stage system, even when the single-stage system is operating at a high temperature [68]. Some of the recent developments regarding these systems will be reviewed in this chapter. • Single-effect solar absorption cycle. Most absorption cooling systems use a singleeffect absorption cycle operating with an H2 O/LiBr working pair and a solar FPC or an ETC with hot water to drive these systems. The single-effect absorption cooling system is based on the basic absorption cycle that contains a single absorber and generator, as shown in Fig. 5.28. In the generator G, the refrigerant is separated from the absorbent by the heat provided by the solar collector. The vapour refrigerant is condensed in condenser C, then laminated in expansion valve EV1 and evaporated at a low pressure and temperature in the evaporator E. The cooled refrigerant is absorbed in the absorber Ab by a weak solution that returns from the generator after the lamination in the expansion valve EV2 . The rich mixture created in the absorber is pumped by pump P and returned in G. A typical SHX can be used to improve the cycle efficiency. A 60% higher COP can be achieved by using the SHX [69]. The absorber is chilled by cooling water because the absorption is exothermic. For low-temperature heat sources, the degassing zone is unacceptably small, the release of the refrigerant-vapour in the generator is slowed down, and the operation of the system becomes unstable or impossible. To improve the COP and to use lower temperatures in generator, a solar resorption cooling system can be used (Fig. 5.30) [38].

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Fig. 5.30 Solar resorption cooling system

In this case, in the generator, the refrigerant is also separated from the absorbent by the heat provided by the SC, but the vapour refrigerant is reabsorbed by a weak solution in the resorber Rb, and the system operates with a cycle similar to the one above. System pressures may be allowed to be as close to atmospheric pressure as possible, which simplifies sealing problems and the manufacture of the pumps and reduces the temperature in generator. The single-effect system is the simplest type of these systems. Design of a singleeffect absorption cooling system depends on the working fluid types. The system shows better performance with a non-volatile working pair, such as H2 O/LiBr. An extra rectifier should be used before the condenser to provide pure refrigerant if the system operates with a volatile working pair, such as NH3 /H2 O [55]. A low cost non-concentrating flat-plate or evacuated tube solar collector is sufficient to obtain the required temperature for the generator. Though economical, its COP is lower. For obtaining a higher COP, multi-effect systems such as double-effect and triple-effect absorption chillers are used, which are run by steam produced from concentrating SCs. Experimental studies. Nakahara et al. [70] developed a single-effect H2 O/LiBr absorption chiller of 7 kW nominal cooling capacity assisted by a 32.2 m2 array of flat-plate SCs. In their system, thermal energy produced by the solar collector was stored in a 2.5 m3 hot water ST. Their experimental results during the summer period showed that the cooling capacity was 6.5 kW. The measured COP of the absorption system was in the range of 0.4–0.8 at a generator temperature of 70 to 100 °C. Another investigation on a H2 O/LiBr absorption system consisting of 49.9 m2 of FPC was performed by Syed et al. [71]. The system performs cooling

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with generation temperatures of 65–90 °C while maintaining a capacity of 35 kW. They achieved an average collector efficiency of approximately ~50%. De-Francisco et al. [72] tested a prototype of a 2-kW solar powered NH3 /H2 O absorption chiller that utilises concentrating collectors and uses a transfer tank instead of a pump. Their experimentation resulted in a COP of 0.05 when the collectors operated at temperatures greater than 150 °C. They suggested that inefficient operation of the transfer tank was responsible for the low COP of their system. Brendel et al. [73] developed an experimental setup for a small-scale solar powered 10-kW NH3 /H2 O absorption chiller. They used plate heat exchangers in the system, except for the generator, which is fabricated as a helical coil heat exchanger inside a cylindrical shell. They reported a COP of 0.58–0.74 for the absorption system operating at a generator temperature ranging from 80 to 120 °C. Rosiek and Batles [74] experimentally investigated the performance of a 70-kW solar absorption chiller operating under two modes of heat rejection from the absorber and condenser of the absorption cycle. The two operation modes were compared in terms of energy consumption, water consumption and CO2 savings. For one cooling period, using the shallow geothermal system reduced the electricity by 31%, reduced water consumption by 116 m3 , and led to a CO2 savings of 833 kg. Simulation studies. El-Shaarawi and Ramadan [75] investigated the performance of a solar powered intermittent NH3 /H2 O absorption system for varying condensation temperature. They reported that decreasing the condenser temperature at any fixed initial solution concentration and temperature results in an increase in the COP of the system. A theoretical simulation has also been conducted by Said et al. [76] of an intermittent solar absorption system designed to provide 120 kWh of cooling effect throughout day and night operation. Their simulation results indicated that the intermittent absorption system can achieve a COP of 0.23 when operating at the generation temperature of 120 °C while producing a cooling effect at a temperature of –9 °C. Recently, El-Shaarawi et al. [77] developed a simplified correlation for an NH3 /H2 O intermittent solar powered absorption refrigeration system. They developed a set of correlations of polynomial form for directly estimating the performance of intermittent absorption systems as a function of the generator, absorber, condenser and evaporator temperatures. They reported that their developed correlation estimates the design parameters of intermittent absorption refrigeration systems with an accuracy of greater than 97%. Chinnappa et al. [78] proposed a conventional vapour-compression airconditioning system cascaded with a solar-assisted NH3 /H2 O absorption system. They concluded that by reducing the R22 condensation temperature to 27 °C, the hybrid system achieved a COP of 5, which is higher than that of the vapour-compression cycle at 2.55. Recently, the approach of direct air cooling of a solar powered NH3 /H2 O chiller has been simulated by Lin et al. [79] for a two-stage absorption system. They tested several arrangements for the series connection of condenser, low-pressure absorber and medium-pressure absorber. The simulation results for the best arrangement indicated a thermal COP of 0.34 under typical summer conditions.

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• Half -effect solar absorption cycle. The half-effect absorption cycle, also called two-stage or double-lift cycle, can provide cold at a relatively low temperature. The name “half-effect” arises from the value of the COP, which is almost half that of the single-effect cycle. A schematic diagram for this cycle is shown in Fig. 5.31. Sumathy et al. [80] proposed a two-stage H2 O/LiBr chiller for cooling purposes in southern China. Test results have proved that the two-stage chiller could be driven by low-temperature hot water ranging from 60 to 75 °C, which can be easily provided by conventional solar hot water systems. Based on the successes of this system, they integrated the solar cooling and heating system with two-stage absorption chiller and with cooling capacity of 100 kW. Operating results from the system indicated that this type of system could be efficient and cost-effective comparing with the conventional cooling system with single-stage chiller. The proposed system with a

Fig. 5.31 Schematic of the half-effect solar absorption cooling system

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two-stage chiller could achieve the same total COP as of the conventional system but with a cost reduction of about 50%. Izquierdo et al. [81] designed a solar double-stage absorption plant with H2 O/LiBr that contained FPCs to feed the generator. The results show that a generation temperature of ~80 °C was required in the absorption system when the condensation temperature reached 50 °C, and they obtained a COP of 0.38 without crystallisation problems. They also performed an exergetic analysis of this system and concluded that the irreversibilities generated by the double-stage thermal compressor will tend to increase with the absorption temperature up to 45 °C. The conclusions show that the doublestage half-effect system has ~22% less exergetic efficiency than the single-effect system and 32% less exergetic efficiency than the double-effect one. Arivazhagan et al. [82] performed an investigation with a two-stage half-effect absorption system operating with an R134a/DMAC working pair. They obtained an evaporation temperature of –7 °C for generation temperatures of 55–75 °C. They concluded that a COP of approximately 0.36 could be achieved within the optimum temperature range (65–70 °C). • Double effect solar absorption cycle. Double-effect absorption cooling technology increases the system performance using a heat source at higher temperatures. Figure 5.32 illustrates a double-effect absorption system with a H2 O/LiBr pair. The cycle begins with generator G-I providing heat to generator G-II. The condenser C rejects the heat and passes the working fluid towards the evaporator E; in this step, the required refrigeration occurs. Then, the fluids pass through the heat exchangers HX-I and HX-II from the absorber Ab to G-I by means of a pump P. Through this process, HX-II can pass the fluids to G-II and then G-II passes them

Fig. 5.32 Solar-assisted double-effect H2 O/LiBr absorption system

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5 Solar Heating and Cooling Systems

to HX-I. The complete cycle includes three different pressure levels: high, medium and low. The combination of two single-effect systems effectively comprises a doubleeffect absorption cooling system. Therefore, the COP of a double-effect system is almost twice that of a single-effect absorption system. For example, an analysis performed by Srikhirin et al. [55] indicates that the COP of a double-effect system is 0.96, whereas the single-effect system has a COP of only 0.6. In the past decade, the COP of double-effect absorption systems has reached values of 1.1–1.2 by using gas-fired absorption technology [62]. Experimental studies. Tierney [83] performed a comparison among four systems with different chiller-collector combinations and at four different latitudes. He concluded that the double-effect chiller with a trough collector had the highest potential savings (86%) among the four systems to handle the demand for a 50 kW load. Simulation studies. Several simulation studies have been conducted using simulation software such as FORTRAN, MATLAB, ASPEN, TRNSYS, EES (Engineering Equation Solver), etc. One recent simulation study was performed by Gomri [84] using mathematical code developed in the FORTRAN programming language. He compared the performance of single-effect and double-effect absorption systems. His results indicated that the double-effect systems have a COP approximately double that of single-effect systems. His case study indicated a COP of 1.22–1.42 for the double-effect systems, whereas the single-effect systems could reach a COP of only 0.73–0.79 when operating under the same conditions. Somers et al. [85] compared the results of simulations using ASPEN software and EES software for the performance of a solar powered H2 O/LiBr system. They successfully modelled the single-effect and double-effect H2 O/LiBr systems using the ASPEN program, and their results indicated errors of less than 3% and 5%, respectively compared to the EES results. • Triple-effect solar absorption cycle. Triple-effect absorption cooling can be classified as having either single-loop or dual-loop cycles. Single-loop tripleeffect cycles are basically double-effect cycles with an additional generator and condenser. The resulting system, with three generators and three condensers, operates similarly to the double-effect system. Primary heat concentrates the absorbent solution in a first-stage generator at approximately 200–230 °C. A fluid pair other than H2 O/LiBr must be used for the high-temperature cycle. The refrigerant vapour produced is then used to concentrate additional absorbent solution in a second-stage generator at approximately 150 °C. Finally, the refrigerant vapour produced in the second-stage generator concentrates additional absorbent solution in a third-stage generator at ~93 °C. The typical solution heat exchangers can be used to improve the cycle efficiency. Theoretically, these triple-effect cycles can obtain COPs of approximately 1.7 [45]. A double-loop triple-effect cycle consists of two cascaded single-effect cycles. One cycle operates at normal single-effect operating temperatures and the other at higher temperatures. The smaller high-temperature topping cycle has a generator

5.3 Solar Thermal Cooling Systems

377

temperature of approximately 200–230 °C. A fluid pair other than H2 O/LiBr must be used for the high-temperature cycle. Heat is rejected from the high-temperature cycle at 93 °C and is used as the energy input for the conventional single-effect bottoming cycle. Theoretically, this triple-effect cycle can obtain an overall COP of approximately 1.8 [45]. Multi-effect cycles are costlier but more energy efficient. Double- and tripleeffect chillers employ an additional generator and heat exchanger to liberate the refrigerant from the absorbent solution with less heat input. Multi-effect absorption cycles require high temperatures above 200 °C that can limit choices in materials and working pairs. To handle the absorption liquid of such high temperature and high pressure, a high-temperature generator must be manufactured as a boiler, and corrosion suppressive measures are needed. The available solar intensity, cooling capacity requirements, overall performance and cost determine the selection of a particular configuration. A combined cooling concept arose due to integrate different pairs or systems for obtaining better cooling performance. Combined solar absorption cooling system refers to the integration of three individual cooling technologies: radiant cooling, desiccant cooling and absorption cooling. Table 5.9 summarises the above-mentioned absorption cooling systems. Solar absorption cooling systems are used in A/C applications, for food preservation and in ice production. • Thermodynamic properties of working pairs. The thermodynamic properties of the refrigerant/absorbent working pair are the most important factor in analysing and optimising the performance of the absorption systems. NH3 /H2 O is one of the most widely used refrigerant/absorbent working pairs in absorption systems. Thus, several correlations for determining the vapour-liquid equilibrium (VLE) thermodynamic properties of the NH3 /H2 O working pair have been proposed by researchers using different methodologies. Park and Sonntag [86] used a generalised equation of state based on a four parameter corresponding states principle to determine the thermodynamic properties of NH3 /H2 O mixtures. Later, Ibrahim and Klein [87] used the Gibbs excess energy to estimate the VLE thermodynamic properties of NH3 /H2 O mixtures. Tillner-Roth and Friend [88] used the approach of the Helmholtz free energy for developing the correlations for estimating the VLE thermodynamic properties of NH3 /H2 O mixtures. Recently, El-Shaarawi et al. [89] used an EES program to develop polynomial forms of explicitly defined thermodynamic property correlations that can be used by any simulation software. The working temperature and pressure range of the VLE thermodynamic properties of NH3 /H2 O working mixtures is summarised in Table 5.10. Patek and Klomfar [90] give a fast calculation of thermodynamic properties. As an example, the bubble point and dew point temperatures of the NH3 /H2 O mixture are found from the correlations in Eqs. (5.3.6) and (5.3.7), developed by Patek and Klomfar [90]:

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Table 5.9 Characteristics of working fluids found from various absorption cooling technologies Absorption cooling systems Working fluids

Results/Reference

Single-effect

– A rectifier is needed to purify the refrigerant if the pair is volatile/[68]

H2 O/LiBr, NH3 /H2 O

– Approximately 60% more COP can be achieved by using a solution heat exchanger/[69] – A system capacity of 70 kW can be achieved by using a vacuum tubular collector (108 m2 ) with FPCs (9124 m2 )/[62] – COP can be increased by 15% using a partitioned hot water tank with a FPC (38 m2 ) and chillers (4.7 kW)/[34] Half-effect

H2 O/LiBr

– Within the optimum temperature range of 65–70 °C, the COP = 0.36 and the evaporation temperature is –7 °C/[82] – The pair is capable of providing the same COP as a conventional cooling system with reducing the cost by half/[80] – The system has 22% lower exergetic efficiency compared to the single-effect system/[81]

Double-effect

H2 O/LiBr

– The system has almost double (0.96) the COP compared to the single-effect system/[55] – The double-effect chillers with trough collectors show the maximum potential savings (86%)/[83]

Hybrid

Combination of mentioned pairs – The types of systems are widely implemented for the cooling of larger places, such as offices, markets or auditorium/[34]

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Table 5.10 Summary of operating temperature and pressure ranges Methodology used

Year

Operating range

Refs.

Temperature (°C)

Pressure (bar)

Generalised equation of state

1990

≤377

≤200

[88]

Gibbs excess energy

1993

≤327

≤110

[89]

Simple functional form

1995

≤180

≤20

[39]

Helmholtz free energy

1998

–

≤400

[90]

Polynomial form of equations

2013

–

≤100

[90]

tb ( p, x) = to

 i

td ( p, y) = to

 i

  po n i ln ai (1 − x) p

ai (1 − y)

mi

m i /4

  po n i ln p

(5.3.6)

(5.3.7)

where t b is the bubble point temperature, in K; t d is the dew point temperature, in K; p is the pressure, in Pa; x is the ammonia mole fraction in liquid phase; y is the ammonia mole fraction in vapour phase; ai , mi and ni are the coefficients; and subscript o represents the ideal gas state.

5.3.2.4

Adsorption Systems

Adsorption technology was first used in refrigeration and heat pumps in the early 1990 s. The adsorption phenomenon results from the interaction between a solid and a fluid (refrigerant) based on a physical or chemical reaction. Physical adsorption (physisorption) occurs when the molecules of the refrigerant (adsorbate) fix themselves to the surface of a porous solid element (adsorbent) due to Van der Waals forces and electrostatic forces, and the molecules are adsorbed onto the surface. By applying heat, the refrigerant molecules can be released (desorption), whereby this is a reversible process. Physical adsorption is nonspecific and occurs for any refrigerantadsorbent system. In turn, the chemical adsorption (chemisorption) results from the ionic or covalent bonds formed between the refrigerant molecules and the solid substance. The bonding forces are much greater than those of physical adsorption, and thus more heat is released. However, the process cannot be easily reversed [91]. The chemisorption process is specific and occurs between a certain gas and a certain corresponding adsorbent solid. When fixed adsorbent beds are employed, these cycles can be operated without any moving parts. The use of fixed beds results in silence, simplicity, high reliability and long lifetime. On the other hand, it leads to intermittent cycle operation with adsorbent beds changing between adsorption and desorption stages, which decreases the system COP. Thus, when a continuous cooling effect is required, two or more adsorbent beds must be operating out of phase [92].

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5 Solar Heating and Cooling Systems

As in the case of absorption, for both physisorption and chemisorption, the process of adsorption is exothermic and is accompanied by the evolution of heat, whereas the process of desorption is endothermic and is accompanied by absorption of heat. These characteristics are used to produce the cooling effect in refrigeration and air-conditioning applications. • Basic solar adsorption refrigeration cycle. Solar energy is the energy source of most adsorption systems operating with the basic cycle. A solar adsorption cooling system based on the basic adsorption refrigeration cycle does not require any mechanical or electrical energy, just thermal energy, and it operates intermittently according to the daily cycle. This refrigerator is a closed system consisting of a SC containing the adsorbent bed, a condenser C, a receiver R equipped with a 2-way valve V, and an evaporator E (Fig. 5.33). In this case, the compressor is an adsorber powered by thermal energy (SC), and the cooling effect is achieved by the evaporation of a refrigerant, while the vapour produced is adsorbed by the adsorbent layer in the adsorber. The basic adsorption cycle consists of four stages (two isobaric and two isosteric lines), which can be represented in the Clapeyron diagram (Fig. 5.34). The process starts at point 1 when the adsorbent is at adsorption temperature t a and at a low evaporation pressure pe , and the content of the refrigerant is at its maximum value X max . The control valve V is closed, and, as heat Qd1 is applied to the adsorbent, both the temperature and pressure increase along the isosteric line 1–2, while the mass of the refrigerant remains constant at the maximum value. Fig. 5.33 Schematic of a solar adsorption cooling device

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381

Fig. 5.34 Basic adsorption cycle

Upon reaching the condensation pressure pc at point 2, the desorption process starts (isobaric line 2–3), in which the progressive heating Qd2 of the adsorbent from point 2 to 3 causes the adsorbent to release the refrigerant vapour, which is liquefied in the condenser (releasing the condensation heat Qc at the condensation temperature t c ) and is then collected in a receiver. This stage ends when the adsorbent reaches its maximum regeneration temperature t d and the refrigerant content decreases to the minimum value X min (point 3). Then, the adsorbent cools along the isosteric line 3–4, while the refrigerant content remains constant at the minimum value. During this phase, the control valve V is opened, allowing for the refrigerant to flow into the evaporator, and the system pressure decreases until it reaches the evaporator pressure pe , thus equalising the refrigerant vaporisation pressure (point 4). Afterward, the adsorption-evaporation phase (isobaric line 4-1) from point 4 to point 1 occurs producing the cooling effect Qe in the evaporator at evaporation temperature t e . At this stage, the vaporised refrigerant in the evaporator flows to the adsorber, where it is adsorbed until the maximum content X max is reached at point 1. During this phase, the adsorbent cools until it reaches the temperature t a by rejecting the sensible-heat and the heat of adsorption Qa . At the end of this phase, the control valve V is closed, and the cycle restarts [91]. In the solar adsorption refrigeration cycle, stages 1–3 correspond to the daytime period, and the stages 3–1 correspond to the night-time period. The adsorption cycle achieves a COP of 0.3–07, depending upon the driving heat temperature of 60–95 °C [93]. The thermal COP of the adsorption cycle can be calculated using following equation: COP =

Qe Qd

(5.3.8)

where Qe is the cooling power, Qd = Qd1 + Qd2 is the heat transferred to the adsorber to promote its regeneration/desorption, and Qd1 and Qd2 are as described above.

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5 Solar Heating and Cooling Systems

The overall COP of a solar adsorption cooling system is defined in Eq. (5.3.9): COPsys =

Qe Qs

(5.3.9)

where Qs is the solar power received by the SC surface. The specific cooling power (SCP), in W/kg, is defined in Eq. (5.3.10): SCP =

Qe ma

(5.3.10)

where Qe is the cooling power, in W, and ma is the mass of adsorbent, in kg. Adsorption refrigeration technology has been used for many specific applications, such as purification, separation and thermal refrigeration technologies. Researchers worldwide are working to improve the performance of adsorption cooling systems in order to overcome its current technical and economic issues. There are many ways: improving working pairs, heat and mass enhancement in adsorbent bed during adsorption and desorption process, optimisation of the adsorbent bed structure and refrigeration cycle. The majority of the current research works is related with the necessity to improve the adsorber-collector operating parameters and to develop new or enhanced working pairs. On the other hand, several projects and research works have been undertaken to overcome these limitations by developing continuously operation systems with higher performances, recurring to multiple adsorbent beds, mass or heat recovery systems, or multi-stage systems. However, such systems usually require a continuous heat source to operate uninterruptedly, and they are also more complex and expensive. • Working pairs. In an adsorption refrigeration technique, the adsorbent/refrigerant working pair plays a vital role in the optimal performance of the system. For any cooling application, the adsorbent must have high adsorptive capacity at ambient temperatures and low pressures but less adsorptive capacity at high temperatures and high pressures. The adsorbents are characterised by surface properties such as surface area and polarity. A large specific surface area is preferable for providing large adsorption capacity, but the creation of a large internal surface area in a limited volume inevitably gives rise to large numbers of small-sized pores between adsorption surfaces. The pore size distribution of micro-pores which determines the accessibility of adsorbate molecules to the internal adsorption surface is important for characterising adsorptivity of adsorbents. The choice of the adsorbent will depend mainly on the following factors: high adsorption and desorption capacity to attain high-cooling effect; good thermal conductivity to shorten the cycle time; low specific heat; chemically compatible with the chosen refrigerant; low cost; and widely available. The selected refrigerant must have most of the following desirable thermodynamics and heat transfer properties: evaporation temperature below 0 °C; highlatent heat per unit volume; high-thermal conductivity; low viscosity; low specific

5.3 Solar Thermal Cooling Systems

383

heat; non-toxic, non-inflammable, non-corrosive nature and chemically stable in the working temperature range. The most commonly used adsorbents are activated carbon, zeolite and silica gel. Activated carbon (AC) offers a good compromise between high-adsorption and desorption capacities. In turn, natural zeolites need to be present in large quantities because only a small amount of refrigerant is desorbed during the temperature increase. Silica gel is expensive and may not be available in most countries. The most commonly used refrigerants are ammonia (NH3 ), methanol and water (H2 O), which have relatively high-latent heat values (1368, 1160 and 2258 kJ/kg, respectively) and low specific volumes (of the order of 10−3 m3 /kg). NH3 is toxic and corrosive, while H2 O and methanol are not, but the latter are flammable. The most commonly used working pairs are: silica gel/water; activated carbon/methanol; activated carbon/ammonia; zeolite/water; activated carbon granular and fibre adsorbent, metal chloride/NH3 , and composite adsorbent/NH3 . The most common working pairs used in hybrid adsorption technology are silica gel/chloride-water and chlorides/porous media/NH3 . Silica gel/water is ideal for solar energy applications due to its low regeneration temperature, thus only requiring low grade heat sources, commonly below 85 °C. Moreover, water has the advantage of having a greater latent heat than the other conventional refrigerants. However, this pair has a low adsorption capacity as well as a low vapour pressure, which can hinder mass transfer. Furthermore, this working pair requires vacuum conditions in the system [62]. Main applications for this working pairs are refrigeration, water cooling and ice-making. Activated carbon/methanol is one of the most common working pairs in adsorption refrigeration systems. It also operates at low regeneration temperatures, while its ad-sorption-evaporation temperature lift is limited to 40 °C. This pair is also characterised by its large cyclic adsorption capacity, low freezing point, low adsorption heat and the high evaporation latent heat of methanol. However, AC has a low thermal conductivity, which decreases the system’s COP. Additionally, methanol has a high toxicity and flammability [91]. Main applications for this working pairs are ice-making, water cooling and ventilation. The activated carbon/NH 3 pair requires regeneration temperatures that can exceed 150 °C. Its adsorption heat is similar to that of activated carbon/methanol, but it requires higher operating pressures, which prevents the infiltration of air into the system and reduces the cycle time. These factors help to increase the specific cooling capacity of the system. However, the AC has a lower adsorption capacity when paired with NH3 than methanol [62, 91]. Main applications for this working pairs are ice-making and refrigeration. The zeolite/water pair requires regeneration temperatures that exceed 200 °C, with an adsorption-evaporation temperature lift up to 70 °C or more. This pair remains stable at high temperatures, and the latent heat of water is much higher than those of methanol or other classical refrigerants. However, a system operating with the zeolite/H2 O pair is more suitable for A/C applications due to the solidification temperature of water, which restrains the freezing process. The specific cooling

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5 Solar Heating and Cooling Systems

capacity of these systems is not very high [62]. Main applications for this working pairs are refrigeration, ice-making and water cooling. In addition to the most common working pairs, other pairs have also been investigated. In Germany, Bansal et al. [94] developed a solar refrigerator with the capacity to produce a daily 4.4 MJ cooling effect operating with strontium chloride as the adsorbent and ammonia as the refrigerant. The maximum solar COP obtained was 0.08 with a daily solar radiation of 26 MJ/m2 . More working pairs have been evaluated the recent years. For example, Jribi et al. [95] simulated the dynamic behaviour of a four-bed adsorption cycle using AC and low global warming potential R1234ze. Table 5.11 provide the summary of a comparison between various solid adsorbent pairs. The main direction for future research work on adsorption working pairs is related to advanced adsorbent technology with high heat and mass transfer performance. Promising results have been obtained with the composite adsorbents and consolidated adsorbents. However, improvements in heat transfer often result in deployment of the mass transfer performance, thus, research should be focused in producing adsorbent where both mass and heat transfer can be satisfactory. Generally, consolidated adsorbent with high density and short mass transfer path has both good heat and mass transfer performance. However, the increase of the volume occupied by the mass transfer channels reduces the amount of the adsorbent that can be placed in a specific space. Table 5.11 Comparison between various solid adsorbent pairs Adsorbent

Refrigerant

Adsorption heat (kJ/kg)

Density of refrigerant (kg/m3 )

Considerations

Activated alumina

H2 O

3000

1000

Water is applicable except for very low-operating pressure

Zeolite

H2 O

3300–4200

1000

NH3

4000–6000

681

CH3 OH

2300–2600

791

Natural zeolite has lower values than synthetic zeolite

Silica gel

CH3 OH

1000–1500

791

Suitable for temperature less than 200 °C

Silica gel

H2 O

2800

1000

Used mostly for descent cooling

Calcium chloride

CH3 OH

1800–2000

791

Used for cooling

Metal hydrides

Hydrogen

2300–2600

1000

Used for air-conditioning

Complex compounds

Salts and NH3 or H2 O

2000–2700

681

Used for refrigeration

5.3 Solar Thermal Cooling Systems

385

Another direction for future research work is the search for working pairs that could be powered by low temperature and could be used to obtain temperatures below –10 °C. • Physical and chemical adsorption. Adsorbents such as silica gel, activated carbon and zeolite are physical adsorbents having highly porous structures with surfaceto-volume ratios on the order of several hundred that can selectively catch and hold refrigerants. When saturated, they can be regenerated simply by being heated. The employed adsorbent/refrigerant working pairs include silica gel/H2 O [96] and AC with methanol or NH3 [97]. Chemical adsorption is characterised by the strong chemical bond between the refrigerant and the absorbent. Therefore, it is more difficult to reverse and thus requires more energy to remove the adsorbed molecules than physical adsorption does. The most commonly used chemical adsorbent in solar cooling applications has been calcium chloride (CaCl2 ). CaCl2 adsorbs NH3 to produce CaCl2 ·8NH3 and water to produce CaCl2 ·6H2 O as a product. • Study of solar adsorption cooling systems. Solar energy can easily be used in adsorption cooling systems. The performance of solar adsorption cooling systems was reported by several researchers. Experimental studies. Some researchers [98–101] reported COP values of 0.10– 0.12 for solar-assisted adsorption systems using zeolite/H2 O, and Critoph [101] reported the COP value of 0.05 using activated carbon/NH3 . Henning and Glase [102] designed a pilot adsorption cooling system using silica gel/H2 O as the working pair. The system was powered with the solar heat produced by vacuum tube collectors having a surface area of 170 m2 . The reported COP varied between 0.2 and 0.3. Sumathy et al. [103] provided literature reviews of the solar adsorption cooling technologies using various adsorption pairs and their performances. Luo et al. [104] used a solar adsorption cooling system for low-temperature grain storage with silica gel/H2 O. They concluded that a COP value ranging from 0.096 to 0.13 could be achieved. González and Rodr´ιguez [105] presented a solar refrigeration system comprising a 0.55 m2 parabolic SC with four parallel tube receptors containing a bed of activated carbon (Fig. 5.35). The cooling water flow rate is promoted by an electrically driven pump powered by a PV module. The evaporator consists of several vertical pipes, each surrounded by a small cylindrical tank containing the water to refrigerate. The test results led to a maximum solar COP of 0.10, while the evaporation temperature reached 1.1 °C for 19.5 MJ/m2 of daily solar radiation. Sapienza et al. [106] developed a new composite sorbent named SWS-9 V (LiNO3 /vermiculite) which was specially designed for low-temperature heat sources (< 70 °C). The experimental results showed that the system had a SCP of 230 W/kg and a COP of 0.66 at t e = 10 °C, t c = 35 °C and t d = 90 °C. Recently, a solar adsorption refrigeration system operating with the silica gel/water pair was developed in Portugal (Fig. 5.36). The system consists of a 1m2 FPC, a condenser, a condensate receiver and an evaporator inside a cold box

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5 Solar Heating and Cooling Systems

Fig. 5.35 Solar refrigerator with parabolic collector

Fig. 5.36 Solar refrigerator operating with silica gel/water

[91]. From the experimental results, it was found that the unit is capable of reaching a solar COP of 0.07, cooling a daily load of 6 kg of water, and still produce a significant amount of ice inside the evaporator to maintain its temperature constant all the time (near 0 °C).

5.3 Solar Thermal Cooling Systems

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Fig. 5.37 Solar refrigerator with cylindrical adsorber 1-solar collector; 2-heat pipe; 3-adsorber; 4-evaporator; 5-condenser; 6-valves; 7-tank; 8-expansion valve

Simulation studies. More recently, Li et al. [107] presented simulation results of a solar refrigerator in which the zeolite is placed inside the evacuated tubes of the SC. The adsorbent can reach 200 °C, and the global system performance is relatively high compared to the previous solar adsorption refrigerators, with the theoretical solar COP values reaching to greater than 0.25. For the summer climate in Morocco, El-Fadar et al. [108] simulated a solar adsorption refrigerator with no moving parts and with a parabolic SC connected to a cylindrical adsorber through a water heat pipe (Fig. 5.37). The influences of several parameters were analysed, and it was determined that the COP increases with the adsorbent mass, up to a critical value of 14.5 kg, which corresponds to a 72.8 cm collector opening and a solar COP of 0.18. Hassan et al. [109] presented more recently in Canada a theoretical simulation model of a tubular solar adsorption refrigeration system using the activated carbon/methanol working pair. The 1-m2 flat-plate SC consists of several steel pipes containing the adsorbent. The test results indicate that the solar COP value was 0.21 for a maximum solar radiation intensity of 900 W/m2 . Table 5.12 summarises the performance of the solar adsorption cooling systems using various adsorption pairs. Figure 5.38 compares the performance of the adsorption cycles using different working pairs. One can notice that silica gel and AC are popular choice for adsorbents.

5.3.2.5

Applications of Solar Sorption Cooling Systems

• Air-conditioning (A/C). The main purpose of most buildings and A/C systems is to provide an acceptable environment that does not impair the health and performance of the occupants. Solar sorption refrigeration systems are suitable for A/C due to their low-installation costs and high-cooling capacities. Experimental studies. In Japan, a solar heating and cooling system with FPCs and absorption refrigeration system was installed [70]. Yeung et al. [110] developed a

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5 Solar Heating and Cooling Systems

Table 5.12 Performance of the solar adsorption refrigeration system Working pair

COPsys

Solar collector

System conditions

Activated carbon/methanol

0.100.12

FPC (A = 6 m2 )

t e = 3 °C, t c = 25 °C, t d [98] = 110 °C

References

Activated carbon/methanol

0.100.12

FPC (A = 6 m2 )

t e = 6 °C, t d = 70 °C78 [102] °C

Zeolite/water

0.11

FPC (A = 20 m2 )

t e = 1 °C, t c = 30 °C, t d = 118 °C

[99]

Zeolite/water

0.100.12

FPC (A = 1.5 m2 )

–

[98]

Activated carbon/ammonia

0.05

FPC (A = 1 m2 )

–

[100]

Activated carbon/water

0.07

FPC (A = 2 m2 )

–

[96]

Silica gel/water

0.200.30

VTC (A = 170 m2 )

–

[101]

Silica gel/water

0.100.13

–

–

[103]

Fig. 5.38 Comparison of the adsorption cycle performance using different working pairs

solar powered absorption A/C system on the campus of the University of Hong Kong. The system consists of a FPC array with a surface area of 38.2 m2 , a 4.7-kW cooling capacity H2 O/LiBr absorption chiller, a 2.75-m3 hot water ST, a cooling tower, a fan coil unit, and an electrical auxiliary heater. It had an annual system COP of 7.8%. The potential energy savings and limitations of solar thermal A/C in comparison to conventional technologies for Europe are illustrated and discussed by Balaras et al. [111]. Bujedo et al. [112] studied different control strategies for a solar powered H2 O/LiBr absorption cycle. A 77.5-m2 collector area was used to drive a 35-kW

5.3 Solar Thermal Cooling Systems

389

chiller with two 2-m3 hot water STs and a 1-m3 cold-storage tank to air-condition 200m2 of offices under Spanish weather conditions. The new strategies had better results than the conventional one. An improvement of the yield of the solar field ranged from 7 to 12%, whereas the improvement in the total system COP was 44-48%. Agyenim et al. [113] designed a solar absorption cooling system with cold storage. A 4.5-kW chiller unit using H2 O/LiBr was driven by 12 m2 of vacuum tube collectors. The chiller was activated at a minimum temperature of 80 °C and it was able to produce chilled water with a temperature in the range of 7–16 °C. The solar cooling system was experimentally tested in Cardiff, UK. It was recommended that to commercialise the system the solar cooling system should be integrated with the domestic hot water and space heating systems used during the winter season. Lizarte et al. [114] introduced a directly air-cooled single-effect H2 O/LiBr absorption chiller that used an innovative adiabatic flat-fan sheet absorber. The flat-fan sheet configuration was also investigated by Palacios et al. [115] and found to exhibit a mass transfer coefficient one order of magnitude higher than that of the falling-film or the spay-type absorbers. The system was used to air-condition a 40-m2 space during the summer season in Madrid. The volume of the absorption unit was 1 m, whereas the hot water ST volume was 1.5 m3 . For the test period, the mean collector efficiency, system COP and solar COP were 0.27, 0.53 and 0.062, respectively. Simulation studies. Al-Alili et al. [116] studied the performance and economic and environmental benefits of a 10-kW NH3 /H2 O absorption chiller under Abu Dhabi’s (United Arab Emirates) weather conditions. The solar A/C system had a specific collector area of 6 m2 /kW and a specific tank volume of 0.10 m3 /kW. The system was found to consume 47% less electricity than the widespread systems with vapourcompression cycles of the same cooling capacity. The economic analysis showed that the collector area was the key parameter in reducing the payback period of the initial investment. Balghouthi et al. [117] assessed the feasibility of using a solar powered H2 O/LiBr absorption system in Tunisia by simulation. TRNSYS and EES programs were used to model the system and the conditioned space. To air-condition a 150 m2 building, an 11-kW absorption cycle using a 30-m2 FPC and a 0.8-m3 hot water tank was used. They studied the effect of the generator inlet temperature and heat transfer coefficient on the COP and cooling capacity. Table 5.13 provides more details regarding the solar absorption A/C cycles. • Refrigeration. The low-temperature applications can also utilise sorption systems. These systems are attractive for refrigeration applications in remote or rural areas of developing countries where access to electricity is impossible. Various solar sorption refrigerators have been developed. Experimental studies. Uppal et al. [118] built in 1986 a small capacity (56 L) solar-driven NH3 /H2 O absorption refrigerator to store vaccines in remote locations. Sierra et al. [119] used a solar pond to power an intermittent absorption system with NH3 /H2 O working fluids. They reported that generation temperatures as high as 73 °C and evaporation temperatures as low as –2 °C could be obtained. The system COP was in the range of 0.24–0.28.

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Table 5.13 Performance of the solar absorption air-conditioning cycles Working fluid

COPsys

Solar collector

System conditions

NH3 /H2 O

0.427

ETC (A = 11 m2 )

t e = –9 °C, t c = 3745 °C, [76] t g = 110 °C

References

NH3 /H2 O

0.550

ETC (A = 6 m2 )

t e = 6 °C, t c = 24 °C, t g = 85 °C

[115]

H2 O/LiBr

0.620

ETC (A = 94 m2 )

t e = 15.5–25 °C, t c = 26.537.7 °C, t g = 90–106 °C

[113]

H2 O/LiBr

0.660

ETC (A = 2.7 m2 )

t e = 10.1 °C, t c = 24 °C, t g = 77.1 °C

[112]

H2 O/LiBr

0.740

FPC (A = 2.7 m2 )

t e = 7.5 °C, t c = 28 °C, t g = 86 °C

[116]

H2 O/LiBr

0.490

FPC&ETC (A = 1.5 m2 )

–

[117]

De-Francisco et al. [72] tested in Madrid a prototype of a 2 kW solar powered NH3 /H2 O absorption chiller for refrigeration in small rural operations that utilises concentrating collectors and uses a transfer tank instead of a pump. Their experimental results showed inefficient operation of the equipment with a COP less than 0.05 when the collectors operated at temperature greater than 150 °C. Lemmini and Errougani [120] presented experimental work to evaluate the performance of a solar adsorption system using the AC35/methanol pair in Rabat, Morocco. The system consists of a FPC, a condenser and a cold-box evaporator. The results indicated that the solar COP ranges between 0.05 and 0.08 for a solar radiation between 12 and 27 MJ/m2 , a daily average temperature between 14 and 18 °C and a lowest temperature achieved by the evaporator between –5 and 8 °C. Simulation studies. Hammad and Habali [121] simulated a solar absorption refrigeration system with NH3 /H2 O as the working mixture to cool a vaccine cabinet in the Middle East. The simulation results indicated that the system had a COP between 0.50 and 0.65 at the generation temperature of 100–120 °C and the cabinet indoor temperature of 0–8 °C. More recently, Abu-Hamdeh et al. [122] developed a model of a solar adsorption refrigeration system operating with the olive-waste/methanol pair. The system comprises a 3.7-m2 parabolic SC, a heat storage tank, an adsorber, a condenser, an evaporator, a throttling valve and a circulating pump. From the simulated results, the lowest temperature attained in the refrigerated space was 4 °C, with a solar COP of 0.03, for a solar radiation flux of 56.2 MJ/m2 . • Ice-making. An absorption or adsorption chiller can also be used for freezing applications that require temperatures below 0 °C. Experimental studies. Sumathy and Li [123] designed a solar ice maker with the AC/methanol pair using a 0.92-m2 flat-plate SC. The system produced 4–5 kg of ice daily at an evaporation temperature of –6 °C for a daily solar radiation between 17 MJ/m2 and 19 MJ/m2 and achieved solar COP values of 0.10–0.12.

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391

In Switzerland, Hildbrand et al. [96] constructed and tested a new high-efficiency solar adsorption system. The working pair is silica gel/H2 O. Cylindrical tubes function as both the adsorber and the solar FPC (2-m2 double glazed). The condenser is air-cooled, and the evaporator contains 40 L of water that can freeze. This ice functions as cold storage for the cabinet. This system has a solar COP of 0.16. Ji et al. [124] built a solar powered solid adsorption refrigeration system with the finned tube absorbent bed collector. Activated carbon/methanol was utilised as the working pair for adsorption refrigeration in the experiments. The experiments achieved the maximum COP of 0.122 and the maximum daily ice-making of 6.5 kg. The cooling efficiency of the solar powered adsorption refrigeration system with a valve control in the adsorption/desorption process was significantly higher than that without a valve control. Simulation study. In Italy, Vasta et al. [125] presented the numerical model of a solar adsorption refrigerator that simulates the different stages of the thermodynamic cycle and the processes occurring in the system components, which are: a 1.5-m2 SC, containing the adsorbent bed, and a condenser and a cold box containing an evaporator, and the water to freeze. It was found that for most of the year (FebruaryOctober) the system has the ability to produce between 4 and 5 kg of ice per day. For the colder months (November-January), it is possible to produce 2–3.5 kg of ice per day. The average monthly solar COP ranged from 0.05 (July) to 0.11 (January), with a yearly average COP of 0.07.

5.3.3 Solar Thermo-Mechanical Cooling Systems 5.3.3.1

Description of the System

In the thermo-mechanical solar cooling system, the thermal energy is converted to the mechanical energy. Then the mechanical energy is utilised to produce the cooling effect. The steam ejector system represents the thermo-mechanical cooling technology. Figure 5.39 illustrates the steam ejector system integrated with a parabolic solar collector SC. The steam produced by the SC is passing through the steam jet ejector E. During this process, the evaporator pressure is reduced, and water is vaporised in the evaporator V by absorbing the heat from the cold water. The ejector is the key component in the cycle. The ejector mainly consists of a nozzle, a mixing chamber and a diffuser, as shown in Fig. 5.40. The working principle of the ejector is based on the expansion of a high-pressure steam jet in the converging/diverging nozzle section. The internal energy of the motive steam is converted to kinetic energy. The high-speed steam jet (primary fluid) entrains the low-pressure secondary steam jet (secondary fluid). The two steam jets enter the mixing section where momentum is transferred from the primary fluid to the secondary fluid causing acceleration of the secondary steam jet. Before exiting

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5 Solar Heating and Cooling Systems

Fig. 5.39 Schematic of steam jet solar cooling system

Fig. 5.40 Schematic of ejector

the ejector, a diffuser is used to convert the mixed steam’s kinetic energy into internal energy in order to reach a pressure higher than the back pressure. When cooling is not needed, the steam turbines can be used to produce electricity. Most of the steam ejector system require steam at pressures in the range of 0.1– 1.0 MPa, and temperatures in the range of 120–180 °C [126]. However, Loehrke [127] proposed and demonstrated that the steam ejector system could be operated using low-temperature solar heat by reducing the operating pressure under atmospheric pressure. The pump does not determine a high growth in cost or electricity consumption (i.e., the required pump power consumption is ~0.18% of the energy received from the SC). However, the pump requires more maintenance than other parts because it is the only moving part in the system. Hence, to replace the pump, several solutions have been found [128]: • gravitational/rotational ejector cooling system; • bi-ejector cooling system; • heat pipe/ejector cooling system.

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393

Fig. 5.41 Heat pipe/ejector cycle

In a gravitational ejector cooling system, the heat exchangers are placed on different vertical positions, equalising the pressure differences between them. The steam generator has the highest pressure, and the evaporator has the lowest pressure. There are also complex mechanisms of self-regulation of the generator, evaporator and condenser. A major drawback of the system is the requirement of height differences (depending on the working fluid and on the temperature differences) and the length of pipes (which causes high friction and heat losses). In the bi-ejector cooling system, a second ejector, which replaces the pump, carries the liquid condensate to the generator. Therefore, the ejector is a vapour/liquid ejector. An interesting technology is the coupling heat pipe/ejector. The coupling of the heat pipe and the ejector technology is interesting because it results in a system that is both compact and with high performance. This system is composed of a heat pipe, an ejector, an evaporator and an expansion valve (Fig. 5.41); the working principles will not be described here because they are the same as those of other ejector cooling systems. A description can be found in the work of Smirnov and Kosov [129].

5.3.3.2

Performance Parameters

Several parameters are used to describe the performance of ejectors in cooling cycles, as provided below. The entrainment ratio ω is the ratio between the secondary fluid mass flow rate ms , in kg/s and the primary fluid mass flow rate mp , in kg/s: ω=

ms mp

(5.3.11)

The compression ratio H c is the static pressure at the exit of the diffuser pc , in Pa, divided by the static pressure of the secondary fluid pe , in Pa: Hc =

pc pe

(5.3.12)

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5 Solar Heating and Cooling Systems

The theoretical COP of the thermodynamic cycle is defined as the ratio between evaporation heat (cooling power) Qe and the total incoming energy in the cycle Qg + Pel : COP =

Qe Q g + Pel

(5.3.13)

where Qg is the generator thermal power, in W and Pel is the electrical power of pump, in W. The ejector efficiency ηej is defined as the ratio between the actual recovered compression energy and the available theoretical energy in the motive fluid [130]: ηej =

(m p + m s )(h c,in − h e,out ) m p (h g,out − h e,out )

(5.3.14)

where: hc,in is the specific enthalpy at inlet of condenser, in kJ/kg; he,out is the specific enthalpy at outlet of evaporator, in kJ/kg and hg,out is the specific enthalpy at outlet of generator, in kJ/kg. The real COP of the thermodynamic cycle (COPr ) is given by: COPr = ηej COP

(5.3.15)

The overall COP of a solar thermo-mechanical cooling system is given by the following equation: COPsys =

Qe Qs

(5.3.16)

where Qs is the solar power received by the SC surface.

5.3.3.3

Working Fluid Selection

The selection of the appropriate refrigerant is of fundamental importance in the design of an ejector cooling system. In the past, the main principle for selection was the maximisation of the performance; more recently, several factors (safety, cost, etc.) are considered, and the final choice depends on the compromise between the performance and the environmental impact. The working fluids can be classified based on the chemical compounds and can be classified into three main groups [131] (Table 5.14): (1) the halocarbon group [i.e., chlorofluorocarbons (CFCs), hydrochlorofluorocarbons (HCFCs), hydro-fluorocarbons (HFCs), and hydro-fluoroolefin (HFO) and the hydro-carbon group (HC)], (2) organic compounds consisting of hydrogen and carbon (i.e., R290, R600, and R600a) and (3) other refrigerants, [i.e., water (R718b), NH3 (R717) and carbon dioxide (R744)].

5.3 Solar Thermal Cooling Systems

395

Table 5.14 Refrigerant classification and safety characteristics Group Halocarbon compounds

Hydrocarbon compounds Other refrigerants

Safety group (toxicity/flammability)

Working fluid

CFC

A1

R11, R12, R113, R114

HCFC

A1–B1

R21, R22, R123, R141b, R142b, R500, R502

HFC

A1–A2

R134a, R152a, R236fa, R245fa

HFO

A2L

R1234yf

HC

A3

R290, R600, R600a

B1

CH3 OH

B2L

R717

A1

R718b, R744

Generally, a suitable refrigerant for a refrigeration system should be able to guarantee high performance for the required operating conditions. Accordingly, working fluid thermo-physical properties must be taken into account. Thermo-physical properties should satisfy some constraints-they should have a large latent heat of vaporisation and a large generator temperature range for limiting the circulation rate per unit of cooling capacity and the fluid should have a high-critical temperature to compensate large variations in generator temperatures. The fluid pressure should not be too high in the generator for the design of the pressure vessel and for limiting the pump energy consumption. Moreover, the viscosity, the thermal conductivity and the other properties that influence the heat transfer should be favourable. A high-molecular mass is desirable to increase ω and ηej . Low-environmental impact, as defined by the global warming potential and the ozone depletion potential is also an important factor for consideration. The fluid should also be non-explosive, non-toxic, non-corrosive, chemically stable, cheap and available on the market. The working fluid used in a solar ejector cooling system leads to different performance depending on operating conditions. To compare the performance of different used working fluids, in Table 5.15 the following values are presented: t g −the generation temperature; t c −the condensation temperature achieved in condenser C (37°C for cooling with cooling tower, 30°C for cooling with cold water); pg −the pressure in the generator G (maximum pressure in the system); pe −the pressure in the evaporator V (minimum pressure in the system); QSC −the heat needed to be supplied by SC in generator to achieve a cooling power of 1.16×104 W; Ac −the SC area, assuming a solar flux of 0.8 kW/m2 and capture efficiency of 0.5, for achieving a cooling capacity of 1.16×104 W. Considering one FPC, the possible temperature for which can easily provide solar heat is t g = 85°C, and for a parabolic-cylinder concentrating collector can be adopted is t g = 130°C. Analysing the COPr values from this table results as the competitive working fluids: H2 O, R11 and R21, among which best is R11. H2 O and R11 have comparable COPr , but operating pressures in the system are very different. Thus, for the use of

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5 Solar Heating and Cooling Systems

Table 5.15 Performances of different working fluids used in solar steam ejector systems Working fluid H2 O

R-11

tg (o C)

ηej (–)

COPr (–)

173

0.913

0.184

0.168

91

1.471

0.217

0.319

62

2.076

0.226

0.469

pg (kPa)

pe (kPa)

37

392.2

0.88

69,130

30

392.2

0.88

36,396

130

37

475.5

0.88

24,717

30

475.5

0.88

17,979

45

2.887

0.223

0.645

85

37

460.8

50.0

63,428

159

0.936

0.196

0.183

30

460.8

50.1

26,356

66

1.947

0.226

0.440

37

784.0

50.1

26,911

67

1.708

0.226

0.386

30

784.0

50.1

17,175

43

3.121

0.216

0.675

754.9

90.2

85,630

215

0.790

0.172

0.135

85

130

QSC (W)

COP (–)

tc (o C)

Ac (m2 )

R-21

85

37 30

754.9

90.2

47,866

120

1.162

0.209

0.242

Propane

85

37

2745

539

298,969

750

0.496

0.078

0.039

30

2745

539

56,585

142

1.038

0.198

0.209

37

882.3

147

302,475

758

0.423

0.091

0.038

30

882.3

147

102,284

256

0.666

0.170

0.113

85

37

2157

520

Not possible solution

130

37

2157

520

2,130,150

0.348

0.016

0.005

Butane NH3

85

5338

FPCs (t g = 85°C), steam ejector cooling system works completely in depression (pe and pg is less than atmospheric pressure). So if H2 O is used as refrigerant leakage problems are to be solved to avoid the air entering the system. Some experimental studies [132, 133] have examined the effect of the operation conditions such as the generator temperature, evaporator temperature and condenser temperature, the geometrical conditions, the system conditions such as refrigerant and collector selections on the performance of the system. Other researchers [134, 135] have presented numerical methods of simulating the ejector and studied the performance of system. Nehad [132, 133] compared the theoretical performance of the ejector system working with R717, R11, R12, R113 and R114. Then he chose R113 as a refrigerant for the experiment since it has a higher COPr , a reasonable operating pressure, and is non-toxic. Vidal et al. [134] analysed the solar ejector system using R141b as its refrigerant by using the TRNSYS and EES simulation software. The system was designed to deliver 10.5 kW of cooling with 80 m2 of FPC tilted 22° from the horizontal and a 4-m3 hot water ST. They reported the maximum COPr of 0.22 at t g = 80 °C, t e = 8 °C and t c = 32 °C. They also concluded that an efficient ejector system could only work in a region with decent solar radiation and where a sufficiently low condenser temperature could be kept.

5.3 Solar Thermal Cooling Systems

397

Fig. 5.42 Comparison of the ejector cycle performance using different refrigerants

Grazzini and Rocchetti [135] theoretically investigated the performance of the two-stage ejector system. They reported that the COPr of the two-stage ejector system ranged from 0.13 to 0.53 at t g = 110–120 °C, t e = 7–12 °C and t c = 30–40 °C. Along with other researches results [136] show that the low-ejection efficiency leads to values of COP for solar ejector cooling systems smaller than in the case of solar absorption cooling systems. The performance of the ejector system depends on the mass flow rate ratio through the motive nozzle and the suction nozzle. Figure 5.42 shows the performance of ejector cycle using different refrigerants [137]. The ejector systems are mostly used in A/C applications, but they can be used in chemical and metallurgical industry for air cooling in areas with higher heat dissipation.

5.3.4 Hybrid Cooling and Heating Systems In solar thermal systems with large capacity, both solar cooling and solar heating are provided synergistically yielding a complete annual utilisation. During the cold season solar heat serves for space heating. During the warm season solar heat is converted into useful cold by means of sorption cooling devices avoiding overheating of the solar thermal system. There are already several hybrid systems using the basic closed sorption cycle for heat and cold production. Many applications of solar A/C will be done in conjunction with solar heating, with the same collector, storage and auxiliary energy system serving both functions and supplying hot water. Figure 5.43 shows a hybrid cooling and heating system using a

398

5 Solar Heating and Cooling Systems

Fig. 5.43 Schematic of a hybrid solar heating, air-conditioning and hot water system AS-auxiliary heat source A/C-air conditioner; CT-cooling tower; PHT-preheat tank; WH-water heater

H2 O/LiBr absorption cooler for A/C, in which solid flow lines are for cooling, dashed lines are for heating and dotted lines are for air-conditioner coolant flow [138]. An important consideration in combined heating and cooling systems is the relative importance of the summer and winter loads. Either one may dictate the needed capacity of the collector and consequently its size and design. Climate is a major determining factor, and cooling requirements will dominate in warm climates. Commercial buildings are likely to have design fixed by cooling loads, even in cool climates. Also important are building design features that can affect relative energy requirements for the two loads. These include fenestration, shading by overhangs, wing-walls and building orientation. Less obvious is the performance of the cooling and heating system; a poor absorption cooler would require a larger collector area than one with a high COP and thus could shift the determination of collector needs from winter heating to summer cooling. Solar cooling systems predominantly cover cooling capacities in the range of 10–30 kW, requiring solar collectors of approximately 30–100 m2 surface area. Wet cooling towers designed for coolant supply/return temperature about 27/35 °C are applied to transfer the heat rejected by absorber and condenser to the ambient. When a dry air cooler is to be used, cooling water temperatures have to be increased to

5.3 Solar Thermal Cooling Systems

399

Fig. 5.44 Solar cooling/heating system with an absorption chiller and latent heat storage

40/45 °C. As a consequence of the increase of the cooling water temperature, the temperature level of the driving heat supplied to the generator of the absorption chiller has to be increased accordingly. Both systems, wet cooling towers and dry air coolers allow for significantly lower coolant temperatures during off-peak hours with moderate ambient air temperatures. Experimental studies. Helm et al. [139] have described the operation of an absorption cooling and heating hybrid system, that involves latent heat storage supporting the heat rejection of the absorption chiller, in conjunction with a dry cooling system as shown in Fig. 5.44. They have indicated low-temperature latent heat storage together with a dry air cooler, as a promising alternative to the conventional wet cooling tower, as it substantially reduces the over-sizing of the SC system. Mammoli et al. [140] used FPCs and ETCs (232 m2 of total area) to drive a 70 kW H2 O/LiBr absorption system. The system was used to provide heating and cooling to the mechanical engineering university building in New Mexico, USA, wherein 34-m3 hot water ST and seven 50-m3 cold water tanks were used. The system implemented four different control strategies for summer daytime, summer night-time, winter daytime and winter night-time operations. The results indicated that the collector field had a daily average efficiency of 0.58, while the chiller had an average COP of 0.63. The hot storage tank was found to be the largest source of heat loss. In China, Wang et al. [97] developed an innovative solar hybrid system for water heating and ice production using the AC/methanol pair (Fig. 5.45). The adsorber bed is immersed in a water tank and is directly heated by a 2-m2 evacuated tube SC. During

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5 Solar Heating and Cooling Systems

Fig. 5.45 Solar hybrid system using the activated carbon/methanol pair

the night, the hot water drained from the tank can be used for domestic purposes. During the adsorption stage, the sensible and adsorption heat from the adsorber are transferred to the water in the tank, producing useful heat. The authors estimated the following results: in the winter case, with a solar radiation of 24.6 MJ/day, the system produces 60 kg of hot water at 98 °C and 10.5 kg of ice at –2.5 °C with a system COP of 0.143 and a heating efficiency of 0.795; in the spring case, with a solar radiation of 22 MJ/day, the system produces 60 kg of hot water at 91.3 °C and 10 kg of ice at –1.8 °C with a system COP of 0.144 and a heating efficiency of 0.797. Simulation studies. Zhang and Wang [141] designed a continuous operation hybrid solar adsorption system for heating and cooling purposes, working with the AC/methanol pair. The results were obtained by simulation. For a solar radiation of 21.6 MJ/day, the system is capable of heating 30 kg of water to 47.8 °C with a heating COP of 0.34, while the evaporation temperature reaches 5 °C with a solar COP of 0.18. The upper bed can reach 80–90 °C, after which the collector is rotated by 180° to replace the upper bed by the lower bed, which is now heated by solar energy, while the bed initially in the upper position is cooled by cold water coming from a water tank, which flows by natural convection. A continuous combined solid adsorption-ejector cooling and heating system driven by solar energy, operating with zeolite/water working pair, also was presented by Zhang and Wang [142]. More recently, Suleiman et al. [143] performed a numerical model of a solar hybrid system for cooling and heating in Nigeria. The system comprises a 2-m2 FPC and operates with the activated carbon/methanol pair. Considering an evaporator temperature of 0 °C and 25 °C in the condenser, the results showed an average cooling capacity of 4815 kJ (regeneration temperature of 86 °C) with a solar COP of 0.02 and a heating efficiency of 0.46.

5.3 Solar Thermal Cooling Systems

401

5.3.5 Comparison of Various Solar Thermal Cooling Systems Balaras et al. [111] described the main results of the European Union project SACE (Solar A/C in Europe), intended to assess the state-of-the-art, future needs and overall prospects of solar cooling in Europe. For this purpose, they collected information on 54 solar powered cooling projects conducted in various locations in Europe. They reported the thermal COP of different solar cooling technologies, as shown in Table 5.16. They concluded that the single-effect absorption systems have a COP in the range of 0.50–0.73, adsorption systems have a lower thermal COP of 0.59, a liquid desiccant system have a COP of 0.51, and a steam jet system have a relatively high COP of 0.85. Regarding the operating temperature of the systems, absorption systems operated at 60–165 °C, adsorption systems operated at 53–82 °C, a liquid desiccant system operated at 67 °C, and a steam jet system operated at 118 °C. For most of these systems operated below 100 °C, flat-plate SCs could be used, while concentrating SCs had to be used to drive temperatures higher than 100 °C. They also compared the annual EER, which is defined as the ratio of the annual cold production and the annual heat input. The H2 O/LiBr absorption systems have the best annual performance, while the adsorption systems have low annual performance. This result Table 5.16 Comparison of solar thermal cooling systems Specification

Process type

System

Liquid desiccant

Solid desiccant

Absorption Adsorption Ejector

Sorbent type

Liquid

Solid

Liquid

Open

Closed

Thermo-mechanical

Solid

–

Working fluid H2 O/CaCl2 , H2 O/silica H2 O/LiBr, (refrigerant/sorbent) H2 O/LiCl gel, NH3 /H2 O H2 O/LiCl

H2 O/silica gel

Steam

COP (-)

0.59

0.85

2.01

2.90

0.74

0.51

0.50–0.73 (single stage) t c ; 2–2 : Isobar cooling in the condenser C at pressure pc from the temperature t 2 to t 2 = t c ; 2 –3: Isotherm–isobar condensation in the condenser C at pressure pc and temperature t c ; 3–4: Isenthalpic lamination in expansion valve EV, leading the refrigerant from 3 states of the liquid at pc , t c in 4 states of wet vapour at p0 , t 0 ; 4–1: Isotherm–isobar evaporation in the evaporator E at pressure p0 and temperature t 0

The specific compression work w, in kJ/kg, the specific cooling power q0 , in kJ/kg, the specific heat load at condensation qc , in kJ/kg, volumetric refrigerating capacity q0v , in kJ/m3 , the coefficient of performance (COP) are calculated for above presented processes as follows: w = h2 − h1

(6.2.1)

q0 = h 1 − h 4 = h 1 − h 3

(6.2.2)

qc = h 2 − h 3

(6.2.3)

q0 = q0 ρ1 v1

(6.2.4)

h2 − h3 qc = w h2 − h1

(6.2.5)

q0v = COP =

Thermal power (capacity) of heat pump Qhp , in kW, is expressed as:

6.2 Energy-Economic Analysis of Building Heating and Cooling …

Q hp = mqc

453

(6.2.6)

The power necessary for the isentropic compression Pis , in kW, may be calculated using the equation: Pis = mw

(6.2.7)

The effective power Pef on the compressor shaft is bigger and is defined as: Pe f =

Pis ηis

(6.2.8)

where ηis is the isentropic efficiency.

6.2.3.2

Real Cycle

The real operational processes (Fig. 6.3) of a vapour compression-based HP deviate from the component processes of the theoretical cycle in the following ways: • the compression process 1–2 in the compressor is adiabatic, but irreversible; • the heat exchange from the evaporator and the condenser is realised with finite temperature differences, imprinting to these processes an irreversible mark; the average temperature of the cold source t s is higher than the evaporation temperature t 0 , with the difference t 0 , and the average temperature of the hot source t u is lower than the condensation temperature t c , with the difference t c . • the refrigerant flow through the system experiences pressure losses; and • the equipment and pipes which the working fluid runs through exchange heat with the environment. The irreversibility of the compression process increases the specific compression work to w and increases the specific thermal load at condensation by qc .

Fig. 6.3 Real operation process in t–s and p–h diagrams

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6 Heat Pumps for Sustainable Heating and Cooling

To assess the deviation in the degree of compression process 1–2 versus 1–2 , the (adiabatic) efficiency ηi of the compressor is defined as: ηi =

w w − qc qc = =1−  1. Additionally, the use of an HP can only be considered if the COPhp > 2.78. The COP of an HP is restricted by the second law of thermodynamics: • in heating mode: COP ≤

tu = C tu − ts

(6.2.29)

ts tu − ts

(6.2.30)

• in cooling mode: COP ≤

where t u and t s are the absolute temperatures of the hot environment (condensation temperature) and the cold source (evaporation temperature), respectively, in K. The maximum value εC of the efficiency can be obtained in the reverse Carnot cycle.

6.2.5.2

Economic Indicators

In the economic analysis of a system, different methods could be used to evaluate the system. Usually the HP achieves a fuel economy C (operating costs) comparatively of the classical system with thermal station (TS), which is dependent on the type of HP. On the other hand, the HP involves an additional investment I HP from the classical system I TS , which produces the same amount of heat. Thus, it can be determined the recovery time (RT), in years, to increase investment, I = I HP −I TS , taking into account the operation saving achieved through low-fuel consumption C = C TS −C HP : RT =

I ≤ RTn C

(6.2.31)

where RTn is normal recovery time. It is estimated that for RTn a time frame within 8–10 years is acceptable, but this limit varies depending on the country’s energy policy and environmental requirements. Another economic indicator is total updated cost (TUC):

6.2 Energy-Economic Analysis of Building Heating and Cooling …

TUC = I0 +

τ

n=1

C (1 + i)n

461

(6.2.32)

where: I 0 is the initial investment cost in the operation, beginning the date of the systems inception; C is annual operation and maintenance cost of the system; i is the discount (inflation) rate; τ is the number of years for which is made an update (20 years). The following equality can be demonstrated rather easily: τ

n=1

1 (1 + i)τ − 1 n = i(1 + i)τ (1 + i)

(6.2.33)

and is defined update rate ur =

1 (1 + i)τ − 1 = i(1 + i)τ CRF

(6.2.34)

where CRF is the capital recovery factor. Taking into account Eqs. (6.2.33) and (6.2.34), Eq. (6.2.32) yields the following equation: TUC = I0 + u r C

(6.2.35)

Net present cost (NPC) of the project over its entire lifespan of operation includes expenses such as components, component replacements, operation and maintenance costs, and initial investment costs. The NPC can be computed using equation: NPC =

TAC CRF

(6.2.36)

where TAC is the total annual cost (sum of all annual costs of each system component).

6.2.5.3

Calculation of CO2 Emissions

HPs driven by electricity from, for instance, hydropower or renewable energy reduce emissions of gases that harm the environment, such as carbon dioxide (CO2 ), sulphur dioxide (SO2 ) and nitrogen oxides (NOx ), more significantly than if the electricity is generated by coal, oil or natural gas power plants.

462

6 Heat Pumps for Sustainable Heating and Cooling

Due to the diversity in each country with respect to heating practices, direct energy use by HPs, and primary energy sources for electricity, country-specific calculations are provided. The annual heating energy provided by HPs is defined as E t . The annual primary energy consumption from HP electricity use is then: E el =

Et SPF

(6.2.37)

The CO2 emissions CCO2 of the HP during its operation can be evaluated with the following equation: CCO2 = gel E el

(6.2.38)

where gel is the specific CO2 emission factor for electricity. The average European CO2 emission factor for electricity production is 0.486 kg CO2 /kWh and for Romania is 0.547 kg CO2 /kWh [22]. Because HP electricity consumption is considered the most important source for CO2 emission, other potential contributors (e.g., HP life cycle, HP refrigerant or borehole construction) are neglected.

6.2.6 Energy-Economic Analysis of Different Systems 6.2.6.1

Assessment of Energy Consumption for an Air-to-Water HP

Annual energy consumption of heating/cooling system for a building contributes to minimizing the life cost of the building. This consumption is obtained by time integration of instantaneous consumption during the cold season, warm season respectively. Instantaneous consumption depends on the efficiency of the HVAC system. For computation of the annual energy consumption of a heating/cooling system can be used the degree-day method or bin method [23]. • Degree-day method. The degree-day method and its generalisations can provide a simple estimate of annual loads, which can be accurate if the indoor temperature and internal gains are relatively constant and if the heating or cooling systems operate for a complete season. The balance point temperature t ech of a building is defined as that value of the outdoor temperature t e at which, for the specified value of the indoor temperature t i , the total heat loss is equal to the heat gain Qap from sun, occupants, lights and so forth: Q ap = U (ti − tech )

(6.2.39)

6.2 Energy-Economic Analysis of Building Heating and Cooling …

463

where U is the heat transfer coefficient of the building, in W/K. Heating is needed only when t e drops below t ech . The rate of energy consumption of the heating system is: Q inc =

U [tech − te (τ)]te t ech ). Equation (6.2.50) is evaluated for each bin, and the total energy requirement E bin , in kWh, is the sum of the Qbin over all of the bins. This method is defined in European Standard EN 15316-4.2 [25]. Knowing the capacity Qhp and the drive power Pe of the HP for each bin temperature interval, the following can be determined: • Heat demand (heat loss) of the building Qinc , in kW: Q inc =

U (tech − te ) 1000

(6.2.51)

• HP efficiency, COPhp : COPhp =

Q hp Pe

(6.2.52)

• HP operation coefficient, f :   Q inc f = min 1, Q hp

(6.2.53)

• Thermal energy provided by the HP, E t , in kWh: E t = f Q hp Nbin

(6.2.54)

• Electrical energy to drive the HP, E el , in kWh: E el = f Pe Nbin

(6.2.55)

466

6 Heat Pumps for Sustainable Heating and Cooling

The energy requirement E bin , in kWh, is obtained by summing the values Qbin given by Eq. (6.2.50). • The energy delivered by the auxiliary source, E aux , in kWh: E aux = E bin − E t

(6.2.56)

• The total energy consumed by the HP and auxiliary source, E, in kWh: E = E el + E aux

(6.2.57)

The computer program METBIN has been elaborated based on this computational model in EXCEL for PC-compatible micro-systems. • Numerical application. For a building heated by an HP, the following is known: the heat transfer coefficient U = 850 W/K and the balance temperature t ech = 17.8 °C. Using these, the energy consumption during the heating period is determined using the METBIN program. The results are summarised in Table 6.2. Figure 6.6 shows the variation of the heat loss and the thermal power of the HP depending on the outdoor temperature. 6.2.6.2

Economic Analysis of Heating for a Building Using a Water-to-Water HP and Other Primary Energy Sources

A study is performed here on the heating of a residential building in a rural area with a water-to-water heat pump, using groundwater as a heat source compared to other sources of primary energy. • Calculation assumptions. A building with a useful area of 240 m2 (basement-floor, ground floor, floor and bridge) from 1993 is heated with radiators from a thermal station (TS) with gas-oil. Indoor air temperatures were considered in accordance with the wishes of the client: +20 °C for the stairway and annex spaces; +22 °C for day rooms and bedrooms; and 24 °C for baths. The construction materials that distinguish the heated spaces are 50 cm brick for the exterior walls, 10 cm concrete and a 15 cm layer of expanded polystyrene insulation for the bridging, and double glazing in oak. The exterior walls will be isolated from the outside with expanded polystyrene (10 cm). The calculation of the heat demand Qinc was performed for the existing building envelope (exterior walls without insulation) and after thermal rehabilitation (exterior walls insulated with 10 cm expanded polystyrene) for different outdoor air temperatures (Table 6.3) to choose an efficient heat source. For the DHW production, it is necessary to consider a heat demand Qdhw of 3 kW (three persons, three bathrooms and a kitchen).

34.8

37.8

40.8

−17

−20

−23

Total

31.8

−5

−14

22.8

−2

25.8

19.8

1

28.8

16.8

4

−11

13.8

7

−8

7.8

10.8

10

5

15

34

77

162

312

497

644

691

650

601

647

34.68

32.13

29.58

27.03

24.48

21.93

19.38

16.83

14.28

11.73

9.18

6.63

4.08

0

0

0

10.2

11.6

12.1

13.3

14.6

16.1

18.2

21.6

24.1

26.8

0

0

0

4.37

4.66

4.76

5.01

5.23

5.47

5.80

6.31

6.58

6.87

7.11

0

0

0

233

2.49

2.59

2.65

2.79

2.95

3.14

3.42

3.66

3.90

4.06

0

0

0

1.00

1.00

1.00

1.00

1.00

0.89

0.64

0.43

0.28

0.15

0.05

0

0

0

336.5

754.6

1485.1

2490.0

3368.1

3349.4

2429.8

1611.7

1171.2

801.1

340.3

54259.47 18138.2

0

0

0

785.45

1879.25

3775.25

6610.15

9402.45

9867.48

7624.50

5517.18

4289.61

3125.28

66827.9

173.4

482.0

1005.7

2081.3

3965.8

6842.2

9631.9

10838.5

9867.5

7624.5

5517.2

4289.6

3125.3

1383.1

12568.4

173.4

482.0

1005.7

1295.9

2086.6

3067.0

3021.8

1430.1

0

0

0

0

0

0

30706.0

173.4

482.0

1005.7

1632.4

2841.5

4552.1

5511.7

4804.2

3349.4

2429.8

1611.7

1171.2

801.1

340.3

1383.12

766

28.9

4.8

13

1.53

1.8

16

904

E t (kWh) E el (kWh) E bin (kWh) E aux (kWh) E (kWh)

Temp. (bin) t ech -t e (°C) Hours N bin Qinc (kW) Qhp (kW) Pe (kW) COPhp Coef. f t e (°C) (h)

Table 6.2 Results provided of computer program METBIN

6.2 Energy-Economic Analysis of Building Heating and Cooling … 467

468

6 Heat Pumps for Sustainable Heating and Cooling

Fig. 6.6 Variation of the heat requirement and HP thermal power with outdoor temperature

Table 6.3 Heat demand for heating

t e (°C)

Qinc (kW) Actual envelope

Rehabilitated envelope

+5

18.9

13.6

0

20.2

15.5

−5

21.6

17.4

−10

23.0

18.3

−15

24.3

19.1

−20

25.6

21.1

• Description of proposed solution. The building heating is realised as follows: – heating of the living spaces (living rooms, bedrooms and stairway) with floor convector-radiator; – bathroom heating with radiators (towel-port); – hot water temperature to radiators and convector-radiator: 50/40 °C; – the supply of radiators and convector-radiators use distributor/collector systems; – the distribution network for the radiators and convector-radiators, pexal made, is placed at the ceiling, basement-floor, ground floor and floor. The heat demand of the building will be provided by a Thermia Eko 180 HP and a boiler with a capacity of 300 L. A mechanical compression HP (scroll compressor) operates with the ecological refrigerant R404A. The heat source is the groundwater aquifers with a minimum temperature of 10 °C. For the operating conditions with t 0 = 8 °C and t c = 50 °C, the thermal power of the HP is Qhp = 21 kW. This capacity covers part of the building heat demand for outdoor temperatures higher than −5 °C for the existing envelope and almost the entire demand (even for an outdoor temperature of −20 °C) for the thermally rehabilitated envelope (exterior walls with additional insulation). To meet the rest of the heat demand (i.e., heating and DHW production), the HP is equipped with three electrical resistances of 3 kW, which operate automatically, depending on the

6.2 Energy-Economic Analysis of Building Heating and Cooling …

469

set indoor temperature. For flow rate control in the hot water distribution network from the heating circuit, the following measures are provided: • a first adjustment of the flow rates that supply the terminal units (radiators or convector-radiators), achieved by progressive reduction of the pipe diameters; • a base adjustment, achieved through the flow control valves for each column; • a final adjustment at the terminal units, developed by the thermostat valves set at the comfort temperature in each room. • Economic analysis. Comparing the solution described for building heating with other possible variants of primary energy sources (liquefied petroleum gas (LPG), gas-oil and natural gas) shows a superior investment for the HP, but also shows an economy in operation costs, which enable the recovery of additional investment. Tables 6.4 and 6.5 summarise the necessary investments and operation costs over a period of 10 years for the considered variants. The recovery time RT of the additional investment for an HP, compared to thermal boilers using Eq. (6.2.31), resulted in the following: • compared to an LPG boiler: RT =

IHP − ITS,LPG 15100 − 6500 = 2.74 years = CTS,LPG − CHP 5033.7 − 1903.2

(6.2.58)

• compared to a gas-oil boiler: RT =

IHP − ITS,gas−oil 15100 − 6500 = 1.88 years = CTS,gas−oil − CHP 6468.7 − 1903.2

(6.2.59)

• compared to a natural gas boiler: RT =

IHP − ITS,natural gas 15100 − 7000 = 8.15 years = CTS,natural gas − CHP 2897.0 − 1903.2

(6.2.60)

Table 6.4 Investment costs I, in e, for HP and different thermal boilers Solution components

HP

Thermal boiler with fuel LPG

Gas-oil

Natural gas

Heat pump/boiler

7700

3000

3000

3000

Groundwater capture

4900

–

–

–

Heat exchanger

1300

–

–

–

Circulation pumps

1200

–

–

–

Fuel tank

–

3500

3500

–

Gas connection

–

–

–

4000

Total

15100

6500

6500

7000

470

6 Heat Pumps for Sustainable Heating and Cooling

Table 6.5 Operation costs C, in e, for HP and different thermal boilers Solution characteristics

HP

Thermal boiler with fuel LPG

Gas-oil Natural gas

Thermal power (kW)

21 + 9 24

24

24

Fuel calorific power (kW/l)

–

6.30

10.0

9.44

2.33

0.90

0.85

0.90

(kW)) 9.00

2.84

TS Efficiency/HP coefficient of performance Hour consumption (fuel (l/h);

(m3 /h)/electricity

4.23

3.02

Annual operation (h/year)

1870a

1700

1700

1700

Fuel price (e/l); (e/m3 )/electricity price (e/kWh)

0.087

0.500

0.900

0.300

Annual consumption (l/year; m3 /year; kWh/year)

16,830 7191

5134

Annual energy cost (e/year)

1464

3595.5 4620.5

1448.5

Estimated increase of energy price in 10 years

1.30

1.40

2.00

Operation costs (10 years), C (e)

1903.2 5033.7 6468.7

1.40

4828

2897.0

a Annual

operation of electrical resistances is considered 10% of the normal operation period, so at the 1700 h/year, 170 h/year is added

Compared to any of the boiler heating solutions, heating with a water-to-water HP has a recovery period of investment RT that is smaller than the normal recovery period RTn of 8–10 years.

6.2.7 Examples of HP Utilisation HPs are used for DHW and building heating (e.g., houses, office buildings, administrative buildings, hotels, hospitals, etc.), in industrial processes and agriculture. HPs can be used in both local and centralised heat supply systems. The connection of HP to the heating systems shows some features determined by their very different structure and heat consumption characteristics. Figure 6.7 shows the schematic of an air-to-water HP used for heating and DHW production for a building with a floor surface of 170 m2 and a heat demand of 16 kW. The heating is performed with fan coil units, and the water supply and return temperatures are 50 °C and 40 °C, respectively. The installation is provided with heat storage and HP (I), which operates for heating until the outdoor temperature is −3 °C, taking heat from the outdoor air. Below this outdoor temperature, HP (II) begins to operate and takes the heat from the heat storage, which contains water heated by liquid refrigerant subcooling from the HP circuit. The evaporation temperature is −10°C, and the condensation temperature is + 55°C. The working fluid used is R22, and the absorbed electric powers by the two compressors are PI = 3.75 kW and PII = 3.0 kW.

6.2 Energy-Economic Analysis of Building Heating and Cooling …

471

Fig. 6.7 Air-to-water HP for a house heating and DHW production. 1—main compressor; 2—condenser; 3—subcooler; 4—fan cooling coil; 5—fast heat storage; 6—slow heat storage; 7—second compressor; 8—evaporator; 9—condenser; 10—defrosting cooling coil water heater; 11—DHW heat exchanger; 12—fan coil units; 13—shower and bathtub

One of the first uses of water-to-water HPs was in Switzerland for the heating of the City Hall building in Zurich [21]. The functional scheme of the system is shown in Fig. 6.8. The working fluid of the HP is ammonia (NH3 ), and the heat source is river water with a temperature in winter of approximately 4 °C. The heat taken up in the evaporator E is yielded in the condenser C to the water radiator circuit R to a temperature of approximately 50 °C. For an outdoor air temperature of −20 °C and a room temperature of +18 °C, the heat demand is 175 kW. The HP only covers the basic heat load of 80 kW for the offices and accommodation heating. The remaining heat demand is covered by an electric heater with a power of 65 kW. The plant is designed to operate with the HP

Fig. 6.8 Water-to-water HP for administrative building

472

6 Heat Pumps for Sustainable Heating and Cooling

for approximately 1500 h/year. During the summer, the system can be used to cool the air from the ventilation circuit of meeting rooms. In the local heat supply, building systems commonly use the geothermal water source HPs for low-water temperatures (those below 40 °C). Water-to-water HPs with the scheme shown in Fig. 6.9 are used to heat multifamily buildings and to produce DHW. They are used with radiant floor heating systems (4). The production of the DHW is made with an immersed coil (5) in the storage tank (7), which is additionally equipped with an electrical resistance heater (8) for periods of maximum hot water consumption. In the summer season when heating is unnecessary, the HP operates exclusively for DHW production. To maintain the productivity parameters of the geothermal source and to maintain ecological balance, the geothermal water must be returned, after cooling in the HP evaporator, to an injection well. Figure 6.10 presents the scheme of an HP system used for heating an individual home. The heat source is the ground, from which heat is absorbed by vertical loops that circulate an antifreeze solution (water-glycol). The antifreeze solution flowing through the HP evaporator is sent to vertical ground heat exchangers (loops). The

Fig. 6.9 Water-to-water HP for house and DHW heating using geothermal water heat source. 1—geothermal production well; 2—injection well; 3—geothermal water circulation pump; 4— radiant floor heating; 5—DHW coil; 6—hot water thermostat; 7—hot water storage; 8—additional electrical resistance

6.2 Energy-Economic Analysis of Building Heating and Cooling …

473

Fig. 6.10 Ground-coupled heat pump for a house heating. 1—ground loops; 2—circulation pump; 3—storage tank; 4—hot water pump; 5—heating system pump; 6—three-way valve

installation includes a storage tank of approximately 10 m3 , where heat may be stored for the periods in which the heating system is not running. A system of two three-way valves allows for heating directly from the HP condenser or from the storage tank or both simultaneously. In all of the HP systems, those with applications in industry are more numerous, characterised by higher power corresponding to the waste energy discharged by industrial technological systems. Figure 6.11 illustrates the functional scheme of a water-to-water HP, used in a factory that produces copper pipes. The water resulting from cooling the extrusion mould has a temperature of ~43°C. Instead of cooling the water in a cooling tower for reuse, this water is employed as a Fig. 6.11 Water-to-water HP used in a copper pipe factory

474

6 Heat Pumps for Sustainable Heating and Cooling

heat source for the evaporator E of an HP. The condenser C produces hot water with a temperature of approximately 88°C, which is accumulated in a buffer tank (BT) of approximately 45,000 L. This hot water is used to heat the soap solution used for the copper pipe lubrication during the manufacturing process. The thermal power of this HP is 1600 kW, the power absorbed by the compressor is 460 kW, and the COP is 3.4. In the case of vapour compression-based refrigeration systems, the refrigerant is situated at the end of compression, in a superheated vapour state, with a temperature higher than the ambient air. One possibility to value the condensation heat and sensitive heat of superheated vapours represents their use by HP systems. Figure 6.12 shows a coupling between an HP and a refrigeration system for a milk factory. The system consists of two cascade refrigeration circuits. The cold water production stage includes the compressor K1 and the evaporator E1 , which operates with R22. The condensation of R22 vapour occurs in the pipes of the intermediate heat exchanger C1 –E2 , which also has part of the evaporator role in the hot water production stage. The second stage operates with R114 and also has a compressor K2 and a condenser C2 . The condensate subcooler SC recovers the subcooling heat to produce DHW at 60 °C. For an annual system operation of 6000 h/year, the fuel savings achieved is 36 toe. Currently, a large number of installations are based on the use of solar energy in combination with HP. For the most efficient use of solar energy throughout the year, the energy is stored in summer and is consumed during the winter. The heat from the sun is stored in water contained in thermal-insulated storage tanks. The heating and hot water system in a solar house (Fig. 6.13) from Essen, Germany uses solar energy as a heat source through the collector plane (5). The hot water from the solar collector circuit heats boiler (1) used for DHW production and boiler (2) used to heat the water for the radiators. When this system is not enough, an HP starts to operate using heated water from the solar collector, producing the hot water in condenser C for the heaters. The installation has the possibility to heat water with electric energy which is not possible with solar energy. Fig. 6.12 Water-to-water HP coupled with a refrigeration system for technological heating/cooling

6.2 Energy-Economic Analysis of Building Heating and Cooling …

475

Fig. 6.13 Solar-assisted water-to-water heat pump for heating and DHW. 1—DHWstorage; 2— heating water storage; 3—additional electric heater; 4—DHW electric heater; 5—flat solar collector

Figure 6.14 presents a radiant floor heating system with a heat pump and a vacuum tube solar collector, operating with water temperatures of 20–30 °C. A groundwater heat pump with horizontal collectors or vertical loops and solar collectors transfers its heat to a stratified hot water tank. Reheating hot water is performed both by an additional heat pump and directly by an electric heater. For a family house with a heat demand of approximately 8000 kWh/year, the solar collector can cover approximately 2000 kWh/year. If taking into account the circulation pumps’ power, the electricity consumption of the HP reaches 1500 kW/year, and the COP of the HP can reach a value of 4.

Fig. 6.14 Radiant floor heating system with HP and solar collector

476

6 Heat Pumps for Sustainable Heating and Cooling

Initially, installation can be realised without the solar collector, leaving the possibility of installing one in the future. Instead, an HP for hot water reheating can be mounted with an electric heater.

6.2.8 Conclusions Correct adaptation of the heat source and the heating system for the operating mode of HPs leads to safe and economical operation of the heating system. Heating systems with HPs consume minimum energy during operation and are certainly a solution for energy optimisation of buildings. The HP mode requires some additional investments. If the capacity of the HP is selected as larger than the condensing capacity in the pure refrigeration mode, the additional capacity costs have to be covered by the savings in energy costs. An HP provides the necessary technical conditions for efficient use of solar heat for heating and DHW production. A combined cooling and heating system with an HP is always more effective than a traditional system if its requirements are taken into the consideration in the design process. For renovation, the applicability is more limited and is always case dependent. The main barrier for the use of HPs for retrofitting is the high-distribution temperature of conventional heating systems in existing residential buildings. Traditional design temperatures of up to 70–90 °C are too high for the present HP generation, with a maximum economically acceptable heat distribution temperature of approximately 55 °C. In addition to the application of existing HPs in already improved standard buildings with reduced heat demand, the development and market introduction of new high-temperature heat pumps is a major task for the replacement of conventional heating systems with HPs in existing buildings.

6.3 General Review of Ground Source Heat Pump Systems 6.3.1 Preliminary Considerations Economical strategy of a sustainable development imposes certainly to promote efficiency and a rational energy use in buildings as the major energy consumer in Romania and the other member states of the European Union (EU). At present heat use is responsible for almost 80% of the energy demand in houses and utility buildings for space heating and hot water generation, whereas the energy demand for cooling is growing year after year. On 17 December 2008, the European Parliament adopted the Renewable Energy Directive. It establishes a common framework for the promotion of energy from

6.3 General Review of Ground Source …

477

renewable sources. This directive opens up a major opportunity for further use of heat pumps (HPs) for heating and cooling of new and existing buildings. Ground source heat pump (GSHP) systems use the ground as a heat source/sink to provide space heating and cooling as well as DHW. The GSHP technology can offer higher energy efficiency for air-conditioning (A/C) compared to conventional A/C systems because the underground environment provides higher temperature for heating and lower temperature for cooling and experiences less temperature fluctuation than ambient air temperature change. The first known record of the concept of using the ground as heat source for an HP was found in a Swiss patent issued in 1912 [26]. The first surge of interest in the GSHP technology began in both North America and Europe after World War Two and lasted until the early 1950s when gas and oil became widely used as heating fuels. At that time, the basic analytical theory for the heat conduction of the GSHP system was proposed by Ingersoll and Plass [27], which served as a basis for development of some of the later design programs. The next period of intense activity on the GSHPs started in North America and Europe in 1970s after the first oil crisis, with an emphasis on experimental investigation. In the ensuing two decades, considerable efforts were made to establish the installation standard and develop design methods for vertical borehole system [28–30]. This section mainly presents a detailed review of GSHP technology, concentrating on the ground-coupled heat pump (GCHP) systems [18]. Initially, the operation principle of an HP and the types of HPs are discussed. Then, a detailed description on GSHPs and its development are performed, the most typical simulation models of the vertical ground heat exchangers currently available are summarised, and a new groundwater HP (GWHP) using a heat exchanger with special construction, tested in laboratory and the possibility to obtain the better energy efficiency with combined heating and cooling by GCHP are well presented. Finally, the energy, economic and environmental performances of a closed-loop GCHP system and the advanced engineering applications of hybrid GCHP systems are also briefly reviewed [17].

6.3.2 Operation Principle of an HP The HP is a thermal installation which is based on a reverse Carnot thermodynamic cycle (consumes drive energy and produces a thermal effect). Any HP moves (pumps) the heat E S from a source with low temperature t s to a source with high temperature t u consuming the drive energy E D . The operation principle of the HP is shown in Fig. 6.15. Energy transfer in the HP is based on the phase change of refrigerant under the constant thermodynamic cycle. The heat is extracted from the source and transferred to the building energy systems. Reverse cycle HPs have a cooling ability as well, by changing the flow direction of the refrigerant, resulting in heat extraction from the building and rejection to the outside source.

478

6 Heat Pumps for Sustainable Heating and Cooling

Fig. 6.15 Principle diagram of an HP

Four main components incorporated within the HP are: the compressor, evaporator, condenser and an expansion valve. The main auxiliary components are fans, piping, controls and housing. HP for heating purposes operates as per the following steps: 1. In the evaporator, the liquid refrigerant extracts heat from a heat source and evaporates. After the evaporator refrigerant is in the state of low-pressure vapour, then the temperature increases slightly. 2. The refrigerant in vapour state flows into the electrical compressor; here the pressure is increased, resulting in the increase of the temperature. 3. High-temperature vapour flows to the condenser. The heat transfer to the building’s heating system causes the refrigerant to cool down and condensate to high pressure and temperature liquid. 4. Hot liquid runs through an expansion valve, where its pressure is reduced, in turn lowering the temperature. The refrigerant returns to the evaporator and the cycle is repeated. The superheaters are included in some HPs performing as an auxiliary heat exchanger supplying heat to a DHW tank (up to 65–70 °C). The superheater is placed at the compressor’s exit; it transfers thermal energy of compressed vapour to water that circulates through a hot water tank, therefore reducing or eliminating the energy required for DHW heating.

6.3.3 Description of HP Types HPs are classified by (1) the heat source and sink; (2) the heating and cooling distribution fluids; and (3) the thermodynamic cycle. The following classifications can be made according to:

6.3 General Review of Ground Source …

479

• function: heating, cooling, DHW heating, ventilation, drying, heat recovery, etc. • heat source: ground, groundwater, water, air, exhaust air, etc. • heat source (intermediate fluid)-heat distribution: air-to-air, air-to-water, waterto-water, antifreeze (brine)-to-water, direct expansion-to-water, etc. The most common type of HP classification is according to the heat source. In general, there are three principal types of HPs based on heat source: an air-source HP (ASHP), ground source HP (GSHP) and the water source HP (WSHP), and they are described in the following sections. The GSHPs are those with electro-compressor. The process of elevating lowtemperature heat to over 38 °C and transferring it indoors involves a cycle of evaporation, compression, condensation and expansion (Fig. 6.15). A non-CFC refrigerant is used as the heat transfer medium, which circulates within the HP.

6.3.3.1

Air-to-Air Heat Pumps

Air-to-air HPs are the most common and are particularly suitable for factory-built unitary HPs. These HPs are also found in controlled dwelling ventilation applications to enable an increase in the heat recovery from the exhaust air, and can even allow for cooling of selected rooms. For these applications, various units are used. Air-to-air HPs have a full-hermetic compressor, finned heat exchangers for the evaporator and condenser, and an expansion valve as well as the necessary safety mechanisms. As the outdoor air temperature decreases the heat demand increases and the HP capacity substantially decreases due to the efficiency reduction.

6.3.3.2

Water-to-Air Heat Pumps

Water-to-air HPs rely on water as the heat source and sink, and use air to transmit heat to or from the conditioned space. They include: • groundwater heat pumps (GWHPs), which use groundwater from wells as a heat source and/or sink; • surface water heat pumps (SWHPs), which use surface water from a lake, pond or stream as a heat source or sink; • solar-assisted HPs, which rely on low-temperature solar energy as the heat source. 6.3.3.3

Air-to-Water Heat Pumps

Air-to-water HPs [4] use outdoor air as their heat source and are mostly operated in bivalent heating systems, as well as for cooling, heat recovery and DHW production. The indoor unit contains the substantial components and is fitted indoors, protected from weather and freezing temperatures. The outdoor unit is connected to the indoor

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6 Heat Pumps for Sustainable Heating and Cooling

unit via refrigeration lines. Through the elimination of air ducts, extremely quiet, energy-efficient fans are made possible. Generally a fully hermetic compressor (piston or scroll) with built-in, internal overload protection is used in these HPs. Stainless steel flat-plate heat exchangers are used for the condenser. Expansion valve, weather-dependent defrost mechanism— preferably hot gas. Copper-tube aluminium finned evaporator. For quiet operation, an axial fan with low speed should be used. Electrical components and the controller are either integrated or externally mounted, depending on the manufacturer and model. Control of the heating system is commonly integrated. The heat demand of a building depends on the climate zone in which it is located. In temperate climate conditions, such as in Romania, the heat demand Qinc evolves from the minimum values in the provisional seasons (spring and autumn) to the maximum value in the cold season (Fig. 6.16). The annual number of hours with the minimum outdoor air temperature represents approximately 10–15% of the total time for heating, which is why the selection of an HP to cover the integral peak load is not recommended. To reduce costs, the HP is selected to cover only 70–75% of the maximum heat demand of the building. The rest of the heat demand is produced by an auxiliary traditional source (electric heater or oil/gas boiler). In this case, the HP operates in bivalent mode (Fig. 6.16), distinguishing three situations: (a) if the outdoor air temperature t e is lower than the limit heating temperature t lim , the HP provides the full heat demand up to the balance point temperature t ech ; (b) if the outdoor air temperature t e is lower than t ech , the HP provides part of the heat demand and the rest is provided by the peak traditional source; (c) when the outdoor air temperature t e reaches the stop-heating temperature t o , the HP is switched off and the traditional source meets the full heat demand. Usually, the balance point corresponds to an outdoor temperature of 0 to +5 °C. For temperate climate zones, the HP covers approximately 2/3 of the annual heat demand. Fig. 6.16 Heat demand provide in function of source temperature. Po —stop heating point; Pech —balance point; Plim —limit heating point

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ASHP (air-to-air or air-to-water) utilising ambient heat is less efficient compared to other types of HPs, when the outdoor air temperature is lower than −10°C. The current level of technical development of ASHP units still suggests these HPs are to be used as a supportive heating source in cold climates. In most cases, ASHP-based systems must be equipped with an additional electric heater or other source of energy to be utilised during the coldest periods of winter.

6.3.3.4

Water-to-Water Heat Pumps

Water-to-water HPs operate as GWHPs or SWHPs. Water-to-water HPs use water (e.g., aquifer-fed boreholes, lakes or water bodies) as the heat source and sink for heating and cooling. Antifreeze-to-water HPs are used in closed-loop ground-coupled installations. Water-to-water and antifreeze-to-water HPs are used for monovalent heating operation, as well as cooling, heat recovery and DHW production. Heating/cooling changeover can be performed in the refrigerant circuit, but it is often more convenient to perform the switch in the water circuits. Several water-towater HPs can be grouped together to create a central cooling and heating plant to serve several air handling units. This application has advantages of better control, centralised maintenance, redundancy and flexibility.

6.3.3.5

Ground-Coupled Heat Pumps

GCHPs use the ground as a heat source and sink. An HP may have a refrigerant-towater heat exchanger or may be direct expansion (DX). In systems with refrigerantto-water heat exchangers, a water or antifreeze solution is pumped through horizontal, vertical or coiled pipes embedded in the ground. DX ground-coupled HPs use refrigerant in DX, flooded or recirculation evaporator circuits for the ground pipe coils. A loop of suitable pipe containing the refrigerant and lubricant is put in direct contact with the ground or water body. The compressor operation circulates the refrigerant directly around this loop, thus eliminating the heat transfer losses associated with the intermediate water-DX heat exchanger found in conventional water source HPs [4]. There is also no need for a source-side circulation pump as the compressor fulfils this role. However, care must be taken to ensure that the DX loops are totally sealed and corrosion-resistant and that the lubricant is adequately circulated to meet the needs of the compressor. A hybrid GCHP is a variation that uses a cooling tower or air-cooled condenser to reduce the total annual heat rejection to the ground coupling. The main advantage of WSHP in comparison to GSHP is lower installation costs. Also, it has better thermodynamic performance than closed-loop systems because of wells that supply groundwater at ground temperature and the heat exchanger delivers heat transfer liquid at temperatures other than ground temperature. Also, the system can be combined with a potable water supply well, in turn decreasing operating costs if water was already pumped for other purposes, such as irrigation.

482

6.3.3.6

6 Heat Pumps for Sustainable Heating and Cooling

Hybrid Air-to-Water Systems

A hybrid air-to-water system integrates an air-to-water HP unit with another nonrenewable heat source, such as a condensation gas boiler, to create a highly energyefficient heating and DHW system. This system can produce water flow temperatures from 25 up to 80 °C, making it suitable for any type of heat emitter, including radiant floor heating and radiators. The intelligent hybrid HP measures the outdoor temperature, automatically adjusting the flow temperature to the emitters and calculating the efficiency of the HP. The system continuously evaluates whether the efficiency of the HP is higher than that of the condensing gas boiler. Based upon this evaluation, the energy source is selected, ensuring that the most efficient heat source is being used at all times. There are three operating conditions for this system [31]: • HP only: for approximately 60% of the year, when the outdoor temperature is mild, the heat pump will supply energy for space heating. The primary energy-based efficiency in this mode is approximately 1.5. • hybrid operation: for approximately 20% of the year, when outdoor temperatures are between −2 and 3 °C, the HP and the condensing gas boiler work together to provide energy for space heating. The system efficiency is approximately 1.0 in this mode. • boiler only: when outdoor temperatures are below −2°C, the condensation gas boiler provides the energy for space heating. Throughout the year, the overall weighted primary energy efficiency is between 1.2 and 1.5, which is 30–60% higher compared with the best gas condensation boiler. The hybrid HP system consists of three main components [31]: 1. The outdoor unit transmits the renewable energy extracted from the air to the indoor unit (hydro-box). The compact and whisper-quiet outdoor unit contains the inverter-driven compressor, which has a modulation ratio from approximately 20–100%. In partial load conditions, the outdoor heat exchanger is over-sized, which increases the efficiency by up to 30%. 2. The hydro-box is mounted on the wall behind the condensing boiler. It contains the water-side elements of the system, such as the expansion tank and pump, as well as the controls for the system and the heat exchanger, which converts the renewable energy extracted from the air into hot water. 3. The condensing gas boiler is installed in front of the hydro-box. The combined dimensions of the boiler and hydro-box are approximately the same as a conventional wall-hung boiler. The hybrid HP has been field-tested in various climates and house types (i.e., size, age and energy rating) with a range of different heat emitters. The seasonal performance factor (SPF) measured during the winter of 2011–2012 varied between 1.25 and 1.6.

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6.3.4 Ground Source Heat Pump Systems Recently, the GSHP system has attracted more and more attention due to its superiority of high-energy efficiency and environmental friendliness [12, 18, 32, 33]. Renewable forms of energy such as solar, wind, biomass, hydro and earth energy produce low or no GHG emissions. The temperature of the ground is fairly constant below the frost line. The ground is warmer in the middle of winter and cooler in the middle of summer than the outdoor air. Thus, the ground is an efficient heat source. A GSHP system includes three principle components: (1) a ground connection subsystem, (2) HP subsystem and (3) heat distribution subsystem. The GSHPs comprise a wide variety of systems that may use groundwater, ground or surface water as heat sources or sinks. These systems have been basically grouped into three categories by ASHRAE [34]: (1) groundwater heat pump (GWHP) systems, (2) surface water heat pump (SWHP) systems and (3) ground-coupled heat pump (GCHP) systems. The schematics of these different systems are shown in Fig. 6.17. Many parallel terms exist: geothermal heat pump, earth energy system and ground source system. The GWHP system, which utilises groundwater as heat source or sink, has some marked advantages including a low-initial cost and minimal requirement for ground surface area over other GSHP systems [35]. However, a number of factors seriously restrict the wide application of the GWHP systems, such as the limited availability of groundwater and the high-maintenance cost due to fouling corrosion in pipes and equipment. In an SWHP system, heat rejection/extraction is accomplished by circulating working fluid through high-density polyethylene (HDPE) pipes positioned at an adequate depth within a lake, pond, reservoir or the suitable open channels. The major disadvantage of the system is that the surface water temperature is more affected by weather condition, especially winter. Among the various GSHP systems, the vertical GCHP system has attracted the greatest interest in research field and practical engineering. Several literature reviews on the GCHP technology have been reported [36, 37].

Fig. 6.17 Schematic of different ground source heat pumps

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6 Heat Pumps for Sustainable Heating and Cooling

In a GCHP system, heat is extracted from or rejected to the ground via a closed loop, i.e., ground heat exchanger (GHE), through which pure water or antifreeze fluid circulates. The GHEs commonly used in the GCHP systems typically consist of HDPE pipes which are installed in either vertical boreholes (called vertical GHE) or horizontal trenches (horizontal GHE). In direct expansion systems, the heat stored in the ground is absorbed directly by the working fluid (refrigerant). These results in an increased COP. Horizontal GHEs are mainly used with this system. The GSHPs work best with heating systems, which are optimised to operate at lower water temperatures than radiator and radiant panel systems (floor, wall and cei-ling). GSHPs have the potential to reduce cooling energy by 30–50% and reduce heating energy by 20–40% [38]. The GSHPs tend to be more cost-effective than conventional systems in the following applications: • in new construction where the technology is relatively easy to incorporate, or to replace an existing system at the end of its useful life; • in climates characterised by high-daily temperature swings, or where winters are cold or summers hot, and where electricity cost is higher than average; • in areas where natural gas is unavailable or where the cost is higher than electricity. 6.3.4.1

Description of SWHP Systems

Surface water bodies can be very good heat source and sinks, if properly used. The maximum density of water occurs at 4.0 °C, not at the freezing point of 0 °C. This phenomenon, in combination with the normal modes of heat transfer to and from takes, produces temperature profile advantageous to efficient HP operation. In some cases, lakes can be the very best water supply for cooling. Various water circulation systems are possible and several of the more common are presented. In a closed-loop system, a water-to-air HP is linked to a submerged coil. Heat is exchanged to or from the lake by the refrigerant circulating inside the coil. The HP transfers heat to or from the air in the building. In an open-loop system, water is pumped from the lake through a heat exchanger and returned to the lake some distance from the point at which it was removed. The pump can be located either slightly above or submerged below the lake water level. For HP operation in the heating mode, this type is restricted to warmer climates. Entering lake water temperature must remain above 5.5 °C to prevent freezing. Thermal stratification of water often keeps large quantities of cold water undisturbed near the bottom of deep lakes. This water is cold enough to adequately cool buildings by simply being circulated through heat exchangers. A heat pump is not needed for cooling, and energy use is substantially reduced. Closed-loop coils may also be used in colder lakes. Heating can be provided by a separate source or with heat pumps in the heating mode. Pre-cooling or supplemental total cooling are also permit-ted when water temperature is between 10 and 15 °C. Advantages of closed-loop SWHPs are (1) relatively low cost because of reduced excavation costs, (2) low-pumping energy requirements and (3) low-operating cost.

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Disadvantages are (1) the possibility of coil damage in public lakes and (2) wide variation in water temperature with outdoor conditions.

6.3.4.2

Description of GWHP Systems

A GWHP system removes ground-water from a well and delivers it to an HP (or an intermediate heat exchanger) to serve as a heat source or sink [34]. Both unitary and central plant designs are used. In the unitary type, a large number of small waterto-air HPs is distributed throughout the building. The central plant uses one or a small number of large capacity chillers supplying hot and chilled water to a two- or four-pipe distribution system. The unitary approach is more common and tends to be more energy efficient. Direct systems (in which groundwater is pumped directly to the HP without an intermediate heat exchanger) are not recommended except on the very smallest installations. Although some installations of this system have been successful, others have had serious difficulty even with groundwater of apparently benign chemistry. The specific components for handling groundwater are similar. The primary items include (1) wells (supply and, if required, injection), (2) a well pump (usually submerged) and (3) a groundwater heat exchanger. The use of a submerged pump avoids the possibility of introducing air or oxygen into the system. A back-washable filter should also be installed. The injection well should be located from 10 to 15 m in the downstream direction of the groundwater flow. In an open-loop system, the intermediate heat exchanger between the refrigerant and the groundwater is subject to fouling, corrosion, and blockage. The required flow rate through the intermediate heat exchanger is typically between 0.027 and 0.054 L/s. The groundwater must either be reinjected into the ground by separate wells or discharged to a surface system such as a river or lake. To avoid damage due to corrosion, the conductivity of the water should not exceed 450 μ Siemens per cm. The ground-water flow rate G must be capable of delivering the full capacity required from the heat source. This depends on the evaporator cooling power Q0 and the water cooling degree and is given by the following equation: G=

Q0 ρw cw (twi − twe )

(6.3.1)

where ρw is the water density; cw is the specific heat of water;t wi and t we are the water temperatures at the HP inlet and the HP outlet, respectively. The values of the flow rate for each HP model are usually provided in the manufacturer’s data sheets. Table 6.6 summarises the calculated COP values of GWHP and SWHP systems, operating as water-to-water HPs. The “Geotherm” system [18] uses a specially built heat exchanger (Fig. 6.18) placed in an extraction well with a 1.0 m diameter and a depth of 2.0 m. The heat

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6 Heat Pumps for Sustainable Heating and Cooling

Table 6.6 The COP of water-to-water GWHP and SWHP systems Water temperature at evaporator inlet t s (°C)

Water temperature at condenser outlet t u (°C) 30

35

40

45

50

5

4.55

4.10

3.70

3.40

3.15

10

5.30

4.65

4.15

3.75

3.45

15

6.25

5.35

4.70

4.20

3.85

20

7.70

6.35

5.45

4.80

4.30

25

9.95

7.80

6.45

5.55

4.85

30

14.10

10.10

7.95

6.55

5.60

Fig. 6.18 Schematic of “Geotherm” GWHP system

exchanger is mounted between a GCHP and a groundwater source with a reduced flow rate and of any water quality. This heat exchanger consists of a set of four coaxial coils made of HDPE tubes with a diameter of 25 mm, immersed in a cylindrical reservoir made of glass fibre reinforced resins (0.8 m diameter and 1.2 m height) supplied with groundwater at the bottom side. The HP used in conjunction with the intermediate heat exchanger is a GCHP system of 10 kW with a COP of 4. The secondary circuit of the heat exchanger (towards the HP) circulates an antifreeze solution (glycol 20%), which enters the HP at 0 °C and leaves at −2 °C, transported by a circulation pump with a flow rate of 0.94 L/s. The glycol flow in the tubes is ensured by the circulation pump within the HP. Outside of the coils, the groundwater from the cylindrical reservoir is involved in a flow among the spires of coils by a submersible pump. The relatively small pressure loss on the secondary

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circuit of the heat exchanger allows the use of a reduced power circulation pump for the glycol. In the primary circuit of the heat exchanger (outside the tubes), groundwater enters with a temperature of 12 °C and is evacuated to approximately 1 °C (in heating mode). Because the temperature drop is 11 °C, compared with 4 °C in the usual systems, it is possible to obtain the same thermal power with a groundwater flow rate nearly three times lower. The pressure loss on the primary circuit of the heat exchanger is 26 kPa for the mentioned flow rate. The heat exchange is realised mainly by the groundwater supply, and the heat exchanged directly with the ground around the extraction well is also important. The heat transfer surface is 20 m2 , and the heat transfer coefficient is 154 W/m2 K. The groundwater is then evacuated through the top of the heat exchanger by gravity in the rejection well. If the rejection well cannot retrieve all of the groundwater flow rate, surface drainage through a network of perforated pipes buried at 50–80 cm or another evacuation solution (lake, river or sewer) is recommended. Regardless of the outdoor air and ground temperature, the HP will always operate at the same optimum temperatures because of the automation. The automation starts the groundwater inlet (electro-valve or submersible pump) only when the return water-glycol temperature goes below 1 °C. The groundwater flow rate is limited to 4–12 L/min depending on the thermal power of the HP (4– 12 kW). During the summer, the intermediate heat exchanger can operate in a passive cooling mode in which the HP only produces DHW using heat recovered from the A/C space. In this case, the heat carrier from the heaters is transported with the circulation pump directly to the intermediate heat exchanger. The main advantages of this Geotherm HP system with intermediate heat exchanger are the following: • • • • •

lower heat pump installation costs; very deep wells or long trenches on large surfaces are not necessary; eliminated drilling of extraction and rejection wells; reduced groundwater flow rate (30–40% of the usual flow rate); the location of the Geotherm heat exchanger in the absorption well improves the thermal state through direct heat exchange with the ground; and • the groundwater quality is not important because heat transfer is made by HDPE. The installation of a GWHP that uses a safety refrigerant is possible in any space that is both dry and protected from freezing temperatures. The system should be installed on an even, flat surface and the construction of a free-standing base is recommended. The placement of the unit should be such that servicing and maintenance are possible. Generally, only flexible connections to the HP should be implemented.

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6.3.4.3

6 Heat Pumps for Sustainable Heating and Cooling

Description of GCHP Systems

The ground serves as an ideal heat source for monovalent heat pump systems. The GCHP is a subset of the GSHP and is often called a closed-loop HP. A GCHP system consists of a reversible vapour-compression cycle that is linked to a GHE buried in the soil (Fig. 6.17). The heat transfer medium, an antifreeze solution (brine), is circulated through the GHE (collector or loop) and the HP by an antifreeze solution pump. The GHE size needs to take into account the total annual heating demand, which, for domestic heating operation, is typically between 1700 and 2300 h in central Europe. The GCHP is further subdivided according to GHE type: horizontal GHE and vertical GHE. • Types of horizontal GHEs. Horizontal GHEs (Fig. 6.19) can be divided into at least three subgroups: single-pipe, multiple-pipe, and spiral. Single-pipe horizontal GHEs consist of a series of parallel pipe arrangements laid out in trenches. Typical installation depths in Europe vary from 0.8 to 1.5 m. Consideration should be given to the local frost depth and the extent of snow cover in winter. Horizontal GHEs are usually the most cost-effective when adequate yard space is available and the trenches are easy to dig. Antifreeze fluid runs through the pipes in a closed system. The values of the specific extraction/rejection power qE for ground [39, 40] are given in Table 6.7. For a specific power of extraction/rejection qE , the required ground area A can be obtained as follows [41]: A=

Q0 qE

(6.3.2)

Fig. 6.19 Horizontal ground heat exchanger

Table 6.7 Specific extraction power for ground

qE (W/m2 )

No.

Type of ground

1

Dry sandy ground

10–15

2

Moist sandy ground

15–20

3

Dry clay ground

20–25

4

Moist clay ground

25–30

5

Ground with groundwater

30–35

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where Q0 = Qhp −Pe is the cooling power of HP. To save required ground area, some special GHEs have been developed [42]. Multiple pipes (two, four or six), placed in a single trench, can reduce the amount of required ground area. The trench collector is vilely used in North America, and less in Europe. The spiral loop (Fig. 6.20) is reported to further reduce the required ground area. This consists of pipe unrolled in circular loops in trenches with a horizontal configuration. For the horizontal spiral loop layout, the trenches are generally a depth of 0.9–1.8 m. The distance between coil tubes is of 0.6–1.2 m. The length of collector pipe is of 125 m per loop (up to 200 m). The ends of parallel coils 1 are arranged by a manifold-collector 2 in a heart 3, and then the antifreeze fluid is transported by main pipes 4 at HP. For the trench collector, a number of pipes with small diameters are attached to the steeply inclined walls of a trench several metres deep. Disadvantages of the horizontal systems are: (1) these systems are more affected by ambient air temperature fluctuations because of their proximity to the ground surface, and (2) the installation of the horizontal systems needs much more ground area than vertical system. • Types of vertical GHEs. There are two basic types of vertical GHEs or borehole heat exchangers (BHE): U-tube and concentric- (coaxial-) tube system configurations (Fig. 6.21). BHEs are widely used when there is a need to install sufficient heat exchanger capacity under a confined surface area, such as when the earth is rocky close to the surface, or where minimum disruption of the landscape is desired. The U-tube vertical GHE may include one, tens or even hundreds of boreholes, each containing single or double U-tubes through which heat exchange fluid is circulated. Typical U-tubes have a nominal diameter in the range of 20–40 mm and each borehole is normally 20–200 m deep, with a diameter ranging from 100 to 200 mm. Concentric pipes, either in a very simple method with two straight pipes of different diameters or in complex configurations, are commonly used in Europe. The borehole Fig. 6.20 Spiral ground coil

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6 Heat Pumps for Sustainable Heating and Cooling

Fig. 6.21 Common vertical GHE designs

annulus is generally backfilled with some special material (grout) that can prevent contamination of groundwater. A typical borehole with a single U-tube is illustrated in Fig. 6.22. The required borehole length L can be calculated by steady state heat transfer equation as follows [34]: L=

Fig. 6.22 Schematic of a vertical grouted borehole

q Rg tg − t f

(6.3.3)

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where: q is the heat transfer rate, in kW; t g is the ground temperature, in K; t f is the heat carrier fluid (i.e., antifreeze, refrigerant) temperature, in K; Rg is the effective thermal resistance of ground per unit length, in (m · K)/kW. The GHE usually are designed for the worst conditions by considering that these need to handle three consecutive thermal pulses of various magnitude and duration: yearly average ground load qa for 20 years, the highest monthly ground load qm for 1 month, and the peak hourly load qh for 6 h. The required borehole length to exchange heat at these conditions is given by [43]: L=

qh Rb + qa R20a + qm R1m + qh R6h tg − (t f + tg )

(6.3.4)

where: Rb is the effective borehole thermal resistance; R20a , R1m , R6h are the effective ground thermal resistances for 20 years, one month, and six hours thermal pulses; t g is the increase of temperature because long-term interference effect between the borehole and adjacent boreholes. The effective ground thermal resistance depends mainly on the ground thermal conductivity and, to a lesser extent, on the borehole diameter and the ground thermal diffusivity. Alternative methods of computing the thermal borehole resistance are presented by Bernier [43] and Hellström [44]. The antifreeze solution (brine) circulation loop normally consists of the following components: collector pipes, manifold, vent, circulation pump, expansion vessel, safety valve, insulation or condensate drainage, and flexible connections to the HP unit (closed system). The piping should be sized such that the fluid velocity does not exceed 0.8 m/s. The antifreeze mass flow rate must be capable of transporting the full thermal capacity required from the heat source. The mass flow rate mb , in kg/s, is given by: mb =

3600 Q 0 cb t

(6.3.5)

where Q0 is the cooling power of the HP, in kW; cb is the specific heat of antifreeze, in kJ/kg K; and t is the temperature difference, in K (e.g., 3 K). Advantages of the vertical GCHP are that it (1) requires relatively small ground area, (2) is in contact with soil that varies very little in temperature and thermal properties, (3) requires the smallest amount of pipe and pumping energy and (4) can yield the most efficient GCHP system performance. The disadvantage is the higher cost because of the expensive equipment needed to drill the borehole.

6.3.4.4

Simulation Model of GHEs

The main objective of the GHE thermal analysis is to determine the temperature of the heat carried fluid, which is circulated in the U-tube and the HP, under certain

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operating conditions. Actually, the heat transfer process in a GHE involves a number of uncertain factors, such as the ground thermal properties, the groundwater flow rate and building loads over a long lifespan of several or even tens of years. In this case, the heat transfer process is rather complicated and must be treated, on the whole, as a transient one. In view of the complication of this problem and its long-time scale, the heat transfer process may usually be analysed in two separated regions. One is the solid soil/rock outside the borehole, where the heat conduction must be treated as a transient process. Another sector often segregated for analysis is the region inside the borehole, including the grout, the U-tube pipes and the circulating fluid inside the pipes. This region is sometimes analysed as being steady state and sometimes analysed as being transient. The analyses on the two spatial regions are interlinked on the borehole wall. The heat transfer models for the two separate regions are as follows. • Heat conduction outside borehole. A number of simulation models for the heat transfer outside the borehole have been recently reported, most of which were based on either analytical methodologies or numerical methods [45]. Kelvin’s line source. The earliest approach to calculating the thermal transport around a heat exchange pipe in the ground is Kelvin’s line source theory, i.e., the infinite line source [28, 46]. According to Kelvin’s line source theory, the temperature response in the ground due to a constant heat rate is given by: t (r, τ) − t0 =

q 4π λ



∞ r2 4aτ

e−u du u

(6.3.6)

where: r is the distance from the line source and τ the time since start of the operation; t is the temperature of the ground at distance r and time τ; t 0 is the initial temperature of the ground; q is the heating rate per length of the line source; λ and a are the thermal conductivity and diffusivity of the ground. The solution to the integral term in Eq. (6.3.6) can be found from the related references [29, 47]. It was estimated that using Kelvin’s line source may cause a noticeable error when aτ/rb2 < 20. Cylindrical source model. The cylindrical source solution for a constant heat transfer rate was developed by Carslaw and Jaeger [48], then refined by Ingersoll et al. [47], and later employed in a number of research studies [49, 50]. In this model, the borehole is assumed as an infinite cylinder surrounded by homogeneous medium with constant properties (ground). It also assumes that the heat transfer between the borehole and ground with perfect contact is of pure heat conduction. Based on the governing equation of the transient heat conduction along with the given boundary and initial conditions, the temperature distribution of the ground can be given in the cylindrical coordinate:

6.3 General Review of Ground Source …

493

∂2t ∂ r2

+ r1 ∂∂ rt = a1 ∂∂ τt rb < r < ∞ −2πrb λ ∂∂ τt = q r = rb , τ > 0 τ = 0, r > r t − t0 = 0

(6.3.7)

where r b is the borehole radius. The cylindrical source solution is given as follows: t − t0 =

q G(z, p) λ

(6.3.8)

where z = aτ/r b , p = r/r b . As defined by Carslaw and Jaeger [48], the expression G(z, p) is only a function of time and distance from the borehole centre. The temperature on the borehole wall, where r = r b , i.e., p = 1, is of interest at it is the representative temperature in the design of GHEs. However, the expression G(z, p) is relatively complex and involves integration from zero to infinity of a complicated function, which includes some Bessel functions. Fortunately, some graphical results and tabulated values for the G(z, p) function at p = 1 are available in some related reference [47]. An approximate method for G was proposed by Hellström [44]. Eskilson’s model. Both the one-dimensional model of Kelvin’s theory and the cylindrical source model neglect the axial heat flow along the borehole depth. A major progress was made by Eskilson [30] to account for the finite length of the borehole. In this model, the ground is assumed to be homogeneous with constant initial and boundary temperatures, and the thermal capacity of the borehole elements such as the pipe wall and the grout are neglected. The basic formulation of the ground temperature is governed by the heat conduction equation in cylindrical coordinates: ∂ 2t 1 ∂t 1 ∂t ∂ 2t + 2 = + 2 ∂r r ∂r ∂z a ∂τ t (r, 0, τ) = t0 t (r, z, 0) = t0   1 D+L ∂t  q(τ) = 2πr λ  dz L D ∂ r r =rb

(6.3.9)

where L is the borehole length, and D is the uppermost part of the borehole, which can be thermally neglected in engineering practice. In Eskilson’s model, the numerical finite difference method is used on a radial– axial coordinate system to obtain the temperature distribution of a single borehole with finite length. The final expression of the temperature response at the borehole wall to a unit step heat pulse is a function of τ/τs and r b /L only: t b − t0 = −

q f (τ/τs , rb /L) 2π λ

(6.3.10)

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6 Heat Pumps for Sustainable Heating and Cooling

where τs = L 2 /9a means the steady state time. The f -function is essentially the dimensionless temperature response at the borehole wall, which was computed numerically. Finite line-source solution. Based on the Eskilson’s model, an analytical solution to the finite line source has been developed by a research group [51] that considers the influences of the finite length of the borehole and the ground surface as a boundary. Some necessary assumptions are taken in the analytical model in order to derive an analytical solution: • the ground is regarded as a homogeneous semi-infinite medium with constant thermo-physical properties; • the boundary of the medium (ground surface) keeps a constant temperature t0 , same as its initial one, throughout the time period concerned; • the radial dimension of the borehole is neglected so that it may be approximated as a line source stretching from the boundary to a certain length L; • as a basic case of study, the heating rate per length of the source q is constant since the starting instant τ = 0. The solution of the temperature excess was given by Zeng et al. [51]:

t (r, z, τ) − t0 =

q 4π λ

 0

⎡ L

⎤ √2 √2 r +(z−l)2 r +(z+l)2 √ √ er f c( ) ) er f c( 2 aτ 2 aτ ⎢ ⎥ −  ⎣  ⎦ dl (6.3.11) 2 2 2 2 r + (z − l) r + (z + l)

Equation (6.3.11) demonstrates that the temperature on the borehole wall, where r = r b , varies with time and borehole length. The temperature at the middle of the borehole length (z = L/2) is usually chosen as its representative temperature. An alternative is the integral mean temperature along the borehole length, which may be determined by numerical integration of Eq. (6.3.11). For the convenience of applications, the former is usually accepted as the representative temperature in the design and analysis program. Other typical numerical models. Hellström [44] and Thornton et al. [52] proposed a simulation model for ground heat stores, which are densely packed ground loop heat exchangers used for seasonal thermal energy storage. This type of system may be directly used to heat buildings with or without a heat pump. Muraya et al. [53] developed a transient finite element model of the heat transfer around a vertical U-tube heat exchanger for a GCHP system to study the thermal interference that occurred between the adjacent legs of the U-tube. Rottmayer et al. [54] presented a finite difference model that simulated the heat transfer process of a U-tube heat exchanger. A geometric factor was introduced to account for the noncircular geometry used to represent the pipes in the borehole. • Heat transfer inside borehole. The thermal resistance inside the borehole, which is primarily determined by thermal properties of the grouting materials and the arrangement of flow channels of the borehole, has a significant impact on the GHE performance. The main objective of this analysis is to determine the entering and

6.3 General Review of Ground Source …

495

leaving temperatures of the circulating fluid in the borehole according to the borehole wall temperature, its heat flow and the thermal resistance. One-dimensional model. A simplified one-dimensional model has been recommended for GHE design, which considers the U-tube as a single “equivalent” pipe [29, 55]. In this model, both the thermal capacity of the borehole and the axial heat flux in the grout and pipe walls are negligible as the borehole dimensional scale is much smaller compared with the infinite ground outside the borehole. Thus, the heat transfer in this region is approximated as a steady state one-dimensional process. Two-dimensional model. Hellström [44] derived the analytical two-dimensional solutions of the thermal resistances among pipes in the cross-section perpendicular to the borehole axis, which is superior to empirical expressions and one-dimensional model. Quasi-three-dimensional model. On the basis of the two-dimensional model above mentioned, a quasi-three-dimensional model was proposed by Zeng et al. [56], which takes account of the fluid temperature variation along the borehole depth. To keep the model concise and analytically manageable, the conductive heat flux in the grout in axial direction, however, is neglected.

6.3.5 Environmental Performances The GSHPs work with the environment to provide clean, efficient, and energy saving heating and cooling year-round. GSHPs use less energy than alternative heating and cooling systems, helping to conserve natural resources. HPs driven by electricity from, for instance, hydropower or renewable energy reduce emissions more significantly than if the electricity is generated by coal, oil or natural gas power plants. The CO2 emissions for different primary energy sources are summarised in Table 6.8 [57]. The GSHPs utilise renewable or solar energy stored in the ground near the surfaces. The renewable component (66%) displaces the need for primary fuels, which, when burned, produce GHGs emissions and contribute to global warming. An analysis Table 6.8 CO2 emissions for different primary energy sources No. System

Efficiency CO2 emission per kWh of CO2 emission per kWh of fuel (kg CO2 /kWh) useful heat (kg CO2 /kWh)

1

Coal boiler

0.70

0.34

0.49

2

Gas-oil boiler

0.80

0.28

0.35

3

LPG boiler

0.80

0.25

0.31

4

Natural gas boiler

0.80

0.19

0.24

5

Air-to-air HP

2.50

0.47

0.19

6

Ground-to-water HP 3.20

0.47

0.15

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6 Heat Pumps for Sustainable Heating and Cooling

was performed [58] to estimate the total equivalent warming impact (TEWI) of GSHPs compared to other heating and cooling systems in residential, commercial and institutional buildings. The modelling results show CO2 emissions reductions of 15–77% through the application of GSHPs in both residential and commercial buildings. The unique flexibility of GSHPs allows them to be used for residential and commercial buildings all across the United States, Canada and Europe. Regarding CO2 emissions, it could be seen that GSHPs do compete with condensing boilers in countries like Germany, United Kingdom and te United States [59]. With increasing proportions of electricity generated from renewable sources, installing heat pumps in existing buildings becomes a more and more attractive option with respect to both primary energy demand and CO2 emissions.

6.3.6 Hybrid GCHP Systems It is known that the GCHP systems can achieve better energy performance in specific locations where building heating and cooling loads are well balanced all the yearround because of the long-term transient heat transfer in the GHEs. However, most buildings in warm-climate or cold-climate areas have unbalanced loads, dominated by either cooling loads or heating loads. An alternative to decrease the initial cost of the GCHP system and, at the same time, to improve the system performance is to employ a supplemental heat rejecter or heat absorber, which is called the hybrid GCHP (HGCHP) system [45].

6.3.6.1

HGCHP Systems with Supplemental Heat Rejecters

Figure 6.23 shows the operation principle of the HGCHP system with a cooling tower, where the cooling tower is connected in series with the GHE loop and is isolated from the building and ground loops with a plate heat exchanger. The ASHRAE manual [35] discussed the advantages of the HGSHP applications for cooling-dominated buildings considering initial costs and available surface are limitations. Kavanaugh and Rafferty [28] have discussed the possibility of the HGCHP system with a fluid cooler as a favourable alternative to lower the initial cost of the GHE installation. They recommended that the hybrid system be sized based on the peak building load at the design condition and the capacity of the cooler be calculated according to the difference between the GHE lengths required for cooling and heating loads. Kavanaugh [60] has proposed a revised design method for sizing fluid coolers and cooling tower for hybrid system on the basis of the design procedure by ASHRAE [35] and Kavanaugh and Rafferty [28]. In addition to sizing the GHE and cooler, this revision also provides a method for balancing the heat flow into the ground on an annual basis.

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497

Fig. 6.23 Schematic diagram of an HGCHP with cooling tower

Yavuzturk and Spitler [61] have investigated the advantages and disadvantages of various control strategies for the operation of an HGCHP system with a cooling tower under different climatic conditions. The investigated control strategies are broadly categorised into three groups: (1) at point control for the HP entering or exiting fluid temperatures to activate the cooling tower; (2) differential temperature control to operate the cooling tower when the difference between the HP entering or exiting temperature and the ambient wet bulb temperature is greater than a set value and (3) scheduled control to operate the cooling tower during the night to accomplish the cool storage in the ground and avoid a long-term temperature rise. The simulation results for a small building indicate that the hybrid application appears to have significant economic benefit compared to the conventional system. A practical hourly simulation model of the HGCHP system with a cooling tower was developed with the aim of analysing and modelling the heat transfer process of its mains components on an hour-by-hour basis by Man et al. [62]. Hourly operation data of the HGCHP system are calculated by the developed computer program based on the hourly simulation model. The impacts of four different control strategies on performances of two different HGCHP systems are compared.

6.3.6.2

HGCHP Systems with Solar Collectors

In heating-dominated climates, the single GCHP system may cause a thermal heat depletion of the ground, which progressively decreases the HP’s entering fluid temperature. As a result, the system performance becomes less efficient. Similar to the cases of cooling-dominated buildings, the use of a supplemental heat supply device, such as a solar thermal collector, can significantly reduce the GHE size and the borehole installation cost. Basically, the GHE is sized to meet the cooling load and the supplemental heater is sized to meet the excess heating load that is unmet by the GHE. Figure 6.24 shows the basic operating principle of the hybrid GCHP system with a solar collector.

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6 Heat Pumps for Sustainable Heating and Cooling

Fig. 6.24 Schematic diagram of an HGCHP system with solar collector

The idea to couple a solar collector to the coil of pipes buried in the ground, by means of which solar energy can be stored in the ground, was first proposed by Penrod in 1956. Recently, a number of efforts have been made to investigate the performance and applications of the solar-assisted GCHP systems. Chiasson and Yavuzturk [63] approached a system simulation to assess the feasibility of the hybrid GCHP systems with solar thermal collectors in heating-dominated buildings. Yuehong et al. [64] conducted experimental studies of a solar-ground heat pump system, where the heating mode is alternated between a solar energy-source heat pump and a ground source heat pump with a vertical double-spiral coil GHE. Ozgener and Hepbasli [65] experimentally investigated the performance characteristics of a solar-assisted GCHP system for greenhouse heating with a vertical GHE. A solar-assisted GCHP heating system with latent heat energy storage tank (LHEST) was investigated by Zongwei et al. [66]. The hybrid heating system can implement eight different operation models according to the outdoor weather conditions by means of alternative heat source changes among the solar energy, ground heat and the LHEST. Finally, it is claimed that the LHEST can improve the solar fraction of the system, and thus the COP of the heating system can be increased.

6.3.7 Better Energy Efficiency with Combined Heating and Cooling by HPs The possibilities of HP solutions in combined cooling and heating systems have been unclear for a major part of the designers of the A/C systems. Therefore, a survey was made to find out a proper dimensioning and disseminate the knowhow. More general study was performed to find out the influence of different factors.

6.3 General Review of Ground Source …

499

A general study was carried out with a simple modelling tool [67]. Because the goal was to compare different systems and sizing of the HP, the required heating and cooling capacities were calculated as the time series using a simple dependence on outdoor temperature and solar radiation. Variations of a heat source temperature of the HP are important for the annual COP. The presumed curves and the influence on COP are shown in Fig. 6.25. When the sizing factor SF of HP increases the COP decreases (Fig. 6.26) because a greater part of heating demand is produced under less favourable conditions, at lower heat source temperature. If the HP is dimensioned only for A/C cooling duty the SF here is 40%. Free cooling using the low temperature of the heat source is an effective way to decrease energy consumption of the compressor-based cooling. The temperature level of the heat source and the annual cooling demand profile determine how big a part can be covered by free cooling as illustrated in Fig. 6.27. Also, the temperature level of the cooling water network has an essential influence: the higher the temperature, the bigger part can be produced by free cooling. Exhaust air as a heat source utilises heat after the normal heat recovery heat exchanger. When the efficiency on the heat exchanger is increased, the temperature Fig. 6.25 Temperature profiles of heat sources as used in modelling

Fig. 6.26 Annual COP as a function of sizing factor SF

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6 Heat Pumps for Sustainable Heating and Cooling

Fig. 6.27 Influence of supply temperature of cooling water network on COP for cooling

before the evaporator falls and required capacity of the HP decreases. However, the electricity usage is almost constant, because COP decreases as shown in principle in Fig. 6.28. The main point is that the total energy consumption decreases. In the model of the evaporator, also the energy loss caused by defrosting was calculated. The method was calculation of the amount of freezing moisture and evaluation of the heat needed to melt the frost with a given efficiency.

Fig. 6.28 Influence of heat recovery efficiency on energy consumption

6.3 General Review of Ground Source …

501

Fig. 6.29 Schematic diagram of a closed-loop HGCHP system

6.3.8 Energy, Economic and Environmental Performances of a Closed-Loop GCHP System 6.3.8.1

Description of System

The closed-loop GCHP system (Fig. 6.29) represents on of the most popular configurations [43]. A working fluid is pumped through a series of vertical boreholes, where heat is collected (rejected) with a corresponding fluid temperature increase (decrease). Borehole dept is project dependent, but is usually in the 50–150 m range and the borehole-to-borehole distance is of 6–8 m. As shown in the cross-section, boreholes are usually filled with a grout to facilitate heat transfer from the fluid to the ground, and to protect groundwater aquifers. Fluid then returns to the building, where HPs either collect (reject) heat in the fluid loop, thereby decreasing (increasing) the fluid temperature. At any given time, some HPs may operate in heating mode while others might be in cooling mode. Thus, it is possible to transfer energy from one section of the building to the other via the fluid loop. Finally, in some situations it is advantageous to design the hybrid GCHP systems (HGCHP), where a supplementary heat rejecter or heat absorber is added to reduce the length of the GHE. The values of COP in heating and cooling for 10 commercially available 10.5 kW water-to-air extended range HPs were considered (Fig. 6.30). In cooling, the inlet fluid temperature should be as low as possible to reduce HP energy consumption. While in heating mode the inlet fluid temperature should be as high as possible.

6.3.8.2

Analysis of System Performances

Bernier [43] considered a building which has an area of 1486 m2 and is located in a warm-climate region, Atlanta, Georgia (a cooling-dominated climate) in the United

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6 Heat Pumps for Sustainable Heating and Cooling

Fig. 6.30 COP values for 10 commercially water-to-air HPs, of 10.5 kW

States. This building is part of the thermal energy systems specialists (TESS) library of the TRNSYS program, and it is assumed to be equipped with 15, 10.5 kW extended range HPs. The building loads were evaluated hourly using the TRNSYS simulation software and are shown in Fig. 6.31. The peak building cooling load is 111 kW. The total annual building heating and cooling loads are 87,000 MJ and 552,000 MJ, respectively. Boreholes have a 150 mm diameter and include two 25 mm HDPE-9 pipes. The borehole-to-borehole distance is set to 8 m. Bernier claimed that showing the influence of different parameters on the GHE length has determined the required length of boreholes using Eq. (6.3.4) for considered building and four design options: • Case 1 uses low-efficiency HPs (bottom performance curve in Fig. 6.30) and a configuration borehole with a low-thermal conductivity grout. • Case 2 is similar to Case 1 except that high-efficiency HPs are used (top curve in Fig. 6.30). • In Case 3, the borehole thermal resistance has been lowered by using a highthermal conductivity grout and spreading the pipes against the borehole wall. Fig. 6.31 Hourly loads for considered building

6.3 General Review of Ground Source …

503

• In Case 4, the GHE length has been reduced and a closed-circuit fluid cooler is used in the fluid loop (Fig. 6.29). Considering that the cooling loads are much greater than the heating loads, the GHE length was determined based on the cooling loads. It is assumed that the maximum acceptable inlet fluid temperature to the HP is 38 °C. Finally, TRNSYS simulations were used to evaluate HP energy consumption every hour over 20 years of operation, and with these results the average annual energy consumption and the value of the SPF was calculated [43]. The numerical results of length determination, summarised in Table 6.9 were examined by an analysis of energy consumption, life cycle costs, and CO2 emissions. Main conclusions of this analysis are presented as follows. • Annual energy consumption. The average annual COP for the low-efficiency HPs (Case 1) are lower than the other three cases, while the COP for Cases 2 and 3 are very similar. With the hybrid system, the ground temperatures, and consequently the inlet fluid temperature to the HPs, are higher than for Cases 2 and 3 on average. Consequently, the cooling COP for Case 4 differs from the ones observed for Cases 2 and 3 even though the same high-efficiency HPs are used. Table 6.9 Comparative numerical results of analysed solutions Specifications

Case 1

Case 2

Case 3

Case 4

Type of HP efficiency

Low

High

High

High

Hybrid system

No

No

No

Yes

Borehole thermal resistance, Rb ((m K)/W)

0.20

0.20

0.09

0.09

Bore field configuration

5×5

5×5

5×4

5×4

Total GHE length, L (m)

3165

2980

2280

1500

Heating annual performance factor, SPF

4.03

5.65

5.74

5.80

Cooling annual performance factor, SPF

3.86

5.44

5.35

4.89

Heat pumps

47,730

34,440

34,760

37,580

Fluid cooler

–

–

–

420

Boreholes

79,855

75,213

63,220

41,630

Heat pumps

27,690

38,080

38,080

38,080

Length determination of GHE

Annual energy consumption, in kWh

Costs, in e

Fluid cooler

–

–

–

8080

Total investment cost

107,545

113,293

101,300

87,790

Operation energy cost (for 20 years)

39,160

28,252

28,514

30,830

Total costs

146,705

141,545

129,814

118,620

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6 Heat Pumps for Sustainable Heating and Cooling

In terms of annual energy consumption, the low-efficiency HPs (Case 1) consume about 30% more energy than the other three cases. Cases 2 and 3 have similar energy consumption while the hybrid system consumes about 10% more energy than Cases 2 and 3. The fluid cooler of the hybrid system operates an average of 125 h per year with an average annual energy consumption of 420 kWh. • Life cycle cost. A life cycle cost analysis is presented in Table 6.9. Numerical results show that Case 4 has the lowest life cycle cost followed by Case 3. The main difference between these two cases has to do with borehole costs. This difference is greater than capital cost of the fluid cooler estimated at 8080 e [61]. Case 2 has the lowest energy consumption followed closely by Case3. The present value of 20 years of operation for low-efficiency HPs (Case 1) is much higher than the three other cases that use high-efficiency HPs. • CO2 emissions. The CO2 emissions of the closed-loop GCHP system considered previously will be compared with a system that uses a gas boiler to provide heat and a conventional chiller for cooling. The hydraulic power plants not have CO2 emissions and coal power plants present high-CO2 emissions. Figure 6.32 illustrates the amount of CO2 emitted by these two systems for heating/cooling of the reference building. For the geothermal system, Cases 1 and 2 are considered (lines a and b). For the gas boiler-chiller system, a gas boiler efficiency of 80% is assumed and two chillers’ COP (4 and 5) is considered (lines c and d). Lines a and d intersect at 360 kg CO2 emissions per MWh of electricity produced. Thus, if the reference building was located in a region with CO2 emissions higher than this value, then the low-efficiency HPs will emit more CO2 than the gas boiler and high-efficiency chiller system. A similar behaviour occurs when lines a and c intersect at 730 kg CO2 per MWh of electricity produced. In that case the lowefficiency HPs emit more CO2 than the gas boiler and the low-efficiency chiller system. Line b is always lower than the other three. This indicates that the operation of high-efficiency HPs leads to the least amount of annual CO2 emissions, even in cases that utilises coal for electricity production. Fig. 6.32 Annual CO2 emissions as a function of CO2 emitted per MWh of produced electricity: a and b HPs with low-efficiency (Case 1) and high-efficiency (Case 2), respectively; c and d gas boiler-chiller system with COPs of 4 and 5, respectively

6.3 General Review of Ground Source …

505

6.3.9 Conclusions The GSHPs are suitable for heating and cooling of buildings and so could play a significant role in reducing CO2 emissions. During the past few decades, a large number of GSHP systems have been widely applied in various buildings around the world due to the attractive advantages of high efficiency and environmental friendliness. The GSHPs have increasingly been used for building heating and cooling with annual rate of increase of 10–12% in recent years. The GWHPs have the low costs, but with some limitations on the big water flow rate and the clogging of extraction well with appreciable sediment quantities. The new GWHP system “Geotherm”, having a COP of 4, removes these disadvantages by using a special heat exchanger. A combined cooling and heating system with a HP is always more effective than a traditional system if its requirements are taken into the consideration in the design process. For renovation, the applicability is more limited and always depending on the case. Besides, the application of existing GSHPs in already improved standard buildings with reduced heat demand, the development and market introduction of new hightemperature HPs is a mayor task for the replacement of conventional heating systems with HPs in existing buildings.

6.4 Simulation of Ground Thermo-Physical Capacity for a Vertical Closed-Loop GCHP System 6.4.1 Preliminary Considerations The ground serves as an ideal heat source for monovalent HP systems [18, 32, 33, 68]. A GSHP system includes three principle components: (1) a ground connection subsystem, (2) HP subsystem and (3) heat distribution subsystem. The GSHPs work best with heating systems, which are optimised to operate at lower water temperature than is radiator and radiant panel systems (floor, wall and ceiling) [38]. The GCHP is a subset of the GSHP and is often called a closed-loop HP. Among the various GSHP systems, the vertical GCHP system has attracted the greatest interest in research field and practical engineering. A GCHP system consists of a reversible vapour-compression cycle that is linked to a ground heat exchanger (GHE) buried in the soil (Fig. 6.33), through which pure water or antifreeze solution (brine) circulates. The GHEs commonly used in the GCHP systems typically consist of high-density polyethylene pipes which are installed in either borehole heat exchanger (BHE) (called vertical GHE) or horizontal trenches (horizontal GHE). In direct expansion systems, the heat stored in the ground is absor-bed directly by the working fluid (refrigerant).

506

6 Heat Pumps for Sustainable Heating and Cooling

Fig. 6.33 Ground-coupled heat pump

The incorrect determination of the vapourisation thermal power needed for the GCHPs with vertical GHE leads to unfavourable effects of these systems [69]. Therefore is very important to know the thermal conductivity of the ground and the borehole thermal resistance for establish the right number of boreholes to be realised, depending on energy to be transferred to the HP. This section presents a working methodology and develops an analytical model for evaluation of the ground thermal conductivity and the borehole thermal resistance using a thermal response test (TRT). Additionally, the Earth Energy Designer (EED) simulation program is used to calculate the fluid temperature for a case study of the GHE, according to the monthly heating and cooling loads, and the borehole thermal resistance. The average fluid temperature in the ground for cooling, heating and domestic hot water (DHW) production thermal power over a period of 25 years is simulated [70].

6.4.2 Ground Thermal Response Test In the case of vertical closed-loop GCHP systems, the determination of the parameters to calculate the vapourisation thermal power that must be provided from the ground is laborious. Evaluating the thermal conductivity of the ground and the effective thermal resistance of the borehole are very important to know how many loops must be set, which is a function of the energy that must be given to the HP. In this respect, taking a TRT of the ground is necessary, using a borehole in which a simple ground loop is placed.

6.4.2.1

Physical Principles of the Test

The thermal field surrounding the vertical GHE is determined with a line-source model, which represents the borehole as a heat line source. Equation of the infinite line heat source with constant intensity can be written as [4]:

6.4 Simulation of Ground Thermo-Physical Capacity …

qE t (rb , τ) = tb − tg = 4πλ

∞ r 2 /4aτ

 2  e−u qE r du = ·E u 4πλ 4aτ

507

(6.4.1)

where t(r b ,τ) is the temperature difference dependent on the borehole radius r b and the time τ; t b is the average temperature of the borehole wall, in K; t g is the undisturbed ground temperature, in K; qE is the specific power of rejection/extraction, in W/m; λ is the thermal conductivity of the ground, in W/(m · K); r is the effective radius, in m; a = λ/ρc is the thermal diffusivity of the ground, in m2 /s; ρ is the ground density, in kg/m3 ; c is the ground specific heat at constant pressure, in J/(kg · K); and τ is the time. The exponential integral function E, for high values of the parameter (aτ/r 2 ), can be approximated with the following expression:  2  4aτ r = ln 2 − γ E 4aτ r

(6.4.2)

For τ > 5r 2p /a Eq. (6.4.1) becomes:   qE 4aτ t (r p , τ) = q E Rg = ln 2 − γ 4πλ rb

(6.4.3)

where Rg is the thermal resistance of the ground, in K/(W/m) and γ is the Euler constant, approximately equal to 0.5772. The temperature difference between the average temperature of the heat carrier fluid t f = (t i + t e )/2 and the temperature on the borehole wall t b is given by: t f − tb = R b q E

(6.4.4)

where Rb is the thermal resistance of the borehole, in K/(W/m). By introducing the borehole thermal resistance Rb into Eq. (6.4.3), the temperature variation between the circulating fluid and the ground can be obtained:    4aτ 1 ln 2 − γ t (rb , τ) = q E (Rb + Rg ) = q E Rb + 4πλ rb

(6.4.5)

To obtain the smallest temperature differences in the borehole requires its thermal resistance to be as small as possible. This can be accomplished by increasing the ground thermal conductivity, using adequate filling materials and/or by increasing the distance between the tubes of the vertical loop.

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6 Heat Pumps for Sustainable Heating and Cooling

Fig. 6.34 Schematic of an equipment for thermal response test

6.4.2.2

Testing Equipment

During an in situ test, a ground electric heater usually provides heat to the circulating fluid (water or glycol) through the ground loop while the inlet (t i ) and outlet (t e ) fluid temperatures are measured (Fig. 6.34). The average of these two instantaneous temperature reading is usually taken to represent the average temperature in the vertical ground loop at a given time. In an ideal test, the measured circulating flow rate and the heat input rate remain constant throughout the test.

6.4.2.3

Data Analysis and Final Evaluation

For the amount of heat rejected/extracted from the ground, a transient state is set up, expressed by Eq. (6.4.3) in the form: tf =

      Q 1 4a Q ln(τ) + ln 2 − γ + Rb + tg 4πλL L 4πλ rb

(6.4.6)

where Q is the total power of rejection/extraction, in W and L is the borehole length, in m. Equation (6.4.6) can be simplified and written as line form: t f = α ln(τ) + n

(6.4.7)

in which: α=

Q 4πλL

(6.4.8)

6.4 Simulation of Ground Thermo-Physical Capacity …

509

Fig. 6.35 Calculation of borehole thermal resistance

    1 4a Q ln 2 − γ + Rb + tg n= L 4πλ rb

(6.4.9)

where α is the late-time slope in a plot of the fluid temperature t f versus the natural logarithm of time τ (Fig. 6.35). The ground thermal conductivity λ is obtained from Eq. (6.4.8): λ=

Q 4πα L

(6.4.10)

The slope α of the interpolation straight-line of the measurements is independent of the borehole resistance Rb . Thus, an estimated thermal conductivity λ of the ground can be used to determine the real thermal resistance of the borehole. Figure 6.36 shows the variation of the ave-rage fluid temperature t f depending on the time τ from the beginning of the test. Replacing the ground thermal conductivity λ obtained from Eq. (6.4.10) with Eq. (6.4.3) results in the equivalent thermal resistance of the borehole: Fig. 6.36 Variation of fluid temperature in time

510

6 Heat Pumps for Sustainable Heating and Cooling

Rb =

  4a 1 1 1 ln(τ) + ln 2 − γ (t f − tb ) = (t f − tg ) − qE qE 4πλ rb

(6.4.11)

Equation (6.4.11) does not allow a proper estimation of the borehole equivalent thermal resistance, as it is influenced by the test duration through ln(τ). In addition, in Eq. (6.4.8), the thermal diffusivity comes in a, as a ratio between the thermal conductivity λ and the thermal capacity C. The thermal conductivity λ is determined by Eq. (6.4.10), but the thermal capacity C, in J/(m3 · K), can be only approximated using the equation:   4πλ 4 τλ t f − t g − q E Rb C = ρc = exp ln 2 − γ − qE rb

(6.4.12)

where ρ is the ground density; c is the ground specific heat; and the borehole thermal resistance Rb is considered equal to 0.1 K/(W/m) for a standard borehole. To estimate the minimum duration τmin of the test, the following equation can be used [71]: 5r 2 τmin = b a

(6.4.13)

where r b is the borehole radius and a is the ground thermal diffusivity. Austin et al. [72] recommend a minimum duration of 50 h based on their experience with field data sets. Gehlin [73] suggests a minimum duration of 60 h, but recommends using 72 h.

6.4.3 Use of EED Simulation Program: Case Study for a BHE The EED program has been developed [44, 71] on the basis of the line-source simulation model of the GHEs [27]. The fluid temperature of the borehole heat exchanger is calculated according to the monthly heating and cooling loads and the borehole thermal resistance. The EED program input data are as follows [4]: • Ground: thermal conductivity 1.90 W/(m K), thermal capacity 2.40 MJ/(m3 K), annual average temperature of the ground surface 10.6 °C, geothermal heat flux 0.07 W/m2 . • Borehole: number of boreholes 1, configuration: 0 (“1:single”), borehole length 80.00 m, collector type: single-U, borehole diameter 110 mm, U-tube diameter 32 mm, U-tube wall thickness 3 mm, U-tube thermal conductivity 0.42 W/(m · K), distance between axes of the tubes 60 mm, thermal conductivity of the filler 0.60 W/(m · K), contact resistance filler-tube 0.00 (m · K)/W.

6.4 Simulation of Ground Thermo-Physical Capacity … Table 6.10 Monthly thermal energy demands, in MWh

Month

511

Heating load Cooling load Ground thermal load

January

0.89

0.00

0.657

February

0.75

0.00

0.556

March

0.67

0.00

0.492

April

0.45

0.00

0.331

May

0.35

0.25

0.001

June

0.35

0.35

−0.099

July

0.35

0.57

−0.312

August

0.35

0.51

−0.254

September 0.35

0.25

0.007

October

0.54

0.00

0.399

November 0.70

0.00

0.514

December 0.83

0.00

0.616

Total

1.93

2.908

6.56

• Circulating fluid: thermal conductivity 0.480 W/(m · K), specific heat 3795 J/(kg · K), density 1052 kg/m3 , viscosity 0.0052 kg/(m · s), freezing temperature −14 °C, flow rate through the probe 0.300 l/s. • The basic load: Seasonal performance factor for: heating 4.00, cooling 99999.0, and DHW 3.70. The values of the monthly thermal energy demand are given in Table 6.10. • The peak load: the peak monthly thermal loads are given in Table 6.11, simulation years: 25, first month of operation: April. The results obtained using the EED program are as follows: Table 6.11 Peak monthly thermal loads, in kW Month

Peak heating load

Duration (h)

Peak cooling load

Duration (h)

January

3.11

24.0

0.00

0.0

February

3.11

24.0

0.00

0.0

March

0.00

0.0

0.00

0.0

April

0.00

0.0

0.00

0.0

May

0.00

0.0

0.00

0.0

June

0.00

0.0

2.15

10.0

July

0.00

0.0

2.15

10.0

August

0.00

0.0

2.15

10.0

September

0.00

0.0

0.00

0.0

October

0.00

0.0

0.00

0.0

November

0.00

0.0

0.00

0.0

December

3.11

24.0

0.00

0.0

512

6 Heat Pumps for Sustainable Heating and Cooling

Table 6.12 Specific extraction power, in W/m

Month

Basic load Peak heating load Peak cooling load

January

11.24

29.16

0.00

February

9.52

29.16

0.00

March

8.42

0.00

0.00

April

5.67

0.00

0.00

May

0.02

0.00

0.00

June

−1.70

0.00

−26.88

July

−5.34

0.00

−26.88

August

−4.35

0.00

−26.88

September 0.12

0.00

0.00

October

6.83

0.00

0.00

November 8.80

0.00

0.00

29.16

0.00

December

10.55

• Thermal resistances: borehole thermal resistance 0.7141 m · K/W, Reynolds number 2972, fluid-tube thermal resistance 0.0139 m · K/W, tube thermal resistance 0.0787 m · K/W, grout-tube thermal resistance 0.0000 m · K/W, fluidground thermal resistance 0.1856 m · K/W, effective borehole thermal resistance 0.1877 m · K/W. • Specific extraction power: Table 6.12 presents the monthly values of the specific extraction power for basic and peak heating and cooling. • The average fluid temperatures: Table 6.13 summarises the monthly average temperatures for the basic thermal load, depending on the year of the simulation. In the 25th simulation year, the minimum average fluid temperature was 5.52 °C Table 6.13 The average fluid temperatures for the basic load, in °C Simulation year

1

2

5

10

25

January

12.07

6.02

5.75

5.63

5.52

February

12.07

6.74

6.48

6.36

6.26

March

12.07

7.23

6.99

6.87

6.77

April

9.26

8.57

8.34

8.23

8.12

May

11.90

11.42

11.20

11.09

10.99

June

12.82

12.44

12.23

12.13

12.02

July

14.70

14.39

14.19

14.09

13.99

August

14.36

14.09

13.90

13.80

13.70

September

11.59

12.20

11.97

11.79

11.69

October

8.80

8.59

8.42

8.32

8.22

November

7.59

7.41

7.24

7.14

7.04

December

6.54

6.37

6.21

6.11

6.01

6.4 Simulation of Ground Thermo-Physical Capacity …

513

in late January, and the maximum average fluid temperature was 15.82 °C at the end of July. Table 6.14 gives the monthly average fluid temperatures for the peak heating load, depending on the year of the simulation. In the 25th simulation year, the minimum average fluid temperature was −0.79 °C in late January, and the maximum average fluid temperature was 13.99 °C is at the end of July. Table 6.15 gives the monthly average fluid temperatures for the peak cooling load, depending on the year of the simulation. In the 25th simulation year, the minimum Table 6.14 The average fluid temperatures for the peak heating load, in °C Simulation year

1

2

5

10

25

January

12.07

−0.28

−0.56

−0.68

−0.79

February

12.07

−0.18

−0.44

−0.55

−0.66

March

12.07

7.23

6.99

6.87

6.77

April

9.26

8.57

8.34

8.23

8.12

May

11.90

11.42

11.20

11.09

10.99

June

12.82

12.44

12.23

12.13

12.02

July

14.70

14.39

14.19

14.09

13.99

August

14.36

14.09

13.90

13.80

13.70

September

12.20

11.97

11.79

11.69

11.59

October

8.80

8.59

8.42

8.32

8.22

November

7.59

7.41

7.24

7.14

7.04

December

−0.01

−0.18

−0.34

−0.44

−0.54

Table 6.15 The average fluid temperatures for the peak cooling load, in °C Simulation year

1

2

5

10

25

January

12.07

6.02

5.75

5.63

5.52

February

12.07

6.74

6.48

6.36

6.26

March

12.07

7.23

6.99

6.87

6.77

April

9.26

8.57

8.34

8.23

8.12

May

11.90

11.42

11.20

11.09

10.99

June

20.76

20.38

20.18

20.07

19.97

July

21.50

21.18

20.99

20.88

20.78

August

21.47

21.20

21.01

20.91

20.80

September

11.59

12.20

11.97

11.79

11.69

October

8.80

8.59

8.42

8.32

8.22

November

7.59

7.41

7.24

7.14

7.04

December

6.54

6.37

6.21

6.11

6.01

514

6 Heat Pumps for Sustainable Heating and Cooling

Fig. 6.37 Average fluid temperature in the ground over a period of 25 years

average fluid temperature was 5.52 °C in late January, and the maximum average fluid temperature was 20.80 °C at the end of August. Figure 6.37 plots the evolution of the average fluid temperature in the ground for cooling, heating and DHW production thermal power over a period of 25 years. Four different scenarios were simulated, two for the winter season (base load and peak load for heating) and two for the summer season (base load and peak load for cooling).

6.4.4 Conclusions In Europe, the ground TRT became a standard instrument to investigate the necessary parameters for the proper designing of vertical loops. Through the ground TRT, the length of the loops is properly determined, the operating performance of the system is provided and supplementary costs (e.g., extra loops, boreholes, glycol, etc.) are avoided. This operation is performed using specialised software. From the cost efficiency point of view, TRT is generally efficient for those situations where 10 or more vertical GHEs are required. Analysing the time evolution of the fluid temperatures in the ground for the peak loads reveals that these values are approximately constant, meaning that the heat source (ground) is fully regenerated and thus the GCHP will maintain high performance in operation.

6.5 Performance Analysis of Different Heating Systems …

515

6.5 Performance Analysis of Different Heating Systems Connected to a GCHP for an Office Room 6.5.1 Preliminary Considerations Buildings are indisputably considered as one of the largest energy consuming sectors. According to the International Energy Agency, the average energy consumed by buildings represents 32% of worldwide energy consumption. European Union (EU) energy consumption patterns reveal that buildings are the greatest energy consumer, using approximately 40% of the total energy demand, followed by industry and transportation, which consume approximately 30% each [74]. Some actions are performed to reduce energy consumption and to protect the environment (e.g., the use of renewable energies for new or retrofitted buildings and passive energy buildings). The Renewable Energy Directive 2009/28/EC of the European Parliament opens up a major opportunity for further use of heat pumps (HPs) for heating and cooling of new and existing buildings [16]. Conversion of heating and cooling systems based to ground source HPs and air-to-water HPs is a well-proven measure to approach nearly zero-energy buildings (nZEBs) requirements. Ground-coupled heat pump (GCHP) systems are a type of renewable energy technology which has been increasingly used in the past decade across Europe to provide air-conditioning (A/C) and domestic hot water (DHW) for the buildings [4, 75]. A number of GCHP systems have been used in residential and commercial buildings worldwide because of their noticeable high efficiency and environmental friendliness [18, 76, 77]. The use of GCHPs in the achievement of adequate temperatures has been studied by several researchers [78–80]. Most existing studies of GCHP systems concentrate on theoretical and simulation model research [81–85] or in situ monitoring of the heat transfer in borehole heat exchanger (BHE) [86–88]. Only a few researchers have investigated the experimental operation performance of GCHP systems. Pulat et al. [89] evaluated the performance of a GCHP with a horizontal ground heat exchanger (GHE) installed in Turkey under winter climatic conditions. Yang et al. [90] reported the heat transfer of a tworegion vertical U-tube GHE after an experiment performed in a solar geothermal multifunctional HP experimental system. Lee et al. [91] conducted experiments on the thermal performance of a GCHP integrated into a building foundation in summer. Man et al. [92] performed an in situ operation performance test of a GCHP system for cooling and heating provision in a temperate zone. The experimental results indicate that the performance of the GCHP system is affected by its intermittent or continuous operation modes. Petit and Meyer [93] compared the thermal performance of a GCHP with an air-source air conditioner, finding that a horizontal or vertical GCHP was more favourable in terms of economic feasibility. Esen and Inalli [94] proposed using the in situ thermal response test to determine the thermal property of the ground for the GCHP applications in Turkey. The widespread distribution of HPs as single generators in heating systems has mainly been in new, rather isolated buildings that have limited unit loads. This has

516

6 Heat Pumps for Sustainable Heating and Cooling

enabled the use of low-temperature terminal units, such as fan coil units and, in particular, radiant systems [4]. After the introduction of plastic piping, the application of water-based radiant heating and cooling with pipes embedded in room surfaces (i.e., floors, walls and ceilings), has significantly increased worldwide. However, to extend the use of these types of heat generators and to benefit from their energy efficiency, working with radiators, which were the most commonly used terminal units in heating systems in the past, is necessary. This section is focused of an experimental study performed to test the energy efficiency of the radiator or radiant floor heating system for an office room connected to a GCHP [95]. The main performance parameters (COP and CO2 emissions) are obtained for one month of operation of the GCHP system, and a comparative analysis of these parameters along with thermal comfort is achieved. Simulations of useful thermal energy and the system COP in heating mode with Transient Systems Simulation (TRNSYS) software are finally performed along 8760 h using Meteonorm weather data and compared to experimental measurements to validate the simulation models.

6.5.2 Description of Office Room Experimental investigations of GCHP performance were conducted in an office room (Fig. 6.38) at the Polytechnic University of Timisoara, Romania, located at the ground floor of the Civil Engineering Faculty building.

Fig. 6.38 Heated office room

6.5 Performance Analysis of Different Heating Systems …

517

Fig. 6.39 Monthly energy demand for office room heating

Timisoara has a continental temperature climate with four different seasons. The heating season runs in Timisoara from 1 October to 30 April. The following data are known: heat transfer resistance (1/U-value) of building components: walls (2.10 m2 K/W), ceiling (0.34 m2 K/W), windows and doors (0.65 m2 K/W); glass walls surface, 8.2 m2 ; total internal heat gain (e.g., from computers, human and lights), 25 W/m2 ; and heat demand, 1.35 kW. The indoor and outdoor air design temperatures are 22 and −15°C, respectively. This space is equipped both with a floor heating system and steel panel radiators to analyse the energy and environmental performances of these systems. These two heating systems are connected to a mechanical compression GCHP, type WPC 5 COOL. In the GCHP system, heat is extracted from the ground by a closed-loop vertical GHE with a length of 80 m. Figure 6.39 illustrates the monthly energy demand for office room heating calculated using Romanian standard NP 048-2000.

6.5.3 Experimental Facilities The GCHP experimental system consisted of a BHE, HP unit, circulating water pumps, floor/radiator heating circuit, data acquisition instruments and auxiliary parts as shown in Fig. 6.40.

518

6 Heat Pumps for Sustainable Heating and Cooling

Fig. 6.40 Experimental GCHP system

6.5.4 Borehole Heat Exchanger The GHE of this experimental GCHP consisted of a simple vertical borehole that had a depth of 80 m. Antifreeze fluid (30% ethylene glycol aqueous solution) circulates in a single polyethylene U-tube of 32 mm internal diameter, with a 60 mm separation between the return and supply tubes, buried in the borehole. The borehole’s overall diameter was 110 mm. The borehole was filled with sand and finished with a bentonite layer at the top to avoid intrusion of pollutants in the aquifers. The average temperature across the full borehole depth tested was 15.1 °C. The ground characteristics are based on measurements obtained from the Banat Water Resources Management Agency [96]. The average thermal conductivity and thermal diffusivity of the ground from the surface to 80 m deep tested were 1.90 W/(m · K) and 0.79×10−6 m2 /s, respectively [97]. The boreholes were completely backfilled with grout mixed with drilling mud, cement and sand in specific proportions. The thermal conductivity and thermal diffusivity of the grout tested by the manufacturer were 2.32 W/(m · K) and 0.93×10−6 m2 /s, respectively.

6.5.5 Heat Pump Unit The HP unit is a reversible ground-to-water scroll hermetic compressor unit with R410A as a refrigerant and the nominal heating capacity of 6.5 kW. The HP unit is a compact type model having an inside refrigeration system. The operation of the HP is governed by an electronic controller, which, depending on the system water return

6.5 Performance Analysis of Different Heating Systems …

519

temperature, switches the HP compressor on or off. The heat source circulation pump was controlled by the HP controller, which activates the source pump 30 s before compressor activation.

6.5.6 GCHP Data Acquisition System The GCHP data acquisition system consists of the indoor and outdoor air temperature, dew point temperature, supply/return temperature, heat source temperature (outlet BHE temperature), relative air humidity and main operating parameters of the system components.

6.5.7 Heating Systems The heating systems are supplied via a five-circuit flow/return manifold as follows. The first two circuits supply the floor heating system. The third and fourth circuits are coupled to a radiator heating system, and the fifth circuit is for backup. The flow/return manifold is equipped with a circulation pump to ensure the chosen temperature of the heat carrier (hot water). A three-way valve and a thermostatic valve are provided to adjust the maximum hot water temperature of the floor’s heating system. Thus, for higher temperatures, the hot water is adjusted to achieve a circulation loop in the heating system. To achieve higher performances of the heating systems, a thermostat is provided for controlling the start/stop command of the circulation pump when the room reaches the set point temperature. At the same height as this thermostat, there is also an ambient thermostat that controls the starting and stopping of the HP to ensure optimum operation of the entire heating system. The start-stop command of the flow/return manifold circulation pump is controlled by an interior thermostat relay, situated at a height of approximately 1.00 m above the floor surface. This height has been determined to provide adequate comfort for the office occupants. The radiant floor heating system consists of two circuits connected to a flow/return manifold (Fig. 6.41a), designed to satisfy the office heating demand of 1.35 kW. The first circuit has a length of 54 m and is installed in a spiral coil, with the closest step distance to the exterior wall of the building to compensate for the effect of the heat bridge, and the second circuit, with a length of 61 m, is mounted in the coil simple. The mounting step of the coils is between 10 and 30 cm. The floor heating pipes are made of cross-linked polyethylene with an external diameter of 17 mm and a wall thickness of 2 mm. The mass flow rate for each circuit is controlled by the flow/return manifold circuit valves. They are adjusted to satisfy the heat demand according to Timisoara’s climate (t e = −15 °C).

520

6 Heat Pumps for Sustainable Heating and Cooling

Fig. 6.41 Schematic of heating systems: a floor heating; b radiator heating

Radiator heating system. The low-temperature radiator heating system (45/35 °C) has two steel panel radiators, each one with two water columns and a length of 1000 mm, height of 600 mm and thermal power of 680 W (Fig. 6.41b), connected to a flow/return manifold and dimensioned to satisfy the office heating demand of 1.35 kW. They are installed on a stand at 15 cm above the floor surface to ensure optimal indoor air circulation. The heating radiator system pipes are made of cross-linked polyethylene with an external diameter of 17 mm and a wall thickness of 2 mm. The mass flow rate for each radiator is controlled by the flow/return manifold circuit valves, adjusted to satisfy the heat demand of office room.

6.5.8 Measuring Apparatus A network of sensors was setup to allow monitoring of the most relevant parameters of the system [97]. Two thermal energy metres were used to measure the thermal energy produced by the GCHP and the extracted/injected thermal energy to the ground. A thermal energy meter was built with a heat computer, two PT500 temperature sensors and an ultrasonic mass flow meter. The two PT500 wires temperature sensors with an accuracy of ±0.15 °C were used to measure the supply and return

6.5 Performance Analysis of Different Heating Systems …

521

temperature for a hydraulic circuit (the water-antifreeze solution circuit or the manifold circuit). Also, an ultrasonic mass flow meter measured the mass flow rate for a hydraulic circuit. The thermal energy metres were AEM metres, model LUXTERM, with a signal converter IP 67 and accuracy 35%. In addition, the PMV index values for the pair 1 met–0.9 clo are lower with 47–94% in the case of the radiant floor heating system than in the case of the radiator heating system. Therefore, the first system leads to increased thermal comfort.

22.10 22.40 22.60 22.70 22.80 22.80

2.5

3.0

3.5

4.0

4.5

5.0

25.50

5.0

21.70

25.50

4.5

21.20

25.30

4.0

2.0

25.20

3.5

1.5

25.00

3.0

20.60

24.70

2.5

1.0

24.30

2.0

Radiator

23.70

1.5

2.16

2.16

2.15

2.14

2.13

2.11

2.08

2.05

2.01

2.34

2.34

2.32

2.32

2.31

2.28

2.26

2.22

PPD (%)

83

83

83

83

82

82

80

79

77

89

89

89

89

88

88

87

86

84

22.80

22.80

22.70

22.60

22.40

22.10

21.70

21.20

20.60

25.50

25.50

25.30

25.20

25.00

24.70

24.30

23.70

23.00

PPD (%) 8 6 6 5 5 5 5 5 5 14 12 11 10 9 8 8 8 8

PMV (−) −0.35 −0.26 −0.18 −0.12 −0.08 −0.06 −0.04 −0.02 −0.02 −0.67 −0.59 −0.53 −0.48 −0.43 −0.41 −0.39 −0.38 −0.38

t r (°C)

2.17

PMV (−)

t r (°C) 23.00

1.0

Radiant floor

1 met−0.90 clo

3.4 met−0.67 clo

Distance from the window (m)

Heating type

Table 6.17 Numerical results of THERMAL COMFORT computer program

22.80

22.80

22.70

22.60

22.40

22.10

21.70

21.20

20.60

25.50

25.50

25.30

25.20

25.00

24.70

24.30

23.70

23.00

t r (°C)

−1.67

−1.67

−1.69

−1.70

−1.74

−1.79

−1.86

−1.94

−2.05

−1.19

−1.19

−1.23

−1.25

−1.28

−1.34

−1.41

−1.51

−1.63

PMV (−)

1.1 met−0.29 clo PPD (%)

60

60

61

62

64

67

70

74

79

35

35

37

38

39

42

46

52

58

6.5 Performance Analysis of Different Heating Systems … 525

526

6 Heat Pumps for Sustainable Heating and Cooling

6.5.11 Numerical Simulation of Useful Thermal Energy and System COP Using TRNSYS Software TRNSYS software [103] is one of the most flexible modelling and simulation tools and can solve very complex problems from the decomposition of the model in various interconnected model components. One of the main advantages of TRNSYS for the modelling and design of GSHPs is that it includes components for the calculation of building thermal loads, specific components for HVAC, HPs and circulating pumps, modules for BHEs and thermal storage, as well as climatic data files, which make it a very suitable tool to model a complete A/C or HP installation to provide heating and cooling to a building. Some model performance indicators, such as the root mean square error (RMSE), the coefficient of variation (cv ), the coefficient of multiple determinations (R2 ) and percentage difference (relative error) er may be used to compare simulated and actual values for model validation, according to relations [104]:  RMSE =

n i=1



ysim,i − ymea,i n

2

RMSE  100 cv =   y¯mea,i  2 n  i=1 ysim,i − ymea,i 2 n R =1− 2 i=1 ymea,i    ymea,i − ysim,i  er = 100% ymea,i

(6.5.3) (6.5.4)

(6.5.5)

(6.5.6)

where n is the number of measured data in the independent data set; ymea,i is the measured value of data point i; ysim,i is the simulated value of data point i; y¯mea,i is the mean value of all measured data points.

6.5.11.1

Simulation of Thermal Energy Used for Office Room Heating

• Definition of the operation scheme. To simulate the thermal energy used to cover the heating load of the office room, the operational connections were established between the building and all internal and external factors. Figure 6.45 presents the operational scheme built in TRNSYS, where the building thermal behaviour was modelled using a “Type 56” subroutine. This subroutine was processed with the TRNBuild interface by introducing the main construction elements, their orientation and surface, shadow factors and indoor activity type.

6.5 Performance Analysis of Different Heating Systems …

527

Fig. 6.45 Schematic of the system model built in TRNSYS to simulate useful thermal energy

Weather data for Timisoara were obtained from the Meteonorm database [105] and the weather data reader “Type 109” and “Type 89d” were used to convert the data in a form readable from TRNSYS. The simulation model took into account the outdoor air infiltrations, heat source type, and interior gains. To extract the results, an online plotter (“Type 65”) is used. • Simulation results and comparison with experimental data. Performing simulations for a one-year period (8760 h), the values of thermal energy used for heating were obtained and are presented beside the measured values in Table 6.18. Statistical indicators such as RMS, cv and R2 are also given in Table 6.18. There was a maximum difference between the measured and TRNSYS simulated values for the heating period of approximately 1.59%, which is very acceptable. The RMSE and cv values in heating mode are 2.722 and 1.41%, respectively. The R2 -values are about 0.9999, which can be considered as very satisfactory. Thus, the simulation model was validated by the experimental data.

528

6 Heat Pumps for Sustainable Heating and Cooling

Table 6.18 Thermal energy used for office room heating Month

Heating energy (kWh)

er (%)

RMSE (−)

cv (%)

R2 (−)

2.72187

1.409

0.99990075

Simulated

Measured

January

252.50

256.24

1.57

February

195.70

195.06

0.32

March

151.61

150.44

0.77

April

49.73

48.95

1.59

May

0.00

0.00

0.00

June

0.00

0.00

0.00

July

0.00

0.00

0.00

August

0.00

0.00

0.00 0.00

September

0.00

0.00

94.85

95.66

0.84

November

174.45

172.62

1.06

December

238.75

240.11

0.57

October

6.5.11.2

COP Simulation of GCHP System

• Definition of the operation scheme. For COP simulation of the GCHP system the operational scheme built in TRNSYS from Fig. 6.46 was utilised. The assembly of GCHP system consists of the standard TRNSYS weather data readers “Type 15-6”, a GCHP model “Type 919”, a BHE “Type 557a”. Also, in the simulation model were defined single-speed circulating pumps “Type 114” for the antifreeze fluid in the BHE and “Type 3d” for heat carrier fluid of the manifold. A “Type 14” for the load profile and a daily load subroutine were created, this approach improving significantly the numerical convergence of the model. Finally, two model integrators (“Type 25” and “Type 24”) were used to calculate daily and total results for thermal energy produced. • Simulation results and comparison with experimental data. COP simulation of the GCHP integrated both with radiator and radiant floor heating system was performed for a 1-month period. The results of the simulation program are presented beside the experimental data in Table 6.19. A comparative analysis of these results indicates that the COPsys values simulated with TRNSYS program were only 3.52% lower than the measured values for radiant floor heating system and only 4.98% lower than the measured values for radiator heating system. Thus, the simulation model is validated experimentally.

6.5 Performance Analysis of Different Heating Systems …

529

Fig. 6.46 Scheme of the system model built in TRANSYS for COP simulation

Table 6.19 The COP values for GCHP system

Heating system

COPsys Simulated

Measured

Relative error er (%)

Radiant floor

5.48

5.68

−3.52

Radiator

5.15

5.42

−4.98

6.5.12 Conclusions The use of HPs in modern buildings with improved thermal insulation and reduced thermal load is a good alternative to traditional heating solutions. This study showed that radiator heating and radiant floor heating systems have small differences (4.5%) in their energy performance coefficient (COPsys ) value, but the ON/OFF switching in the case of a radiator heating system is almost three times higher than that for a radiant floor heating system, leading to higher wear on the HP equipment. In addition, the radiator heating system showed 10% higher energy consumption and CO2 emissions compared to the floor heating system under the same operating conditions. The developed TRNSYS simulation models can be used as a tool to determine the GCHP performance connected with different heating systems to optimise their energy efficiency and ensure the user’s comfort throughout the year.

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6.6 Performance of an Experimental Vertical GCHP System for Heating, Cooling and DHW Operation 6.6.1 Preliminary Considerations Due to the heat capacity of the ground, ambient air temperature variations are directly reflected only in the surface ground temperature, and their effect is reduced at deeper layers. According to the reports of the 2010 World Geothermal Congress, GCHP systems have the largest energy use and installed capacity, accounting for 69.7 and 49.0% of the worldwide capacity and use, respectively. Almost all of the installations occur in North America, Europe and China, increasing from 26 countries in 2000, 33 countries in 2005 and all the way up to the present 43 countries. Sweden, Denmark, Switzerland, Austria and the United States are the leaders in this field [106]. The number of installed GCHP systems has grown continuously by 10–30% annually in recent decades [18, 32, 45, 68] reaching 70 million installed units in Europe by 2020 [107]. The use of GCHPs to achieve adequate temperatures has been studied by several researchers [78, 79]. Most existing studies of GCHP systems concentrate on theoretical and simulation model research [45, 85, 108] or in situ monitoring of heat transfer in the BHE [32, 56, 68, 87]. Only a few researchers have investigated the experimental operational performance of GCHP systems [89, 91, 92]. This section is focused on the energy and environmental analysis and modelling of a geothermal experimental plant from a continental temperate climate [109, 110]. The system consists of a reversible vertical GCHP. One of the main innovative contributions of this study is in the achievement and implementation of an energy-operational optimisation device for the GCHP system using quantitative adjustment with a buffer tank (BT) and a variable speed circulating pump. Experimental measurements are used to test the performance of the GCHP system at different operating modes. The main performance parameters (energy efficiency and CO2 emissions) are obtained for one month of operation using both classical and optimised adjustment of the GCHP system. A comparative analysis of these performances for both heating and cooling and DHW with different operation modes is performed. Additionally, two simulation models of thermal energy consumption in heating/cooling and DHW operation were developed using TRNSYS software. The simulations obtained using TRNSYS software are analysed and compared to the experimental measurements.

6.6.2 Description of Experimental Laboratory Experimental investigations of GCHP performance were conducted in a laboratory (Fig. 6.47) at the Polytechnic University of Timisoara, Romania, located at the ground floor of the Civil Engineering Faculty building with six floors and a heated basement. The city has a continental temperature climate with four different seasons.

6.6 Performance of an Experimental Vertical GCHP System …

531

Fig. 6.47 Experimental laboratory

The heating season in Timisoara runs from 1 October to 30 April, and the cooling season runs from 1 May to 30 September. The laboratory room has an area of 47 m2 , and its height is 3.70 m. The envelope (external walls) is made of 200 mm porous brick with a 100-mm thermal insulating layer and 20 mm lime mortar. The thermal transmittances (U-values) are as follows: walls, 0.345 W/m2 K and double-glazed windows, 2.22 W/m2 K. The area of the windows is 16 m2 , and the area of the interior door is 2.1 m2 . The indoor air design temperature is 20 °C for the heating season and 26 °C for cooling season. The outdoor air design temperature is −15°C for the heating season and 32.6 °C for the cooling season. The GCHP installed in this experimental laboratory heated and cooled through a fan coil system. With the mentioned input data, a heating load of 3.11 kW and a cooling load of 2.15 kW were obtained. The laboratory area was assimilated with a three-person apartment area in Timisoara. Considering the DHW daily mean consumption of 50 L/person, a tank hot water temperature of 45 °C and a cold water temperature of 20 °C, a DHW load of 4.36 kW was determined. Figure 6.48 illustrates the monthly energy demand for laboratory heating (positive values) and cooling (negative values).

6.6.3 Description of the Experimental System The GCHP experimental system consisted of a BHE, HP unit, BT, circulating water pumps, fan coil units, sink, data acquisition instruments and auxiliary parts, as shown in Fig. 6.49. The heat carrier fluid can be delivered towards two fan coils units in two flow rate adjustment modes:

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6 Heat Pumps for Sustainable Heating and Cooling

Fig. 6.48 Monthly energy demand for laboratory heating/cooling

Fig. 6.49 Schematic of the experimental GCHP system with optimised flow rate adjustment

1. Direct, by a recirculation pump connected inside of the HP unit of the GCHP system (classical solution); 2. Indirect, by a fixed-speed circulating pump connected to a BT. The GCHP automation can control the operation of the circulating pump connected to the BT by on/off switching. This assembly improves the entire system operation. The BT allows decreasing the GCHP on/off switching because of its thermal inertia, and thus, the energy efficiency increases. The solution for heat carrier fluid flow rate adjustment was optimised using an automatic control device of circulating

6.6 Performance of an Experimental Vertical GCHP System …

533

Fig. 6.50 Schematic of a control device of the variable speed pump

pump speed [111]. The main components of an automatic device for pump speed control are shown in Fig. 6.50 [52]. For the proposed setting, different values of the heat demand were calculated, using the Romanian standard SR 1907 and of the cold demand, using the Romanian standard SR 6648, depending on the temperature difference t between inside and outside as follows: • for heating, a range of outdoor air temperature was considered between −20 and 22 °C, taking into account that the indoor air temperature is constant (t i = 22 °C), and the outdoor air temperature varies depending on the day-night and seasonal alternation; • for cooling, a range of the outdoor air temperature was considered to be between 26 and 42 °C, taking into account that the indoor air temperature is constant (t i = 26 °C), and the outdoor air temperature varies depending on the day–night and seasonal alternation. For each value of the heat and cold demand corresponds a flow rate of heat carrier fluid that must be pumped in the system by the circulating pump at a certain speed ν of its motor and in this way the speed control of the circulating pump attached to the BT is controlled. Following the calculations performed, in fact, the variation curve, by points, of the frequency ν, in Hz, of the frequency converter was obtained depending on the temperature difference t, in °C. Applying the geometric interpolation by the numerical method of the smallest squares [112], the analytical expression of this curve was determined, under the forms: • for heating: ν = 7.652t 0.284

(6.6.1)

ν = 14.845t 0.175

(6.6.2)

• for cooling:

Figure 6.51 presents a schematic of the automatic control device of the circulating pump speed according to heating/cooling demand of the room. In comparison with the classical solution, in which the circulating pump on/off switching is controlled

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Fig. 6.51 Schematic of the automatic control device for the circulating pump

by the GCHP automation, the optimised solution assures both the on/off switching and the speed control of the circulating pump. The temperature difference between the inside and outside of the heated/cooled space is measured by temperature sensors TS1 and TS2 connected to a programmable logic controller (PLC). In the PLC internal memory, an algorithm based on Eqs. (6.6.1) and (6.6.2) is implemented for calculating the frequency of the frequency converter, which depends on the measured temperature difference. The PLC sends to the frequency converter the corresponding frequency value to ensure the fluid flow rate according to heating/cooling load at that time. In addition, the PLC allows on/off switching control of the circulating pump. For simultaneous on/off switching of the circulating pump and GCHP, common temperature values of this process were established.

6.6 Performance of an Experimental Vertical GCHP System …

6.6.3.1

535

Borehole Heat Exchanger

The GHE of this experimental GCHP consisted of a simple vertical borehole that had a depth of 80 m and was described in Sect. 6.5.4.

6.6.3.2

HP Unit Equipment

The HP unit was a reversible ground-to-water scroll hermetic compressor unit with R410A as a refrigerant. The nominal heating and cooling capacities were 6.5 kW (35 °C supply/0 °C return) and 3.8 kW (23 °C return/15 °C supply), respectively. The HP unit was a compact type model having an inside refrigeration system and DHW tank with a 175-l capacity. The operation of the HP was governed by an electronic controller, which, depending on the building water return temperature, switched the HP compressor on or off. The heat source circulation pump was controlled by the HP controller, which activates the source pump 30 s before compressor activation. The COP of the GCHP system (COPsys ) is defined by Eq. (6.2.12), where E el is the energy consumption of the GCHP system, which includes the energy consumption of the compressor of heat pump unit, circulating pumps, fan coil units, frequency converter and PLC. The CO2 emission (CCO2 ) of the heating system during its operation is calculated with Eq. (6.2.38). To obtain the COPhp or COPsys and CO2 emission, it is necessary to measure the heating/cooling energy E t and electricity E el used by the HP unit or the GCHP system.

6.6.3.3

Water Circulation Pumps

The water circulating loops of the GCHP consisted of a GCHP-BT water loop and BT-fan coil unit water loop. Two centrifugal pumps with rated flow of 2.8 and 5.5 m3 /h were chosen for the first and the second water circulating loop, respectively. The first circulating pump (fixed-speed circulating pump connected to HP unit) was controlled by the GCHP automation, and the second pump (variable speed circulating pump connected to BT) was controlled by an automatic control device.

6.6.3.4

Fan Coil Units

Two parallel-connected fan coil units were utilised as terminal units of the GCHP. The total thermal power of these two fan coil units was 3.2 kW.

536

6.6.3.5

6 Heat Pumps for Sustainable Heating and Cooling

GCHP Data Acquisition System

The GCHP data acquisition system consists of the indoor and outdoor air temperature, supply/return temperature, heat source temperature (outlet BHE temperature), DHW temperature, relative air humidity and main operating parameters of the system components.

6.6.4 Measuring Apparatus Two thermal energy metres were used to measure the thermal energy produced by the GCHP and the extracted/injected thermal energy to the ground. A thermal energy meter was built with a heat computer, two PT500 temperature sensors and an ultrasonic mass flow meter. The two PT500 wires temperature sensors with an accuracy of ±0.15 °C were used to measure the supply and return temperature for a hydraulic circuit (the water-antifreeze solution circuit or the fan coil circuit). Also, an ultrasonic mass flow meter was used to measure the mass flow rate for a hydraulic circuit. The thermal energy metres were AEM metres, model LUXTERM, with a signal converter IP 67 and accuracy 4, and the GCHP system operating in heating or cooling and DHW mode had a 3 < COPsys < 4 for both cases. 3. In classical and optimised adjustment cases, the COPhp values for heating and DHW provision tests were 3.81 and 3.95, respectively and for heating operation tests, they were 4.82 and 5.06, respectively. 4. When using the circulating pump speed control, electricity savings and a reduction of the CO2 emission of 3% for laboratory heating and 5% for laboratory cooling were obtained at the same time as DHW production. 5. If the GCHP is used to produce only DHW for a family at different temperatures between 40 and 60 °C, then the COPhp would decrease to approximately 2, and the CO2 emission level would vary between 6.11 and 13.16 kg. 6. For an instantaneously consumed hot water volume, the energy performance of the GCHP can be decreased by up to 23% when the hot water temperature in DHW tank must be increased to 25 °C. 7. The developed TRNSYS simulation models can be used as a tool to determine the GCHP performance in different operation modes to optimise the system energy efficiency and ensure the user’s comfort throughout the year. 8. A limitation of this study is that the optimised solution for regulating the flow rate of heat-carrying fluid using a buffer tank and an automatic control device of the circulation pump speed is applicable only to residential buildings. 9. In order to possibly improve the energy efficiency of the GCHP system, in-depth research is needed in the future, aimed at integrating solar photovoltaic collectors into the system, which will produce electricity to drive the circulation pump in the water pumping process.

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Chapter 7

Thermal Energy Storage

Abstract This chapter is focused on the analysis of TES technologies that provides a way of valorising solar heat and reducing the energy demand of buildings. The principles of several energy storage methods and calculation of storage capacities are described. Sensible heat storage technologies, including the use of water, underground and packed-bed are briefly reviewed. Latent heat storage (LHS) systems associated with phase change materials (PCMs) and thermo-chemical storage, as well as cool thermal energy storage are also discussed. Finally, an abridged version of the comprehensive review published on the development of LHS systems focused on heat transfer and enhancement techniques employed in PCMs to effectively charge and discharge latent heat energy, and the formulation of the phase change problem are provided.

7.1 Generalities The recent projections predict that the primary energy consumption will rise by 48% in 2040 [1]. The achievement of Europe’s climate energy targets, which are included in the European Commission Energy Roadmap 2050, is made possible by using energy storage technology [2]. On the other hand, the depletion of fossil resources in addition to their negative impact on the environment had accelerated the shift towards sustainable energy sources. Renewable energy sources (RES) like solar radiation, ocean waves, wind, biogas, etc. have been playing a major role in reforming the natural balance and providing the needs of growing population demand [3]. However, due to the climatic vagaries, means to store these types of RES have become urgent [4]. These reasons lead to the need of developing efficient and sustainable methods of storing energy. The use of thermal energy storage (TES) in the energy system allows to conserving energy and increase the overall efficiency of the systems. Energy storage has become an important part in renewable energy technology systems such as solar systems. TES is a technology that stocks thermal energy by heating or cooling a storage medium so that the stored energy can be used at a later time for heating and cooling applications [5] and power generation. TES systems © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 I. Sarbu, Advances in Building Services Engineering, https://doi.org/10.1007/978-3-030-64781-0_7

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7 Thermal Energy Storage

are used particularly in buildings and industrial processes. Advantages of using TES in an energy system are the increase of the overall efficiency and better reliability, but it can also lead to better economics, reducing investment and running costs and less pollution of the environment, i.e. fewer carbon dioxide (CO2 ) emissions [6]. Solar thermal systems, unlike photovoltaic systems with striving efficiencies, are industrially matured, and utilise major part of sun’s thermal energy during the day. Yet, it does not have enough (thermal) backup to keep operating during the low or no solar radiation hours. TES is becoming particularly important for electricity storage in combination with concentrating solar power (CSP) plants where solar heat can be stored for electricity production when sunlight is not available. In Europe, it has been estimated that around 1.4 million GWh/year could be saved and 400 million tons of CO2 emissions avoided, in the building and industrial sectors by more extensive use of heat and cold storage [7]. Storage density, in terms of the amount of energy per unit of volume or mass, is an important issue for applications in order to optimise a solar ratio (how much of the solar radiation is useful for the heating/cooling purposes), efficiency of the appliances (solar thermal collectors and absorption chillers) and energy consumption for space heating/cooling. For these reasons, it is worth to investigate the possibility of using phase change materials (PCMs) in solar system applications. The potential of PCMs is to increase the energy density of small-sized water storage tanks, reducing solar storage volume for a given solar fraction or increasing the solar fraction for a given available volume [8]. It is possible to think of thermal storage in the hot and/or in the cold side of the plant. The former allows the storage of hot water from the collectors (and from the auxiliary heater) to be supplied to the generator of the absorption chiller (in cooling mode) or directly to the users (in heating mode). The latter allows the storage of cold water produced by the absorption chiller to be supplied to the cooling terminals inside the building. It is usual to identify the three situations just described as, respectively, “hot”, “warm”, and “cold” storage because of the different temperature ranges. Typically, a hot tank may work at 80–90 °C, a warm tank at 40–50 °C and a cold tank at 7–15 °C [9]. While heat storages in the hot side of solar plants are always present because of heating and/or domestic hot water (DHW) production, cold storages are justified in bigger size plants. Cold storages are used not only to get economic advantages from the electricity tariffs (in case of electric compression chiller) depending on the time-of-the-day but also to lower cooling power installed and to allow more continuous operation of the chiller [10]. Support for research and development (R&D) of new storage materials, as well as policy measures and investment incentives for TES integration in buildings, industrial applications and variable renewable power generation, is essential to foster its deployment. This chapter is focused on the analysis of TES technologies that provides a way of valorising solar heat and reducing the energy demand of buildings [11– 13]. The principles of several energy storage methods and calculation of storage capacities are described. Sensible heat storage (SHS) technologies, including the use of water, under-ground and packed-bed are briefly reviewed. Latent heat storage

7.1 Generalities

561

(LHS) systems associated with PCMs and thermochemical storage (TCS), as well as cool thermal energy storage are also discussed. Finally, an abridged version of the comprehensive review published by Sarbu and Dorca [13] on the development of LHS systems focused on heat transfer and enhancement techniques employed in PCMs to effectively charge and discharge latent heat energy, and the formulation of the phase change problem is provided.

7.2 An Overview of Thermal Energy Storage This section provides an overview of the main TES technologies, including SHS, LHS associated with PCMs, TCS and cool thermal energy storage (CTES) systems [11].

7.2.1 Classification and Characteristics of Storage Systems The main types of thermal energy storage of solar energy are presented in Fig. 7.1. An energy storage system can be described in terms of the following characteristics: • Capacity defines the energy stored in the system and depends on the storage process, the medium and the size of the system; • Power defines how fast the energy stored in the system can be discharged (and charged);

Fig. 7.1 Types of thermal energy storage of solar energy

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7 Thermal Energy Storage

• Efficiency is the ratio of the energy provided to the user to the energy needed to charge the storage system. It accounts for the energy loss during the storage period and the charging/discharging cycle; • Storage period defines how long the energy is stored and lasts hours to months (i.e., hours, days, weeks, and months for seasonal storage); • Charge and discharge time defines how much time is needed to charge/discharge the system; and • Cost refers to either capacity (e/kWh) or power (e/kW) of the storage system and depends on the capital and operation costs of the storage equipment and its lifetime (i.e., the number of cycles). Capacity, power and discharge time are interdependent variables and in some storage systems, capacity and power can also depend on each other. Typical parameters for TES systems are shown in Table 7.1 [14], including capacity, power, efficiency, storage period and cost. High-energy storage density and high power capacity for charging and discharging are desirable properties of any storage system. It is well known that there are three methods for TES at temperatures from—40 °C to more than 400 °C: sensible heat, latent heat associated with PCMs, and thermo-chemical storage associated with chemical reactions (Fig. 7.2) [15]. The choice of storage medium depends on the nature of the process. For water heating, energy storage as sensible heat of stored water is logical. If air-heating collectors are used, storage in sensible or latent heat effects in particulate storage Table 7.1 Typical parameters of TES systems TES system

Capacity (kWh/t)

Power (MW)

Efficiency (%)

Storage period

Cost (e/kWh)

Sensible (hot water)

10–50

0.001–10

50–90

Days/months

0.1–10

PCM

50–150

0.001–1

75–90

Hours/months

10–50

Chemical reactions

120–250

0.01–1

75–100

Hours/days

8–100

Fig. 7.2 Methods of thermal energy storage: a sensible heat; b latent heat; c thermochemical reactions

7.2 An Overview of Thermal Energy Storage

563

units is indicated, such as sensible heat in a pebble-bed heat exchanger. In passive heating, storage is provided as sensible heat in building the elements. If photovoltaic or photochemical processes are used, storage is logically in the form of chemical energy.

7.2.2 Sensible Heat Storage Sensible heat storage (SHS) (Fig. 7.2a) is the simplest method based on storing thermal energy by heating or cooling a liquid or solid storage medium (e.g., water, sand, molten salts, or rocks), with water being the cheapest option. The most popular and commercial heat storage medium is water, which has a number of residential and industrial applications. Underground storage of sensible heat in both liquid and solid media is also used for typically large-scale applications. SHS has two main advantages: it is cheap and without the risks derived from the use of toxic materials. SHS system utilises the heat capacity and the change in temperature of the storage medium during the process of charging and discharging. The amount of heat stored depends on the specific heat of the medium, the temperature change and the amount of storage material [16]. tf Qs =

mcp dt = mcp (tf − ti )

(7.2.1)

t

where: Qs is the quantity of heat stored, in J; m is the mass of heat storage medium, in kg; cp is the specific heat, in J/(kg·K); t i is the initial temperature, in °C; t f is the final temperature, in °C. The SHS capacity of some selected solid-liquid materials is shown in Table 7.2. Water appears to be the best SHS liquid available because it is inexpensive and has a high specific heat. However above 100 °C, oils, molten salts and liquid metals, etc. are used. For air-heating applications rock bed-type storage materials are used. Table 7.3 shows the main characteristics of the most commonly used solid state thermal storage materials [17], including sand-rock minerals, concrete, fire bricks and ferroalloy materials. These materials have working temperatures from 200 °C to 1200 °C, and have excellent thermal conductivities: 1.0–7.0 W/(m·K) for sandrock minerals, concrete and fire bricks, 37.0–40.0 W/(m·K) for ferroalloy materials. The materials shown in Table 7.3 are all low cost, ranging from 0.05 to 5.00 $/kg. The only disadvantage is their heat capacities being rather low, ranging from 0.56 to 1.3 kJ/(kg·°C), which can make the storage unit unrealistically large.

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Table 7.2 List of selected solid-liquid materials for sensible heat storage Medium

Fluid type

Temperature range (°C)

Density (kg/m3 )

Specific heat (J/(kg·K))

Rock

–

20

2560

879

Brick

–

20

1600

840

Concrete

–

20

1900–2300

880

Water

–

0–100

1000

4190

Calorie HT43

Oil

12–260

867

2200

Engine oil

Oil

≤160

888

1880

Ethanol

Organic liquid

≤78

790

2400

Propane

Organic liquid

≤97

800

2500

Butane

Organic liquid

≤118

809

2400

Isotunaol

Organic liquid

≤100

808

3000

Isopentanol

Organic liquid

≤148

831

2200

Octane

Organic liquid

≤126

704

2400

Table 7.3 Solid state sensible heat storage materials Storage materials

Working temperature (°C)

Density (kg/m3 )

Thermal conductivity (W/(m K))

Specific heat (kJ/(kg·°C))

Sand-rock minerals

200–300

1700

1.0

1.30

Reinforced concrete

200–400

2200

1.5

0.85

Cast iron

200–400

7200

37.0

0.56

NaCl

200–500

2160

7.0

0.85

Cast steel

200–700

7800

40.0

0.60

Silica fire bricks 200–700

1820

1.5

1.00

Magnesia fire bricks

3000

5.0

1.15

7.2.2.1

200–1200

Water Tank Storage

The use of hot water tanks is a well-known technology for thermal energy storage. Hot water tanks serve the purpose of energy saving in water heating systems based on solar energy and in co-generation (i.e., heat and power) energy supply systems. State-of the-art projects [18] have shown that water tank storage is a cost-effective storage option and that its efficiency can be further improved by ensuring optimal water stratification in the tank and highly effective thermal insulation. Today’s R&D

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565

Fig. 7.3 A typical system using water tank storage

activities focus, for example, on evacuated super-insulation with a thermal conductivity of 0.01 W/(mK) at 90 °C and 0.1 mbar and on optimised system integration. A typical system in which a water tank is used is shown in Fig. 7.3. The energy storage capacity of a water (or other liquid) storage unit at uniform temperature (i.e., fully mixed, or no stratified) operating over a finite temperature difference is given by Eq. (7.2.1) redefined as Qs = mcp ts

(7.2.2)

where Qs is the total heat capacity for a cycle operating through the temperature range t s and m, cp is the mass and the specific heat, respectively of water in the unit. The temperature range over which such a unit can operate is limited at the lower extreme for most applications by the requirements of the process. The upper limit may be determined by the process, the vapour pressure of the liquid, or the collector heat loss. An energy balance on the no stratified tank is mcp

dts = Qu − QL − Us As (ti − ta ) dτ

(7.2.3)

where: Qu and QL are rates of addition or removal of energy from the collector and to the load; U s is the heat loss coefficient of storage tank; As is the storage tank surface area; t a is the ambient temperature for the tank; τ is the time. Equation (7.2.3) is to be integrated over time to determine the long-term performance of the storage unit and the solar process. Useful long-term analytical solutions are not possible due to the complex time dependence of some of the terms. There are many possible numerical integration methods. Using simple Euler integration is usually satisfactory (i.e., rewriting the temperature derivative as (t s -t i )/τ and solving for the tank temperature at the end of a time increment): ts = ti +

 τ  Qu − QL − Us As (ti − ta ) mcp

(7.2.4)

Equation (7.2.4) can be used to predict water storage temperature as a function of time. Once the tank temperature is known, other temperature-dependent quantities can be estimated.

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7 Thermal Energy Storage

Fig. 7.4 Schematic of a solar combisystem with solar collectors and a boiler charging water storage tank

Hot water storage systems used as buffer storage for DHW supply are usually in the range of 500 L to several cubic metres (m3 ). This technology is also used in solar thermal installations for DHW combined with building heating systems (combisystems). Large hot water tanks are used for seasonal storage of solar thermal heat in combination with small district heating systems. These systems can have a volume up to several thousand cubic metres. Charging temperatures are in the range of 80–90 °C. The usable temperature difference can be enhanced by the use of heat pumps for discharging (down to temperatures around 10 °C). A more complex system with tank storage is shown in Fig. 7.4; a solar combisystem where water store is the central part. The so called combistore is charged with solar collectors and a second heating source, for example, a bio-fuel or gas boiler, and heat is extracted to two heat sinks of very different characteristics: DHW and space heating [19]. Solar combisystems including combistores were also the topic of the European project Combisol, whose goal was the promotion and standardisation of solar combisystems in Europe [20]. High specific heat capacity, wide availability, chemically stability and low cost make water a good storage media suitable for low-temperature solar cooling applications (e.g., single stage absorption chillers and desiccant systems). Due to the boiling point constraint (100 °C at 1 bar), use of water as SHS medium for high-temperature application (double effect and triple effect chillers) requires increasing the system pressure [21].

7.2 An Overview of Thermal Energy Storage

7.2.2.2

567

Underground Storage

Underground thermal energy storage (UTES) is also a widely used storage technology, which makes use of the ground (e.g., the soil, sand, rocks, and clay) as a storage medium for both heat and cold storage. Means must be provided to add energy to and remove it from the medium. This is done by pumping heat transfer fluids (HTFs) through pipe arrays in the ground. The pipes may be vertical U-tubes inserted in wells (boreholes) that are spaced at appropriate intervals in the storage field or they may be horizontal pipes buried in trenches. The rates of charging and discharging are limited by the area of the pipe arrays and the rates of heat transfer through the ground surrounding the pipes. If the storage medium is porous, energy transport may occur by evaporation and condensation and by movement of water through the medium, and a complete analysis of such a store must include consideration of both heat and mass transfers. These storage systems are usually not insulated, although insulation may be provided at the ground surface. Boreholes (ground heat exchangers) are also frequently used in combination with heat pumps where the ground heat exchanger extracts low-temperature heat from the soil. Aquifer storage is closely related to ground storage, except that the primary storage medium is water, which flows at low rates through the ground. Water is pumped out of and into the ground to heat it and extract energy from it. Water flow also provides a mechanism for heat exchange with the ground itself. As a practical matter, aquifers cannot be insulated. Only aquifers that have low natural flow rates through the storage field can be used. A further limitation may be in chemical reactions of heated water with the ground materials. Aquifers, as with ground storage, operate over smaller temperature ranges than water stores. Most applications deal with the storage of winter cold to be used for the cooling of large office buildings and industrial processes in the summer. Cavern storage and pit storage are based on large underground water reservoirs created in the subsoil to serve as TES systems. Caverns are the same in their principles of operation as the tanks discussed in previous section. Energy is added to or removed from the store by pumping water into or out of the storage unit. The major difference will be in the mechanisms for heat loss and possible thermal coupling with the ground. These storage options are technically feasible, but applications are limited because of the high investment costs. For high-temperature (i.e., above 100 °C) SHS, the technology of choice is based on the use of liquids (e.g., oil or molten salts, the latter for temperatures up to 550 °C). For very high temperatures, solid materials (e.g., ceramics, concrete) are also taken into consideration. However, most of such high-temperature-sensible TES options are still under development or demonstration.

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7.2.2.3

7 Thermal Energy Storage

Pebble-Bed Storage

A pebble-bed (packed-bed) storage unit uses the heat capacity of a bed of loosely packed particulate material to store energy. A fluid, usually air, is circulated through the bed to add or remove energy. A variety of solids may be used, rock and pebble being the most widely used materials. A pebble-bed storage unit is shown in Fig. 7.5. In operation, flow is maintained through the bed in one direction during addition of heat (usually downward) and in the opposite direction during removal of heat. Note that heat cannot be added and removed at the same time; this is in contrast to water storage systems, where simultaneous addition to and removal from storage is possible. A major advantage of a packed-bed storage unit is its high degree of stratification. The pebbles near the entrance are heated, but the temperature of the pebbles near the exit remains unchanged and the exit-air temperature remains very close to the initial bed temperature. As time progresses a temperature front passes through the bed. When the bed is fully charged, its temperature is uniform. A packed-bed in a solar heating system does not normally operate with constant inlet temperature. During the day, the variable solar radiation, ambient temperature, collector inlet temperature, load requirements and other time-dependent conditions result in a variable collector outlet temperature. Many studies are available on the heating and cooling of packed beds. The first analytical study was by Schumann [22] and the basic assumptions leading to this model are one-dimensional plug flow, no axial conduction or dispersion, constant properties, no mass transfer, no heat loss to the environment and no temperature gradients within the solid particles. The differential equations for the fluid and bed temperatures (t f , t b ) are: ρf cp,f ε

Fig. 7.5 Pebble-bed storage system

mf cp,f ∂tf ∂tf =− + kv (tb − tf ) ∂τ A ∂x

(7.2.5)

7.2 An Overview of Thermal Energy Storage

ρb cp,b (1 − ε)

569

∂tb = kv (tf − tb ) ∂τ

(7.2.6)

where: ρf is the fluid density; cp,f is the specific heat of fluid; ε is the bed void fraction; mf is the fluid mass; A is the bed cross-sectional area; k v is the volumetric (per unit bed volume) heat transfer coefficient between the bed and the fluid; and τ is the time. For an air-based system, the first term on the left-hand side of Eq. (7.2.5) can be neglected and the equations can be written as [23]: ∂tf = NTU (tb − tf ) ∂(x/L)

(7.2.7)

∂tb = NTU (tf − tb ) ∂Θ

(7.2.8)

NTU =

kv AL mf cp,f

(7.2.9)

and the dimensionless time is Θ=

τ mf cp,f ρb cp,b (1 − ε)AL

(7.2.10)

where: A is the bed cross-sectional area; L is the bed length; NTU is the effectiveness. Analytical solutions to these equations exist for a step change in inlet conditions and for cyclic operation. For the long-term study of solar energy systems, these analytical solutions are not useful and numerical techniques as finite difference method must be employed.

7.2.3 Latent Heat Storage The energy storage density increases and hence the volume is reduced, in the case of LHS (Fig. 7.2b) comparatively with SHS (materials that don’t change phases). The heat is mainly stored in the phase change process (at a quite constant temperature) and it is directly connected to the latent heat of the substance. The use of a LHS system using PCMs is an effective way of storing thermal energy and has the advantages of high-energy storage density and the isothermal nature of the storage process. The main advantage of using LHS over SHS is their capacity of storing heat at almost similar temperature range. Initially, these materials act similar to SHS materials where the temperature rises linearly with the system enthalpy, but later, heat is absorbed or released at almost constant temperature with a change in physical state. LHS is based on the heat absorption or releases when a storage material undergoes a phase change from solid to liquid or liquid to gas or vice versa. The storage capacity Qs , in J, of the LHS system with a PCM medium [16] is given by

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7 Thermal Energy Storage

  Qs = m cps (tm − ti ) + f q + cpl (tf − tm )

(7.2.11)

where: t m is the melting temperature, in °C; m is the mass of PCM medium, in kg; cps is the average specific heat of the solid phase between t i and t m , in kJ/(kg K); cpl is the average specific heat of the liquid phase between t m and t f , in J/(kg K); f is the melt fraction; q is the latent heat of fusion, in J/kg. For example, Glauber’s salt (Na2 SO4· ·10H2 O) has cps ≈ 1950 J/(kg·°C), cpl ≈ 3550 J/(kg·°C) and q = 2.43 × 105 J/ kg at 34 °C. The measurement techniques presently used for latent heat of fusion and melting temperature of PCMs are: (1) differential thermal analysis (DTA), and (2) differential scanning calorimeter (DSC) [24]. As depicted in Fig. 7.1, the phase change process takes place in different modes: solid-solid, liquid-gas and solid-liquid. In the first case, heat is stored by transition between different kinds of crystallisation forms. For liquid-gas systems latent heat is very high, but there are some problems in the storage control due to the high volume variations during a phase change. The most widespread are the solid-liquid PCMs that have a limited volume variation during exchange (generally less than 10%) and a fairly high melting latent heat. Melting processes involve energy densities of 100 kWh/m3 (e.g., ice) compared to a typical 25 kWh/m3 for SHS options. PCMs can be used for both short-term (daily) and long-term (seasonal) energy storage, using a variety of techniques and materials. Possible applications of PCMs are: • implementation in gypsum board, plaster, concrete, or other wall-covering material being part of the building structure to enhance the TES capacity, with main utilisation in peak load shifting (and saving) and solar energy [25]. In this application typical operating temperature is 22–25 °C but it can vary as a function of climate and heating/cooling loads; • cold storage for cooling plants (operating temperature 5–18 °C) [26]; • warm storage for heating plants (45–60 °C) [27]; • hot storage for solar cooling and heating (>80 °C) [28]. 7.2.3.1

PCMs Used for Energy Storage in Buildings

Storage concepts applied to the building sector have been classified as active or passive systems [29]. Passive thermal energy systems can enhance effectively the naturally available heat energy sources in order to maintain the comfort conditions in buildings and minimise the use of mechanically assisted heating or cooling systems [30]. The use of active thermal energy systems provides a high degree of control of the indoor conditions and improves the way of storing heat energy. These systems are usually integrated in buildings to provide free cooling or to shift the thermal load from on-peak to off-peak conditions in several applications, such as DHW applications [31] or heating, ventilation and air-conditioning (HVAC) systems [32].

7.2 An Overview of Thermal Energy Storage

571

Fig. 7.6 Schematics of a storage Trombe wall

• Passive technologies. The use of thermal energy storage as passive technology has the objective to provide thermal comfort with the minimum use of HVAC energy. When high thermal-mass materials are used in buildings, passive sensible storage is the technology that allows the storage of high quantity of energy, giving thermal stability inside the building. Materials typically used are rammed earth, alveolar bricks, concrete, or stone. Standard solar walls, also known as Trombe walls, and solar water walls also use sensible storage to achieve energy savings in buildings [33]. Trombe wall (Fig. 7.6) is a wall with high thermal capacity, shielded by a glass pane. A greenhouse effect is created, reducing thermal losses from the wall, heating the air between wall and glass that can be introduced into the room with a natural draught due to the chimney effect of the heated air. The temperature of the wall increases as energy is absorbed, and time-dependent temperature gradients are established in the wall. Energy is lost through the glazing and is transferred from the room side of the wall to the room by radiation and convection. This storage wall can be considered as a set of N nodes connected together by a thermal network, each with a temperature and capacitance [34]. Heat is transferred by radiation across the gap and by convection between air flowing in the gap and the absorbing surface and the inner glazing. Energy balances are written for each node of thickness x, resulting in a set of ordinary differential equations with terms that represent its time-dependent temperature and energy flows to all adjacent nodes. The general energy balance for any node i in the wall is λ dti = (ti−1 + ti+1 − 2ti ), i = 2, . . . , N − 1 dτ ρcp x2

(7.2.12)

where: λ is the thermal conductivity of wall; ρ is the wall density; cp is the specific heat of wall; and τ is the time.

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7 Thermal Energy Storage

Equations for nodes 1 and N must take into account the node half-thickness and the convection and radiation heat transfer. The set of N equations are simultaneously solved for the time-dependent temperatures at each of the nodes, and from this the energy stored in the wall (relative to a base temperature t room ) can be calculated. If there is air flow through vents and to the room, the energy added to the room by this mechanism will be ma cp,a (t o −t r ), where t o is the outer glazing temperature and t r is the room temperature. PCM can be incorporated in construction materials using different methods, such as direct incorporation, immersion, encapsulation, micro-encapsulation and shapestabilisation. A new approach in PCM wallboards is the addition of an aluminium honeycomb in a containing micro-encapsulated PCM wallboard (Fig. 7.7) [35]. Another approach to incorporate PCM in building walls is its mixture with insulation materials. In masonry wall, the PCM incorporation can be, for example, within clay bricks (Fig. 7.8) [36]. • Active technologies. The use of thermal energy storage in building active systems is an attractive and versatile solution for several applications for new or Fig. 7.7 Micro-encapsulated PCM honeycomb wallboard

Fig. 7.8 Clay bricks including PCM macro-capsules

7.2 An Overview of Thermal Energy Storage

573

Fig. 7.9 Operational mode of the ventilated facade with PCM

retrofitted buildings, such as the implementation of RES in the HVAC for space heating/cooling, the improvement in the performance of the current installations or the possible application of peak load shifting strategies [37]. The integration of the TES in the building can be done using the core of the building (core, floor, walls), in external solar facades, in suspended ceilings, ventilation systems, PV systems and water tanks. Moreover, the thermal energy storage of solar energy in active building systems is extended to integrate solar air collectors in building walls or use PCM in ventilated facades (Fig. 7.9) [38].

7.2.3.2

TES for Concentrated Solar Power Plants

Concentrated solar power (CSP) systems use mirrors to concentrate sunlight from a large area to a small area where it is absorbed and converted to heat at high temperatures. The high-temperature heat is then used to drive a power block (usually a steam turbine connected to an electrical power generator) similar to the power block of a conventional thermal power plant. A major advantage of CSP plants over solar photovoltaic power plants is that CSP plants may be coupled with conventional fuels and can utilise TES to overcome the intermittency of solar energy. Several TES technologies that have been implemented for CSP plants are mainly two-tank and single-tank systems. In a two-tank system, the fluid is stored in two tanks, one at a high temperature and the other at a low temperature. Fluid from the low-temperature tank flows through the solar collector or receiver, where solar energy heats it to a high temperature and it then flows to the high-temperature tank for storage. Fluid from the high-temperature tank flows through a heat exchanger, where it generates steam for electricity production. The fluid exits the heat exchanger at a low temperature and returns to the low-temperature tank. These systems are called two-tank direct systems. An indirect system, on the other hand, uses different fluids for heat transfer and storage. An indirect system is used in plants in which the heat transfer fluid (HTF) is too expensive or not suited for use as the storage fluid. The storage fluid from the low-temperature tank flows through an extra heat exchanger, where it is heated by the high-temperature HTF. The high-temperature

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7 Thermal Energy Storage

Fig. 7.10 Schematic of a parabolic trough power plant with two-tank molten salt storage

storage fluid then flows back to the high-temperature storage tank. The fluid exits this heat exchanger at a low temperature and returns to the solar collector or receiver, where it is heated back to a high temperature. Storage fluid from the high-temperature tank is used to generate steam in the same manner as the two-tank direct system. Figure 7.10 shows a two-tank TES system integrated into a parabolic trough power plant [39]. Single-tank systems, mostly thermocline systems store thermal energy in a solid medium, most commonly silica sand, in a single tank. At any time during operation, the top part of the medium is at high temperature, and the bottom part is at low temperature. The hot- and cold-temperature regions are separated by a temperature gradient or thermocline. High-temperature HTF flows into the top of the thermocline and exits the bottom at low temperature. This process moves the thermocline downward and adds thermal energy to the system for storage. Reversing the flow moves the thermocline upward and removes thermal energy from the system to generate steam. Buoyancy effects create thermal stratification of the fluid within the tank, which helps to stabilise and maintain the thermocline. Using a solid storage medium and only needing one tank reduces the cost of this system relative to the two-tank systems. This system was demonstrated at the Solar One central receiver CSP system in California, where steam was used as the HTF and mineral oil was used as the storage fluid.

7.2 An Overview of Thermal Energy Storage

575

7.2.4 Chemical Energy Storage The TCS uses thermochemical materials (TCM) that store and release heat by a reversible endothermic/exothermic reaction process (Fig. 7.2c). During the charging process, heat is applied to the material A, resulting in a separation of two parts B + C. The resulting reaction products can be easily separated and stored until the discharge process is required. Then, the two parts B + C are mixed at a suitable pressure and temperature conditions and energy is released. The products B and C can be stored separately, and thermal losses from the storage units are restricted to sensible heat effects, which are usually smalls compared to heats of reaction. Thermal decomposition of metal oxides for energy storage has been considered by Simmons [40]. These reactions may have the advantage that the oxygen evolved can be used for other purposes or discarded and oxygen from the atmosphere used in the reverse reactions. Two examples are the decomposition of potassium oxide 4KO2 ↔ 2K2 O + 3O2 which occurs over a temperature range of 300–800 °C with a heat of decomposition of 2.1 MJ/kg, and lead oxide, 2PbO2 ↔ 2PbO + O2 which occurs over a temperature range of 300-350 °C with a heat of decomposition of 0.26 MJ/ kg. There are many practical problems yet to be faced in the use of these reactions. Energy storage by thermal decomposition of Ca(OH)2 has been extensively studied by Fujii et al. [41]. The reaction is Ca(OH)2 ↔ CaO + H2 O. The forward reaction will proceed at temperatures above about 450 °C; the rates of reaction can be enhanced by the addition of zinc or aluminium. The product CaO is stored in the absence of water. The reverse exothermic reaction proceeds easily. An example of a photochemical decomposition reaction is the decomposition of nitrosyl chloride, which can be written as NOCl + photons → NO + Cl The atomic chlorine produced forms chlorine gas, Cl2 , with the release of a substantial part of the energy added to the NOCl in decomposition. Thus the overall reaction is 2NOCl + photons → 2NO + Cl2 The reverse reaction can be carried out to recover part of the energy of the photons entering the reaction.

576

7 Thermal Energy Storage

Table 7.4 Some chemical reactions for thermal energy storage Reaction

Temperature (°C)

Energy density (kJ/kg)

Methane steam reforming

CH4 + H2 O = CO + 3H2

480–1195

6053

Ammonia dissociation

2NH3 = N2 + 3H2

400–500

3940

Thermal dehydrogenation of metal hydrides

MgH2 = Mg + H2

200–500

3079 (heat); 9000 (H2 )

Dehydration of metal CA(OH)2 = CAO + hydroxides H2 O

402–572

1415

Catalytic dissociation SO3 = SO2 + ½O2

520–960

1235

Processes that produce electrical energy may have storage provided as chemical energy in electrical storage batteries or their equivalent. Thermo-chemical reactions, such as adsorption (i.e., adhesion of a substance to the surface of another solid or liquid), can be used to store heat and cold, as well as to control humidity. The high storage capacity of sorption processes also allows thermal energy transportation. Table 7.4 lists some of the most interesting chemical reactions for TES [42]. While sorption storages can only work up to temperatures of about 350 °C, chemical reactions can go much higher.

7.2.5 Cool Thermal Energy Storage The CTES has recently attracted increasing interest in industrial refrigeration applications, such as process cooling, food preservation and building air-conditioning systems. CTES appears to be one of the most appropriate methods for correcting the mismatch that occurs between the supply and demand of energy. Cool energy storage requires a better insulation tank as the energy available in the cool state is expensive, compared to the heat available in a hot storage tank. Cheralathan et al. [43] investigated the performance of an industrial refrigeration system integrated with CTES. The researchers have indicated significant savings in capital and operating cost, in thermal storage integrated systems. The size of the PCM-based CTES system was also considerably reduced when compared with that of a chilled water system. The sorption phenomenon can also be applied for TES. In that case, a heat source promotes the dissociation (endothermic process) of a working pair, whose substances can be stored separately. When they come into contact again, heat is released (exothermic process). Therefore, the energy can then be stored with virtually no loss because the heat is not stored in a sensible or latent form but rather as potential energy, as long as the substances are kept separate.

7.2 An Overview of Thermal Energy Storage

577

Fig. 7.11 Seasonal adsorption thermal storage system

Adsorption TES is a promising technology that can provide an excellent solution for long-term TES in a more compact and efficient way. Solar thermal energy or waste heat from several processes can be used to regenerate the adsorbent and promote the energy storage [44]. The adsorption cycle has already been used in several research projects to promote thermal energy storage. In 1990, Kaubek and Maier-Laxhuber [45] patented an adsorption apparatus to be used as an electro-heating storage, working with the zeolite/water pair and reporting a 30% savings in energy consumption. The system can be used as an air-heating device or combined with a hot water tank. Hauer [46] presented a seasonal adsorption thermal energy storage system, working with the silica gel/water pair (Fig. 7.11). During the summer, while the system is charging, the heat from the solar collectors is conducted to three adsorbent beds, promoting the desorption stage. In the winter, the low temperatures in the solar collector promote the evaporation of the water in the evaporators/condensers, and the heat of adsorption is released to the building heating system. A cascade storage system offers vast potential for the improvement of a solar cooling system performance. In a cascaded storage system, PCMs with different melting temperatures are arranged in a series to store heat in different temperatures. In comparison with a conventional single PCM-based storage system, a cascaded multiple PCM-based storage system would improve solar collecting efficiency as the lower temperature at the bottom of the tank is connected to the inlet of the solar collector. The numerical results from the parametric study investigated by Shaikh and Lafdi [47] indicated that the total energy charged rate can be significantly enhanced by using composite PCMs as compared to the single PCM. Figure 7.12 shows the different TES technologies: sensible heat (i.e., water as an example); latent heat (i.e., different materials); and thermo-chemical (i.e., sorption and chemical reactions).

578

7 Thermal Energy Storage

Fig. 7.12 Storage capacity depending on temperature for TES

7.2.6 Conclusions and Future Trends SHS is applicable to domestic systems, district heating and industrial needs. The most popular and commercial heat storage medium is water, which has a number of residential and industrial applications. Underground storage of sensible heat in both liquid and solid media is also used for typically large-scale applications. However, TES systems based on SHS offer a storage capacity that is limited by the specific heat of the storage medium. Furthermore, SHS systems require proper design to discharge thermal energy at constant temperatures. PCMs can offer a higher storage capacity that is associated with the latent heat of the phase change. TCS can offer even higher storage capacities. Thermo-chemical reactions such as adsorption can be used to accumulate and discharge heat and cold on demand, as well as to control humidity in a variety of applications using different chemical reactants. At present, TES systems based on sensible heat are commercially available while TCS and PCM-based storage systems are mostly under development and demonstration. In CTES, materials with subzero temperatures are identified, but their thermal reliability, phase segregation and subcooling issues are not deeply studied. Studies on industrial (large scale) level thermal cold storage PCMs are hardly tested. Support for R&D of new storage materials, as well as investment incentives for TES integration in buildings, industrial applications and variable renewable power generation is essential to foster its deployment. In future greenhouses, TES solutions can combine heating–cooling-dehumidification functions and provide polygeneration possibilities. Further research on the possibility of TCS and better development of PCM is needed for this option to be widely adopted in a more cost-effective manner.

7.3 Heat Transfer Analysis in TES Using LHS Systems and PCMs

579

7.3 Heat Transfer Analysis in TES Using LHS Systems and PCMs 7.3.1 Preliminary Considerations TES has recently attracted increasing interest to thermal applications such as space and water heating, waste heat utilisation, cooling and air-conditioning. Energy storage is essential whenever there is a mismatch between the supply and consumption of energy [48, 49]. Various TES techniques have been developed over the past four decades. TES can be achieved through three distinct ways: sensible, latent, or thermochemical heat storage. The classification of energy storage and the materials used are detailed by Sarbu and Sebarchievici [50]. In the sensible heat storage (SHS), the temperature of the storage material increases as the energy is stored, whereas the latent heat storage (LHS) makes use of the energy stored when a substance changes from one phase to another. The internal energy increases when energy in the form of heat is added to a substance. The well-known consequence is an increase in temperature (sensible heating) or change in phase (latent heating). LHS may be classified based on the phase change process as solid-solid, solidliquid, solid-gas and liquid-gas. Solid-gas and liquid-gas transformations are generally not employed for energy storage despite their high latent heats, because gases occupy large volumes. In solid–solid transitions, heat stored as the material is transformed from one crystalline form to another. These transitions generally have small latent heats making such materials less desirable. LHS by solid-liquid phase transition is a particularly attractive technique as it provides a high-energy storage density. Moreover, it has the capacity to store energy as latent heat of fusion at a constant temperature corresponding to the phase transition temperature of the phase change material (PCM). Hence, it can potentially lower the cost [51]. The temperature of the PCM remains nearly constant during melting (charging) and solidification (discharging), which is desirable. PCMs used for the storage of thermal energy as latent heat are special types of advanced materials, which substantially contribute to the efficient use and conservation of waste heat and solar energy. The study of PCMs was pioneered by Telkes and Raymond [52]; however, PCMs did not receive much attention until the energy crisis in the early 1980s, when they were extensively researched for use in different applications especially for solar heating systems [53–56]. The LHS, using PCMs, is in full development. Towards 2030 the intention is to have industrial process heat applications with TES [57]. The use of PCMs is one of the novel methods that have been proposed to achieve the objective of high storage density with higher efficiency. PCMs have been widely used in LHS systems for heat pumps, solar engineering and spacecraft thermal control applications. The use of PCMs for heating and cooling applications in buildings has been investigated in the past decade [58]. There are many PCMs that melt and solidify at a wide range of temperatures, making them attractive for many applications. A

580

7 Thermal Energy Storage

proper design of TES systems using PCMs requires quantitative information on the heat transfer and phase change processes in the PCM. This section provides a comprehensive theoretical study on the development of LHS systems focused on heat transfer and enhancement techniques employed in PCMs to effectively charge and discharge latent heat energy, and the formulation of the phase change problem [13]. The main categories of PCMs are classified and briefly described, including the main characteristic properties and selection criteria. The heat transfer enhancement technologies, namely dispersion of low-density materials, use of porous materials, metal matrices and encapsulation, incorporation of extended surfaces and fins, utilisation of heat pipes (HPs), cascaded storage and direct heat transfer techniques, are also discussed in detail. Additionally, a twodimensional heat transfer simulation model of an LHS system is developed using the control volume technique to solve the phase change problem. Furthermore, a three-dimensional numerical simulation model of an LHS is built to investigate the quasi-steady state and transient heat transfer in PCMs and several future research directions are provided.

7.3.2 Latent Heat Thermal Energy Storage LHS materials are known as PCMs because of their property of releasing or absorbing energy with a change in physical state. The energy storage density increases and hence, the volume is reduced in the case of LHS. The main advantage of LHS over SHS is the high storage density within a small temperature band. Figure 7.13 gives a comparison between a SHS system and a LHS system made of a single PCM. For the small temperature difference covering the phase change, there is a factor of 3 between the heat stored in the LHS system and the SHS system. For a large temperature difference, the advantage of the LHS shrinks to 6:4 = 1.5 [17]. The heat storage capacity Q, in J, of an LHS system is given by [49, 58, 59]: Fig. 7.13 Comparison of stored heat between SHS and LHS with a single PCM

7.3 Heat Transfer Analysis in TES Using LHS Systems and PCMs



tm

Q= ti

 Mcp dt + MfL +

581

tf

Mcp dt

(7.3.1)

tm

where t m is the melting temperature, in °C; t i is the initial temperature, in °C; t f is the final temperature, in °C; M is the mass of PCM medium, in kg; cp is the specific heat capacity, in J/(kg·°C); f is the melt fraction; and L is the latent heat of fusion, in J/kg. In contrast to SHS in which the materials have a large temperature rise/drop when storing/releasing thermal energy, LHS can work in a nearly isothermal way, owing to the phase change mechanism. This makes LHS favourable for applications that require stringent working temperature requirements. However, the main disadvantage of LHS is its low thermal conductivity, which mostly falls in the range of 0.2-0.7 W/(m·K); therefore, effective heat transfer enhancement technologies must be adopted [60].

7.3.2.1

System Components

A LHS system consists of the following three main components: 1. a PCM suitable for the desired temperature range; 2. container for the PCM (encapsulation of PCM); 3. heat exchange surface area for transferring heat from the heat source to the PCM and from the PCM to the heat sink. The integration of LHS containers into specific heating or cooling systems can be classified according to the heat transfer fluid (HTF) used, i.e. air or liquid. The LHS containers could be integrated in conventional central heating systems with water radiators when the HTF used is water; this is ideal to retrofit when changing a gas boiler to a heat pump (Fig. 7.14a) [61]. The LHS containers can be integrated into centralised ventilation systems when the HTF used is air, typical in large office areas and commercial buildings [62] (Fig. 7.14b).

Fig. 7.14 Schematic of the integration of LHS into water space heating systems (a) and centralised air space heating systems (b)

582

7 Thermal Energy Storage

Fig. 7.15 Cross sections of a compact tube in tube (a), an encapsulated packed-bed (b) and encapsulated staggered cylinders (c) LHS containers

Most LHS containers can be classified into two groups: compact and encapsulated. Figure 7.15 shows the cross sections for three different types of LHS containers suitable to be integrated with heating systems. In compact LHS systems, the PCM is enclosed in a large container with an embedded heat exchanger. The general configuration used is the shell-and-tube type (Fig. 7.15a). Compact LHS systems are generally designed to integrate with water heating systems. Encapsulated systems (Fig. 7.15b, c) are those in which the PCM is contained in small containers, over which the HTF flows, leading to a heat storage system that contains a greater component of SHS than compact LHS systems in the same temperature range. Such encapsulated models have the versatility to be integrated with both air and water heating systems, owing to their shape versatility and leak proof construction.

7.3.2.2

Phase Change Materials

Many PCMs are known to melt with a high heat of fusion in any required temperature range. However, their use as heat storage material depends on the desirable characteristics related to • thermo-physical properties (latent heat of transition and thermal conductivity should be high, and density and volume variations during phase transition should be, respectively, high and low in order to minimise storage volume),

7.3 Heat Transfer Analysis in TES Using LHS Systems and PCMs

583

Table 7.5 Main desirable characteristics of PCMs Thermal properties

Kinetic properties

Chemical properties

Economics

(1) Melting (1) Small vapour tem-perature in pressure at desired operating opera-ting range temperatures

(1) Little or no super-cooling during freezing

(1) Chemical stability

(1) Abundant

(2) High latent heat (2) Small volume of fusion per unit variation on volume phase change

(2) High nucleation rate to avoid super-cooling

(2) Complete reversible freezing/melting cycle

(2) Large-scale availabilities

(3) High specific heat

(3) Adequate rate of crystallisation

(3) Compatibility with container materials

(3) Effective cost

(4) High thermal conductivity of both phases

Physical properties

(3) High density

(4) No toxic, no flammable and no explosive material

• kinetic and chemical properties (super-cooling should be limited to a few degrees, and materials should have long-term chemical stability, compatibility with materials of construction, no toxicity, and no fire hazard), and • economic advantages (low cost and large-scale availability of PCMs are also very important). The main characteristics required for PCMs are indicated in Table 7.5 [49]. PCMs can be used for both short-term (daily) and long-term (seasonal) energy storage, using various techniques and materials. • Classification. LHS materials are broadly classified based on their physical transformation for heat absorbing and desorbing capabilities. Several authors have carried out investigations on a wide range of PCMs, subdividing them into organic, inorganic and eutectics [49]. PCMs are classified into different groups depending on the material nature (paraffin, fatty acids, salt hydrates, etc.) (Figure 7.16). A comparison of the advantages and disadvantages of different categories of PCMs is presented in Table 7.6 [51]. Organic PCMs can melt and solidify many times without phase segregation, and because of the degradation of their latent melting heat, they crystallise with little or no super-cooling, and they are usually non-corrosive. The two main groups are as follows: 1. Paraffin waxes: they consist of a mixture of mostly straight chain n-alkenes CH3 – (CH2 )–CH3 . The crystallisation of the (CH3 )- chain releases a large amount of latent heat. Both the melting point and latent heat of fusion increase with chain length. Owing to cost consideration, however, only technical grade paraffin’s could be used as PCMs in LHS systems. Paraffin is safe, reliable, predictable, less expensive, non-corrosive and available in a large temperature range (5–80 °C) [49].

584

7 Thermal Energy Storage

Fig. 7.16 Classification of phase change materials Table 7.6 Comparison of different categories of PCMs Classification

Advantages

Disadvantages

Organic PCMs

Availability in a large temperature range

Low thermal conductivity

High heat of fusion

Relative large volume change

No super-cooling

Flammability

Non-corrosive Chemically stable and recyclable Good compatibility with other materials Inorganic PCMs

High heat of fusion

Super-cooling

High thermal conductivity

Corrosion

Low volume change Availability in low cost Eutectics

Sharp melting temperature High volumetric thermal storage density

Lack of currently available test data of thermo-physical properties

7.3 Heat Transfer Analysis in TES Using LHS Systems and PCMs

585

2. Non-paraffin organic PCMs: they are the most numerous of the PCMs with highly varied properties. A number of esters, fatty acids, alcohols and glycols suitable for energy storage have been identified [63]. Some of the main features of these organic materials include high heat of fusion, inflammability, low thermal conductivity, low flash points and instability at high temperatures. Fatty acids have a high heat of fusion compared to paraffin’s, and they have reproducible melting and freezing behaviours with little or no super-cooling. However, fatty acids are more expensive than technical grade paraffin’s, and they are mildly corrosive and possess an unpleasant odour [49]. Inorganic PCMs are used in high-temperature solar applications and one of their most reported challenges is maintenance. At low temperatures, they freeze and at high temperatures, they are difficult to handle. These PCMs do not super-cool appreciably and their melting enthalpies do not degrade with cycling. The two main types are as follows: 1. Salt hydrate with the general formula AB·nH2 O are alloys of inorganic salts (AB) containing n kmol of water of crystallisation. During phase transformation, dehydration of the salt occurs, forming either a salt hydrate that contains fewer water molecules: AB · nH2 O → AB · mH2 O + (n − m)H2 O

(7.3.2)

or to its anhydrous form: AB · nH2 O → AB + nH2 O

(7.3.3)

Salt hydrate melting is classified as congruent, incongruent and semi-congruent [59]: • congruent melting occurs when the salt is soluble in the hydration water at the melting temperature; • incongruent melting occurs when the salt is only partially soluble in the hydration water at the melting temperature; • semi-congruent melting occurs when the solid and liquid phases that are in equilibrium have different compositions during the melting process because of the transformation of the salt hydrate to a salt hydrate with a lesser amount of hydration water. Salt hydrates have been extensively studied in heat storage applications [64] because of their positive characteristics: high latent heat of fusion per unit volume, relatively high thermal conductivity (almost double that of paraffin), low corrosiveness and compatibility with plastics. These materials dissociate into anhydrous salts, release water vapour when subjected to a heat source and store the energy supplied for dehydration upon heating. A numerical study was conducted to investigate the performance of three different salt hydrates, namely magnesium sulphate (MgSO4 ·7H2 O),

586

7 Thermal Energy Storage

cupric sulphate (CuSO4 ·5H2 O) and gypsum (CaSO4 ·2H2 O), to investigate their abilities to efficiently store thermochemical energy. It was shown that cupric sulphate had the highest efficiency and required the least heating time to initiate a chemical reaction. 2. Metallic PCMs include low-melting point metals and their alloys. This category offers the potential for high-density and high-temperature thermal energy storage. Metallic PCMs have high thermal conductivity, which relate to high charging and discharging rates in TES systems, and they can operate at temperatures exceeding 560 °C. They also have high thermal diffusivity, which eliminates the need for large heat exchange surfaces. As noted by Kenisarin [65], the two most important material properties of PCMs are the melting temperature and heat of fusion. By plotting the melting temperature and heat of fusion of each material on a chart (Fig. 7.17), it is possible to select the PCM with the most favourable characteristics for the design. The largest phase transition heat, on a mass or volume basis, has been found for binary and ternary alloys of the relatively plentiful elements Al, Cu, Mg and Zn, but not all of the potential materials are suitable for use in TES systems [66]. Huang et al. [67] determined the specific heat of the liquid and solid forms and the latent heat of fusion of Al–Si, Al–Si-Mg and Al–Si-Cu alloys. In a study performed by Kotzé et al. [68] a eutectic aluminium-silicon alloy, AlSi12 is identified as a good potential PCM. AlSi12 has a heat of fusion of 560 J/g and a melting temperature of 577 °C, which is above the working temperature of regular HTFs.

Fig. 7.17 Latent heats and melting temperatures of metallic PCMs

7.3 Heat Transfer Analysis in TES Using LHS Systems and PCMs

587

Eutectics materials are combinations of two or more low-melting point materials with similar (congruent) melting and freezing points; eutectics nearly always melt and freeze without segregation and have high thermal conductivities and densities. The weight percentage of each material can be varied to obtain different melting points of the resulting eutectic mixture [49]. For this reason, they are a promising type of PCM for the future, even if they are actually less diffused than the other groups. However, they have low latent and specific heat capacities [69]. The temperature range is one of the main criteria for the suitability of a PCM in any application. There are numerous thermal energy storage applications that use PCM, which all fit a particular range suitable for their optimum thermal performance. Figure 7.18 shows a brief classification system based on melting temperatures, which can help in deciding which PCM to use [70] based on the desired application. • Thermo-physical properties. Table 7.7 presents the thermo-physical properties of organic compounds identified based on quoted stability and enthalpy of phase change, whereas Table 7.8 summarises the thermo-physical properties for a selection of salt hydrates [15, 25]. Table 7.9 presents the physical properties of selected eutectic compounds in the 0–250 °C range [61, 71]. Owing to the lack of experimental data for some of the thermo-physical properties of eutectic mixtures, weighting methods have been used to predict missing values [75, 76]. The weighting correlations used to obtain the thermo-physical properties, namely melting enthalpy (h), specific heat capacity (cp ), thermal conductivity (λ) and density (ρ), are presented in Eqs. (7.3.4)–(7.3.9), which use available properties of the mixture and its constituents, molar ratio (x i ), molecular mass (M i ), mass ratio (wi ), volumetric ratio (zi ), and their melting point (t m ) to predict the unknown values. A comparison of some eutectic salts with available experimental data was made; the difference between predictions and measurements was less than 10% [61]. Fig. 7.18 Category of PCM based on melting point

588

7 Thermal Energy Storage

Table 7.7 Thermo-physical properties of selected organic compounds Compound

Melting point (°C)

Melting enthalpy (kJ/kg)

Specific heat (kJ/(kg·K))

Thermal conductivity (W/(m·K))

Density (kg/m3 )

Refs.

Solid

Liquid

Solid

Liquid

Formic acid

8

277

1.00

1.17

0.30

0.27

1227

[71]

Acetic acid

17

192

1.33

2.04

Lauric acid

44

212

2.02

2.15

0.26

0.19

1214

[71]

0.22

0.15

1007

[71] [72]

Stearic acid

54

157

1.76

2.27

0.29

0.17

940

Palmitic acid

61

222

1.69

2.20

0.21

0.17

989

[71]

Parrafin wax

0–90

150–250

3.00

2.00

0.20

–

880–950

[71]

Acetamide

82

260

2.00

3.00

0.40

0.25

1160

[71]

Erythritol

117

340

2.25

2.61

0.73

0.33

1450

[72]

HDPE

130

255

2.60

2.15

0.48

0.44

952

[71] [72]

Urea

134

250

1.80

2.11

0.80

0.60

1320

Maleic acid

141

385

1.17

2.08

–

–

1590

[72]

d-Mannitol

165

300

1.31

2.36

0.19

0.11

1490

[73]

Hydroquinone

172

258

1.59

1.64

–

–

1300

[71]

wi = xi Mi

 

−1 xi Mi

(7.3.4)

i

 −1 wi  wi zi = ρi ρi i

(7.3.5)

cp,eutectic =

cp,i wi

(7.3.6)

ρi zi

(7.3.7)

λzi i

(7.3.8)

 i

ρeutectic =

 i

λeutectic =

 i

heutectic = tm,eutectic

 hi wi i

tm,i

(7.3.9)

• Measurement of thermal properties of PCMs. The methods used for measuring the thermal properties of PCMs are very important. There are many existing measurement techniques, among which, the differential scanning calorimetry (DSC) and differential thermal analysis (DTA) are the most commonly used. In DSC and DTA techniques, a sample and a reference material are heated at constant rate. The

7.3 Heat Transfer Analysis in TES Using LHS Systems and PCMs

589

Table 7.8 Thermo-physical properties of selected salt hydrates Compound

Melting point (°C)

Melting enthalpy (kJ/kg)

Specific heat (kJ/(kg·K))

Thermal conductivity (W/(m·K))

Density (kg/m3 )

Refs.

Solid

Liquid

Solid

Liquid

Water

0

333

3.30

4.18

1.60

0.61

920

[71]

Calcium chloride hexahydrate

30

125

1.42

2.20

1.09

0.53

1710

[71]

Sodium sulphate decahydrate

32

180

1.93

2.80

0.56

0.45

1485

[71]

Sodium thiosulfate pentahydrate

46

210

1.46

2.39

0.76

0.38

1666

[71]

Sodium acetate trihydrate

58

265

1.68

2.37

0.43

0.34

1450

[71]

Barium hydroxide octahydrate

78

280

1.34

2.44

1.26

0.66

2180

[71]

Magnesium nitrate hexahydrate

89

140

2.50

3.10

0.65

0.50

1640

[71]

Oxalic acid dihydrate

105

264

2.11

2.89

0.90

0.70

1653

[72]

Magnesium chloride hexahydrate

117

150

2.00

2.40

0.70

0.58

1570

[71]

temperature difference between them is proportional to the difference in heat flow between the two materials and is recorded as the DSC curve. The recommended reference material is alumina (Al2 O3 ). The latent heat of fusion is calculated using the area under the peak and the melting temperature is estimated by the tangent at the point of greatest slope on the face portion of the peak. The DSC method can also be used for analysing the thermal properties of PCM wallboards. Through a DSC test, the melting temperature and heat of fusion of a PCM can be obtained. In addition, the distribution of PCM in the wallboard, heat storage capacity of the PCM wallboard, and effect of multiple thermal cycling on the thermal properties of PCMs can be tested. • Criteria for PCM selection. When developing a TES system, the selection of a PCM is an important task, and the selected PCM must fit the requirements of the system. The melting temperature and phase change enthalpy of existing PCMs are shown in Fig. 7.19 [77]. In building applications, as an example, PCMs

14–86

82–18

71–29

85–15

15–85

77–23

90–10

89–11

56–44

53–6–41

48–52

62–38

58–42

45–50–5

LiNO3 MgNO3 ·(H2 O)6

Urea-LiNO3

Urea-NaNO3

Urea-NH4 Cl

Urea-K2 CO3

Urea-KNO3

Urea-NaCl

Urea-KCl

KNO3 –NaNO2

KNO3 –NaNO3 –NaNO2

KNO2 -NaNO3

LiNO3 –NaNO2

LiNO3 –KCl

LiNO3 –NaNO3 –KCl

38–62

Urea-acetamide

59–41

61–39

Mg(NO3 )2 ·(H2 O)6 NH4 NO3

83–17

60–40

Urea CH3 COONa·(H2 O)3

Stearic acid–acetamide

67–33

CaCl2 ·(H2 O)6 MgCl2 ·(H2 O)6

Mg(NO3 )2 ·(H2 O)6 -MgCl2 ·(H2 O)6

Mass ratio

Compound

160

160

156

149

142

141

115

112

109

102

102

83

76

72

65

59

53

52

30

25

266

272

233

124

110

97

227

230

195

206

214

187

218

180

213

132

224

125

200

127

Melting point Melting (°C) enthalpy (kJ/kg)

Table 7.9 Thermo-physical properties of selected eutectic compounds

1320

1260

1570

1050

1170

1180

1690

1720

1600

1660

1770

1600

1770

2380

1800

2290

1920

2130

1750

1690

1350

1910

1630

1730

1740

1960

2020

1910

2020

2090

2030

2020

2900

2400

2810

2660

2670

2210

0.880

1.310

1.120

0.580

0.720

0.730

0.830

0.820

0.810

0.780

0.760

0.750

0.850

0.700

0.300

0.670

0.510

0.590

0.630

0.930

0.590

0.590

0.660

0.520

0.570

0.570

0.660

0.600

0.580

0.580

0.580

0.590

0.600

0.510

0.180

0.530

0.340

0.500

0.480

0.550

Liquid

Solid

2270

Liquid

Solid 1620

Thermal conduct. (W/(m·K))

Specific heat (kJ/(kg·K))

2297

2196

2296

2080

2006

1994

1370

1372

1416

1415

1348

1502

1438

1713

972

1610

1216

1672

1370

1661

Density (kg/m3 )

(continued)

[61]

[71]

[61]

[74]

[74]

[74]

[61]

[61]

[61]

[61]

[61]

[61]

[49]

[61]

[61]

[71]

[51]

[59]

[59]

[71]

Refs.

590 7 Thermal Energy Storage

49–51

87–13

80–20

55–45

27–73

6–67–27

55–45

13–87

9–91

86–14

LiNO3 –NaCl

KNO3 -KOH

KNO3 –NaNO3

LiBr–LiNO3

LiOH–NaNO3 –NaOH

NaNO2 –NaNO3

CaCl2 –LiNO3

LiCl–LiNO3

NaNO3 –NaOH

19–81

LiOH–LiNO3

LiNO3 –NaNO3

Mass ratio

Compound

Table 7.9 (continued)

250

244

238

233

230

228

222

214

208

194

183

160

342

317

163

184

279

110

83

369

262

352

Melting point Melting (°C) enthalpy (kJ/kg)

1350

1190

1580

1500

1310

1300

1340

1010

1030

1540

1720

1860

1610

1530

2130

2000

1380

1490

1350

1560

0.660

1.370

1.370

0.590

0.780

1.140

0.730

0.880

1.350

0.870

1.330

0.600

0.640

0.690

0.640

0.670

0.570

0.510

0.540

0.630

0.590

0.690

Liquid

Solid

2000

Liquid

Solid 1600

Thermal conduct. (W/(m·K))

Specific heat (kJ/(kg·K))

2241

2351

2362

2210

2154

2603

2028

1905

2350

2317

2124

Density (kg/m3 )

[71]

[61]

[61]

[61]

[61]

[74]

[61]

[71]

[71]

[74]

[74]

Refs.

7.3 Heat Transfer Analysis in TES Using LHS Systems and PCMs 591

592

7 Thermal Energy Storage

Fig. 7.19 Melting temperature and phase change enthalpy for existing PCMs

with a phase change temperature range of 18–30 °C are preferred to meet the requirements of thermal comfort. From the point of melting temperature, it can be observed that for LHS in building applications, the potential PCMs are paraffin, fatty acids, salt hydrates and eutectic mixtures. Zalba et al. [51], Abhat [63], and Jegadheeswaran et al. [78] described the main criteria that govern the selection of a PCM. To be a suitable material for LHS systems, the following criteria, namely physical, kinetic, chemical and economic properties, need to be met (Table 7.5). A visual combination of important thermal properties (Fig. 7.20) of a few types of PCMs was produced by Li et al. [79]. • Long-term stability. Insufficient long-term stability of the storage materials and containers is a problem that has limited the widespread use of LHS. Long-term stability of PCMs is required in practical applications of LHS; therefore, major changes in their thermal properties after undergoing numerous thermal cycles should not occur. Thermal cycling tests to check the stability of PCMs in LHS systems were carried out by many researchers for organics, salt hydrates and salt hydrate mixtures [80, 81]. Some potential PCMs were identified to have good stability and thermo-physical properties. Recently, Shukla et al. [82] carried out thermal cycling tests for some organic and inorganic PCMs and their results showed that organic PCMs tend to have better thermal stabilities than inorganic PCMs.

7.3 Heat Transfer Analysis in TES Using LHS Systems and PCMs

593

Fig. 7.20 Thermal properties of various PCMs

7.3.2.3

Heat Transfer Enhancement Technologies

There are several methods of enhancing the heat transfer in a latent heat thermal storage: thermal conductivity enhancement using low-density materials such as carbon fibres and paraffin composites [78], porous materials either as a metal foam (copper, steel or aluminium) or as porous material like graphite [83], metal matrices [84], and encapsulation methods using graphite, polymers, or the nickel film coating of PCM copper spheres [85]; enhancement with fins (extended metal surface) [86], HPs [87], and cascaded storage (multiple PCMs) [78]; and direct heat transfer techniques [88]. The most common enhancement techniques involve the use of extended surfaces such as fins and HPs or using multiple PCMs of different melting points [89]. The general review of some these techniques was performed by Ibrahim et al. [89], which revealed that enhancement in heat transfer can be accomplished either by increasing the heat transfer area of the storage system or by increasing the thermal conductivity of the storage material. The reasons behind this selection are the result of the detailed assessment, which summarises as given below.

594

7 Thermal Energy Storage

Fig. 7.21 Use of carbon fibres to enhance heat transfer: a fibre cloth, b fibre brush, c no carbon fibre

7.3.2.4

Low-Density Materials

To enhance the heat transfer in TES systems, the insertion of high thermal conductivity materials including metal structures has been tested [90]. Metal structures possess relatively high densities, and this usually leads to their settlement at the bottom surface of the PCM container. Hence, many researchers consider other alternatives such as low-density and high-conductivity additives for PCMs. Carbon fibres can be better alternatives to enhance the thermal performance of LHS systems as they have relatively lower densities than metals, and the thermal conductivities are almost equal to those of aluminium and copper [78]. Carbon fibres also exhibit a high corrosive resistance potential and hence are compatible with most PCMs. Nakaso et al. [91] tested the use of carbon fibres to enhance heat transfer in thermal storage tanks, reporting a twofold rise in effective thermal conductivities. Their carbon cloths and carbon brushes are shown in Fig. 7.21. Frusteri et al. [92] randomly dispersed carbon fibres of different lengths into an inorganic PCM to increase its thermal conductivity. Their results indicated that the composite PCM-fibre had enhanced heat diffusion. Sanusi et al. [93] investigated the thermal performance of a paraffin/graphite nanofiber (GNF) composite PCM during the solidification period. They found that impregnating GNF into paraffin-based PCMs is an effective means for reducing its solidification time and enhancing the TES.

7.3.2.5

Porous Materials

Incorporation of porous materials to PCMs increases their thermal conductivity and hence improves the thermal performance of LHS systems [83]. This is primarily due to the higher thermal conductivity of porous materials compared to pure PCMs. Paraffin/expanded graphite (EG) composites were introduced, and they can be made to incorporate even more carbon. Sari and Karaipekli [94] compared two samples: the first made from pure paraffin and the second from a paraffin/EG composite. They found that the paraffin/EG composites with mass fractions of 2%, 4%, 7% and 10% EG had increased their effective thermal conductivities by 81.2%,

7.3 Heat Transfer Analysis in TES Using LHS Systems and PCMs

595

136.3%, 209.1% and 272.7%, respectively. However, the main disadvantage of EG is its structural discontinuity, which means that heat cannot be transferred very smoothly and efficiently. Zhou and Zhao [95] investigated the heat transfer enhancement of PCMs by using EG and metal foams. They found that both increased the heat transfer rate significantly, but metal foams showed a better performance than EG. The reason is that the structures inside the EG are sparse, whereas metal foams have a much more continuous matrix than EG, which means that heat can be easily transferred to PCMs. Lafdi et al. [96] studied experimentally the heat transfer characteristics of a paraffin wax/aluminium foam composite PCM and investigated the effect of the foam porosity and pore size on the melting rate of the PCM. The results indicated that the higher porosity aluminium foam accelerates the attainment of a steady state temperature as compared with the foams with lower porosity. Li and Wu [97] conducted a numerical investigation on the thermal behaviour of sodium nitrate (NaNO3 ) as a PCM using the computational fluid dynamics (CFD) software FLUENT. Fleming et al. [98] compared the thermal performance of two shell-and-tube LHS units, with one composed of aluminium foam. The experimental results showed that the foam significantly increased the heat transfer during both melting and solidification in terms of the overall heat transfer coefficient.

7.3.2.6

Metal Matrices

A metal matrix, such as a porous matrix, has been used to enhance the heat transfer rate in TES. A porous matrix is characterised by two parameters, i.e. the porosity and the cell size which refer respectively to the percentage of volume that will be occupied by PCM and the size of the pore, expressed in pores per inch. For the first parameter, Mesalhy et al. [99] indicated that the performance improvement depends on both the porosity of the matrix and its conductivity. Low values of porosity lead to a higher effective thermal conductivity, resulting in an increased performance enhancement. However, a decrease in the porosity has the opposite effect because the low porosity of the matrix hampers the movement of the liquid PCM and the natural convection. For the second parameter, Elgafy et al. [100] showed how the mean pore size of the additives could be of critical importance on the system performance. If it is too small, the PCM molecular motion will be hindered, thereby it will be very difficult to impregnate the porous media with the PCM, which will adversely affect the LHS capacity. Metals with the highest thermal conductivities are silver, copper, gold and aluminium, which turn them into a desirable option for metal matrix production to LHS systems. Their characteristics are given in Table 7.10 [101]. Due to their lower prices in comparison with gold and silver, copper and aluminium are most commonly used. Steel wool is more feasible for improving the thermal conductivity of PCMs compared to EG. However, it is not as compactable as graphite.

596

7 Thermal Energy Storage

Table 7.10 Metals with high thermal conductivities Metal

Melting point (°C)

Specific heat (J/(kg·K))

Thermal conductivity (W/(m·K))

Density (kg/m3 )

Silver

961.9

237

429.0

10490

Copper

1084.6

381

387.6

8978

Gold

1064.4

129

401.0

19300

660.2

910

237.0

2800

1450.0

440

90.3

8910

Aluminium Nickel

7.3.2.7

Encapsulation

The encapsulation method for heat transfer enhancement consists of confining the PCM as a core covered by a shell of another type of material. The classification of encapsulation techniques is dependent on the size of the capsules: macro-encapsulation (1–10 mm), micro-encapsulation (1–1000 μm), and nanoencapsulation ( 2200)

(7.3.13)

All correlations showed the same general trend with small differences in values recorded for the lower Reynolds numbers in the turbulent regime. The major deviations increased with the increase in Nusselt and Reynolds numbers.

7.3.3.2

Phase Change Problem Formulation

• Moving boundary condition. In addition to the fixed boundaries of the PCM domain, the phase change process of PCMs involves moving the boundary between phases and is generally known as the Stefan or moving boundary condition. Melting and solidification are the two thermal processes for LHS systems. Melting occurs when a solid PCM receives and absorbs heat energy, which represents the actual storage. Recovery of the latent heat energy from the PCM is accomplished through solidification (freezing) of the liquid. The PCM phase transition proceeds from a solid to a mushy state and then to a liquid state during the melting process and vice versa during the solidification process. The heat transfer mechanisms associated with the melting and solidification processes can be either conduction- or convection-controlled (natural convection in most situations) or simultaneous conduction/convection-controlled. The main difficulty in solving liquid-solid phase change problems lies in the Stephan condition [155]. The numerical treatment of the moving boundary condition can be used to classify numerical methods for melting problems into deforming and fixed grid schemes [156]. In deforming grid schemes the position of the interface is determined by rearranging the mesh, whereas in fixed grid schemes the phase boundary is not explicitly tracked. Instead, an additional variable called the phase fraction is introduced. It is expressed as a function of the temperature or the enthalpy and determines the position of the phase boundary. The problem of predicting the behaviour of phase change systems is difficult due to its inherent non-linear nature at moving interfaces, for which displacement rate is controlled by the latent heat lost or absorbed at the boundary. The following energy equation, known as the Stephan condition, describes this transition process [49, 85, 155]: ρL

δts δtl ds(τ ) = λs − λl dτ δτ δτ

(7.3.14)

where ρ is the density of PCM (it is not specified if it is solid or liquid); L is the latent heat of fusion of PCM; s(τ ) is the surface position; λs and λl are the thermal

608

7 Thermal Energy Storage

conductivities of the solid and liquid PCM respectively; t s and t l are the solid and liquid phase temperatures respectively; and τ is the time. Boundary integral methods are very convenient to use for the solution of Stephan condition. In these methods, nodal points are located only on the boundaries and move together with the phase change interface. This means that there is no need for any mesh adjustment. For multidimensional problems, mesh adjustment is necessary but much easier to perform than in standard domain methods. Shamsundar and Sparrow [157] demonstrated the equivalence between the energy conservation equation applied in three zones (solid, liquid, and solid/liquid) and the enthalpy formulation method. These are solved through a finite difference method and the solidification is analysed in a square plate cooled by convection. This method is applicable for both phase change in a single temperature and phase change in a range of temperatures (mixtures or alloys). Meyer [158] studied the problem of phase change conduction, establishing that the classic Stefan problem implies the resolution of the temperature range and carrying out a review and comparison of explicit and implicit methods. Hunter [159] confirmed that the enthalpy formulation method is the most suitable for real substances on the condition that there is no alteration to the numerical scheme in the boundary. • Energy conservation equation forms. The analysis of heat transfer problems in phase change processes is complex because the solid-liquid boundary moves depending on the speed at which the latent heat is absorbed or lost at the boundary. Solutions to phase change problems include analytical, experimental and numerical using one-, two-, or three-dimensional models to solve the energy conservation equation, which is formulated in various ways with the phase change being considered in different representations. Examples of some formulations by various researchers are given below: • Solomon [146]:  a ∂ ∂t ∂t = w rw ; r(τ ) ≤ r ≤ l; t = tcr ; r ≤ r(τ ) ∂τ r ∂r ∂r

(7.3.15)

⎧ ⎪ ⎨ 0 for a PCM slab insulated at one end in which 1 + w = lA/V with w = 1 for a PCM cylinder ⎪ ⎩ 2 for a PCM sphere where r is the radius, in m and t cr is the critical temperature, in °C or K. • Lacroix [160]:   ∂h 1 ∂ ∂k ∂ ∂k ∂f = ar + a − ρL ∂τ r ∂r ∂r ∂z ∂z ∂τ

(7.3.16)

7.3 Heat Transfer Analysis in TES Using LHS Systems and PCMs

609

t with phase change: H(t) = h(t) + ρl f (t)L, where h(t) = tm ρcp dt, f (t) is the liquid fraction of melted PCM, t m is the melting temperature, in K, and r, z are the radial and axial coordinates, in m, respectively. • Gong and Mujumdar [161]:  ρHTF cp,HTF

∂tHTF ∂tHTF +υ ∂τ ∂x

=

4k ∂ 2 tHTF (tPCM − tHTF ) + λHTF d ∂x2

(7.3.17)

and   1 ∂ ∂ ∂tPCM ∂tPCM ∂hPCM = λPCM r + λPCM ∂τ r ∂r ∂r ∂x ∂x

(7.3.18)

where x and r are the axial and radial coordinates. • Morrison and Abdel-Khalik [162]: Solid phase of PCM: ∂u UP λ s ∂ 2 ts + = (tHTF − ts ) ∂τ ρs ∂x2 ρs A

(7.3.19)

where u, t s , λs and ρs are the specific internal energy, temperature, thermal conductivity and density of PCM respectively; t HTF , U, and P are the HTF temperature, overall heat transfer coefficient between the fluid and PCM, and wetted perimeter respectively. Heat transfer fluid: m UP ∂tHTF ∂tHTF + = (ts − tHTF ) ∂τ ρHTF AHTF ∂x ρHTF AHTF cp,HTF

(7.3.20)

where m, ρHTF , AHTF and cp,HTF are the mass flow rate, density, flow area and specific heat of fluid, respectively. It has been shown that axial conduction during flow is negligible and if the fluid capacitance is small, Eqs. (7.3.19) and (7.3.20) become [23]: ∂u = NTU (ts − tHTF ); ∂Θ

∂tHTF = NTU (tHTF − ts ) ∂(x/l)

(7.3.21)

with ratio = τmcp,HTF / ρs Al and effectiveness NTU = UPl/ (mcp,HTF ), where A is the cross-sectional area of the material, in m2 and l is the length in the flow direction, in m.

610

7 Thermal Energy Storage

• Verlaj et al. [163]: ρ

  1 ∂ ∂t 1 ∂ λ ∂t ∂H = λr + ∂τ r ∂r ∂r r ∂θ r ∂θ

(7.3.22)

with phase change formula: – solid region (t ≤ t m − ε): H = cp t, – interface (t m − ε ≤ t ≤ t m + ε): H = cp t + (L/2ε)t − t m + ε, – and liquid region (t ≥ t m + ε): H = cp t + L, where r is the radial coordinate, θ is the angular coordinate, and ε is the remittance. • Faden et al. [164]:

cp

∂t + cp ∇( ut) − ∇ · ∂τ



λ ∇t ρ



 ∂f = −L + ∇( uf ) ∂t

(7.3.23)

where: cp is the mixture heat capacity, in J/(kg K); t is the temperature, in K; τ is the time, in s; u is the velocity vector, in m/s; λ is the mixture thermal conductivity, in W/(m K); ρ is the mixture density, in kg/m3 ; L is the latent heat of fusion, in J/kg; and f is the phase fraction.

7.3.3.3

Mathematical Modelling and Numerical Simulation of LHS Systems

Generally, the heat transfer analysis of phase change problems is much more complex than single-phase problems owing to (1) non-linearity of the problem due to the motion of the solid-liquid interface during phase change, (2) inadequate knowledge of the heat transfer process at the solid-liquid interface because of buoyancy-driven natural convection in the liquid, (3) uncertainty of the interface thermal resistance between the container and the solid PCM, (4) volume change with change in phase and (5) the presence and configuration of holes in a solid. The enthalpy formulation method is the most suitable for typical applications under the restriction that there is no alteration to the numerical scheme at the interface. This method is one of the most popular fixed-domain methods for solving the phase change problem. The major advantage is that the method does not require explicit treatment of the moving boundary.

7.3 Heat Transfer Analysis in TES Using LHS Systems and PCMs

611

1. Two-dimensional heat transfer simulation model Enthalpy formulation. Enthalpy function h, defined as a function of temperature, is given by Voller [165]. For a phase change process, the energy conservation can be expressed mathematically in terms of the total volumetric enthalpy and temperature for constant thermo-physical properties, as follows [122, 166, 167]: ∂H = ∇(λk (∇t)) ∂τ

(7.3.24)

where H is the total volumetric enthalpy, in J/m3 ; τ is the time, in s; λk is the thermal conductivity of phase k in PCM, in W/(m·K); and t is the temperature, in K. The total volumetric enthalpy is the sum of the sensible and latent heat of PCM [49]: H (t) = h(t) + ρl f (t)L

(7.3.25)

where h is the sensible volumetric enthalpy, in J/m3 ; ρl is the density of liquid PCM, in kg/m3 ; f is the melt fraction; and L is the latent heat of fusion, in J/kg. The sensible volumetric enthalpy is expressed as [167]:  h=

t

ρk ck dt

(7.3.26)

tm

where ρk is the density of phase k in PCM, in kg/m3 ; ck is the specific heat of phase k in PCM, in J/(kg K); t is the temperature, in K; and t m is the melting temperature, in K. In the case of isothermal phase change, the liquid fraction of melt is given by [166]: ⎧ if t < tm (solid) ⎪ ⎨ 0, if t = tm (mushy) (7.3.27) f = 0 − 1, ⎪ ⎩ 1, if t > tm (liquid) Using Eqs. (7.3.25) and (7.3.26), the enthalpy of PCM is  H=

t

ρs cs dt, t < tm (solid)

(7.3.28)

tm

H = ρl fL, t = tm (melting)  H=

t tm

ρl cl dt + ρl L, t > tm (liquid)

(7.3.29) (7.3.30)

612

7 Thermal Energy Storage

Solving Eqs. (7.3.28)–(7.3.30) for the PCM temperature, we obtain  H=

t

ρl cl dt + ρl L, t > tm (liquid)

(7.3.31)

tm

t = tm , 0 ≤ H ≤ ρl L (interface) t=

tm + (H − ρl L) , H > ρl L (liquid) ρl cl

(7.3.32) (7.3.33)

Using Eqs. (7.3.25) and (7.3.26), an alternative form of Eq. (7.3.24) for a twodimensional heat transfer in PCM can be obtained as   ∂ ∂h ∂ ∂h ∂f ∂h = α + α − ρl L (7.3.34) ∂τ ∂x ∂x ∂y ∂y ∂τ and for the heat exchanger container material, it is   ∂hf ∂hf ∂hf ∂ ∂ = αf + αf ∂τ ∂x ∂x ∂y ∂y

(7.3.35)

where τ is the time, in s; x and y are the space coordinates, in m; α is the thermal diffusivity of PCM, in m2 /s; αf is the thermal diffusivity of container material, in m2 /s; and hf is the sensible volumetric enthalpy of container material, in J/m3 . Numerical solution. The control volume discretisation technique developed by Voller [165] has been used to solve the energy conservation equation. The domain is divided into elementary control volumes and then the equation is integrated in these control volumes. Equation (7.3.34) is solved using a fully implicit finite difference method. The finite difference equation for PCM is obtained by integrating Eq. (7.3.29) over each control volume. The discretisation of Eq. (7.3.29) for x = y leads to the following scheme (Fig. 7.28): hP = hoP + αR(hE − 4hP + hW + hN + hS ) + ρl L(fPo − fPk )

(7.3.36)

aE hE + aW hW + aP hP + aN hN + aS hS = Q

(7.3.37)

aE = aW = aN = aS = −αR aP = 1 − aE − aW − aP − aN − aS

(7.3.38)

with

Q = hoP + ρl L(fPo − fPk ) , R =

dt (dx)2

(7.3.39)

7.3 Heat Transfer Analysis in TES Using LHS Systems and PCMs

613

Fig. 7.28 Two-dimensional domain

where hoP , fPo refer to the enthalpy and the melt fraction, respectively, from the previous time step and W, E, P, N, S are the west, east, centre, north and south nodes respectively. Equation (7.3.37) can be solved using a three-diagonal matrix algorithm. The basis feature of the present fixed grid enthalpy method is the source term Q, which keeps track of the latent heat evolution, and its driving element is the melt fraction. Its value is determined iteratively from the solution of the enthalpy equation. Hence, after the (k + 1)th numerical solution of the enthalpy equation of the Pth node, Eq. (7.3.37) could be rearranged as aP hP = −aE hE − aW hW − aN hN − aS hS + hoP + ρl L(fPo − fPk )

(7.3.40)

If phase change occurs about the Pth node (i.e., 0 ≤ f ≤ 1), the (k + 1)th estimate of the melt fraction needs to be updated such that the left side of Eq. (7.3.40) is zero, i.e. 0 = −aE hE − aW hW − aN hN − aS hS + hoP + ρl L(fPo − fPk )

(7.3.41)

Equation (7.3.41) could be rearranged as fPk+1 =

−aE hE − aW hW − aN hN − aS hS + hoP ρl L + fPo

(7.3.42)

The melt fraction update Eq. (7.3.42) is applied at every node after the (k + 1)th solution of Eq. (7.3.37) for sensible volumetric enthalpy h, along with under/over correction, i.e.

614

7 Thermal Energy Storage

 f =

0, if (f )k+1 ≤ 0 1, if (f )k+1 ≥ 1

(7.3.43)

Convergence at a given time step is declared when the difference in the total enthalpy fields falls below an admissible error, i.e.   k+1 H − H k ≤ω ρk ck

(7.3.44)

The typically value ω = 10−4 of admissible error was used. 2. Three-dimensional heat transfer simulation model Centralised LHS systems offer potential benefits in energy efficiency, load shifting and emergency heating/cooling load systems. This section reports the development of a mathematical model of a centralised finned LHS for analysing the thermal performance of the melting process for both quasi-steady state and transient conjugate heat transfer problems [168]. The model utilises a PCM technology that stores and retrieves energy at almost a constant temperature and is subjected to constant convective boundary conditions of free air stream based on a specific ventilation air flow rate. The numerical solution is conducted using the FLUENT software [169]. The numerical simulation results using paraffin RT20 are compared with available experimental data for cooling and heating of buildings. A numerical technique is employed to simulate the PCM heat transfer within a certain range of phase change temperature, which typically uses the enthalpy-porosity theory to deal with solid-liquid interface. In this method, a mixed solid-liquid phase region is present during the phase change. The region is described using a parameter called liquid fraction with a value which varies from 0 to 1. The porosity effect is found to be similar to that of the liquid volume fraction of the porous media at the mushy region [170]. Based on multiphase flow models such as the volume of fluid method (VFM), mixture and Euler model, only the VFM and solidification/melting model can be applied simultaneously. For simplicity, the following assumptions are considered: (1) The axial conduction and viscous dissipation in the fluid are negligible and are ignored. (2) The PCM and porous matrix material are considered homogeneous and isotropic. (3) The thermo-physical properties of the PCM and HTF are independent of temperature; however, the properties of the PCM could be different in the solid and liquid phases. (4) The PCM is considered at a single mean melting temperature t m . (5) The effect of radiation heat transfer is negligible.

7.3 Heat Transfer Analysis in TES Using LHS Systems and PCMs

615

Governing equations. The density and dynamic viscosity of the liquid PCM depend on its temperature. The density ρ of PCM, in kg/m3 , is approximated by [168]: ρ=

ρref βt (t − tm ) + 1

(7.3.45)

where ρref is the reference density of PCM at the melting temperature t m , and βt is the expansion factor. The value of βt = 0.001 K−1 can be selected. The dynamic viscosity μ of the liquid PCM, in kg/(m·s), can be calculated using the following equation:  1790 μ = exp −4.25 + t

(7.3.46)

where t is the temperature of PCM, in K. The energy equation is written in terms of the sensible enthalpy as follows [166]:  h=

t

cp dt

(7.3.47)

tref

or  λ ∂ρ h + div(ρ u¯ h) = div grad h + Qh ∂x cp

(7.3.48)

where h is the sensible enthalpy, in J/kg; u¯ = (u, v, w) is the velocity, in m/s; λ is the thermal conductivity, in W/(m·K); cp is the specific heat at constant pressure, in J/(kg·K); and Qh is the latent heat source term. To describe the fluid flow in the full liquid and mushy regions, the conservation equations of momentum and mass are required. In the enthalpy-porosity approach, the energy equation source term, Qh , which accounts for the latent heat term, could be written in the following form [168]: Qh =

∂(ρ H ) + div(ρ u¯ H ) ∂t

(7.3.49)

where H = F(t) is the latent heat content, in J/kg, and is recognised as a function F of temperature t. The value of F(t) can be generalised as follows: ⎧ t ≥ tl ⎪ ⎨ L, F(t) = L(1 − fs ), tl ≥ t ≥ ts ⎪ ⎩ 0, t < ts

(7.3.50)

where L is the latent heat of phase change, in J/kg; f s is the local solid fraction; t l is the liquid phase temperatures, in K; and t s is the solid phase temperatures, in K. Assuming a Newtonian laminar flow, the continuity and momentum equations are

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7 Thermal Energy Storage

∂ρ + div(ρ u¯ ) = 0 ∂τ

(7.3.51)

∂(ρ u) ∂p + div(ρ u¯ u) = div(μgrad u) − + A0 u ∂τ ∂x

(7.3.52)

∂p ∂(ρ v) + div(ρ u¯ v) = div(μ grad v) − + A0 v + Qg ∂τ ∂y ∂p ∂(ρ w) + div(ρ u¯ w) = div(μ grad w) − + A0 w ∂τ ∂z

(7.3.53) (7.3.54)

where u¯ = (u, v, w) is the velocity, p is the effective pressure, and μ is the viscosity. The parameter A0 in Eqs. (7.3.52)–(7.3.54) is defined so that the momentum equations are forced to mimic the Carman-Koseny formula [171]: A0 =

C(1 − φ)2 φ3 + Ω

(7.3.55)

where C is a constant of 1.6 × 105 accounting for the mushy-region morphology, ϕ is the porosity between 0 and 1, and  = 10−3 is a constant introduced to avoid division by zero. Assuming the Boussinesq approximation, the gravity source term, Qg can be written as [170]: Qg =

ρref βt (h − href ) cp

(7.3.56)

where βt is the thermal expansion coefficient, in K−1 ; cp is the liquid specific heat, in J/(kg·K); href and ρref are reference values of enthalpy, in J/kg and density, in kg/m3 , respectively. Darcy’s law is used to describe the flow of fluid through the porous medium as u¯ = −

kp grad p μ

(7.3.57)

where k p is the permeability, which is considered as a function of porosity. The total enthalpy H of the PCM is the sum of the sensible heat, h = cp t, and latent heat H: H = h + H The liquid fraction f can be expressed as

(7.3.58)

7.3 Heat Transfer Analysis in TES Using LHS Systems and PCMs

⎧ 0 t < tl ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ f = 1 t > tl ⎪ ⎪ ⎪ ⎪ t − ts ⎪ ⎩ t s < t < tl tl − ts

617

(7.3.59)

The latent heat content of the PCM can be written in the following form: H = fL

(7.3.60)

In the enthalpy-porosity technique, the mushy region is treated as a porous medium. For the purpose of methodology development, it is worthwhile to consider the entire cavity as a porous medium. In fully solidified regions, the porosity (ϕ) is set as zero and takes the value ϕ = 1 in fully liquid regions, whereas in mushy regions, ϕ lies between 0 and 1. Accordingly, the flow velocity is linked to the porosity state and is defined as u = ϕui , where ui is the flow velocity. Physical model. A schematic of the three-dimensional physical model of a centralised storage unit filled with PCM is shown in Fig. 7.29. Two different fins made of aluminium are used to increase the thermal performance of the storage unit. They are connected to the metal box from both sides of the lower and upper faces. The same fin structure that is outside the box is extended into the PCM. The fins on the external side of the box are aimed at increasing the exposed area for convective heat flux whereas fins inside the box are for boosting the thermal conduction heat flux. The box is filled with paraffin RT20 with a melting point of 22 °C, heat storage

Fig. 7.29 Geometrical configuration of LHS: a schematic of LHS system; b three-dimensional computational domain; c cross-section of computational domain

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7 Thermal Energy Storage

capacity of 172 kJ/kg within an operating temperature range of 11-26 °C, and specific heat capacity of 1.8 and 2.4 kJ/(kg·K) for solid and liquid, respectively [172]. Model description. The three-dimensional computational domain storage unit filled with PCM with aluminium fins are arranged orthogonal to the axis of the unit. The HTF flows in the vicinity of such unit. The model has three zones: (1) air box with airflow around the fins and system, (2) PCM box (fluid/solid), and (3) fin box (solid). All boxes are coupled to each other as one geometrical body. The air and PCM are coupled so that the energy transfers from the air to fin and then from the fin to PCM. Owing to the symmetrical structure of the considered unit, the computational domain is simplified to only one symmetry unit cell in which the planes of symmetry are in the middle of the fin and are in the middle between two subsequent fins, as illustrated in Fig. 7.29. Model validation. To verify the model, the numerical simulation of the evolution of fraction of melted phase was compared with the experiment of Gua et al. [173], who measured the performance of a physical model in a rectangular cavity with a length of 88.9 mm and a height of 63.5 mm filled with another PCM (gallium). The melting temperature of gallium was assumed to be 29.8 °C. At the initial time, the left wall temperature suddenly increased to 38 °C and remained constant while the temperature at the right wall was maintained constant at 28.3 °C. Table 7.15 provides the properties of paraffin, gallium, air and aluminium. The model employed a single precision, unsteady solver to solve the implicit scheme of second order; the time step was set as 0.2 s. The numerical solution was performed using FLUENT software. The computational domain of the two-dimensional physical model was meshed to 44 × 32 using the Gambit software. Figure 7.30 shows the solid-liquid interface positions for 2 min, 6 min, 10 min and 17 min of melting process. The numerical simulation results are in good agreement with the experimental results as shown in Fig. 7.30. Thus, the numerical model demonstrates great potential to predict the fluid flow and heat transfer performance of a centralised LHS system. Table 7.15 Properties of paraffin, gallium, air and aluminium used for calculation Materials

ρ (kg/m3 )

Paraffin

cp (J/(kg K))

t PCM (°C)

L (J/kg)

μ (kg/(m s))

740/(0.001 × 0.15 (t − 293.15) + 1)

RT20(DSC)

20–22

172.000

0.001 × exp (–4.25 + 1970/t)

Gallium

6093

32

381.5

29.78

80.160

1.81×10−3

Air

1.2×10−5 t2

0.0242

1006.43

–

–

1.7894× 10−5

2024

871

–

–

–

0.01134t + 3.498 Aluminium

2719

λ (W/(m K))

−

7.3 Heat Transfer Analysis in TES Using LHS Systems and PCMs

619

Fig. 7.30 Comparison between experimental and numerical results

7.3.4 Conclusions and Future Research Directions The use of TES systems based on the latent heat capacity of PCMs is an efficient method for storing thermal energy. This has been the topic of extensive research for few decades and many strategies have been considered to overcome the drawbacks linked to the use of PCMs to widen the potential of this technology. PCMs enable a target-oriented solidification temperature that is set by the constant temperature of the phase change. Melting temperature, latent heat of fusion and PCM thermo-physical issues are three basic factors influencing the selection of PCMs in any application. Two primary requirements in the selection approach are high heat of fusion and precise melting/solidification temperature. This study showed that enhancement in heat transfer can be accomplished by either increasing the heat transfer area of the storage system or increasing the thermal conductivity of the PCM. From the literature review, it is clear that the phase change rate (melting/solidification) can be increased considerably by adding porous, high- conductivity and low-density materials. Additionally, the most common enhancement techniques involve the use of extended surfaces such as fins and HPs or using multiple PCMs of different melting points. The micro-encapsulation and nano-encapsulation of PCMs with inorganic and organic shells can increase the heat transfer surface area and solve the phase segregation in salt hydrates. The use of other approaches, such as metallic foam–HPs, metallic foam–fins, or fins–multiple PCMs are relatively new and therefore, could be potential research areas for future studies. Heat transfer is considered mainly from a theoretical point of view, considering different simulation techniques. Numerical methods appear to be a suitable approach to solving phase change problems although most of the available solutions to such problems apply only to one- or two-dimensional systems owing to the complexity of the equations involved in the phase change. A common approach observed in the solution of phase change problems has been the use of an enthalpy formulation that

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7 Thermal Energy Storage

facilitates the implementation of a numerical algorithm. The presented numerical simulation models are of real use to researchers in their future work. The use of CFD for thermal conductivity enhancement of PCMs involving porous, high-conductivity and low-density materials is recommended. Encapsulating materials that offer a strong and durable shell around the PCM and provide good bonding with the construction material, i.e. concrete, need to be investigated. Additionally, the application of micro-encapsulated PCMs is not widely tested in various climatic conditions with various heat loads to determine their long-term thermal stability, which is a potential area of future research. Majority of the studies on HP are numerical and therefore, experimental works on the use of HP for heat transfer enhancement in LHS systems require more attention for future studies in this area. Additionally, the use of extended surfaces (fins, HP) together with addition of high-conductivity materials for heat transfer enhancement of LHS systems is also recommended for future researches. Life cycle analysis, both economical and energetic, should be performed on systems to determine into which conditions energy storage systems involving PCMs should be used.

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Chapter 8

Hydraulic Simulation and Optimisation of Water Transmission and Distribution Systems

Abstract This chapter presents a detailed theoretical study on hydraulic simulation and optimal design and energy efficiency optimisation of water transmission and distribution systems focused on looped distribution systems in steady state and transient conditions, including the development of new, high-performance models for hydraulic analysis of looped networks using variational formulations, original models for optimising design and choosing their optimal route using deterministic methods such as linear, non-linear and dynamic programming, as well as proposing solutions to optimise the energy efficiency of these systems (zoning procedures, potential elements). Additionally, an overview of the multi-objective optimisation of water distribution networks is also included.

8.1 Generalities Water and energy are essential elements for the well-being of the societies. Providing hygienic-sanitary and comfort conditions in residential and sociocultural buildings are related, among others, to the design, execution and proper operation of the water supply system. Water, sanitary and waste services represent a substantial proportion of the cost of construction, averaging 10% of the capital costs of building and with continuing costs in operation and maintenance. A water supply system is a set of structures, facilities and services that produces and distributes water to consumers; the distributed water must be compatible with the needs associated with the domestic consumption, utilities and other industrial consumption in both quantity and quality. Physically, the system is composed of a set of reservoirs (natural sources of raw water, storage and distribution tanks), pipes (water mains, distribution network pipes), civil structures (mainly in water treatment plants) and hydro-mechanical (pumps, valves) and electrical (motors) equipment (Fig. 8.1). Piping, storage and the supporting infrastructure are together referred to as the water distribution system (WDS). While some components are used as the source of energy (e.g., pumps and reservoirs) the others (e.g., pipes, valves and tanks) are used to convey and store energy and water in the system.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 I. Sarbu, Advances in Building Services Engineering, https://doi.org/10.1007/978-3-030-64781-0_8

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8 Hydraulic Simulation and Optimisation of Water Transmission …

Fig. 8.1 Schematic of a centralised water supply system. 1−catchment; 2, 6−pumping; 3−adduction; 4−treatment plant; 5−reservoir; 7−distribution main; 8−distribution network; 9−compensatory tank

The volume of water provided to consumers includes a large amount of energy required for the treatment, distribution and the various internal technological processes of the water supply system. On the other hand, there is squandering of potable and industrial water nationally, to which is added the losses of water in the networks and in the interior installations. Thus, the energy consumption for the operation of the water supply systems is approximately 5% of the country’s total energy consumption. Water and energy resources are fundamental to human existence, and are regularly subject to economic, technological, demographic and social pressures. The world energy consumption for water distribution is about 7% of the global energy [1]. Additionally, it is estimated that 2–3% of the worldwide electricity consumption is used for pumping in WDSs [1], while 80–90% of this consumption is absorbed by motor-pump sets [2, 3]. This cost represents one of the major operational costs associated with water supply systems. A fundamental question in WDS energy– water nexus is whether to minimise the excess energy or generate electricity from the excess energy in the system. Nowadays an increased distance between populations and water sources is observed due to population growth, leading to fast expansions of several water networks. At the same time, the global water consumption has quadrupled in the last 50 years and it is expected that this value would continue to increase [4]. Consequently, the immediate consumers supply without any planned strategy has led to inefficient operated systems, increasing the energy costs for water supply and distribution. The estimative of water loss in the world is around 30%, meaning that a similar portion of energy is also lost [5]. Multiple factors contribute to these energy losses in the water sector [5]: inefficient pump stations, poor design of the networks, installations and maintenance, old pipes with head loss, bottlenecks in the networks, excessive pressures and inefficient operation strategies. According to Feldman [5], the main improvements in energy efficiency can be obtained with: (1) pump stations design improvement, (2) systems design improvement, (3) variable speed drives (VSD) installation, (4) efficient operation of pumps and (5) leakages reduction through pressure modulation. However, it is important to notice that WDSs should always satisfy the requirements of several consumption sectors, responding to demand in each place, at each time and with appropriate pressures [6]. For this reason, computational modelling

8.1 Generalities

631

and optimisation becomes an important auxiliary tool for these more complex studies of energy efficiency in water supply systems [7]. Given the importance and spread of WDSs, since the last century, there have been intense concerns to improve their calculation, implementation and operation methods. In the present era, distribution systems have become complex, large-scale systems with very high costs and high requirements for their design, analysis and operation. Modern computers have provided the ability to process calculation to a higher level, and have enabled new formulations and requirements for the design and operation of WDSs. This chapter presents a detailed theoretical study on hydraulic analysis and optimal design and energy efficiency optimisation of water transmission and distribution systems focused on looped distribution networks in steady state and transient conditions, including different optimisation and hydraulic simulation models of these systems [8–17]. Additionally, an overview of the multi-objective optimisation of water distribution networks is also included [18].

8.2 Nodal Analysis of Urban Water Distribution Networks 8.2.1 Preliminary Considerations Supplying water resources for the growing population of urban areas has been a major challenge in recent years. Distribution network is an essential part of all urban water supply systems and its cost may be equal to or greater than 60% of the entire cost of the project [19–21]. Water supply of large urban and industrial centres is made by distribution networks sized bigger and bigger, being necessary that, in order to ensure greater uniformity and stability of pressure lines with favourable economic and energy effects, to be achieved in a more complex structure (looped networks, several supply sources, booster pumps, inner potential elements, etc.). Also, network extension design or redesign of networks for energy optimisation of their operation lead to complicating the general scheme of the system and thus increase the difficulties of calculation it. Formulation of appropriate mathematical models, which allow the determination of flow rate and pressure distribution in looped networks with non-standard components is essential both for accurate and efficient resolution of design stage, and network analysis in different operating conditions (normal or emergency state). These cases occur especially in the design of network expansions or the redesign of any networks for operational and energy optimisation. There are three methods for looped water distribution network analysis (the loop (cycle) method, the node method and the pipe method) taking into consideration hydraulic parameters chosen as unknown. These methods belong to two types of network analysis problems with increasing capabilities: the forward and inverse problems. In the forward problem, the system’s hydraulic behaviour (i.e., the flow in each

632

8 Hydraulic Simulation and Optimisation of Water Transmission …

pipe, the pressure at each node and the operating heads for pumps) is determined for specified pipe system characteristics as well as water demand and operating conditions. In the inverse problem, selected pipe system characteristics are treated as variables and are determined to meet designated flow and/or pressure specifications [22]. This section addresses a version of the prime type. For all these methods the non-linear system of equations can be solved by iterative procedures: Hardy–Cross method [19, 23, 24], Newton–Raphson method [25–28] and linear theory method [29, 30]. Dynamic programming is also used primarily to solve tree-shaped networks [31, 32] and could be extended to solve looped systems [33]. Analytical procedures have already been developed by Gofman and Rodeh [34] and Boulos et al. [35]. Shamir and Howard [36, 37] and Bhave [38] proposed heuristic rules for model solvability. The previous rules were restricted to solving acyclic networks (i.e., no flow circulation exists around any of the network loops) in the presence of pressure constraints only. Up to now the uncertainty of the input variables for the analysis of a hydraulic network has been addressed in various ways. Lansey et al. [39] proposed a model that directly considered the uncertainties of nodal demands, pressure heads and pipe roughness coefficients for minimum cost design of a pipe network. In order to exploit the entire probability density function, other scientists [40] proposed the use of the Monte Carlo simulation method both in the water distribution analysis and the water distribution network optimisation problems. Urban water distribution network has a known configuration, resulted from its design, and service pressures set according to adopted construction types. In time, to an existing network, could be added consumers and potential elements that alter the original pressure distribution and, therefore is necessary an analysis to find solutions to ensure service pressures in all consumer nodes. Using a sufficient number of simulations can determine the appropriate settings for the piezometric head (heads) of the supply node (nodes) as well as other necessary measures for service pressure to ensure the energy optimisation of the network. For such a purpose, the use of nodal analysis, in which the unknowns are generally the hydraulic heads at the nodes of the network, is efficient. The water demand and the diameters and roughness coefficients of the pipes are considered to be known and precise values. Although in the node method, the equations number is greater than that in the loop method, the density of non-zero elements of the node equations matrix is less than that of the loop equations [41]. The nodal equations system is easier to be formulated, forming a “sparse” matrix of coefficients [42]. In this section, a generalised classic model is developed for the nodal analysis of complex looped systems with non-standard network components and the solvability of new problems, along with the determination of the pressure state in the system [8]. Additionally, a different approach is presented to solving this problem by using the variational formulation method for the development of a new analysis model based on unconditioned optimisation techniques. This model has the advantage of using a specialised optimisation algorithm that directly minimises an objective multivariable function without constraints and that can be implemented in a computer program. In addition, the two proposed models are compared with the classic Hardy–Cross

8.2 Nodal Analysis of Urban Water …

633

method, with the results indicating a good performance of these models. Finally, a study regarding the implications of long-time operation of a pipe network on energy consumption is performed using the proposed models.

8.2.2 Steady State Network Equations A distribution network may be represented by a direct-connected graph composed of a finite number of arcs (pipes, pumps and fittings) and a set of nodes as well as reservoirs and pumps or pipe intersections (junction nodes). In the case of a complex topology for a looped network, with reservoirs and pumps at the nodes, the total number of independent loops (closed loops, possibly containing booster pumps installed in the pipes, and pseudo loops), M, is given by the following formula: M = T − N + NR P

(8.2.1)

where: T is the number of pipes in network; N is the number of nodes; N RP is the number of pressure generating facilities, equal to the number of nodes with known hydraulic grade. Each open loop (pseudo loop) makes the connection between a node with a known piezometric head (reservoir) or with a determined relation discharge-piezometric head (pumping station), and another node with a known piezometric head or a determined relation discharge-piezometric head. In the classical analysis of a complex looped network, fundamental equations of the computational model express: – discharge continuity at nodes:

fj =

N 

Qi j + q j = 0

( j = 1, . . . , N − N R P )

(8.2.2)

i=1 i= j

where: f j is the residual discharge in node j; Qij is the discharge through pipe ij, with the sign (+) when entering node j and (–) when leaving it; qj is the consumption discharge (demand) at node j with the sign (+) for node inflow and (–) for node outflow.

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8 Hydraulic Simulation and Optimisation of Water Transmission …

– energy conservation in loops:

h m =

T 

εi j h i j − f m = 0

(m = 1, . . . , M)

(8.2.3)

i j∈m i j=1

where: hm is the residual head loss (divergence) in loop m; hij is the hydraulic head loss of the pipe ij; εij is the orientation of flow through the pipe, having the values (+1) or (–1) as the water flow sense is the same or opposite to the path sense of the loop m, and (0) value if ij∈m; / f m is the pressure head introduced by the potential elements of the loop m, given by the equations: • simple closed loops: fm = 0

(8.2.4)

• closed loops containing booster pumps installed in the pipes: fm =

T 

εi j H p,i j

(8.2.5)

i j∈m i j=1

• open loops with pumps and/or reservoirs at nodes: fm = Z I − Z E

(8.2.6)

where: Z I , Z E are piezometric heads at pressure devices at the entrance or exit from the loop; H p,ij is the pumping head of the booster pump integrated on the pipe ij, for the discharge Qij , approximated by parabolic interpolation on the pump curve given by points:   H p,i j = A Q i2j + B  Q i j  + C

(8.2.7)

The coefficients A, B and C can be determined from three points of operating data [38]. The hydraulic head loss is given by the Darcy–Weisbach functional equation: hi j =

Li j 8 λi j r Q i2j 2 π g Di j

(8.2.8)

where g is the gravitational acceleration; λij is the friction factor of pipe ij, which can be calculated using the Colebrook−White formula or the explicit equation proposed

8.2 Nodal Analysis of Urban Water …

635

by Arsenie [43] for the transitory turbulence flow; Dij and L ij are the diameter and the length, respectively, of pipe ij; and r is the exponent having the value 5.0. Flow equation (8.2.8) is difficult to use in the case of pipe networks and therefore it is convenient to write it in the following general form: β

h i j = Ri j Q i j

(8.2.9)

where Rij is the hydraulic resistance of pipe ij, expressed by the following expression: Ri j =

8 λ∗ L i j π 2 g Dirj

(8.2.10)

The variation of the hydraulic parameters λ* and β has been determined for different pipe materials and water temperatures [44]. Specific consumption of energy for water distribution wsd , in kWh/m3 , is obtained by referring the hydraulic power dissipated in pipes to the sum of node discharges: T 

wsd = 0.00272

i j=1

 β +1 Ri j  Q i j  N      q j 

(8.2.11)

j=1 q ω : ⎪ ⎪ ⎪ N ⎪ x−1   −1  ⎪ ⎪ ⎪ Ri j Z i − Z j + i j  Z i − Z j + i j  + q j = 0; ⎪ ⎪ ⎨ i= j   f j = i=1  Z i − Z j + i j  ≤ ω : ⎪ ⎪ ⎪ 2  ⎪ N ⎪ Z i −Z j +i j ⎪ x −x Z i −Z j +i j ⎪ ω R [(x − 1) + 3 − x] + q j = 0 ⎪ ij ω ω ⎪ ⎩ i= j

(8.2.19)

i=1

where x = 1/ β and ω is chosen conveniently (10−4 −10−5 ). Partial derivatives are obtained from Eq. (8.2.19) as follows:  ⎧  Z i − Z j + i j  > ω : ⎪ ⎪   ⎪ ⎪  Z i − Z j + i j x−1 ; ⎨ x Ri−x j ∂fj ∂ fi   = =  Z i − Z j + i j  ≤ ω :  ⎪ ∂ Zi ∂Zj 2  ⎪ ⎪ Z −Z + ⎪ 3 ⎩ ω x Ri−x (x − 1) i ωj i j + j ω



.

(8.2.20)

3−x ω

N  ∂fj ∂fj =− ∂Zj ∂ Zi i= j

(8.2.21)

i=1

• After the examination of Eq. (8.2.14), the fulfilment of the discharge continuity at the nodes can be accomplished by admitting as variables not only piezometric heads, Z j , but also hydraulic resistances, Rij , and concentrated discharges in nodes, qj , conditioned such that the sum of all of those unknown is N–N RP . Therefore, the use of the model can be extended to solve new problems. Noting the unknowns resistances  of piezometric heads Z = {Z1 …Zw }, hydraulic   ¯ at nodes q = q R = Ri j . . . R pr and concentrated discharges . . . qn and j   (0) (0) (0) , starting from the initial vector X(0) = Z 1(0) . . . Z w(0) Ri(0) j . . . R pr q j . . . qn corrections can be determined for each iteration from the linear system:

⎤ ∂ f1 ∂ f1 ······ ⎫ ⎧ ⎫ ⎥⎧ ⎢ ∂ Z1 ∂qn ⎥⎪ δ Z 1 ⎪ ⎪ − f 1 ⎪ ⎢ ⎪ ⎥⎪ ⎢ .. ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎥⎪ ⎢ .... ⎪ ⎪ ⎪ ⎪ ⎪ .. .. ⎪ ⎪ ⎥⎪ ⎢ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ . . ⎪ ⎥⎪ ⎢ ⎪ ⎪ ⎨ ⎨ ⎬ ⎬ ⎥ ⎢ ∂ f w+1 ∂ f w+1 ⎥ ⎢ · · · · · · δ R − f = i j w+1 ⎢ ∂ Z1 ⎪ ⎪ ⎪ ∂qn ⎥ ⎪ ⎪ ⎥⎪ ⎢ ⎪ ⎪ ⎪ ⎪ ⎪ .. .. ⎪ ⎪ ⎥⎪ ⎢ .. ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎥⎪ ⎢ .. ⎪ ⎪ . . ⎪ ⎪ ⎪ ⎪ ⎪ ⎥⎪ ⎢ .. ⎪ ⎪ ⎩ ⎩ ⎭ ⎭ ⎥ δq ⎢ − f n N ⎦ ⎣ ∂ fN ∂ fN ······ ∂ Z1 ∂qn ⎡

(8.2.22)

8.2 Nodal Analysis of Urban Water …

639

in which the partial derivatives on Rij and qj have the expressions:

∂fj ∂ Ri j

⎧   Z i − Z j + Πi j  > ω : ⎪ ⎪  x−1 ⎪ ⎪ ⎨ −x Ri−(x+1) (Z i − Z j + Πi j ) Z i − Z j + Πi j  ; j   = Z − Z + Π  ≤ ω : j ij ⎪ ⎪ i 2  ⎪ ⎪ ⎩ −x ω−x R −(x+1) Z i −Z j +Πi j [(x − 1) Z i −Z j +Πi j + 3 − x] ij ω ω ∂fj =1 ∂q j

(8.2.23)

(8.2.24)

The algebraic system of Eq. (8.2.22) has no solution for the combinations of unknowns that lead to the existence of lines or columns in the matrix of the system when all terms are null. Therefore, the choice of these combinations must respect some rules: • for each node, at least one of the following must exist as an unknown: the concentrated discharge at node, the piezometric head for that node or any adjacent node or the hydraulic resistance of any pipe that meet in the node; • a node that has an unknown concentrated discharge shall be connected to at least one other node with a known discharge; and • a pipe with an unknown hydraulic resistance must not have more than one unknown at the nodes that define it (either piezometric head or consumed discharge in the node). The use of the Newton–Raphson algorithm for solving the system of linear Eq. (8.2.19) has the following advantages: – the Jacobean matrix contains at most N+2T non-zero elements [20], which indicates the property of “sparse matrix” [42]; – in most cases, this matrix is symmetric, irreducible and weakly dominant diagonal, which ensures the existence of an inverse matrix; and – the matrix inverse is a positive matrix, a property that provides the qualities of numerical stability in solving the linear algebraic system of Eq. (8.2.22). Based on the nodal analysis model in the classic formulation, a computer program, ANOREC was elaborated [22, 46] in the FORTRAN programming language for use in PC-compatible micro-systems.

8.2.4.2

Variational Formulation

If instead of the classical equations in (8.2.14) the relations of (8.2.3) and (8.2.13) along with the performance function that express energy consumption are used, then the network analysis can be performed using an unconditional optimisation model. Thus, in the variation formulation of the nodal analysis of looped networks, the determination of the piezometric heads, Z j , is performed on the criterion of

640

8 Hydraulic Simulation and Optimisation of Water Transmission …

minimising the energy consumption in the network per time unit (power), expressed analytically by the objective function [44, 47]: Z h i j T N  j   Fe = ( Q i j dh i j ) − ( q j dZ j ) → min i j=1 0

(8.2.25)

j=1 0

subject to constraints (Eq. 8.2.3) of energy conservation in the loops. After substituting Eq. (8.2.13) into Eq. (8.2.25) and after calculating the integrals, the constraints can be eliminated, and the problem can be simplified to determining the minimum of a function with N–N RP variables (Z i , Z j ) without constraints: Fe =

β+1 T N   β β  − β1  Ri j Z i − Z j + Πi j  − q j Z j → min β + 1 i j=1 j=1

(8.2.26)

Using the extremum conditions ∂F e /∂Z j = 0 (j = 1,…,N–N RP ) one obtains the system of node Eqs. (8.2.14). The variation formulation considerably reduces the magnitude of the problem, simplifying it from a system with N–N RP independent non-linear equations with N– N RP unknowns and M constraints to a function with only N–N RP unknowns, that is without constraints. To minimise direct the function (8.2.26), the conjugate gradient algorithm is used [48–50]. The permissible error in the calculation ε is considered to be equal to 10−5 . Having determined the piezometric head at the nodes, the available pressure head H j at the nodes is calculated using the equation: Hj = Z j − Z Tj

(8.2.27)

Then, the discharges, Qij , through the pipes are determined using the functional Eq. (8.2.13) along with the other hydraulic parameters of the network. Based on the nodal analysis model in the variation formulation, a computer program ANOREV was developed [20, 46] in the FORTRAN programming language for PC-compatible micro-systems.

8.2.5 Numerical Examples The looped distribution network with the topology from Fig. 8.2 is considered. The network is made of cast iron and is supplied with a discharge of 0.50 m3 /s. The following data are known: pipe length L ij , in m; pipe diameter Dij , in m; elevation head ZT j , in m; industrial concentrated discharges in the nodes qj , in m3 /s; piezometric head at the “critical node” Z 1 = 124 m; and the exponent, β = 1.936.

8.2 Nodal Analysis of Urban Water …

641

Fig. 8.2 Schematic of analysed distribution network

8.2.5.1

Determination of the Discharge and Pressure Distribution in a Looped Network

For the water distribution network considered in Fig. 8.2, the pumping head, discharges and pressures distribution must be determined using the classic Hardy– Cross procedure and the two nodal analysis models (ANOREC, ANOREV) developed above. The results of the numerical solution performed by means of a computer, referring to the hydraulic characteristics of the pipes and nodes, are presented in Tables 8.1 and 8.2, respectively. Table 8.1 presents the discharges and head losses through the pipes established by using the three mentioned models of computation (the iterative tolerance imposed is 10−5 ). It can be observed that the results are very close. The difference between the discharges obtained with Hardy–Cross model and those given by ANOREC vary between 0.01% (pipe 9–8) and 1.8% (pipe 8–11), and the difference between discharges obtained using Hardy–Cross and ANOREV varies from 0% (pipe 7−6) to 2.8% (pipe 9−8). The specific consumption of energy for water distribution is 0.00705 kWh/m3 for all three computational models used. Table 8.2 summarises the values for the piezometric head Z j and the residual pressure head H j at the nodes determined by using the classic procedure and the two new computational models. The piezometric head at node 13 has the values of 131.435 m, 131.356 m and 131.363 m, which correspond to residual pressure head values of 29.435 m, 29.356 m and 29.363 m, respectively, each of which is sufficient for the supply of water to the consumers. The divergence of the piezometric line on the network contour is 0.216 m for Hardy–Cross, 0.001 m for ANOREV and only 0.0 m for ANOREC.

642

8 Hydraulic Simulation and Optimisation of Water Transmission …

Table 8.1 The discharges and head losses through pipes Pipe i −j

Computational model HARDY–CROSS

ANOREC

Q (m3 /s)

h (m)

Q (m3 /s)

h (m)

ANOREV Q (m3 /s)

h (m])

2−1

0.01210

3.955

0.01219

3.754

0.01204

3.915

3−2

0.03618

0.895

0.03616

0.915

0.03605

0.889

4−3

0.06957

1.217

0.06902

1.251

0.06916

1.203

13−4

0.11413

1.369

0.11358

1.437

0.11371

1.356

6−5

0.03770

1.443

0.03762

1.428

0.03776

1.447

7−6

0.08206

0.907

0.08174

0.938

0.08206

0.907

8−7

0.13518

0.521

0.13496

0.559

0.13531

0.521

9−8

0.17542

0.261

0.17544

0.288

0.18034

0.276

13−9

0.25264

1.064

0.25318

1.172

0.25266

1.065

11−10

0.01589

2.495

0.01614

2.469

0.01610

2.558

12−11

0.04797

2.156

0.04798

2.206

0.04806

2.163

13−12

0.09503

1.122

0.09504

1.192

0.09501

1.122

5−1

0.01655

3.124

0.01647

2.972

0.01661

3.147

7−2

0.02618

1.578

0.02628

1.584

0.02625

1.587

9−3

0.02549

1.461

0.02603

1.516

0.02579

1.495

6−10

0.01673

3.120

0.01649

2.291

0.01661

3.075

8−11

0.01329

1.951

0.01353

1.938

0.01327

1.945

Table 8.2 The piezometric head and available pressure head at nodes Node

Computational model

j

HARDY–CROSS

ANOREC

Z j (m)

H j (m)

Z j (m)

H j (m)

Z j (m)

H j (m)

1

124.000

24.000

124.000

24.000

124.000

24.000

2

127.955

27.455

127.754

27.254

127.915

27.415

3

128.850

27.850

128.6681

27.668

128.804

27.804

4

130.066

29.066

129.920

28.920

130.007

29.007

5

127.124

26.624

126.972

26.472

127.147

26.647

6

128.566

28.566

128.399

28.399

128.594

28.594

7

129.533

28.533

129.338

28.338

129.502

28.502

8

130.053

28.553

129.896

28.396

130.023

28.523

9

130.371

28.371

130.184

28.184

130.299

28.299

10

125.446

25.446

125.490

25.490

125.520

25.520

11

128.157

27.157

127.958

26.958

128.078

27.078

12

130.313

28.813

130.165

28.665

130.241

28.741

13

131.435

29.435

131.356

29.356

131.363

29.363

ANOREV

8.2 Nodal Analysis of Urban Water …

8.2.5.2

643

Implications of the Extended Operation of the Pipes on the Pumping Energy

The developed computational models, together with those existing in literature, were primarily used to solve the problems of the analysis or design of distribution networks, using computers and removing the calculation difficulties created by the complexity and the different operating assumptions of the networks; as a result, specialists now focus their efforts on establishing accurate basic data, which affect the precision of the model results. Special attention should be paid to the sufficiently accurate assessment of the pipe roughness, which influences the calculation of the head losses. These losses have a significant energy influence on the optimal network solution in a water supply system. In the distribution network design process, new, clean and properly mounted pipes are considered, and the roughness of the pipes is assigned according to the characteristics of the pipe material. Many measurements that have been performed by different researchers [51, 52] indicate an increase in pipe roughness due to corrosion, deposition of material and ageing, which leads, as a consequence, to the reduction of the transport capacity for pipes of up to 50%. To achieve discharge established in the design calculation, the hydraulic slope and thus the proportional pumping energy must be increased. In addition, iron and minerals residues deposited in pipes and their corrosion products lead to changes in the water quality from the network. For water pipes, accounting for the properties of water in connection with the formation of deposits in pipes, Kamerstein proposed a division of the water characteristics into five groups of natural water, which correspond to the same number of average increases in the rate of roughness [52], each determining the reduction percentage of the pipe transport capacity. The reduction of the transported flow by pipes, along with its operating duration, can be expressed by the equation:   m0 Q i j = Q i(0) j 1 − 0, 01 n 0 τ

(8.2.28)

where Q i(0) j is the calculated transport capacity of the pipe; τ is the operating duration, in years; and n0 and m0 are the addiction parameters of the physical–chemical properties of water having the most likely mean values given in Table 8.3. The pipe roughness variation, depending on the number of operating years, can be expressed by the equation obtained based on the results of Sharp and Walski [53]:  = 0 + ω τ

(8.2.29)

where:  is the pipe roughness at age τ; 0 is the roughness when the pipe was new (τ = 0); ω is average rate of roughness change with values from Table 8.3; τ is the pipe age.

644

8 Hydraulic Simulation and Optimisation of Water Transmission …

Table 8.3 Values of parameters ω, n0 , m0 depending on physic-chemical properties of water Group

Water properties

ω (mm/year)

I

Poorly mineralised water, non-corrosive. Water containing little organic matter and dissolved iron

0.025

2.3

0.50

II

Poorly mineralized water, corrosive. Water containing dissolved organic matter and iron less than 3 mg/dm3

0.070

2.3

0.50

III

Corrosive water containing little amount of chlorides and sulphates. Water with iron content of over 32 mg/dm3

0.200

6.4

0.50

IV

Corrosive water with high content of chlorides and sulphates (over 500−700 mg/dm3 ). Untreated water with high content of organic substances

0.510

11.6

0.40

V

Highly mineralised water (fixed mineral residue over 2000 mg/dm3 ) and corrosive, with high carbonate hardness and permanent hardness reduced

0.800

18.0

0.35

n0

m0

Because the change rate of the roughness, expressed as a factor of time, depends on several factors and the determination of the real roughness values in the laboratory is difficult, the direct determination of the precise value of pipe roughness of the operating networks is required. In the absence of reliable data from tests under realistic conditions, calculations can be performed using the values given by Eq. (8.2.29). Based on this equation, the variation of friction factor λ* and discharge exponent β as a function of ω was determined for pipes manufactured by different materials (reinforced concrete, cast iron, steel, PVC and PE–HD) with operating durations of 10, 25, 50 years, for an average water temperature of 15 °C. The results are illustrated in Fig. 8.3. The material deposits (clogging) and the corrosion or the erosion of pipe material are the main phenomena that occur during operation, which leads to an increase of the pipe roughness. Very low or zero velocity of water for long periods of time facilitates the clogging and consolidation of deposits in the presence of carbonate. In addition, mechanical clogging and biological clogging occur. The main causes leading to the formation of deposits in pipes are: • suspended substances in water, for untreated industrial water networks; • temporary hardness of water; • corrosive action of transported water, which leads to the formation of iron oxide deposits; and • biological action due to the ferruginous bacteria and some protozoa. Both the corrosion and the clogging of pipes by increasing the roughness increase the energy loss, with negative effects on the pressure and flow distribution in the network. In this case, the result is a preferential water supply at some points over others.

8.2 Nodal Analysis of Urban Water …

645

Fig. 8.3 Variation of hydraulic parameters λ* and β with roughness increase rate for pipes. a reinforced concrete and cast iron; b steel; c PVC and PE-HD

646

8 Hydraulic Simulation and Optimisation of Water Transmission …

Defining the pressure distribution stability, σH , as a ratio between the minimum pressure (at the maximum consumption at the critical point) and the maximum pressure (for zero consumption): σH =

Hmin Hmax

(8.2.30)

and taking into account the similarity of the relationships of centrifugal pumps, the discharge distribution stability is defined as:  Q min σQ = = Q max

Hmin Hmax

(8.2.31)

To illustrate the above-mentioned processes, the water distribution network in Fig. 8.2 is considered. For this considered network, the parameters calculated using the computer program ANOREV are: (1) the available pressure head at nodes after 10, 25 and 50 years of operation with two rates of roughness change and (2) the pressure and discharge stability. The numerical results are presented in Table 8.4. After an operating time of 10 years, with a roughness change rate of 0.025 mm/ year, relatively little growth in the hydraulic slope was determined, from 4.1% (pipe 9–8) to 17.3% (pipe 2–1), but after an operating time of 50 years and a roughness change rate of 0.2 mm/year, the hydraulic slopes increased significantly, reaching values from 175% (pipe 9–8) to 259% (pipe 5–1). The pressure distribution stability decreased by 4.7−69.7%, and the discharge distribution stability decreased by 2.4−45%. To maintain the transport capacity of the pipes in the case of the analysed network, a pumping head increase is required, resulting in an increase in the pumping electricity consumption from 3.9% (ω = 0.025 mm/year, τ = 10 years) to 56.7% (ω = 0.2 mm/year, τ = 50 years) and, accordingly, the increase of the specific energy for the water distribution in the network from 15.6 to 206%. The effect of the change of pipe roughness for the increasing the network operation time on the pressure distribution consists of a more pronounced increase in the hydraulic slopes than those expected from the design, with the following implications: • significant reduction of the discharge for the consumption points, leading to difficulties in water use and often the necessity to over-equip the pump stations as well as to incorrectly design the extensions or rehabilitations of networks in which the pipes have been already in operation; • increase of the pressure in the network to achieve the same transported flow, resulting in a greater energy consumption and the modification of the optimal calculation; and • generation of an additional water loss in the network, which can be significant because the amount of damage increases up to the end of the material lifetime.

8.2 Nodal Analysis of Urban Water …

647

Table 8.4 Available pressure head at nodes H j , in m Node j

ω [mm/year] 0.00

0.025

0.200

Project

τ [years]

τ [years]

10

25

50

10

25

1

24.000

22.859

22.371

20.453

18.202

13.364

7.284

2

27.455

26.502

26.295

25.485

24.548

22.587

20.213

3

27.850

26.528

26.374

25.776

25.087

23.651

21.920

4

29.066

28.855

28.770

28.443

28.069

27.293

26.364

5

26.624

26.021

25.754

24.719

23.525

21.024

17.986

6

28.566

28.283

28.122

27.498

26.784

25.312

23.568

7

28.533

28.224

28.231

27.831

27.375

26.443

25.355

8

28.553

28.415

28.338

28.043

27.709

27.034

26.248

9

28.371

28.213

28.151

27.912

27.643

27.099

26.467

10

25.446

24.731

24.353

22.870

21.133

17.416

12.773

11

27.157

26.645

26.438

25.631

24.695

22.724

20.315

12

28.813

28.644

28.576

28.312

28.008

27.379

26.824

13

29.435

29.435

29.435

29.435

29.435

29.435

29.435

σH

0.815

0.777

0.760

0.695

0.618

0.454

0.247

σQ

0.903

0.881

0.872

0.834

0.786

0.674

0.497

0.0071

0.0082

0.0086

3.9

5.5

wsd

(kWh/m3 )

Pumping energy increase (%)

0.0103 12.0

0.0123 19.7

0.0165 36.1

50

0.0216 56.7

If, for new pipes, the roughness is considered unchanged for a period of 10−12 years, after this operating period, it is absolutely necessary to consider a change of roughness for the inner walls of the pipes.

8.2.6 Conclusions The three analysis methods of looped networks (loop method, nodal method and pipe method) are theoretically equivalent. The mathematical model for all of these networks is based on the conservation equations of the discharges in the nodes and energy in the loops and on the functional equation head loss–discharge in the component elements of the network. In the case in which the unknowns of a network are the nodal piezometric heads, concentrated consumption in nodes and/or hydraulic resistances, the nodal method is preferred as the hydraulic analysis method.

648

8 Hydraulic Simulation and Optimisation of Water Transmission …

Because of the possibility of introducing unknown amounts of consumption at the nodes and the hydraulic resistances of some pipes, the nodal analysis model ANOREC offers greater flexibility compared to loop analysis, which enables its use for new problems. Such problems could be: the study of existing networks for establishing the possibility of connecting new consumers or identifying hydraulic resistance and the determination of the pressure stage in a network to ensure the service pressure. The mathematical model expressed by the objective functions (8.2.26) constitutes a new form of hydraulic analysis of complex looped networks based on unconditioned optimisation techniques. This model replaces the solution of the non-linear system of Eqs. (8.2.2), (8.2.3) and (8.2.9) with the direct minimisation of a multivariable function, without constraints, that expresses the energy consumption across the network. The computer program ANOREV includes this particular aspect and contains the conjugate gradient algorithm, which give it efficiency, especially in the operational analysis of complex distribution networks. This new method is computationally more efficient and consequently assists the designer to obtain the best design of WDSs with less effort.

8.3 Hydraulic Analysis of Looped Networks Using Variational Formulations 8.3.1 Preliminary Considerations There are three methods for analysing flow and pressure distribution in looped water supply networks (the loop method, the node method, the element method) taking into consideration hydraulic parameters chosen as unknown. For all these methods the non-linear system of equations can be solved by iterative procedures: Hardy–Cross method [54–57] or Newton–Raphson method [58–61]. Analytical procedures have already been developed by Gofman and Rodeh [62] and Boulos et al. [35]. Shamir and Howard [37, 63] and Bhave [38] proposed heuristic rules for model solvability. The previous rules were restricted to solving acyclic networks (i.e., no flow circulation exists around any of the network loops) in the presence of pressure constraints only. This section shows a different approach to this problem by using the method of variational formulations for hydraulic analysis of water distribution networks [44]. This method has the advantage that it uses a specialised optimisation algorithm which minimises directly an objective multivariable function without constraints, implemented in two computer programs. These optimisation models can serve as a guideline to supplement existing procedures of network analysis.

8.3 Hydraulic Analysis of Looped Networks …

649

8.3.2 Basis of Hydraulic Analysis In classical analysis of looped networks, fundamental equations of the computational model express discharge continuity at nodes (Eq. 8.2.2) and energy conservation in loops Eq. (8.2.3). The head loss in the pipes is given by the Darcy–Weisbach flow equation written in the following general form: β

h i j = Ri j Q i j

(8.3.1)

where Rij is the hydraulic resistance of pipe ij, having the succeeding expression: Ri j =

8 λ∗ L i j π 2 g Dirj

(8.3.2)

The variation of hydraulic parameters λ* and β has been determined for different pipe materials and water temperatures θ (Fig. 8.4), using a computer program [64]. Flow equation (8.3.1) can be written as follows:  β −1 β h i j = Z i − Z j = Ri j Q i j = Ri j Q i j  Q i j 

(8.3.3)

or: −

Q i j = Ri j

1 β

1

−

h iβj = Ri j

1 β



 1−β   Z i − Z j + Πi j ×  Z i − Z j + Πi j  β

(8.3.4)

where Z i and Z j are the piezometric heads at nodes i and j and ij is the active pressure introduced by the intermediate pump on the pipe ij. If a circulation flow Qm is associated to each loop m and an initial flow distribution Q i(0) j is chosen so as to satisfy Eq. (8.2.1) then it can be written as: Q i j = Q i(0) j +

M 

εi j Q m

(i j = 1, . . . , T )

(8.3.5)

i j∈m m=1

and for simple loops (f m = 0) the system of Eqs. (8.2.1), (8.2.2), (8.3.1), (8.3.5) is equivalent to the following:  β−1   M     (0)   (0) εi j Ri j (Q i j + εi j Q m ) Q i j + εi j Q m  = 0 (m = 1, . . . , M)   i j∈m i j∈m (m)   M 

m=1

m=1

(8.3.6)

650

8 Hydraulic Simulation and Optimisation of Water Transmission …

Fig. 8.4 Variation diagram of hydraulic parameters λ* and β: a—reinforced concrete and cast iron; b—steel; c—PE-HD; d—PVC

8.3 Hydraulic Analysis of Looped Networks …

651

Substituting Eqs. (8.3.4) in (8.3.1) one gets a system of N–N RP equations at nodes with N–N RP unknown: N 

−

1 β

Ri j

  1−β (Z i − Z j + Πi j ) Z i − Z j + Πi j  β + q j = 0 ( j = 1, . . . , N − N R P )

i= j i=1

(8.3.7) Specific consumption of energy for water distribution wsd , in kWh/m3 , is obtained by referring the hydraulic power dissipated in pipes to the sum of node discharges: T 

wsd = 0.00272

i j=1

 β +1 Ri j  Q i j  (8.3.8)

N      q j 

j=1 q 0, it results that ∂ 2 Fc /∂h i2j > 0. For practical values of α and β, (βα−r)/r < 0, so it results that ∂ 2 Fc /∂ Q i2j < 0. Consequently, in all cases the objective function F c has a convex–concave form for its definition range, and, therefore, has no extreme. To establish an extreme, a set of variables should be specified (Qij or hij ). Thus, if the flow discharges in pipes are known, the values hij are to be determined by minimising the objective function F c . If only the head losses are the given values, the variables Qij are to be determined by maximising the objective function F c . Considering variables hij to be unknown, pipes discharges (Qij ) are to be calculated according to optimisation model described in Sect. 8.9.3. By solving the non-linear system of Eqs. (8.9.2), (8.9.21) and (8.9.24) using the gradient method [156], the head losses through pipes (hij ) and piezometric heads at the supply nodes (Z IPP,j ) are determined. The optimal diameters Dij of pipes are computed using Eq. (8.9.19) and their approximation to the closest commercial values is performed. Finally, the hydraulic balance of pipe network is performed with Hardy−Cross method using the results of a new computation of the head losses with Eqs. (8.9.15) or (8.9.16). If the head losses (hij ) are the given values, the unknown variables Qij are to be determined by solving the system of Eqs. (8.9.1), (8.9.23) and (8.9.26), and used to calculate the optimal diameters in Eq. (8.9.19). The piezometric heads Z n at the node n can be determined starting from a node of known piezometric head. The residual pressure head H n at the node n is calculated from the equation: Hn = Z n − Z Tn

(8.9.30)

where ZT n is the elevation head at the node n. For an optimal design, the piezometric (hydraulic grade) line of a path of NT j pipes, situated in the same pressure zone, must represent a polygonal line which resembles as closely as possible the optimal form expressed by the equation:

8.9 Optimisation Models of Looped Urban Water Supply Networks

⎤ β α ⎞ α+r +1 ⎥ N Tj ⎢ ⎜ ⎟ ⎥ ⎢ ⎜ ⎟ d ⎥ ⎢ ⎟ 1 − − ⎢1 − ⎜ hi j ⎥ ⎜ ⎟ N T j ⎥ ⎢  ⎝ ⎠ i j=1 ⎦ ⎣ Li j ⎡

Z n = Z I P P, j

713

⎛

(8.9.31)

i j=1

where Z n is the piezometric head at the node n, and d is the distance between node n and the pressure device j. The computer program OPNELIRA has been elaborated [157] based on the NOM, in the FORTRAN programming language for PC-compatible micro-systems.

8.9.7 Linear Optimisation Model For the evaluation of the energy dissipated in pipes with variable discharge on route, a complex computational equation has been established by specialised studies [79]. The equation takes into account the complete hydrodynamic effects including the secondary (branch) ones, in the zones of consumption nodes. In particular, for pipes with uniform outflow along their length, the expression for head loss between extreme ends takes the form: $ % 8 α0 Q c Q 2c ∗ 2 − 2 (2 Q 0 − Q c ) (8.9.32) h i j = Ri j Q 0 − Q 0 Q c + 3 π g Di4j where: Dij , Rij are the diameter and hydraulic resistance of the pipe ij; Q0 is the inflow in the initial section of the pipe ij; Qc is the outflow along the length of the pipe ij; α0 is the non-uniformity coefficient of velocity distribution in the cross-section of the pipe. The second term of the flow equation (8.9.32) represents the energy loss due to variation of outflow along the length of the pipe and determines a diminishing of the total head loss. The discharge in the pipes of a network could be considered constant, equalising head loss in a pipe with uniform outflow along its length with head loss in a simple pipe with concentrated outflow: $ % Qc 2 = Re,i j Q i2j h i∗j = Re,i j Q 0 − 2

(8.9.33)

where Re,ij is the equivalent hydraulic resistance of the pipe ij, and Qij is the discharge through pipe ij. By equating Eq. (8.9.32) and (8.9.33), from elementary computations, the following expression of the equivalent hydraulic resistance is arrived at:

714

8 Hydraulic Simulation and Optimisation of Water Transmission …

Re,i j = Ri j

1 2 θ 3 ij

− (1 − ωi j ) θi j + 1 − 2 ωi j  2 θ 1 − 2i j

(8.9.34)

in which the following non-dimensional characteristics have been used: – for outflow: θi j =

Qc Q0

(8.9.35)

– for pipe:

θi j =

Qc Q0

(8.9.36)

The total length of a pipe ij, with the discharge Qij , may be divided into sij segments (k) of Dk,ij diameters and x k,ij lengths. Taking into account the Darcy–Weisbach’s functional equation, the friction slope J k,ij for each segment k of the pipe ij can be calculated, in the hypothesis of concentrated outflow, with the equation: Jk,i j =

Q i2j h k,i j 8 = 2 λk,i j r xk,i j π g Dk,i j

(8.9.37)

where: r is an exponent having the value 5.0; g is the gravitational acceleration; λk,ij is the friction factor of segment k in pipe ij, can be calculated using the Colebrook– White formula, or the explicit equation proposed by Arsenie [154] for the transitory turbulence flow. Since in real conditions the discharge decreases from one cross-section to another in the sense of outflow, an increase of pressure is accomplished at the outlet of the pipe, by a phenomenon similar to rebound, which has the effect of diminishing the head loss. Thus, Eq. (8.9.34) is taking into account and the notations 8.9.38 are introduced in Eq. (8.9.37): Θi j =

2 4 α0 Dk,i j 4 θi j − 3θi j + 3 ; Ωk,i j = 2 3 (2 − θi j ) λk,i j (2 − θi j )

(8.9.38)

The expression of friction slope in each segment k of the pipe ij, for the uniform outflow along the length of the pipe, is rewritten as: ∗ Jk,i j =

h ∗k,i j xk,i j

$ % Ωk,i j = Jk,i j Θi j − xk,i j

(8.9.39)

8.9 Optimisation Models of Looped Urban Water Supply Networks

715

Table 8.15 Energy-economical factors E min and E max No.

Pipe material

ATC

UTC

EC

E min

E max

E min

E max

E min

E max

1

Reinforced concrete

0.46

2.28

0.21

1.46

0.34

1.38

2

Cast iron

0.24

1.11

0.14

0.78

0.20

0.80

3

Steel

0.46

2.28

0.21

1.46

0.34

1.38

4

PVC

0.28

1.20

0.13

0.90

0.17

0.51

5

PE–HD

0.28

1.22

0.13

0.95

0.17

0.55

For ij = 1 and k,ij = 0, the general Eq. (8.9.39) takes the particular form of Eq. (8.9.37), valid for pipes with constant discharge. The discharges Qij are determined for each operating (loading) condition. The distribution of discharges is optimised by using Eq. (8.9.12) with γ = 2. The series of commercial diameters which can be used Dk,ij ∈ [Dmax,ij , Dmin,ij ] for each pipe ij are established using the limit values of optimal diameters Dmax,ij and Dmin,ij , computed by Eq. (8.9.40) for pumping operation networks or Eq. (8.9.41) for gravity networks: 1

1

β

α +r α +r Q iαj +r Dmax (min),i j = E max (min) Q p

 Dmax (min),i j =

4 Qi j π Vmin (max ),i j

(8.9.40)

(8.9.41)

where: Qij is the optimal discharge of the pipe ij; Qp = Qp,j is the pumped discharge; V min , V max are the limits of the economic velocities; E is the energy-economical factor of the pipes [122, 152], which has a maximum value E max and a minimum value E min (Table 8.15), corresponding to the limit values of the variation of energy-economical parameters (p1 , p2 , η, f , σ, e, τ, k ) for the distribution system. A penalty coefficient pij is used when optimising diameters in the case of extending a network, which has the value equal to the value of the corresponding imposed diameter, for pipes with fixed diameters (designated pipes), resulting in Dk,ij = pij . It is admitted that a pipe ij of length L ij of a pumping operation network made up of T pipes can be divided into sij segments (k) of diameters Dk,ij and lengths x k,ij and are performed the notations: ∗ α ck,i j = ξ 1 (a + b Dk,i j )

Z I P P, j = (



h i j + H0 ) j

The objective function expressed by Eq. (8.8.7) takes the form:

(8.9.42) (8.9.43)

716

8 Hydraulic Simulation and Optimisation of Water Transmission …

min Fc =

{X,Z}

si j T  

∗ ck,i j x k,i j + ψ

i j=1 k=1

NP 

Q p, j Z I P P, j

(8.9.44)

j=1

where: F c is the objective function to be minimised; X is the vector of unknown lengths x k,ij ; and Z is the vector of unknown pressurised device piezometric heads Z IPP,j . Therefore, the unknowns of the objective function are the decision variables x k,ij  and Z IPP,j , being N P + iTj=1 si j in number. When the pressure device is comprised of one or more reservoirs (ψ = 0), then Eq. (8.9.44) of the objective function becomes: min Fc = {X}

si j T  

∗ ck,i j x k,i j

(8.9.45)

i j=1 k=1

This objective function has as unknowns the decision variables x k,ij , and minimises the included energy or the network cost. Hence, the values of the decision variables must be determined in order to minimise the objective function F c , subject to: • constructive constraints which are introduced to ensure that the sum of all pipe segments between any two nodes is equal to the length between those nodes: si j 

xk,i j = L i j

(i j = 1, . . . , T )

(8.9.46)

k=1

• operational constraints which are written for each operating situation, and which must provide the necessary pressure HN o at the critical nodes, starting on different path from the pressure devices IPPj (Fig. 8.25):

Fig. 8.25 Scheme of a path IPPj – critical node O

8.9 Optimisation Models of Looped Urban Water Supply Networks N T j si j

Z I P P, j −



N Tj

εi j Θi j Jk,i j xk,i j ≥ Z To + H No −

i j=1 k=1

717

s

ij   ( εi j Ωk,i j Jk,i j + H p,i j )

i j=1 k=1

(8.9.47) where: NT j is the pipes number of a path IPPj – O; ZT o is the elevation head at the critical node O; Z IPP,j is the available piezometric head at the pressure device j; H p,ij is the pumping head of the booster pump mounted on the pipe ij, having the expression of Eq. (8.9.6). • hydraulic constraints which are characteristic only for looped networks, expressing the energy conservation in loops: T 

εi j Θi j Jk,i j xk,i j =

i j∈m i j=1

T 

εi j Ωk,i j Jk,i j + f m

(m = 1, . . . , M)

(8.9.48)

i j∈m m=1

where εij is the orientation of the pipes, and the pressure head f m is given by Eqs. (8.9.3), (8.9.4) and (8.9.5). In the case that the available piezometric heads Z IPP,j are known, and it being unnecessary to determine them by optimisation, the objective function (Eq. 8.9.44) takes the form of Eq. (8.9.45), while values Z IPP,j are contained in the free term of constraints (Eqs. 8.9.47 and 8.9.48). As Eqs. (8.9.44) or (8.9.45) of the objective function and the constraints (Eqs. 8.9.46−8.9.48) are linear with respect to the unknowns of system, the optimal solution is determined according to the LP method [158], using the Simplex algorithm [159]. Computing the unknowns Z IPP,j by optimisation, for pumping operation networks, results in the corresponding pumping head: H p, j = Z I P P, j − Z S P, j

(8.9.49)

where Z SP,j is the water level in the suction basin of IPPj . Taking into account head loss H IPP,j-n on the path IPPj – n: HI P P, j−n =

N T j si j   i j=1 k=1

Θi j Jk,i j xk,i j −

N T j + si j   i j=1

, Ωk,i j Jk,i j + H p,i j

(8.9.50)

k=1

the piezometric head Z n at the node n is determined from the equation: Z n = Z I P P, j − HI P P, j−n

(8.9.51)

718

8 Hydraulic Simulation and Optimisation of Water Transmission …

where ZT n is the elevation head at the node n. The residual pressure head H n at the node n can be calculated using Eq. (8.9.30). The computer program OPLIRA has been elaborated [157] based on the LOM, in the FORTRAN programming language for PC-compatible micro-systems.

8.9.8 Numerical Application The looped distribution network with the topology from Fig. 8.26 is considered. It is made of cast iron and is supplied with a discharge of 1.22 m3 /s provided from two pump stations (Qp,1 = 0.806 m3 /s, Qp,2 = 0.404 m3 /s). The following data is known: pipes length L ij , in m, elevation head ZT j , in m, and necessary pressure HN j = 24 m. A comparative study of network dimensioning is performed using the models EVM, MOM, NOM, and LOM, the last being applied in the hypothesis of concentrated outflow (LOM–C), as well as of uniform outflow along the length of the pipes (LOM–D). Computation was performed considering a transitory turbulence regime of water flow and the optimisation criterion used was UTC (minimum updated total costs). The results of the numerical solution performed by means of a PC micro-system, referring to the hydraulic characteristics of the pipes (discharge, diameter, head loss, velocity) are summarised in Tables 8.16 and 8.17.

Fig. 8.26 Plan of the designed distribution network

540

460

515

450

350

485

545

470

180

220

500

475

530

10−9

11−10

12−11

32−12

14−13

15−14

16−15

17−16

18−17

32−18

20−19

21−20

470

8−7

9−8

470

410

5−4

380

450

4−3

12−6

560

3−2

6−5

480

2−1

(m)

ij

Pipe i–j

0.08192

0.03088

0.27757

0.22695

0.19425

0.14540

0.11293

0.04911

0.42005

0.23271

0.16874

0.11621

0.06848

0.02729

0.15178

0.12616

0.10431

0.07719

0.04476

0.01372

350

200

500

500

500

450

350

250

600

500

400

350

300

200

400

350

350

300

250

150

1.087

2.582

1.777

0.527

0.319

0.812

2.088

2.066

1.097

1.133

2.177

1.864

1.722

2.010

1.306

2.235

1.345

1.812

1.992

2.370

0.85

0.98

1.41

1.16

0.99

0.91

1.17

1.00

1.49

1.19

1.34

1.21

0.97

0.87

1.21

1.31

1.08

1.09

0.91

0.78

0.15016

0.05114

0.25322

0.15660

0.13865

0.07548

0.07325

0.02912

0.26445

0.13028

0.08398

0.06718

0.04405

0.01984

0.09861

0.07299

0.08931

0.07195

0.04467

0.01488

Qij (m3 /s)

V ij (m/s)

MOM hij (m)

Qij L (m3 /s)

LDij (mm)

EVM

450

300

500

400

400

350

400

300

500

400

350

350

350

300

350

350

350

400

400

300

Dij (mm)

Table 8.16 Pipe hydraulic characteristics determined with EVM, MOM and NOM

1.260

1.137

1.928

1.066

0.684

1.078

0.578

0.377

1.472

1.509

1.462

0.836

0.422

0.169

1.487

1.008

1.316

0.460

0.221

0.097

hij (m)

0.94

0.72

1.29

1.25

1.10

0.78

0.58

0.41

1.35

1.04

0.87

0.70

0.46

0.28

1.03

0.76

0.93

0.57

0.36

0.21

V ij (m/s)

0.14410

0.06085

0.26553

0.16457

0.14401

0.06911

0.07628

0.02019

0.28601

0.13969

0.10410

0.07668

0.03863

0.01934

0.11076

0.08514

0.08692

0.07005

0.04557

0.01715

Qij (m3 /s])

NOM

450

350

600

450

450

350

350

200

700

450

400

350

250

200

400

350

400

350

250

200

Dij (mm)

0.900

0.549

0.640

0.484

0.305

0.694

0.974

1.159

0.236

0.720

0.850

0.830

1.444

1.034

0.707

1.039

0.477

0.682

2.062

0.838

hij (m)

(continued)

0.91

0.63

0.94

1.04

0.91

0.72

0.79

0.64

0.74

0.88

0.83

0.80

0.79

0.62

0.88

0.89

0.69

0.73

0.93

0.55

V ij (m/s)

8.9 Optimisation Models of Looped Urban Water Supply Networks 719

300

8−2

345

310

7−1

15−9

340

32−31

320

400

31−30

340

250

30−29

14−8

190

28−29

13−7

440

27−28

370

510

27−26

11−5

490

26−25

335

300

31−24

320

420

23−24

10−4

550

22−23

9−3

430

21−22

(m)

ij

Pipe i–j

0.01101

0.01728

0.01655

0.01582

0.00845

0.00811

0.00934

0.01009

0.07343

0.03376

0.00399

0.00791

0.03105

0.07723

0.03270

0.00833

0.01337

0.05587

0.10602

125

150

150

150

125

125

125

125

250

250

100

125

200

300

200

125

150

300

350

2.836

2.470

2.415

2.408

1.577

1.526

1.795

2.154

3.176

0.824

0.914

0.825

2.417

2.056

2.976

1.440

1.973

1.183

1.456

0.90

0.98

0.94

0.90

0.69

0.66

0.76

0.82

1.50

0.69

0.51

0.64

0.99

1.09

1.04

0.68

0.76

0.79

1.10 350

−0.07448

300

−0.05624

0.04076

0.03550

0.02285

0.05399

0.01821

0.01325

0.01059

0.00893

0.25816

0.13064

300

300

300

300

200

200

200

200

600

400

350

250

−0.02257 0.08290

350

300

0.07319

0.03873

400

300

−0.04011 0.09618

300

Dij (mm)

0.03066

Qij (m3 /s)

V ij (m/s)

MOM hij (m)

Qij L (m3 /s)

LDij (mm)

EVM

Table 8.16 (continued)

0.525

0.369

0.162

0.987

0.843

0.468

0.268

0.196

0.516

1.349

0.691

−0.550

−0.542

1.099

0.673

0.548

−0.938

−0.810

0.370

hij (m)

0.58

0.50

0.32

0.76

0.58

0.42

0.34

0.28

0.91

1.04

0.86

0.80

0.46

0.76

0.55

0.77

0.77

0.57

0.43

V ij (m/s)

0.02864

0.04179

0.02108

0.03946

0.01869

0.01605

0.01196

0.00666

0.22622

0.11834

0.07939

−0.05534

−0.01942

0.08074

0.03619

0.07654

−0.05484

−0.01985

0.02680

Qij (m3 /s])

NOM

250

250

200

250

200

200

150

125

600

450

400

300

250

400

250

400

350

250

300

Dij (mm)

0.518

0.996

0.883

1.031

0.659

0.516

1.138

0.969

0.319

0.464

0.244

−0.401

−0.315

0.515

1.155

0.273

−0.397

−0.410

0.226

hij (m)

(continued)

0.58

0.85

0.67

0.80

0.60

0.51

0.68

0.54

0.80

0.74

0.63

0.78

0.40

0.64

0.74

0.61

0.57

0.40

0.38

V ij (m/s)

720 8 Hydraulic Simulation and Optimisation of Water Transmission …

330

340

360

350

340

330

320

370

340

330

320

320

290

16−10

18−11

25−13

26−14

27−15

16−28

17−29

18−30

19−25

20−26

21−27

22−28

23−30

(m)

ij

Pipe i–j

0.00453

0.01097

0.18657

0.01080

0.00632

0.00518

0.01101

0.00447

0.02977

0.00470

0.00315

0.00234

0.00489

100

125

400

125

100

100

125

100

200

100

100

100

100

1.353

2.612

1.646

2.615

3.009

2.231

2.632

1.500

1.721

1.753

0.842

0.453

1.784

0.58

0.89

1.49

0.88

0.81

0.66

0.90

0.57

0.95

0.60

0.40

0.30

0.62

200

−0.00465

300 150

−0.00360

450

300

0.03159

0.18891

0.05878

250

125

−0.00375 0.02657

350 250

0.08977

300

300

300

300

Dij (mm)

−0.02669

0.04261

0.02944

0.05818

0.05038

Qij (m3 /s)

V ij (m/s)

MOM hij (m)

Qij L (m3 /s)

LDij (mm)

EVM

Table 8.16 (continued)

−0.139

0.292

1.204

1.044

0.581

−0.064

−0.438

−0.568

1.103

0.582

0.286

1.053

0.767

hij (m)

0.20

0.45

1.19

0.83

0.54

0.15

0.31

0.54

0.93

0.60

0.42

0.82

0.71

V ij (m/s)

−0.00299

0.00747

0.19690

0.04302

0.03628

0.00352

−0.00114

−0.00482

0.08705

0.03694

0.03661

0.05435

0.04025

Qij (m3 /s])

NOM

125

250

500

350

250

150

100

250

400

250

250

350

300

Dij (mm)

−0.199

0.038

0.582

0.196

0.805

0.138

−0.112

−0.018

0.397

0.858

0.867

0.316

0.377

hij (m)

0.24

0.15

1.00

0.45

0.74

0.20

0.15

0.10

0.69

0.75

0.75

0.57

0.57

V ij (m/s)

8.9 Optimisation Models of Looped Urban Water Supply Networks 721

722

8 Hydraulic Simulation and Optimisation of Water Transmission …

Table 8.17 Pipe hydraulic characteristics determined with LOM−C and LOM−D Pipe i–j

LOM−C Qij (m3 /s)

k

x k,ij Dk,ij hk,ij (m) (mm) (m)

V k,ij Qij (m/s) (m3 /s)

k

x k,ij Dk,ij hk,ij (m) (mm) (m)

2–1

0.01678

1

480 250

0.260

0.34

0.01698

1

480 250

0.306

0.35

3–2

0.04538

1

27

400

0.009

0.36

0.04585

1

22

400

0.001

0.37

2

534 350

0.351

0.47

2

538 350

0.343

0.48

4–3

0.07099

LOM−D

1

273 400

0.216

0.57

2

177 350

0.275

0.74

0.07217

V k,ij (m/s)

1

183 400

0.107

0.57

2

267 350

0.358

0.75

5–4

0.08745

1

410 400

0.483

0.70

0.08943

1

410 400

0.443

0.71

6–5

0.07716

1

470 400

0.435

0.61

0.07890

1

470 400

0.407

0.63

12–6

0.10278

0.10452

1

185 500

0.096

0.52

2

195 400

0.313

0.82

1

96

300

0.029

0.28

103 500

0.020

0.53

277 400

0.377

0.83

1

28

300

0.001

0.28

8–7

0.01996

2

374 250

0.282

0.41

2

442 250

0.355

0.41

9–8

0.04966

1

540 350

0.422

0.52

0.04957

1

540 350

0.397

0.52

10–9

0.07172

1

379 400

0.305

0.57

0.07285

1

225 400

0.144

0.58

2

81

350

0.128

0.75

2

235 350

0.312

0.76

11–10 0.09208 12–11 0.12788

1

6

500

0.002

0.47

2

509 400

0.663

0.73

1

319 500

0.251

0.65

0.01987

1 2

0.09797 0.13111

1

94

500

0.012

0.50

2

421 400

0.544

0.78

1

236 500

0.141

0.67

2

131 400

0.322

1.02

2

214 400

0.420

1.04

32–12 0.26622

1

350 600

0.450

0.94

0.27119

1

350 600

0.360

0.96

14–13 0.02521

1

485 300

0.227

0.36

0.02526

1

485 300

0.231

0.36

15–14 0.05825

1

159 450

0.047

0.37

0.05872

1

72

0.003

0.37

0.06994

16–15 0.07150

1

389 400

0.311

0.57

2

81

350

0.127

0.74

1

66

500

0.048

0.63

2

114 400

0.263

0.98

1

43

500

0.040

0.71

2

177 400

0.514

1.11

32-18 0.25872

1

500 600

0.609

20-19 0.05466

1

475 350

21-20 0.14958

1

480 500

2

50

17–16 0.12354 18–17 0.13930

21-22 0.05292

400

450

1

206 400

0.118

0.56

2

264 350

0.334

0.73

0.12257

1

180 400

0.297

0.98

0.13864

1

220 400

0.491

1.10

0.92

0.26230

1

500 600

0.524

0.93

0.447

0.57

0.05439

1

475 350

0.407

0.57

0.513

0.76

0.14945

1

452 500

0.411

0.76

0.165

1.19

2

78

400

0.086

1.19

1

430 450

0.068

0.25

−0.03627 1

262 350

−0.097 0.38

1

340 450

0.085

0.33

2

90

350

0.079

0.55

22-23 −0.03393 1

51

350

−0.019 0.35

0.03930

(continued)

8.9 Optimisation Models of Looped Urban Water Supply Networks

723

Table 8.17 (continued) Pipe i–j

LOM−C Qij (m3 /s)

LOM−D k

x k,ij Dk,ij hk,ij (m) (mm) (m)

2

499 300

23-24 −0.06466 1

420 450

31-24 0.08636 26-25 0.03711

V k,ij Qij (m/s) (m3 /s)

k

x k,ij Dk,ij hk,ij (m) (mm) (m)

−0.412 0.48

2

388 300

−0.153 0.41

−0.06678 1

270 450

−0.082 0.42

2

150 350

−0.145 0.69

1

300 400

0.302

1

34

500

0.013

0.44

2

266 400

0.306

0.69

1

227 350

0.102

0.39

2

263 300

0.257

0.53

1

510 400

0.536

0.66

27-28 −0.03953 1

440 350

−0.223 0.41

27-26 0.08245

0.08848 0.03721 0.08173

V k,ij (m/s)

−0.245 0.51

0.70

1

221 350

0.082

0.39

2

269 300

0.235

0.53 0.65

1

510 400

0.477

−0.03837 1

262 350

−0.106 0.40

2

178 300

−0.148 0.54

28-29 −0.06559 1

190 350

−0.254 0.68

−0.06957 1

190 350

−0.221 0.72

30-29 0.09444

250 400

0.342

0.09810

1

4

500

0.001

0.50

2

246 400

0.289

0.78

1

250 500

0.150

0.66

31-30 0.12749

1

0.75

1

365 500

0.286

0.65

0.13003

2

35

400

0.087

1.02

2

150 400

0.252

1.04

32-31 0.24520

1

340 600

0.373

0.87

0.24985

1

340 600

0.296

0.88

7-1

0.00703

1

310 250

0.033

0.14

0.00683

1

310 250

0.037

0.14

8-2

0.01178

1

300 250

0.084

0.24

0.01151

1

300 250

0.086

0.23

9-3

0.01493

1

335 250

0.146

0.30

0.01422

1

335 250

0.139

0.29

10-4

0.01910

1

320 300

0.089

0.27

0.01830

1

138 300

0.027

0.26

2

182 250

0.103

0.37

11-5

0.04796

1

370 350

0.271

0.50

0.04820

1

370 350

0.244

0.50

13-7

0.02083

1

41

300

0.013

0.29

0.02072

1

68

300

0.009

0.29

2

299 250

0.245

0.42

2

272 250

0.208

0.42

14-8

1

133 350

0.043

0.32

2

187 300

0.131

0.44

0.04350

1

345 350

0.210

0.45

16-10 0.04771

1

46

450

0.010

0.30

15-9

0.03120

0.03094

1

237 350

0.063

0.32

2

83

300

0.031

0.44

0.04157

1

345 350

0.170

0.43

0.04216

1

330 350

0.166

0.44

2

284 350

0.205

0.50

18-11 0.06265

1

340 350

0.416

0.65

0.06555

1

340 350

0.397

0.68

25-13 0.03134

1

302 350

0.099

0.33

0.03117

1

119 350

0.028

0.32

2

58

300

0.041

0.44

2

241 300

0.182

0.44

1

350 350

0.271

0.51

1

350 350

0.294

0.51

26-14 0.04940

0.04871

(continued)

724

8 Hydraulic Simulation and Optimisation of Water Transmission …

Table 8.17 (continued) Pipe i–j

LOM−C Qij (m3 /s)

27-15 0.08148

LOM−D k

x k,ij Dk,ij hk,ij (m) (mm) (m)

V k,ij Qij (m/s) (m3 /s)

k

x k,ij Dk,ij hk,ij (m) (mm) (m)

V k,ij (m/s)

0.65

0.65

1

340 400

0.350

1

340 400

0.299

16-28 −0.03515 1

330 350

−0.134 0.37

0.08158

−0.02902 1

326 350

−0.102 0.30

17-29 −0.00595 1

320 200

−0.076 0.20

−0.00563 1

320 250

−0.027 0.20

18-30 0.01368

1

370 250

0.137

0.28

0.01501

1

370 250

0.174

0.31

19-25 0.03009

1

340 300

0.223

0.43

0.02983

1

330 350

0.343

0.57

21-27 0.17292

1

320 500

0.452

0.88

0.17347

1

320 500

0.363

0.88

22-28 0.04767

1

320 450

0.065

0.30

0.03639

1

320 450

0.041

0.23

23-30 −0.00724 1

290 200

−0.099 0.23

−0.00746 1

290 200

−0.127 0.24

The significance of (–) sign of discharges and head losses in Tables 8.16 and 8.17 is the change of flow sense in the respective pipes with respect to the initial sense considered in Fig. 8.26. Figure 8.27 illustrates, starting from the node source 32 to the control node 1, on the path 32–18–17–16–15–14–13–7–1, the piezometric lines obtained using the four mentioned computation models, evidencing their deviation from the optimal theoretical form. Figure 8.27 also includes the corresponding values of the objective Fig. 8.27 Hydraulic grade lines along the path 32–18– 17–16–15–14–13–7–1

8.9 Optimisation Models of Looped Urban Water Supply Networks

725

function F c , pumping energy W e , as well as specific energy consumption for water distribution wsd . According to the performed study it was established that: • all the pipes of the network are operating in a transitory turbulence flow; • there is a general increase of pipes diameters achieved by optimisation models (MOM, NOM, LOM) with respect to EVM, because the classical model does not take into account the minimum consumption of energy and the diversity of economical parameters; • in comparison with the results obtained by EVM, the ones obtained by optimisation models are more economical, a substantial reduction of specific energy consumption for water distribution is achieved (MOM—29.9%, NOM— 59.8%, LOM-C—70.9%, LOM-D—74.3%) as well as a reduction of pumping energy (MOM—18.4%, NOM—18.6%, LOM-C—27.2%, LOM-D—27.8%), at the same time the objective function has also smaller values (MOM—5.8%, NOM—6.6%, LOM-C—4%, LOM-D—4.8%); • the optimal results obtained using LOM are superior energetically to those offered by MOM and NOM, leading to pumping energy savings of 11% even if the objective function has an insignificant increase (not more than 3%); • also, the application of LOM for uniform outflow along the length of the pipes, has led to the minimum deviation from the optimal form of the piezometric line, especially to a more uniform distribution of the pumping energy, by elimination of a high level of available pressure at some nodes even at maximum consumption. The smallest value of the specific energy consumption, namely that of 0.0041 kWh/m3 , also supports this assertion; • reduction of the pressure in the distribution network achieved in this way, is of major practical import, contributing to the diminishing of water losses from the system.

8.9.9 Conclusions The mathematical programming, as a fundamental procedure for optimising the structures in general, together with graph theory and the increasing implication of computers in solving mathematical formulations have created conditions for solving efficiently some optimisation problems of WDSs design. The different types of programming which exist (linear, non-linear, whole, geometric, etc.) provide multiple possibilities for solving specific problems. Some main conclusions have been drawn from the evaluation of results presented in this study: (1) The implementation of the NOM or LOM coupled with the mathematical model of optimal discharges (Eqs. 8.9.12−8.9.14) into a computer program for optimal design of looped networks, leads not only to optimal diameters, but also guarantees high security of supply in their operation.

726

8 Hydraulic Simulation and Optimisation of Water Transmission …

(2) The provided results of the LOM in the assumption of distributed discharge on route confirms that the designed water supply pipe networks using this model have an energy performance higher than the designed networks applying any other discussed models. (3) The developed optimisation models, very general and practical, offers the possibility of optimal design of water supply networks using multiple objectives and considers the transitional or turbulent flow regime. It has the advantage of using not only cost criteria, but also energy consumption, consumption of scarce resources and other criteria can be expressed by simple options in the objective function (Eq. 8.9.7). (4) The LOM could be applied to any looped or tree-shaped network, either when piezometric heads at pressure devices (pump stations or reservoirs) must be determined or when these heads are given. It permits the determination of an optimal distribution of commercial diameters between each pair of network nodes and the length of pipe segments corresponding to these diameters. Also, this facilitates the consideration of uniform outflow along the length of the network pipes. A more uniform distribution of pumping energy is achieved so that the head losses and the parameters of pump stations can be determined more precisely. (5) For other analysed larger size networks, the energy savings due to diminishing pressure losses and operation costs when applying the LOM represents about 5−25%, this is of great importance, considering the general energy issues. (6) Further studies must be done to investigate the application of the proposed optimisation models to classical test cases in order to compare its performance with other previous works. The presented study attempts to obtain a near-complete solution to the problem of optimal design of distribution networks. The proposed models are capable of handling almost all standard and non-standard components of pipe networks (i.e., pipes, source and booster pumps, reservoirs, check and pressure-reducing valves). The optimisation approach used in this study does not require calculation of derivatives. This makes the methods more efficient and consequently serves the designers to get the best design of even the most complicated WDSs with fewer efforts.

8.10 Multi-objective Optimisation of Water Distribution Networks 8.10.1 Preliminary Considerations Distribution system costs within any water supply scheme may be equal to or greater than 60% of the entire cost of the project [21, 160]. These observations highlight

8.10 Multi-objective Optimisation of Water Distribution Networks

727

the need for an efficient and safe water distribution network (WDN). The reduction of the cost and energy consumption of the WDN can be achieved through its design and operational optimisation. An important stage of network design is to find the optimum network layout which satisfies requirements such as pressure, power consumption and demands at different nodes and also to minimise cost while meeting a performance criterion. The development of WDNs without the use of optimisation provides non-optimal structures, based essentially on the immediate response to the growing water demand of population and industry [21]. These non-optimal structures are translated into nonefficient systems in terms of design and operation. The unpredictability of growing water demand also creates a challenge for optimisation techniques. For these reasons, recourse to the optimisation tools is crucial. For the optimal design of WDNs both steady and transient states must be taken into consideration. Optimisation problems can be solved using conventional trial and error methods or more effective optimisation methods. However, in WDNs, the optimisation process by trial and error methods can present difficulties due to the complexity of these systems such as multiple pumps, valves and reservoirs, head losses, large variations in pressure values, several demand loads, etc. For this reason, innovative linear [161], non-linear [162–164] and heuristic [165–171] optimisation algorithms are becoming more widely explored in optimisation processes of the WDNs. In the solution procedure, each algorithm is linked with a hydraulic analysis solver of WDNs to obtain the optimum solution. Consideration of reliability in WDNs also has been drawing increasing attention over the past few years [172–174]. WDN design requirements have been shifting from a single objective of economic considerations in early years to a comprehensive multi-objective design in recent years [175]. This section provides a survey of the most approached method, models and numerical examples for multi-objective optimisation of WDNs design and operation [18]. The main deterministic and heuristic optimisation techniques are synthesised, a single- and multi-objective optimisation problem is generally formulated, and the main optimisation objectives, decision variables and constraints for the design, rehabilitation and operation of WDNs are discussed. Additionally, some deterministic and heuristic multi-objective optimisation models for WDN design and rehabilitation is included and numerically exemplified. Finally, the advantages and disadvantages of the optimisation techniques and models used for designing WDNs are presented along with some recommendations on future research directions.

8.10.2 Methods and Techniques of Optimisation Due to the complexities in the optimal design of WDNs, many researchers have applied diverse suitable calculation methods to solve the problem. The optimisation methods and techniques can be classified into two main categories: (1) deterministic methods, based essentially on the computation of the objective function gradient and/or function evaluations and (2) heuristic techniques, based essentially

728

8 Hydraulic Simulation and Optimisation of Water Transmission …

on exploratory search and natural phenomena or even on artificial intelligence. Heuristic searches that use the heuristic function in a strategic way are referred to as meta-heuristic techniques. The deterministic methods most applied in WDN optimisation comprise linear programming (LP), integer linear programming (ILP), non-linear programming (NLP), integer non-linear programming (INLP) and dynamic programming (DP). Optimisation problems that combine continuous and integer values are referred to as mixed-integer programming (MIP). These kinds of algorithms enable finding the exact position of an optimal solution. However, they usually converge to local optimal solutions which may not be the global optimum. In addition, the need of derivative evaluations can, in some cases, complicate the optimisation process. The heuristic techniques usually provide only suboptimal solutions because they do not attempt to escape from local optimum. These drawbacks have led to the introduction of meta-heuristics. In fact, the prefix “meta”, which means “upper level methodology”, indicates that meta-heuristic algorithms can be viewed as “higher level” heuristics. A number of meta-heuristic algorithms have been developed and extensively applied, including genetic algorithms (GAs), evolutionary algorithms (EAs), differential evolution (DE), cross-entropy (CE), simulated annealing (SA), tabu search (TS), particle swarm optimisation (PSO), ant colony optimisation (ACO), harmony search (HS), shuffled complex evolution (SCE), shuffled frog leaping algorithm (SFLA), etc. These techniques provide the advantages of not requiring derivatives calculations and do not rely on the initial choice of values for the decision variables. Due to the exploratory nature of the heuristic algorithms, the probability of finding global optimal solutions using these advanced techniques is higher than in the case of deterministic methods. The main disadvantage of these techniques is related to the higher computational effort [176]. The previously described existing meta-heuristic techniques can be divided into three classes [177] summarised in Table 8.18. Local search meta-heuristics operate on a single complete solution and iteratively improve it by making small adjustments called moves. Population-based meta-heuristics operate on a set of solutions and find better solutions by combining solutions from that set into new ones. Finally, constructive meta-heuristics build a solution by working with a single, unfinished, solution and adding one solution element at a time.

8.10.3 Objective of Optimisation A general optimisation problem is defined as the minimisation (or maximisation) of an objective function F subject to equality and/or inequality constraints and can be expressed as [190]: F(X) → min (or max) subject to :

8.10 Multi-objective Optimisation of Water Distribution Networks

729

Table 8.18 Classification of meta-heuristic methods Local search meta-heuristics

Population-based meta-heuristics

Constructive meta-heuristics

Methods

Authors

Methods

Authors

Methods

Authors

SA

Kirkpatrick et al. [178]

GA

Holland [181], Goldberg [182]

PSO

Kennedy and Eberhart [187]

TS

Glover [179, 180]

DE

Storn and Price [183]

ACO

Dorigo and Gambardella [188]

CE

Rubinstein [184] HS

SCE

Liong and Atiquzzaman [185]

SFLA

Eusuff and Lansey [186]

Geem and Kim [189]

φi (X) ≤ 0; i = 1, 2, ... p φ j (X) = 0 j = 1, 2, ...m

(8.10.1)

where X = {x 1 , x 2, …,x n } is the vector of decision variables (continuous or discrete) with dimension n; p is the number of inequality constraints ϕi , and m is the number of equality constraints ϕj . An objective function to which optimisation is performed consists of a mathematical function with real values that expresses a linear or non-linear relationship between the decision variables The goal of a multi-objective problem (MOP) is to optimise (minimise and/or maximise) a number of objective functions simultaneously. The general formulation of a MOP can be stated as: F(X) = F( f 1 (X), . . . , f k (X)) → min (or max) subject to : φi (X) ≤ 0; i = 1, 2, . . . p φ j (X) = 0 j = 1, 2, . . . m

(8.10.2)

where k is the number of objective functions. Multi-objective optimisation methods have the advantage of providing a set of optimal solutions, called Pareto front [190], which shows the trade-offs between the different objectives, especially the conflicting ones, and after their analysis, only one solution is selected based on an additional criterion. EAs are usually the most used to solving MOPs.

730

8 Hydraulic Simulation and Optimisation of Water Transmission …

Optimisation problem for WDNs arises when it is desired to solve the design, rehabilitation/extension or operation problem based on an optimisation criterion expressed by the objective function, subject to a set of practical constraints. Many aspects related to the application of the multi-objective heuristic techniques for optimal design or rehabilitation of WDNs were investigated, such as: GA [191, 192], PSO [193], ACO [194] and SFLA [195]. Objectives of a general optimisation model of WDN design can be divided into four groups: (1) economic objectives such as total costs (capital and operation) [196, 197] and rehabilitation costs [198], (2) performance objectives, reflecting the pressure deficit at demand nodes [199] and reliability and resilience of the system [200], (3) community objectives, which include a benefit function of the solution (i.e., rehabilitation, expansion) [201], water quality deficiencies [202] and hydraulic failure of the system [203], (4) environmental objectives namely greenhouse gas (GHG) emissions consisting of capital and operating emissions [204]. • Design optimisation. Typically, in design optimisation problem of WDNs, the objective function is expressed as a function of costs that can be associated to distinct water supply components or even costs associated to energy consumption. Annual total cost (capital and energy costs) (ATC) can be defined by a singleobjective function expressed with equation [160]:

ATC = β0 (Cn + C p ) + Cop

(8.10.3)

Cop = p1 Cn + p2 C p + Ce

(8.10.4)

in which

where β0 = 1/T r is the discount (amortisation) rate of the operation period T r ; C n is the network investment cost, obtained by adding the capital costs of each compound pipe; C p is the pumping station capital cost, proportional to the installed power; C e is the pumping energy cost; C op is the annual operation cost; p1 and p2 are the service and maintenance rates for network pipes and pumping stations, respectively. Recently, more focus has been laid on the life cycle cost (LCC) defined as: LCC = Cn + C p + u r Cop

(8.10.5)

in which ur is the update rate (present value factor or discount factor). • Rehabilitation. For an existing pipe network, rehabilitation consists of the replacement of pipes with the same or larger diameter, cleaning or cleaning and lining of existing pipes. To formulate a network rehabilitation problem [198] some studies consider only a single economic objective, while other investigations apply a multi-objective optimisation framework considering the network benefit [201],

8.10 Multi-objective Optimisation of Water Distribution Networks

731

violations of pressure at network nodes [199], velocity constraints in pipes [205] and water quality deficiencies at network nodes [206]. • Operational optimisation. The objective function of the operational optimisation problem of WDNs can assume various forms. For example, the objective can be to maintain the minimum pressure on the network or to minimise the pumping costs through the use of pumps with variable speeds [207] or to maximise energy efficiency of a supply system that uses water and wind turbines for power generation [208]. • Reliability and resilience of the system represent performance characteristics of a WDN in relation to current and most importantly future uncertain conditions. As reliability measure can be considered hydraulic availability index [209] or hydraulic performance index [172]. Numerous researchers proposed indirect reliability indices as surrogate reliability measures (SRMs). Two of the most employed SRMs are the resilience index [173], related to the WDN energy surplus and the entropy index [210] related to the flow path uniformity within the WDN. The resilience can be defined in broadest terms as the ability of a WDN to adapt to or recover from a significant disturbance, which can be internal (e.g., pipe failure) or external (e.g., natural disaster). Prasad and Park [211] used the network resilience index (NRI) proposed by Todini [173], whose maximisation can be considered one of the objectives of multi-objective optimisation in WDN design [212].

8.10.4 Decision Variables and Constraints The decision variables define the characteristics of each hydraulic component in the design such as pipe diameters [213], pipe lengths [161], pipe roughness [214], pressure heads at nodes [215], number of pumps [216], pump head [217], tank volumes or elevations and valve settings [218]. In a looped pipe network in steady state, the objective function is conditioned by hydraulic constraints given by physical laws governing the water flow (mass and energy conservation) and minimum pressure head requirements at the demand nodes [160]. Additional constraints can be the operational constraints (e.g., minimum/maximum pressure at nodes [219], minimum/maximum water velocity in pipes [220] and minimum/maximum allowable residual chlorine concentration at nodes [221]) and constraints on decision variables (e.g., minimum pipe diameters and use of a discrete set of commercially available diameters [202], limits on pipe segment lengths [161] and pump station capacities [222]). Additionally, in transient state the continuity and momentum equations [223] are considered as constraints.

732

8 Hydraulic Simulation and Optimisation of Water Transmission …

8.10.5 Overview of the Multi-objective Optimisation Models in Literature In most researches, optimal design, operation and rehabilitation of WDNs have been investigated at a specific time (statically) regardless of the relationship between them (separately). Some researches are focused on optimal design of WDNs [224] and some of them focus on optimal operation scheduling of WDNs [225]. Additionally, some researches have focused on rehabilitation of WDNs [226]. In literature, most MOPs applied to WDN optimisation are represented by combinations of two objectives such as: minimising design cost and maximising hydraulic benefits [201]; minimising rehabilitation cost and transient impacts (through a surge damage potential factor-SDPF) [171] or combinations of three objective, such as minimising LCC and life cycle GHG emissions (LCE), and maximising NRI [212]. Cenedese and Mele [145] applied a mathematical approach based on the reduced gradient (RG) with multi-objective analysis to select the optimal solution for the hydraulic networks. Walski et al. [227] were the first to use multi-objective evolutionary optimisation to solve a WDN design problem. They dealt with minimisation of network costs and pressure. Several other multi-objective optimisations for least-cost design (LCD) and maximum resilience of WDNs were approached in the literature [173, 211, 228–232]. Kapelan et al. [233] performed the optimal design of a new WDN considering two objectives, the construction costs and network reliability, using NSGA-II. This methodology was tested on several cases, all based on the New York tunnels network reinforcement problem. The results obtained demonstrate that the proposed methodology is capable of identifying robust Pareto optimal solutions despite significantly reduced computational effort. Wu et al. [197] considered the use of variable speed pumping during the optimisation of network design using multi-objective GA for the reduction of total costs and GHG emissions and concluded that variable speed pumps are effective for achieving the multiple objectives. Chandramouli [174] provided a detailed methodology on the development of an optimisation model including reliability for design of WDNs using GAs and hydraulic simulator EPANET [234] in MATLAB. A new parameter was proposed to determine the overall network reliability using network nodal demands and their corresponding satisfaction indices. The proposed methodology was tested on a Hanoi network. Yazdi et al. [170] developed a hybrid algorithm for multi-objective design of WDNs. This method combines the global search schemes of DE with the local search capabilities of HS to enhance the search proficiency of EAs. This method was compared with other multi-objective EAs and the results showed that the proposed hybrid method provided better optimal solutions and outperformed the other algorithms.

8.10 Multi-objective Optimisation of Water Distribution Networks

733

El-Ghandour and Elansary [171] recently investigated the problem of optimal rehabilitation of WDNs for both steady and transient state. Two objectives are considered: minimising rehabilitation cost by considering pipe diameters as decision variables and minimising the transient impacts by minimising an SDPF. A multi-objective ACO model was developed to solve this problem. This model was verified using the well-known New York tunnels network. In general, there are few researches in WDNs, which consider the relationship between the design and renovation planning of WDN during its life cycle. Ghajarnia et al. [235] introduced multi-objective dynamic design of WDNs. The first objective was to minimise the total cost of dynamic design and rehabilitation of the network and the second objective was to maximise the network fuzzy reliability index. The developed method was tested on two sample networks. Results showed that the dynamic design method had a positive performance on more decreasing the design costs and increasing reliability of the network. Siew et al. [236] presented penalty-free multi-objective evolutionary optimisation approach for the phased whole-life design and rehabilitation of WDNs. An external hydraulic analysis model based on EPANET 2 called EPANET-PDX (pressuredependent extension) was used. Results for two sample networks showed that the algorithm was stable and could find optimal and near-optimal solutions for reliably and efficiently. Shirzad et al. [237] used an approach for simultaneous optimization of initial design and rehabilitation scheduling of WDNs during their life cycle. The optimization model consists of a multi-objective ACO algorithm linked to a pressure-analysis model. The first objective is to minimise the total cost of dynamic design and renovation of the network and the second objective is to maximise the network reliability index. To evaluate the dynamic design in comparison to the static design, a small sample network and a real WDN have been used. The results showed that the dynamic design produces more reliable and lower costs in comparison to the static design or rehabilitation scheduling separately. Dini and Tabesh [238] developed a multi-objective ACO meta-model by the combination of ACO algorithm, hydraulic simulator EPANET and an artificial neural network (ANN) within MATLAB. Comparison of the results in the sample network showed that the design and rehabilitation planning of the network during its life cycle can create lower costs and higher reliability. Huang et al. [239] developed a multi-objective optimisation model of WDN design that includes four objectives: minimising transient adverse impacts (for two objectives), minimising network cost and maximising hydraulic reliability. The non-dominated sorting genetic algorithm III (NSGA-III) was adopted to solve this multi-objective optimisation problem. Table 8.19 summarises the main researches developed especially in the last two decades for multi-objective optimisation of WDNs.

734

8 Hydraulic Simulation and Optimisation of Water Transmission …

Table 8.19 Previous multi-objective optimisation studies Author(s)

Year

Objectives

Optimisation method

Application

Walski et al.

1988

• Minimum cost • Minimum pressure

EA

Design

Halhal et al.

1997

• Minimum total cost Messy GA • Maximum hydraulic benefit

Design

Todini

2000

• Minimum cost • Maximum resilience

GA

Design

Prasad and Park

2004

• Minimum cost • Maximum resilience

GA

Design

Kapelan et al.

2005

• Minimum cost • Maximum resilience

NSGA-II

Design

Creaco and Franchini

2012

• Minimum total cost GA and LP • Maximum resilience

Design

Wu et al.

2012

• Minimum total cost GA • Minimum GHG emissions

Design and operation

Ghajarnia et al.

2012

• Minimum total cost Honey-bee mating • Maximum network optimisation fuzzy reliability index

Dynamic design

Wang et al.

2014

• Minimum cost • Maximum resilience

Multi-objective EAs (MOEAs)

Design

Zheng et al.

2014

• Minimum cost • Maximum resilience

Self-adaptive multi-objective DE

Design

Siew et al.

2014

• Minimum total cost NSGA-II and • Maximum demand EPANET-PDX satisfaction ratio

Design and rehabilitation

Wang et al.

2015

• Minimum cost • Maximum resilience

Design

Chandramouli

2015

• Minimum total cost GAs and EPANET • Maximum resilience

Design

Piratla

2016

• Minimum LCC • Minimum LCE • Maximum NRI

Design

NSGA-II

GANetXL

(continued)

8.10 Multi-objective Optimisation of Water Distribution Networks

735

Table 8.19 (continued) Author(s)

Year

Objectives

Optimisation method

Application

Yazdi et al.

2017

• Minimum cost • Maximum resilience

DE and HS

Design

Shirzad et al.

2017

• Minimum cost • Maximum resilience

ACO and EPANET-PDX

Design and rehabilitation

El-Gahandour and Elansary

2018

• Minimum cost • Minimum SDPF

ACO

Rehabilitation for steady and transient states

Beygi et al.

2019

• Minimum total cost NSGA-II and • Maximum EPANET resilience

Dini and Tabesh

2019

• Minimum total cost ACO, EPANET and Design and • Maximum ANN Rehabilitation combined network reliability index

Hang et al.

2020

• Minimum cost NSGA-III • Minimum transient adverse impacts • Maximum hydraulic reliability

Design and operation

Design

8.10.6 Examples of WDN Design Optimisation 8.10.6.1

Single-Objective Optimisation

In this example, the optimal design problem of a distribution network, supplied by pumping or gravity from one or more node sources is formulated as a nonlinear objective function subject to linear and non-linear constraints [161]. A nonlinear optimisation technique is used in which the minimum total capital cost in terms of pipe diameters and reservoir elevations or pump heads is considered as a single-objective function. The minimum and maximum sizing of pipe diameters, pipe flow velocities and nodal pressures with the hydraulic analysis equations of the network are considered as constraints. This technique has the advantage that it uses a specialised optimisation algorithm which minimises directly an objective multivariable function without constraints. Additionally, the optimisation technique is coupled with a hydraulic analysis performed by the iterative Newton–Raphson method [135]. • Optimisation model. Total capital costs of the distribution network consist of: (a) Cost of the pipes and their installations and (b) Cost of the pressure generating facilities. The objective function F c with constraints, that express the minimum total capital costs, can be written as follows [240]:

736

8 Hydraulic Simulation and Optimisation of Water Transmission …

Fc (Di j , Z IP,k ) = f 1 (Di j ) + f 2 (Z IP,k )

(8.10.6)

and is subject to Dmin ≤ Di j ≤ Dmax (i j = 1, ..., T ) Vmin ≤ Vi j ≤ Vmax (i j = 1, ..., T ) Hmin ≤ H j ≤ Hmax ( j = 1, ..., N )

(8.10.7)

ZIP min ≤ Z IP,k ≤ Z IP max (k = 1, ..., N R P ) where: ZIP,k is the reservoir piezometric head or pump dynamic head; V ij is the flow velocity in pipe ij; H j is the pressure head at node j; V min , V max are the minimum and maximum allowable flow velocities in pipes, respectively; H min , H max are the minimum and maximum allowable nodal pressure heads, respectively; Z IPmin , Z IPmax are the minimum and maximum allowable reservoir piezometric heads/pump dynamic heads, respectively; T is the total number of pipes in the network; N is the total number of nodes; N RP is the number of pressure generating facilities. Discharge continuity and energy must be also conserved for the network. The objective function F c can be changed to unconstrained optimisation problem by using the following transformation [241]: • for pipe diameters:

Di j = Dmin + (Dmax − Dmin ) sin2 di j

(8.10.8)

• for reservoir elevations: Z IP,k = Z IP min + (Z IP max − ZIP min ) sin2 z k

(8.10.9)

where d ij and zk are new transformed variables. The concept of the penalty function (ω) was used and, hence, a generalised objective function can be introduced as: Γ (Di j , Vi j , H j , Z IP,k , ω) = f 1 (Di j ) + f 2 (Z IP,k )+ ⎡ % %2 T $ T $   Vi j 2 Vi j 1− +ω⎣ ++ −1 + Vmax Vmin i j=1 i j=1 ⎤ % %2 N $ N $  Hj 2  Hj + 1− + − 1 ⎦ → min Hmax Hmin j=1 j=1

(8.10.10)

8.10 Multi-objective Optimisation of Water Distribution Networks

737

The objective function of Eq. (8.10.10) can be minimised by the conjugate direction method [242]. The coupled hydraulic and optimisation analysis of pipe networks can be summarised as follows: (a) Assume pipe diameters and reservoir piezometric heads/pump dynamic heads (preliminary design). (b) Do the hydraulic analysis by initially solving the non-linear system of equations at nodes via the Newton−Raphson method to get the piezometric heads at all nodes. Then, discharges, head losses of all pipes and residual pressure heads at the nodes can be determined easily. (c) Compute the objective function of Eq. (8.10.10). (d) Use Powell’s conjugate direction method to minimise the total capital cost objective function. If the objective function is not minimal, pipe diameters and reservoir piezometric heads should be changed. Then, repeat the cycle from stage (b). • Numerical application. A complex network that consists of two fixed-head reservoirs, sixteen pipes, a booster pump and a check valve as shown in Fig. 8.28 is considered. It is supplied with a discharge of 0.165 m3 /s provided from two sources, and for all pipes use ductile iron material. The input data (L ij , in m, qj , in m3 /s, and ZT j , in m) of pipe network is given in Fig. 8.28 and the constraints is imposed from Table 8.20. Results of the numerical solution performed by means of a computer, referring to the hydraulic characteristics of the pipes (optimal diameter Dij , discharge Qij , head loss hij , velocity V ij ) and the nodes (consumed discharge qj , elevation ZT j ,

Fig. 8.28 Schematic of the designed network

738

8 Hydraulic Simulation and Optimisation of Water Transmission …

Table 8.20 Constraints

Value

Allowable diameter (mm)

Allowable velocity (m/s)

Allowable pressure head (m)

Minimum

80

0.15

15.0

Maximum

750

2.50

95.0

piezometric head Z j and pressure head H j ) are presented in Tables 8.21 and 8.22 [75]. The value of the minimised function F c = 1.51×109 . The significance of the (–) sign of discharges and head losses in Table 8.21 is the change of flow sense in the respective pipes with respect to the initial sense considered in Fig. 8.28. The mathematical model expressed by the objective function (8.10.10) based on unconditioned optimisation techniques is capable of handling almost all standard and non-standard components of pipe networks (i.e., pipes, source and booster pumps, reservoirs, check and pressure-reducing valves). Table 8.21 Hydraulic characteristics of the pipes (Optimal continuous solution) Pipe i-j

L ij (m)

Dij (mm)

Qij (m3 /s)

H ij (m)

V ij (m/s)

2–1

2200

381.0

0.07660

2.70

0.67

7–2

2100

361.2

0.07092

2.87

0.69

4–3

600

401.0

0.02003

0.08

0.16

7–4

600

254.6

−0.00997

−0.23

0.21

6–5

1100

424.6

0.03572

0.38

0.25

7–6

1200

287.8

0.04172

3.70

0.64

10 – 7

1800

128.7

0.00693

5.09

0.53

9–8

600

376.9

−0.12371

−3.37

1.11

10 – 9

600

309.0

−0.10371

−6.39

1.38

11–10

Pump

–

0.12836

37.79

–

13–11

750

352.5

0.12836

3.49

1.32

13–12

1200

384.0

0.21074

9.22

1.82

14–13

700

354.5

0.08840

1.59

0.90

15 – 5

1200

380.4

0.03272

0.50

0.29

10–15

1500

382.6

0.02972

0.51

0.26

8–3

1800

304.9

0.05003

4.82

0.69

12 – 8

900

310.8

0.18574

15.33

2.45

8.10 Multi-objective Optimisation of Water Distribution Networks

739

Table 8.22 Hydraulic characteristics of the nodes Node j

Qj (m3 /s)

ZT j (m)

Zj (m)

Hj (m)

1

−0.0766

200.0

230.58

30.58

2

0.006

180.0

197.39

17.39

3

0.030

140.0

194.36

54.36

4

0.030

135.0

194.28

59.28

5

0.003

138.0

190.44

52.44

6

0.006

138.0

190.82

52.82

7

0.012

130.0

194.52

64.52

8

0.012

130.0

199.18

69.18

9

0.020

128.0

195.82

67.82

10

0.012

135.0

189.43

54.43

11

0.000

135.0

227.23

92.23

12

0.025

145.0

214.52

69.52

13

0.006

165.0

223.73

58.73

14

−0.0884

210.0

225.32

15.32

8.10.6.2

Two-Objective Optimisation

• Optimisation model. The optimal rehabilitation of WDNs under both steady and transient states is expressed as a double-objective optimisation problem. The first objective, Eq. (8.10.11), is the least rehabilitation cost; while the second objective, Eq. (8.10.12), is to minimise the expected damage occurred by transient events by minimising the surge damage potential factor (SDPF). These two equations can be represented as follows [171]:

Cn =

T 

ci j (Dk )L i j ; (k = 1, . . . N D ) → min

(8.10.11)

i j=1

 ⎧-  ∗ ∗ N ⎨ dτ if H j (τ ) > Hmax H j (τ ) − Hmax  ∗ ∗ SDPF = → min 0 if Hmin  ≤ H j (τ ) ≤ Hmax ∗ ⎩-  ∗ j=1 Hmin − H j (τ ) dτ if H j (τ ) < Hmin

(8.10.12)

where: cij (Dk ) is the cost of unit length of pipe ij corresponding to diameter k; L ij is the length of pipe ij; N D is total commercially available diameters; N is total number ∗ is the maximum of nodes; H j (τ ) is the pressure head at node j and instant τ; Hmax ∗ allowable pressure head; Hmin is the minimum required pressure head. The network pipe diameters are the decision variable and the hydraulic constraints suggested by Jung et al. [243] are considered.

740

8 Hydraulic Simulation and Optimisation of Water Transmission …

An ACO algorithm was used by El-Ghandour and Elansary [171] to perform the double-objective optimisation in this study. Both a steady state hydraulic analysis model, based on extended linear graph theory [244], and a developed transient analysis model [245] are linked with previous model to evaluate the potential solutions. • Numerical application. The case study of the New York tunnel network (Fig. 8.29) gravity-driven, given by Jung et al. [243], was used to verify the developed model by El-Ghandour and Elansary [171], and the results are compared. The network needs rehabilitation actions by adding new pipes parallel to the existing ones to increase the pressure heads at some demand nodes. The previous optimisation model was applied to the New York tunnel network to determine which of the 21 existing pipes is needed to be duplicated and determining the size of each duplicated pipe from 15 available pipe sizes achieving both the least rehabilitation cost and the minimum SDPF. The layout of the network and the corresponding data are given by Dandy et al. [246]. A transient condition in the network is introduced by sudden demand increase (from 28.3 l/s to 4817.6) at node 10 during a time equal to 1 s. This increase in demand may be due to: a temporary increase in water consumption, a fire flow or a burst pipe. Table 8.23 shows the total cost of the pipes and the pipe sizes selected in the optimisation corresponding to zero SDPF for both the model developed by El-Ghandour and Elansary [171] and the corresponding one given by Jung et al. [243]. Fig. 8.29 New York tunnel network

8.10 Multi-objective Optimisation of Water Distribution Networks

741

Table 8.23 Total cost of the pipes and the selected pipe sizes corresponding to zero SDPF Model

Total cost

Pipe size (mm)

($ millions) 7 Jung et al. [243]

49.1

El-Ghandour and 47.2 Elansary [171]

−

9

15

16

17

18

19

21

3,900 3,000 2,100 3,000 2,100 3,000 1,500

2,700 4,200 −

2,700 3,000 1,800 2,100 1,800

The results showed that the rehabilitation strategy of the network satisfies the constraints with a cost $2 million lower than Jung et al. [243]. Both studies identified the same locations to be duplicated except for one location only. The transient pressure head profiles obtained using the results of the two Pareto optimal solutions summarised in Table 8.23 at most critical nodes 17 and 19 are shown in Fig. 8.30. For the purpose of comparison with the optimal rehabilitation of the network in steady state only, the results given by Dandy et al. [246] is adopted and the transient head profiles for the two nodes are calculated and drawn on the figure.

Fig. 8.30 Transient pressure head profile at nodes 17 and 19

742

8 Hydraulic Simulation and Optimisation of Water Transmission …

From the results shown, the El-Ghandour and Elansary [171] model seems perfectly able to determine pipe sizes with lower total rehabilitation costs and SDPF than those that were presented by Jung et al. [243].

8.10.6.3

Three-Objective Optimisation

This example presents a three-objective optimisation model for the investigation of various sustainable and resilient design alternatives for water distribution networks [212]. This study combines three parameters such as life cycle cost, resilience and environmental impacts (CO2 emissions) in a multi-objective model to obtain various sustainable and resilient design alternatives. The model is validated on a three-loop benchmark network that was previously studied. • Optimisation model. A three-objective function is proposed to design WDNs by: (1) minimising LCC; (2) minimising life cycle CO2 emissions (LCE); and (3) maximising NRI. The constraints are the discharge and pressure requirements. The decision variables are pipe diameters and pump sizes. The network topology and the operational parameters such as required pressures and water demands are assumed to be given [212]. Objective 1: Minimum LCC obtained by minimising Eq. (8.10.5), in which: Cn =

T 

ci j L i j ; C p =

i j=1

NP 

0.4 K p Q 0.7 p,i H p,i ; C op =

i=1

NP 

T p e Pi

(8.10.13)

i=1

where: cij is the pipe cost of diameter Dij per unit length; L ij is the length of pipe ij; K p is a constant for pump capital cost with the value of 700,743 [247]; Qp,i and H p,i are the rated discharge and head (i.e., the discharge and head at the best efficiency) of pump i; T p is number of operating hours in a year (8760); e is the cost of electricity (0.12 $/kWh [248]); Pi is the power expended by pump i. Objective 2: Minimum LCE: LCE = C E n + C E op → min

(8.10.14)

where CE n is the emissions related to the embodied energy of network pipe materials estimated using an emissions coefficient ge ; CE op is the emissions related to the operational pumping energy over the design life time. Emissions related to pumping energy are estimated using an emissions coefficient gp = 0.5566 kg/kWh [249].

8.10 Multi-objective Optimisation of Water Distribution Networks

743

Objective 3: Maximum NRI as proposed by Prasad and Park [211]:   ψ j q j H j − H j,min /  NRI = . NP NR − Nj=1 q j H j,min Q H + /γ ) (P k k i k=1 i=1 N

j=1

(8.10.15)

with N Tj ψj =

i j=1

Di j

N T j max{Di j }

(8.10.16)

where N is the number of nodes in the network; N R is the number of reservoirs; N P is the number of pumps; Pi is the operating power of the pump i; Qk is the discharge from reservoir k; H k is the pressure head supplied at the source node by reservoir k; qj is the demand at node j; H j is the pressure head in normal operating conditions at node j; H j,min is the minimum pressure head constraint at node j; γ is the specific weight of water; ψj is the nodal uniformity coefficient; NT j is the number of pipes connected to node j; Dij is the diameter of pipe ij. Constraints: H j ≥ H j,min (“ node j). Optimisation algorithm: A GA-based optimisation tool called GANetXL, linked with EPANET software, initially developed by Savic et al. [250] was used to perform the three-objective optimisation. • Numerical application. The three-objective optimisation model previously described was applied using a benchmark network, shown in Fig. 8.31 [212], which was originally used by Costa et al. [247] to demonstrate a SA model for the design of this network. The same network was later used by Geem [248] to demonstrate an HS optimisation model. This three-loop network has 9 nodes, 11 pipes, and is supplied by a reservoir and a pump. Each pipe is 2500 m long, and a value of 130 is chosen for the Hazen–Williams Fig. 8.31 Schematic of the benchmark WDN

744

8 Hydraulic Simulation and Optimisation of Water Transmission …

Table 8.24 List of candidate pipes for the decision variables Candidate number, i

Di (mm)

Ci ($/m)

Ge (kg/m)

Break rate (break/(km·year))

Break repair cost ($)

1

152.4

42

140.62

0.41

5000

2

203.2

58.4

185.44

0.25

5500

3

254

73.8

238.17

0.15

6000

4

304.8

95.8

305.84

0.10

6500

5

355.6

118.8

355.06

0.08

7000

6

406.4

143

433.28

0.06

7500

7

457.2

169

502.71

0.05

8000

8

508

197.2

593.23

0.04

8500

9

609.6

252.6

710.12

0.02

9000

10

762

346.1

1015.09

0.01

9500

coefficient. The hydraulic constraints that need to be met are the demands qj (m3 /h) at each node j as shown in Fig. 8.31 with a minimum allowable pressure head of 30 m at each node. The elevation heads ZT j , in m, at each node are also presented in Fig. 8.31. Ten candidate diameters for pipes and nine pump curves in addition to the option of “no pump” are considered as shown in Table 8.24. The candidate pipe diameters are adapted from the previous studies that used the same three-loop benchmark network. The algorithm previously described was tested on the optimisation presented by Geem [248] for the design of pump-included WDNs by minimising LCC (for a 20 year period), and using an HP algorithm for obtaining the optimal solution. The same optimal solution was converged upon in approximately 875 generations [248] using the GANetXL algorithm. The solution which is called the “least cost solution” or “S1 ” can be seen in Table 8.25. The corresponding LCC, LCE and NRI values are for a 50-year design period. The use of either larger diameter pipes or larger capacity pumps improves redundancy in the system, and subsequently NRI values are expected to increase with LCC. The challenge however is to choose a solution that will provide the highest benefit to the user. The comparison of the most beneficial solution (S3 ) to the least-cost solution (S1 ), presented in Table 8.25, shows that both LCC and LCE of S3 are marginally greater than those of S1 , but the NRI of S3 is significantly greater than of S1 . The benefits from such a significant rise in NRI outclassed the slight increase in cost and emissions. This study along with several others point out the fact that capital costs should not be the sole criteria while making design decisions.

8.10 Multi-objective Optimisation of Water Distribution Networks

745

Table 8.25 Comparison of solutions in several scenarios Solution

S1

S3

S89

S123

S282

S324

1

609.6

609.6

609.6

609.6

609.6

762

2

254

355.6

406.4

406.4

457.2

457.2

3

152.4

254

254

254

304.8

254

4

457.2

406.4

457.2

406.4

457.2

457.2

5

152.4

152.4

254

254

254

304.8

6

152.4

203.2

203.2

203.2

254

254

7

355.6

254

254

254

254

304.8

8

254

152.4

254

203.2

254

254

9

254

304.8

304.8

304.8

304.8

304.8

10

254

152.4

152.4

152.4

203.2

203.2

11

152.4

254

254

203.2

203.2

203.2

Pump

4

4

4

5

5

4

LCC (million $)

5.683

5.738

5.998

6.058

6.361

6.448

LCE (kilo tonne)

56.949

57.144

57.913

61.848

62.740

59.300

Resilience (NRI)

0.127

0.163

0.226

0.241

0.291

0.298

8.10.7 Conclusions In this survey, the general optimal WDN design problem was presented with all the additional complexities and various successful models were reviewed. The optimisation of pipe networks under steady state conditions has been studied and different researchers proposed the use of mathematical programming techniques (LP, NLP, DP) to identify the optimal solution for WDNs. However, these deterministic methods either use some gradient information or require restrictive assumptions such as linearity, convexity and differentiability of the objective function, which cannot be generally satisfied and they usually converge to local optimal solutions that may not be the global optimum. Recently, the focus of the research in this area has shifted to the meta-heuristic based optimisation methods like GA, SA, ACO, PSO, SFLA, DE, HS, etc. As metaheuristic optimisation methods use only the values of the objective function in the search for optimal solutions, a large number of numerical simulations are required to reach these solutions. This is time consuming for small problems, but for larger problems it may be the only feasible way, and in that sense the required computational effort is actually the benefit of this approach. Multi-objective optimisation methods, based on different design criteria, have the advantage of providing a set of optimal solution, called Pareto front, instead of a unique optimal solution. Heuristic algorithms are usually the most used for solving MOPs. While the heuristic methods deal with a set of solutions during the search procedure, allowing to obtain a set of Pareto optimal solutions in a single run,

746

8 Hydraulic Simulation and Optimisation of Water Transmission …

the deterministic methods only lead to a single solution and can not guarantee the generation of different points on the Pareto front. Further research in heuristic optimisation methods should focus on hybrid methods, which combine the specific advantages of different approaches. These studies should also contain the use of hyper-heuristic techniques for optimising WDNs, which are more general and can solve a wider series of problems compared to the current meta-heuristic methods specialised in a narrow class of problems.

8.11 Numerical Simulation of Unsteady Flow in Water Distribution Networks 8.11.1 Preliminary Considerations A water distribution system (WDS) is the process which from the water source supplies or distributes to meet the end users’ demands. This process is attained by operations of pumps, main and service pipes, storage tanks or reservoirs, and related equipment while under pressure in a closed system. Water supplies of large urban and industrial centres consist of increasingly larger distribution networks that are necessary to ensure the greater uniformity and stability of pressure lines, with favourable economic and energy effects. The optimisation of pipe networks under steady flow conditions has been studied and various researchers have proposed the use of innovative linear [251] non-linear [164] and heuristic [169] optimisation techniques in order to identify the optimal solution for WDSs [160]. An unsteady flow in pipe networks is usually a transient state from one steady state to another, including to and from resting state. Therefore, a hydraulic transient is the flow rate and pressure condition that occurs in a pipe network between an initial steady state condition and a final steady state condition. When velocity changes rapidly because a flow control component changes status (for example, a valve closing or pump turning off), the change moves through the system as a pressure wave. She is perfectly able to find weak spots and cause damage to pipes, supports, machinery, etc., because the wave front is steeper, and the pressure rises (or drops) a lot. The primary objectives of transient analysis are to determine the values of transient pressures that can result from flow control operations and to establish the design criteria for system equipment and devices (such as control devices and pipe wall thickness) so as to provide an acceptable level of protection against system failure due to pipe collapse or bursting. Because of the complexity of the equations needed to describe transients, numerical computer models are used to analyse transient flow hydraulics. This section presents the basic concepts associated with transient flow, discusses the theoretical background of water hammer, and introduces aspects of system design that should be considered during transient analysis. Additionally, several analysis models of transient flows are developed including the transient analysis and design

8.11 Numerical Simulation of Unsteady Flow in Water Distribution Networks

747

optimisation for pipe networks using genetic algorithm (GA) method. Finally, the versatility of this approach is demonstrated solving a numerical example [252].

8.11.2 Overview of Transient Evaluation Examples of system flow control operations include opening and closing valves, starting and stopping pumps and discharging water in response to fire emergencies. These operations cause transient flow phenomena, especially if they are performed too quickly. Proper design and operation of a hydraulic system is necessary to minimise the risk of system damage or failure due to hydraulic transients. When a flow control operation is performed, the established steady state flow condition is altered. The values of the initial flow conditions of the system, characterised by the measured velocity V and pressure p at positions along the pipe x, change with time t until the final flow conditions are established in a new steady state condition. The physical phenomenon that occurs during the time interval T T between the initial and final steady state conditions is known as the hydraulic transient. In general, transients resulting from relatively slow changes in flow rate are referred to as surges, causing a mass oscillation and those resulting from more rapid changes in flow rate are referred to as water hammer events. For typical water distribution main installation, transient analysis may be necessary even if velocities are low. System looping and service connections may amplify transient effects and need to be studied carefully. Transient analysis should be performed for large, high-value pipes, especially those with pumping stations. Evaluating a system for potential transient impacts involves determining the values of head (H max and H min ) at incremental positions in the system. These head values correspond to the minimum and maximum pressures of the transient pressure wave, depicted as pmax and pmin in Fig. 8.32. Computation of these head values through the system allows the engineer to draw the grade lines for the minimum and maximum hydraulic grades expected to occur due to the transient. If the elevation Z along the pipe is known, then the pipe profile can be plotted together with the hydraulic grades and used to examine the range of possible pressures throughout the system. Figure 8.32 shows a pumping system in which an accidental or emergency pump shutdown has occurred. The extreme values indicated by the hydraulic grade lines were developed by reviewing the head versus time data at incremental points along the pipeline. The grade lines for H min and H max , which define the pressure envelope or head envelope, provide the basis for system design. If the H min grade line drops significantly below the elevation of the pipe, as shown in a portion of the system in Fig. 8.32, then the engineer is alerted to a vacuum pressure condition that could result in column separation and possible pipe collapse. Pipe failure can also result if the transient pressure in the pipe exceeds the pipe’s pressure rating. Maximum (or minimum) transient

748

8 Hydraulic Simulation and Optimisation of Water Transmission …

Fig. 8.32 Grade lines for a pumping system during an emergency shutdown

pressure can be determined for any point in the pipe by subtracting the pipe elevation Z from H max (or H min ) and converting the resulting pressure head value to the appropriate pressure units. Specialised programs are necessary to perform transient analysis in water distribution systems. Hydraulic transients can be analysed using one of two model types: a rigid model or an elastic model [160]. The rigid model has limited applications in hydraulic transient analysis because the resulting equation does not accurately interpret the physical phenomenon of pressure wave propagation caused by flow control operations, and because it is not applicable to rapid changes in flow. Water hammer is considered as a hydraulic transient phenomenon and is defined as unsteady flow, which is transmitted as a pressure or water hammer wave in the pipe system. Water hammer can be generated by operating system devices including valves and pumps, and by events such as pipe rupture. The complete equations for water hammer are one-dimensional unsteady pressure flow equations given by [253, 254]: a2 ∂ Q ∂H + =0 ∂t gA ∂x

(8.11.1)

8.11 Numerical Simulation of Unsteady Flow in Water Distribution Networks

∂Q ∂H λQ|Q| + gA + =0 ∂t ∂x 2D A

749

(8.11.2)

where: H is the total head in a pipe, in m; t is the time, in s; a is the characteristic wave celerity of the liquid, in m/s; g is the gravitational acceleration, in m/s2 ; A is the crosssectional area of pipe, in m2 ; Q is the flow rate, in m3 /s; λ is the Darcy−Weisbach friction factor; D is the pipe diameter, in m. Transient modelling essentially consists of solving Eqs. (8.11.1) and (8.11.2) for a wide variety of boundary conditions and system topologies. The equations cannot be analytically solved, so various approximate methods have been developed over the years: arithmetic method [255]; graphical method [256]; method of characteristics [257, 258]; algebraic method [259]; wave-plan analysis method [260]; implicit method [261]; perturbation method [262].

8.11.3 Considerations on Pipe System Design The emergency flow control scenarios should be analysed and tested during the design phase because they affect the pipe system design and the selection of system equipment. Steel, polyvinyl chloride (PVC), high-density polyethylene (HDPE) and thin-wall ductile iron pipes are susceptible to collapse due to vapour separation, but any pipe that has been weakened by repeated exposure to these events may experience fatigue failure. A pipe weakened by corrosion may also fail. Where very low pressures are possible during transient events, a more expensive material to preclude the chance of collapse can be used. For example, for largediameter pipes under high pressures, steel is usually more economical than ductile iron. However, the engineer may select ductile iron because it is less susceptible to collapse. It is always best to avoid vapour pressure conditions through surge protection measures regardless of the type of pipe used. Pipe systems constructed above ground are more susceptible to collapse than are buried pipes. With buried pipes, the surrounding bedding material and soil provide additional resistance to pipe deformations and help the pipe resist structural collapse. Another important consideration when designing a system to protect against hydraulic transients is the use of air valves. Using air valves to avoid vacuum conditions requires careful analysis of possible transient conditions to ensure that the air valve is adequately sized and designed. Other factors that influence extreme transient heads are wave celerity and liquid velocity. Selecting larger diameters to obtain lower velocities with the purpose of minimising transient heads is acceptable for short pipe systems delivering relatively low flows. However, for long pipe systems, the diameter should be selected to optimise construction and operating costs. Long pipe systems almost always require transient protection devices.

750

8 Hydraulic Simulation and Optimisation of Water Transmission …

After considering these factors during the conceptual and preliminary designs of the system, the project should move into the final design phase. Any changes to the system during final design should be analysed with the transient model to verify that the previous analysis results and specifications are still appropriate.

8.11.4 Transient Analysis in Pipe Networks The process of obtaining an unsteady solution for a specific problem in which the water demands or pressure heads are specified functions of time consists of the following steps [262]: (1) The time T, over which the unsteady solution is to be obtained, is divided into T /t time increments, where t is the time step. (2) The discharges in all pipes and the pressure heads at all nodes are assigned initial values that are chosen from a steady state solution that has the same demands, and all other data as the unsteady solution has at time zero. (3) All water demands over each time increment must be specified. (4) Over each new time increment, define and evaluate the functions and the Jacobean matrix of derivatives of these functions. (5) Solve the resulting linear equation system. The solution of this equation system is then subtracted from the set of unknown values, according to the Newton−Raphson method [41]. (6) Steps (4) and (5) are repeated iteratively, until the specified convergence criterion has been satisfied. (7) Write the solution for the discharges and the nodal heads for this time increment, and then repeat steps (3) through (7) until the unsteady solution spans the entire time period. The steps from (1) through (7) are the general method for analysing an unsteady flow in a pipe system. This system is consisted of pipes, reservoirs, pumps, tanks, etc. In the following subsection, the governing equation for each component and some of their boundary conditions will be mentioned. The unsteady flow inside the pipes is described in terms of the unsteady mass balance (continuity) equation and unsteady momentum equation, which define the state variables as the discharge Q or velocity V, and pressure head H.

8.11.4.1

Equations Describing Unsteady Flow in Pipes

Using the method of characteristics for analysing the unsteady flow in pipe networks, a pair of equations to find H and V in a pipe divided in n segments at the interior point P, starting from point 2 to point N (point 1 is related to the boundary condition) is developed [262]:

8.11 Numerical Simulation of Unsteady Flow in Water Distribution Networks

  1 g λt (VL + VR ) + (HL − H R ) − (VL |VL | + VR |VR |) 2 a 2D   1 a a λt HP = (VL − VR ) + (HL + H R ) − (VL |VL | − VR |VR |) 2 g g 2D VP =

751

(8.11.3) (8.11.4)

where the subscripts L and R are considered as the left and right points on the characteristic grid with respect to certain point P and located at the same distance from it.

8.11.4.2

Reservoir Boundary Condition (Upstream End of Pipe)

For a pipe exiting from a reservoir and neglecting the entrance head losses, the H equation is the following: H P1 = H0

(8.11.5)

where H 0 is the head of the reservoir water surface. In addition, the velocity V P1 can be calculated as V P1 = V2 +

8.11.4.3

g λt (H0 − H2 ) − V2 |V2 | a 2D

(8.116)

Three Pipes Connected in One Junction

For a pipe junction with one inflow (pipe 1), two outflows (pipes 2 and 3) and an external demand q at the junction, the equations that describe the relationships between the six unknowns are: V P1 = V2 +

g λt (H0 − H2 ) − V2 |V2 | a 2D

(8.11.7)

Pipe 1, C+ : V P1 = C1 − C2 H P1

(8.11.8)

V P2 = C3 + C4 H P2

(8.11.9)

Pipe 2, C− :

752

8 Hydraulic Simulation and Optimisation of Water Transmission …

Pipe 3, C− : V P3 = C5 + C6 H P3

(8.11.10)

V P1 A1 = V P2 A2 + V P3 A3 + q

(8.11.11)

H P1 = H P2 = H P3

(8.11.12)

Conservation of mass:

Work-energy:

Solving this linear set of equations leads to: H P1 = H P2 = H P3 =

C 1 A1 − C 3 A2 − C 5 A3 − q C 2 A1 + C 4 A2 + C 6 A3

(8.11.13)

where: H P and V P are the pressure head and velocity, respectively at a specific point P in a specific end of the three connected pipes; C 1 − C 6 are the pipes constants; and A1 , A2 and A3 are the pipe cross-sectional areas. In the same manner equations can be obtained for four or five pipes connected at the same junction.

8.11.4.4

Valve in the Interior of a Pipe

The internal boundary condition for equal cross-sectional areas of pipe on both sides of valve (Fig. 8.33) is described by the equations: Pipe 1, C+ : V P1 = C3 − C4 H P1 Fig. 8.33 Valve in a pipe with constant diameter

(8.11.14)

8.11 Numerical Simulation of Unsteady Flow in Water Distribution Networks

753

Pipe 2, C− : V P2 = C1 + C2 H P2

(8.11.15)

V P1 = V P2

(8.11.16)

Conservation mass:

Work-energy: H P1 = H P2 + ζv

V P22 2g

(8.11.17)

where ζv is the valve minor loss coefficient. The equation obtained by combining Eqs. (8.11.14)−(8.11.17) is: V P22

$ % $ % 2g 1 1 2g C3 C1 V P2 − =0 + + + ζv C 4 C2 ζv C 4 C2

(8.11.18)

While keeping ζv separate, definition of the coefficients: % % $ 1 1 C3 C1 ; C6 = 2g + + C5 = 2g C4 C2 C4 C2 $

(8.11.19)

leads to the velocity expression: V P1 = V P2

 0 1 C5 4C6 ζv = −1 + 1 + 2ζv C52

(8.11.20)

This equation is correct so long as the flow is in the original downstream direction. If the flow reverses, then the following equation is obtained: V P1 = V P2

8.11.4.5

 0 1 C5 4C6 ζ  v =  1− 1− 2ζ v C52

(8.11.21)

Source Pumping Station at Upstream End of Pipe

Discharge side, C− : V Pd = C3 + C4 H Pd

(8.11.22)

754

8 Hydraulic Simulation and Optimisation of Water Transmission …

Conservation mass: N P Q = V Pd Ad

(8.11.23)

Z P S + H p = H Pd

(8.11.24)

  Hp Q C = n + C ss 7 8 n 2p np

(8.11.25)

Work-energy:

Pump characteristics:

with    H p /n 2p A − H p /n 2p B       ; C8 = −C7 Q/n p B + H p /n 2p B  C7 =  Q/n p A − Q/n p B 

(8.11.26)

where: N P is the number of pumps in parallel; Ad is the area of delivery pipe; Z PS is the pump elevation head; H p is the head delivered by pump; np is the pump speed at the transient state; nss is the pump speed at the steady state; C 3 −C 8 are constants; and A, B are two points on the pump characteristic curve (H p − Q). From the previous equations, following solution is obtained for the pressure head at a specific point H P : HP =

8.11.4.6

Z PS +

n ss n p C3 C7 Ad + n ss n 2p C8 NP n ss n p 1 − N P C 4 C 7 Ad

(8.11.27)

Nodal Equations of Looped Networks

Looped networks are reduced to virtual branched networks by fictitious sectioning of pipes. Thus, there are created additional nodes called apparent nodes (A) in which, of course, the boundary and connection conditions at any moment t are reduced to the identity of the discharges and pressures on the left and right of the applied section (Fig. 8.34). Therefore, the following nodal equations result [257]:

8.11 Numerical Simulation of Unsteady Flow in Water Distribution Networks

755

Fig. 8.34 Transformation of a looped network into a virtual branched network. a looped network with apparent nodes; b junction node

• junction node:   (t+1) (t) (t) H j,i − H j−1,i = −m j−1,i Q (t+1) − Q (i = 1, 2, . . . , I ) j,i j−1,i   (t+1) (t) H j,k − H j+1,k = m j,k Q (t+1) − Q (t) (k = 1, 2, . . . , K ) j,k j+1,k (t+1) (t+1) H j,i = H j.k = H j(t+1) I 

Q (t+1) = j,i

i=1

K 

Q (t+1) + q (t+1) j,k j

(8.11.28)

k=1

where: t is the time of calculation; m = a/(gA) is the wave resistance; I is the number of inflow pipes in node; K is the number of outflow pipes in node; qj is the consumed discharge at node j, which may vary over time depending on the pressure head H j from the node. For example, in the case of a hydrant or overpressure valve, the connection between qj and H j is precisely the characteristic curve of the device:   qj = qj Hj

(8.11.29)

• apparent node:   (t) H j(t+1) − H j−1 = −m j−1 Q (t+1) − Q (t) j j−1   (t) (t) H j(t+1) − H j+1 = m j Q (t+1) − Q j j+1 = −Q (t+1) Q (t+1) j,i j,k

(8.11.30)

756

8 Hydraulic Simulation and Optimisation of Water Transmission …

Equations (8.11.30) result from Eqs. (8.11.28) substituting I = K = 1 and qj = 0. A system of computer programs for the calculation of unsteady flows in single wire pipes and piping systems was developed by a team of specialists from the Technical University of Civil Engineering in Bucharest [263].

8.11.5 Optimisation of Pipe Networks 8.11.5.1

Objective Function and Constraints

Water distribution network design problem is formulated and solved as a singleobjective optimisation problem with the selection of pipe diameters as the decision variables. The main parameter is subject to minimisation which is the capital cost of the network. The optimisation problem is solved using a single-objective GA. The objective of the optimal design model is to minimise total capital costs under the constraint of minimum pressure head requirements in steady state condition and minimum and maximum pressure heads requirements in transient condition (water hammer). The latter is included in order to protect the system from negative or positive transient pressures. More specifically, the optimisation problem is to minimise the objective function F c . It is the summation of the network cost and penalty cost in both cases: steady state and water hammer (transient state): Fc = Cn + C p−ST + C p−T R → min

(8.11.31)

with Cn =

T  i j=1

ci j L i j =

T 

(a + b Diαj )L i j

(8.11.32)

i j=1

where: C n is the capital cost of the network; C p-ST is the penalty cost in case of steady state; and C p-TR is the penalty cost in case of transient condition; T is the number of pipes in a network; cij is the specific cost of pipe ij; a, b and α are the cost parameters depending on the network pipe material [20]; Dij , L ij are the diameter and the length of pipe ij, respectively. Penalty cost in case of steady state C p-ST is described as follows [264]:

C p−ST =

⎧ ⎨0 ⎩ CNn

N  



if Hmin −ST − H j ≤ 0

Hmin −ST − H j if Hmin −ST − H j > 0

(8.11.33)

j=1

where: N is the number of node in network; H min-ST is the minimum allowable pressure head for water hammer; and H j is the pressure head at node j.

8.11 Numerical Simulation of Unsteady Flow in Water Distribution Networks

757

The total penalty cost in case of water hammer C p-TR is described as follows: C p−T R = C p−T R,max + C p−T R,min

(8.11.34)

with C p−T R,max =

⎧ ⎨0 ⎩ Cn

N  



if H j,max − Hmax −T R ≤ 0

H j. max − Hmax −T R if H j,max − Hmax −T R > 0

j=1

(8.11.35) C p−T R,min =

⎧ ⎨0 ⎩ Cn

N  



if Hmin −T R − H j,min ≤ 0

Hmin −T R − H j,min if Hmin −T R − H j,min > 0

(8.11.36)

j=1

where: C p-TR,max is the penalty cost in case of water hammer when the pressure head exceeds the maximum allowable pressure head limit; C p-TR,min is the penalty cost in case of water hammer when the pressure head decreases below the minimum allowable pressure head limit; H max-TR is the maximum allowable pressure head for water hammer; and H min-TR is the minimum allowable pressure head for water hammer Generally, the penalty cost in case of steady state is a function of minimum allowable pressure head at each node, pressure head at each node and number of nodes violating the criteria. The minimisation of the objective function in Eq. (8.11.31) is subject to: (a) Discharge balance constraint, as described in Eq. (8.9.1). (b) Energy balance constraint, as described in Eq. (8.9.2). (c) Design constraint is the pipe diameter bounds (maximum and minimum) and given as: Dmin ≤ Di j ≤ Dmax

(i j = 1, . . . , T )

(8.11.37)

where Dij is the discrete diameter of pipe ij, selected from the set of commercially available pipe sizes, and T is the total number of pipes. (d) The hydraulic constraints for steady state and water hammer are given as: H j ≥ Hmin−ST

( j = 1, . . . , N )

Hmin−T R ≤ Hk ≤ Hmax−T R (k = 1, . . . , N∗ )

(8.11.38) (8.11.39)

758

8 Hydraulic Simulation and Optimisation of Water Transmission …

where: H j is the pressure head at node j; H min-ST is the minimum allowable pressure head at node j for the steady state: H min-TR and H max-TR are the minimum and maximum allowable pressure heads at node k for the transient state; and N * is the number of segment into which the pipe is divided. Using GA to solve the optimisation problem in Eq. (8.11.31), constraints (a), (b), (c) and (d) can be automatically satisfied by linking GA to the deterministic water distribution network solver such as Newton−Raphson method and transient analyser that has implemented the method of characteristics.

8.11.5.2

Implementation of Genetic Algorithm Over Pipe Network

The flow chart in Fig. 8.35 shows the sequence of the basic operators used in GAs. The first generation is randomly selected from the start. Every string in this generation is evaluated according to its quality, and a fitness value is assigned. Next, a new generation is produced by applying the reproduction operator. Pairs of strings of the new generation are selected and crossover is performed. With a certain probability, genes are mutated before all solutions are evaluated again. This procedure is repeated until a maximum number of generations are reached. While doing this, the all time best solution is stored and returned at the end of the algorithm. The GA serves as a framework which provides the outer cycle of the search or optimisation process. The brief idea of GA is to select population of initial solution points scattered randomly in the optimised space, then converge to better solutions by applying in iterative manner the following three processes (reproduction/selection, crossover and mutation) until a desired criteria for stopping is achieved. The optimisation program Genetic Algorithm Steady Transient network (GASTnet) was written in FORTRAN language and it links the GA, the Newton−Raphson simulation technique for the steady state hydraulic simulation and the transient analysis [265]. Fig. 8.35 Genetic algorithm flow chart

8.11 Numerical Simulation of Unsteady Flow in Water Distribution Networks

759

A brief description of the steps in using GA for pipe network optimisation, and including water hammer is as follows: (1)

Generation of initial population. The GA randomly generates an initial population of coded strings representing pipe network solutions of population size n. Each of the n strings represents a possible combination of pipe sizes. (2) Computation of network capital cost. For each n string in the population, the GA decodes each substring into the corresponding pipe size and computes the total material cost. The GA determines the costs of each trial pipe network design in the current population. (3) Hydraulic analysis of each network. A steady state hydraulic network solver computes the pressure heads and discharges under the specified demands for each of the network designs in the population. The actual nodal pressure heads are compared with the minimum allowable pressure heads, and any pressure deficits are noted. The Newton–Raphson technique is used. (4) Computation of penalty cost for steady state. The GA assigns a penalty cost for each demand if a pipe network design does not satisfy the minimum pressure head constraints. The pressure violation at the node at which the pressure deficit is maximum, is used as the basis for computation of the penalty cost. The maximum pressure deficit is multiplied by a penalty factor (C n /N), as described in Eq. (8.11.33). (5) Transient analysis of each network. A transient analysis solver computes the transient pressure heads resulting from the pump power failure, sudden valve closure or sudden demand change as best described in the Sect. 8.10.4 by Eqs. (8.11.3)−(8.11.27). The minimum and maximum pressure heads are estimated in each pipe of the network and compared with the minimum and maximum allowable pressure heads, and any pressure deficits are noted. (6) Computation of penalty cost for transient state. The GA assigns a penalty cost if a pipe design does not satisfy the minimum and maximum allowable pressure heads constraints. The penalty cost is estimated as the pressure violation multiplied by a penalty factor equals to the cost of the pipes, as described by Eqs. (8.11.34)−(8.11.16). (7) Computation of total network cost. The total cost of each network in the current population is taken as the sum of the network cost (Step 2), the penalty cost of steady state (Step 4), plus the penalty cost of transient state (Step 6). This step is an expression to Eq. (8.11.31). (8) Computation of the fitness. The fitness of the coded string is taken as some function of the total network cost. For each proposed pipe network in the current population, it can be computed as the inverse or the negative value of the total network cost from Step 7. (9) Generation of a new population using the selection operator. The GA generates new members of the next generation by a selection scheme. (10) The crossover operator. Crossover occurs with some specified probability of crossover for each pair of parent strings selected in Step 9.

760

8 Hydraulic Simulation and Optimisation of Water Transmission …

(11) The mutation operator. Mutation occurs with some specified probability of mutation for each bit in the strings, which have undergone crossover. (12) Production of successive generations. The use of the three operators described above produces a new generation of pipe network designs using Steps 2 to 11. The GA repeats the process to generate successive generations. The last cost strings (e.g., the best 20) are stored and updated and cheaper cost alternatives are generated. These steps for the optimisation of water networks considering both steady state and transient conditions are illustrated in the flow chart of the GASTnet program (Fig. 8.36) [265]. After the model has been constructed and calibrated, it is ready to be used in design. To get the most benefit from the model, the designer should examine a broad range of alternatives.

Fig. 8.36 Flow chart of the GASTnet program

8.11 Numerical Simulation of Unsteady Flow in Water Distribution Networks

761

8.11.6 Numerical Example The water supply pipe network with the topology from Fig. 8.37 is considered. The system comprises six nodes, six pipes and two reservoirs at nodes 5 and 6, with constant level, equal to 311 m and 305 m, respectively. It is supplied with a flow rate of 0.136 m3 /s provided from two reservoirs (Q5-1 = 0.108 m3 /s, Q6-3 = 0.028 m3 /s). The following data are known: pipe length L ij , in m; pipe diameter Dij , in mm; elevation head ZT j , in m; and the water demands at nodes qj , in m3 /s. The roughness height of pipes and wave speed are 0.051 mm and 914 m/s, respectively. The water demand was suddenly increased at node 2 from 0.028 m3 /s to 0.057. For the steady state, the required minimum pressure head at all nodes is 24 m and for the transient conditions, the minimum and maximum pressure heads are 24 m and 55 m, respectively. Applying the GASTnet program in the transient-optimisation mode, the optimal diameters for the network against the original ones are summarised in Table 8.26. The least cost is 267,000.00 units after optimisation against 348,000.00 units, which is equal to 0.767 times the original cost.

Fig. 8.37 Typical pipe network for sudden water demand change

Table 8.26 Optimal and original diameters for the sudden water demand change

Pipe (i−j)

Original diameter (mm) Optimal diameter (mm)

5−1

254

305

1−2

203

203

3−2

203

152

6−3

254

152

3−4

203

152

1−4

203

152

Cost (units)

348,000.00

267,000.00

Run time (s) 30

150

762

8 Hydraulic Simulation and Optimisation of Water Transmission …

Table 8.27 Pressure heads at nodes for the steady state using the optimal diameters

Node

Pressure head (m)

1

46.22

2

39.65

3

37.35

4

37.25

5

12.00

6

12.00

Table 8.27 presents the corresponding nodal pressure heads for the steady state. These heads fulfil the minimum pressure constraint of 24 m at all nodes except the reservoirs nodes. The two reservoirs at nodes 5 and 6 have pressure heads of 12 m. Figure 8.38 illustrates the pressure head variation depending on time at all nodes before and after optimisation. The dashed curves represent the results for transientsimulation using the original network pipes diameters. It is clear that the pressure

Fig. 8.38 Pressure head versus time for various demand nodes

8.11 Numerical Simulation of Unsteady Flow in Water Distribution Networks

763

fluctuations are very significant and destructive as it crosses the pressure limits of 24−55 m. The results in transient-optimisation mode (continuous curves) reveal that the pressure fluctuations have been contained within the predetermined pressure head limits 24−55 m. As observed from Fig. 8.38, the convergence to steady state caused by sudden demand change is rapid. The choice of the time of the transient flow simulation as 60 s was sufficient to obtain nearly steady state condition at the end of this time.

8.11.7 Conclusions When designing WDSs, the engineer needs to consider economic and technical factors such as acquisition of property, construction costs, site topography and geological conditions of the land where the pipe system will be constructed. The previous studies were concerned with the optimisation of networks under steady state conditions in spite of the fundamental importance of transients. The optimisation of a transient flow for WDSs is investigated relatively recently. In this paper, the transient flow is introduced to the water network by the pump power failure, sudden valve closure and sudden demand change. The technique of the optimal pipe diameter selection is very economical as the network design can be achieved without using anti-water hammer protection devices. This technique is not only crucial to water networks design and performance, but also effective in minimising costs.

8.12 Optimisation of Water Distribution System Energy Efficiency Using Potential Elements 8.12.1 Preliminary Considerations As a vital part of water supply systems, water distribution networks represent one of the largest infrastructure assets of industrial society. According to Watergy [266], approximately 2–3% of the worldwide electricity consumption is used for pumping in water supply systems, while 80–90% of this consumption is absorbed by motorpump sets [267]. Coelho and Andrade-Campos [268] provides several strategies to improve the energy efficiency of the water distribution systems (WDSs). Most WDSs require the operation of pumps to deliver the necessary quantity of water with the adequate pressure to the final consumers. As reported by Bene et al. [269] and Vilanova and Balestieri [270], the electricity used to pump water is a significant part of the total operation in WDSs. WDSs equipped with pumping stations are characterised by energy consumption greater than 60% of the energy consumed by the operation of the entire supply system

764

8 Hydraulic Simulation and Optimisation of Water Transmission …

of large urban centres [271]. As a result, a great increase in the energetic system load occurs especially during peak water consumption hours. Pumping systems are found to have a significant potential for energy efficiency improvements [272–275]. In most cases, optimisation of operations has only considered fixed-speed pumps and the cost savings that may be obtained by exploiting a multi-pattern electric tariff [276–279]. Pump and motor upgrades to more efficient solutions, either being technologically more advanced or because they are more properly adjusted to the system, often allow significant energy savings [267]. Vogelesang [280] quantitatively discussed the energy saving potential of applying variable speed pumps and indicated a possible energy reduction of 27% only with a 10% of pump speed decrease. Variable speed drives (VSDs) have been shown to be an effective way to reduce the pumping energy, especially in systems that require a wide range of flow rates [281] in absence of elevated tanks. Energy optimisation of parallel-connected, rotational speed-controlled pumps has been studied to some extent [282, 283]. Viholainen et al. [284] developed a pumping control strategy for most of the scenarios considered (two pumps in parallel, two frequency converters and one programmable logic controller) using frequency converters that close to high efficiency. Several studies provide other alternatives to improve energy efficiency in WDSs. A model for decision systems regarding the quantification, location and opening adjustment of control valves in a distribution network, to minimise pressures and leakage levels in network is developed in [285]. Carravetta et al. [286] present a real case study (flow rate less than 1440 m3 /h) and suggest the installation of pumps in the supply pipes that act as micro-hydro turbines to generate electric power. These turbines may be used to provide pressure control instead of using pressure control valves. Diniz et al. [287] present an analysis of energy efficiency in supply systems based on modelling and optimisation. Other researchers have successfully applied genetic algorithms to control hydraulic pressure in the water distribution network [288]. However, these models require that the functions satisfy certain restrictive conditions that cannot be generally guaranteed for any WDS. The assessment of energy efficiency in WDSs is strongly influenced by the sitedependent nature of the water–energy nexus in pressurised networks [289]. Understanding this link requires a systematic energy analysis to separately evaluate the influence of pumping stations, the network and water loss and to highlight inconsistencies in the design and management that are reflected in both of the resources, namely water and energy. The hourly variations in water demand during the day are much greater compared to the average daily demand. For a domestic consumer water requirement is more during morning and evening hours than the noon demand. The hourly variation in demand has also an influence on the residual pressures in the system. In the case of water distribution for Romanian consumers, the available pressure is greater at the periphery consumers, where the lower pressure is necessary, while in central zones, the pressure is insufficient. Often, the absence of water at consumers can be observed during certain hours in a 24-hour period due to system under dimensioning, increased

8.12 Optimisation of Water Distribution System …

765

water consumption by some users, inadequate operation of pumping stations, or a combination of these factors. These disadvantages are amplified by the overlapping of peak hours for water, heat and electricity consumption, especially between 7:00 and 9:00 in the morning and between 17:00 and 21:00 in the evening, contributing to increasing operation expenses. During peak hours, the energy cost is 2−3 times more expensive than during the hours of minimum consumption. Therefore, it is very interesting to provide a reduction of energy consumption during peak hours. A technical solution for this reduction can be a decrease in the pumping power (even stopping pumps if it is possible) during peak hours, along with an extensive delivery outside of these hours. Consequently, distribution systems must be equipped with pumped storage tanks. An important goal is the absolute reduction of pumping energy, which is possible by dividing the system into zones. For this purpose, a special form of parallel zoning procedure or a vertical division into zones with intermediary pumps mounted on the distribution mains, or a combined solution with more potential elements, can be used [290]. This section presents several comparative studies of energy efficiency in WDSs considering distinct configurations of the networks and also considers utilisation of the variable speed pumps [291]. The main aim of the paper is to search for possible optimal network configurations that reduce electricity consumption and improve energy efficiency using potential elements (pumped storage tanks, intermediary pumping stations integrated on distribution mains, elevated storage tanks floating on the system) and control systems to vary pump speed drive according to water demand. The improving energy efficiency of water pumping is briefly reviewed providing a representative real case study. In addition, a hydraulic analysis of the optimisation strategies with potential elements is performed and an analytical model is developed to estimate the optimal location of a pumped storage tank. Finally, certain optimisation solutions to reduce pumping energy are analysed in a detailed manner through the use of a case study to ascertain their energy and economic efficiencies.

8.12.2 Improving Energy Efficiency of Water Pumping 8.12.2.1

A Brief Review of Previous Works

Some pumping stations comprise parallel-connected pumps with fixed-speed and flow rate controlled by the number of pumps in operation. In this procedure, it is very difficult to define a pump’s operating schedule with minimal energy cost without compromising the full delivery of daily demand and ensuring a suitable reservoir level for the next work cycle. According to Feldman [5], the main improvements in energy efficiency can be obtained with: (1) pumping stations and system design improvement; (2) VSDs installations; (3) efficient operation of pumps; and (4) minimisation of water losses through pressure control.

766

8 Hydraulic Simulation and Optimisation of Water Transmission …

The power absorbed by a pump in a water supply system P, in W, and the electricity consumption E p , in Wh, can be calculated using following equations: γ Q Hp η

(8.12.1)

E p = P Tp

(8.11.2)

P=

where γ is the water specific weight, in N/m3 ; Q is the pump discharge, in m3 /s; H p is the pump head for the operating point, in m; η is the global efficiency of the pumping station; and T p is the operation period, in h. The specific energy consumption w, in %, for an optimal operation period T p of the pumps can be estimated as: T

∫ p Pdt · 100 w = 24 0  Q i Hi γ T p ηi

(8.12.3)

i=1

where Qi , H i and ηi are the pump characteristics in classical operation at the i-th -T hour of a day; 0 p P dt is the energy consumption during interval T p at discharges different from Qi . Most existing pumping stations requiring flow control make use of bypass lines, throttling valves or pump speed adjustments. Most water distribution systems are fed through some type of centrifugal pumps characterised by a head-flow (H−Q) curve. A centrifugal pump has a motor that spins a piece within the pump called an impeller. If the pump used is a fixed-speed pump, the operating point is forced to move along the pump curve corresponding to the constant nominal speed. There are two methods to adjust the water flow rate in a pipe network with a fixed-speed pump: • Bypassing part of the water flow rate. • Introducing a supplementary pressure loss using a control valve [292] that can lead to higher energy efficiency of the water supply system when the nominal pump head is lower than the optimal value. Additionally, valves can be a source of emissions and suffer from corrosion, erosion, plugging, cavitation and leakage. Speed can be controlled in a number of ways, either the most popular type of VSD being the variable frequency drive (VFD) or variable speed controller. Using VSDs to replace fixed-speed pumps has the possibility to save electrical energy. The decreasing energy consumption can be reduced the cost related to pump operation. Variable speed pumps can prevent over-pressurising of the WDS that has no storage floating on the system (that is, no tank where the hydraulic grade line (HGL) in the tank is the same as the HGL in the system) [271].

8.12 Optimisation of Water Distribution System …

767

Fig. 8.39 Flow rate adjustment using pump speed control

Variable speed pumps are coupled with a motor that is controlled by a VFD. The most common form of VFD is the voltage-source, pulse-width modulated (PWM) frequency converter. The principal duty of the VFD is to alter the main supply to vary the speed of the motor while delivering the required torque at higher efficiency. As a result, as the pump speed changes, the pump curve is adjusted for different operating conditions. The flow control (Fig. 8.39) is achieved by changing the pump curve H (at different pump speeds n1 and n2 ) on the fixed system curve H r . Pipe work curve H r start from point (0, H g ), where H g is the geodesic head. The operating point F2 corresponds to the reduced pump head H F2 . The approximation introduced into the power–speed relation implies that the efficiency will remain constant for speeds n1 and n2 , i.e., that the efficiency curve will only be shifted to the left in the case of speed reduction. The efficiency variation depending on the pump speed is provided by the following analytical relationship [293]: $

n1 η2 = 1 − (1 − η1 ) n2

%0.1 (8.12.4)

where n1 and n2 are two different speeds and η1 , η2 are the corresponding efficiencies. Therefore, as indicated in [293], for the particularly case of the large pumps the changes in efficiency can be neglected if the changes in speed rate do not exceed 1/3 from the nominal pump speed. Figure 8.40 shows the variation curves of H, Q, P and η for centrifugal pumps depending on pump speed n. It can be observed that a reduction of 20% of the pump speed will lead to the decreasing of power demand of 50% at constant pump efficiency. Thus, the possibility exists to reduce the pumping energy consumption by using VSDs.

768

8 Hydraulic Simulation and Optimisation of Water Transmission …

Fig. 8.40 Variation of the centrifugal pump curves

Variable speed pumps are useful in applications requiring operational flexibility, such as when flow rates change rapidly, but the required pressure remains constant [271]. These pumps can take advantage of the different required operating conditions in water distribution systems. In particular, the reduction in energy consumption exploits the possibility of reducing the head or flow rate in the system. Figure 8.39 shows the case in which the required flow rate is smaller than the actual operating point. This situation can be the case of a water transmission system, where the pumps are used to move water from a lower to an upper tank. Because the pumping at a particular time of the year may be sized for a peak-day demand, the pump will deliver a flow rate associated with the operating point, despite the fact that the required demand is decreased. However, this operating strategy can be economically convenient if the system has a sufficient storage volume so that pumps can be switched on only during the off-peak-tariff period. Parallel-connected centrifugal pumps are often implemented in the pumping systems with a widely varying flow rate demand [294, 295]. The output of the parallel-connected centrifugal pumps in a system can be adjusted with an on-off, throttle, or rotational speed control methods. In the simplest case, parallel-connected pumps are operated with an on-off control method, where additional parallel pumps are started and stopped according to the desired flow rate. In the systems where more accurate flow regulation is required, the adjustment can be performed by applying throttling or rotational speed control for a single pump, while the other pumps are controlled with the on-off method. VSD has a motor that can change the pump speed in response to the system conditions. The majority of electric motors used in pump applications are induction types. The most common type of VFD controls the flow of electricity to the pump motor and therefore controls the rate at which the pump rotates. Note that in variable drive systems, additional losses are generated in the motor by the VFD. Another problem could be in the lower reliability of the pumps, both for the lower quality of the electric pulse and for operational conditions diverging from the best efficiency point (BEP) line.

8.12 Optimisation of Water Distribution System …

769

The general expression of variable speed pump system efficiency is given by Marchi et al. [296]: η = ηm ηVFD η p

(3.12.5)

where ηm is the motor efficiency; ηVFD is the efficiency of the VSD; and ηp is the pump efficiency. The flow variation in pumping systems may occur as a result of several situations, such as the need to turn pumps on only when required (partial load operation), the use of a bypass to return a portion of the pumped discharge to the suction tank, the use of a suction tank with a variable level, the insertion of head losses in the system through the throttling of control valves, changes in the pump speed by hydraulic or electrical coupling between the pump and motor or the use of pumps operating in parallel [297]. According to Gibson [298], VSDs are an energy-efficient alternative for controlling pump flow rates. The author reported that the effectiveness of VSDs on flow control depends on the interaction between the characteristic curve (H−Q) and the system curve. This includes the use of the magnitude of required speed variation to obtain the maximum and minimum required flow rates in addition to the unstable regions in the pump curve, which are usually located in the range below 33% of the nominal flow. To correlate the pumped discharge with the water demand and to ensure the required pressure using minimum energy, an automatic control device of pump speed designed and described in [293] or a supervisory control and data acquisition (SCADA) system deployed in industry can be utilised. If several pumps are to operate in parallel connection, the rotational speed can be modified for a single pump (while the other pumps operate at nominal speed and nominal discharge), and the frequency converter automatically connects to the other pumps. Thus, the pumping station must be equipped with np = nc +nv number of pumps, where nc is the number of classical (fixed-speed) pumps (pf ) and nv is the number of variable speed pumps (pv ).

8.12.2.2

Case Study

A case study is presented to demonstrate the efficiencies of the previously analysed control methods (valve and speed control). The case study consists of a pumping station operating with 6 pumps of 12 NDS-1450 types in the water distribution system of a large urban centre in Romania, which must ensure the daily water supply of 172,800 m3 . The obtained numerical results that are based on the characteristic curves plotted in Fig. 8.41 for different parallel-connected pump designs are presented in Table 8.28. This table compares the specific energy consumption w and the energy savings W obtained during a 360-day operation period (T p ) by applying throttling or rotational

770

8 Hydraulic Simulation and Optimisation of Water Transmission …

Fig. 8.41 Characteristic curves H−Q, η−Q and the operating points for different parallel-connected pumps Table 8.28 The specific energy consumption and energy savings obtained with control methods Adjustment method

Period (h)

Number Pumped of flow Q operating (m3 /s) pumps

Pump Absorbed Consumed head power P energy E p H p (m) (kW) (kWh/day)

Specific energy consumption w (%)

1. Classical (start– stop)

0:00–4:00

3 pf

1.47

38.6

696.3

31,705.6

100

4:00–10:00

6 pf

2.48

49.8

1730.8

10:00–14:00 4 pf

1.91

42.5

995.4

14:00–17:00 5 pf 17:00–22:00 6 pf

2.18

45.7

1303.1

2.48

49.8

1730.8

22:00–24:00 4 pf

1.91

42.5

995.4

0:00–5:00

3 pf

1.47

38.6

696.3

27,970.5

88

5:00–6:00

6 pf

2.25

53.0

1424.0

6:00–7:00

6 pf

2.48

49.8

1730.8

7:00–8:00

6 pf

2.25

53.0

1424.0

8:00–10:00

2. Throttle valve control

5 pf

2.08

47.5

1138.2

10:00–12:00 4 pf

1.91

42.5

995.4

12:00–13:00 5 pf

1.81

56.0

1181.6

13:00–15:00 4 pf 15:00–16:00 6 pf

1.91

42.5

995.4

2.08

47.5

1138.2

16:00–20:00 6 pf

2.25

53.0

1424.0

20:00–23:00 6 pf

2.46

50.0

1544.1

23:00–24:00 4 pf

1.81

43.0

1122.6 (continued)

8.12 Optimisation of Water Distribution System …

771

Table 8.28 (continued) Adjustment method

3.

Period (h)

Number Pumped of flow Q operating (m3 /s) pumps

Pump Absorbed Consumed head power P energy E p H p (m) (kW) (kWh/day)

Specific energy consumption w (%)

2pf + 1pv

1.42

37.6

655.2

80

5pf + 1pv

2.25

45.5

1222.5

6:00–7:00

6 pf

2.48

49.8

1730.8

7:00–8:00

5pf + 1pv

2.25

45.5

1222.5

8:00–10:00

5 pf

0:00–5:00 Rotational speed 5:00–6:00 control

2.08

43.0

1030.3

10:00–12:00 4 pf 12:00–1:00 3pf + 1pv

1.91

42.5

995.4

1.81

40.0

708.9

13:00–15:00 4 pf 15:00–16:00 5pf

1.91

42.5

995.4

2.08

43.0

1030.3

16:00–20:00 5pf + 1pv

2.25

45.5

1222.5

20:00–23:00 5pf + 1pv

2.46

49.6

1534.5

23:00–24:00 3pf + 1pv

1.81

40.0

708.9

Energy saving, E p,2-1 Energy saving, E p,3-1 Energy saving, E p,3-2

(MWh/year)

1345.0

(%)

11.6

(MWh/year)

2280.0

(%)

20

(MWh/year)

935.0

(%)

8.4

25,375.5

speed control and the classical control (start-stop). The system head curve H r1 corresponds to the start-stop control. Shutting partially the pumps outlet by valve control the system curve becomes H r2 . The results show the potential gain in energy efficiency using rotational speed control in the pumping system. It should be noted that the optimised operation of the pumping station using the rotational speed control leads to a specific energy consumption of 80% compared with 88% when valve control is used. In comparison with the classical pumping station operation, the rotational speed control ensures energy savings of 2280 MWh/year (20%), and the valve control provides savings of 1345 MWh/year (11.6%). In summary, the pump speed control ensures a supplementary energy savings of approximately 9% compared to the throttle valve control.

772

8 Hydraulic Simulation and Optimisation of Water Transmission …

8.12.3 Energy Optimisation Methodology 8.12.3.1

Pumped Storage Tanks

A pumped storage tank requires a buried tank coupled with a pump (repumping station) to deliver water from the tank to the distribution system and a control valve to gradually fill the tank without seriously affecting the pressure in the surrounding system. These buried tanks are known as “zone tanks”, and the repumping stations are known as “internal pumping stations”. With pumped storage, the distribution storage has a head lower than the hydraulic grade line (HGL) required by the system, so the water must be pumped out of the zone tank to be used. The pumped storage pump pressurises water from the storage facility for delivery to customers within the pressure zone. This procedure consists of the optimal spacing of a few buried storage tanks on some of the distribution mains of the distribution system. These tanks are supplied with the required discharge for downstream consumers through some low-pressure transmission mains, even by means of gravity, if possible. From these storage tanks, the required discharge is repumped into the distribution network at the relatively low pressure of the transmission mains in the junction point. This process does not incur a considerable energy loss, which would occur if the tanks are filled from the distribution network. Using this procedure, a subdivision of pumped discharge Qp and pumping heads H pe,j of external pumping stations is achieved as follows. • from the total discharge Qp delivered by NP external pumping stations, a part Qpn is transported through the distribution mains of pressurised network, and another part Qpa is transported through transmission mains at NT buried storage tanks, according to the following equation: NP  j=1

Q p, j =

NP  j=1

Q pn, j +

NT 

Q pa,k

(8.12.6)

k=1

• pump heads H pe,j of the external pumping stations are decreased at the values hpe,j . The total pump station power P is computed using Eq. (8.12.7) if the transmission mains are operated by gravity or using Eq. (8.12.8) if the transmission mains operate by pumping: NP NT  γ  P= ( Q pn, j h pe, j + Q pa,k H pi,k ) η j=1 k=1

P=

NP NT NT   γ  ( Q pn, j h pe, j + Q pa,k H pa,k + Q pa,k H pi,k ) η j=1 k=1 k=1

(8.12.7)

(8.12.8)

8.12 Optimisation of Water Distribution System …

773

where γ is the water specific weight; η is the aggregated and averaged efficiency of the pumping stations; Qpa,k is the discharge of the pumped storage pump (internal pumping station) k; H pi,k is the pumping head corresponding to the pressure zone served by the internal station k; and H pa,k is the pumping head at the external station for water delivery through transmission mains at storage tank k. Pump heads hpe,j are much lower than pump heads H pe,j because the head losses are changing in proportion with the square of the ratio Qpn,j /Qp,j < 1. Thus, the power of the external pumping stations decreases by reducing the discharge as well as by reducing the pressure, and total power is decreased by: P =

NP γ  Q p, j H pe, j − P) ( η j=1

(8.12.9)

and the electrical energy saving is  E p . If the location of a pumped storage (zone storage tank coupled with a pumping station PSi ) on a distribution main (Fig. 8.42) is moved towards the upstream extreme of distribution main (i.e., towards larger and larger discharges), the power Pi of the internal station PSi increases and the power Pe of the external station PSe decreases greatly because the head losses in upstream segments of distribution main are reduced according to the Darcy–Weisbach formula [6]. As a result, the optimal location of the zone storage tank is given by the minimum value of the power of the external and internal pumping stations (Fig. 8.42d). For evaluation of the power, an analytical model was developed, which assumes as known the length L of the distribution main (Fig. 8.42a), the discharge distribution along it (Fig. 8.42b), and the diameters DM and Dm of the supply section A and terminal section O, respectively. In section A, the distribution main is unloaded with discharge Q(x 0 ) by means of a transmission main located between section A and X0 . A pumped storage (buried tank and PSi ) is located in section X0 . The head loss H(x) that occurs until a computing section X (Fig. 8.42c) is evaluated with the following equation: x H (x) =

R0 (x)Q β x dx

(8.12.10)

0

where x is the abscissa of the computing section, reported at an upstream extremity of the distribution main; Q(x) is the pipe discharge in section X; R0 (x) is the specific (per unit length) hydraulic resistance [271, 299] of the distribution main in section X; and β is an exponent with values in the range of 1.85–2.0, that depends on the Reynolds number and the relative pipe roughness [300]. The variations of the discharge Q(x) and the hydraulic resistance R0 (x) are estimated as:

774

8 Hydraulic Simulation and Optimisation of Water Transmission …

Fig. 8.42 Optimal location of a pumped storage tank. a schematic of the distribution main; b discharge distribution; c head loss variation; d power variation of the external and internal pumping stations

8.12 Optimisation of Water Distribution System …

775

Q(x) = q0 + ax α

(8.12.11)

R0 (x) = r0 − bx 2

(8.12.12)

where the real constants q0 , r 0 and b are computed from the boundary conditions: x = 0, Q(0) = q0 , R0 (0) = 8λ/(π 2 g Dm5 ), and x = L, R0 (L) = 8λ/(π 2 g D 5M ) in which λ is the pipe friction factor, R0 (x) is the hydraulic resistance per length unit of the pipe, and the parameters a and α are determined statistically [301] based on the discharge distribution along the distribution main. Substituting Eqs. (8.12.11) and (8.12.12) into Eq. (8.12.10) and integrating, the resulting equation until section X0 is obtained: β

β

H (x0 ) = r0 q0 x0 −

bq0 3 r0 a β βα+1 ba β βα+3 x0 + x0 x − 3 βα + 1 βα + 3 0

(8.12.13)

To describe the hydraulic regime upstream of section X0 , the discharge equation can be written under a simple form: Q  (x) = Q(x) − Q(x0 ) = a(x α − x0α )

(8.12.14)

This equation results in the piezometric head (HGL) in the supply node of the distribution main: H (L) = H (x0 ) +

r0 a β βα+1 ba β r0 a β βα+1 ba β βα+3 L L βα+3 − x0 x − + βα + 1 βα + 3 βα + 1 βα + 3 0

(8.12.15) and the expressions of the pump stations’ power: γ Q(x0 )H (x0 ) η

(8.12.16)

γ [Q(L) − Q(x0 )][H (L) − H (x0 )] η

(8.12.17)

Pi = Pe =

Taking into account Eqs. (8.12.16) and (8.12.17), the total power P = Pe + Pi can be expressed as: P=

γ {[Q(L) − Q(x0 )][H (L) − H (x0 )] + Q(x0 )H (x0 )} η

(8.12.18)

The optimal solution for the location of a pumped storage tank coupled with PSi is determined by the value of x 0 , for which the total power P expressed by Eq. (8.12.18) becomes minimum (Fig. 8.42d):

776

8 Hydraulic Simulation and Optimisation of Water Transmission …

min P =

γ βα+1 (c0 + c1 x0 + c2 x0α + c3 x0α+1 + c4 x03 + c5 x0α+3 + c6 x0 + η α+βα+1

+ c7 x0

βα+3

+ c8 x0

α+βα+3

+ c9 x0

)

(8.12.19)

where c0 … c9 are the coefficients of the objective function depending on the parameters a, b, α, β, r 0 , q0 , and L as shown in [20]. The minimum of the objective function in Eq. (8.12.19) is evaluated using an interpolation numerical method, based on a searching algorithm with an accelerated step coupled with square interpolation (modified Broyden–Fletcher–Goldfarb–Shann general method) [302], which were implemented in a computer program.

8.12.3.2

Intermediary Pumping Stations Integrated on the Distribution Mains

Direct integration of pumps on the network main pipes is a rational possibility for preservation of the energy used in the water distribution process. On the distribution mains where a repumping station is mounted with parallelconnected pumps, water is taken over at a lower pressure p1 and repressed at a higher pressure p2 , and the pumping head is H pi = (p2 −p1 )/γ. Use of serial-connected intermediary pumping stations on some distribution mains amplifies the discharge through these pipes. These pumping stations also generate a low-pressure zone upstream in the suction node but ensure an important increase in pressure downstream in the pressure node. In this mode, favourable local increases in the piezometric head (HGL) in the system are generated. The repumping station is located almost at the suction node, and connection of the service lines at the upstream pipes is not made from the suction node but rather immediately downstream from the pump. Considering that in a distribution system served by NP external pumping stations (PSe ) intermediary pumping stations are directly serial-connected on a number of NA distribution mains, the total power in the system is: P=

NP NA  γ  ( Q p, j h pe, j + Q pa,k H pi,k ) η j=1 k=1

(8.12.20)

where Qp,j and hpe,j are the discharge and pumping head, respectively, for external pumping station j, and Qpak and H pi,k are the discharge and pumping head, respectively, for intermediary pumping station k. Because the pumping heads of the external pumping stations are decreased (hpe,j 1: λ=



 2(1 + α)m 1 +

1 1 − 2 2(2α − 1)m 8(4α − 3)m 4

 (10.2.13)

(b) For m < 1 and α = 2: λ=



 1+α  4−3α 8α 2 − 8.25α + 1.625 1  α 1 + m 1−α − 1 + m 1−α − 1 2(1 + α) m 2(α−1) (4α − 3)(2α − 1) α 8(3α − 4)

(10.2.14)

822

10 Hydraulic Calculation of Open Channels …

(c) For m < 1 and α < 1 (α= 2):  2 

1+α 8α − 8.25α + 1.625 1 α + m 1−α − 1 − 2(1 + α) m 2(α−1) (4α − 3)(2α − 1) α  2−α  4−3α  1 1 1−α 1−α m m −1 + −1 (10.2.15) 2(α − 2) 8(3α − 4)

λ=

– Hydraulic radius: √ α A = 2 R= Pu λ



m h 1+α

(10.2.16)

• Semi-elliptic channel in Fig. 10.3 is defined by the general ellipse with the following equation [17]: (z − a)2 x2 + −1=0 a2 b2

(10.2.17)

where: a is the major semi-axis; b is the small semi-axis. The following expressions for cross-section elements are obtained: – Section width at water free-surface: B = 2b – Water depth:

Fig. 10.3 Semi-elliptic channel

(10.2.18)

10.2 General Analytical Model for Hydraulic Computation …

823

h=a

(10.2.19)

– Cross-sectional area: A=

π π ab= Bh 2 4

(10.2.20)

– Wetted perimeter [18]:

Pu = π

3 a + b 1√ − ab 2 2 2

 (10.2.21)

– Hydraulic radius: R=

B A  Pu 1.5 B + 2 − 2 B h h

(10.2.22)

The following dimensionless parameters ϕ = B/h, ψ = A/h2 , and f = Pu /h are defined as: 1. for trapezoidal section: β=

b ; φ = β + 2 m; ψ = β + m; h

f =β+2



1 + m2

(10.2.23)

2. for parabolic section: α2 m ; φ = 2 α m; ψ = 2 1+α

√ f = 2λα



m 1+α

(10.2.24)

  π 1.5 (φ + 2) − 2φ 4

(10.2.25)

3. for semi-elliptic section: φ=

B π ; ψ = φ; h 4

f =

Each dimensional geometrical element can be expressed depending on one sole dimensional element and two other dimensionless parameters, according to Table 10.1. For m = 0 and β = 0, in Eq. (10.2.23), the particular case of a rectangular channel and a triangular channel, respectively, is obtained. Substituting ϕ = 2 in Eq. (10.2.25) correspond to the case of a semi-circular channel.

824

10 Hydraulic Calculation of Open Channels …

Table 10.1 Geometrical element expression of simple cross-sections Elements

A function of:

h

h

B

h

1 φ

A B

B

A

ψh 2

ψ φ2

Pu

fh

1 φ

ψ f h

R

10.2.2.2

ψ 0,5 φ ψ 0,5

φh

B

1

B2

√

Pu

R

A

1 f

Pu

f ψ

A

φ f

Pu

ϕ f ψ

ψ f2

A 1 ψ 0,5

B

ψ φf

√

ψ 0,5

B

√ √

f

A

Pu

A

ψ f2

Pu2

R

f2

ψ

f2 ψ

Pu

R R2 R

R

Hydraulically Optimal Section

The hydraulically optimal cross-section [19] of an open channel is a section that for the same area A, the same bottom slope i and the same roughness coefficient n, conveys the maximum discharge Q. Maximum discharge is obtained when the hydraulic radius is maximal or when the wetted perimeter is minimal. For the trapezoidal channel, the value b = A/h-mh is substituted in the expression of wetted perimeter Pu and writing the minimum condition:  A dPu = − 2 − m + 2 1 + m 2 = 0, dh h

(10.2.26)

is obtained: b = 2h tg

θ 2

(10.2.27)

Equation (10.2.27) shows that the hydraulically optimal cross-section, for a given slope, corresponds to: βo =

θ b = 2 tg h 2

(10.2.28)

If the minimal perimeter condition is imposed, then θ = 60o . For the parabolic channel, the hydraulically optimal cross-section condition is obtained by determining the minimum of function in Eq. (10.2.12), considering A = const., which is reduced to calculate the minimum of function λ(α, m). For this purpose, the values λ(α, m) were calculated using Eqs. (10.2.13)–(10.2.15) for 80 values of α and 340 values of m using a computer program. The minimum value λ(α, m) for a given degree α of the generic parabola corresponds to the reverse optimal side slope mo , of which the values are presented

10.2 General Analytical Model for Hydraulic Computation …

825

Table 10.2 Optimal value mo for various α for parabolic channels α

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

6.0

7.0

8.0

9.0

mo 0.851 0.521 0.517 0.425 0.356 0.307 0.272 0.241 0.198 0.167 0.145 0.128

Table 10.3 Optimal value αo for various m for parabolic channels m

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

αo

5.5

4.0

3.1

2.6

2.2

1.9

1.7

1.4

1.3

in Table 10.2 and represent the condition of hydraulically optimal parabolic cross-section. The minimal value λ(α, m) for a given slope 1/m also corresponds to αo being the optimal degree of a generic parabola. The optimal value αo is listed in Table 10.3 and represent the hydraulically optimal parabolic cross-section condition for a given side slope. For the semi-elliptic channel, the hydraulically optimal section condition is obtained by considering A = const. and determining the minimum of function in Eq. (10.2.21) rewritten under general form: √

 φ+2 √ √ π 1.5 √ − 2 A, Pu = 2 φ

(10.2.29)

The following is obtained: φo = 2 ,

(10.2.30)

Condition expressed by Eq. (10.2.30) leads to the limit case when the semi-ellipse tends to a semi-circle.

10.2.2.3

Mathematical Model

Expressing water velocity V using Chézy’s formula (10.2.31) and adopting the Pavlovski’s formula (10.2.32) for the hydraulic resistance coefficient C yields the well-known Q discharge semi-empirical Eq. (10.2.33) [3–6]: V =C C= Q =VA=

√

Ri

1 y R n

1 A R y +0,5 i 0,5 n

(10.2.31) (10.2.32) (10.2.33)

826

10 Hydraulic Calculation of Open Channels …

where: Q is the volumetric discharge; n is the Manning’s roughness coefficient; A is the cross-sectional area; R is the hydraulic radius; i is the channel bottom slope; and y is an exponent in Pavlovski’s formula, calculated with the following equation: y = 2.5

√

n − 0.13 − 0.75

√ √

R n − 0.10

(10.2.34)

Equation (10.2.34) is valid for R between 0.1 and 0.3 and for n between 0.011 and 0.040. Substituting the A and R expressions depending on h (Table 10.2) in Eq. (10.2.33), the general equation for hydraulic computation of simple cross-section channels with steady state uniform flow is obtained: Q=

1 ψy n fy

+1.5 +0.5

hy

+2.5 0.5

i

(10.2.35)

The flow is steady if the mean velocity of one cross-section remains constant within a certain period of time. If the mean velocity between the two cross-sections is constant at a certain moment, the flow is uniform. If the water velocity V obtained after design is not enclosed between admissible limits indicated in the literature [4], such as minimum permissible velocity V m , that avoids the deposition of sediment and suspensions, and maximum permissible velocity V M, that are safe against erosion, the channel bottom slope i is increased or decreased according to Eq. (10.2.36) obtained from the Chézy’s formula (10.2.31): i=

2 n 2 Vm(M)

R 2y+1

(10.2.36)

and the water depth h is determined with the following equation:  1 h = 0.5 ψ

Q Vm(M)

(10.2.37)

The design of a channel with a given shape requires determination of the variables h, B and V when the elements Q, i, n and parameters α and p or m (parabolic section), ϕ (semi-elliptic or semi-circular section), m and β (trapezoidal section), m (triangular section), or β (rectangular section) are known. This can be easily performed applying the iteration method. In the case of the operation checking problem, the geometrical elements B, h, i, n, m and α are given and the hydraulic elements Q and V are computed. Taking into account the calculation formulas presented, an algorithm to solve the outstanding problems of the hydraulic computation of simple cross-section (linear and curve) open channels with steady state uniform flow was developed. On the basis of this algorithm the computer program CANDES1 [20] was elaborated in FORTRAN programming language for PC micro-systems.

10.2 General Analytical Model for Hydraulic Computation …

827

10.2.3 Compound Channels 10.2.3.1

Geometrical Elements of the Channels with Flat Sides and a Cylindrical Bottom

The channel with flat sides and a cylindrical bottom (round-bottomed triangle) is a form usually created by excavation with shovels. Taking into account the notations in Fig. 10.4 and the tangency condition of trapezium sides to the circle arch, the cross-section elements can be deduced [21]: m = ctgθ

(10.2.38)

b = 2r sin θ = f 1 (m)r

(10.2.39)

h = 2r sin2

θ = f 2 (m)r 2

H − h = αr H=

α + f 2 (m) h = [α + f 2 (m)] r f 2 (m)

B = b + 2m(H − h) = [2mα + f 1 (m)] r

(10.2.40) (10.2.41) (10.2.42) (10.2.43)

in which: f 1 (m) =

4 m

 m = 2 1 + m2 f 2 (m) = 1 −

Fig. 10.4 Channel with flat sides and a cylindrical bottom

2m m

(10.2.44) (10.2.45) (10.2.46)

828

10 Hydraulic Calculation of Open Channels …



H H − f 2 (m) = f 2 (m) −1 α= r h

(10.2.47)

where: θ is the side angle; m is the reciprocal of the side slope; r is the circle arch radius; H is the water depth; B is the section width at the water free-surface. Using Eqs. (10.2.42) and (10.2.43), the following is obtained: β=

2mα + f 1 (m) B = H α + f 2 (m)

(10.2.48)

f 1 (m) − f 2 (m) β β − 2m

(10.2.49)

α=

According to Eq. (10.2.47), if h = H (circular channel) and h = 0 (trapezoidal channel), then α has the value 0 and ∞, respectively. Introducing restrictions α = 0 and α = ∞ in Eq. (10.2.48), the problem’s compatibility condition is obtained: 2m < β
β. Feurich and Bosch [28] have developed, following experimental research, a diagram of the variation of water velocity in sewer columns according to the water head. From the analysis of this diagram were determined the values of the resistance coefficient β = v/v0 depending on the column height H, where v is the real velocity of water in columns, and v0 is the velocity of water in vacuum. The results were represented in graphical form in Fig. 10.5.

10.3 A New Calculation Model for Design of Sewer Columns in Buildings

835

Fig. 10.5 Diagram of variation of the resistance coefficient β

10.3.3 Computational Model Considering the flow at the partially full section and the known calculation flow rates, from the continuity equation: Q = Av,

(10.3.12)

taking into account the Eq. 10.3.10 and explaining the area A of the section occupied by water with thickness δ (Fig. 10.6), the equation for calculating the diameter D of a sewer column is obtained: D=

Q +δ √ π δβ 2g H

(10.3.13)

In order to avoid the phenomena that produce depressions or overpressures higher than 40 mm H2 O in the sewer columns, it is recommended that: Fig. 10.6 Cross-section through the vertical column

836

10 Hydraulic Calculation of Open Channels …

δ ≤ 0.25D

(10.3.14)

With the condition expressed by Eq. (10.3.14), for g = 9.81 m/s2 , the Eq. (10.3.13) for calculating the diameter D, in m, becomes:  D = 0.62

Q βH 0.5

(10.3.15)

Taking into account the variation graph of the resistance coefficient β in Fig. 10.5, the authors drew up on the basis of Eq. (10.3.15) the diagram for the dimensioning of the sewer columns illustrated in Fig. 10.7, where D is in mm. For the case when the presented diagrams are not available, analytical relations of calculation of the coefficient β have been deduced, usable on the computer, in the general form: β = αHψ

(10.3.16)

Determining the constants α and ψ by numerical method of the smallest squares [29], for four characteristic variation domains of the resistance coefficient β, the following expressions of it resulted, depending on the column height H, in m:

Fig. 10.7 Diagram for sizing vertical sewer columns

References

837

β = 0.24H 0.54 (H < 3)

(10.3.17)

β = 0.30H 0.25 (3 ≤ H < 7)

(10.3.18)

β = 0.457H 0.034 (7 ≤ H ≤ 15)

(10.3.19)

β = 1.879H −0.484 (15 < H ≤ 30)

(10.3.20)

The diameter of the column is established by choosing the maximum size from the variants proposed in the study, depending on the calculation flow rates and the heights of the column. It must be taken into account that the diameters of the sewer columns are at least equal to those of the pipes connecting to the sanitary objects, or of the branches afferent to the horizontal pipes. It is recommended that the connection to the horizontal collectors always be made with elbows of maximum 45°, as much as possible with the insertion of a straight piece. As it has resulted from experimental research [28], a column with a straight path to the horizontal collector pipe is much superior from a functional point of view to any other solution and consequently must be tended towards this constructive way of achieving it. If changes of direction cannot be avoided, they will be made with elbows at 15°, 30° or at most 45°.

10.3.4 Conclusions The diagram proposed for sizing the vertical columns shows the decrease of the diameter with the height, for the same calculation flow rate, which is explained by the increase of the water flow velocity and by the storage effect of the sewer column. The proposed model for sizing the sewer columns has the advantage that it takes into account not only the influence of the flow rate transported through the column but also its height. The diagrams elaborated for this purpose offer the designer the possibility to perform a fast and efficient calculation in comparing the constructive variants. On the other hand, the calculation model is usable on computers, on the basis of which a computer program can be drawn up, which will lead to an increase in the accuracy of the calculations and to a significant reduction in working time compared to manual calculation.

838

10 Hydraulic Calculation of Open Channels …

References 1. Mateescu C (1963) Hydraulics. Didactic and Pedagogic Publishing House, Bucharest (in Romanian) 2. Blidaru V, Blidaru E, Cismaru E (1996) Contributions regarding section shape selection of concrete steel prefabricated troughs for irrigations. Hydrotechnics 41(7):205–213 3. Chaudhry MH (1993) Open channel flow. McGraw-Hill, New Jersey, USA 4. Chow WT (1973) Open channel hydraulics. McGraw-Hill, New York, USA 5. Subramanya K (1998) Flow in open channels. McGraw-Hill, New Delhi, USA 6. French RH (1994) Open-channel hydraulics. McGraw-Hill, New York, USA 7. Swamee PK, Bhatia KG (1972) Economic open channel section. J Irrig Power 29(2):169–176 8. Loganathan G (1991) Optimal design of parabolic canals. J Irrig Drain Eng ASCE 117(5):716– 735 9. Monadjemi P (1994) General formulation of best hydraulic channel section. J Irrig Drain Eng ASCE 120(1):27–35 10. Froehlich DC (1994) Width and depth-constrained best trapezoidal section. J Irrig Drain Eng ASCE 120(4):828–835 11. Turan ME, Yurdusev MA (2011) Optimization of open canal cross sections by differential evolution algorithm. Math Comput Appl 16(1):77–86 12. Kaveh A, Talatahari S, Azar BF (2012) Optimum design of composite open channels using charged system search algorithm. Iran J Sci Technol Trans B Eng 36(C1):67–77 13. Sarbu I, Iosif A (2018) A general analytical model for hydraulic computation of open channels with steady state uniform flow. Int J Adv Appl Sci 5(1):1–7 14. Sarbu I (1986) Considerations on the hydraulic calculation of channels with parabolic crosssection. Hydrotechnics 9:283–285 15. Swamee PK (1995) Optimal irrigation canal sections. J Irrig Drain Eng ASCE 121(6):467–469 16. Sarbu I, Retezan A (1985) Considerations on the hydraulic calculus of the asymmetric natural beds. Hydrotechnics 30(10):308–310 17. Sarbu I (1986) Regarding the hydraulic calculation of semi-elliptical channels. Hydrotechnics 11:345–347 18. Elipsa (2016) http://www.imatematica.ro/geometrie/elipsa.php. Accessed 16 Oct 2016 19. Arsenie M, Arsenie D (1981) Channel profiles with remarkable characteristics: hydraulically optimal profile. Hydrotechnics 26(6):182–188 20. Sarbu I, Kalmar F (2000) Computer aided design of building services. Mirton Publishing House, Timisoara, Romania (in Romanian) 21. Sarbu I (1986) About the optimal hydraulic calculation of the channels with flat sides and cylindrical bottom. Hidrotechnics 2:36–38 22. Dumitrescu L (1980) Sanitary installations for ensembles of buildings. Technical Publishing House, Bucharest (in Romanian) 23. Mateescu Th (1996) Calculation of sanitary installations. Iasi, Romania: “Gh. Asachi” Publishing House (in Romanian) 24. Giurconiu M, Mirel I, Carabet A, Chivereanu D, Florescu C, Staniloiu C (2002) Hydro-urban constructions and installations. West Publishing House, Timisoara, Romania (in Romanian) 25. Retezan A, Sarbu I (1986) Considerations on the sizing of sewer columns. Constructions 9(10):68–70 26. Sommer F, Hanslin R (1969) Wastewater distribution in vertical columns. Sanitär-und Heizungs-technik 33(12):34–48 27. Giurconiu M, Mirel I, Retezan A, Sarbu I (1989) Hydraulics of hydro-urban constructions and installations. Facla Publishing House, Timisoara, Romania (in Romanian) 28. Feurich H, Bösch K (1979) Sanitary engineering. Kramer-Verlag, Dusseldorf, Germany 29. Sarbu I (2010) Numerical modelling and optimisations in building services. Polytechnic Publishing House, Timisoara, Romania (in Romanian)

Chapter 11

Numerical Modelling of Heat Transfer

Abstract In this chapter two numerical simulation models based on finite or boundary elements of conductive thermal fields generated or induced into solid body in steady state are developed and the velocity and temperature fields due to laminar forced heat convection in a concentric annular tube with constant heat flux boundary conditions are studied using dual reciprocity method. Additionally, a numerical simulation model of change in time along the pipe of ice layer formed inside outdoor pressurised pipes, under non-stationary atmospheric regime is described.

11.1 Generalities Modern computational techniques facilitate solving problems with imposed boundary conditions using different numerical methods [1–8]. The numerical analysis of heat transfer [9–11] has been independently, though not exclusively, developed in four main streams: the finite difference method (FDM) [12, 13], the finite volume method (FVM) [14], the finite element method (FEM) [15–17] and the boundary element method (BEM) [18–20]. The dual reciprocity method (DRM) is another method with boundary elements, proposed for Poisson equations and different from the standard BEM due to the use of radial interpolation functions [21]. The FDM is based on using Taylor series expansion to find approximation formulas for derivative operators. The basic concept of the FVM is derived from physical conservation laws applied to control volumes. The FDM, FVM and FEM depend on the mesh that discretises the domain via a special scheme. The FEM and BEM are based on the integral equation for heat conduction. This equation can be obtained from the differential equation using the variational calculus. Several scientists worked on the combination of BEM and FEM. A combined BEM–FEM model for the velocity-vorticity formulation of the Navier–Stokes equations was developed by Žuniˇc et al. [22] to solve 3D laminar fluid flow. In the field of viscous fluid flow numerical simulation, an important work was done by Young et al. [23] using primitive variable formulation of Navier–Stokes equations. They computed pressure field with BEM and momentum equation with three steps FEM.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 I. Sarbu, Advances in Building Services Engineering, https://doi.org/10.1007/978-3-030-64781-0_11

839

840

11 Numerical Modelling of Heat Transfer

In this chapter two numerical simulation models based on FEM or BEM of conductive thermal fields generated or induced into solid body in steady state are developed [24] and the velocity and temperature fields due to laminar forced heat convection in a concentric annular tube with constant heat flux boundary conditions are studied using DRM method [25]. Additionally, a numerical simulation model of change in time along the pipe of ice layer formed inside outdoor pressurised pipes, under non-stationary atmospheric regime is described [26].

11.2 Numerical Simulation of 2D Steady State Heat Conduction Using Finite and Boundary Element Methods 11.2.1 Preliminary Considerations Though thermal phenomenons are produced in three-dimensional bodies, the resulted thermal fields have preponderant variations on certain directions. That is why the analysis of thermal fields from plane or cylindrical walls usually is performed using two-dimensional computation models. The temperature variation in space and time within an inhomogeneous, anisotropy and linear (constant thermal conductivity) material is expressed by Fourier conduction differential equation. Analytical integration of this equation is very involved and even impossible in case of domains with sophisticated geometry. Also, the analysis of non-linear conductive thermal fields by classic mathematical methods is very involved. Analytical solutions that can be obtained with Kirchhoff and Boltzmann transformations [27] are only for the simple cases. In these situations numerical methods should be applied. The FEM and BEM are based on the integral equation for heat conduction. This equation can be obtained from the differential equation using the variational calculus. In the first case, the temperature values will be calculated on the finite elements. Then, based on these partial solutions, the solution for the entire volume will be determinate. Using this method we can divide into elements also fields with unregulated border. FEM algorithms are very robust and generally converge with reasonable amounts of computation. The BEM uses a fundamental solution to convert a partial differential equation to an integral equation. In the BEM only the boundary is discretised and an internal point’s position can be freely defined. This method has the immediate advantage of reducing the dimensionality of the problem by one. In addition, the BEM naturally handles the problems caused by dynamic geometry. Unlike the FEM, which requires that the domain be meshed, the BEM only discretises the boundary. Therefore, the amount of data necessary for solving a problem can be greatly reduced [19, 20, 28, 29]. A complete review of the BEM’s domain integrals is presented in [30].

11.2 Numerical Simulation of 2D Steady State Heat Conduction …

841

The BEM, an effective and promising numerical analysis tool due to its semianalytical nature and ability to reduce a problem’s dimension, has been successfully applied to the homogeneous linear heat conduction problem [31]. This section aims to use both FEM and BEM for solving steady state heat conduction problems [32, 33]. The temperature distribution in some solid bodies, with linear variation of the properties and in pipe insulation is analysed. Numerical examples are presented to demonstrate the accuracy and efficiency of the developed numerical simulation models. The present research efforts aiming at the establishment of the FEM’s and BEM’s applicability to heat conduction are confirmed and could eventually be extended to the study of other heat transfer systems.

11.2.2 Analytical Model of Heat Conduction The temperature in a solid body is a function of the time and space coordinates. The points corresponding to the same temperature value belong to an isothermal surface. This surface in a two-dimensional Cartesian system is transformed into an isothermal curve. The heat flow rate Q represents the heat quantity through an isothermal surface S in the time unit:  (11.2.1) Q = q ds S

in which the heat flux q is given by the Fourier law: q = −λ

∂t = −λ grad t ∂n

(11.2.2)

where λ is the thermal conductivity of the material. The thermal conductivity of the building materials is a function of temperature and variation can accordingly be expressed as: λ = λ0 [1+b(t − t0 )]

(11.2.3)

where λ0 is the thermal conductivity corresponding to the t 0 temperature and b is the material constant. If there is heat conduction within an inhomogeneous and anisotropy material, considering the thermal conductivity constant in time, the temperature variation in space and time is given by the Fourier equation:       ∂ ∂t ∂t ∂t ∂t ∂ ∂ = ρc λx + λy + λz + Q0 ∂τ ∂x ∂x ∂y ∂y ∂z ∂z

(11.2.4)

842

11 Numerical Modelling of Heat Transfer

Fig. 11.1 Boundary conditions

where t is the temperature; τ is the time; ρ is the material density; c is the specific heat of material; λx , λy , λz are the thermal conductivity in the directions x, y and z; Q0 is the power of internal sources. To solve the differential equation it is necessary to have supplementary equations. These equations contain the geometrical conditions of the analysis domain, the starting conditions (at τ = 0) and the boundary conditions. The boundary conditions (Fig. 11.1) describe the interaction between the analysed domain and the surroundings. In function of these interactions different conditions are possible: • the Dirichlet (type I) boundary conditions give us the temperature values on the boundary surface S t of the analysed field like a space function constant or variable in time: t = f (x, y, z, τ )

(11.2.5)

• the Neumann (type II) boundary conditions give us the value of the heat flux through the S q boundary surface of the analysed field: q = λx

∂t ∂t ∂t n x + λ y n y + λz n z ∂x ∂y ∂z

(11.2.6)

where nx , ny , nz are the cosine directors corresponding to the normal direction on the Sq boundary surface. • the Cauchy (type III) boundary conditions gives us the external temperature value and the convective heat transfer coefficient value between the S α boundary surface of the body and the surrounding fluid: α (t − te ) = λx

∂t ∂t ∂t n x + λ y n y + λz n z ∂x ∂y ∂z

(11.2.7)

11.2 Numerical Simulation of 2D Steady State Heat Conduction …

843

where α is the convective heat transfer coefficient from S α to the fluid (or inversely); t e is the fluid temperature. The analytical model described by the Eqs. (11.2.4)–(11.2.7) can be completed with the material equations which provide us information about variation of the material properties depending on temperature. For the materials with linear physical properties (λ = const.), these equations are not used in the model. Solving the heat conduction differential equation (Eq. 11.2.4) can determine the temperature values in each point of the body. However, if body has a boundary surface of sophisticated geometry, the Eq. (11.2.4) cannot be solved using analytical methods. In this case numerical methods should be applied. The increasing availability of computers has also lead into the direction of more frequent use of these methods.

11.2.3 Numerical Model with Finite Elements The transformation of Eqs. (11.2.4)–(11.2.7) into integral model is necessary to use the FEM. To realise this transformation variation calculus can be used. The temperature t(x, y, z, τ) which represents a solution for Eq. (11.2.4) with conditions (11.2.5)–(11.2.7), also represents a solution for the steady state equation in the V field: δF = 0

(11.2.8)

where F is the functional of heat conduction. Integration of Eq. (11.2.4) with conditions (11.2.5)–(11.2.7) is mathematically equivalent with the minimisation of the functional:     2  2     ∂t 2 ∂t ∂t ∂t 1 ρc − Q 0 t dV − + λy + λz dV + λx F= 2 ∂x ∂y ∂z ∂τ V V     1 (11.2.9) t − te dS q t dS + α t 2 

Sq

Sα

where Q0 is positive when the internal sources produce heat and negative when these sources absorb heat; q is positive when the body receives heat and negative when the body yields heat to the surrounding fluid; α is positive on the surfaces where the heat transfer happens from the body to the fluid and it is negative inversely. The minimisation of the functional is performed correspondingly to each finite element. The solution for the entire field is obtained by joining the partial solutions. Though the heat conduction is carried out within three-dimensional bodies, the temperature distribution variation is significant only in certain directions. Thus, the analysis of temperature distribution in bars, plane or cylindrical walls is performed using a two-dimensional model.

844

11 Numerical Modelling of Heat Transfer

In the steady state heat transfer processes the temperature does not depend on the time, thus ∂t/∂τ = 0 in Eq. (11.2.9). In addition, at two-dimensional problems, the temperature does not vary on z direction, thus ∂t/∂z = 0.

11.2.3.1

General Equations of the FEM

Equation (11.2.9) can be expressed as:    2        1 ∂t 2 ∂t 2 ∂t F= + λy + λz − Q 0 t dV − λx 2 ∂x ∂y ∂z V     1 (11.2.10) t − te dS qtdS + αt 2 Sq

Sα

Taking into account that the temperature function is not continuous on the entire field, the Eq. (11.2.10) can be integrated only on the finite elements. On the entire field the functional F can be written as a sum of m functional F e , where m is the number of finite elements: F=

m

Fe

(11.2.11)

e=1

⎧    e 2    m ⎨ ∂ te 2 ∂t 1 + λy dV − Q 0 t e dV − F= λx ⎩ 2 ∂x ∂y e=1 V Ve e ⎫   ⎪   ⎬ 1 (11.2.12) qt e dS + αt e t e − te dS ⎪ 2 ⎭ Sqe

Sαe

where the “e” exponent refers to a finite element. For a given finite element the temperature t e can be calculated based on the temperature values in the nodes: t e = N1 t1 + N2 t2 + · · · + Nn tn = [N ]{t}e

(11.2.13)

where: n is the number of the finite element nodes; [N] is the form matrix of the finite element; {t}e is the vector of temperature values in the nodes. In Eq. (11.2.12) appear the partial derivates of the temperature, therefore the Eq. (11.2.13) should be derived:

11.2 Numerical Simulation of 2D Steady State Heat Conduction …

 {B} =

∂t e ∂x ∂t e ∂y



 =

∂ N1 ∂ N2 ∂x ∂x · · · ∂ N1 ∂ N2 ∂ y ∂y · · ·

845

⎧ ⎫ ⎪ t ⎪ ⎨ 1⎬ t2 = [J ]{t}e ⎪ ⎭ ⎩t ⎪ n

∂ Nn ∂x ∂ Nn ∂y

(11.2.14)

If the thermal conductivities are written in matrix form:   λx 0 [D] = 0 λy

(11.2.15)

then Eq. (11.2.12) can accordingly be expressed as: 

1 ([J ]{t}e )T [D][J ]{t}e dV − 2

F = e

Ve



α ([N ]{t}e )2 dS − 2

Sαe



 Q o [N ]{t}e dV −

Ve



q[N ]{t}e dS+ Sqe

αte [N ]{t}e dS

(11.2.16)

Sαe

Because ([J ]{t}e )T ={t}eT [J ]T ([N ]{t}e )2 =([N ]{t}e )T ([N ]{t}e ) = {t}eT [N ]T [N ]{t}e

(11.2.17)

Equation (11.2.16) can be expressed as:  Fe =

1 T T {t} [J ] [D][J ]{t}e dV − 2 e

Ve





α T {t} [N ]T [N ]{t}e dS − 2 e

Sαe



 Q o [N ]{t}e dV −

Ve

q[N ]{t}e dS+ Sqe

αte [N ]{t}e dS

(11.2.18)

Sαe

If it is derived the matrix Eq. (11.2.18) the further equation is obtained: ⎛ ∂ Fe ⎜ =⎝ ∂{t}e



[J ]T [D][J ]dV +

⎞

 Sαe

Ve



⎟ α[N ]T [N ]d S ⎠{t}e −

Ve

Q o [N ]T dV −



Sqe

q[N ]T d S −



αte [N ]T d S

Sαe

(11.2.19) Because dV = hdA and dS = hdL result: ⎛ ∂ Fe ⎜ = h⎝ ∂{t}e



Ae

[J ]T [D][J ]d A +

 Le

⎞ ⎟ α[N ]T [N ]d L ⎠{t}e − h

 Ae

Q o [N ]T d A−h

 Le

q[N ]T d L − h



αte [N ]T d L

Le

(11.2.20)

846

11 Numerical Modelling of Heat Transfer

where: h is the thickness of the finite element, dA is the area of the finite element and dL is the length of the finite element side. The finite element thickness h is considered constant and equal to 1 m. Equation (11.2.20) can be written as in compressed form: ∂ Fe = [k]{t}e − { p} ∂{t}e

(11.2.21)

in which:  [k] = h  { p} = h

 α[N ]T [N ]dL

[J ]T [D][J ]dA + h Ae

L αe



Q 0 [N ]T dA + h Ae

(11.2.22)



q[N ]T dL + h L qe

αte [N ]T dL

(11.2.23)

L αe

where: [k] is the matrix of the heat transfer corresponding to a finite element, the first term is related to conduction and the second term to convection on the L αe side of the S αe boundary surface; {p} is the vector of heat sources containing the internal sources Q0 , the heat flux q on the S qe boundary surface, and the convection on the S α boundary surface. The minimisation of the F functional supposes the equality with zero of the first derivate in each point of the studied field. Taking into account of Eq. (11.2.11) results: ∂F ∂ e ∂F F = = ∂{t} ∂{t} e=1 ∂{t}e e=1 m

m

(11.2.24)

Substituting Eq. (11.2.21) in Eq. (11.2.24) is obtained the equation system corresponding to the entire field: [K ] {t} = {P}

(11.2.25)

in which: [K ] =

m 1

[k];

{P} =

m

{ p}

(11.2.26)

1

where: [K] is the matrix of heat conduction of the entire field; {P} is the vector of heat sources corresponding to analysed field; {t} is the vector of unknown temperatures. Equation (11.2.25) represents the form with finite elements of the heat conduction differential equation, which contains a number of equations equal to the node number with unknown temperatures.

11.2 Numerical Simulation of 2D Steady State Heat Conduction …

11.2.3.2

847

Matrix of Heat Conduction

If there are used finite elements with triangle form in a certain point of finite element, using Eq. (11.2.13) the t e temperature (Fig. 11.2), can be written as: ⎧ ⎫ ⎨ ti ⎬  t e = Ni ti + N j t j + Nk tk = Ni N j Nk t j = [N ]{t}e ⎩ ⎭ tk 

(11.2.27)

where: t i , t j , t k are the temperatures in i, j, k nodes (nodes of triangle finite element); [N] is the form matrix of the finite element [34]. The conduction matrix of a finite element is: [k] = [k1 ] + [k2 ]

(11.2.28)

with:  [k1 ] = h

 [J ]T [D] [J ]dA; [k2 ] = hα

Ae

[N ]T [N ]dL

(11.2.29)

L αe

The [J] matrix, using Eq. (11.2.14) can be expressed as:  {B} =

∂ te ∂x ∂ te ∂y



 =

⎧

⎫

 t ⎪ ∂ Ni ∂ N j ∂ N k ⎪ ⎨ i⎬ ∂x ∂x ∂x ∂ Ni ∂ N j ∂ Nk ⎪ t j ⎪ = [J ]{t}e ∂ y ∂ y ∂ y ⎩ tk ⎭

There are derived the expressions of form functions: Fig. 11.2 Finite element with triangle form

(11.2.30)

848

11 Numerical Modelling of Heat Transfer

  ∂ Ni  [J ] =  ∂∂Nxi  ∂y

∂ N j ∂ Nk ∂x ∂x ∂ N j ∂ Nk ∂y ∂y

    1 bi b j bk  =  2 Ae ci c j ck

(11.2.31)

where Ae is the area of the finite element, and the b respective c can be written as [34]: bi = yi − yk ; b j = yk − yi ; bk = yi − y j ci = xk − x j ; c j = xi − xk ; ck = x j − xi

(11.2.32)

Consequently, the [J] matrix is constant. Because the λx and λy thermal conductivities do not vary for a finite element, the [D] matrix is also constant, thus:  [k1 ] = h

[J ]T [D][J ] dA = h[J ]T [D][J ]Ae

(11.2.33)

Ae

Substituting the expression of [J] matrix from Eq. (11.2.31) and the expression of [D] matrix from Eq. (11.2.15) in Eq. (11.2.33) results: ⎡ ⎤ λ b b + λ y ci ci λx bi b j + λ y ci c j λx bi bk + λ y ci ck h ⎣ x i i [k1 ] = λx b j bi + λ y c j ci λx b j b j + λ y c j c j λx b j bk + λ y c j ck ⎦ 4 Ae λx bk bi + λ y ck ci λx bk b j + λ y ck c j λx bk bk + λ y ck ck

(11.2.34)

The matrix [k 2 ] from Eq. (11.2.28) can be written as: ⎡

⎤ Ni Ni Ni N j Ni N k ⎣ N j Ni N j N j N j Nk ⎦ dL N k Ni N k N j N k N k

 [k2 ] = h α L αe

(11.2.35)

Using the L–natural coordinates and considering that convective heat transfer exists on the jk side of the finite element, result:  [k2 ] = h α L αe

⎡

⎤ 0 0 0 ⎣ 0 L j L j L j L k ⎦ dL 0 L j Lk Lk Lk

(11.2.36)

To solve Eq. (11.2.36), the following relation should be used: X j Xi

β

L iα L j dx =

α!β!(X j − X i ) (α + β + 1) !

Consequently for products with the same indices j or k is obtained:

(11.2.37)

11.2 Numerical Simulation of 2D Steady State Heat Conduction …



 L j L j dL = L αe

 L k L k dL =

L αe

L 2j dL = L αe

2!0! L αe L αe = 3 (2+0 + 1) !

849

(11.2.38)

and for products with different indices j and k is obtained: 

 L j L k dL =

L αe

1!1! L αe L αe = 6 (1+1 + 1) !

L k L j dL = L αe

(11.2.39)

Substituting into Eq. (11.2.36) results: ⎡ ⎤ 000 hα L αe ⎣ [k2 ] = 0 2 1⎦ 6 012

(11.2.40)

If convective heat transfer exists the ij or ki sides of the finite element are: ⎡ ⎤ 210 hαL αe ⎣ [k2 ] = 1 2 0 ⎦; 6 000

⎡ ⎤ 201 hαL αe ⎣ [k2 ] = 0 0 0⎦ 6 102

(11.2.41)

The matrix [k 2 ] exists only in the case when at least, o none side of the finite element heat transfer is realised by convection.

11.2.3.3

Vector of Heat Sources

This vector is based on Eq. (11.2.23) from three terms, which can be calculated using the L–natural coordinates. Supposing that Q0 is constant for a finite element, using the following relation:  Ae

β

γ

L iα L j L k dA =

α!β!γ ! 2 Ae (α+β+γ +2) !

(11.2.42)

is obtained: ⎧ ⎫ ⎪ Ni ⎪  ⎨  ⎬ p Q = h Q o [N ]T dA = h Q o N j dA = h Q o ⎪ ⎩N ⎪ ⎭ k Ae Ae Ae !



⎧ ⎫ ⎧ ⎫ ⎪ ⎪1⎪ ⎨ Li ⎪ ⎬ h Q o Ae ⎨ ⎬ L j dA = 1 ⎪ 3 ⎪ ⎩L ⎪ ⎭ ⎩1⎪ ⎭ k

(11.2.43) The second term, for a certain heat flux, corresponds to the heat transfer on the boundary surface of the studied field. Supposing that the body receives the heat flux

850

11 Numerical Modelling of Heat Transfer

through L ki = L qe side of the finite element, using Eq. (11.2.37) result: 

!

pq = h L qe

⎧ ⎫ ⎧ ⎫ ⎧ ⎫  ⎨ Ni ⎬  ⎨ Li ⎬ ⎨1⎬ hq L qe q[N ]T dL = hq 0 dL = hq 0 dL = 0 ⎩ ⎭ ⎩ ⎭ 2 ⎩ ⎭ Nk Lk 1 L qe L qe (11.2.44)

The third term, from Eq. (11.2.23), corresponds to convective heat transfer on the jk (L jk = L αe ) side of the finite element. Using Eq. (11.2.37) is obtained:  { pα } = h L αe

⎧ ⎫ ⎧ ⎫ ⎧ ⎫ ⎪ 0 ⎪ ⎪  ⎨  ⎪ ⎬ ⎨ 0 ⎪ ⎬ ⎨0⎪ ⎬ hαt L e αe αte [N ]T dL = hαte N j dL = hαte L j dL = 1 ⎪ ⎪ ⎪ ⎪ 2 ⎩N ⎪ ⎭ ⎩L ⎭ ⎩1⎪ ⎭ k k L αe L αe

(11.2.45) It could be observed that the element zero in the vector {pq } and {pα } expressed by Eqs. (11.2.44) and (11.2.45), respectively can occupy any position, corresponding to the side of finite element with heat transfer. Based on the equation systems obtained for the finite elements, they can realise the equation system for the entire studied field. This system can be solved using analytical or iterative methods. In present there are different programs on the software market which permit numerical analysis of the temperature distribution (e.g., WAEBRU) but these programs are too expensive and our department cannot buy them. In this context to analyse the temperature distribution in a solid body under steady state heat transfer using the numerical model developed above the computer program TAFEM has been elaborated. The equation system is solved using the Gauss method.

11.2.4 Numerical Model with Boundary Elements In the case of a plane wall, inside the analysis field, the heat transfer in steady state is modelled by the Laplace equation [28]: ∇2t = 0

(11.2.46)

On t portion of boundary of the analysis field Dirichlet boundary conditions are imposed and leftover portion q Neumann boundary conditions are imposed. In order to determine the temperature on boundary of the analysis field is used the following integral equation [28, 35, 36]:

11.2 Numerical Simulation of 2D Steady State Heat Conduction …

 c(ξ )t (ξ ) +

o

o

o

t ( X )q ∗ (ξ, X )d ( X ) =





851

o

dt ( X ) o

o

dn( X )



o

u ∗ (ξ, X )d ( X )

(11.2.47)

where: ζ is the point in which is written the integral equation (source point); c(ζ) is a o

o

o

coefficient; X is the current integration point; u ∗ (ζ, X ) = (1/2π ) ln[1/r (ζ, X )] is the fundamental solution; v∗ = ∂u ∗ /∂n is the normal derivative of this solution. o

o

The distance r(ζ, X ) between the current point X and the source point ζ is calculated with the equation: o

r (ξ, X ) = [x − x(ξ )]2 + [y − y(ξ )]2

! 21

(11.2.48)

Boundary is discretised into N constant boundary elements for which are considered temperatures t j , respectively the normal derivative (∂t/∂n)j constant and equal to the mid point (node) value of the element. Thus the integral equation is obtained under the following discretised form: ci ti +

N j=1

 tj

o

o

q ∗ (ξ, X )d ( X ) =

  N  dt j=1

j

dn

j

o

o

u ∗ (ξ, X )d ( X )

(11.2.49)

j

or ci ti +

N

Aˆ i j t j =

j=1

N

 Bi j

j=1

dt dn

 (11.2.50) j

where coefficients Aˆ i j and Bij have the expressions: Aˆ i j =



o

o

q ∗ (ξ, X )d ( X ); Bi j =

j



o

o

u ∗ (ξ, X )d ( X ), i = j

(11.2.51)

j

When i = j these become: Aii =

1 + Aˆ ii ; 2

Bii =

  li li 1 − 1n 2π 2

(11.2.52)

Explicitly, Eq. (11.2.50) generates a linear and compatible system of N equations with 2 N unknowns (t j and (∂t/∂n)j ) and after implementing the boundary conditions, the number of unknowns is reduced to N. In the case of constant boundary elements, coefficient ci has the value 1/2. Coefficients Aˆ i j and Bij from Eq. (11.2.51) are computed using a Gauss quadrature:

852

11 Numerical Modelling of Heat Transfer m m lj ∗ lj ∗ qk wk ; Bi j = u wk Aˆ i j = 2 k=1 2 k=1 k

(11.2.53)

where lj is the length of the j boundary element. o

Introducing notations: nx = cos(n, x); ny = cos(n, y) and using, for ∀ X ∈ , the parametric equations: x = Aη + B;

y = Cη + D, η ∈ [−1, 1]

(11.2.54)

where: x∈[x j , x j+1 ] and y∈[yj , yj+1 ], the following relations are obtained: nx = √

−C A2

+

C2

; ny = √

A A2

(11.2.55)

+ C2

where (x j , yj ) and (x j+1 , yj+1 ) are the extremities of the boundary element j. The analysis field is transformed into a dimensionless one by replacing the dimensional variables (x, y) with dimensionless ones (x * , y* ): x∗ =

x ; xmax

y∗ =

y xmax

(11.2.56)

where x max is the maximum extension of the analysis field after axis Ox. To determine the temperature inside of the analysis field is used the integral representation:  t (ξi ) =

o

o

o

dt ( X ) dn ∗ ( X )

o

o

u ∗ (ξi , X )d ( X ) −



o

o

o

t ( X )q ∗ (ξi , X )d ( X )

(11.2.57)



o

o

where ζi ∈ , and  represent the inside of the analysis field  ( = ∪ ). After the discretisation of boundary into N constant boundary elements is obtained the integral equation under discretised form:    N  N o o o o dt ∗ ti (ξi ) = u (ξi , X )d ( X ) − t j q ∗ (ξi , X )d ( X ) (11.2.58) ∗ dn j j=1 j=1

j

j

which can be written as such: ti =

N j=1

B¯ i j



dt dn ∗

 − j

N

A¯ i j t j

j=1

Coefficients A¯ i j and B¯ i j are evaluated using a Gauss quadrature:

(11.2.59)

11.2 Numerical Simulation of 2D Steady State Heat Conduction … m lj ∗ q wk ; A¯ i j = 2 k=1 k

m lj ∗ B¯ i j = u wk 2 k=1 k

853

(11.2.60)

where m is the number of Gauss type points and wk is the weight coefficients. Temperatures t i from points ζi are easily determined taking into account that values t j and (∂t/∂n* )j are known on the analysis field boundary, and coefficients A¯ i j and B¯ i j are computed with Eq. (11.2.54). By knowing values t j and t i of temperature on the analysis field boundary, the group of coordinate points (x * , y* ) for which t = const. represents the isothermal curves. This numerical model based on BEM has been implemented in computer program TABEM, developed in FORTRAN programming language, for PC compatible systems.

11.2.5 Applications 11.2.5.1

Temperature Distribution in Orthotropic Body

The temperature distribution was analysed in a solid body 500 × 400 mm sectional dimensions (Fig. 11.3) using FEM. The body receives heat flux on two sides: qx = 2320 W, qy = 928 W. On the other two sides the body transmit heat by convection

Fig. 11.3 Analysis domain for solid body

854

11 Numerical Modelling of Heat Transfer

Table 11.1 Temperature values in the nodes Node

Coordinates x

t (°C)

Node

y

Coordinates x

t (°C) y

1

0.0

0.0

49.063

16

30.0

0.0

78.094

2

0.0

10.0

65.543

17

30.0

10.0

103.400

3

0.0

20.0

79.955

18

30.0

20.0

124.892

4

0.0

30.0

93.393

19

30.0

30.0

143.586

5

0.0

40.0

107.704

20

30.0

40.0

160.357

6

10.0

0.0

58.153

21

40.0

0.0

90.677

7

10.0

10.0

77.100

22

40.0

10.0

119.105

8

10.0

20.0

94.157

23

40.0

20.0

142.159

9

10.0

30.0

109.882

24

40.0

30.0

161.681

10

10.0

40.0

125.446

25

40.0

40.0

178.732

11

20.0

0.0

67.581

26

50.0

0.0

107.376

12

20.0

10.0

89.601

27

50.0

10.0

137.498

13

20.0

20.0

109.025

28

50.0

20.0

161.191

14

20.0

30.0

126.452

29

50.0

30.0

181.013

15

20.0

40.0

142.752

30

50.0

40.0

198.159

αx = αy = 23.2 W/(m2 ·K). The material of the body has orthotropic properties with the following values of the thermal conductivities: λx = 11.6 W/(m·K), λy = 5.8 W/(m·K). The analysed field is divided into 40 finite elements with 30 nodes. Running the TAFEM program the values of temperatures in the nodes have been obtained and summarised in Table 11.1. The temperature distribution in the body is illustrated in Fig. 11.4. Wood is the only one orthotropic material which is used in civil engineering, and this property should be taken into account in computation of building heat losses (e.g., heat flux direction perpendicular or parallel on the fibre).

11.2.5.2

Temperature Distribution in Pipe Insulation

The temperature distribution in pipe insulation (Fig. 11.5) was analysed using the TAFEM program. The calculus was performed for a pipe with 800 mm nominal diameter and the hot water temperature was 150 °C. The ambient temperature was considered 1 °C. To obtain results which describe the real situation as exactly as possible the convective heat transfer coefficient on the external insulation surface was considered variable with values between 10 and 25.6 W/(m2 ·K).

11.2 Numerical Simulation of 2D Steady State Heat Conduction …

855

Fig. 11.4 Temperature distribution in studied body

Fig. 11.5 Insulation 1–pipe wall; 2a, 2b–insulation layers; 3–protection coat

In Fig. 11.6 the temperature distribution is illustrated in the pipe section. It can be observed that due to the variable boundary conditions on the insulation surface the isotherm curves are not circular curves, which are obtained when the classical calculus [27] is used.

856

11 Numerical Modelling of Heat Transfer

Fig. 11.6 Temperature distribution in pipe insulation

11.2.5.3

Temperature Distribution in Metallic Plaques

In Figs. 11.7 and 11.8 two variants of a metallic plaque, with dimensions 40× 40×70 mm are considered, for which was determined the temperature distribution using BEM and analytical method (AM). Figures 11.9 and 11.10 illustrate the dimensionless analysis domains together with mixed boundary conditions for these boundaries. Fig. 11.7 Simple metallic plaque

Fig. 11.8 Metallic plaque with a semi-cylindrical cut-out

11.2 Numerical Simulation of 2D Steady State Heat Conduction …

857

Fig. 11.9 Boundary conditions for simple plaque

Fig. 11.10 Boundary conditions for plaque with semi-cylindrical cut-out

For metallic plaque in Fig. 11.7 the boundary is discretised into N = 16 boundary elements and 9 internal points (Fig. 11.11), and is applied the computational model based on BEM. For metallic plaque in Fig. 8, the boundary is discretised into N = 56 constant boundary elements (Fig. 11.12) and using BEM was determined isothermal curves illustrated in Fig. 11.13.

Fig. 11.11 Boundary discretisation and internal points for simple plaque

858

11 Numerical Modelling of Heat Transfer

Fig. 11.12 Boundary discretisation for plaque with semi-cylindrical cut-out

Fig. 11.13 Temperature distribution for plaque with semi-cylindrical cut-out

The numerical results achieved by means of TABEM program are summarised in Table 11.2, comparatively with the ones obtained with AM [37]. The developed model performance was evaluated using three statistical indices: the coefficient of multiple determinations (R2 ), the root mean square error (RMSE) and the relative error (er ), as defined below [38, 39]. These performance criteria were used to compare simulated and analytical (exact) values of the temperature and its normal derivative to validate the model.

11.2 Numerical Simulation of 2D Steady State Heat Conduction …

859

Table 11.2 The values t j and (∂t/∂n ∗ ) j (∂t/∂n ∗ ) j

Point

Coordinates

t j (°C)

j

x ∗j

y ∗j

BEM

1

0.125

1.000

93.052

93.750

0.747

0.000

0.0

0.0

2

0.375

1.000

80.705

81.250

0.671

0.000

0.0

0.0

3

0.625

1.000

68.299

68.750

0.656

0.000

0.0

0.0

4

0.875

1.000

55.821

56.250

0.763

0.000

0.0

0.0

5

1.000

0.875

50.000

50.000

0.0

– 51.704

– 50.0

3.408

6

1.000

0.625

50.000

50.000

0.0

– 48.290

– 50.0

3.420

7

1.000

0.375

50.000

50.000

0.0

– 48.290

– 50.0

3.420

8

1.000

0.125

50.000

50.000

0.0

– 51.704

– 50.0

3.408

9

0.875

0.000

55.821

56.250

0.763

0.000

0.0

0.0

10

0.625

0.000

68.299

68.750

0.656

0.000

0.0

0.0

11

0.375

0.000

80.705

81.250

0.671

0.000

0.0

0.0

12

0.125

0.000

93.052

93.750

0.745

0.000

0.0

0.0

13

0.000

0.125

98.776

100.000

1.224

50.000

50.0

0.0

14

0.000

0.375

99.308

100.000

0.692

50.000

50.0

0.0

15

0.000

0.625

99.308

100.000

0.692

50.000

50.0

0.0

16

0.000

0.875

98.776

100.000

1.224

50.000

50.0

0.0

17

0.250

0.250

86.836

87.500

0.759

0.000

0.0

0.0

18

0.250

0.500

86.876

87.500

0.713

0.000

0.0

0.0

19

0.250

0.750

86.836

87.500

0.759

0.000

0.0

0.0

20

0.500

0.,250

74.521

75.000

0.639

0.000

0.0

0.0

21

0.500

0.500

74.536

75.000

0.619

0.000

0.0

0.0

22

0.500

0.750

74.521

75.000

0.505

0.000

0.0

0.0

23

0.750

0.250

62.205

62.500

0.472

0.000

0.0

0.0

24

0.750

0.500

62.240

62.500

0.416

0.000

0.0

0.0

25

0.750

0.750

62.205

62.500

0.472

0.000

0.0

0.0

AM

er (%)

BEM

AM

er (%)

RMSE

0.58256

–

0.68280

–

R2

0.99994

–

0.99883

–

The coefficient R2 presents the overall concordance between analytical and simulated (predicted) time series, ranges from 0, for a poor model, to 1 for a perfect model, and is expressed as: "n R =1− 2

#

ysim, j − yanal, j "n 2 j=1 yanal, j

j=1

$2 (11.2.61)

860

11 Numerical Modelling of Heat Transfer

where: n is the number of analytical data points; yanal,j is the analytical value of data point j; ysim,j is the simulated value of data point j. The RMSE is a measure of overall performance across the entire range of the data set expressed by the formula % RMSE =

"n j=1

#

ysim, j − yanal, j n

$2 (11.2.62)

Greater or equal to 0, the RMSE indicates an ideal model fit when it equals 0. The relative error er measures overall agreement between analytical and simulated values and is always a positive number, with 0 representing a perfect model fit to analytical values. It is expressed as a percentage using the equation:    yanal, j − ysim, j  100% er = ysim, j

(11.2.63)

where yanal,j is the analytical solution at data point j and ysim,j is the predicted value at point j by the numerical model. Taking into account the results from Table 11.2 the BEM solutions agree well with the exact solutions, and for relative error er acceptable values have been achieved (er < 1.3% for temperature and er < 3.5% for its normal derivative) even if the number of boundary elements considered is small. The values of the RMSE are 0.5826 and 0.6828 for temperature and its normal derivative, respectively. The R2 -values are approximately 0.9999 for temperature and 0.9988 for its derivative, respectively, a result that is very satisfactory. Thus, the simulation model is analytically validated.

11.2.6 Conclusions In practice there are many situations where it is indispensable to know the temperature distribution in a body (e.g., in different mechanic and electronic components). In civil engineering it is important to analyse the temperature distribution in thermal bridges, pipe walls and insulation materials [40]. In mechanical engineering, for instance, also it is important to study the heating of rail wagon wheels running in braking state. The simulations with numerical models developed based on FEM and BEM represent an efficient way to obtain temperature distribution in steady state conductive heat transfer processes. The numerical results were shown to be in excellent agreement with exact solutions and the simulation models were analytically validated. The numerical computation of the temperature field, on the basis of the BEM, has led to close values to the ones determined analytically even if a small number of boundary elements and internal points of the analysis domain were used.

11.2 Numerical Simulation of 2D Steady State Heat Conduction …

861

Using the proposed numerical models, different simulation programs could be realised what makes it possible to effectuate a lot of different numerical experiments of practical problems. This study shows that the FEM and BEM have strong potential for further applications. Extension of the present approach to 3-D problems is easily be achieved by using fundamental solution u* and normal derivative υ* corresponding to the axisymmetric problems.

11.3 Numerical Simulation of the Laminar Forced Convective Heat Transfer Between Two Concentric Cylinders 11.3.1 Preliminary Considerations The BEM has been used to solve the direct and inverse heat conduction problems [19, 41, 42]. However, its extension to non-homogeneous and non-linear problems is not straightforward. Therefore, applications of the BEM to heat convection problems have not been sufficiently studied and are still in the development stage. Because the effects of convection are of considerable importance in many heat transfer phenomena, more research should focus on them. The drawbacks of applying the BEM to such problems are that the required fundamental solution depends on the thermal conductivity and that it is difficult to model heat generation rates (due to heat sources) because they introduce domain integrals [43]. Recently, the radial integration method (RIM) has been developed by Gao [44], which not required the fundamental solutions to basis functions and can remove various singularities appearing in domain integrals. However, although the radial integration BEM is very flexible in treatment of the general non-linear and nonhomogeneous problems, the numerical evaluation of the radial integrals is very timeconsuming compared to other methods [29, 45, 46], especially for large 3D problems. To approximate a solution to the heat conduction equation using boundary integrals, the DRM introduced by Nardini and Brebbia [21] can be used. The DRM preserves the advantages of the BEM: a shorter computational time than the FEM and a reduced number of boundary elements. Since its introduction, the DRM has been applied to engineering problems in many fields [47–49]. In the DRM, an available fundamental solution is used for the complete governing equation, and the domain integral arising from the heat source-like term is transferred to the boundary using radial interpolation functions [50–52]. In this section, the velocity and temperature fields due to laminar forced heat convection in a concentric annular tube with constant heat flux on the boundaries are determined using the DRM [25] to solve the governing equation, which is expressed mathematically in the form of a Poisson equation. A test problem is employed to verify the DRM solutions with different boundary element discretisations and

862

11 Numerical Modelling of Heat Transfer

different numbers of internal points, and the results of the numerical simulations are discussed and compared with exact analytical solutions to determine their convergence and accuracy. A concentric annular tube is chosen because of its simplicity and ability to provide an exact solution, allowing the basic nature of the proposed model for convection problems to be analysed in detail [53, 54]. Therefore, present research efforts aiming at the establishment of the DRM’s applicability to heat convection are confirmed and could eventually be extended to the study of other heat transfer systems.

11.3.2 Physical Problem and Its Mathematical Formulation Consider an incompressible Newtonian fluid of density ρ, thermal conductivity λ and specific heat c contained between two stationary concentric cylinders (i.e., in a concentric annular tube). The inner and outer cylinders have radii of Ri and Ro , respectively. Figure 11.14 shows a schematic of the annular tube and coordinate system. In the system to be analysed, the z coordinate represents the axial direction and the x–y co-ordinate plane is attached to the cross-sectional surface. To simplify the problem and its solution, the steady laminar flow is assumed to be fully developed with constant transport properties and negligible body forces. Under these conditions the Navier-Stokes equation becomes the simple pressure-driven Poiseuille flow equation. Because the flow is fully developed, the axial flow velocity is a function of only the x and y coordinates, and the axial pressure gradient is constant. In the energy equation, the viscous dissipation and axial heat conduction are neglected.

11.3.2.1

Governing Equations

The governing equations of the laminar fluid flow, expressed in the form of a Poisson equation, are obtained from the momentum and energy conservation equations [55]: Fig. 11.14 Schematic of the concentric annulus and coordinate system

11.3 Numerical Simulation of the Laminar Forced Convective …

863

∇2w =

∂ 2w ∂ 2w 1 dp + 2 = ∂x2 ∂y η dz

(11.3.1)

∇2t =

∂ 2t ∂ 2t w dt + = 2 2 ∂x ∂y a dz

(11.3.2)

where w is the axial velocity of the flow; η is the dynamic viscosity; p is the pressure; t is the temperature; and a = λ/ρc is the thermal diffusivity. For the fully developed thermal flow with constant heat flux on the boundaries and using the mixed mean temperature t m [54], Eq. (11.3.2) becomes: ∇2t =

∂ 2t ∂ 2t w dtm + 2 = 2 ∂x ∂y a dz

(11.3.3)

where ∂t/∂z = dt m /dz is a constant derived from the given conditions.

11.3.2.2

Boundary Conditions

The boundary conditions associated with Eqs. (11.3.1) and (11.3.3) are: w = 0 at r = Ri and r = R0

(11.3.4)

t = ti at r = Ri ; t = t0 at r = R0

(11.3.5)

where Ri is the radius of the inner cylinder and R0 is the radius of the outer cylinder. To solve for the temperature, the velocity is first obtained from Eq. (11.3.1); then Eq. (11.3.3) can be solved because the assumption of negligible buoyancy decouples the momentum and energy equations.

11.3.3 Numerical Model 11.3.3.1

The DRM Formulation

To solve using the BEM, Eqs. (11.3.1) and (11.3.3) subject to Eqs. (11.3.4) and (11.3.5) can be generalised as the following type of Poisson equation [48]: ∇ 2 u(x, y) = b(x, y), (x, y) ∈  with the boundary conditions:

(11.3.6)

864

11 Numerical Modelling of Heat Transfer

u(x, y) = u, ¯ q(x, y) =

(x, y) ∈ 1

(11.3.7)

∂u(x, y) = q, ¯ (x, y) ∈ 2 ∂n

(11.3.8)

and the convective heat transfer problem is represented by: 1 dp = const. η dz w dtm u(x, y) = t, b(x, y) = a dz

u(x, y) = w, b(x, y) =

(11.3.9)

where: 1 + 2 = is the total boundary of the domain ; n is normal to the boundary; u¯ and q¯ are the values specified at each boundary. Applying the usual boundary element technique to Eq. (11.3.6), an integral equation can be derived as described in [18]:  ci u i +

∗





uq d −

∗



qu d =



bu ∗ d

(11.3.10)



where the constant ci depends on the geometry at point i as follows: ⎧ ⎨ 1 ci = ⎩ θ 2π

pentru (xi , yi ) ∈  pentru (xi , yi ) ∈

(11.3.11)

where θ is the internal angle at the source point. The key part of the DRM is to calculate the domain integral term of Eq. (11.3.10) on the boundary and remove the need for a complicated domain discretisation. To accomplish this, the source term b(x, y) is expanded using its values at each node j and a set of interpolating functions f j as in [47, 48]: b(x, y) ∼ =

N +L

αj f j

(11.3.12)

j=1

where: αj is a set of initially unknown coefficients; N and L are the number of boundary nodes and internal points, respectively. Using Eq. (11.3.12), the coefficients αj can be expressed in terms of the nodal values of the function b(x, y) in matrix form as: α = F−1 b

(11.3.13)

11.3 Numerical Simulation of the Laminar Forced Convective …

865

where F is a matrix with coefficients f j and b = {bi }. The radial basis functions f j are linked with the particular solutions uˆ j to the equation: ∇ 2 uˆ j = f j

(11.3.14)

Substituting Eq. (11.3.14) into Eq. (11.3.12) and applying integration by parts to the domain integral term of Eq. (11.3.10) twice leads to [8]:  ci u i +



uq ∗ d −



qu ∗ d =

N +L

    α j ci uˆ i j + uˆ j q ∗ d − qˆ j u ∗ d



j=1



(11.3.15) ˆ qˆ can be derived as: On a two-dimensional domain, u* , q* and u, 1 −1 1 ln( ); q ∗ = ∇r · n

2π r 2π r

(11.3.16)

r r2 r2 r3 + ; qˆ = ( + )∇r · n

4 9 2 3

(11.3.17)

u∗ = uˆ =

where r is the distance from a source point i or a DRM collocation point j to a field point (x, y). As for Eq. (11.3.14), an interpolating function is chosen as a radial basis function (RBF). Two relevant expressions for RBFs are frequently used for this purpose in the engineering community: f = 1+r and f = 1+r + r 2 [50, 51]. In the numerical solution of the integral Eq. (11.3.15), u, q, uˆ and qˆ are modelled using the linear interpolation functions as follows: 

∗

k



uq d = ∗

k



uˆ j q d =

1 u k h ik

+

2 u k+1 h ik ;

k

 1 uˆ k j h ik

+

2 uˆ (k+1) j h ik ;



1 2 qu ∗ d = qk gik + qk+1 gik

(11.3.18)

1 2 qˆ j u ∗ d = qˆk j gik + qˆ(k+1) j gik (11.3.19)

where:  1 h ik =

k

 1 = gik

k

2 ϕ1 q ∗ d , h ik =

2 ϕ1 u ∗ d , gik =

 

k

k

ϕ2 q ∗ d

(11.3.20)

ϕ2 u ∗ d

(11.3.21)

The first subscript in Eqs. (11.3.20) and (11.3.21) refers to the specific position of the point where the flow velocity or temperature is evaluated. The second subscript

866

11 Numerical Modelling of Heat Transfer

refers to the boundary element over which the contour integration is performed. The superscripts 1 and 2 designate the linear interpolation functions 1 and 2 , respectively, with which the u* and q* functions are weighted in the integrals in Eqs. (11.3.18) and (11.3.19). When the boundary = 1 ∪ 2 is discretised into N elements, the integral terms in Eq. (11.3.15) can be rewritten as: 



uq ∗ d = qu ∗ d =

N  k=1 k N  k=1 k

uq ∗ d =

N &

Nn N ' 2 1 u = + h ik Hik u k sau = Hik uˆ k j pentru uˆ j h i(k−1) k

k=1

qu ∗ d =

k=1

N &

N ' 2 1 q = + gik G ik qk sau = gi(k−1) k

k=1

j=1 Nn

k=1

G ik qˆk j pentru qˆ j

(11.3.22) (11.3.23)

j=1

2 2 where h i0 = h i2N and gi0 = gi2N . Substituting Eqs. (11.3.22) and (11.3.23) into Eq. (11.3.15) after several manipulations yields the dual reciprocity boundary element equation:

ci u i +

N k=1

Hik u k −

N

G ik qk =

k=1

N +L

( α j ci uˆ i j +

j=1

N

Hik uˆ k j −

k=1

N

) G ik qˆk j

k=1

(11.3.24)

11.3.3.2

Numerical Solution

Equation (11.3.24) can now be written in a matrix-vector form as: ˆ − GQ)α ˆ HU − GQ = (HU

(11.3.25)

where H and G are matrices with elements H ik and Gik with ci incorporated into the ˆ Q ˆ correspond to vectors with principal diagonal element; U, Q and their terms U, elements uk and qk , and matrices with uˆ k j and qˆk j as the jth column vectors. Substituting α from Eq. (11.3.13) into the above equation yields: ˆ − GQ)F ˆ −1 b HU − GQ = (HU

(11.3.26)

Introducing the boundary conditions into the nodes of the uk and qk vectors and rearranging by moving known quantities to the right-hand side and unknown quantities to the left-hand side lead to a system of linear equations of the form: A = Y

(11.3.27)

11.3 Numerical Simulation of the Laminar Forced Convective …

867

Using the DRM matrix equation, a numerical solution to the problem of laminar convective heat transfer between two concentric cylinders can be readily obtained for the flow velocity w from the momentum equation and the temperature t from the energy equation or for their normal derivatives. This numerical model has been implemented as a computer program in the FORTRAN programming language for PC-compatible microsystems.

11.3.3.3

Testing the Model

The geometry illustrated in Fig. 11.15 is used for testing purposes. To simplify the problem, the surface temperatures of the two cylinders are assumed to be equal. Thus, the solution satisfies the following boundary conditions: w(x, y)| R=Ri = w(x, y)| R=R0 = 0   t ∗ (x, y) R=Ri = t ∗ (x, y) R=R0 = 0 t ∗ = tw − t, tw = ti = t0

Fig. 11.15 Boundary element nodes and internal points

(11.3.28)

868

11 Numerical Modelling of Heat Transfer

For the numerical test case, the following numerical values are introduced to Eqs. (11.3.1) and (11.3.3) from [56], in which the spectral collocation method is used to analyse heat convection in an eccentric annulus: Ri = 0, 030 m,

R0 = 0, 055 m

(dp/dz)/η = −836 m−1 s−1 a = 1.3418 × 10−9 m2 /s dtm /dz = 0.47 ◦ C/m

(11.3.29)

To confirm the accuracy of the DRM for the actual heat convection problem, the boundaries of the external and internal surfaces are discretised into 36, 48, 60, 72 or 84 elements. The nodes on every boundary and at the internal points of the analysis domain are located as shown in Fig. 11.15. Therefore, the total number of internal points used in the analysis is 90, 120, 150, 180 and 210 in the 36, 48, 60, 72 and 84 boundary element cases, respectively. The developed DRM is evaluated by means of some statistical indicators of model performance, such as the root mean square error (RMSE), the coefficient of variation (cv ), the coefficient of multiple determinations (R2 ) and the relative error (er ), which may be used to compare simulated and analytical (exact) values of the flow’s velocity and temperature to validate the model. The error can be estimated using the RMSE, defined as [38]: % RMSE =

"n i=1

#

ysim,i − yanal,i n

$2 (11.3.30)

In addition, the coefficient of variation cv , in %, and the coefficient of multiple determinations R2 are defined as follows: RMSE  100% cv =   y¯anal,i  $2 "n # i=1 ysim,i − yanal,i 2 "n R =1− 2 i=1 yanal,i

(11.3.31)

(11.3.32)

where: n is the number of analytical data points; yanal,i is the analytical value of data point i; ysim,i is the simulated value of data point i; y¯anal,i is the mean value of all of the analytical data points. The relative error er is calculated using the following formula:    yanal,i − ysim,i  er = 100% ysim,i

(11.3.33)

11.3 Numerical Simulation of the Laminar Forced Convective …

869

where yanal,i is the analytical solution at point i, and ysim,i is the predicted value at point i by the numerical model.

11.3.4 Simulation Results and Discussion To obtain the axial flow velocity w(x, y), Eq. (11.3.1) is solved first. The results for the boundary and internal nodes are shown in Tables 11.3 and 11.4 for the RBFs f = 1 + r and f = 1 + r+r 2 , respectively. In these tables, the normal derivative of the velocity w at the boundary is also listed, and all of the numerical solutions are compared with the exact solutions [53] to determine their accuracy. In addition, statistical values such as the RMSE, cv and R2 corresponding with different numbers of boundary elements in the analysed system are given in Tables 11.3 and 11.4. Figures 11.16 and 11.17 show the convergence of the DRM’s solutions for the velocity and its normal derivative as the numbers of boundary elements and internal points increase. The DRM solutions agree well with the exact solutions, and the relative errors are within 2.3% when the number of elements is greater than 36. The values of the RMSE and cv are between 0.00014 and 0.00074 and 0.40 and 2.01%, respectively, for the two radial basis functions. The R2 -value for any number of boundary elements is approximately 0.9997 for both of the radial basis functions, a result that is very satisfactory. Thus, the simulation model is analytically validated. As noted in Fig. 11.16, the velocities calculated at r = 0.0508 m and r = 0.0342 m are less accurate than the others, and the solution at r = 0.0342 is less accurate than it is at r = 0.0508. The solutions for the normal derivative of the velocity on the boundary at r = 0.055 m is less accurate than it is at r = 0.030 m, as shown in Fig. 11.17. This is because the outer boundary elements are larger than the inner boundary elements, and the distribution of internal points becomes sparse in the outward direction, whereas a rapid change in the velocity occurs at the inner and outer boundaries, as shown in Figs. 11.15 and 11.18. Therefore, the magnitude of the solution’s error in the radial direction is closely related to the physical and the mathematical aspects of the problem and the overall accuracy of the solution is fairly acceptable. Thus, when 36 elements are used, the solution has a maximum error of 2.34% at radial position r = 0.0342 m, and the next step results in an accurate solution for the temperature. The DRM solutions for the velocity are, in turn, used in the energy equation (Eq. 11.3.3) to solve for the temperature distribution. Tables 11.5 and 11.6 show the simulation results for the temperature and statistical values such as the RMSE, cv and R2 . The DRM solutions are in excellent agreement with the exact solutions and the relative errors er are within 5% when 36 elements are used (Figs. 11.19, 11.20 and 11.21). The cv values are in the range of 0.3–5.0% and the R2 -value is approximately 0.999 for the two radial basis functions with any of the tested numbers of boundary elements, which is very acceptable. Thus, the simulation model is validated by the analytical solutions.

−11.931682

−11.961390

0.030

0.999724

0.035084

0.0508

R2

0.057611

0.0466

2.018

0.066727

0.0425

0.000741

0.061518

0.0383

cv %

0.040336

0.0342

36

RMSE

w

−9.614363

−9.570611

0.055

∂w/∂n

48

0.999908

1.162

0.000427

0.034883

0.057196

0.066320

0.061112

0.039937

Number of boundary elements

DRM solution

Radial location r (m)

Variable

0.999962

0.749

0.000275

0.034733

0.057006

0.066133

0.060926

0.039755

−11.910987

−9.632446

60

0.999981

0.521

0.000191

0.034638

0.056908

0.066030

0.060825

0.039656

−11.902295

−9.646733

72

0.999988

0.405

0.000149

0.034606

0.056853

0.065973

0.060760

0.039614

−11.900702

−9.649446

84

Table 11.3 DRM results and analytical solution for the boundary and internal points in flow velocity simulation (f = 1 + r)

–

–

–

0.034439

0.056682

0.065803

0.060591

0.039413

−11.883840

−9.667904

Analytical solution

870 11 Numerical Modelling of Heat Transfer

−11.929878

−11.960900

0.030

0.999725

0.035080

0.0508

R2

0.057609

0.0466

2.015

0.066725

0.0425

0.000740

0.061519

0.0383

cv %

0.040334

0.0342

36

RMSE

w

−9.615427

−9.570477

0.055

∂w/∂n

48

0.9999087

1.160

0.000426

0.034880

0.057193

0.066321

0.061112

0.039938

Number of boundary elements

DRM solution

Radial location r (m)

Variable

0.999961

0.750

0.000276

0.034726

0.057012

0.066136

0.060927

0.039754

−11.906732

−9.632632

60

0.999982

0.516

0.000189

0.034635

0.056906

0.066031

0.060820

0.039654

−11.899952

−9.647164

72

0.999989

0.397

0.000146

0.034604

0.056850

0.065974

0.060761

0.039601

−11.898130

−9.651780

84

Table 11.4 DRM results and analytical solution for the boundary and internal points in flow velocity simulation (f = 1 + r+r 2 )

–

–

–

0.034439

0.056682

0.065803

0.060591

0.039413

−11.883840

−9.667904

Analytical solution

11.3 Numerical Simulation of the Laminar Forced Convective … 871

872

11 Numerical Modelling of Heat Transfer

Fig. 11.16 Accuracy of the solution for the velocity at the internal points: a Radial basis function f = 1+r; b Radial basis function f = 1+r + r 2

Fig. 11.17 Magnitude of the error in the solution for the normal derivative of the velocity at the boundaries: a Radial basis function f = 1 + r; b Radial basis function f = 1 + r+r 2

Although the convergence trend shown in Fig. 11.20 is not monotonic and the radial location’s effect on the magnitude of the error does not exactly follow the trend shown in the previous case, the solution trends can be considered indistinguishable within 1% relative error. These test results validate the power of the dual reciprocity boundary element method and the accuracy of its solutions because the numerical solution for the velocity was used as an input in Eq. (11.3.3) and the source-like function b(x, y) of Eq. (11.3.12) in Eq. (11.3.3) was approximated using interpolating functions and the nodal values of internal points.

11.3 Numerical Simulation of the Laminar Forced Convective …

873

Fig. 11.18 Comparison of velocity profile obtained using analytical solution and DRM results: a Radial basis function f = 1 + r; b Radial basis function f = 1 + r+r 2

As a final note, all of the numbers of elements tested are adequate for solving this problem. The amount of error in the solutions for the velocity and temperature is acceptable. Using the fourth-order RBFs, the accuracy of the DRM is increased insignificantly so that only minor differences are observed between errors (0.2%). The errors can be decreased only using a higher adequate number of boundary elements and internal points limited by computational capacity.

11.3.5 Conclusions A numerical simulation model based on the DRM has been developed for the solution of the laminar heat convection problem between two concentric cylinders with a constant imposed heat flux. The DRM is different than the standard implementation as was proposed for Poisson-type equations due to the use of RBFs. The DRM matrix was formulated to perform the numerical computation, and five boundary element discretisations were tested with corresponding numbers of internal points. Five radial locations were selected at which solution for the velocity and temperature was obtained. The numerical results were shown to be in excellent agreement with exact solutions for the 36-element case and the simulation model was analytically validated. This numerical model was successfully used to solve the laminar convective heat transfer problem in a concentric annular tube. This study also shows that the DRM has strong potential for further applications. Although this method has been applied to 2D problems, an extension of the approach to 3D problems is straightforward.

233420.45

0.030

0.998102

711.52

0.0508

R2

1180.68

0.0466

5.298

1383.48

0.0425

42.3739

1268.86

0.0383

cv %

804.26

0.0342

36

RMSE

t*

172056.38

0.055

∂t*/∂n

0.999571

2.518

20.1408

730.65

1209.26

1413.28

1298.52

828.59

229217.02

170824.22

48

Number of boundary elements

DRM solution

Radial location r (m)

Variable

0.99934

0.986

7.8869

741.78

1224.48

1426.46

1311.65

847.40

230340.65

171362.75

60

0.999986

0.451

3.6070

746.86

1230.46

1429.68

1315.86

853.78

230698.70

171600.75

72

Table 11.5 DRM results and analytical solution for boundary and internal points in temperature (f = 1+r)

84

0.999993

0.309

2.4750

747.90

1231.92

1431.26

1317.26

855.04

230771.22

171628.56

–

–

–

750.34

1234.96

1433.69

1320.13

858.72

229506.90

170484.20

Analytical solution

874 11 Numerical Modelling of Heat Transfer

233300.36

0.030

0.998243

713.38

0.0508

R2

1182.72

0.0466

5.098

1385.24

0.0425

40.7741

1271.14

0.0383

cv %

805.85

0.0342

36

RMSE

t*

171989.88

0.055

∂t*/∂n

0.999613

2.390

19.1179

731.68

1210.64

1414.58

1299.86

829.69

229286.02

170768.08

48

Number of boundary elements

DRM solution

Radial location r (m)

Variable

0.999946

0.891

7.1300

742.87

1225.78

1427.24

1312.24

848.14

230294.05

171293.14

60

0.999988

0.415

3.3248

747.12

1230.98

1430.02

1316.04

854.14

230618.22

171535.45

72

Table 11.6 DRM results and analytical solution for the boundary and internal points in temperature (f = 1 + r+r 2 )

84

0.999995

0.268

2.1458

748.03

1232.04

1431.76

1317.68

855.78

230708.55

171598.75

–

–

–

750.34

1234.96

1433.69

1320.13

858.72

229506.90

170484.20

Analytical solution

11.3 Numerical Simulation of the Laminar Forced Convective … 875

876

11 Numerical Modelling of Heat Transfer

Fig. 11.19 Accuracy of the solution for the temperature at the internal points: a Radial basis function f = 1 + r; b Radial basis function f = 1 + r+r 2

Fig. 11.20 Accuracy of the solution for the normal derivative of the temperature at the boundaries: a Radial basis function f = 1 + r; b Radial basis function f = 1 + r+r 2

11.4 Numerical Simulation of Water Freezing in Outdoor Pressurised Pipes 11.4.1 Preliminary Considerations Using outdoor pipes in water supply systems (adductions, valley and river crossings [57], etc.) during cold periods, severe difficulties can occur. They are due, either to water freezing which may lead to the formation of an ice layer on the inner pipe wall, affecting the flow due to hydraulic characteristics desired, or to permanent deformations induced by this phenomenon.

11.4 Numerical Simulation of Water Freezing …

877

Fig. 11.21 Comparison of temperature profile t * obtained using analytical solution and DRM results: a Radial basis function f = 1 + r; b Radial basis function f = 1 + r+r 2

Therefore, if the water flow is interrupted to perform various maintenance operations in the system and the pipe is full of water, after some time the whole water mass in the pipe will freeze. To prevent this phenomenon in practice there is a tendency to ensure a permanent minimum discharge through the pipe. For resting atmospheric regime (wind velocity negligible), an equation to calculate the minimal discharge to prevent water freezing was determined [34]: G min =

2π R L[9, 74 + 0, 075(tw0 + tw − 2te )] −te ρw cw ln ttw0w −t e

(11.4.1)

where: Gmin is the minimum protection discharge; R, L are the inner radius and the length of pipe, respectively; ρw is the water density; cw is the specific heat of water; t w0 , t w are the initial and final temperature of water; t e is the outdoor air temperature. This precaution, in most cases, ensures free flow in the pipe, but does not stop the formation of an ice layer on the pipe inner wall, as for a water temperature near 0 °C it is impossible to avoid water freezing, even for flow velocities over 10 m/s. Therefore, we must study if the pipe is able to transport the minimal protection discharge for a non-stationary atmospheric regime, without affecting the hydraulic characteristics of the flow. Also, even in the case of a normal operation with a given discharge, it is necessary to study the capacity of the pipe to transport the discharge, considering the ice volume that can be formed inside. If the pipe is not adequate, it must be protected through outside protective thermal covers. This section offers a theory on the ice layer formation in outdoor pipes in nonstationary atmospheric regime, and provides some numerical examples. A mathematical model for numerical simulation of changes in time along the pipe of ice layer formed inside outdoor pressurised pipes, under non-stationary atmospheric regime is developed [26]. This model can be used for obtaining economical solutions of the problem to protect these pipes from frost.

878

11 Numerical Modelling of Heat Transfer

11.4.2 Elements of Thermal Energy In Fig. 11.22 is presented the longitudinal section of a frozen pipe with elementary length dx, and its characteristic thermal features. The direction of x-coordinate coincides with flow direction. By examining the thermal phenomena inside the pipe, we conclude that the main terms of thermal energy to be considered in calculating the thermal balance for a unit length pipe, are: • Heat flow water, Qw [J/day]:

Q w = 86400Gρw cw tw

(11.4.2)

where: G is the discharge through the pipe; t w is the water temperature (average value in the cross-section). • Heat developed by friction, Qf [J/(m day)]:

Q f = 86400ρw gG J =

54600πρw g 2.67 1.5 r J n

(11.4.3)

where: g is the gravitational acceleration; J is the hydraulic slope; n is the Manning roughness coefficient; r is the radius of inside cross-section available to discharge. • Heat transmitted by water to outdoor air through pipe wall, Qp [J/(m day)]:

Qp =

86400 × 2π(t1 − t N +1 ) N" −1 r 1 1 + ln rj+1 + αe1r N αi r1 λj j j=1

Fig. 11.22 Longitudinal section through a pipe with frozen layer

(11.4.4)

11.4 Numerical Simulation of Water Freezing …

879

where: αi , αe are the coefficients of internal and external convection, respectively; λj is the thermal conductivity of material layer j of the pipe; N is the number of material layers. The thermal resistance of convective heat transfer from water to pipe (αi have high values) and the thermal resistance of the pipe wall can be neglected due to their reduced influence on the thermal flow: Qp =

86400 × 2π(t1 − t N +1 ) 1 ln Rr + αe1R λg

(11.4.5)

where λg is the thermal conductivity of ice, and R is the inner radius of pipe. Considering the expression for the coefficient of external convection [37]: αe = 3.77

w0.7 , R 0.3

(11.4.6)

and using the substitution: 1 1 R =− ln αe R λg Rf

(11.4.7)

can be determined a fictitious radius Rf , which considers the disturbances of the outdoor air flow: 0.7

R f = R · e0.615/(w R)

(11.4.8)

where w is the wind velocity. Introducing the relations for temperatures t 1 = t g = 0 °C and t N+1 = t e , Eq. (11.4.5) takes the form: Qp =

−86400π te − 2λ1 g ln Rr f

(11.4.9)

where t e is the outdoor air temperature, and t g is the ice melting temperature. • Solidification heat of water, Qg [J/m]: Q g = π ρg (R 2 − r 2 )L w

(11.4.10)

where ρg is the ice density and L w is the specific solidification heat of water.

880

11 Numerical Modelling of Heat Transfer

• Heat transmitted by water to ice, Qt [J/(m day)]: Q t = 86400 × 2πr αi (tw − tg )

(11.4.11)

The coefficient of internal convection α i can be determined with the following equation [26]: αi = 416

G 0.75 r 1.75

(11.4.12)

where G is the water discharge through the pipe. Ice melting temperature varies with water pressure head in the pipe [58]: tg = −0.784 × 10−3 H

(11.4.13)

where H is the water pressure head. Substituting Eqs. (11.4.12) and (11.4.13) into Eq. (11.4.11) the following expression is obtained: Q t = 72 × 10 π(tw + 0.784 × 10 6

−3



G H) r

0.75 (11.4.14)

11.4.3 Thermal Balance The thermal balance of the water through the pipe— ice— external environment system can be expressed as: −

∂ Qg ∂ Qw + Q f − Qp + =0 ∂x ∂τ

(11.4.15)

where τ is the time. For the ice—pipe system, the thermal balance can be written as: Qt − Q p +

∂ Qg =0 ∂τ

(11.4.16)

The thermal balance equation of water flow through the pipe is expressed as follows: −

∂ Qw + Q f − Qt = 0 ∂x

(11.4.17)

11.4 Numerical Simulation of Water Freezing …

881

11.4.4 Mathematical/Numerical Model Due to water temperature and pressure variation in time along the pipe, the ice layer depth will vary as well. Therefore, generally, r = r(x,τ). In the numerical simulation, the following values of parameters are used: ρw = 1000 kg/m3 , g = 9.81 m/s2 , cw = 4185 J/(kg K), L w = 333.3×103 J/kg, ρg = 917 kg/m3 , λg = 2.32 W/(m K), n = 0.01. • Constant ice layer depth along the pipe. For pipes with large length (x → ∞) one may assume a cylindrical ice cover formed on the inner pipe wall: ∂r dr = ∂τ dτ

∂r = 0; ∂x

(11.4.18)

Defining the relative radius of ice (non-dimensional parameter): r∗ =

r Rf

(11.4.19)

and considering the hydraulic slope J, according to the Chézy-Manning formula: J = 0.255

n2 G 2 1 r∗5.33 R 5.33 f

(11.4.20)

as well as Eqs. (11.4.2), (11.4.3), (11.4.9) and (11.4.10), Eq. (11.4.15) takes the form: −86400Gρw cw

ρw gn 2 G 3 1 ∂tw dr∗ 86400π te + 22000 =0 − 1 − 2πρg L w R 2f r∗ 5.33 ∂x r dτ R 5.33 ln r ∗ ∗ f 2λg (11.4.21)

Using Eqs. (11.4.9), (11.4.10) and (11.4.14), Eq. (11.4.16) becomes: 72 × 106 π(tw + 0.784 × 10−3 H )



G Rf

0.75

1 r∗0.75

−

86400π te 1 2λg ln r∗

− 2πρg L w R 2f r∗

dr∗ =0 dτ

(11.4.22) Taking into account Eq. (11.4.20) pressure head gradient is expressed as: n2 G 2 1 ∂H = J p − J = J p − 0.255 5.33 5.33 , ∂x r∗ Rf where J p is the pipe slope.

(11.4.23)

882

11 Numerical Modelling of Heat Transfer

The expression of the parameter t w is determined from Eq. (11.4.22) and is derived with respect to x as follows: ( ) ∂tw n2 G 2 1 −3 = −0.784 × 10 J p − 0.255 5.33 5.33 , ∂x r∗ Rf

(11.4.24)

Substituting Eq. (11.4.24) and the values of known parameters into Eq. (11.4.21), the following differential equation is obtained: Jp G 1 dr∗ G3 1 te 1 = 0.148 2 + 7.48 × 10−6 7.33 6.33 − 0.66 × 10−3 2 dτ R f r∗ R f r∗ ln r∗ R f r∗ (11.4.25) which allows the study of ice layer depth variation in time. Since water temperature must be, generally, known in practice, it can be expressed by substituting Eq. (11.4.24) in Eq. (11.4.21): 0.75 tw = 1.256J p G 0.25 R 0.75 + 0.636 × 10−4 f r∗

G 2.25 1 − 0.784 × 10−3 H 4.58 r R 4.58 ∗ f (11.4.26)

The derivative dr * /dτ from Eq. (11.4.25), under certain given conditions, varies only versus the relative radius r * . The graph of this function (Fig. 11.23) intersects the axis of coordinates (dr * /dτ = 0) for the following value: Fig. 11.23 Graph of function dr * /dτ

11.4 Numerical Simulation of Water Freezing …

883

r∗ = r∗ lim

(11.4.27)

this represents the relative limit radius towards which the ice surface in the pipe tends, under the given conditions. By the forming of ice on the pipe wall, the roughness coefficient decreases, so that for a certain thickness of ice, characterised by the maximal admitted relative radius: r∗ ad = 0.705

R Rf

(11.4.28)

the transportation capacity can be maintained without endangering the system by strongly increasing water velocity through the pipe. Frost protection so as to obtain a completely free ice pipe can result in extremely high investment costs for insulation. Therefore, if for certain given (specified) conditions it results that: r∗ lim ≥ r∗ ad

(11.4.29)

then the pipe can operate without thermal insulation. If condition expressed by Eq. (11.4.29) is not satisfied, it is recommended to determine the thickness of thermal insulation layers accepting the formation of an ice layer characterised by the relative radius equal to r *ad . In this case, Eq. (11.4.3) is also used. For G = 0 in Eq. (11.4.25), and integrating the resulting equation with the boundary condition: r * = R/Rf , for τ = 0, and r * = r *ad , after introducing Eq. (11.4.28), it is obtained the expression of maximum admissible time of water stagnation in the pipe τmax , in days:   R R2 0.503 ln − 0.076 τmax = 758 te Rf

(11.4.30)

• Variable ice layer depth along the pipe. For pipes operating at constant hydraulic and thermal characteristics for a long time (τ → ∞) the assumption of the forming of an ice layer of variable depth along the pipe is considered: ∂r = 0; ∂τ

∂r dr = ∂x dx

(11.4.31)

In this case, the expressions (11.4.21) and (11.4.22) of thermal balance Eqs. (11.4.15) and (11.4.16) take the forms: −86400Gρw cw

ρw gn 2 G 3 1 ∂tw 86400π te + 22000 − 1 =0 5.33 5.33 ∂x r∗ Rf ln r∗ 2λg

(11.4.32)

884

11 Numerical Modelling of Heat Transfer

72 × 106 π(tw + 0.784 × 10−3 H )



G Rf

0.75

1 r∗0.75

−

86400π te =0 1 ln r∗ 2λg

(11.4.33)

Using Eq. (11.4.33) can be obtained:  tw = 0.00559te

Rf G

0.75

r∗0.75 − 0.784 × 10−3 H ln r∗

(11.4.34)

) n2 G 2 1 J p − 0.255 5.33 5.33 x r∗ Rf

(11.4.35)

with: ( H = Ho +

where H o is the hydraulic head available of the pipe. Deriving Eq. (11.4.34) with respect to x and substituting in Eq. (11.4.32) the known values, the following differential equation is obtained: dr∗ G 2.75 (− ln r∗ )2 = − 0.00714 × 10−3 − 5.08 [1 + 0.75(− ln r )] dx te R 6.08 r ∗ ∗ f − 0.625 × 10−3

J p G 0.75 r∗0.25 (− ln r∗ )2 1 r∗0.25 (− ln r∗ ) − 0.1407 0.75 0.25 1 + 0.75(− ln r ) 1 + 0.75(− ln r∗ ) ∗ G Rf te R 0.75 f

(11.4.36)

which describes ice layer variation along the pipe. The graph of the function (11.4.36) intersects the axis of coordinates (dr * /dx = 0) for the value of r *lim . The solutions of differential Eqs. (11.4.25) and (11.4.36) can be obtained using the Runge-Kutta numeric integration method [59] implemented into computer program EVGHECA [34]. Separating the variables in differential Eq. (11.4.32) and integrating with the boundary conditions: x = 0 for t w = t wo and x = x a for t w = t wa , abscissa x a of cross-section in which the freezing begins (r * = R* = R/Rf ) is determined by: xa =

A ln C





B−C 0, 00559te

Rf G

0,75

B − C(tw0 − te )  * & + ' 0,75 R∗ −3 H + Jc − 0, 255 n 2 G 2 xa − te − 0, 784 × 10 0 0,75 R 5,33 ln R∗

(11.4.37)

where: A = 86400 Gρw cw ;

B = 22000

ρw gn 2 G 3 86400 × 2π ; C= # $0.75 5.33 R 0.0024 GR + λ1g ln

R Rf

(11.4.38)

11.4 Numerical Simulation of Water Freezing …

885

Equation (11.4.37) can be solved by applying well-known numeric methods (secant method, Newton method, and iteration method). For x = x a and x = L (r * = r *lim ), using Eq. (11.4.34) the water temperatures t wa and t wlim , respectively are determined. By equating Eqs. (11.4.2) and (11.4.4) written in differential form, after integration with the boundary conditions of the variables: t w = t wo for x = 0 and t w = t wL for x = L, the minimal discharge to prevent water freezing is obtained: G min =

6.12π L(w R)0.7 wo −te ρw cw ln ttwL −te

(11.4.39)

where L is the pipe length and t wL is the water temperature in the final cross-section. • Variable ice layer depth in time along the pipe. However, generally, the ice layer formed on the pipe wall varies both in time and along the pipe: r * = r * (x,τ). In this case Eqs. (11.4.16) and (11.4.17) of the thermal balance take the forms: ( 72 × 106 π(tw + 0.784 × 10−3 H )

G Rf

)0.75

1 r∗0.75

−

86400π te 1 2λg ln r∗

− 2πρg L w R 2f r∗

∂ r∗ =0 ∂τ

∂tw ρw gn 2 G 3 1 − + 22000 ∂x R 5,33 r∗5,33 f  0,75 1 G =0 −72 × 106 π(tw + 0, 784 × 10−3 H ) Rf r∗0,75

(11.4.40)

−86400Gρw cw

(11.4.41)

where water pressure head H has the expression (11.4.35). By Eq. (11.4.40) the expression of the parameter t w is determined, which then is derived with respect to x. Substituting in Eq. (11.4.41) the relations thus obtained and the values of known parameters, the second-order differential equation results in: A

∂r∗ ∂r∗ ∂r∗ ∂r∗ ∂ 2 r∗ +B +C +D +E =0 ∂ x ∂τ ∂ x ∂τ ∂x ∂τ

where A, B, C, D and E are the functions of r * and x defined as follows: 1.75 A = −3069.8 × 109 G 0.25 R 2.75 f r∗ 0.75 B = −5372.2 × 109 G 0.25 R 2.75 f r∗

C = −2.02 × 109 te G 0.25 R 0.75 f D = −1.92 × 109 R 2f r∗

3 0.75 ln r∗ − 1 x −6 G − 0.106 × 10 5.33 r∗0.25 (ln r∗ )2 R f r∗6.33

(11.4.42)

886

E = −1.264 × 106

11 Numerical Modelling of Heat Transfer

te G3 1 + 2.088 × 105 5.33 5.33 + 0.283 × 109 J p G (11.4.43) ln r∗ R f r∗

Ice layer variation in time along the pipe is described by the hyperbolic partial differential Eq. (11.4.42). The resolution of this equation consists in determining the function r * = r * (x,τ), which satisfies both the given equation and the initial conditions: r * (x,0) = R* = R/Rf and ∂r * (x,0)/∂τ = 0. The solution of the partial differential equation can be obtained using numerical finite-difference integration (grids method) by “crossways” procedure [60]. The values r *i,j for the function r * (x i ,τj ) are computed at the nodes (i,j) of a straight-line grid (i = x/h, j = τ/s) from the plane xOτ, where h and s are the length and the time step.

11.4.5 Numerical Applications and Results Suppose a metallic outdoor pipe has the following characteristics: G = 2.0 m/s, J p = 0.015, R = 0.60 m, L = 4000 m, H o = 10 m, t e = −10 °C, w = 4.96 m/s. The numerical simulation model developed above is used. 0.7 Fictitious radius is determined by Eq. (11.4.8): R f = 0.60e0.615/(4.96 · 0.6) = 0.80 m, then for ratio R* = R/Rf = 0.6/0.8 = 0.75, using Eq. (11.4.28) the relative admissible radius results: r *ad = 0.705 × 0.75 = 0.528. In the initial assumption of a constant external heat exchange on the circumference of the pipe the computer program EVGHECA is used to solve the differential Eq. (11.4.25), and it is obtained r *lim = 0.529 and τlim = 27 days (for an admissible error of 0.00005). Additionally, the maximum admissible time of water stagnation in the pipe determined by the computer program is τmax = 6.01 days. Based on the obtained numeric results, in Fig. 11.24 the variation diagram for the ice layer during its forming is represented, which has as asymptote the horizontal line r *lim = 0.529. Figure 11.25 shows water temperature variation along the pipe Fig. 11.24 Ice layer depth variation in time

11.4 Numerical Simulation of Water Freezing …

887

Fig. 11.25 Water temperature variation along the pipe with a constant ice layer depth (for τ = τlim )

for τlim = 27 days. The following values are obtained for water temperature: 0.0190 °C in input cross-section (x = 0) and 0.0037 °C in the final cross-section (x = L). Therefore, after the time τ = τlim , for an input water temperature t wo = 0.0190 °C a constant ice layer along the pipe will be formed. This ice is characterised by the relative radius r *lim . Considering then an input water temperature t wo = 0.1 °C and solving the differential Eq. (11.4.36) and as well as Eqs. (11.4.37) and (11.4.34) using the computer program, the following values are obtained: r *lim = 0.529, t wlim = 0.0037 °C for x = L = 4000 m and x a = 607.5 m, t wa = 0.0646 °C. Based on the computed results, in Figs. 11.26 and 11.27, the variation diagrams for ice layer and water temperature along the pipe are illustrated. Final numerical results obtained by solving the partial differential Eq. (11.4.42) in more than 2000 computational nodes, using a computer program, are represented in Fig. 11.28. Since r *lim = 0.529 > r *ad = 0.528, the pipe can operate without thermal insulation. Water velocity in the pipe has the maximum value: vmax = G/[π(Rf r *lim )2 ] = 3.79 m/s. Considering water temperature in the final cross-section t wL = 0 °C, the minimal protection discharge Gmin = 3.96 m3 /s is obtained by Eq. (11.4.39). For this discharge the relative limit radius and the water velocity have the following values: r *lim = 0.704 and v = 3.98 m/s. Therefore, in this case ice is formed on the pipe wall in a thin layer (R-Rf r *lim = 3.68 cm) and as a result the flow velocity does not increase significantly (13.7%), at given flow velocity in the pipe without ice (vo = 3.5 m/s). Fig. 11.26 Ice layer depth variation along the pipe (t wo = 0.1°C)

888

11 Numerical Modelling of Heat Transfer

Fig. 11.27 Water temperature variation along the pipe with a variable ice layer depth (for τ = τlim )

Fig. 11.28 Ice layer depth variation vs time along the pipe (t wo = 0.1°C)

11.4.6 Conclusions The numerical model for simulating variation in time along the pipe of ice layer in outdoor pressurised pipes has an increased generalisation and accuracy level because it considers the disturbances of the external air flow. Additionally, the model developed in this study offers the possibility to choose an optimal protection solution for the pipes against water freezing based on an economic calculation, and to prevent this phenomenon in operation. Hence, it is recommendable to install along the pipes exposed to wind a control system formed of sufficient number of thermometers with automatic signal and transmission, which indicates the moment when the water temperature reaches limit of 0 °C.

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