Exergy Analysis of the Air Handling Unit at Variable Reference Temperature: Methodology and Results 3030978400, 9783030978402

Citation preview

Vytautas Martinaitis Giedrė Streckienė Juozas Bielskus

Exergy Analysis of the Air Handling Unit at Variable Reference Temperature Methodology and Results

Exergy Analysis of the Air Handling Unit at Variable Reference Temperature

Vytautas Martinaitis · Giedr˙e Streckien˙e · Juozas Bielskus

Exergy Analysis of the Air Handling Unit at Variable Reference Temperature Methodology and Results

Vytautas Martinaitis Department of Building Energetics Vilnius Gediminas Technical University—VILNIUS TECH Vilnius, Lithuania

Giedr˙e Streckien˙e Department of Building Energetics Vilnius Gediminas Technical University—VILNIUS TECH Vilnius, Lithuania

Juozas Bielskus Department of Building Energetics Vilnius Gediminas Technical University—VILNIUS TECH Vilnius, Lithuania

ISBN 978-3-030-97840-2 ISBN 978-3-030-97841-9 (eBook) https://doi.org/10.1007/978-3-030-97841-9 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 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

Preface

Exergy (Ex) builds a link between the states of the system under consideration, which are described by the first law of thermodynamics (FLT) and the second law of thermodynamics (SLT), and the state of the chosen reference environment (REN) that, as a case in point, can be defined by the temperature of that environment. The product here is the parametric function of Ex = f(FLT, SLT, REN). The characteristics of a particular system determine which of the three integrated variables will have a larger effect on the result. Buildings and their technical systems have their own specific combinations of said variables in exergy analysis. Due to its nature, exergy analysis should become a valuable tool for the assessment of building sustainability, first of all considering their scope, and the dependence of their energy demands on the local environmental and climatic conditions. Nonetheless, methodological bottlenecks do exist, and a solution to some of them is proposed in this monograph. First and foremost, there is the still-missing thermodynamically viable method to apply the variable reference environment temperature in exergy analysis. The book demonstrates that a correct approach to the directions of heat exergy flows, when the reference temperature is considered variable, allows reflecting the specifics of energy transformation processes in units of heating, ventilation, and air-conditioning systems in a thermodynamically viable way. The outcome of the case analysis, which involved coordinated application of methodologies based on the Carnot factor and coenthalpies, was exergy analysis indicators—exergy efficiency and exergy destroyed—obtained for air handling units and their components. These methods can be used for the purposes of analysing and improving heating, ventilation, and air-conditioning systems that, as a rule, operate at a variable environment temperature. Exergy analysis becomes more reliable in designing dynamic models of such systems and their exergy-based control algorithms. This would improve the possibility to deploy them in building information modelling (BIM) technologies and the application of life cycle analysis (LCA) principles in designing buildings, thus improving the quality of the decision-making process. Furthermore, this would benefit other systems where variable reference environment plays a key role.

v

vi

Preface

The target audience of the book includes researchers, specialists, and students who are interested in the sustainable development of technical systems of energy, mechanics, and construction, as well as preservation of natural resources.

Vilnius, Lithuania January 2022

Vytautas Martinaitis

Acknowledgements

We would like to extend our gratitude to a lot of our colleagues, students, and collaborators who have made all kinds of contributions to this work. It all began with an ambition to employ thermodynamic analysis for the purposes of the assessment of heating, ventilation, and air-conditioning systems. It was over a couple of decades ago that this course appeared on the master’s curriculum of the Building Energetics Department at VILNIUS TECH. Since then, the active and inherent curiosity of a large number of students has helped improve both the contents and the methodology of learning. This first of all helped us design an application of the variable reference temperature for exergy analysis. These efforts of our team have had the support from our colleagues at the department—we like to think this to be the number one reason why this book has come to see the light of day. We would like to thank our reviewers, Dr. Audrius Bagdanaviˇcius from the Department of Engineering at University of Leicester, and Doc. Dr. Liutauras Vaitkus, Energy Department at Kaunas University Technology, for drafting the text of this publication. Their spot on tips have been instrumental in making this book reader-friendlier. We wish to extend our thanks to the co-authors of publications on exergy, Doc. Dr. Giedrius Šiupšinskas, Doc. Dr. Darius Biekša, and Doc. Dr. Violeta Miseviˇci¯ut˙e. We furthermore want to acknowledge Gintautas Baceviˇcius, who bound the illustrations that had been picked by the authors of this monograph in various publications and tailor made specifically for this book into one single whole. We want to thank the Research Council of Lithuania for the funding of the research that has some of its results featured in this publication. And last but not least, we would like to thank our spouses, Aldut˙e, Alvydas, and R¯uta, our families who had accommodated our efforts in expanding this knowledge and writing this book for years.

vii

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Building Technical Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Exergy as Quality of Energy for Buildings . . . . . . . . . . . . . . . . . . . . . 1.3 State of the Environment and Exergy . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Variable Ambient Temperature and Exergy Flows . . . . . . . . . . . . . . . 1.5 Monograph Chapters at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Theoretical Foundation of the Exergy Analysis Methodology at Variable Reference Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Direction of Exergy Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Exergy Efficiency of the Heat Transfer Process . . . . . . . . . . . . . . . . . 2.3 Energy—Enthalpy, Exergy—Coenthalpy . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Coenthalpy as a Parameter of State in Exergy Transfer . . . . 2.3.2 Energy and Entropy Balance of the Heat Exchanger . . . . . . . 2.4 Exergy Efficiency and Destroyed Exergy . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Exergy Balance of the Heat Exchanger . . . . . . . . . . . . . . . . . . 2.4.2 Exergy Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Air Handling Unit as a Thermodynamic System . . . . . . . . . . . . . . . . 2.5.1 The Technological Diagrams of the Air Handling Unit Under Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2 Heat Exchangers of the Air Handling Unit . . . . . . . . . . . . . . . 2.5.3 A Preliminary Comparison of Air Handling Unit Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Summary of This Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Exergy Analysis of the Heat Recovery Exchanger of the Air Handling Unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 When Exergy Flows Are Calculated with the Carnot Factor . . . . . . . 3.1.1 Typical Cases of Exergy Analysis of the Heat Recovery Exchanger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Numeric Indicators of Exergy Analysis of Heat Recovery Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 2 3 4 6 8 17 17 21 22 22 25 28 28 29 31 32 35 38 41 43 44 46 50 ix

x

Contents

3.1.3 A Case of Comparison with the Prior Method . . . . . . . . . . . . 3.2 When Exergy Flows Are Calculated Using Coenthalpy as a State Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Formulation of the Heat Recovery Exchanger . . . . . . . . . . . . 3.2.2 The Algorithm of Exergy Analysis of the Heat Recovery Exchanger with Coenthalpy . . . . . . . . . . . . . . . . . . . 3.2.3 Exergy Efficiency for the Thermomechanical Flows of the Heat Exchanger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.4 The Results of Calculations Using the Exergy Analysis Algorithm of the Heat Recovery Exchanger . . . . . . 3.3 Cases of Functional Exergy Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Characteristic Values of Coenthalpies of the Heat Recovery Exchanger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Three Cases of Functional Exergy Efficiency . . . . . . . . . . . . . 3.3.3 Calculation Results for the Three Cases of Exergy Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Summary of This Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Analysis of the Modes of Operation of the Heat Pump of the Air Handling Unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 The Thermodynamic Analytical Correlations of the Air Handling Unit Heat Pump Components . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Energy Balances of the Heat Pump Components . . . . . . . . . . 4.1.2 Exergy Balance and Exergy Efficiency of Heat Pump Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.3 Correlation Between the Parameters of the Heat Transfer Process in the Heat Pump Evaporator and Condenser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Parametric Analysis of the Modes of Operation of the Heat Pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Characteristics of Parametric Analysis . . . . . . . . . . . . . . . . . . 4.2.2 The Logic and Alternatives of Optimising Processes Within the Air Handling Unit . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Heat Recovery Processes Between the Two Cooling Air Flows in the Heat Pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Results of Parametric Analysis of the Heat Pump as an Air Handling Unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Results of the Analysis of the Exergy Parameters of the Heat Pump as an Air Handling Unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Summary of This Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54 56 56 58 64 69 75 76 79 83 87 89 89 90 92

95 98 98 99 101 104 106 107

Contents

5 Comparative Exergy Analysis of Cases of the Air Handling Unit . . . . 5.1 General Input Data of the Cases of the Air Handling Unit . . . . . . . . 5.2 Graphic Interpretation of Exergy Analysis with Methods Based on the Carnot Factor and Coenthalpies . . . . . . . . . . . . . . . . . . . 5.3 Comparison of the Mode Characteristics of the Four Diagrams of the Components of the Air Handling Unit . . . . . . . . . . . 5.4 Comparison of the Exergy Indicators of the Four Diagrams of the Components of the Air Handling Unit . . . . . . . . . . . . . . . . . . . . 5.4.1 Exergy Destroyed in Air Handling Units . . . . . . . . . . . . . . . . 5.4.2 Exergy Efficiency of Air Handling Units . . . . . . . . . . . . . . . . 5.5 Summary of This Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Seasonal Thermodynamic Efficiency of the Air Handling Unit . . . . . . 6.1 Determining Seasonal Indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.1 Determining Local Climatic Conditions . . . . . . . . . . . . . . . . . 6.1.2 Determining Seasonal Indicators of the Air Handling Unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Analysis of Individual Cases of Air Handling Units . . . . . . . . . . . . . 6.2.1 Air Handling Unit Where the Heat Recovery Exchanger Is the Main Component . . . . . . . . . . . . . . . . . . . . . 6.2.2 Assessing the Impact of Climatic Conditions: The Results of the Parametric Analysis . . . . . . . . . . . . . . . . . . . . . . 6.2.3 Air Handling Unit with a Heat Recovery Exchanger and a Heat Pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.4 Air Handling Unit with a Heat Recovery Exchanger and a Heat Pump at Variable Refrigerant Isotherms . . . . . . . 6.2.5 Comparison of the Results for Different Climate Zones . . . . 6.2.6 Investigation of the Impact of the Temperature Efficiency of the Heat Recovery Exchanger Under Different Climatic Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Summary of This Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xi

111 112 115 123 127 127 132 137 141 142 142 143 144 144 152 154 158 160

162 172

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

About the Authors

Prof. Dr. Habil. Vytautas Martinaitis is a chief research fellow at the Department of Building Energetics Vilnius Gediminas Technical University—VILNIUS TECH, Lithuania. He graduated from Kaunas University of Technology (Lithuania) with a diploma of Certified Civil Engineer (CCEng., Heating, Ventilation, Air Conditioning), at Polytechnic Institute of Byelorussia, Minsk, he defended his doctoral (Dr. sc. eng., Energy and Thermal engineering), and at the Lithuanian Energy Institute, Kaunas, his Doctor Habilitus (Dr. hab., Energy and Thermoengineering) degree. The title of his habilitus thesis is Thermodynamic Analysis Model of Building Life Cycle. He did a six-month internship at the Swiss Federal Institute of Technology Lausanne. He has dedicated most of his professional career to lectures and research. He was a docent at Kaunas Technology University, the University of Constantine (Algiers). In 1989, he became a docent and later a professor at the Department of Building Energetics Vilnius Gediminas Technical University—VILNIUS TECH. He has held the dean’s position at the Faculty of Environmental Engineering. For several years, he was CEO at a consultancy company that focused on boosting the energy efficiency of buildings. He was a Lithuanian nominated expert in the European Union 7 FP 2007– 2013 “Energy” and H2020 2014–2018 “Safe, clean, and efficient energy” research programmes committees. Currently, he is a professor emeritus.

xiii

xiv

About the Authors

His research papers cover studies aimed at assessing and improving the efficiency of energy and the interaction of construction technological processes by applying and structuring methods of thermodynamic (exergy), life cycle, environmental, and multi-criteria analysis. This makes it possible to produce a quantitative expression of an approach to cohesive development in assessing a design solution or an operational system. Assessment models for exergy analysis at a variable reference temperature, the two-factor method of the assessment of the energy efficiency and physical condition of a building, the algorithm of actual energy consumption data analysis, the expert system of more efficient resource consumption in a building, and technologies transforming renewable energy sources of the site already have their application or have attracted attention from the international academia. These models are structured and developed to accommodate the purposes of the information modelling of the technical systems of a building. This work was done in supervision of national and international projects and 13 doctoral dissertations, all of them defended successfully, in the fields of energy, construction, and mechanics. He has published dozens of articles in the Web of Sciences publications, and he is the author of several patents and has written numerous technical reports and also 12 books on thermodynamics, heat production, and energy efficiency of buildings. Giedr˙e Streckien˙e has a doctoral degree in thermal engineering and energy from Vilnius Gediminas Technical University (VILNIUS TECH), where in 2011 she defended her doctoral dissertation titled Research of Heat Storage Tank Operation Modes in Cogeneration Plant. In 2011, she became a docent, and in 2020, a professor at VILNIUS TECH’s Building Engineering Department. In 2017, she was awarded the educational title of a docent. Her research fields include heat accumulation, technologies of renewable energy sources, and the modelling and thermodynamic analysis of energy systems. She was a co-author of more than 35 articles published in international journals, has read reports at international conferences in Denmark, Germany, France, and Latvia, has authored two educational books on heat transmission, and is a co-author of two national patents. She

About the Authors

xv

is a reviewer of international journals Energies, Buildings, Energy, Journal of Building Engineering, Sustainability, Building and Environment, Applied Thermal Engineering, and a member of the reviewers’ board of the Applied Sciences magazine. She is a lecturer to master and bachelor undergraduates in thermodynamic analysis, technical thermodynamics, heat and mass exchange, building energy system modelling, and a supervisor of their final theses. She is the supervisor of one doctoral student in mechanical engineering. She has also given lectures at T.E.I. Patras (Greece), Riga Technical University (Latvia), and the South-Eastern Finland University of Applied Sciences (Finland). Juozas Bielskus has a master’s degree in energetics (2012) and a doctoral degree in technological sciences, mechanical engineering (2017) from Vilnius Gediminas Technical University (VILNIUS TECH). He has defended a doctoral dissertation titled Thermodynamic and Functional Efficiency Analysis of Solar Energy Using Indoor Climate System. Since 2018, he is a docent at the Building Engineering Department of VILNIUS TECH and has held an associate, a lecturer, and a research fellow positions. In 2021, he was awarded the educational degree of a docent. The field of his research covers the application and development of knowledge of engineering thermodynamics, mechanics of fluids, heat transfer in solving problems of increasing the efficiency of energy consumption, and utilisation of renewable energy sources in buildings. The results of these studies have been published in nearly twenty publications in the Clarivate Analytics Web of Science database and more than 20 articles in other scientific publications. He is a coauthor of three national patents and is involved both in research funding competition projects of the Research Council of Lithuania and in contract investigative work in the areas of HVAC and usage of renewable energy sources on orders from business. He is a lecturer to master and bachelor undergraduates in hydraulic systems, renewable energy technologies, modelling buildings energy systems with computational fluid dynamics, and the supervisor of their final theses.

Abbreviations

AHU BIM BSS BTS CM CN COP EV Fe FLT Fs HP HRE HVAC LCA MEP REC REN RET SCOP SLT TV WAH ZLT

Air handling unit Building information modelling Building service systems Building technical systems Compressor Condenser Coefficient of performance Evaporator Fan (exhaust air) First law of thermodynamics Fan (supply air) Heat pump Heat recovery exchanger Heating, ventilation, and air conditioning Life cycle analysis Mechanical, electrical, and plumbing Reference coenthalpy Reference environment Reference temperature Seasonal coefficient of performance Second law of thermodynamics Throttle valve Water-to-air heat exchanger Zero law of thermodynamics

xvii

Nomenclature

Variables A cp e E˙ h k l L˙ M˙ M¯ T T¯ q Q Q˙ Q˙¯ s S S˙  S˙ irr P z Z p Tln m ηC εF εiC

Surface area (m2 ) Specific heat capacity at constant pressure (kJ/kg·K) Specific exergy (kJ/kg) Exergy flow rate (kw) Enthalpy (kJ/kg) Coenthalpy (kJ/kg) Specific destroyed exergy (kJ/kg) Destroyed exergy (kw) Mass flow rate (kg/s) Mass flow rate ratio (–) Temperature (K or °C, when specified) Non-dimensional temperature (–) Specific thermal energy (kJ/kg) Heat (kJ) Heat transfer flow rate (kw) Relative heat transfer flow rate (–) Specific entropy (kJ/kg·K) Entropy (kJ/kg) Entropy flow rate (kw/K) Produced entropy rate (kw/K) Pressure (Pa) Distribution function (–) Cumulative distribution frequency function (-) Pressure losses (Pa) Logarithmic mean temperature difference (K) Carnot factor (–) Power consumption efficiency of the fan (–) Isentropic efficiency of the compressor (–)

xix

xx

εT ηex η Fs ηF ηU

Nomenclature

Temperature efficiency (–) Exergy (thermodynamic) efficiency (–) Functional exergy efficiency of sector i (–) Functional exergy efficiency (–) Universal exergy efficiency (–)

Subscripts a AHU c CN CNizot consum, cons e E EV EVizot f F FN Fe Fs h HP HRE i j in k l M¯ min out q p prod R sez HP V w Win

Air Air handling unit Cooler fluid Condenser Isotherm in the condenser Consumed State of reference environment State of exhaust air temperature after AHU Evaporator Isotherm in the evaporator Refrigerant, in some cases a specific freon Final Fan Exhaust fan Supply fan Hotter fluid Heat pump Heat recovery exchanger State of fluid Fluid j Input Coenthalpy Destroyed exergy Mass flow rate ratio Minimum Output or outgoing Heat transfer Pressure Produced Room Seasonal Heat pump Ventilation Water Water inlet

Nomenclature

Wout WAH 1 2 

xxi

Water outlet Water-to-air heat exchanger State “1” or “in” State “2” or “out” Total

Superscripts c h q + –

Cooler fluid Hotter fluid Heat transfer To the system Out of the system

Chapter 1

Introduction

The building sector is Europe’s second largest consumer of energy, utilising about 40% of primary energy. Especially considering that buildings account for 36% of the end-consumption and nearly 40% of all CO2 emissions globally. The enormous share of global energy consumption that goes into creating a microclimate on the premises inside buildings has been rightfully getting an increasing amount of attention from the world’s community and political figures. Fundamental political and technological measures geared towards reducing energy consumption and increasing its efficiency in buildings are driven by developed industrial countries, the European Union (EU). No other sector of economy has most likely been the subject of such focused political decision when it comes to minimising the overall consumption of energy and fossil fuels and transitioning to nearly zero energy buildings in the EU since 2020. The constantly growing requirements for building energy efficiency and the tightening of environmental standards are forcing designers, manufacturers, and operators of energy-consuming equipment to review the established engineering solutions by applying the higher complexity component solutions, and to improve the strategies for the control thereof. On the other hand, the building sector is unique in the way that the building envelope and its technological systems designed and deployed it in remain in use for a relatively long period of time without major alterations. Renovation or replacement of conventional systems and solutions can only be made possible through modernisation of the existing or construction of new buildings. Some of the measures are quire costly and global practice of attaining this kind of experience and its dissemination is highly supported. Thanks to significant volumes of energy consumption and the search for rational solutions, both the sector of new and existing buildings and its problems will remain a priority in terms of sustainability research on an international level.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 V. Martinaitis et al., Exergy Analysis of the Air Handling Unit at Variable Reference Temperature, https://doi.org/10.1007/978-3-030-97841-9_1

1

2

1 Introduction

1.1 Building Technical Systems Be as it may, the overall trends are positive. Application of building information modelling (BIM) technologies and life cycle analysis (LCA) principles in building design boosts the quality of decisions made. The thermal characteristics of envelopes have been improving for over a decade now, fossil fuel is being supplanted by renewable energy resources, the methods and measures to evaluate the heaviest energy consumers among building systems are becoming more sophisticated. For instance, owing to the dramatic drop in the need of thermal energy for heating purposes and the prevalence of LEDs in lighting systems, increasing the energy efficiency of ventilation, air conditioning, and hot water supply systems in modern buildings becomes priority number one. The energy services of these systems are directly connected with the human physiology, and personal needs for fresh air and water that has been handled properly are increasing rather than decreasing. They are affected by architectural structural solutions of buildings to a much lesser extent. So, buildings take a relatively short time to build or renovate, and remain in use for long periods. It is the use of buildings that produces those disturbing figures of energy consumption. Energy-demanding services for buildings are created by processes taking place within the building technical systems (BTS). Notably, BTS are almost synonymous to building services systems (BSS) or heating, ventilation, and air conditioning (HVAC) or mechanical, electrical, and plumbing (MEP) systems. This latter acronym has become widespread with the advent of the BIM technology. For the purposes of this book, any differences between these terms are irrelevant, and their potential characteristics will be discussed on a case-by-case basis. The energy chain of building energy services begins with initial/natural energy sources and ends with BTS. Over the last decade, there has been a substantial shift both in the approach to the technological constitution of the chain as such and in the solutions adopted and implemented for project purposes. Heating based on burning fuel in efficient and automated gas boilers has become a rather limited solution already. The forms of energy—work and heat—take place in a multitude of transformational processes along this chain. These processes take place in units that have a complicated technological makeup: renewable energy transformers, heat pumps, heat exchangers, energy storage units, accumulators, heat transfer fluid circulation pumps, control and adjustment equipment, and so on. This variety of processes and their transformation in time as well as the underlying technologies require an objective and universal evaluation in terms of energy efficiency. One of the key goals of scientific research for the purposes of ensuring sustainable renovation and development of the building sector is the energy efficiency of BTS and a quest for technological combinations to accommodate that purpose (Schmidt 2009; Stremke et al. 2011). Sustainability or cohesive development should be first and foremost perceived as a goal to minimise the consumption of primary energy (PE) in the energy supply chain or, in other words, improve its thermodynamic efficiency. For the purposes of technological choice and BTS energy consumption, it is critical that the year-on-year demand for primary energy be reduced (Dincer and Rosen 2007; Molinari 2012).

1.2 Exergy as Quality of Energy for Buildings

3

1.2 Exergy as Quality of Energy for Buildings The long-prevalent concept of energy efficiency, which covers the energy volumes of processes, is being developed with the help of a qualitative structure of energy. This physical analysis of the processes of energy transformation is supported ever so broadly by exergy analysis, an approach to measuring energy-consuming devices and the processes that take place in them, which is rapidly gaining an increasing amount of popularity. Right after the first oil crisis, this thermodynamic method was noted as a viable option for buildings, focusing on their BTS. Applied science publications covering this subject appeared in different countries, including (in a chronological order) (Rant 1963; Baehr 1980; Gaggioli and Wepfer 1981; Shukuya 1994; Gertis 1995; Martinaitis 1996; Pons et al. 1999). Between the 2000s and this day, the number of publications on the overarching subject of exergy and BTS has been following a geometric progression. A special mention should be reserved for (Hepbasli and Akdemir 2004; Schmidt 2004; Zmeureanu and Wu 2007) who also joined this field. One important indication of the perception of this issue became the international cooperation in implementing the International Energy Agency’s projects Low Exergy Systems for Heating and Cooling of Building (IEA ECBCS 2007) and Low Exergy Systems for High Performance Buildings and Communities (IEA ECBCS 2011). However, this specific area of the building’s technical systems and of buildings is closely linked to the general context of sustainable development (Angelotti and Caputo 2007; Dincer and Rosen 2007; Khalid et al. 2015), and exergy is considered to be one of the criteria for assessing sustainable development (Schmidt 2009; Balta et al. 2010). The application of exergy analysis allows defining the most thermodynamically efficient conditions for the process to take place. And these data can serve as a point of reference for the purposes of developing equipment and solving the problems of managing integrated systems in which seasonal climatic characteristics are factored in (Martinaitis et al. 2010; Razmara et al. 2015). It is this particular feature that renders an assessment based on exergy a useful tool when it comes to measuring the quantitative parameters of sustainable development (Balta et al. 2010). The usual economic analysis of the physical indicators that it produces is supplemented by a life cycle analysis. These methods blend to produce combinations such as exergoeconomics (Tsatsaronis 1993) and emergy analysis (Wang et al. 2020). The benefits offered by the application of exergy analysis are at their highest when the analysis is applied in a consistent evaluation of the chain of energy transformations (Biekša et al. 2006; Laukkanen et al. 2016), from primary energy and up to the end energy service provided (room air temperature, humidity, illumination, and so on). A consistent thermodynamic analysis of the process chain allows identifying sites of energy losses, mapping the specific points where the efficiency of energy consumption could be improved, just as it is done when dealing with industrial energy production processes (Rosen and Tang 2008). Hence, the exergy analysis of the energy chain of energy service technologies of buildings is the most effective if it extends from the assessment of primary energy resources to the services for the

4

1 Introduction

end-user. With the method of thermodynamic analysis applied to assess the internal energy processes of units, it is critical that the assessment methodology, perceived and applied unanimously across the energy chain, be approached in a unified manner. First of all, by preserving and promoting the principles of thermodynamics as a fundamental science. An overview of the sources of scientific insights covering this subject suggests that BTS solutions are regarded as viable options in the application of methods of thermodynamic or exergy analysis increasingly often (Biekša and Martinaitis 2004; Yucer and Hepbasli 2011; Shukuya 2013). Exergy efficiency as a technical energy indicator of BTS performance has a relatively broad application for the purposes of identifying strategies of optimal system management (Marachlian et al. 2011; Du et al. 2015; Razmara et al. 2015), choosing combinations of hardware components (Baldini et al. 2014; Kim et al. 2014; Khalid et al. 2015), or comparing energy transformation processes within BTS (Wei and Zmeureanu 2009; Laverge and Janssens 2012; Martinaitis and Streckiene 2016).

1.3 State of the Environment and Exergy The material presented in this book focuses on the analysis of the characteristic BTS processes. Exergy is presented as a part of energy that could be used to achieve work in a defined state of the surrounding environment. For the purposes of thermodynamic analysis of energy transformation systems, exergy and the related indicators are given a broader interpretation and are connected to the quality of the processes in question. Work as a thermodynamic indicator of process is also a unit of measure of its quality. One or several specific parameters of the state of the environment (such as temperature, pressure, concentration, and so on) are called the state of reference. The exergy results obtained for the system in question are a function of the parameters of the state of the system and the chosen reference environment (REN) bound by the first law of thermodynamics (FLT) and the second law of thermodynamics (SLT): Ex = f(FLT, SLT, REN). The characteristics of a particular system determine which of these three complex variables will have the greater impact on the result. Generally, or under the first approach, these variables are to be considered equivalent for the purposes of thermodynamic analysis. Of course, in practice thermodynamic analysis does not even touch upon any presumptions regarding this equivalency. At textbook level, too, these variables are often given the following inequivalent order of priority: SLT, FLT, REN. By its methodical nature, owing to the size of buildings and the dependency of their energy demands on climatic conditions on the one hand, and relying on the parameters of the state of the environment (hence, the climate) on the other, exergy analysis should become an important tool when it comes to the assessment of building sustainability. Still, this is yet obstructed by a number of bottlenecks

1.3 State of the Environment and Exergy

5

that science is gradually bringing down. They are covered here briefly, with a more detailed discussion presented in the appropriate chapters. The characteristics of the surrounding environment and the impact of the potential shift in its parameters merit renewed interest. There is an increasing number of articles, their authors pointing to the fact that the choice of the reference environment [or a particularly frequent application of the reference temperature (RET)] has a major effect on the outcomes of exergy valuation. The passage of several decades has seen some musings over the benchmark environment. Wepfer and Gaggioli clearly postulate that, by contrast to the benchmark variables of the thermodynamic and thermochemical tables, the benchmark environment of exergy analysis cannot be chosen at will (Wepfer and Gaggioli 1980). The analysis of the theory and practice of the benchmark environment of chemical exergy in the article by Gaudreau et al. (2012) identifies two fundamental theoretical approaches to reference environment as formulated by Ahrendts (1980) and Szargut et al. (1988), presenting the strengths and weaknesses of these approaches and their effect on the making of decisions grounded on sustainability. The term ‘environment’ is covered in a systematic and concise manner by Serova and Brodianski (2004), who draw a comparison between cases of exergy analysis deliberately chosen. Dincer and Cengel (2001) noted that fundamental models of the environment can be defined as follows: natural-environment-subsystem; reference-substance; equilibrium and constrained-equilibrium; process-dependent. The publication referenced above shows that the choice of REN for processes covered by the analysis is based on assumptions. Suggestions are made as to solutions and concepts, yet the results of the exergy flows and efficiency indicators obtained in the wide range of REN are left out. Unfortunately, there is no mention of the process-depended model, which is omitted in a wide range of calculations, because it was never proposed. It is worth noting here that even if one were to ignore any kind of thermodynamic knowledge, mathematical logic alone would suggest that the further the parameters of the subject system are removed from the parameters of the state of the environment, the lesser impact these latter have on the outcomes of exergy analysis. And vice-versa, which is important for the purposes of the study at hand. The problem of the variation in environmental conditions is particularly relevant when it comes to analysing the processes of heat and work transformation within the engineering systems of buildings. The processes in question take place within these systems at temperatures that are close to the environment temperature. The choice of a reference environment affects the quantity of exergy transformed, and this impact can be significant considering the low level of exergy that can often be observed in buildings (Marmolejo-Correa and Gundersen 2012). Whereas for the purposes of exergy analysis of electric and industrial processes transforming high-quality energy as key input and output, the influence of the RET is smaller (Blanco 2011). HVAC specialists first raised this question a way back (Krakow 1991). Unfortunately, collective studies carried out two decades later (Annexes 37 and 49) (IEA ECBCS 2007, 2011) offer a proper description of the problem yet are limited to general recommendations without moving towards a thermodynamically viable universal

6

1 Introduction

methodical solution. Dividing approaches into static and dynamic (or using only the latter) by way of analysis does not resolve this problem. Calculations done for that purpose at temperature that changes over time ignore the ‘thermodynamic control’. If the middle of the algorithm, even the smallest of its interim phases feature negative exergy destroyed or exergy efficiencies are obtained outside the limits of 0–1, there are no longer any thermodynamics in this problem, and only maths remain. The report (IEA ECBCS 2011) discusses the grounds for calculating the flows of energy and exergy required for a building and its system with different sources of reference environment: the universe as a nearly absolute zero; room air inside the building; undisturbed soil; the outdoor air surrounding the building. Based on the results obtained, it recommends using the surrounding outdoor air as the reference environment. But that is a purely logical recommendation that does not have a thermodynamic algorithm. It also suggests a source of how ‘thorough analysis of different suitable benchmark environments’ provides examples with negative exergy destroyed or exergy efficiencies outside the limits of 1. Without giving any comments on how it is thermodynamically unacceptable and without any suggestions of how to address this. For want of generally accepted algorithms to resolve the problem of energy analysis in a variable REN, any search is limited to solutions that apply to a specific technology in question: heat pumps, heat exchangers, storage units, humidifiers or driers, and so on. Ergo, when it comes to conducting exergy studies, different authors differ in their interpretations of environmental conditions, and it all stays in the phase of scientific discussion for now. At this stage of the application of exergy analysis to buildings, the discussions and the publications that represent them are covered at length in the works of (Bonetti 2017; Bonetti and Kokogiannakis 2017). The authors of the article are not categorical or biased towards the choice of the REN; instead, they accentuate that with buildings, we have two groups of heat transfer processes: steady and unsteady. Of course, the authors dub these latter as ‘dynamic’, a name that hardly can be seen as appropriate in terms of the classics of heat transfer. They say that ‘achieving a mutual agreement on the status of the exergy analysis of buildings requires further discussion grounded on theoretical and practical considerations.’ Inherent building processes are the unsteady processes of energy accumulation and custom-built energy storage units that take place within the structural framework of the building.

1.4 Variable Ambient Temperature and Exergy Flows BTS equipment is home to relatively fast-paced energy transformation processes that directly depend on the ambient temperature and should be considered quasisteady. One characteristic member of this family is ventilation and air conditioning hardware. The two process groups and the equipment that falls into them, directly or indirectly, tend to follow a pattern of merging into a single system of creating comfort (indoor microclimate) in the building. The exergy analysis of this type of integrated system calls for methods grounded on assumptions that adequately take the physical

1.4 Variable Ambient Temperature and Exergy Flows

7

properties of the phenomenon into consideration. With quasi-steady processes, the suggested method would be that of an exergy analysis based on a variable REN as introduced in the case of the air heat exchanger (Martinaitis et al. 2016). The same article introduces a case where the choice of a variable REN alone does not guarantee that the algorithm will fit into the boundaries of thermodynamic laws. The directions of exergy flows need to be approached in a manner that is adequate for the shift in the REN. One example of a deeper approach to exergy analysis of unsteady processes could be the studies by (Pons 2009, 2019). The thermodynamic arguments that they introduce evolve into mathematic arguments, with numeric calculations used to prove the convergence of exergy analysis and energy optimisation. Variations in the environment temperature are considered to by the periodic day cycle. The author tends to favour the choice of a constant reference temperature determined with this method. It is a noteworthy interpretation for the exergy analysis of unsteady heat transfer in structural units of buildings and their energy storage units. For the purposes of exergy analysis, it is important to identify exergy flows that go into and out of the system, their balance used as an identification of exergy destroyed, and their relationship, as that of the exergy performance of the unit and the process taking place in it. It is a statement that is relatively easy to understand and is acceptable to many. Still, in hands-on application, especially with the benchmark temperature below, above, or crossing the working temperatures of the working fluids in cases of energy accumulation or with all of the above, the identification of these values lays at the tier of scientific discussion. Shaped by a steady flow of thermal energy, the flow of exergy in this case changes both in size and in direction. In turn, this affects the outcome of exergy balance (Martinaitis and Streckiene 2016). A categorisation of ‘cold’ or ‘hot’ exergy flows would be rather figurative, yet hardly capable of achieving a singular formalisation in the algorithm. The matter of assessment of the flow of thermal exergy will be discussed elsewhere in this monograph. Exergy efficiency is the most common exergy-based parameter for the purposes of the comparison of different energy conversion systems. The exergy efficiency indicator provides more information than the energy efficiency value. It has more use when it comes to pinpointing system weaknesses or analysing potential improvements to the systems (Chengqin et al. 2002). Still, the concept of exergy efficiency needs a clear and unambiguous definition, one that would be independent of individual assumptions chosen by different authors. This value has to be the clearly denominated, compared, and determined result of an assessment procedure. In this case, it emerges that exergy analysis employs two definitions of exergy efficiency (Woudstra 2002; Lior and Zhang 2007; Marmolejo-Correa and Gundersen 2012; Nguyen et al. 2014): • Universal: the ratio of all incoming and outgoing exergy flows; • Functional: the ratio between the amount of exergy created (produced) and received (consumed) by the system. The main limiting conditions arising out of the fundamental principles of thermodynamics say that the exergy efficiency of the process of energy transformation lies within the limits of 0 and 1, and the actual exergy destroyed can only be above zero.

8

1 Introduction

Just like a below-zero amount of exergy destroyed, a value of the exergy efficiency ratio that is above 1 should be approached critically. As the example in (Martinaitis et al. 2016) shows, disregard for these limiting conditions may be beneficial in a local context of analysis, yet it damages and prevents further correct application of exergy analysis in the chain of energy transformations.

1.5 Monograph Chapters at a Glance The material of this publication has been deliberately drawn as an algorithm for the exergy analysis of the key units and processes of heating, ventilation, and air conditioning (HVAC). This is evident in the sequence in which the material is presented, and in the level of its detail. The publication in general and its individual chapters are preceded by theoretical, analytical grounds, an explanation of the presumptions for the analysis and/or the properties of the processes, and conclude with numeric results, examples, and a discussion thereof. The equations used in the calculations are presented and described with the level of detail and in the sequence so as to enable those who seek and have the necessary resources to continue developing and improving the tools of and the instruments for modelling the exergy analysis of HVAC systems. On the other hand, it is not a handbook; the contents of this publication require the reader to have a certain degree of knowledge of thermodynamic, exergy analysis and experience in its application. Knowledge obtained through university studies of engineering thermodynamics and HVAC systems and the processes taking place within them should be enough to accommodate that purpose. The application of this knowledge should avoid dogmas that often take shape in the environment of specific studies or are built on the basis of insufficient knowledge of theoretical foundations. It is respect for thermodynamics first, and respect for formulas and figures obtained on their basis second. In this era, exergy analysis should not be considered as a classic of thermodynamic analysis; as a result, one should invest some time in getting to understand the thermodynamic concept of the indicators obtained and to study their broader and more variegated interpretations. The introductory chapter (this chapter) transitions from the problem of high levels of energy consumption in buildings to the specifics of the application of exergy analysis to resolve it. The applied value of the exergy analysis of engineering systems is higher when it covers a possibly longer chain of energy transformation, from primary energy to the energy service for the consumer. The analysis of this chain and its elements should have identical methodological validation. The occurring solutions of individual chain components, which are fragmented yet defined by a certain degree of analytical detail, lack presentation of their assumptions and interpretation of the results from the viewpoint of thermodynamic fundamentals. The status of the reference environment in exergy analysis can be considered constant when it can be reasonably demonstrated that its factual variation within the boundaries of chosen reliability has no effect on the outcome. In other words,

1.5 Monograph Chapters at a Glance

9

assessment based on the application of a steady state of the environment has to be thermodynamically justified in its own right. HVAC equipment is dominated by heat transfer processes that can largely be considered quasi-steady for the purposes of their efficiency analysis. The study highlights that the temperatures that trigger these processes are relatively similar to the variable environment temperature, which at the same time is close to the reference temperature (RET) for the purposes of the exergy analysis of these processes. The study furthermore applies thermodynamic logic to show that the flows of energy and exergy differ both in their numeric value and their unique rules of directional shift. The rapid innovation in the field of low-exergy systems for buildings demands thermodynamically accepted analytical descriptions for exergy transformation process in the chain of HVAC systems. This exergy analysis can provide a more reliable set of system design and optimal control algorithms that would allow obtaining the target function of minimal destruction of exergy. The study in question is part of work in progress in that direction. Chapter 2 presents the concept of the shift in the direction of exergy flow and the grounds for preparing its algorithm, when the varying environment air temperature is also the RET. The direction of the thermomechanical exergy flow is always aligned with the ambient temperature. It changes its aspect towards the temperatures of air intended or consumed for ventilation purposes by being above, below, or parallel to them, and sometimes all three at once within a particular HVAC unit. This quality merits some attention in the exergy analysis of HVAC, because this mode makes up a substantial portion of operation of these systems during the year. It is important to realise that with at least two constant temperatures that trigger a steady flow of heat, the exergy flows that define that heat transfer and are connected with each of the temperatures are always aligned with the ambient temperature and follow its shift. Which means that they can change both in their direction and in their volume, even when the temperature that triggers heat transfer is steady. The use of coenthalpy and a thermodynamic state parameter that directly constitutes the potential of the exergy flow and the numeric and graphic interpretations of its variation are instrumental for the purposes of the analysis of ongoing processes. Direct analysis of exergy flows and their reflection in the case of a variable potential-building RET opens up possibilities to observe the specifics of the exergy transformation process, and the above-mentioned directional shifts first and foremost. The air handling units and the choice of component combinations to be used in it must provide a particular flow of heat for the air that will be used to ventilate the room. For the purposes of any kind of technological arrangement, the primary variable that is independent on the AHU energy transformation processes and the amount of this energy is the outdoor air temperature (and the reference temperature (RET) at the same time). Just like the constant rather than variable air flow rate required for ventilation and the air temperature inside the room (the air supplied to and exhausted from it). These two indicators are chosen as constant for the purposes of the study. The main energy transformers within the air handling unit are the heat exchangers—heat recovery exchangers, water-to-air and electric heat exchangers, heat pump condensers, and evaporators. The temperatures of the heat transfer fluid

10

1 Introduction

in them can be above, below, or equal to the ever-varying environment temperature, hence, the RET. Event the temperature of the heat transfer fluid that flows into the same unit at any given moment can be either of the three at different locations. As it was mentioned, this defines the direction and volume of the exergy flow. For methodological demonstration purposes this study features a thermodynamic analysis of processes of energy transformation in four technologically different AHUs. In addition to the aforementioned heat exchangers, the function of air transportation in them is accommodated by two fans. They are supplemented by a compressor (CM) and a throttle valve (TV) in the heat pump. The action of these specific individual components of AHU schemes is explained in terms of the methodology that is being presented, complete with the equations necessary for AHU thermodynamic analysis purposes, as well as brief commentary thereon. The underlying fundamental thermodynamic stance here is that regardless of the scope of the thermodynamic system, the exergy efficiency ratio of the energy transformation process in the outcome of the application of the exergy analysis methodology is always within the limits of 0 and 1, and the exergy actually destroyed can only be above zero. Chapter 3 introduces the exergy analysis of the heat recovery exchanger of the air handling unit. The heat recovery unit is very important from the technological and efficiency point of view—what is more, it may well be the main energy transformer of the AHU. It generates about 50–80% of the thermal flow within the air handling unit. On the FLT level, the temperature efficiency that defines its performance level ideally should be as high and as stable as possible within the annual environment temperature shift range. It is the number one task for HRE developers and manufacturers, and the main expectation of the users. In terms of the exergy analysis methodology, the authors found the HRE instrumental for the purposes of showcasing the concept of the shift in the direction of the exergy flow at variable RET as presented in this chapter, as well as providing its consistent analytical description. To determine the exergy efficiency of the process taking place within the HRE and the amount of exergy destroyed in it, HRE exergy analysis is performed by expressing exergy flows both with the Carnot factor and with coenthalpies. The Carnot factor has broad application and recognition when it comes to measuring the exergy of thermal flows. The methodology of the ventilation heat recovery exchanger exergy analysis combines non-dimensional data to produce a more universal set of data. Here they are tied with the entropy generated during the process, as well as other indicators. These are, first and foremost, the Carnot factor as such and the relative heat flow. This latter is the expression of the interaction of three Carnot factors (two heat transfer fluids and the environment, amounting to zero) in cases of directional variation of exergy flows. Non-dimensional temperature binds the ambient temperature and the temperature of the heat transfer process, both of them relevant for the purposes of exergy analysis. Temperature efficiency, a value that defines heat recovery exchangers in engineering practice, was employed as well. It cannot testify directly as to the exergy efficiency of the process, but as it represented BTS by nature, it is convenient to use in the exergy analysis of heat recovery exchangers.

1.5 Monograph Chapters at a Glance

11

If enthalpy as a state parameter is the potential of the energy flow, then coenthalpy is the direct potential of exergy flow. Other comparable potentials are pressure for the mass flow rate, temperature for the heat flow, voltage for the electrical current. Unfortunately, due to a lack of effort to plunge its depths, coenthalpy is not a properly prevalent parameter for the purposes of exergy analysis. Both methods reinforce the reliability of each other’s methodology and results, and reveal the importance of coenthalpy as thermodynamic potential. The use of the coenthalpy parameter and the numeric and graphic interpretations of its variation are instrumental for the purposes of visualisation, analysis of the ongoing processes and information exchange. While moving straight to the values of exergy flows without visualising the potentials that create them sometimes cuts short the possibilities to observe the specifics of this process. This is what happens in energy transformation processes at near-ambient temperature. Especially when the temperature changes and constitutes the RET for exergy analysis at the same time. In each case, we also have coenthalpy as a reference parameter of the environment of exergy analysis, REC. It is always lower than (or sometimes equal to) any other coenthalpy of the heat transfer fluid involved in the process in question. This is the key difference between the REC and the RET, the state of reference environment defined by temperature, which can be lower or higher (for instance, in the case of ventilation) than any temperatures of the flows involved in the processes. If with the task at hand this temperature is only lower or only higher than the temperatures of the heat transfer fluids, then this property of REC as a reference parameter of exergy analysis loses some of its relevance, because heat transfer fluid coenthalpies behave in a manner similar to that of temperatures. But in the AHU or HRE analysis discussed in this study, when the reference temperature is equal to a temperature of heat transfer fluids or falls between several of them, this property becomes methodologically significant and exceptional. Application of coenthalpy as a parameter of the thermodynamic state allows: determining the value of exergy flow directly based on the differences of the coenthalpies of heat transfer fluid states; deciding on the direction of exergy flow: from a medium with a higher coenthalpy value to one with a lower coenthalpy; relying on the reference coenthalpy (REC) as the coenthalpy value that is always the lowest and independent on the state of heat transfer fluids. A special focus was placed on the calculations of the universal and the functional exergy efficiencies, which are often encountered in the exergy analysis, all the while relying on the formal logic of their definition grounded on the ‘output–input’ exergy flows for universal efficiency, and ‘produced–consumed’ exergy flows for functional efficiency. A deeper essence of this methodology and the universal character of the algorithm were revealed by presenting detailed equations for the calculation of HRE exergy, the universal and the three functional exergy efficiencies at variable RET. The origin of the equation was supported with evidence and the results were illustrated. A numeric and graphic analysis of coenthalpy diagrams, exergy efficiency and the tendencies of their variation provides deeper insights into the properties of

12

1 Introduction

the processes. The study involved a broad analysis of the universal and the functional exergy efficiencies in terms of HRE, which revealed their properties and specifics. It is clear that the exergy efficiencies obtained are more sensitive to the specifics of the process than the universal exergy efficiency. The methodology and the algorithm that were developed contribute to solving problems with the concepts of exergy efficiency when they are applied to project valuation and process improvement. The application of this approach can go beyond the scope of HRE. First of all, it is relevant when processes of energy transformation take place at a varying environment temperature. Chapter 4 introduces a parametric study of combinations of the power ratings and energy amounts of the components of the heat pump at reference room and outside air temperature conditions characteristic to ventilation. The processes of heat recovery with a heat pump between two ventilation air flows are analysed. The characteristic resulting indicators for the purposes of this study are considered to be the states of the refrigerant of the heat pump (HP) in the condenser (CN), evaporator (EV), compressor (CM), and throttle valve (TV). They are described by temperatures and other supplementing or derivative parameters (enthalpies, entropies, coenthalpies, pressures, and so on). The thermodynamic analytical ties among the components of the heat pump of the air handling unit are described, beginning with the energy balances of the heat pump components. The chapter then proceeds to deal with the balance of the exergy heat pump components, the exergy efficiency, keeping in line with the analytical descriptions, definitions of exergy flows and exergy efficiency, wordings, and expressions presented in the previous chapters. The heat transfer process between the air used for ventilation purposes and the refrigerant in the evaporator and in the condenser is limited to the ventilation task. It is defined by the amount of air for ventilation, the outside and the room temperatures, and the resultant heat flows, their values shifting as the outside air temperature varies. The optional, variable, or constant parameters would be the refrigerant evaporation and condensation temperatures (isotherms), the temperature differences between the air and the refrigerant. The derivative parameters would be the inherent heat flows of the evaporator and the condenser, the flow rate of the refrigerant, the power of the compressor, the efficiency indicator of the heat pump. The chapter furthermore presents a system of equations connecting these parameters in the ventilation air heat recovery task. It is thermodynamically desirable to assess the sensitivity of said indicators to the distance between the refrigerant’s isotherms. The fact that these isotherms are controlled with throttle (hence, simplicity) has an adverse effect on exergy indicators, and other types of control could lead to technological difficulties (hence, complexity). The parametric analysis performed helped reveal the parameters that affect the preparation of this algorithm, analyse the impact a shift in the reference environment and technical parameters has on an exergy-efficient solution. For the purposes of this analysis, the alternative isotherms were the steady and variable temperature refrigerant isotherms in the evaporator and the condenser. The result obtained was that isotherms that are shifting in a defined manner point to a

1.5 Monograph Chapters at a Glance

13

possibility to have high and table heat pump efficiency indicators at variable environment temperature. The alternatives were illustrated with the way the parameters and indicators, such as temperatures, the Carnot factors, and coenthalpies, which are used in the exergy analysis methodology, varies inside this unit. The parametric analysis produced parameters of the delimiting or the resultant state, focusing on air heating or the interaction of HP components. The variation of the values of the universal and the functional exergy efficiencies, coefficient of performance (COP) of the heat pump in a wide range of variation of the environment air temperature was obtained. The search algorithm that was developed purportedly opens up opportunities for a deeper optimisation of the cycle of the heat pump engaged in a ventilation task as well as for addressing the technological tasks of managing this cycle. Chapter 5 presents the results from the numeric case of the four technological schemes of the AHU introduced in this chapter, which were obtained through the application of the methodology for the determination of exergy efficiency that was developed. It is a known fact that the operation of HVAC systems depends on climatic conditions and on the environment temperature in particular. The results that were presented earlier in the book already confirm that, when it comes to thermodynamic analysis, exergy transfers and destruction depend significantly on the environment temperature, which is also the reference temperature (RET). On the other hand, the RET is so far usually considered constant for the purposes of this analysis, and published attempts to use it as a variable are not without flaw. This chapter integrates the results of the exergy analysis of the heat recovery exchanger (Chap. 3) and the heat pump (Chap. 4); these results overlap in places, because they are the main components of AHU energy transformation. Only the additional equations needed for the exergy analysis of the AHU, complete with a brief commentary thereon, are presented here. A lot of other analytical expressions that were used were already introduced in prior chapters. The numeric analysis of these AHU cases is rather biased towards drawing a comparison between the mutual exergy indicators of AHU schemes under similar or approximate conditions. The air flow for ventilation and the room temperature are constant for all schemes. The overall amount of heat needed for the air supplied is proportionate to the environment temperature and is identical for all schemes. The absolute indicators accepted in these cases have little direct impact on the efficiency indicators that are addressed below. The chapter provides graphic illustrations of the methods presented above (based on the Carnot factor and coenthalpies) that were not clearly shown side by side in the same numeric cases. The reciprocal positions of the statuses of the air and the refrigerant in the heat exchangers (HRE, CN, EV), the heat flows inside them, and other mode characteristics are showed in a wide range of outdoor air temperatures. These characteristics constitute indicators such as the heat transfer fluid state parameters, flow rates, power ratings, and so on. In other words, these are values that do not point to the outcomes of exergy analysis directly. The fact that the dependence of some of the mode characteristics on varying reference temperature is straight-line in nature is not something new; however, the proportions of those indicators and their impact in different technological schemes when they perform the same function—ventilation

14

1 Introduction

at a steady flow rate—merits some attention. The examples presented in the chapter constitute some of the potential future cases of a more profound parametric analysis that the methodology showcased here reveals. The main technological schemes’ efficiency indicators of choice are their coefficient of performance (COP) and universal and functional exergy efficiency. In addition to direct exergy efficiency, another indicator in exergy analysis is the amount of exergy destroyed, as well as its structure by components and processes taking part in them. That is why the chapter presents and deals with the variation of entropy produced in separate components, which has a direct effect in the amounts of exergy destroyed. The universal and intrinsic indicators of the entire AHU and its components are discussed, providing a commentary on their interaction in terms of these indicators. Summary results of the exergy destroyed by each AHU scheme are provided for the purposes of comparison of the cases, and each combination can be subjected to further scrutiny. The detailed distribution of exergy destroyed in the subject AHU schemes as presented in this chapter shows that, within the chosen range of variable RET, the portion of exergy destroyed by individual components changes two and more times. Integrated values for the exergy efficiency of the whole AHU are presented, their specifics discussed. When it comes to analysing the exergy efficiency of these AHUs, it is worth knowing and seeing the exergy efficiencies of the components that constitute them. Paired with the exergy destroyed by those components as discussed above, this allows revealing the impact the components have on the coefficient of performance and exergy efficiency of the whole unit. And at the same time identify the components that need improving in terms of their efficiency first and foremost. AHU exergy efficiencies under the effect of fans and with the impact of fans ignored are presented. Their impact on the AHU’s thermodynamic efficiency is revealed as well. The use of a variable RET shows that fans with a steady rate (power output) are one of the factors that have a negative effect on the COP or exergy efficiency. The COP of the HRE has the biggest effect on the air handling unit’s COP, universal and functional exergy efficiencies. As a result, the choice of the appropriate HRE should be based on exergy analysis, aligning it with other AHU components and considering the shift of the RET at a particular location. Process parameters in the AHU and the components of its HP shift within the range of RET variation. The prevalent tendency is that with the RET going up, many indicators decrease. Nonetheless, each component is unique by the nature of its entropy produced, exergy destroyed, and the variation in its exergy efficiency. The generation of entropy, albeit it is not an indicator that allows drawing a comparison of the AHU COP, shows the distribution of the irreversible nature of processes in the components and the characteristics of their variation. Furthermore, it allows making checks of the interim results of the process of exergy analysis. Notably, when temperatures within heat exchangers are changing on a near straight-line basis, meaning when the shift is insignificant, HVAC exergy analysis can be done using methods that are both on the Carnot factor and coenthalpies. The choice depends on the available information.

1.5 Monograph Chapters at a Glance

15

In other words, with the variable RET model, when the reference temperature equals the temperature of the outdoor air used for ventilation, the COP, the values of the universal and the functional exergy efficiencies, and exergy destroyed clearly indicate which of the subject AHU systems is the more efficiency at different environment temperatures. This information helps develop computational algorithms for determining and measuring seasonal operation of HVAC systems further. Chapter 6 deals with the seasonal thermodynamic efficiency of the air handling unit as obtained on the methodological basis of the exergy analysis laid down in the book. Equipped with an AHU methodology of how thermodynamic analysis should be performed at a chosen temperature and having examined the tendencies in the variation of exergy flows, exergy destroyed, and exergy efficiency at variable RET, one can proceed to calculate the seasonal indicators of choice. The average seasonal long-term coefficient of performance is something that usually is of interest not only to researchers, but to designers and users of the equipment as well. The only difference is that some of them can be rather concerned about the individual ratios of the process and the impact the different parameters have on the indicator, while others are rather more interested in and attach practical significance to the efficiency of the operation of the whole solution or unit at a specific location. The ultimate goal here being to determine the exergy efficiency and coefficient of performance of a particular component or the whole unit in general during a certain season or another period of choice. The thermodynamic efficiency of building technical systems is closely connected to the local climate, one its parameters—the environment air temperature—virtually never losing its significance. For instance, the amounts and proportions of energy consumption in buildings depend on the climatic conditions of a particular location, the building practice and consumer behaviour, the level of the economy, and the existing custom in building houses. The important thing is to determine the ambient temperature when the amounts of exergy consumed and destroyed are at their largest. From the practical standpoint, such information creates a possibility to move on towards economic indicators, because seasonal indicators are proportionate to the costs to maintain room microclimate as well as the consumption of natural resources. The analysis performed shows a connection between exergy indicators and the characteristics of the local climatic conditions. This assessment of seasonal characteristics helps determine the intensity of use of the unit, the frequencies of distribution in the course of the year or another period of choice, as well as the period that requires more attention. It informs the search for the optimal operation of the unit in a particular location. The quantitative and qualitative system assessment reveals that even though their energy balance (i.e., FLT) lends more appeal to air handling units equipped with heat pumps (HPs), this advantage diminishes with the application of exergy analysis. The comparison of different AHU schemes on the basis of energy and exergy clearly shows that the use of the heat pump has its appeal only when systems are approached in terms of the coefficient of performance (COP). For AHUs with a HP, this indicator is higher compared to systems equipped with water-to-air heat exchangers (WAH).

16

1 Introduction

Exergy analysis shows that with air handling units equipped with heat recovery exchangers and water-to-air heat exchangers, the amount of exergy destroyed is smaller, and the exergy coefficient of performance is higher. This reveals the necessity to improve the available heat pump control algorithms and the controls of their implementation. The developed tools of exergy analysis can be used to probe the processes taking place in HP components for possibilities to minimise exergy destroyed. In this regard, the results obtained train the spotlight on the evaporator and fans. Analysis of individual cases highlights the role the heat recovery exchanger plays in the entire process of air handling unit operation, because it determines the power outputs of other components, the amounts of exergy destroyed, and the efficiency of the whole unit. Analysis and comparison of AHU schemes showed that when it comes to system analysis, seasonal exergy efficiency as a comparative indicator is more sensitive to external variables than the seasonal coefficient of performance (SCOP). All in all, seasonal-climatic assessment involving exergy indicators demonstrates its added value for the purposes of investigating the operation of HVAC equipment in different climate zones. On the basis of the numeric results of case analysis, the study showed that the appropriate approach to the directions of heat exergy flows when the reference temperature is considered to be variable, and the determination of their values based on methodologies formulated in reliance on the Carnot factor and coenthalpies allow designing algorithms for the dynamic modelling of HVAC systems and reflecting the specifics of the energy transformation processes in HVAC units in a thermodynamically reasonable way. The methodology developed by the authors and presented in this study shows that all of the parameters grounded on exergy, such as the universal and the functional exergy efficiencies and the absolute destruction of exergy are highly sensitive to changes in the reference temperature (RET). At the same time, the results are in line with the key axioms of thermodynamic (exergy) analysis. Therefore, the proposed methodology can be applied for the purposes of analysing and improving heating, ventilation, and air conditioning systems that, as a rule, operate at shifting ambient temperatures, as well as designing dynamic models for such systems and their exergybased control algorithms. The research summarised in this work has been published in the course of more than a decade in the publications that were contextually specified in the preface, as well as in (Martinaitis et al. 2018a, b; Streckien˙e et al. 2019). Some of the featured illustrations have been adapted for this book based on publications from the publishing houses of Elsevier, Inderscience, MDPI, AIP Publishing as referenced by the authors. Even though the illustrations in this monograph are not identical to their respective counterparts that previously appeared elsewhere, they are used in the book courtesy of the publishing houses.

Chapter 2

Theoretical Foundation of the Exergy Analysis Methodology at Variable Reference Temperature

The applied value of the exergy analysis of engineering systems is the higher when it covers a possibly longer chain of energy transformation, from primary energy to the energy service for the consumer. The analysis of this chain and its elements should have identical methodological validation. The occurring solutions of individual chain components, which are fragmented yet defined by a certain degree of analytical detail, lack presentation of their assumptions and interpretation of the results from the viewpoint of thermodynamic fundamentals. This book shows that the flows of energy and exergy vary in their numeric values just as they follow their own unique rules of directional shift. The state of the reference environment can be factored in if it can be proven that its factual variation does not have any effect on the outcome within the limits of chosen reliability. Furthermore, the underlying fundamental principle of thermodynamics is that the exergy efficiency of the process of energy transformation lies within the limits of 0 and 1, and the amount of exergy destroyed in the actual process can only be above zero.

2.1 Direction of Exergy Flow The question of heat exergy direction becomes relevant when the temperatures that trigger heat transfer are similar to the variable environment temperature. The difference in the temperatures of the warm and cold sources of heat creates a heat flow moving in the direction from the higher temperature to the lower. The size of these flows is proportionate to the difference of said potentials and does not depend on the environmental conditions. What about the heat flow exergy? Does its flow follow the flow of heat? Are their directions aligned at all times? It is important when it comes to performing mathematical operations with exergy flows. We can easily agree that when the temperature of the heat source matches the temperature of the environment, it has no thermal exergy flow, meaning that the exergy flow equals zero. Let us assume that the temperature © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 V. Martinaitis et al., Exergy Analysis of the Air Handling Unit at Variable Reference Temperature, https://doi.org/10.1007/978-3-030-97841-9_2

17

18

2 Theoretical Foundation of the Exergy Analysis Methodology …

of the heat source stays constant. When the environment temperature moves away from the temperature of the heat source, maintaining the temperature of that source will require compensating the exergy flow leaving the thermodynamic system. It happens both when the environment temperature rises above and falls below that of the heat source. Therefore, in the temperature coordinates the heat exergy flow goes in the direction away from any the heat source of any temperature (hot or cold) to the environment temperature. This is in line with the logical statement that if you want to have within the control volume (such as a room) a temperature other than the ambient temperature, you will need to use thermal, chemical, mechanical or other types of energy to compensate for the exergy flow lost in the room. So, the exergy flow leaves the room with a temperature different (higher or lower) from that of the environment. As a result, low-temperature heating or high-temperature cooling is considered thermodynamically efficiency because it leads to the lowest exergy flows and costs—lower consumption of resources. Moving on to a more formal, quantitative thermodynamic assessment of heat transfer, let us use a diagram that includes the zero law of thermodynamics (ZLT), the first law of thermodynamics (FLT), and the second law of thermodynamics (SLT) and is quite known in classical technical thermodynamics. The authors first came across this diagram in a book by Baehr H. D. (Baehr 1962). Of course, the exergy approach includes both the FLT and the SLT. The suggestion is that said diagram be expanded in the direction of the development of thermodynamic analysis towards exergy with some modification, and be construed as a stationary flow of heat. This diagram is showed in Fig. 2.1. We have a steady heat transfer process triggered by constant temperatures Th = 20 °C and Tc = −20 °C. They were chosen to approximate the natural environment. The process is interpreted in terms of the zero law of thermodynamics (ZLT), the first law of thermodynamics (FLT), the second law of thermodynamics (SLT), and exergy. In the part representing the ZLT, we can see the temperatures Th > Tc , which generate the heat flow Q˙ ch . It represents the FLT, with only heat passing the boundaries of the thermodynamic system. The irreversibility of the process is assessed under the SLT, its quantitative assessment is done by the equation of the  balance  of its entropies, its interior entropy gain (entropy 1 h h 1 ˙ ˙ produced)  Sc irr = Q c Tc − Th > 0. Expanding this problem to include exergy analysis requires the previously excluded reference temperature Te . Confining the problem in question to heat transfer (q) only, the (+) assigned to the abstract system and the exergy () flows resulting from the processes taking place in it are combined ˙ Here, L˙ = Te S˙irr ≥ 0 is the by the exergy flow balance equation  E˙ q+ +  E˙ q− = L. exergy destroyed as a result of the process irreversibility, which always amounts to 0 or more under the SLT. In some isolated cases, the resultant exergy may not exist, for instance, when the heat flow runs towards the environment. In the case of heat loss in the room, meaning the process of transmission of heat to the outside via the wall of the room, the exergy balance equation would be  E˙ q+ = L˙ ≥ 0. With most of the different energy transformer exergy analysis problems, Te < Th and Te < Tc as often as not. Processes in room heating, cooling, and ventilation hardware at temperatures are close to the ambient temperature and may be Th ≥

2.1 Direction of Exergy Flow

19

Fig. 2.1 The heat transfer process from the ZLT, the FLT, and the SLT, and the exergy standpoint, when the environment temperature is close to the heat source temperature

Te ≥ Tc , as well as Te > Th , meaning that they can be both lower and higher than the environment temperature. At the top of the diagram, Te is shown to be within the limits of Th ≥ Te ≥ Tc , but it can change its position within said mathematically defined limits by attaining any value in the coordinates where the x axis signifies temperature. This allows supplementing the thermodynamic system represented by said classical diagram with data about the exergy flows that take place in it. Notably, this diagram does not show the wall of the building, and the process of heat transfer as such is not related to the outside air temperature, i.e. Tc = Te or Th = Te . Furthermore, in the case of the ZLT, the FLT, and the SLT, the Te is not a state parameter that affects the indicators of the heat transfer process. In terms of the FLT, we have a constant heat flow Q˙ ch = const, and with the SLT, Sch irr = const. The exergy analysis of the process features a RET, which is the outdoor air temperature Te , which is shown as variable on the x axis. In the case at hand, usingthe Carnot    factor, the exergy flow triggered by the temperature Th would be E˙ h = Q˙ ch  1 − TThe ,     and the exergy flow triggered by the temperature Tc , E˙ c = Q˙ ch  1 − TTec , meaning that the constant heat flow is multiplied by the absolute values of the Carnot factor ηC = 1 − TTei that mirrors the subject temperatures Ti . The process exergy balance equation is E˙ h = E˙ c + L˙ ch . The dependence of these three terms of the equation on

20

2 Theoretical Foundation of the Exergy Analysis Methodology …

Te is show in the exergy part of the diagram. In this interpretation of Fig. 2.1, the SLT links the flow of exergy destroyed in the process, which is straight-line dependant on Te and is always positive: L˙ ch = Te  S˙ch irr ≥ 0. Within the Th ≥ Te ≥ Tc temperature range, the exergy flows triggered by both temperatures are assigned to the system E˙ h+ and E˙ c+ , which is marked with the upper index ‘+’. There is no resultant exergy flow leaving the system here. We have the case of E˙ h+ + E˙ c+ = L˙ ch . This interpretation of how the direction of exergy flows in the steady heat transfer process triggered by temperatures depends on the location of the T e vis-à-vis these temperatures. In other words, the two exergy flows describing the process of heat transfer are always aligned with the environment temperature and follow its shift. It should be reminded that we are talking about steady heat transfer at constant temperatures triggering the heat flow. There can also be a different kind of interpretation. When the Te equals any of these temperatures (Te = Tc or Te = Th ), the relevant exergy flows are 0. In this case, no supply of exergy is needed to maintain one of the temperatures, because that is the temperature of the environment. In the rest of the cases, exergy has to be supplied to the system to maintain the temperatures of Th and Tc that trigger the heat transfer process (to compensate exergy flows). The known diagram is enhanced with the values of the terms of this equation within the shifting range of the temperature Te from Te < Tc to Te > Th on the left, ant at temperatures that approximate those that actually shape the energy needs of buildings, such as T h = 20 °C, T c = −20 °C. Expanded to the thermodynamically fringe conditions from Te = 0 K to Te  Th , this case is showcased in Fig. 2.2. In it, the exergy flow data from Fig. 2.1 are highlighted with a dotted line. When the Te amounts to any of these temperatures (Te = Th or Te = Tc ), the relevant exergy flows are 0. Exergy destroyed is proportionate to the Te and is always positive, because entropy generated and the absolute temperature are always positive. If the thermodynamic analysis algorithm of the system or its subsystems within the broad Te range points to a negative value of exergy destroyed; hence, regardless of what the correct mathematics might be, the thermodynamic Fig. 2.2 Terms of the exergy balance in the heat transfer process within the broad Te range

2.1 Direction of Exergy Flow

21

assumptions still need fixing. In other words, the master and the servant are yet to reach an understanding.

2.2 Exergy Efficiency of the Heat Transfer Process One important attribute of the exergy analysis of the thermodynamic process is the thermodynamic (exergy) efficiency of the process as such. In the most general case, it is the ratio between the (resultant) exergy leaving the system and the exergy supplied, L˙ h E˙ − ηex = E˙ + or ηex = 1 − E˙ +c . With the steady heat transfer process taking place in the thermodynamic system portrayed in Fig. 2.1 (when T h = 20 °C, and T c = − 20 °C), the character of the shift of this indicator within the temperature range of 30 ◦ C ≥ Te ≥ −30 ◦ C is shown in Fig. 2.3 (on the left), and with this range expanded to purely theoretical due to thermodynamic interpretation, the indicator is shown in Fig. 2.3 (on the right). we can see that the dependence has its highest value, ηex = 1, and its lowest value, ηex = 0; besides, in the general case, it is asymmetrical towards 0 °C (the T h = 20 °C, T c = −20 °C average). The highest value is always aligned with T e = 0 K. The minimum of ηex = 0 is always within the range of Te = Th and Te = Tc , which in this case is T h = 20 °C, T c = −20 °C. The case of E˙ h+ = E˙ c+ (the point of intersection of the values of the exergy flows in Fig. 2.1) is not quantitatively symmetrical vis-à-vis temperatures (in this case, it does not amount to 0 °C), and instead constitutes the so-called harmonised average of h Tc and differs from one combination of these temperatures to another. Te,E h =Ec = T2Th +T c In the numeric case at hand, it is −1.46 °C.

Fig. 2.3 The thermodynamic (exergy) efficiency of the heat transfer process between temperatures the T h = 20 °C, T c = −20 °C with the ambient temperature shifting: (on the left) 30 ◦ C ≥ Te ≥ −30 ◦ C, (on the right) from T e = 0 K and up

22

2 Theoretical Foundation of the Exergy Analysis Methodology …

The numeric case of the heat transfer process testifies that this kind of interpretation of the direction of exergy flows matches the underlying axioms of thermodynamic (exergy) analysis): 1. 2. 3.

Exergy destroyed is always L˙ ≥ 0 and with  S˙irr = const, they are proportionate to Te . The exergy efficiency of the system and the process taking place in it is 0 ≤ ηex ≤ 1. The direction of the heat exergy flow is from the heat source towards the environment.

Our goal is making an objective, universal thermodynamic assessment of this and any other process. Prepared and tested in this manner, the element solution can be applied with a high degree of reliability for the purposes of thermodynamic (exergy) analysis of the HVAC system energy transformation chain.

2.3 Energy—Enthalpy, Exergy—Coenthalpy It is thermodynamically accepted that the flows of energy and mass are generated by a different in potentials. For instance, a difference in pressures triggers mass flows that travel from a higher potential towards a lower potential—pressure. It is a known fact that the amount of thermomechanical exergy in energy is first of all affected by the difference between the potential of the medium that carries the energy and that of the reference environment (temperatures, pressures, concentrations). For the purposes of this book, it has been assumed that no exergy generated by the difference in the potentials of pressures or concentrations exists, or that it is not measured. In that case, the second temperature potential of the exergy generated by the temperatures of the heat transfer media of the heat recovery exchanger is the ambient temperature Te . It is also the state of the reference environment for the purposes of exergy analysis, yet it is unique in a way that it is variable in the BTS analysis.

2.3.1 Coenthalpy as a Parameter of State in Exergy Transfer At the FTL level, the intensity of heat transfer and the potential that generates it consist of the enthalpies or temperatures of the heat transfer media and the difference thereof. In the exergy analysis covering the FTL and the STL, according to (Borel 1984; Borel and Favrat 2010), this potential (and a state parameter at the same time) is coenthalpy. Thermodynamically speaking, the historical system state parameters are temperature (T ) and pressure (P). They are definitely enough to describe the state of a simple thermodynamic system (such as a close-ended ideal gas system). Volume (V ) and internal energy (u) augment these two attributes of state. The way it is

2.3 Energy—Enthalpy, Exergy—Coenthalpy

23

postulated in (Moran and Shapiro 2006), ‘in many thermodynamic analyses the sum u i + Pi vi occurs so frequently in subsequent discussions, it is convenient to give the combination a name, enthalpy’. In short, enthalpy is the energy potential of a system (both close- and open-ended). It is a system parameter derived from the combination of the state parameters u, v, and P. We can compare the origins of enthalpy with L. Borel’s understanding and suggestion of the concept of coenthalpy k. He gave this name to the combination of state parameters h, Te , and s, considering it as the potential of the system’s exergy. Enthalpy and coenthalpy are easier to understand when they are applied in field (Borel et al. 2012). In this book, we expand the field of application of coenthalpy as a state parameter to resolve the problems applied by describing the objective methodology of assessment of exergy of the ventilation units of an air conditioning system. Then, when referred to purely as a parameter of the state of the system—the temperature Ti , the coenthalpy of the state i of the heat transfer medium (its mass flow rate) is calculated under the following formula: ki = h i − Te si ,

(2.1)

where h i is the enthalpy of the heat transfer medium and its mass flow rate, kJ/kg; si is its entropy, kJ/kg K; Te is the thermodynamic reference environment (outside air) temperature (RET) for the purposes of exergy analysis, K. Traditionally, the comparative exergy flow used (estimated and analysed) for the purposes of exergy analysis would then be the one that occurs when the process moves from state 1 to state 2 e12 = k1 − k2 = (h 1 − h 2 ) − Te (s1 − s2 ),

(2.2)

the difference in coenthalpies clearly perceived as the potential that generates the flow of exergy. In terms of the reference environment, air as an ideal gas, enthalpy h i = c p Ti , Ti , kJ/kg K; the temperature of the environment Te and kJ/kg; entropy si = c p ln 273,15 air as the heat transfer medium Ti , K. Within the framework of this book, the thermodynamic reference environment for the purposes of exergy analysis is the temperature Te (RET). In that case, the relevant derivative state parameters that define the reference environment (the outside air surrounding the buildings) would be: Reference environment enthalpy for the ideal gas, h e = c p Te ; Reference environment entropy for the ideal gas, se = c p ln Reference environment coenthalpy generally

Te ; 273, 15

(2.3) (2.4)

24

2 Theoretical Foundation of the Exergy Analysis Methodology …

 ke = h e − Te se , or for ideal gas ke = Te c p 1 − ln

 Te . 273, 15

(2.5)

Furthermore, the coenthalpy of the state i of the heat transfer medium that has its temperatures directly affected by the properties of the ideal gas (its mass flow rate) for the ideal gas would be:  ki = c p

 Ti Ti − Te ln . 273, 15

(2.6)

The comparative exergy flow, assessed in terms of the surrounding air: ei = ki − ke = (h i − h e ) − Te (si − se ).

(2.7)

Again, we wish to note that the comparative flow of energy amounts to the difference in coenthalpies, just as the comparative flow of energy to the difference in enthalpies, and the comparative flow of heat to the difference in temperatures. This state parameter should be approached as a significant contributing factor to successfully balancing between the conventional thermodynamic analysis and exergy analysis. With the thermodynamic parameter of state, the size of exergy flow is defined by the difference in the potentials of that flow—the difference in the coenthalpies of states. The exergy flow has a clear-cut direction, going from the medium with a higher coenthalpy rating to the medium where the coenthalpy is lower. In a particular problem, the reference coenthalpy (REC) ke is always the lowest, its amount independent on the state of the heat transfer medium. Using the parameter of coenthalpy as well as the numeric and graphical interpretations of its shift is instrumental for the purposes of visualising and analysing the ongoing processes. Whilst moving straight to exergy flows without visualising the potentials that generate them first sometimes constructs the possibilities to observe the fine points of the process and to avoid mistakes. This is what happens when energy transformation processes take place at temperatures close to the environment. Among other things, that temperature shifts and is the RET for the purposes of exergy analysis. In each case, ke is a reference parameter in exergy analysis, plus it is always lower than (or sometimes equal to) any of the coenthalpies of the heat transfer medium involved in the process at hand. This is the key difference between the attribute ke and the state of the reference environment expressed as temperature, because Te can be lower and higher (such as in the case of ventilation) than any other temperature of the flows involved in the processes. If in the problem at hand this temperature is only lower or only higher than the temperatures of the heat transfer media, then this ke as a minimum reference attribute of exergy analysis becomes less relevant, because the coenthalpies of heat transfer media will always be higher. But, as we will see in the next problem, when the reference temperature intersects with at least one temperature of heat transfer media or falls between any two of them, this attribute becomes methodically important and unique.

2.3 Energy—Enthalpy, Exergy—Coenthalpy

25

As we will see in Chap. 3, the application of coenthalpy as the potential of exergy flow clearly allows addressing the aforesaid matter of the direction of exergy flow in steady heat transfer processes when the a REN is variable.

2.3.2 Energy and Entropy Balance of the Heat Exchanger Heat exchangers are important energy transformers within HVAC units. In Fig. 2.4, we can see diagrams of counter flow heat exchangers where the heat transfer process is given two different definitions. In the figure on the left we have heat transfer defined by the heat flow transferred and the input and output temperatures of the heat transfer media. The heat balance equation for this type of heat exchanger is as follows: The equation of the heat exchanger energy balance comparing the heat flows consumed and produced is as follows: Q˙ ch = M˙ h c ph (Th1 − Th2 ) = M˙ c c pc (Tc2 − Tc1 ) or Q˙ ch = M˙ h (h h1 − h h2 ) = M˙ c (h c2 − h c1 ). (2.8) The energy balance can be recorded by presenting and contrasting the heat transfer medium flows involved in the process as the input and output flows: Q˙ ch = M˙ h h h1 + M˙ c h c1 = M˙ h h h2 + M˙ c h c2 .

(2.9)

Assuming that M = Mh /Mc , these two cases can also be presented as follows: + = q− qch = M h h1 − M h h2 = h c2 − h c1 or qconsum pr od ,

(2.10)

+ − qch = M h h1 + h c1 = M h h2 + h c2 or qin = qout .

(2.11)

The upper indices show the inflow into (+) and the outflow from (−) the system. For the purposes of energy balance and analysis confined into its brackets this kind of twofold record would seem excessive, however in exergy analysis, the exergy flow pairs of ‘consumed–produced’ and ‘input–output’ are not always comparable.

Fig. 2.4 Diagram of the heat transfer process in an ideally insulated heat exchanger; state parameters

26

2 Theoretical Foundation of the Exergy Analysis Methodology …

In the second case (right), with flow entropies expressed as S˙i = M˙ i si , the entropy produced is measured as follows: h = S˙h1 + S˙c1 − S˙h2 − S˙c2 .  S˙c,irr

(2.12)

The expression of entropy in the heat transfer process is d S q = δ Q/T . For the purposes of this problem, we will assume that the temperatures follow straight-line variation, because otherwise questions that may be involved at later phases could overshadow the logic behind the solution. Ergo, the selected straight-line approach allows expressing the entropy produced as the difference between the average entropy of the cold heat transfer medium and that of the hot heat transfer medium:     1 Q˙ ch 1 Q˙ ch Q˙ h Q˙ h h (2.13) = + c − + c .  S˙c,irr 2 Tc1 Tc2 2 Th1 Th2 This result can already be linked to exergy analysis to find exergy destroyed, which is generally expressed as follows: h L˙ ch = Te  S˙c,irr ≥ 0.

(2.14)

Combining these formulas, the amount of exergy destroyed during the process in the case on the right can be expressed through the values of the Carnot factor ηCi = 1 − TTei as follows: L˙ ch

= E˙ h − E˙ c =

h1  h2

  c2  Te Te h 1− δ Q˙ c − 1− δ Q˙ ch . Th Tc

(2.15)

c1

A graphic interpretation of areas expressed as integrals for formula 2.15 is shown in Fig. 2.5. Fig. 2.5 Graphic expression of exergy destroyed in the heat exchanger of the process, L˙ ch = f (ηCi , Q˙ ch )

2.3 Energy—Enthalpy, Exergy—Coenthalpy

27

The calculation for the heat transfer media “c” in the figure above should be split in two, based on the two lines. Even if the deviation from the straight-line approach were greater, this method involving separate sections could still be applied to improve the accuracy of the calculation by using the Carnot factor for exergy estimations. The left-hand term of Eq. (2.15) shows the size of exergy flow supplied to the system, while its right-hand counterpart, the size of exergy flow acquired by the system. Notably, regardless of the positioning of the ηC = 0 value vis-à-vis the other ηCi (such as between the values of the hot and the cold heat transfer media), the exergy destroyed that defines this process will nonetheless amount to the area between the two curves (see Fig. 2.5). The choice of method to estimate exergy destroyed depends on the set of statedefining parameters that we have at our disposal. In case number one, there may be some problems with the differences in the reference states of entropies for different heat transfer media. Based on the obtained average of exergy destroyed, the comparison should involve units with a similar output rating. Still, we do not have a universal efficiency ratio that we could use for comparison purposes. In addition to  S˙irr or L˙ ch , determining exergy efficiency ηex also requires knowing the flow of exergy supplied to the system in the process at the very least. Variable RET has an impact on the exergy analysis procedures. Obviously, entropy  S˙irr produced at variable temperature Te does not change, and only the analysis outcomes pointing to it remain limited. As it was already demonstrated even when the heat flow is steady in terms of size and direction, with the RET shifting, the exergy flow changes both in its size and direction. When we can apply ideal gas formulas to estimate state parameters of heat transfer media (which is very often the case for air inside HVAC systems), the necessary difference in entropies can be found as follows: s12 = c p ln

T1 T2

(2.16)

or s12 = c p

T12 − T22 . 2T1 T2

(2.17)

The origin of case number two has to do with the application of the Carnot factor to determine the amount of exergy in the heat flow. Within the T1 /T2 range of 2 to 0.5 (which largely covers HVAC technologies), the results obtained with the two formulas are very similar.

28

2 Theoretical Foundation of the Exergy Analysis Methodology …

2.4 Exergy Efficiency and Destroyed Exergy 2.4.1 Exergy Balance of the Heat Exchanger The formulation of exergy balance equations for the heat exchanger shown in Fig. 2.4 is similar to that of the energy balance in (2.10) and (2.11). The indices applied in Fig. 2.4 will be used with the comparative exergy flows ei and coenthalpies ki . The exergy balance expressed with the components of the ‘consumed–produced’ exergy flows is as follows: + ˙ = E˙ − E˙ consum pr od + L  ,

(2.18)

and expressed with comparative exergy flows + − − + − M˙ h eh2 = M˙ c ec2 − M˙ c ec1 + L. M˙ h eh1

(2.19)

Expressed with the state parameter—coenthalpies as per Eq. 2.2 and M = Mh /Mc , econsum M = M(kh1 − kh2 ) e pr od M = kc2 − kc1 .

(2.20)

The exergy balance expressed with the components of the ‘input–output’ exergy flows is as follows: + − = E˙ out + L˙  , E˙ in

(2.21)

and expressed with comparative exergy flows + + − − + M˙ h eh1 = M˙ c ec2 + M˙ h eh2 + L. M˙ c ec1

(2.22)

Expressed with the state parameter—coenthalpies and M = Mh /Mc ,  ein M = kc1 + Mkh1 − 1 + M ke ,

(2.23)

 − eout = kc2 + Mkh2 − 1 + M ke . M

(2.24)

It can be observed that in this case the expression of the terms of the balance includes the reference coenthalpy ke , which is determined under Eq. 2.5. Compared to energy balances (Eqs. 2.10 and 2.11), where the values of energy flows are identical, the exergies of ‘consumed–produced’ and ‘input–output’ have different values. Exergy destroyed in the heat transfer process in question is as follows:

2.4 Exergy Efficiency and Destroyed Exergy + − + − E˙ out = E˙ consum − E˙ − L˙  = E˙ in pr od ,

29

(2.25)

Expressed with comparative exergy flows, + + − − + − − + + M˙ h eh1 − M˙ c ec2 − M˙ h eh2 = M˙ h eh1 − M˙ h eh2 − M˙ c ec2 + M˙ c ec1 . L˙  = M˙ c ec1 (2.26)

It follows from this equation and M = Mh /Mc , that  + − − + = ec2 M eh1 − eh2 − ec1 + l M .

(2.27)

Expressed with the state parameter—coenthalpies as per Eq. 2.7 and M = Mh /Mc , l M = M(kh1 − kh2 ) − (kc2 − kc1 ).

(2.28)

With identical heat transfer medium flow rates, Mh = Mc or M = 1 could be formulated as follows: l = (kh1 − kh2 ) − (kc2 − kc1 ).

(2.29)

Exergy destroyed in heat transfer depends on the coenthalpies of the original states of the heat transfer media, which under Eq. 2.6 are affected by the RET, or Te , which is variable by choice.

2.4.2 Exergy Efficiency This book focuses on the exergy efficiency of buildings. Two cases of exergy balance + + ) or incoming ( E˙ in ) exergy flows were demonusing the sum of consumed ( E˙ consum strated. As a result, as far as exergy efficiency is concerned, we are able to study two cases: • Functional (practical, consumed–produced, rational, or desirable) exergy efficiency defined as the ratio between exergy created (produced) and supplied (consumed) in the system; • Universal (input–output, forced, general, or total) exergy efficiency defined as the ratio of all outgoing and incoming exergy flows. Therefore, the differences between the universal and the functional efficiencies require individual expressions of efficiency to be assessed, considering the variable reference conditions. Exergy efficiency formulas for calculating the universal and the functional efficiency including the above flow indicators as per above are presented below.

30

2 Theoretical Foundation of the Exergy Analysis Methodology …

Efficiencies first should be expressed for the simplified energy transformer with two equal flow rates of the same material M˙ h = M˙ c (an ideally insulated heat exchanger) as shown in Fig. 2.4 M˙ h = M˙ c . Exergy destroyed: + + − + − + − − e−pr od = ein − eout = ec1 − ec2 + eh1 − eh2 . l = econsum

(2.30)

Universal exergy efficiency: − − − + eh2 ec2 eout l = + + + =1− + + . ein ec1 + eh1 ec1 + eh1

ηU =

(2.31)

Functional exergy efficiency: ηF =

e−pr od + econsum

=

− + − ec1 ec2 l + − =1− + − . eh1 − eh2 eh1 − eh2

(2.32)

In a more general case of heat exchangers, where heat transfer medium flow rates are not equal ( M˙ c = M˙ h ), and in this case, we have the ratio between these mass flow rates M in the equations. Exergy destroyed:  + − − + − ec2 − eh2 + ec1 . l M = M eh1

(2.33)

Universal exergy efficiency: ηU =

− − − + Meh2 ec2 eout l = 1 − + M + . + = + + ein ec1 + Meh1 ec1 + Meh1

(2.34)

When expressed with heat transfer medium state parameters—coenthalpies: − eout M

ηU =

ein M

 kc2 + Mkh2 − 1 + M ke =  . kc1 + Mkh1 − 1 + M ke

(2.35)

When M˙ c = M˙ h (such as in the case of the HRE): ηU =

− eout kc2 + kh2 − 2ke = . ein kc1 + kh1 − 2ke

(2.36)

Functional exergy efficiency: ηF =

e−pr od + econsum

=

− − e+ ec2 l  + c1− = 1 −  + M − . M eh1 − eh2 M eh1 − eh2

(2.37)

2.4 Exergy Efficiency and Destroyed Exergy

31

When expressed with heat transfer medium state parameters—coenthalpies: ηF =

e−pr od M + econsum M

=

kc2 − kc1 M(kh1 − kh2 )

.

(2.38)

When M˙ c = M˙ h (such as in the case of the HRE): ηF =

e−pr od + econsum

=

kc2 − kc1 . kh1 − kh2

(2.39)

In both of these cases, exergy destroyed is proven to be thermodynamically incapable of depending on the constitution of the exergy efficiency chosen for the analysis.

2.5 Air Handling Unit as a Thermodynamic System To ensure the correct living and working conditions in buildings, a thermal comfort has to be achieved on the premises by heating, cooling, and conditioning the air supplied. Modern buildings achieve this through the use of the air handling (ventilation) unit (AHU). In the broader sense of functionality, the AHU is a multi-component engineering unit used for the purposes of indoor ventilation by purifying, heating, cooling, humidifying, or drying the air supplied. At the first level of dissection, it is made up of air transportation and heating–cooling components. The principal diagram of energy and mass flows of the AHU is shown in Fig. 2.6. The processes taking place in the thermodynamic system delineated with the dotted line as well as the units that bring them to fruition can be different. These are fans, HRE (heat

Fig. 2.6 Diagram of mass and energy flows of the air handling unit

32

2 Theoretical Foundation of the Exergy Analysis Methodology …

recovery exchanger), air heat exchangers, electric motors, air purification filters, automated control equipment. When necessary, the unit can be kitted with additional components such as the air cooler, humidifier, an additional heat exchanger, and so on. Still, the basic function of the AHU is to supply the room with the necessary quantity of fresh air that satisfies the necessary parameters (temperature being parameter number one), which are shown in the principal diagram.

2.5.1 The Technological Diagrams of the Air Handling Unit Under Analysis Exergy is a thermodynamic property that depends on the state of the system under analysis and on the environment, the so-called reference environment, or the reference temperature (RET) of thermal systems. Determining exergy efficiency becomes problematic when RETs differ and can be lower, higher than, or equal to the temperatures of working fluids, as it is the case with the diagrams of the air handling unit (AHU). The characteristic technological examples of the AHU of the HVAC system are shown in Fig. 2.7a–d. In this book, the action of the individual AHU components shown in the diagrams is explained both in terms of the analysis conducted, and the methodology presented, avoid textbook or online explanations and only sticking to the equations necessary for the study at hand and possibly a brief commentary thereon. For methodology demonstration purposes, this book offers a thermodynamic analysis of processes of energy transformation in these technologically variegated AHUs. In the AHU diagrams shown here, the energy transformers are the HRE and an auxiliary unit (a heat exchanger: a coil unit—water-to-air heat exchanger (WAH), a heat pump (HP), and so on) that provides the air with the necessary amount of heat following the process that takes place within the HRE. Air transportation is served by two fans (Fs and Fe ). The possible heat exchanger options in these AHU diagrams are as follows: water-to-air heat exchanger (WAH) for diagram a and b, a heat recovery exchanger (HRE) for diagram b and d, and, with an HP present (c and d), a condenser (CN) and an evaporator (EV). Inside the heat pump, they are supplemented by a compressor (CM) and a throttle valve (TV). The heat transfer media bound in the AHU energy transformation processes are the air needed for ventilation, the water in the water-to-air heat exchanger, the refrigerant in the heat pump. This latter unit consists of a condenser and an evaporator that are connected by a compressor and a throttle valve to run in the reverse cycle. The interaction of these components under the characteristic AHU usage conditions is analysed in this book. Within the framework of this study, characteristic usage conditions are perceived as the states of the outdoor air and the air inside the ventilated room and the HP refrigerant that are primarily defined by temperatures and other

2.5 Air Handling Unit as a Thermodynamic System

33

Fig. 2.7 Technological diagrams of the ventilation AHU: a only WAH, b WAH-HRE, c only HP, d HP-HRE

34

2 Theoretical Foundation of the Exergy Analysis Methodology …

ancillary or derivative parameters (such as enthalpies, entropies, coenthalpies, pressures, and so on). For the purposes of indexation of state parameters while discussing AHU operation, it is assumed that refrigerant parameters are indexed with digits, and air parameters, with letters. This book presents only equations that are necessary for the thermodynamic analysis of the AHU, as well as brief commentary on them. When it comes to any kind of technological makeup, the primary variable that is independent of the AHU energy transformation processes is the air temperature [reference temperature (RET)], Te and the rather constant rather than variable air flow rate needed for ventilation, M˙ V and the temperature of air inside (supplied to and extracted from) the room, TR . For the purposes of the book, these two indicators are considered to be constant. The AHU and the chosen combinations of its components must ensure a specific heat flow of the fresh air to be used for the ventilation of the room: Q˙ AHU = M˙ V c pa (TR − Te )

(2.40)

q AHU = h R − h e .

(2.41)

or

One of the characteristics is that this heat flow is always in shift based on the environment temperature that depends on the local climatic conditions. As a result, the outcome of thermodynamic analysis depends on the outdoor temperature at a specific location, something that must have a reflection in the calculation methodology. For the purposes of this book, the following AHU efficiency indicators were adopted: coefficient of performance (COP) and exergy efficiency ηex . The AHU coefficient of performance is limited to BTS and in essence corresponds to the widely accepted concept of heat pump, considering the sameness of electricity and exergy: C O PAHU =

Q˙ AHU , E˙ + AHU

(2.42)

where E˙ + AHU is the flow of exergy supplied outside of the AHU as a thermodynamic system both in the form of work and heat. It can be used by fans, the compressor, and additional heat exchangers or coolers that use external heat transfer media or electricity and were left outside of the diagram. This COP is slightly different from the AHU COPs that are becoming widespread in engineering practice and do not involve any electricity in the denominator. Yes, it constitutes a pure flow of exergy, but other potential energy inputs (such as coolness and heat) should be assessed at their thermodynamic value (exergy). A characteristic indicator of the heat pump compressor is its isentropic efficiency εiC , while fans that have to overcome losses of pressure P, are defined by the power consumption coefficient ε F . Numerically speaking, the properties of

2.5 Air Handling Unit as a Thermodynamic System

35

the chosen refrigerant are important, yet it is assumed that their effect on the AHU processes is in no way unique compared to other instances of a reverse cycle. The AHU operates within different, albeit narrow, ranges of temperatures and the thermodynamic processes of all heat exchangers (WAH, HRE, HP condenser or evaporator) are similar. The energy balance equations of these heat exchangers are presented below. The specific thermal energy q ± = Q˙ ± / M˙ V and the specific exergy e± = E˙ ± / M˙ V will later be used in the calculations. The plus sign (+) in the upper index shows that energy (or exergy) is supplied to the system, while the minus sign (−) indicates that the direction of the energy (or exergy) flow transcends the limits of the system. Another AHU efficiency indicator is its exergy efficiency that is addressed below. In the most general case (of the AHU as a whole or its components), this would be the ratio between the (resultant) exergy that leaves the system in question, E˙ − and the exergy supplied to it, E˙ + : ηex =

E˙ − E˙ +

or

ηex = 1 −

L˙ ch , E˙ +

(2.43)

where L˙ ch is the exergy destroyed in the process. In the following section, examples of these two heat exchangers will be used to demonstrate how the methodology that this book suggests can be applied to AHU exergy analysis, when REN is the environment temperature that varies within the limits of specific climatic conditions.

2.5.2 Heat Exchangers of the Air Handling Unit Follow energy (FLT) balance equations for AHU heat exchangers as well as the compressor and the throttle valve that will be used to introduce the methodology and numeric cases of exergy analysis in the subsequent chapters. In the AHU diagrams presented here we have the following heat exchangers: • a water-to-air heat exchanger (WAH) and possibly an electric air heat exchanger in diagram a and b; • a heat recovery exchanger (HRE) in diagram b and d; • a condenser (CN) and evaporator (EV) in the heat pump in diagram c and d. In the case of the heat pump, there is also a compressor and a throttle valve involved in the transformation of energy. At the FLT level, energy transformation inside heat exchangers is measured with an equation of heat transfer from the hotter heat transfer medium, h to the cooler, c: Q˙ ch = AU Tln m ,

(2.44)

36

2 Theoretical Foundation of the Exergy Analysis Methodology …

Fig. 2.8 Diagrams of energy calculation and energy balances of AHU components. is the water flow rate, kg/s; is the flow rate of air used in ventilation; is the refrigerant flow rate, kg/s; is the enthalpy, kJ/kg

as well as a heat balance equation: Q˙ ch = M˙ c c pc (Tc1 − Tc2 ) = M˙ h c ph (Th2 − Th1 ).

(2.45)

The heat exchangers in the AHU are the heat recovery exchanger (HRE) and the water-to-air heat exchanger (WAH). Their diagrams are presented in Fig. 2.8, which also shows their energy balance equations expressed as enthalpies. M˙ W (h Win − h Wout ) = M˙ A (h K − h c ).

(2.46)

M˙ V (h h − h W ) = M˙ V (h c − h e ).

(2.47)

M˙ f (h 1 − h 5 ) = M˙ V (h E − h W ).

(2.48)

M˙ f h 4 = M˙ f h 5 .

(2.49)

M˙ f (h 2 − h 4 ) = M˙ V (h K − h c ).

(2.50)

2.5 Air Handling Unit as a Thermodynamic System

37

The energy balance equation for the WAH is as follows: Q˙ W AH = M˙ W c pW (TW in − TW out ) = M˙ V c pa (TK − Tc ) or M˙ W qW AH = (h W in − h W out ) = h K − h c . M˙ V

(2.51)

HRE energy flows do not appear in Fig. 2.7, because they do not go outside the boundaries of the thermodynamic systems. Nonetheless, the HRE is a key AHU component. The HRE energy balance equation is as follows: Q˙ H R E = M˙ V c pa (Th − Tw ) = M˙ V c pa (Tc − Te ) or q H R E = h h − h w = h c − h e . (2.52) Energy balance in the condenser: M˙ f Q˙ C N = M˙ f (h 2 − h 4 ) = M˙ V c pa (TK − Tc ) or qC N = (h 2 − h 4 ) = h c − h e . M˙ V (2.53) Energy balance in the evaporator: M˙ f Q˙ E V = M˙ f (h 1 − h 5 ) = M˙ V c pa (Tw − TE ) or q E V = (h 1 − h 5 ) = h w − h E . M˙ V (2.54) The efficiency indicators that match the technical level of individual components are rather stable. These include the HRE temperature efficiency, too. The HRE is a specific heat exchanger. In it, heat transfer takes place between air flows that have the same rates, with exhaust air heating the air that is supplied to replace it. In engineering practice, the temperature efficiency of the HRE between the hot (h) and the cold (c) air flows that have the same rate is generally estimated with the following formulas: εT =

Th1 − Th2 Th1 − Tc1

(2.55a)

εT =

Tc2 − Tc1 . Th1 − Tc1

(2.55b)

or

Notably, in the AHU technological diagrams presented here, air enters the HRE at outside temperature Te = Tc1 ; in that case, the appropriate indicators used in the

38

2 Theoretical Foundation of the Exergy Analysis Methodology …

equations change to reflect the data of Fig. 2.8: εT =

Th − Tw Th − Te

(2.56a)

εT =

Tc − Te . Th − Te

(2.56b)

or

The following presentation and numeric examples of the exergy analysis methodology deal with more generic cases (as introduced by formulas 2.55a and 2.55b).

2.5.3 A Preliminary Comparison of Air Handling Unit Diagrams The process of air handling can be briefly described under diagram b as follows. The amount of air necessary for ventilation, M˙ V is supplied to and extracted from the room at temperature TR . Air transportation is served by two—supply and exhaust— fans (Fs and Fe ). Air taken from the outside at temperature Te enters the HRE where it is heated from Te to Tc . Then this air is heated to TK in the AHU and is later heated some more in the supply fan (Fs ) and then is supplied to the room at temperature TR . Air is exhausted from the room at temperature TR and is heated to Th in the exhaust fan, and then releases heat to the air supplied in the HRE by cooling down to Tw . The air is then released at temperature Tw = TE . A process that is more connected with the WAH could be described as follows. Water for this heat exchanger can be handled in the building’s boiler room or supplied from the district heating system. This heat exchanger can be replaced with an electric heat exchanger or a heat pump (HP) as shown in diagram c or d. Air is then heated to temperature TK in the HP condenser (CN), then heated some more in the supply fan (Fs ) and supplied to the room at temperature TR . Air is exhausted from the room at temperature TR and is heated to Th in the exhaust fan, and the HRE releases heat to the air supplied by cooling down to Tw . The air then continues to release heat in the HP evaporator (EV) by cooling down to TE and is then exhausted. A process that more connected with the HP can be described as follows. The HP runs in the reverse cycle of compression–expansion of refrigerant vapour. This unit heats outside air to the required temperature in the condenser (CN), and the Fs supplies the air to the room after giving it a little bit of heat. In the evaporator (EV), the refrigerant evaporates owing to the relatively high temperature of exhaust air Tw . Therefore, in addition to heat exchangers, we also have the compressor (CM) and the throttle valve (TV) as energy transformers in the heat pump. The transformation of the air and refrigerant temperatures in the AHU with an HP (diagram c and d) is shown in more detail in Figs. 2.9 and 2.10. The HP circuit

2.5 Air Handling Unit as a Thermodynamic System

39

Fig. 2.9 Process constituting the heat pump cycle in the P–h diagram of the refrigerant

filled with a refrigerant is home to the processes that constitute its cycle as shown in diagram P–h of Fig. 2.9. Inside the evaporator, the refrigerant boils, evaporates, and may be overheated by several degrees under isobaric pressure PE V and at isothermal temperature TE V i zot , yet it can stay in its dry satiated state T1 . The refrigerant is then compressed inside the compressor. The refrigerant is pressurised to T2 , the state of vapour overheated by pressure PC N . This compression takes place a little to the right of the ideal isentropic process, based on the CM’s internal isentropic efficiency εiC . The refrigerant’s temperature rises to dozens of °C. The refrigerant in its overheated vapour state then enters the CN, and during the isobaric process under pressure PC N releases the heat flow required to heat the air from Tc to TK . At the beginning of the CN, the refrigerant cools down to the dry satiated vapour state T3 . Later on, it condenses during the isobaric–isothermal process at temperature TC N i zot . The condensation can continue to a boiling state, the satiated fluid state T4 (as it is in the case at hand), or the refrigerant condensate may get ‘subcooled’. In this last case, the refrigerant’s temperature is several degrees below TC N i zot . After that, as it expands in an isenthalpic manner from PC N to PE V in the TV, the refrigerant cools down to the temperature of the EV isotherm, T5 = T1 . The process of air heating and cooling under diagram d is as follows. The amount of air necessary for ventilation, M˙ V is supplied to and extracted from the room at temperature TR . Outdoor air at temperature Te enters the HRE, where it is heated from Te to Tc . This air is then heated to temperature TK in the HP condenser, then

40

2 Theoretical Foundation of the Exergy Analysis Methodology …

Fig. 2.10 The transformation diagrams of air and refrigerant state in the ventilation AHU: top—with integrated HP (diagram c in Fig. 2.7); bottom—with HP and HRE (diagram d in Fig. 2.7)

heated some more in the supply fan and is supplied to the room at temperature TR . Heated to temperature Th in the exhaust fan, the exhaust air releases heat to the supply air in the HRE by cooling down to Tw . The air then continues to release heat in the HP evaporator by cooling down to TE and is then exhausted. In diagram (c), the air heating and cooling process is less intricate. There is no HRE here, and the outdoor air enters the heat pump condenser, and the room air, the evaporator directly. The main difference between the heat pumps used in diagram c and d for the purposes of accomplishing the same task of air handling (with the amount of air and its outdoor and room temperatures identical) is their power output. In diagram d, part of the air heating task will be performed by the HRE, hence the power output of the condenser will be lower by an appropriate amount. The power output of the evaporator and the compressor will in turn be lower. This is the right moment for a reminder that the HRE virtually requires no external power supply for the system to work. Figure 2.10 shows a diagram of the shift in the air and refrigerant temperatures for the identical air heating and cooling task that these two cases are set to achieve. The ordinate axis shows the numeric values of the temperatures, the abscise axis

2.5 Air Handling Unit as a Thermodynamic System

41

shows power outputs. The power outputs are based on proportions among real data without specifying their exact value. The amount of the air heating power output covered by the HRE directly depends on its efficiency as measured with Eqs. 2.56a and 2.56b. As a result, the power output of the heat pump can be reduced several times. The situation with the distribution of thermal power outputs in diagrams a and b is similar. Here, the power output of the WAH or a substitute electrical air heat exchanger is reduced on the basis of the possibilities that the HRE has to offer. The exergy analysis of these diagrams is described in more detail in Chap. 5.

2.6 Summary of This Chapter The rapid expansion of innovation in the field of low-exergy building systems requires new thermodynamically accepted analytical descriptions to be able to analyse the processes of exergy transformation that are taking place in the chain of HVAC systems. The availability of this exergy analysis would improve the reliability of system design and optimal management algorithms that would allow obtaining the target result of the minimum amount of exergy destruction. HVAC equipment is dominated by heat transfer processes that can be largely considered quasi-stationary for the purposes of the analysis of their efficiency. Notably, the processes that trigger these processes are relatively close to the varying environment temperature—the RET for exergy analysis purposes. It is important to understand that when at least two of the temperatures that generating a stationary heat flow are constant, the exergy flows that describe that heat transfer and are related to each temperature will always be aligned with the environment temperature and will follow its shift. Therefore, exergy flow can change both in its direction and in its size, when the temperatures triggering the transmission of heat and the heat flow as such are constant. The application of coenthalpy as a thermodynamic state parameter and the direct potential of exergy flow as well as the numeric and graphic interpretations of its transformation are instrumental for the purposes of analysing the ongoing processes. Direct analysis of exergy flows without visualising the potentials that generate them at varying RET reduces the possibilities to observe the fine points of the process of energy transformation, and the aforesaid changes in the direction of the exergy flow first and foremost. The main energy transformers in the air handling unit are heat (recovery) exchangers, water-to-air or electrical heat exchangers, heat pump condensers, and evaporators. The temperatures of heat transfer media or refrigerants inside them can be higher or lower than, or equal to the constantly shifting environment temperature; ergo, the RET. Even the temperature of the fluid that passes the same unit at any given time can demonstrate all three of the above states at different locations. As it was already mentioned, this determines the direction and size of exergy flow.

42

2 Theoretical Foundation of the Exergy Analysis Methodology …

As always, the underlying principle is that regardless of the size of the thermodynamic system, the exergy efficiency of the process of energy transformation in the results of the application of exergy analysis lies within the limits of 0 and 1, and the amount of exergy destroyed in the actual process can only be above zero.

Chapter 3

Exergy Analysis of the Heat Recovery Exchanger of the Air Handling Unit

The material presented in this chapter serves two purposes. As far as technology and efficiency is concerned, the HRE is an important and potentially the main energy transformer in the AHU, generating around 50–80% of the unit’s heat flow. On the FLT level, the temperature effectiveness that defines its efficiency ideally should be as high and stable as possible within the range of annual variation of the environment temperature. It is the number one task of HRE developers and the main expectation of the users. From the methodological standpoint of exergy analysis, the HRE was instrumental for the authors to be able to use the concept of the shift in the exergy flow direction, which was introduced in Chap. 2, and the mechanism of developing its algorithm when the variable environment temperature is also the REN. It changes its position against the temperatures of the air intended for ventilation and the air used and can be above, below, or equal to these temperatures, or all of the above at the same time in a specific HRE. This characteristic merits some attention for the purposes of HRE exergy analysis, because such reciprocal temperature positions take up a significant part of the HRE, HVAC system operation during a year. This can be used for the purposes of determining the potential for improving exergy efficiency in the process of designing HVAC systems and implementing controls of their exergy-optimal operation. On top of that, for the purposes of this work, HRE exergy analysis that involves determining the exergy efficiency of the process taking place within the HRE and the amount of exergy destroyed in it is done with exergy flows expressed both with the Carnot factor and with coenthalpies. The state parameter of coenthalpy is the direct potential of exergy flow that is not yet properly dominant in the process of exergy analysis. Both methods reinforce the reliability of the methodology and the results of each other. A special emphasis is placed on the calculations, cases, and qualities of the universal and the functional exergy efficiency.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 V. Martinaitis et al., Exergy Analysis of the Air Handling Unit at Variable Reference Temperature, https://doi.org/10.1007/978-3-030-97841-9_3

43

44

3 Exergy Analysis of the Heat Recovery Exchanger of the Air …

3.1 When Exergy Flows Are Calculated with the Carnot Factor The problem of the thermodynamic (exergy) analysis based on the FLT and the SLT is solved for the heat recovery exchanger that has its diagram presented in Fig. 3.1. This heat exchanger has two heat transfer media with the same physical properties (dry air) and the same flowrate, meaning that the capacity flowrates of the heat transfer media are the same on both sides of the heat transfer surface, M˙ h c ph = M˙ c c pc . The heat balance equation of this heat exchanger under the FLT is: M˙ h c ph (Th1 − Th2 ) = M˙ c c pc (Tc2 − Tc1 ) = Q˙ H R E .

(3.1)

It is assumed that the heat flow transferred at the beginning of the heat exchanger (on the side where the temperatures of both mass flowrates, Th1 and Tc2 , are the highest—the ‘beginning’) amounts 0, and at the end of the heat exchanger (where the temperatures of both mass flowrates, Th1 and Tc2 , are the lowest—the ‘end’), the heat flow transferred reaches the entire amount transferred, Q˙ F . With any heat flow transferred, heat exchanger temperatures can be calculated with the formulas ˙ ˙ ˙ Thi = Th1 −(Th1 −Th2 ) Q˙ Q i and Tci = Tc2 −(Tc2 −Tc1 ) Q˙ Q i , or with Q˙ Q i = Q˙ i , and H RE

H RE

H RE

we would have Tci = Tc1 +(Tc1 −Tc2 )(1− Q˙ i ). As it was already mentioned, with the heat transfer medium of the same physical properties and the same flow rate, the ratio between temperatures is reduced to Th1 − Th2 = Tc2 − Tc1 or Th1 − Tc2 = Th2 − Tc1 . The thermodynamic analysis of heat exchangers addresses the general case when the temperature of the air entering the heat exchanger is not the environment temperature, i.e. Te = Tc1 . Of course, the case of these two temperatures being equal can happen quite often in the engineering practice and would involve the outdoor—ambient, environment—air supplied to the heat exchanger. For the purposes of heat exchanger exergy analysis, the usual and classical case would be when Te = const  Th1 , Tc1 , meaning that when all of the heat exchanger temperatures are considerably higher than the environment (reference) temperature, which assumed to be constant. The dependency of the above heat transfer medium temperatures and the heat flow transferred by them is shown in Fig. 3.2, together with the environment temperature Te . The thermal exergy released by the heating heat transfer medium to the system is: Fig. 3.1 A heat exchanger with comparable mass flowrates

3.1 When Exergy Flows Are Calculated with the Carnot Factor

45

Fig. 3.2 The shift in the heat exchanger temperatures (on the left) and the values of the Carnot factor (one the right) depending on the heat flow transferred, when Te  Th1 , Tc1

E˙ h+

1 =

1  Q˙ H R E ηCh δ Q˙ i = M˙ h c ph (Th1 − Th2 ) 1−

0

0



Te

δ Q˙ i .

Th1 − (Th1 − Th2 ) Q˙ i

(3.2) The resultant flow of exergy transferred to the heat-receiving heat transfer medium is: E˙ c−

1 =

1  Q˙ H R E ηCc δ Q˙ i = M˙ c c pc (Tc2 − Tc1 ) 1−

0

0

Te Tc2 − (Tc2 − Tc1 ) Q˙ i

 δ Q˙ i . (3.3)

The exergy balance equation for the heat exchanger is E˙ h+ = E˙ c− + L˙ ch . The amount of exergy destroyed in the heat exchanger, L˙ ch is the difference between the exergy supplied and the resultant exergy and is always above 0. For the sake of E˙ + E˙ + numeric analysis, the values eh+ = M˙h and ec+ = M˙c can be used with a high degree of h c convenience. The thermodynamic (exergy) efficiency of this thermal transfer process in the heat exchanger is: ηex =

E˙ c− e− L˙ ch lh = c+ = 1 − + = 1 − c+ . + eh eh E˙ h E˙ h

(3.4)

46

3 Exergy Analysis of the Heat Recovery Exchanger of the Air …

3.1.1 Typical Cases of Exergy Analysis of the Heat Recovery Exchanger Equations (3.2) and (3.3) show that the values of the terms of the exergy balance equation with a given heat exchanger (when the flowrates and the inlet and outlet temperatures are available) depend on the respective Carnot factors, ηCi = 1 − TTei . When Ti = Te , then ηCi = 0. These dependencies are shown in Fig. 3.2 (right), and the area between the lines showing the Carnot factors that mirror exergy flows is proportionate to the amount of exergy destroyed in the process, L˙ ch . The cases when Te < Tc1 < Tc2 , as shown in Fig. 3.2 are typical of most of the problems of exergy analysis of various energy transformers. Contrary to classical heat exchangers, with air handling unit heat exchangers owing to the variation of Te , we have cases similar to the heat transfer that was introduced in the beginning. However, within the limits of the problem at hand, the environment temperature shifts and can be Te > Th1 > Th2 or Th1 ≥ Te ≥ Tc1 . The case in Fig. 3.2 then transforms into the cases depicted in Figs. 3.3 and 3.4. There is the problem of identifying the direction of thermal exergy flows and the amount of exergy destroyed, which will be addressed later. As it was already discussed, in the case of heat transfer via the wall, the direction in which the heat and exergy of the of heat transfer media is received and released can overlap; however, it can also differ. The direction of exergy release and reception can even differ within the same heat exchanger: for instance, when exergy is transferred at the beginning by the heat transfer medium with a higher temperature rating to another heat transfer medium, the exergy flow changes its direction at a certain point in the heat exchanger. Using the (right) case from Fig. 3.4, the direction of the thermal exergy flow of any heat transfer medium runs in the direction towards ηCi = 0, and the area between

Fig. 3.3 The characteristics of heat exchanger heat transfer media when Te > Th1 > Th2 , with the temperatures on the left, and Carnot factors on the right

3.1 When Exergy Flows Are Calculated with the Carnot Factor

47

Fig. 3.4 The characteristics of heat transfer media of the heat exchanger when Th1 ≥ Te ≥ Tc1 , with the temperatures on the left, and Carnot factors on the right

the Carnot factor lines equals the amount of exergy destroyed. First of all, to be able to solve this kind of exergy analysis problem, it is important to determine whether the line (Ti = Te ) of the Carnot factor ηCi = 0 crosses the values of any of the heat transfer media ηCh = 1 − TThe and ηCc = 1 − TTec . The product is the solution for the heating heat transfer medium: Th1 − Te , Q˙ h,ηC =0 = Th1 − Th2

(3.5)

and the heated heat transfer medium: Tc2 − Te , Q˙ c,ηC =0 = Tc2 − Tc1

(3.6)

when these values are within the range of 0 ≤ Q˙ i ≤ 1. Furthermore, Q˙ h,ηC =0 > Q˙ c,ηC =0 , because at a specific Q˙ i , the values of the temperature of the heat transfer medium h (the heat-releasing transfer medium) and the Carnot factor will always be greater than the respective values of the heat transfer medium c (the heat-receiving transfer medium). Considering the above assumptions regarding the directions of thermal exergy flows, Fig. 3.5 shows one of the cases when Th1 ≥ Te ≥ Tc1 , or, as far as exergy analysis is concerned, the Carnot factor ηCi = 0 line crosses the values of the heat transfer medium Carnot factors ηCh and ηCc . We have exergy flows above the ηCi = 0 line et+ and et− (‘top’) and below the ηCi = 0 line eb+ and eb− (‘bottom’). In this case, the exergy efficiency of the process is:

48

3 Exergy Analysis of the Heat Recovery Exchanger of the Air …

Fig. 3.5 A case when the Carnot factor ηCi = 0 line crosses the values of the heat transfer medium Carnot factors ηCh and ηCc

η=

et− + eb− lch = 1 − , et+ + eb+ et+ + eb+

(3.7)

    and exergy destroyed lch = et+ + eb+ − et− + eb− is shown as the area between the Carnot factor lines that match the exergy flows. With these reciprocal positions of the three Carnot factors, the same rationale of resolving the problem applies, albeit some of the areas may no longer be there. The block graph for calculating exergy efficiency in cases depicted in Figs. 3.2, 3.3, 3.4 and 3.5 is presented in Fig. 3.6. Non-dimensional criteria used for the purposes of interpretation of the above material could produce heat recovery exchanger exergy analysis data that are more ˙ that universal in nature. First of all, these would be the relative heat transfer flow Q i was already mentioned above. In engineering practice, heat exchangers are described on the basis of their temperature efficiency εT =

Th1 − Th2 . Th1 − Tc1

(3.8)

In that case, knowing the temperature efficiency of the heat exchanger and at least three of the above heat transfer medium temperatures, we are able to determine the one of the above four temperatures that is unknown, e.g., Th2 = (Th1 −εT (Th1 −Tc1 )). c1 The non-dimensional temperature T e = TTh1e −T should be selected as value number −Tc1 three. With these values, the equations in (3.2), (3.3), (3.5), and (3.6) are transformed exclusively into equations that bind the original temperatures of the heat transfer media Th1 and Tc1 , the temperature efficiency of the heat exchanger εT , and the non-dimensional temperature T e : eh+

 E˙ + = h = c ph (εT (Th1 − Tc1 )) M˙ h 0

1

 1−

T e (Th1 − Tc1 ) + Tc1 Th1 − (εT (Th1 − Tc1 )) Q˙ i

 δ Q˙ i . (3.9)

3.1 When Exergy Flows Are Calculated with the Carnot Factor

49

Fig. 3.6 The block graph for the determination of the exergy efficiency of the heat recovery exchanger

The resultant exergy flow transferred to the heat-receiving heat transfer medium is ec−

 E˙ − = c = c pc (εT (Th1 − Tc1 )) M˙ c 0

1

 1−

T e (Th1 − Tc1 ) + Tc1 Tc1 + εT (Th1 − Tc1 )(1 − Q˙ i )

 δ Q˙ i . (3.10)

The value of the relative heat transfer flow matching the heating heat transfer medium ηCi = 0 is

50

3 Exergy Analysis of the Heat Recovery Exchanger of the Air …

1 − Te , Q˙ h,ηC =0 = εT

(3.11)

and for the heat transfer medium heated, εT − T e . Q˙ c,ηC =0 = εT

(3.12)

3.1.2 Numeric Indicators of Exergy Analysis of Heat Recovery Exchangers The above methodology was used to perform calculations of the exergy indicators of the heat recovery exchanger covering a broad range of physical parameters of the air and the environment that nonetheless can be present in the process of ventilation. The chosen temperatures of the heat recovery exchanger’s heat transfer media (based on the tags in Fig. 3.2) Th1 are within the range of (20–30) °C, and Tc1 is within the range of −10 and +10 °C. The range of variation of outdoor temperatures Te is within the range of −30 and 40 °C. The range of variation of the heat exchanger temperature efficiency indicator εT is between 40 and 90%. General presentation of this sample of indicators is based on non-dimensional temperature (9), which varies within the limits of −2.5 and +2.5. Cases of the numeric results of the methodology prepared are discussed below, complete with a graphical visualisation of the universal characteristics of relation ηex = T e , εT . The key formulas used for the purposes of the calculations were (3.7)–(3.12). The calculations of the above sample of data based on the diagrams in Figs. 3.5 and 3.6 are presented in Fig. 3.7.

Fig. 3.7 The dependency of the exergy efficiency of the heat recovery exchanger on the original temperature of the hot heat transfer medium, when εT = 60% and Tc1 = 5 °C: depending on the environment temperature (on the left); depending on the non-dimensional temperature (on the right)

3.1 When Exergy Flows Are Calculated with the Carnot Factor

51

This figure shows the dependency of the exergy efficiency of the heat recovery exchanger on values of the original temperature Th1 of the hot heat transfer medium (which could be the temperature of the exhaust air in the process of ventilation). These temperatures vary in increments of 2 °C, while the temperature efficiency coefficient εT = 60%, and the original temperature of the hot heat transfer medium Tc1 = 5 °C. In this case, it does not necessarily equal the outside air temperature. First of all, it should be noted that as the temperature Tc1 shifts, the value of exergy efficiency remains steady at the same non-dimensional temperature (Fig. 3.7 (on the right)). In this case, the chosen value Tc1 = 5 °C is clearly reflected in the coordinates of both the dimensional and non-dimensional temperature. In the first case (on the left), when the environment temperature Te = 5 °C, the exergy efficiencies of the heat transfer process within the heat exchanger are the same at any original temperature of the hot heat transfer medium (in this case, ηex ≈ 0.43). On the other hand, this value matches the numeric value of the non-dimensional temperature T e = 0 in the figure (on the right). Different Tc1 values would produce comparable dependencies in terms of this temperature. As the figure (on the left) shows, with the temperature Th1 rising the minimum exergy efficiency also moves to the right—towards the higher environment temperature. To better understand the process of the dependencies of exergy efficiency as calculated with the proposed method, Fig. 3.8 shows another combination of samples. Figure 3.8 shows the exergy efficiency of the heat recovery exchanger as the original temperature of the cold heat transfer medium Tc1 changes in increments of 5 °C. In the process of ventilation, this could be the temperature of air taken from the outside and heated in the electric heater or in the condenser of the heat pump before it even enters the heat exchanger covered in this analysis. This also includes a case when no such heating occurs and this temperature equals the environment temperature, Tc1 = Te . Other parameters chosen for the purposes of this example: the temperature efficiency coefficient of the heat exchanger εT = 60%, the original temperature of the hot heat exchanger Th1 = 22 °C. Just like in the previous case, the coordinates

Fig. 3.8 The dependency of the exergy efficiency of the heat recovery exchanger on the original temperature of the hot heat transfer medium, εT = 60% and Th1 = 22 °C: depending on the environment temperature (on the left); depending on the non-dimensional temperature (on the right)

52

3 Exergy Analysis of the Heat Recovery Exchanger of the Air …

of the non-dimensional temperature show a uniform and universal dependency of all these Tc1 on the exergy efficiency of these processes as shown in Fig. 3.8 (on the right). The highest values of this efficiency are always < 1, and the lowest value of 0.5 exists at non-dimensional temperature. In the figure (on the left), when the environment temperature Te = Th1 = 22 °C, the exergy efficiencies are the same at any original temperature of the cold heat exchange medium Tc1 , and have a ‘point of overlap’ (ηex ≈ 0.40). On the other hand, this value of exergy efficiency exists at the numeric value of the non-dimensional temperature T e = 1 as shown in the figure (on the right). The lowest value of exergy efficiency of the process in question moves towards the higher environment temperature, as the temperature Tc1 rises. In general, it can be said that this lowest value of exergy efficiency moves towards the higher environment temperature as the original temperature of the two heat transfer media rises. Besides, the lowest and the highest values of exergy efficiency swap places in the interval between the lowest point and the point of overlap. In the examples provided so far, the heat exchanger’s temperature efficiency coefficient εT was stable and more or less aligned with the seasonal efficiency rating of an average-quality unit in engineering practice. The effect that the variation of this indicator εT has on exergy efficiency is shown in Fig. 3.9. To showcase the methodology, the heat transfer medium temperatures of Tc1 = 5 °C and Th1 = 22 °C were chosen for this variable. The range for εT = (40–90)%, shifting in 10% increments. The lowest value of the exergy efficiency of the process in question is at a steady location of the environment temperature defined with the numeric values of Th1 = 22 °C Tc1 = 5 °C, both in terms of dimensional, and non-dimensional temperature. Generally, this temperature amounts to the average of the original or the final temperature of the heat transfer media (Th1 + Tc1 )/2 = (Th2 + Tc2 )/2. Therefore, with the original temperatures of the heat transfer media available, it is easy to determine the environment temperature at which the exergy efficiency of the heat transfer process will be the lowest. What is more, this gives us the knowledge that the temperature

Fig. 3.9 The dependency of the exergy efficiency of the heat recovery exchanger on the temperature efficiency coefficient εT , when Th1 = 22 °C Tc1 = 5 °C: depending on the environment temperature (on the left); depending on the non-dimensional temperature (on the right)

3.1 When Exergy Flows Are Calculated with the Carnot Factor

53

combination of (Th1 + Tc1 )/2 = Te is to be avoided in the processes lest the exergy efficiency of the heat exchanger be at a low. Obviously, both the lowest value and other values of exergy efficiency are lower when the values of εT are lower. At values below εT = 50%, the lowest value of exergy efficiency reaches zero. It was already highlighted in the previous chapters that one quality of exergy analysis of the heat recovery exchanger is that it operates at temperatures that are close to that of the environment, Te . Analytical expressions must take account of this quality when the environment temperature and the heat transfer medium temperature are linked as follows: Th1 ≥ Te ≥ Tc1 . To sum up, it can be said that this relationship between the temperatures exists at any time when the line of the Carnot factor ηCi = 0 crosses the Carnot factor line of any (or both) of the heat transfer media. In all of the calculation examples presented, this matches the 0–1 range of the non-dimensional temperature T e . It is within this range that the values of exergy efficiency are the lowest. A technological or control solution to be found during the design phase to help prevent the heat exchanger from operating within this range or abridge the duration of this operation would improve the heat exchanger’s seasonal exergy efficiency. It is not the aim of the authors to suggest any such technological or control solution; instead, they aim to show that an exergy analysis performed under the method proposed allows revealing the qualities of the process and the potential for and limits of its improvement. To perform the thermodynamic test of the methodology presented here, a fringe case is selected, with the environment temperature Te = 0 K on the left, and Te  Th on the right. There is also an equivalent of this kind of calculation for the coordinates of non-dimensional temperature. The results are shown in Fig. 3.10.

Fig. 3.10 Calculation of the exergy efficiency of the heat recovery exchanger on the basis of the Carnot factor within the theoretically extreme limits of variation of the Te value (between Te = 0 K and Te  Th ): depending on the dimensional temperature (on the left); depending on the non-dimensional temperature (on the right)

54

3 Exergy Analysis of the Heat Recovery Exchanger of the Air …

The key result that favours this methodology is that with Te far to the left or to the right of the usual temperature values that are close to those of the environment, the overall exergy efficiency of the heat exchanger becomes closer, but not above 1.

3.1.3 A Case of Comparison with the Prior Method To evaluate how valid the method proposed is, exergy efficiency values estimated on the basis of the methodology provided herein are compared with the methodology designed by Boelman et al. (2009). For the purposes of this comparison, the same fundamental parameters and limiting conditions are used: • the reverse-flow heat exchanger and only the perceptible heat transfer are taken into consideration; • the heat transfer between two dry air flows, their temperatures, and heat transfer coefficients are stable and uniform; • the temperature difference Th − Tc is steady throughout the heat exchanger; • the cold air mass flow rate is 1 kg/s and the hot air mass flow rate is 1 kg/s; • the specific heat capacity of dry air is 1.005 kJ/(kg K); • the heat transfer efficiency of the heat exchanger ε is a parameter at 70%; • the heat exchanger is well insulated, the dynamic effect of the air flow is ignored and only thermal exergy is considered. The thermal exergy of the ideal gas flow:    T E˙ = M˙ · c p (T − Te ) − Te ln , Te

(3.13)

where M˙ is the mass flow rate; c p is the specific heat capacity; T is temperature; and Te is the ambient air temperature. Under the method employed by Boelman et al. (2009), the efficiency of the heat exchanger can be defined as the ratio of the input of all products and all sources. When the aim is to increase the thermal exergy of cold air by transferring hot air, the thermal exergy of cold air increases (E c ) as the net output of the product, while the absolute value of the thermal exergy of hot air goes down. (E h ) is considered as the net source input: ηex =

E c E c2 − E c1 . = |E h | E h1 − E h2

(3.14)

This comparison is presented in more detail in Table 3.1. The exergy efficiency estimated under the two methods under certain conditions is shown in Fig. 3.11. The environment temperature Te is within the range of −30 and 40 °C. When the environment temperature is at −3.5 °C, exergy efficiency is the same. However,

3.1 When Exergy Flows Are Calculated with the Carnot Factor

55

Table 3.1 Calculation results for the comparison of exergy efficiency at four different environment temperatures Te (°C)

−3.5

Th1 (°C)

22

Tc1 (°C)

5

10.0

15.2

30.5

22

ηex (proposed method)

0.751

0.278

0.195

0.728

ηex (Boelman et al. 2009)

0.752

0.154

−5.399

−1.376

E h1 (kJ)

1.140

0.249

0.079

0.121

E h2 (kJ)

0.334

0.000

0.046

0.721

E c1 (kJ)

0.132

0.045

0.186

1.140

E c2 (kJ)

0.739

0.083

0.005

0.316

Fig. 3.11 A comparison of exergy efficiencies when −30 °C < Te < 40 °C, εT = 70%, Th1 = 22 °C, and Tc1 = 5 °C

differences occur as it moves forward. Owing to the second value of the environment temperature (10.0 °C), both effects are still positive, yet different. When the environment temperature rises (the third point, 15.2 °C), exergy efficiency calculated under the methodology presented in this document is still between 0 and 1 (ηex = 0.195). However, exergy efficiency measured with Eq. (3.14) is below 0 (ηex = − 5.399). The last (fourth) point (Te = 30.5 °C) reflects a situation when the value of negative exergy efficiency is −1.376, if we use the method provided by Boelman et al. (2009). Unfortunately, this research is described by IEA ECBCS (2011) as a “thorough analysis of different relevant reference environments”. The authors leave the results without any comment that this is thermodynamically unacceptable, or without a suggestion as to how this can be resolved. Considering that the heat exchanger is involved in the technological energy chain, including negative exergy efficiency values in the entire BTS exergy analysis is a difficult thing to do. In cases like that, the applicable exergy efficiency methodology should involve the value of this efficiency indicator of between 0 and 1.

56

3 Exergy Analysis of the Heat Recovery Exchanger of the Air …

3.2 When Exergy Flows Are Calculated Using Coenthalpy as a State Parameter The use of the parameter of coenthalpy and numerical and graphical interpretation of its variation benefit the visualisation and analysis of the ongoing processes. While moving straight to exergy flows without visualising the potentials that generate them sometimes narrows down the possibilities to observe the fine points of the process. This is what happens when energy transformation processes occur at temperatures close to that of the environment. As it was said, that temperature shifts and is the RET for the purposes of exergy analysis. In each case, ke is a reference parameter for exergy analysis; what is more, it is always lower than (or, in some isolated cases, equal to) any of the coenthalpies of the heat transfer medium involved in the process under analysis. This is the key difference between the property ke and the state of the reference environment defined by temperature, because Te can be lower or higher (for instance, in the case of cooling) than some of the temperatures of the flows involved in the process. If, in the problem at hand, this temperature is only lower or only higher than heat transfer medium temperatures, then this property of the lowest value of ke as a reference parameter of exergy analysis loses some of its relevance, because the ‘behaviour’ of heat transfer medium coenthalpies is similar to that of temperatures. Besides, as we will see in the problem that we are discussing here, when the reference temperature is equal to the temperature of the heat transfer media at least at one point or is located between them, this property becomes methodologically important and exceptional.

3.2.1 Formulation of the Heat Recovery Exchanger The methodological outline presented in Chap. 2 is applied to solve the problem of thermodynamic (exergy) analysis of the air handling unit’s heat recovery exchanger that has its diagram shown in Fig. 3.12. Just like in Fig. 3.1, it is a heat exchanger with two heat transfer media that have the same physical properties (dry air) and the same mass flowrates, meaning that the heat capacity flowrates of the heat transfer media are the same on both sides of the heat transfer surface: M˙ h c ph = M˙ c c pc . Fig. 3.12 The diagram of exergy evaluation of the heat recovery exchanger of the air handling unit

3.2 When Exergy Flows Are Calculated Using Coenthalpy …

57

˙ of the hot (h) and the cold (c) heat The arrows show the mass flowrates ( M) transfer media, with only the states of those mass flowrates are indicated with the appropriate coenthalpies k, as well as the direction of the heat flow transferred within the heat exchanger, Q˙ H R E . Under the FLT, the heat balance equation of this heat exchanger is: M˙ h c ph (Th1 − Th2 ) = M˙ c c pc (Tc2 − Tc1 ) = Q˙ H R E .

(3.15)

As with the Carnot factor (see Sect. 3.1), when we apply a relative heat flow, we obtain the following main dependencies between the temperatures: Thi = Th1 − (Th1 − Th2 ) Q˙ i and Tci = Tc2 − (Th1 − Th2 ) Q˙ i .

(3.16)

The equation of exergy balance with coenthalpies applied, when the borders of the system in question (in this case, the counter-flow heat exchanger) are crossed by the flows of the heat transfer medium only, would generally look like this: M˙ h+ kh1 + M˙ c+ kc1 = M˙ h− kh2 + M˙ c− kc2 + L˙ ch .

(3.17)

Considering the two expressions of exergy efficiency (as shown in the methodological outline), it can also be formulated as follows: M˙ h (kh1 − kh2 ) = M˙ c (kc2 − kc1 ) + L˙ ch .

(3.18)

In that case, exergy destroyed would be: L˙ ch = M˙ h (kh1 − kh2 ) − M˙ c (kc2 − kc1 ).

(3.19)

However, in the case of the HRE, the environment temperature varies and may place between the original temperatures of the heat transfer media, as well below or above these temperatures. The non-dimensional environment temperature will be furthermore be used, and will constitute the non-dimensional RET at the same time for the purposes of this monograph: Te =

Te − Tc1 . Th1 − Tc1

(3.20)

In engineering practice, the HRE is defined by its temperature efficiency εT =

Th1 − Th2 . Th1 − Tc1

(3.21)

58

3 Exergy Analysis of the Heat Recovery Exchanger of the Air …

˙ as presented in Sect. 3.1, these nonIn addition to the conditional heat flow Q i dimensional parameters bestow a higher degree of universality on the methodology being developed.

3.2.2 The Algorithm of Exergy Analysis of the Heat Recovery Exchanger with Coenthalpy The algorithm of the HRE exergy analysis with coenthalpies is presented as follows. A commentary of the process of energy transformation happening inside the unit and an explanation of its properties affecting the algorithm are presented. These are followed by a description of the rationale behind the making of the HRE exergy analysis algorithm. Analytical expressions of the specific states (lowest coenthalpy values, equality, limitations, and so on) of the processes are presented. The presentation closes with a demonstration of numeric cases.

3.2.2.1

Characteristics of Energy and Exergy Transformation in the Heat Recovery Exchanger

Heat transfer in heat recovery exchangers of ventilation units takes place at a temperature close to environments, which constantly shifts. The universal algorithm that has been developed is geared towards exergy analysis of such cases (exergy balance, exergy destroyed, exergy efficiency). Combining the material on temperatures and coenthalpies that was laid down in Chap. 2, we are able to visualise the change in these parameters of state the length of the HRE, from the initial moment of heat transfer to the very end of the process (Fig. 3.12), demonstrating Te and the coenthalpy ke in the process, as well. The cases shown in Fig. 3.13 explain the relationship among the temperatures of the three media (two heat transfer media and the environment), a characteristic attribute of the exergy analysis of the heat transfer process. These three cases represent the typical cases of exergy analysis for most of the problems relating to different other energy transformers, when Te < Tc1 < Th2 . What makes the case of the ventilation unit heat recovery exchanger differ from the usual heat recovery units is the changing Te . Figure 3.13 also shows one of the several possible cases of Th1 ≥ Te ≥ Tc1 . These would be the distinguishing characteristics of the operation and exergy analysis of heat exchangers of air handling units. In all cases, the changes in heat transfer medium temperatures are typical of the HRE chosen, yet the limits of RET variation depend on the climatic conditions: the specific geographic location. In example (a), the environment temperature, hence the reference temperature, is 0 °C; in example (f ) it is 16.9 °C, and in (i), as high as 30 °C.

3.2 When Exergy Flows Are Calculated Using Coenthalpy …

59

Fig. 3.13 Cases of reciprocal positions of HRE heat transfer medium temperatures and RET Te used for the purposes of discussion of the detailed diagrams of coenthalpies in Fig. 3.14 (Th1 = 22 °C, Tc1 = 5 °C, Th2 = 10.1 °C, Tc2 = 16.9 °C, which match εT = 0.7)

In case (a), the RET is below the temperature of any of the heat transfer media and this is a usual case of exergy analysis of heat exchangers. Case (i), when this temperature is above the temperature of the two heat transfer media, should also be considered conventional. Whereas in diagram (f), the environment temperature crosses temperature Q˙ i / Q˙ H R E = 0 of one of the heat transfer media and is between the two heat transfer medium temperatures within the range of up to ≈0.4. This is the only case when an accurate numeric solution can be obtained, yet this would require a universal algorithm. All the more as the values to be obtained need to be thermodynamically correct (i.e. in terms of exergy flows, exergy destroyed, the efficiency or the entire HRE or any part of it) at any Te position vis-à-vis the temperatures of the heat transfer media. The reciprocal temperature positions were already covered in cases (a), (f ), and (i) of Fig. 3.13; however, the coenthalpy diagrams in Fig. 3.14 show more cases of specific processes. We have the diagrams of the coenthalpies kh , kc , ke of the heat exchange (heat transfer) process taking place in the HRE (cases a–i) at different characteristic values of the varying reference temperature as specified in each diagram. In every case shown, as the Te changes, the parameters that define the heat transfer process, Th1 = 22 °C, Tc1 = 5 °C and εT = 0.7 remain constant. In the first case, (a), Te = 0 °C, meaning that Te < Tc1 . In case I, Te is the average of Thi and Tc1 , and in case (i), Te = 30 °C, meaning that Te > Thi . The Te values for each case are specified in the rectangle in the diagram. In all cases, the ambient air ke is a reference parameter for the purposes of exergy analysis. It—ke —is always lower than (or sometimes equal to) any of the coenthalpies of the heat transfer media involved in the process. That is the number one difference between ke and temperature as a reference parameter, because Te can be above as well as below the heat transfer medium temperature (for

60

3 Exergy Analysis of the Heat Recovery Exchanger of the Air …

Fig. 3.14 Coenthalpy diagrams along the HRE: cases of reciprocal positions of the environment coenthalpy (REC) ke and the coenthalpies of the heat transfer media

instance, in the case of cooling). This REC property becomes relevant when it is universal for all cases of exergy analysis. With coenthalpy as a parameter, numeric and graphical interpretations of its fluctuations help visualise and analyse the processes that are taking place. The choice to move straight to the analysis of exergy flows without visualising the potentials that generate them restricts the possibility to observe the characteristics of the processes: the changes in the directions of exergy flows. This is what happens when energy transformation processes take place at temperatures close to the environment. Besides, this environment temperature varies and serves as the RET (or the REC) for the purposes of exergy analysis. This is particularly relevant to the HRE and other HVAC components. We emphasise and stand by the hypothesis that the directions in which heat and mass flowrates and the flow of their exergy travel may not always overlap. It depends on the reciprocal Thi ,Tci , and Te positions in the HRE, and the direction of thermomechanical exergy is always aligned towards Te . With coenthalpies, the flow of this exergy travels from the state ki to the state ke , because ki > ke at all times, and the reference point matches kmin = ke . Unfortunately, there is no such unambiguous relation among temperatures.

3.2 When Exergy Flows Are Calculated Using Coenthalpy …

3.2.2.2

61

Sectors of Exergy Flow Directional Combinations in the Heat Exchanger

As we can see from Fig. 3.14, we have cases when the coenthalpy of the same (or one and/or the other) the heat transfer medium drops, reaches its lowest value, and rises again as it travels the length of the heat exchanger. In one part, the exergy of the HRE heat transfer medium increases, and drops in another—hence the change in the direction of the exergy flow, even though the directions of the heat and mass flowrate did not change. The limits of the sectors of directional changes are marked with vertical dotted lines in Fig. 3.14. As we can see, there are no changes in the directions of exergy flows along the HRE in cases a, b, h, and i. It follows that solving these cases in exergy analysis can be done on the basis of the algorithms that have been used so far, even regardless of whether the RET used is variable or not. Meanwhile, case e has four directional combinations of exergy flows between the heat transfer media; cases g and c have two, cases d and f three. Follows presentation of the methodological principles as suggested in the study that provide the basis for the summarised algorithm for the exergy assessment of the heat exchanger of the air handling unit (even when the environment temperature varies and is similar to the temperatures of the heat transfer media) based on coenthalpies. Its further interpretation relies rather exclusively on two characteristic cases, (a) and (f ), which are shown in Fig. 3.15. Here, in addition to the above graphs of coenthalpy variation, comparative exergy flows e− , e+ are shown with reference as to when the system receives (‘into the system, + ’) or loses (‘out of the system, −‘) that flow. In individual cases, references are made to Fig. 3.14.

Fig. 3.15 Two cases of variation of the heat exchanger heat transfer medium state parameters (temperatures and coenthalpies) used for the purposes of the discussion of the exergy analysis algorithm

62

3 Exergy Analysis of the Heat Recovery Exchanger of the Air …

The diagram in Fig. 3.13 hints towards the temperature mode of the chosen cases (a) and (f ). In both of these cases, the shift in the transfer medium temperatures follows a pattern that is typical to the HRE, even though the practical limits of RET variation depend on the local climatic conditions. In case (a), the environment (reference) temperature is 0 °C, in (f ) 16.9 °C. In the first case, it is below any of the heat transfer medium temperature and represents a typical case of heat exchanger exergy analysis. Case (i), when this temperature is above the temperatures of the two heat transfer media, is to be considered typical as well. In case (f ), the environment temperature intersects with the temperature of one heat transfer medium, and is wedged in between the temperatures of both heat transfer media in the left part of the heat exchanger. A numeric solution to this particular case can indeed be found, but there must be a uniform algorithm for all these cases. It needs to be able to generate thermodynamically correct values (for the exergy balance components, exergy destroyed, the exergy efficiency of the heat exchanger or any part of it) in any Te position vis-à-vis the heat transfer medium temperatures. We stand by the above hypothesis that the directions in which heat and mass flowrates and the flow of their exergy travel may not always overlap. It depends on the reciprocal position of Thi , Tci , and Te in the part of the heat exchanger concerned, while the direction of the thermomechanical exergy flow is always aligned towards Te . In the case shown in Fig. 3.15, in the direction of the mass flowrate M˙ c on the left, its coenthalpy approaching the coenthalpy of the reference environment (the coenthalpy of the heat transfer medium decreases in the direction of the heat transfer medium flow), this mass flowrate releases exergy e+ to the system (exergy is taken from the heat transfer medium). By contrast, if its coenthalpy moves further away from the coenthalpy of the reference environment in the process of exergy transformations taking place within the system (or its sector), the system releases exergy e− to this flowrate (the flow receives, and the system loses exergy). The case on the right is more complex and is divided into sectors. It is similar to case (f ) in Fig. 3.14. Along the heat exchanger with a constant direction of heat release, we have cases of exergy release ea− to the heat transfer medium that receives the heat (a sector) and ec− to the heat transfer medium that gives away the heat (b sector). In summary, it can be said that for analysis purposes, a unit where the environment temperature varies and is close to the temperature of heat transfer the media should be split into subsystems—sectors. The boundaries of such sectors will lay where the change of the coenthalpy of one of the flows that exchange exergy changes its direction or where the coenthalpies of both flows overlap. In our case (f, Fig. 3.14), we have three sectors. Notably, for HVAC in general and the heat exchanger of the air handling unit in particular, as the reference temperature Te constantly varies, the boundaries and the number of these sectors vary as well. As it was already mentioned, the goal is to find a uniform calculation algorithm, or universal rules, to cover all of the cases.

3.2 When Exergy Flows Are Calculated Using Coenthalpy …

3.2.2.3

63

Phases of Developing an Exergy Analysis Algorithm for the Heat Recovery Exchanger

The rationale behind the algorithm ideally could be explained by a mechanistic analogy of potential energy, albeit with significant losses for friction (similar to the destruction of exergy). All of the exergy provided in the process cannot be taken in, and the losses for friction are relatively small in a mechanical system, such as a pulley unit. The reference system—the ‘sea level’—matches kmin = ke . It is important to emphasise that there is no state expressed with coenthalpy that would be lower than this. The areas below the coenthalpy lines within the limits of this problem are ‘meaningless’: everything depends on the altitude of the point of the heat transfer medium’s coenthalpy and its variation along the heat exchanger. Cases where the coenthalpy of the same (one and/or the other) heat transfer medium along the heat exchanger drops, reaches its lowest value, and then rises again, merit more attention. The introductory rules for the development of an exergy analysis algorithm for the air handling exchanger using coenthalpies would be as follows: 1.

2.

3.

4.

5. 6. 7. 8.

We divide the heat exchanger into sectors to be separated via the states or both or any of the heat transfer media, kmin = ke and kh = kc . As a result, the locations of such characteristic coenthalpies expressed with the relative heat flow Q˙ i are determined. We calculate the coenthalpies of these states on the boundaries of the subsystem for both heat transfer media. We determine the highest coenthalpy in the sector (regardless of the heat transfer medium) and deduct from it the lower coenthalpy of the same heat transfer medium. We then have e+ , the value of exergy released to the sector. We determine the highest coenthalpy of the other heat transfer medium in the same sector and deduct from it the lower coenthalpy of the same heat transfer medium. We then have e− , the value of exergy received in the sector. From the exergy released (e+ ) we deduct the amount of exergy received (e− ) to obtain the amount of exergy destroyed in the process that took place between the heat transfer media, lch . We calculate the functional exergy efficiency of each i sector (which we will refer to as sectoral efficiency as a result), η Fs,i = (1 − lch /e+ ). We sum up the exergy destroyed for all sectors to obtain the amount of exergy destroyed for the entire HRE, l H R E . We calculate the amount of exergy released to the heat exchanger as the sum of the exergies previously released, e+ H RE . We calculate the functional exergy efficiency of the heat exchanger, η F = (1 − l H R E /e+ H R E ).

64

3 Exergy Analysis of the Heat Recovery Exchanger of the Air …

3.2.3 Exergy Efficiency for the Thermomechanical Flows of the Heat Exchanger 3.2.3.1

Universal and Functional Exergy Efficiency of the Heat Recovery Exchanger

As it was said in the introduction, the universal and the functional ηex often occurs in exergy analysis (Woudstra 2002; Lior and Zhang 2007; Marmolejo-Correa and Gundersen 2012; Nguyen et al. 2014). Our study aims to show the instrumentality of the application of coenthalpy for the purposes of determining ηex . With coenthalpies as parameters of the state, the equations of the universal (input–output) and the functional (produced–consumed) ηex of the counter-flow heat exchanger (as per Fig. 3.12) would be: ηU =

ηF =

− E˙ out e− kc2 + kh2 − 2ke (kc2 − ke ) + (kh2 − ke ) or ηU = = out , + = + kc1 + kh1 − 2ke (kc1 − ke ) + (kh1 − ke ) ein E˙ in (3.22)

E˙ − e−pr od (kc2 − ke ) − (kc1 − ke ) (kc2 − kc1 ) pr od or η F = . (3.23) = = + + (kh1 − ke ) − (kh2 − ke ) (kh1 − kh2 ) econs E˙ cons

Unfortunately, under the conditions of a varying RET, coenthalpies on the external boundaries of the HRE as a thermodynamic system do not reflect the characteristics of energy transformations inside the HRE. If these are ignored, the formula (3.23) applied to the functional ηex in question can even produce negative values of this efficiency (Boelman et al. 2009). The methodological outline of exergy efficiency was introduced in Sect. 2.4. Section 3.1 presented the method for calculating the exergy efficiency of the heat exchanger based on the Carnot factor. It approaches the exergy direction of the heat flow in a universal manner, which is important when the temperatures of heat transfer media in the processes in question are below or above or match the environment temperature. However, the application of the Carnot factor is not limited to just an assessment of the resultant heat flow of the process. For the purposes of the exergy analysis of the processes presented here and its results, the application of the Carnot factor is directly limited by the heat transfer medium flow rates and their state parameters. This monograph puts forth a functional sectoral exergy efficiency, its determination relying on the identification of the processes of transformation of exergy flows that occur in varying directions within the HRE. Thus, the HRE can be divided into up to 4 sectors (sub-systems) based on the reciprocal positions of the varying RET and the temperatures of the heat transfer media. The integral functional sectoral efficiency of the entire HRE is determined by identifying the values, directions, and functional exergy efficiency of exergy flows for each of them. While the functional efficiency of the entire unit is calculated on the basis of state parameters on the

3.2 When Exergy Flows Are Calculated Using Coenthalpy …

65

boundaries of the unit as a thermodynamic system, the sectoral efficiency is based on the boundaries of the sector. When exergy flows do not change their direction inside the unit (one sector identical to the whole HRE), then the total functional and sectoral efficiency will be the same. When exergy flows change their direction in the unit’s sectors, then the sectoral (local) functional efficiency and the total efficiency will be different. Its universal formula could be put down as follows:

 k −j − ki− . =

+ + k − k j i i, j

η Fs

i, j

(3.24)

There the denominator is the sum of coenthalpy differences in sectors that receive exergy, and the numerator, the sum of coenthalpy differences in sectors that provide exergy. In other words, the same heat transfer medium receives exergy in one sector and releases it in another. This can be seen in Fig. 3.5 concerning the application of the Carnot factor. As will be shown in the algorithm to be presented later, the denominator and the numerator of functional exergy efficiency can swap places depending on Te . The functional sectoral exergy efficiency of the HRE at the combination of the given heat transfer medium and environment temperatures shows the highest exergy efficiency that can be achieved in theory. Whereas the difference between the traditional general functional efficiency and the sectoral efficiency suggested here shows the potential for increasing the exergy efficiency in the process of HRE design and its exergy-optional control.

3.2.3.2

Determining the Characteristic States of the Process in the Heat Recovery Exchanger

Figures 3.14 and 3.15 already show that, in addition to their values at the time of entering and leaving the heat exchanger, heat exchanger coenthalpies also have other characteristic values within the range of 0 ≤ Q˙ i ≤ 1. These are the lowest values of the functions ki = F( Q˙ i ) for one and the other heat transfer medium within said range, as well as the Q˙ i value when the heat transfer medium coenthalpies are equal, i.e. Q˙ i,kh =kc . In the first case, Eqs. (3.16), (3.20) and (3.21) are used to analytically determine the lowest kh and kc values, their solution for the heating (or cooled) heat transfer medium being: Th1 − Te 1 − Te = , Q˙ h,k=min = Th1 − Th2 εT and for the heated (or cooling) heat transfer media being:

(3.25)

66

3 Exergy Analysis of the Heat Recovery Exchanger of the Air …

Tc2 − Te εT − T e = . Q˙ c,k=min = Tc2 − Tc1 εT

(3.26)

Therefore, knowing the temperature efficiency and the non-dimensional RET of the heat exchanger alone makes it possible to pinpoint the parts of the exchanger where coenthalpies change the direction of their variation. The relationship between Q˙ i and the non-dimensional RET T e that mirrors the equality of heat transfer medium coenthalpies (their cusp as per example in Fig. 3.15) within the range of 0 ≤ Q˙ i ≤ 1 is expressed with the following equations: Q˙ i,kh =kc



−Th1 )(1−εT ) − Tc1 (Th1 + εT (Tc1 − Th1 )) exp T(Tc1+(T h1 c1 −Th1 )T e



  = , )(1−εT ) − 1 εT (Tc1 − Th1 ) exp T(Tc1+−TT h1−T h1 ( γ 1 h1 ) T e

(3.27)

or  T e,kh =kc =

Th1 −εT (Th1 −T c1 ) Q˙ i  Th1 +εT (Th1 −Tc1 ) 1− Q˙ i

(1 − εT )(Th1 − Tc1 ) − Tc1 ln   Th1 −εT (Th1 −T c1 ) Q˙ i  (Th1 − Tc1 ) ln ˙

 .

(3.28)

Tc1 +εT (Th1 −Tc1 ) 1− Q i

With the heat exchanger operating under definite conditions (given its temperature efficiency of εT and the original heat transfer medium temperatures of Th1 and Tc1 ), Eqs. (3.27) and (3.28) show when the heat transfer medium coenthalpies are equal within the heat exchanger. In other words, they show the conditions when the heat transfer media that supply and receive exergy swap their roles. With the above data of the heat exchanger, this happens in a particular combination of the reference temperature (or T e ) and heat transfer medium temperatures, with the value Q˙ i expressing the part of the heat exchanger where it happens. Equation (3.27) is used to determine the location of equal coenthalpies based on the value Q˙ i at the given reference temperature. Equation (3.28) is used to determine the reference temperature at which the coenthalpies of the heat transfer media are equal based on the value Q˙ i . In both cases, the solutions only have meaning within the range of 0 ≤ Q˙ i ≤ 1. These expressions are needed to realise the algorithm for the calculation of exergy analysis indicators, because these locations impact the choice of one or formula or the other. These analytical expressions retain their relevance in the course of addressing matters of exergy-optimal control in HVAC systems equipped with heat exchangers. The HRE’s typical range of T e values is narrower than 0–1, in which process the amount of exergy supplied equals the amount of exergy destroyed, and the functional exergy efficiency η F = 0. This interval T e,l=k + ≤ T e ≤ 1 − T e,l=k + depends on the HRE’s temperature efficiency εT and on the original temperatures of the heat transfer media and is determined with the value

3.2 When Exergy Flows Are Calculated Using Coenthalpy …



T e,l=k + = ln

εT Tc1 +εT (Th1 −Tc1 ) Tc1

−

Tc1 . (Th1 − Tc1 )

67

(3.29)

With coenthalpies used for the purposes of the algorithm of the exergy analysis of the air handling heat exchanger, the suggested sequence of analytical steps is as follows: 1.

2.

3.

4.

5.

6.

We use Eq. (3.20) to check the value of the non-dimensional RET T e in terms of the 0–1 range. This control value depends exclusively on the original heat transfer medium temperatures and the environment temperature and is not tied to the heat exchanger’s efficiency εT . At no point does the environment temperature cross the temperatures of the heat transfer media when T e ≤ 0 is below or T e ≥ 1 is above them. It is worth noting that depending in this indicator, for the purposes of determining the sectoral exergy efficiency, the heat transfer media swap their roles of releasing and receiving energy. A control calculation of Q˙ h,k=min and Q˙ c,k=min is performed with formulas (3.25) and (3.26) to determine whether the process is devoid of a case where heat transfer medium coenthalpies attain the lowest values of the coenthalpy of the reference environment. Their numeric values in the solution covered in item one should also be outside of the limits of the range of 0–1. With the control indicator 0 < T e < 1, the sequence of the algorithm is primarily determined by the existence of the lowest coenthalpy values of one or both of the heat transfer media and the equality of the heat transfer medium coenthalpy in the process. We determine the values of indicators (3.25), (3.26), and (3.27) that allow us to verify this fact. When only one of these values is within the range of 0–1, we will split the process within the heat exchanger into two sectors, and with two values within said range, the number of sectors will be three. If all indicators are within the range of 0– 1, the process is divided into four sectors based on those locations of the two lowest values of heat transfer medium coenthalpies and coenthalpy equality (Fig. 3.14), and exergy analysis indicators are determined for the process of each of them. They are used to determine the indicators of all processes taking place within the heat exchanger (the hypothetical highest exergy efficiency). We cannot see more than four process sectors in the problem at hand. It can formally be summed up that the heat exchanger is divided into n + 1 sectors, where n is the number of values obtained with formulas within the range of 0 < T e < 1. A decision is made as to how the amount of exergy destroyed should be approached within the limits of the range determined with formula 3.29 (case d, e, f in Fig. 3.14). Once the appropriate coenthalpies are determined for the purposes of measuring exergy flows, exergy efficiencies are determined.

An analytical summary of the calculations of exergy efficiency by dividing the unit into three sector is presented in Table 3.2.

68

3 Exergy Analysis of the Heat Recovery Exchanger of the Air …

Table 3.2 Equations for the calculation of the universal and the functional exergy efficiency of the HRE with coenthalpies, when the environment reference parameter is variable Value

Expression

Input exergy

+ ein = (kc1 − ke ) + (kh1 − ke )

Output exergy

− eout = (kc2 − ke ) + (kh2 − ke )

Universal exergy efficiency (3.22)

ηU = (kc2 + kh2 − 2ke )/(kc1 + kh1 − 2ke ) T e < T e,l=k +

T e,l=k + ≤ T e ≤

T e < 1 − T e,l=k +

+ econs = eh+ = kh1 − kh2

+ econs = (kh1 − kh2 ) + (kc1 − kc2 )

− e− pr od = ec = kc2 − kc1

− e− e− pr od = 0 pr od = eh = Cases (d), (e), (f ) Fig. 3.14 kh2 − kh1

1 − T e,l=k + Consumed exergy Produced exergy

Functional exergy efficiency (3.23)

ηF =

(kc2 −kc1 ) (kh1 −kh2 )

ηF =

e− pr od + econs

=0

+ econs = ec+ = kc1 − kc2

ηF =

(kh2 −kh1 ) (kc1 −kc2 )

Solutions of exergy analysis indicators are found here using the coenthalpy differences that were basically introduced in the methodological outline. Based on the cases shown in Fig. 3.15, Table 3.2 presents expressions of calculating the universal and the functional ηex . The expressions are based on the hypothesis of measuring the direction of exergy flow in determining the potential as formulated in this monograph. Depending on the heat exchanger, the heat transfer medium with a higher coenthalpy value (Fig. 3.14 or Fig. 3.15) transfers exergy to the system until its coenthalpy reaches ke (REC) in the direction of the flow of the medium or leaves the heat exchanger, regardless of whether the heat transfer medium is ‘cold’ (c) or ‘hot’ (h).

3.2.3.3

Exergy Destroyed Inside the Heat Recovery Exchanger

Speaking of the determination of the process ηex , it is important to know the character of the transformation of exergy destruction in the process. The amount of exergy destroyed is calculated with Eq. (3.19) obtained from the equation of exergy balance on the system boundaries. On other words, the difference between the denominator and the numerator in exergy efficiency equations is the amount of exergy destroyed. Even though the numeric values of the universal (3.22) and the functional (3.23) exergy efficiencies differ, the analysis has showed that the amount of exergy destroyed in the process is comparable in both cases and totals: + − + − eout = econsum − e−pr od = (kh1 − kh2 ) − (kc2 − kc1 ). l = ein

(3.30)

This is in line with the thermodynamic logic that the amount of exergy destroyed in the process should not depend on the interpretations of efficiency indicators.

3.2 When Exergy Flows Are Calculated Using Coenthalpy …

69

With exergy destroyed expressed through the original heat transfer medium temperatures used for the purposes of this study, the relative reference temperature (3.20), and the temperature efficiency of the heat exchanger (3.21) and without splitting the HRE into sectors (i.e. by only applying the state parameters of input and output), the equation of exergy destroyed is: lH RE

  Tc1 + εT (Th1 − Tc1 ) ¯ = (Te (Th1 − Tc1 ) + Tc1 )c p ln Tc1   Th1 . − ln Th1 − εT (Th1 − Tc1 )

(3.31)

Numeric cases of the application of the algorithm suggested and their commentaries are presented below.

3.2.4 The Results of Calculations Using the Exergy Analysis Algorithm of the Heat Recovery Exchanger When it comes to presenting numeric cases of HRE exergy analysis, it is worth remembering the conditions of the processes in question. The HRE is where steady heat transfer from one heat transfer medium to the other takes place. The heat transfer medium temperatures are steady at the given location in the HRE. Only the ambient temperature changes, assuming different positions in terms of the heat transfer medium temperatures. The interpretation of the exergy analysis of heat transfer inside the heat exchanger that is presented here covers the transformation of the coenthalpies of the two heat transfer media along the heat exchanger as the environment temperature varies, which formally could be formulated as follows: ki = f (Ti , Q˙ i , T e , εT ).

3.2.4.1

(3.32)

The Nature of Transformation of Exergy Destroyed

The solutions of the equation of exergy destroyed (3.31) at different Te and εT values are shown in Fig. 3.16. In this numeric example as well as in other cases, the original temperatures of the heat transfer media (1 kg of dry air) are Th1 = 22 ◦ C and Tc1 = 5 ◦ C, with εT within the range of 0–1. Notably, when the environment temperature reaches the absolute zero, this amount of exergy destroyed is also zero. This is in line with the general thermodynamic concept of exergy. The analysis and the numeric case in the figure show that the amount of exergy destroyed is identical to the ‘symmetrical’ εT , meaning that they are matching at 0.7 and 0.3.

70

3 Exergy Analysis of the Heat Recovery Exchanger of the Air …

Fig. 3.16 Exergy destroyed in the HRE at different T e and εT values (when Th1 = 22 °C and Tc1 = 5 °C)

It is the amount of exergy destroyed that reflects the target efficiency potential to be achieved with design and control measures by splitting the process into sectors for the purposes of analysis. Figure 3.17 shows the extent to which the amount of exergy destroyed decreases when the HRE is split into sectors. We can see that breaking the process down into sectors reveals the theoretical potential of the process to reduce the destruction of exergy and, at the same time, to increase the amount of exergy provided, with T e in the range of 0–1 (dotted line). The HRE’s characteristic range of T e values is narrower than between 0 and 1, in which process the amount of energy provided equals the amount of energy destroyed, and functional energy efficiency η F = 0 is determined with Eq. (3.29). Fig. 3.17 The amount of exergy destroyed in the whole and sectored HRE

3.2 When Exergy Flows Are Calculated Using Coenthalpy …

71

When it comes to estimating the functional sectoral exergy efficiency, it is the amount of exergy destroyed that reflects the target potential of increasing the efficiency to be achieved with design and control measures. Figure 3.17 shows the extent to which the amount of exergy destroyed decreases when the HRE is divided into sectors and the sectors are measured adequately. Measured this way, the amount of exergy destroyed is below the amount of exergy destroyed in the whole of the HRE measured in an integral manner, based on the heat transfer medium states on the system boundaries. In other words, without a sectoral calculation, the total amount of exergy destroyed cannot be revealed. This ‘extra’ destruction of exergy can also be said to be evident from the difference between the universal and the functional exergy efficiencies. It is found in its continuous process of operation when the environment temperature (which is also the RET) shares its value with any of the heat transfer media un the heat exchanger. The engineering constructive and process control solution is omitted here, yet the available potential is indeed determined. This will be apparent in the following discussion of energy efficiencies.

3.2.4.2

Exergy Efficiency of the Heat Recovery Exchanger

It follows from the above material that, for the purposes of exergy analysis based on the suggested algorithm, once exergy flows (provided, received, and exergy destroyed) are determined, the next step is to calculate exergy efficiencies. The cornerstone formulas to accommodate that purpose are presented in Table 3.2. It is worth adding that the formulas in the table are designed to be used when the boundaries of the thermodynamic system correspond to Fig. 3.12. That case analysis has constant Th1 = 22 °C, Tc1 = 5 °C, and the temperature efficiency of the HRE εT (Eq. 3.21) determines the temperatures of air flows leaving the HRE, Th1 and Tc2 . Therefore, the universal and the functional efficiencies are calculated based on coenthalpy values on the physical boundaries of the HRE. To obtain a universal algorithm for determining the exergy efficiency of the HRE at a variable Te , the proposed sectoral exergy efficiency takes account of the exergy transformation processes taking place inside the HRE and, among other things, reveals the limits of potential to propose and exercise control over those processes throughout the year. Figures 3.18 and 3.19 show numeric examples of ηex as covered in this monograph. The values of said exergy efficiencies for the numeric example in question are shown in Fig. 3.18 and concern the cases of εT = 0.7 and εT = 0.3. In this particular case, we can see that the algorithm proposed and coenthalpy as the chosen state parameter for its realisation allow conducting exergy analysis in line with its principal requirement that the efficiencies must lay within the range of 0 and 1. A fragment of the calculation of the functional η F done under the methodology proposed in the study (Boelman et al. 2009) is shown in Fig. 3.18 demarcated with the red dotted line. There, calculations of functional exergy efficiency produce exergy efficiency values that are even below −1 or above 1. The range between the values of η F and η Fs shows the theoretical potential to boost the exergy efficiency of the process, for

72

3 Exergy Analysis of the Heat Recovery Exchanger of the Air …

Fig. 3.18 The dependency of the universal and the functional exergy efficiencies of the HRE on the RET (with εT = 0.3 on the left, and εT = 0.7 on the right)

Fig. 3.19 Universal ηU (a) and functional η F (b), when the HRE temperature efficiency, εT varies between 0 and 1, (Th1 = 22 °C, Tc1 = 5 °C)

3.2 When Exergy Flows Are Calculated Using Coenthalpy …

73

instance, by exercising its control or applying other engineering measures. On the other hand, due to the sectoral division of the HRE and with reduced exergy flows, the degree of reduction of the amount of exergy destroyed at εT < 0.5 is relatively high (Fig. 3.17), resulting in a rather high functional sectoral exergy efficiency as a relative value. Figure 3.18 shows that ηU has the same values in the case of εT = 0.7 and εT = 0.3. This points to ηU having low sensitivity to the process characteristics. Whereas η F in these two cases is clearly different. The difference between the values of η F and ηU has a particularly high significance in the central part of the diagram. Clearly, as εT increases, the ineffective range shrinks. In Fig. 3.19, numeric results are presented in a wider range of variables. The examples aim to show that the choice of coenthalpy and the rationale behind the direction of exergy flows have kept us on track of the thermodynamic axiom that neither the universal nor the functional ηex is outside the limits of 0–1 in a broad range of variables. Figure 3.19 shows the numeric values of ηex as calculated with the newly developed algorithm within the range of the numeric values of εT between 0 and 1. Figure 3.19 (a) shows the ηU values. This efficiency is clearly symmetrical to εT and 1 − εT . The ηU has limited informative value and sensitivity, because it possesses the same values both at low and high εT . There is a significant and visible difference between the functional efficiency (b) and the universal efficiency (a), when the Te values are at the η F symmetry axis (Thi + T c1 )/2. The range where η F = 0 is wider when the temperature efficiency εT is lower. In the process taking place there, HRE exergy flows travel in opposite directions and destroy exergy. This working range deserves special attention when it comes to achieving the perfection of the control and design solution. This is where the above division of the process HRE into sectors comes in handy. The measurement of exergy efficiency in the HRE when its temperature efficiency εT < 0.5 has little engineering value but points to a logical theoretical foundation. The values of exergy efficiency are enhanced in Fig. 3.20 with the addition of a functional sectoral exergy efficiency to the numeric examples shown in Figs. 3.18 and 3.19. Figure 3.21 shows calculations done with the newly developed algorithm within the range of εT numeric values between 0 and 1. The figure (a) shows the sectoral variation of exergy destroyed in the HRE (by the same analogy as in Fig. 3.17, but in a wider range) at different temperature efficiencies εT . Even though the main plane descends symmetrically from the highest value at εT = 0.5, the reduction in the amount of exergy destroyed at high εT as revealed with the application of sectors is not that significant. The figure (b) enhances the results covered on the basis of Fig. 3.18. The characteristics of the functional sectoral exergy efficiency at εT < 0.5 are clearly visible. Poor temperature efficiencies of the HRE reveal both a substantial difference between the functional and the functional sectoral efficiencies and a significant potential for the improvement of its control and design. Measuring exergy efficiency when the temperature efficiency of the HRE εT < 0.5 ought to be considered reasonable from a theoretical rather than engineering point of view.

74

3 Exergy Analysis of the Heat Recovery Exchanger of the Air …

Fig. 3.20 Change in the universal, functional, and functional sectoral exergy efficiency of the HRE at different non-dimensional environment temperatures (εT = 0.3 on the left, εT = 0.7 on the right)

Fig. 3.21 Exergy destroyed (a) and exergy functional sectoral efficiency (b), when the HRE temperature efficiency εT varies between 0 and 1

3.2 When Exergy Flows Are Calculated Using Coenthalpy …

75

The values of universal exergy efficiencies as shown once again confirm the opinion of other authors that its stability and lack of sensitivity limit its practicality for the purposes of the exergy analysis of the process; ergo, the exergy analysis of the HRE as well.

3.3 Cases of Functional Exergy Efficiency The application of coenthalpy as a parameter of thermodynamic state allows: • determining the amount of exergy flow based directly on the difference of the coenthalpies of the states of the heat transfer media; • judging the direction of exergy flow: from the medium with a higher coenthalpy rating to the medium with a lower coenthalpy; • relying on the reference coenthalpy (REC) ke as the coenthalpy that permanently has the lowest value that does not depend on the heat transfer medium state. These statements regarding the direction of exergy flow could be expended as follows. In the process of heat transfer (in a specific part of the heat exchanger) exergy is delivered to the system by the heat transfer medium with the higher coenthalpy rating, when its coenthalpy (exergy potential) decreases in the direction of the flow of the heat transfer medium (its flowrate). Depending on the shifting RET (and REC at the same time), the heat transfer medium with the same range of temperatures may release exergy at one RET, and receive exergy at another. And this can occur regardless of what the heat transfer medium does with the heat—whether it releases or receives it. Therefore, the directions of heat, mass, and exergy flows are not and cannot be seen as identical. The process of heat transfer between two air flows in the chosen HRE case is simplified to equal values of heat transfer medium flowrates. Employing this example to convey the idea and principles of the methodology presented here makes it easier to transpose and expand the methodological nuances to cases that are more generic in nature and involve different flowrates or other heat exchangers. In general, there are several types of the exergy analysis problem involving the chosen HRE (or another type of heat exchanger). Things to look into include: i.

ii. iii.

the change in the exergy potential (exergy flow—its size and direction) of each heat transfer medium in the process along the heat exchanger or in one of its sector, as the RET shifts; the change in the exergy interaction (exergy transfer) of the heat transfer media in the process along the heat exchanger or in one of its sector, as the RET shifts; the change in the exergy efficiency of the unit (the HRE or another type of heat exchanger) within the chosen range of RET variation.

To solve the first problem, it might be enough to merely calculate the state parameters—coenthalpies (ki and ke )—of the heat transfer media and draw HRE coenthalpy diagrams (Eq. 3.32). Such diagrams were shown for the HRE case in Fig. 3.14 and

76 Table 3.3 The key numeric values of cases of heat transfer in the HRE addressed in the monograph

3 Exergy Analysis of the Heat Recovery Exchanger of the Air … Medium temperature (°C)

Temperature efficiencies of heat recovery exchangers (Eq. 3.21) εT = 0.4

εT = 0.7

εT = 0.9

Heating (hot) medium Th1

22

Th2

15.2

10.1

6.7

16.9

20.3

Heated (cool) medium Tc1

5

Tc2

11.8

will be discussed in detail later. Based on these diagrams, the size and variation of the coenthalpy of the available exergy potential can be analysed. For the second and the third problem, the key issue is making an exergy balance for the system under the given conditions. In other words, the amount of exergy supplied, released, and destroyed within the entire unit or in its separate parts has to be determined. When presenting the methodology (based on the example of HRE exergy analysis), it is worth remembering the conditions of the processes under analysis. The HRE plays host to steady heat transfer from one heat transfer medium to the other. Which means that the heat transfer medium temperatures change along the HRE, but are constant in its particular part. Only the environment temperature (hence the RET) changes, placing in different positions (below, same as, above) vis-à-vis the temperatures of the heat transfer media. Follows an explanation and illustrations of Fig. 3.14 with cases when the environment temperature (used as the reference state for the purposes of exergy analysis) ranges between 0 °C below (a, b), same as (c, d, e, f, g), and 25 °C above (i, h) the temperatures of the working (heat transfer) media. Examples of the coenthalpy diagrams presented (Eq. 3.32) were only provided, with comments, for the case of εT = 0.7 (Fig. 3.14). This section will present HRE cases defined by temperatures (Th ,Tc ), and the temperature efficiency of the heat exchanger (εT ) in Table 3.3, also covering a broader range of values that describe such units.

3.3.1 Characteristic Values of Coenthalpies of the Heat Recovery Exchanger Even though the first and the second problem had different goals formulated for them, the solution in both cases was based on analysis of coenthalpy diagrams. Figure 3.13 contains a temperature diagram for the case of εT = 0.7, showing the characteristic RET cases (a, f, i) out of the nine cases presented in Fig. 3.14. The discussion begins with the case when the environment temperature is below the mass flowrate temperature (a, Fig. 3.14). In this case, the coenthalpy of the hot heat transfer medium (shown in red) has the highest value and decreases along the entire heat exchanger,

3.3 Cases of Functional Exergy Efficiency

77

yet always stays above the coenthalpies of the cold heat transfer medium (shown in blue). Whereas the coenthalpy of the cold heat transfer medium consistently increases in the direction of its flow. This is a classic case of the heat exchanger (that has been dissected in great detail in exergy analysis and is not a subject of any discussion). The amount of exergy released equals the difference between the original and the final coenthalpies of the heat transfer medium. This approach (this rule of calculating the amount of exergy released) holds until the variable RET becomes Tc1 (b, Fig. 3.14), and the coenthalpies, kc1 = ke . As the RET continues to rise, the next state is (c), when the heat transfer medium coenthalpies on the right of the heat exchanger ( Q˙ i = 1) equalise and become kh = kc (c, Fig. 3.14). The nature of transformation of the coenthalpy of the hot heat transfer medium does not change and the coenthalpy consistently decreases. Whereas the original coenthalpy in the direction of the mass flowrate starts to drop in the beginning, reaches ke , and then rises again. As the process continues (the RET continues to rise), this equality of kh = kc moves from right to left in the coenthalpy diagram (one of the d cases, Fig. 3.14), until they move to a central, symmetrical position (e) and reach the heat exchanger’s limit Q˙ i = 0, (g, Fig. 3.14). The numeric value of these equal coenthalpies does not change as such. As the RET continues to rise, another characteristic case would be the temperature of the hot heat transfer medium becoming equal to the environment temperature, when Th1 becomes equal to the RET. Its coenthalpy then becomes equal to the REC: kh1 = ke (h, Fig. 3.14). The sequence in which these characteristic points appear and their numeric values depend on the original conditions: Th1 , Tc1 , and εT . The coenthalpy of the hot heat transfer medium was decreasing in the direction of the flow in the beginning of the process in question (releasing exergy), and then started to climb, and the ke location in the heat exchanger shifted to the left compared to the case with a lower RET (cf. the sequence of d, e, f, g in Fig. 3.14). With the RET rising still, the coenthalpies of the two heat transfer media decrease in the direction of the flow (they both release exergy in the system), reach ke and then start to rise (e, f, g in Fig. 3.14). As the RET continues to rise, we reach the ‘mirror’ process on the other side of the heat exchanger that was covered above. We consistently stick by the rule that exergy is released by the heat transfer medium with the higher coenthalpy rating if its coenthalpy drops in the direction of its flow. Obviously, it never happens in the heat exchanger so that both heat transfer media release heat, however, both of them can release exergy to the system at certain RET values. Formally, in different parts of the HRE and in different proportions, this occurrence takes place between the heat transfer media within a particular RET range: for instance, within the range between Tc1 = Te and Th1 = Te (or at a non-dimensional temperature of T e ≤ 0 and T e ≥ 1). The methodologies referred to in the introduction cannot be (and probably need not) universally applied to measure the changes in the directions of these exergy flows for the purposes of exergy analysis at varying RET. The characteristic ranges of RET values are discussed below in the presentation of three cases of functional exergy efficiency and are shown in Table 3.4. The commentary presented in Sect. 3.3.1 shows a possible way of finding answers to the above questions of the first and the second problems of exergy analysis. Due to the differences in the universal and

Functional exergy efficiency C

Functional exergy efficiency B

Functional exergy efficiency A

Universal exergy efficiency

T e,l=k + ≤ T e ≤

0 < T e < T e,l=k + (kh1 − kh2 ) + (kc1 − ke ) kc2 −ke (kh1 −kh2 )+(kc1 −ke )

Te ≤ 0

kh1 − kh2

(kh2 −ke )+(kc2 −ke ) (kh1 −ke )+(kc1 −ke )

Temperature ranges

Exergy consumed, + econs

kc1 −kc2 kh1 −kh2

kh1 − kh2

Exergy consumed, + econs

Exergy efficiency, η FC (Eq. 3.34)

T e < T e,l=k +

Temperature ranges

Exergy efficiency, η FB (Eq. 3.34)

0

(kh1 − kh2 ) + (kc1 − kc2 )

1 − T e,l=k +

T e,l=k + ≤ T e ≤

(kh2 −ke )+(kc2 −ke ) (kh1 −ke )+(kc1 −ke )

kh2 −kh1 kc1 −kc2

kc1 − kc2

T e > 1 − T e,l=k +

kh2 −ke (kh1 −ke )+(kc1 −kc2 )

(kh1 − ke ) + (kc1 − ke ) (kh1 − ke ) + (kc1 − kc2 )

1 − T e,l=k + < T e < 1

kh2 −kh1 kc1 −kc2

(kh2 −kh=c )+(kc2 −kh=c ) (kh1 −kh=c )+(kc1 −kh=c )

kc2 −kc1 kh1 −kh2

1 − T e,l=k +

kc1 − kc2

(kh1 − kh=c ) + (kc1 − kh=c )

kh1 − kh2

Exergy consumed, + econs

Exergy efficiency, η FA (Eq. 3.34)

T e > 1 − T e,kh =kc

T e,kh =kc ≤ T e ≤ 1 − T e,kh =kc

T e < T e,kh =kc

Temperature ranges

(kc2 + kh2 − 2ke )/(kc1 + kh1 − 2ke ) or 1 − ((kh1 − kh2 ) + (kc1 − kc2 ))/((kh1 − ke ) + (kc1 − ke ))

+ − + l H R E = ein − eout = econsum − e− pr od = (k h1 − k h2 ) + (kc1 − kc2 )

Exergy destroyed

Exergy efficiency, ηU (Eq. 3.33)

− eout = (kc2 − ke ) + (kh2 − ke )

Output exergy

Equation

+ ein = (kh1 − ke ) + (kc1 − ke )

Input exergy

Value

(kh2 −ke )+(kc2 −ke ) (kh1 −ke )+(kc1 −ke )

kc1 − kc2

Te ≥ 1

Table 3.4 Equations for the calculation of universal and functional exergy efficiencies of the HRE at variable reference temperature T e (or Te )

78 3 Exergy Analysis of the Heat Recovery Exchanger of the Air …

3.3 Cases of Functional Exergy Efficiency

79

the functional efficiencies, based on the conditions of the reference environment, separate expressions of efficiency should probably be used as well. Thermodynamically speaking, exergy destroyed l H R E cannot depend on the format of the exergy efficiency chosen for the purposes of the analysis. Efficiency + + (incoming) or econsum (consumed). With could be expressed with exergy flows ein these values, the universal and the functional efficiency could be expressed as follows: lH RE + , ein

(3.33)

lH RE . + econsum

(3.34)

ηU = 1 − and ηF = 1 −

Table 3.4 presents formulas for the calculation of the universal and the functional exergy efficiencies of exergy flows and the amount of exergy destroyed that correspond to the processes visualised in Fig. 3.14. They are instrumental if we are to unequivocally understand the contemplations about the amount of exergy supplied in different cases of exergy efficiency that follow. Here, the differences in the assessment of exergy consumed in the cases of the functional efficiency of the process are demonstrated in a formal way. Getting a grasp of the characteristics of the coenthalpy diagrams that were presented in the commentaries above (Fig. 3.14) makes understanding them and applying them to other heat exchangers really easy. Universal exergy efficiency indeed enjoys a degree of general understanding, yet its lack of sensitivity to system changers limits its use for the purposes of exergy analysis. In this book, its calculation is presented in the general methodological context (Table 3.4, top), but is not covered at length. Functional exergy efficiency depends on the configurational changes of the internal system and has more practicality when it comes to use and/or application, subject to some presumptions.

3.3.2 Three Cases of Functional Exergy Efficiency The monograph proposes three cases of functional exergy efficiency: A, B, C. They are explained hereinafter with the same diagrams of heat transfer medium coenthalpies and temperatures (Fig. 3.14). Analysis of these coenthalpy diagrams offers a certain degree of interpretation in terms of measuring the exergy efficiency of the process. The amount of exergy destroyed within the whole system (HRE) is unambiguous and does not depend on any considerations regarding some presumptions. It is determined as the sum of the differences between the original (input) and the final (output) coenthalpies of the heat transfer medium (Eq. 3.30). The amount of exergy released in the system during the process—the rules and presumptions as to what should be considered the exergy consumed in the system—is up to interpretation.

80

3 Exergy Analysis of the Heat Recovery Exchanger of the Air …

The important thing is that the results of the interpretations do not infringe the principles of thermodynamics (the exergy efficiency is between 0 and 1, and the amount of exergy destroyed is independent on interpretation and is always >0). Otherwise (unless these limitations are observed), the analysis and the indicators could serve local, fragmented (in terms of the energy system or chain) engineering purposes, but it should not be considered a thermodynamic or exergy analysis nonetheless. Functional exergy efficiency A (see Table 3.4). In the chosen part of the heat exchanger (within the range of 0 ≤ Q˙ i ≤ 1), exergy is provided to the system by the heat transfer medium that has the higher coenthalpy rating at that spot, if its coenthalpy decreases in the direction of the heat transfer medium’s flow. Exergy consumed in the system may come from any one (a, b, c, g, h, i, Fig. 3.14) or both (d, f Fig. 3.14) of the heat transfer medium, generally regardless of what they ‘do’ with the heat: release it or receive it. In our case, heat is always released by the heat transfer medium with the index ‘h’, and received by the one with the index ‘c’. In case A of exergy efficiency we consider that exergy is being released by the heat transfer medium as long as, with the RET varying, its coenthalpy reduces in the direction of the flow or until it becomes equal to the coenthalpy of the heat-releasing heat transfer medium at Q˙ i,kh =kc . When designing a calculation algorithm, this location is in each particular case determined with the equation formulated herein (3.27). Heat transfer medium coenthalpies are only equal at T e (hence, RET) values that produce the result of this equation within the range of 0 ≤ Q˙ i ≤ 1. Further solution only requires calculating the value of coenthalpies kh = kc at that part of the HRE. Functional exergy efficiency B (see Table 3.4). The most common attribute of this functional exergy efficiency would be this: heat transfer media release energy to the system either separately (a, b, h, i, Fig. 3.14) or as a pair (c, d, f, g, Fig. 3.14) for as long as its coenthalpy decreases in the direction of the flow and reaches the REC value ke . In terms of T e , this functional exergy efficiency has five characteristic ranges as presented in Table 3.4. With symmetry factored in, it can be said that the number of ranges is three. These symmetrical ranges are T e ≤ 0 and T e ≥ 1. Exergy released within these ranges is estimated as the difference between the coenthalpies of one or the other heat transfer medium. In the range of T e,l=k + ≤ T e ≤ 1 − T e,l=k + , the differences between the original coenthalpies of one and the other heat transfer medium and ke are added together. In the rest of the cases, the difference between the coenthalpies of one of the heat transfer media are added to the difference between the coenthalpy of the other heat transfer medium and ke . The resulting Eq. (3.29) allows determining the limits of this range of T e values. Notably, for the purposes of estimating functional exergy efficiency B within this central range, exergy consumed amounts to the input exergy of the universal exergy efficiency. The specific formulas are presented in Table 3.4, and the results of the calculations, in Figs. 3.22, 3.23, 3.24 and 3.25, together with the other functional exergy efficiencies. Functional exergy efficiency C (see Table 3.4). As the environment temperature rises and the RET increases at the same time, the hot heat transfer medium supplies exergy until the original and the final coenthalpies of the receiving heat transfer

3.3 Cases of Functional Exergy Efficiency

81

Fig. 3.22 Exergy flows and exergy destroyed in the HRE at a temperature efficiency of εT = 0.7

Fig. 3.23 The values of the universal and the three functional exergy efficiencies of the HRE at a temperature efficiency value of εT = 0.7

82

3 Exergy Analysis of the Heat Recovery Exchanger of the Air …

Fig. 3.24 The values of the universal and functional exergy efficiency B at different (40%, 70%, 90%) temperature efficiencies of the HRE

Fig. 3.25 The values of the universal and functional exergy efficiencies B and C at different (40%, 70%, 90%) temperature efficiencies of the HRE

3.3 Cases of Functional Exergy Efficiency

83

medium (which has the lower coenthalpy rating) equalise: kc1 = kc2 . As the environment temperature continues to rise in different parts of the heat exchanger, the two heat transfer media both release and receive exergy, swapping roles along the heat exchanger (b, c Fig. 3.14), until they reach kh1 = kh2 (the cases between f and g, Fig. 3.14). In this range (at environment temperatures that match these cases), the entire amount of exergy consumed within the heat exchanger equals the amount of exergy destroyed. With the environment temperature rising, the transformation of the entire exergy supplied within the heat exchanger into exergy destroyed is complete when the coenthalpy of the heat transfer medium that receives exergy (and has the lower exergy rating) starts to increase in the direction of its flow (g, h, i, Fig. 3.14). Therefore, for the purposes of determining functional exergy efficiency C within the range between T e,l=k + and 1 − T e,l=k + , the amount of exergy consumed will equal the amount of exergy destroyed. This characteristic RET value that delineates this range can be obtained with formula (3.29). The specific formulas are presented in Table 3.4, and the results of the calculations, in Figs. 3.22, 3.23, 3.24 and 3.25, together with the other functional exergy efficiencies.

3.3.3 Calculation Results for the Three Cases of Exergy Efficiency Formulas (3.27) and (3.29) for determining the limits of characteristic ranges that were obtained during the study allow estimating the functional exergy efficiencies for exergy analysis—which efficiencies are covered here—in a wide range of chosen parameters at variable RET (or REC). Figures 3.22, 3.23, 3.24 and 3.25 shows some examples of calculations done on the basis of the methodology designed within the scope of this work. Analysis of this visualisation makes it easier to grasp the logic behind the cases that were presented above. The input and output flows were determined for the numeric values in Table 3.3 and with formulas from Table 3.4. The rationale behind designing these formulas and the rules for their application was explained in the comments on the coenthalpy diagrams the individual cases (A, B, C) of functional exergy efficiency. Some of the results are presented for different cases (0.4; 0.7; 0.9) of εT . Exergy flows and exergy destroyed are presented in Fig. 3.22 at a HRE temperature efficiency of εT = 0.7. The line close to the horizontal shows the amount of exergy destroyed, which is not dependant on the RET in a wide range of temperatures by a lot. It is worth remembering that as the RET changes, the heat flow in the HRE is constant in its size and direction (the way it is in our examples), but the amount of the thermal exergy flow shifts. It is worth remembering that the directions of exergy and heat flows should not be seen as identical for the purposes of calculation or illustration or commentary. It may be worth comparing them, but considering them identical would not be thermodynamically correct.

84

3 Exergy Analysis of the Heat Recovery Exchanger of the Air …

So does the direction of exergy flow, which is always aligned with the reference environment temperature. The symmetry axis (generally, T e = 0.5) divides the diagram into the sum of hot and cold heat transfer medium exergy flows as shown on the left, which is dominated by the amount of exergy flow from the hot heat transfer medium. The RET here is below the heat transfer medium temperatures. The comment for the right-hand side of the diagram would take on a ‘mirror’ aspect. The central part of the diagram shows cases when the RET value the temperatures of the heat transfer media overlaps to a certain degree. Here, inside the HRE, we have exergy flows travelling in opposing directions in certain parts of the unit. Their sums draw close to or even become equal with the amount of exergy destroyed. They differ (in certain parts of the diagram or across the board) for every functional exergy efficiency and universal exergy efficiency alike. The rules for their determination were covered in the introduction of every exergy efficiency above, and the formal characteristic boundaries of their variation are presented in Table 3.4. We can see that the values of all exergy flows that are relevant for the purposes of calculating functional exergy efficiencies overlap both on the right, T e ≤ 0 and on the left, T e ≥ 1. They intersect in the middle, mirroring the above interpretations as to what should be considered exergy consumed in each individual case. In the range of T e,l=k + ≤ T e ≤ 1 − T e,l=k + , the flow values for universal and functional exergy efficiency B meet. The flow of exergy consumed in that range for functional efficiency B amounts to exergy destroyed. Obviously, determining these flows is key for the purposes of HRE exergy analysis, owing to the fact that the indicators of exergy efficiency are derivative and are based on Eq. (3.33) for universal exergy efficiency and Eq. (3.34) for functional exergy efficiency. Figure 3.23 offers a chance to compare the values of the universal and the three functional exergy efficiencies in the case covered in Fig. 3.22. Most of the comments match for both figures. On top of that, it can be observed, first and foremost, that in the central part of the diagram, functional exergy efficiency A and C is more susceptible to the properties of the process. It is there that a process with a higher degree of complexity in terms of exergy analysis takes place. Ergo, the goal of having as many as two indicators with a level of sensitivity above the universal exergy efficiency has been achieved. Case B in the middle matches universal efficiency. Figure 3.24 offers a chance to compare the values of universal and functional exergy efficiency B at different HRE temperature efficiencies. When εT < 0, 5, exergy efficiency B, which has been overlapping so far, breaks away from the universal exergy efficiency, thus demonstrating its characteristic in exergy analysis. It reaches the range of a zero value there. Furthermore, it is much more sensitive than the universal efficiency both on the right, T e ≤ 0, and on the left, T e ≥ 1, of the diagram. Of course, this attribute is characteristic to all three functional exergy efficiencies. Figure 3.25 shows a comparison of the values of functional exergy efficiency B and C at different HRE temperature efficiencies. As it was already mentioned, they meet in the T e ≤ 0 and T e ≥ 1 parts of the diagram.

3.3 Cases of Functional Exergy Efficiency

85

Indicator C remains sensitive within a broad range of temperature efficiencies in the central part of the diagram. Figures 3.26 and 3.27 present general spatial images of the cases of HRE exergy analysis covered above. Figure 3.26 shows the spatial surfaces of the solutions + ) = 0 and exergy destroyed (b) of the incoming exergy flow (a) F(Te , εT , ein F(Te , εT , l H R E ) = 0. Figure 3.27 shows spatial surfaces F(Te , εT , η) = 0 for three functional exergy efficiencies A, B, and C and the universal exergy efficiencies within a broad range of cases. Further to previous commentary, it can be added that the differences between the universal exergy efficiency and functional exergy efficiency B are small. Evaluation of the importance of these differences requires a broader analysis of the input range. Considering cases A and C, a conclusion can be made that with the results of the analysis presented here available, their indicators diverge on a much broader scale. Case C appears to be sensitive within the practice, effective range of HRE operation. These results of case study could have a practical application aiming to improve exergy efficiency in designing HVAC systems and implementing optimal functions

Fig. 3.26 Exergy flow (a) and exergy destroyed (b) at a HRE temperature efficiency range of εT = 0–1 and RET = (−10 to 30) °C

86

3 Exergy Analysis of the Heat Recovery Exchanger of the Air …

Fig. 3.27 The values of three functional A (a), B (b), C (c) and the universal (d) exergy efficiencies of the HRE within the range of temperature efficiency of εT = 0–1 and at RET = (−10 to 30) °C

3.3 Cases of Functional Exergy Efficiency

87

of controlling their exergy. Exergy analysis in the field of technical engineering of HVAC systems is only performed in the initial stage of penetration; however, interpreting the process of heat transfer in the HRE within the thermodynamically acceptable limits allows obtaining cases that favour the analysis (such as by way of looking for minimum or zero exergy efficiency areas) and supports the chosen design solutions. The results obtained show that the processes that are addressed here need better solutions supported with in-depth reasoning within the range of non-dimensional temperature of 0–1. It is within this process range that the values of exergy efficiency are the lowest. If the process were to continue for an extended period of time considering the local climatic conditions, avoiding this process would call for better use of the design or control tools. Ways to avoid this process of relatively low exergy efficiency already lie outside of the scope of this case study.

3.4 Summary of This Chapter Two methods for the calculation of functional exergy efficiencies of the heat recovery exchanger considering the variation of the environment temperature were prepared based on the Carnot factor and coenthalpies. The non-dimensional temperature used in both cases connects the environment temperature and the temperature of the heat exchange process (these are important for the purposes of exergy analysis) and the temperature efficiency that defines heat exchangers in engineering practice. With these non-dimensional indicators combined, the exergy analysis data for the heat exchanger become more universal in nature. For the methodology based on the Carnot factor first of all, these indicators are the relative heat flow and Carnot factor as such. This latter expresses the interaction of three Carnot factors (two heat transfer media and the environment, amounting to zero). The non-dimensional temperature connects the environment temperature and the temperature of the heat exchange process, which are important for the purposes of exergy analysis. Temperature efficiency, which defines heat exchangers in engineering practice, was used as well. By nature, it is within the limits of the FLT and cannot bear direct testimony to the exergy efficiency of the process but can be conveniently used for the purposes of heat exchanger exergy analysis. The choice of the coenthalpy parameter as the direct thermodynamic potential of exergy flow and the numeric and graphical interpretation of its variation benefit the exergy analysis of energy transformation processes taking place in the AHU or other devices, and those of a quasi-stationary nature first and foremost. It is worth accentuating the change in the amounts and directions of the exergy flow based on the variable RET. For that purpose, diagrams depicting the shift in the coenthalpy of the heat recovery unit can be generated in the initial stage of the new algorithm already, showing the direct potential, size, and direction of the exergy flow at a variable RET. A deeper meaning of this methodology and the universal nature of the algorithm were revealed by providing in-depth equations for the calculation of HRE exergy and the universal and the three functional exergy efficiencies against a variable RET. The

88

3 Exergy Analysis of the Heat Recovery Exchanger of the Air …

origin of the equations was supported with arguments, the results of their applications were illustrated. A numeric and graphical analysis of the coenthalpy diagrams, exergy flows, exergy efficiency, and the trends of their variation provides a better insight into the characteristics of the processes. The broad analysis of the universal and the functional exergy efficiencies with regard to the HRE revealed their properties and unique features. The functional exergy efficiencies obtained are clearly seen to have a higher degree of sensitivity compared to the universal process efficiency of the HRE. The two newly formulated exergy analysis algorithms of the range of variation of the processes taking place within the HRE remain universal and can be extrapolated to the complete energy chain of the building’s needs. They are in line with the fundamental tenets of thermodynamics: the exergy efficiency of processes can be within the range of 0 and 1, and the amount of exergy destroyed in them can only be above 0. When it comes to designing HVAC systems and applying exergy-optimal solutions to control their operations, these algorithms objectively take account of the possibilities to use exergy in an efficient manner. They fully cover the exergy transformation processes taking place in these HREs and also show the limits of possibilities for designing HVAC and choosing the controls for such processes throughout the year. In a more narrow sense, this provided a possibility to conduct the exergy analysis of the AHU and its components as presented in this book. The methodology and the algorithm that have been developed help resolve problems with the clarity of the concept of exergy efficiency when they are applied for the purposes of design assessment and process improvement. This approach could have a broader scope of application that goes beyond the HRE. First of all, it can be used in cases where energy transformation processes take place at temperatures close to the environment and exergy analysis aims to factor in the varying reference temperature.

Chapter 4

Analysis of the Modes of Operation of the Heat Pump of the Air Handling Unit

In Chap. 2, the AHU as a thermodynamic system was presented in four diagrams, the first of them serving as a methodological baseline, and in the remaining three, the energy transformers worthy of analysis were the air heat exchanger (water-to-air or electric), the heat recovery exchanger, and the heat pump. Chapter 3 presented methods of the original exergy analysis of the AHU heat exchanger, where the main highlight was the variable RET that followed the shifting pattern of the outdoor air temperature used in ventilation. One of them relies on the application of the Carnot factor, the other, coenthalpy as a parameter of the state. This chapter deals with analytical research of the combinations of powers outputs and energy amounts of the condenser (CN), the evaporator (EV), the compressor (CM), and the throttle valve (TV) of the heat pump (HP). It was done under the characteristic baseline ventilation conditions pertaining to the temperature of the room and the outdoor air. Within the framework of this research, the characteristic resultant conditions are considered to be the states of air and the HP refrigerant that are primarily defined by temperatures and other ancillary or derivative parameters (such as enthalpies, coenthalpies, pressures, and so on). The graphical representation of the results of the parametric analysis shows the limiting or resulting values of state parameters with a focus on air heating and the interaction of the HP components to achieve that purpose. It furthermore presents indicators of operating efficiency: the coefficient of performance, exergy destroyed, and exergy efficiency.

4.1 The Thermodynamic Analytical Correlations of the Air Handling Unit Heat Pump Components In general, the heat pump consists of two heat exchangers and two pressure transformers. These are heat exchangers—the heat-receiving evaporator and the heatreleasing condenser. As the refrigerant flows from the evaporator to the condenser, © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 V. Martinaitis et al., Exergy Analysis of the Air Handling Unit at Variable Reference Temperature, https://doi.org/10.1007/978-3-030-97841-9_4

89

90

4 Analysis of the Modes of Operation of the Heat Pump …

Fig. 4.1 The heat pump transferring heat between two air flows

the compressor increases its pressure, and as it flows from the condenser to the evaporator, its pressure is reduced by the throttle valve. A diagram of the heat pump exchanging energy with the air flow is shown in Fig. 4.1. The combination of these processes makes a reverse cycle as shown in Fig. 2.9. The heat pumps and their heat exchangers—the evaporator and the condenser—operating in HVAC units do so in modes of heat transfer medium state parameters that approximate the variable Te , hence the RET. Of course, the heat transfer medium temperatures within the condenser are often above the temperature of the outdoor air: T2 > T4 > Te , and are lower in the evaporator: T5 ≈ T1 < Te , as shown in Fig. 2.10. Also, as it was already mentioned, heat transfer medium parameters are indexed with numbers, and air parameters, with letters. The energy balance of this heat pump is: Q˙ C N = E˙ C M + Q˙ E V .

(4.1)

Or, if expressed with heat transfer medium state parameters: M˙ f (h 2 − h 4 ) = M˙ f (h 2 − h 1 ) + M˙ f (h 1 − h 5 ).

(4.2)

The energy efficiency of the heat pump as expressed with its coefficient of performance (COP) is: C O PH P =

Q˙ H P Q˙ C N h2 − h4 = + = . + ˙ ˙ h2 − h1 EH P EC M

(4.3)

4.1.1 Energy Balances of the Heat Pump Components Figure 4.2a and b shows diagrams of the evaporator and the condensers as counterflow heat exchangers where the heat transfer process is defined by the heat flow

4.1 The Thermodynamic Analytical Correlations of the Air …

91

Fig. 4.2 Diagrams of the heat pump components

transferred and the parameters of the input and output state of the heat exchangers: the difference between temperatures or enthalpies. Figure 4.2c and d shows diagrams of pressure alternators: the compressor and the throttle valve. The specific feature of the compressor is that it is supplied with work (exergy) E˙ C M , which allows changing the state of the refrigerant. The specific feature of the throttle valve is that it is host to the flow process, also known as throttling, only; the refrigerant and the environment exchange neither work nor heat at this stage. Energy (heat) balance equations for heat exchangers (indices as per Figs. 4.1 and 4.2) EV : M˙ f (h 1 − h 5 ) = M˙ V (h E − h w ),

(4.4)

CN : M˙ f (h 2 − h 4 ) = M˙ V (h K − h c ).

(4.5)

The energy balance equations for the heat pump pressure alternators CM : E˙ C M = M˙ f (h 2 − h 1 ),

(4.6)

TV : M˙ f h 4 = M˙ f h 5 .

(4.7)

92

4 Analysis of the Modes of Operation of the Heat Pump …

The heat exchanger energy balance equations based on a comparison of the flows of heat consumed and produced EV : Q˙ E V = M˙ f (h 1 − h 5 ) = M˙ V (h E − h w ),

(4.8)

CN : Q˙ C N = M˙ f (h 2 − h 4 ) = M˙ V (h K − h c ).

(4.9)

Assuming that the relative mass flowrate is M H P = M˙ f / M˙ V , these cases can also be presented in the following format EV : q E V,V = M H P (h 1 − h 5 ) = (h E − h w ),

(4.10)

CN : qC N ,V = M H P (h 2 − h 4 ) = (h K − h c ).

(4.11)

4.1.2 Exergy Balance and Exergy Efficiency of Heat Pump Components The exergy balance equations for the heat exchangers shown in Fig. 4.2 are formulated in a way similar to (2.10) and (2.11) in the case of energy balance. Comparable exergy flows ei and coenthalpies ki will be subject to the indices applied in Fig. 4.2. The exergy balance expressed as the components of the consumed–produced exergy flows: + ˙ = E˙ − E˙ consum pr od + L  .

(4.12)

When expressed with comparable exergy flows EV : M˙ f eh+1 − M˙ f eh−5 = M˙ V eh+E − M˙ V eh−w + L˙ E V ,

(4.13)

CN : M˙ f eh+2 − M˙ f eh−4 = M˙ V eh+K − M˙ V eh−c + L˙ C N .

(4.14)

4.1 The Thermodynamic Analytical Correlations of the Air …

93

When expressed with coenthalpies as a parameter of the state under Eq. 2.7 EV : = M H P (k1 − k5 ), e+ E V consum,M

(4.15)

CN : eC N consum,M = M H P (k2 − k4 ).

(4.16)

e E V pr od,M = k E − kw ,

(4.17)

eC N pr od,M = k K − kc .

(4.18)

The amount of exergy destroyed in the heat transfer process concerned, L˙  = + − E˙ − E˙ consum pr od for the evaporator and the condenser EV :     L˙ E V = M˙ f eh+1 − eh−5 − M˙ V eh+E − eh−w ,

(4.19)

CN :     L˙ C N = M˙ f eh+2 − eh−4 − M˙ V eh+K − eh−c .

(4.20)

Using coenthalpies as a parameter of the state, it follows from these equations that EV : l E V,M = M H P (k1 − k5 ) − (k E − kw ),

(4.21)

CN : lC N ,M = M H P (k2 − k4 ) − (k K − ec ).

(4.22)

The amount of exergy destroyed in heat transfer depends on the coenthalpies of the original states of the heat transfer media, which under Eq. 2.6 depend on the variable Te , which is considered to be the RET. The exergy balance equation for the heat pump pressure alternators CM : E˙ C M = M˙ f (k2 − k1 ) + L˙ C M , TV :

(4.23)

94

4 Analysis of the Modes of Operation of the Heat Pump …

M˙ f (k4 − k5 ) = L˙ T V .

(4.24)

As was the case with the evaporator or the condenser, these equations can be used to obtain the necessary derivative values for the compressor and the throttle valve. The functional exergy efficiency of the heat pump components expressed in coenthalpies as parameters of the heat transfer medium state EV : η F,E V =

k E − kw M H P (k1 − k5 )

,

(4.25)

.

(4.26)

CN : η F,C N =

k K − kc M H P (k2 − k4 )

CM : η F,C M =

M˙ f (k2 − k1 ) , E˙ C M

(4.27)

L˙ T V = 0. ˙ M f (k4 − k5 )

(4.28)

TV : η F,T V = 1 −

The comparable indicators of the HP exergy efficiency are the universal (ηU ) and the functional (η F ) exergy efficiencies that were presented in Sect. 2.4 and the exergy destroyed, L˙ H P . The instance of the heat pump addressed in this case and shown in Fig. 4.1 would be as follows. The universal exergy efficiency would be determined as the ratio between the exergy flows of the out and in states of air transformed in the heat pump. We supply the heat pump running in the AHU with the exergy flows of the compressor’s power and the room air: + = eC M + (k R − ke ). ein

(4.29)

This heat pump allows us to obtain exergy flows for the outdoor and the room: − = (k R − ke ) + (k E − ke ). eout

(4.30)

In this case, the universal exergy efficiency of the heat pump is: ηU =

− eout (k R − ke ) + (k E − ke ) . + = eC M + (k R − ke ) ein

(4.31)

4.1 The Thermodynamic Analytical Correlations of the Air …

95

The functional exergy efficiency is determined as the ratio between the exergy flows produced and consumed by the system. In the heat pump running within the AHU, we consume the compressor’s power and the exergy flow generated by the differences in the coenthalpies of the room air and the air leaving the evaporator: + = eC M + (k R − k E ). econsum

(4.32)

That way, we generate the exergy flow of the heat pump measured as the difference between the coenthalpy of the room air and the coenthalpy of the outdoor air ke as REC: e−pr od = k R − ke .

(4.33)

In that case, the functional exergy efficiency of the heat pump is: ηF =

e−pr od + econsum

=

(k R − ke ) . eC + (k R − k E )

(4.34)

As it was mentioned in the case of heat exchangers, the amount of exergy destroyed is identical in both cases: l H P = eC − (k E − ke ).

(4.35)

Numeric results of these indicators are presented in Sect. 4.5.

4.1.3 Correlation Between the Parameters of the Heat Transfer Process in the Heat Pump Evaporator and Condenser The shift of the refrigerant’s state within the heat pump cycle is shown in Fig. 2.9. It occurs in the course of heat transfer processes taking place in the condenser (CN) and the evaporator (EV) between the refrigerant and the air. The reciprocal position of their temperature variation is shown in Fig. 4.3. The heat transfer processes taking place both in the condenser and in the evaporator are described using the same set of equations at their respective (chosen or estimated) specific heat flows (AU )C N and (AU ) E V . This monograph is limited to these two indicators that express the values of these heat exchangers. For the purposes of this problem, the thermohydrodynamic processes (and heat release and transfer indicators first and foremost) are considered to be similar for each of the heat exchangers, as they take place within a rather limited range of temperatures. As a result, they are not subject to analysis, and neither is the constructional calculation of the heat exchangers. The equations that connect the parameters of the state of the air and the

96

4 Analysis of the Modes of Operation of the Heat Pump …

Fig. 4.3 The shift of air and refrigerant temperatures in the condenser and the evaporator

refrigerant and the size of the heat exchangers are presented in Table 4.1, without repeating the substitution of temperatures with enthalpies, and vice-versa. The dependencies of the shift in the differences between isotherms and temperatures are connected with equations of energy balance and heat transfer. For the sake of simplicity of the solution (as necessary rather than always), the refrigerant temperature is assumed to be constant in the entire length of the CN and the EV (Fig. 4.3, there are no ‘breaking’ points, e.g. T3 ). In reality, they would happen nonetheless, although their impact on the outcomes of this problem is not significant. The resultant equations are presented in Table 4.2; together with the equations in Table 4.1, they make the analytical foundation of this chapter. The independent parameters stemming from the AHU’s functionality are the air flowrate M˙ V , its specific heat c pa , the air supplied to and exhausted from the room Table 4.1 Equations of heat transfer processes in the CN and the EV Condenser (CN) Q˙ C N = M˙ V c pa (TK − Tc ), Heat flow released to (CN) or by (EV) air (4.36) Heat flow released to (EV) or by Q˙ C N = M˙ f (h 2 − h 4 ), (4.38) (CN) refrigerant Q˙ C N = (AU )C N TC N , Heat flow transferred (4.40) Specific heat flow

(AU )C N = (4.42)

M˙ V c pa (TK −Tc ) , TC N

Evaporator (EV) Q˙ E V = M˙ V c pa (Tw − TE ), (4.37) Q˙ E V = M˙ f (h 1 − h 5 ), (4.39) Q˙ E V = (AU ) E V TE V , (4.41) (AU ) E V = (4.43)

M˙ V c pa (Tw −TE ) TE V

4.1 The Thermodynamic Analytical Correlations of the Air … Table 4.2 Parametric dependencies of CN and EV isotherms

Equations of refrigerant isotherms

Condenser (CN)

Evaporator (EV)

TC N i zot =

TE V i zot =

Tc +TK 2

Tw +TE 2

+ TC N ,

− TE V ,

(4.45)

(4.44) TC N i zot =

Heat pump equation

97

Tc +TK 2

+

TE V i zot =

Tw +TE 2

M˙ V c pa (TK −Tc ) M˙ V c pa (Tw −TE ) , (4.46) , (AU )C N (AU ) E V (AU ) E V TC N C O PH P −1 (AU )C N = TE V C O PH P . (4.48)

−

(4.47)

at a steady temperature TR . εT , the temperature efficiency of the HRE, which is technologically connected to the HP and is an independent value as well. It defines the variation of temperatures Tc , Tw , which are independent in terms of the HP process problem, in the equations that follow. The variable parameters depend on the evershifting environment air temperature Te as the RET. When the climatic conditions require the largest amount of exergy, we have the estimated (baseline) temperature Te0 . Besides, the room temperature, the temperature downstream of the CN towards the room TK , and the temperature going from the room in the direction of the HRE Th are the same. They would be different if the diagram accounted for the air supply and exhaust fans. Rearranged equations from Table 4.2 expressing the values of the isotherm and the temperature difference of the CN and the EV of the heat pump integrated in the AHU are presented in Table 4.3. For the purposes of HP analysis, the simplified, fanless AHU diagram option ‘d’ is selected. Methodologically, it allows using air parameter indices with the same physical values throughout the work. The HRE temperature efficiency for the Table 4.3 The value of the CN isotherm and the difference between the air and the refrigerant temperature CN refrigerant isotherm equation

TC N i zot =

Th (1+εT )+Te (1−εT ) 2

+

M˙ V c pa (1−εT )(Th −Te ) , (AU )C N

(4.49) CN temperature difference equation TC N = TC N i zot − EV refrigerant isotherm equation

εT Th +TK +Te (1−εT ) , 2

TE V i zot =  Th − εT (Th − Te ) − TE V

(AU )C N

(4.51) Temperature difference equation Air temperature after of evaporator

(4.50)

TE V = TC N , (4.52)   )E V . (4.53) TE = Tw − TEMV˙ (AU c V pa

TC N C O PH P −1 T E V C O PH P

2 M˙ V c pa

 +1 ,

98

4 Analysis of the Modes of Operation of the Heat Pump …

equations presented in this chapter above (Tables 4.1, 4.2 and 4.3) εT = 0. It means that there is no heat recovery exchanger in place.

4.2 Parametric Analysis of the Modes of Operation of the Heat Pump Considering that the analytical description of the processes at hand, which are measured with Eqs. 4.1–4.43, has many parameters, the quest for more efficient or optimal combination continues through parametric analysis. Some of the parameters used in the equations vary to some extent in the analytical model; however, that is as yet impossible to achieve in the real-life unit (for instance, the size of the heat exchangers, or rather their specific heat flow). Variation of other parameters can be achieved but it would require an algorithm to control them that would guarantee relatively high and stable indicators of their energy and exergy efficiency. Thermodynamically speaking, said indicators should have their sensitivity to the distance between the refrigerant’s isotherms measured. Controlling their position and the distance between them with throttling (hence, simplicity) negatively affects exergy indicators. Doing so otherwise could create technological difficulties in process control (hence, complexity). The parametric analysis has made it possible to reveal the parameters that affect the development of this algorithm. The following chapters present graphical material of the numeric results of this analysis, accompanied by commentary and interpretations that the authors consider to be relevant. Combinations of the parameters of HP heaters/coolers that are thermodynamically optimal for the AHU considering its characteristic conditions of operation were established.

4.2.1 Characteristics of Parametric Analysis The AHU must supply a variable heat flow that is defined with Eq. 2.40, its production directly split between the condenser and the heat exchanger of the heat pump. Indirectly, generating this heat flow also involves the evaporator and fans. The purpose of the parametric analysis presented in this chapter is to evaluate the modes and efficiency of the heat pump. The problem of parametric analysis is formulated considering the technical ability of heat pumps to alter the parameters of the unit and the process with the RET continuously varying. Here, the optimisation criteria would be the coefficient of performance (COPHP , Eq. 4.3), exergy efficiency (Eqs. 4.24, 4.25, 4.31, and 4.34), and the amount of exergy destroyed (Eqs. 4.21, 4.22, and 4.35). The scope of this book does not include solving the optimisation problem directly in an analytical way. The analysis is based on state-of-the-art unit efficiency indicators, which are presented for the whole of the AHU at the end of Sect. 5.3. Research and engineering

4.2 Parametric Analysis of the Modes of Operation of the Heat Pump

99

experience or information provide the foundation on which process alternatives are built with possibilities for the exergy optimisation of the operation of the HP and the AHU general imbedded in them. In general, they can be described as follows: the HP integrated in the AHU must supply a constantly shifting heat flow that is independent of Te (and of εT to some extent). The possibilities for it to run in a stopand-go mode are very limited, because air needs to be supplied and adequately heated on an ongoing basis, and storing heat is virtually inacceptable. On the other hand, before the matter of storing heat can be addressed, the HP’s specific possibilities in this process need to be identified. As it was mentioned in Sect. 2.5, the room temperature TR and the amount of air for ventilation M˙ V are considered to be constant. The temperatures of the heat transfer media (the air and the refrigerant) and/or the differences between them have the ability to change. Increasing the compressor efficiency εiC M has a limited potential. Other parameters should possibly remain steadier at the parametric combinations limited by the FLT. These parameters are, first of all, the specific heat flows (AU )C N and (AU ) E V . It is, indirectly, the physical value and the thermal power of the CN and the EV.

4.2.2 The Logic and Alternatives of Optimising Processes Within the Air Handling Unit The heat pump of the air handling unit in question uses Freon R410A as refrigerant, its diagram p–h in Fig. 4.4 showing the boundaries of the HP processes concerned. With constant isotherms, the condenser isotherm TC N i zot ≈ 30 °C and the evaporator isotherm TE V i zot ≈ −30 °C. This choice is based on the temperature of the air necessary for the room, which is above 20 °C, and, in the case of cold climate, the temperature of the outdoor air, which sometimes can be close to −30 °C. This corresponds to the red lines in Fig. 4.4. The direction of the isotherms of the other refrigerant in parametric analysis is displayed here as well. The aim is finding a cycle control algorithm with a high efficiency rating. In this case, the parameters of the refrigerant of the regulated HP cycle fluctuate between the red lines (at low outdoor air temperatures) and the blue lines (at outdoor air temperatures that are similar to those of the room temperature), depending on the environment temperature. This is discussed in more detail in the next chapters. The option of overcooling the refrigerant in the condenser or overheating it in the evaporator is not on the table. The solutions of the equations in Tables 4.1, 4.2 and 4.3 are not unambiguous and demand additional conditions (assumptions, limitations, revisions). Figure 4.3 and the formulas in Table 4.1 show that the HP heat flows in the CN and the EV depend on the refrigerant’s flowrate M˙ f , and isotherms TE V i zot = T4 = T3 , and the difference between the CN and EV isotherms defines the power output of the compressor, the HP’s COP, and, in combination with Te , the HP

100

4 Analysis of the Modes of Operation of the Heat Pump …

Fig. 4.4 The boundaries of the heat pump cycle parameters in examples of numeric analysis

ηex . With this in mind, alternatives for the analysis are developed, based on options of HP isotherm TC N i zot and TE V i zot variation. Alternatives of parametric analysis of the heat pump operating in the AHU: • alternative C: TC N i zot = const ≈ 30 °C, TE V i zot = const ≈ −30 °C. • alternative V: analysis of the numeric results of alternative C is followed by a choice of TC N i zot = var, TE V i zot = var. In both cases, the flowrate of the air for ventilation is 560 m3 /h. The ventilated room does not have any heat inflow, its air temperature is 22 °C. The estimated reference environment temperatures are within the range of Te = −30 to 10 °C. These absolute indicators are shared by all alternatives and do not have any major direct impact on the relative indicators that are addressed below. This choice is primarily based on the variation of the resultant indicators (AU )C N and ( AU ) E V of the CN and the EV of the heat exchangers in alternative C. Technically speaking, the CN and the EV in the heat pump have a steady geometrical shape and dimensions, yet following the inherent modes of AHU operation (i.e., the FLT

4.2 Parametric Analysis of the Modes of Operation of the Heat Pump

101

between its components first and foremost), they change under the conditions of calculation for alternative C. They can be sized for a particular AHU so as not to undermine the functionality of the whole unit. Their size would amount to the lowest value obtained in the calculations at the very least (which is the acceptable engineering practice). That size would be sufficient in other cases. Barring further analysis, it is evident that these unit reserves (in terms of their size and/or power output) are the reserves of the possibilities of the optimal solutions for units that operate in a variable mode. The initial analysis of the results of alternative C is followed by the following logical sequence in alternative V: Eqs. 4.46 and 4.47 are applied to obtain (AU )C N 0 at the assumed Te0 , which mirrors the highest exergy demand of the AHU or its HP, depending on the climatic data on a particular locale. That is covered in Chap. 6, which deals with seasonal efficiency. At the assumed Te0 , we have Q C N 0 = (AU )C N 0 TC N 0 . These are the conditions under which TC N and TE V are chosen, assuming that TE V 0 = TC N 0 (Eq. 4.52). Following the correlation between the prior choices in the energy balance Eq. (4.48), COPHP0 is selected. As a result of these choices, the specific heat flow of the EV, (AU ) E V 0 = (AU )C N 0

TC N 0 C O PH P0 − 1 . TE V 0 C O PH P0

(4.54)

becomes a definite value. With Te continuing to change, (AU)KN0 remains nearly constant in these equations, and the main variable (4.51) is TE V i zot = f (Te ). The variation of T KN is partly limited by the engineering practice; however, its reduction as Te increases (and the amount of the heat flow needed to supply air for ventilation at the same time) does not create any technical problems. Other methods of choosing an initial TE V i zot (at the lowest Te ) and their justification cannot be ruled out. On the other hand, the method proposed here can be enhanced with exergoeconomic valuations of the heat exchangers or the whole AHU that would allow obtaining unambiguous values of T and initial TE V i zot . Therefore, with alternative V, the refrigerant isotherms TC N i zot = var are within the range of (40–27) °C, TE V i zot = var, within the range of (−45 to 6) °C. Their operation is analysed within the typical range of temperatures of the heating season: between Te −30 and 10 °C. Detailed modal and efficiency indicators of the two alternatives are presented below.

4.3 Heat Recovery Processes Between the Two Cooling Air Flows in the Heat Pump A diagram of the heat pump transferring heat between two flows of ventilation air was introduced in Fig. 4.1 in the beginning of this chapter. The figures below showcase how the parameters and indicators—temperatures, Carnot factors, and

102

4 Analysis of the Modes of Operation of the Heat Pump …

coenthalpies—applied for the purposes of exergy analysis covered by this book vary within this unit. Figure 4.5 demonstrates alternative C of constant-temperature isotherms in the evaporator and the condenser. Figure 4.6 shows alternative V of variable-temperature isotherms in the evaporator and the condenser. These calculation results are presented for three cases of the environment (reference) temperature Te (RET): −30; −20, and 10 °C. Each of the temperatures is matched by a vertical case in the figures. An identical scale of power on the abscise axis was maintained whenever possible, even though this was not the case for 10 °C. The figures introduce limited analytical information yet they reveal the correlation between and the specifics of the indicators used in the methodology. The diagram of the temperatures of the heat transfer process shows that the outdoor air temperature Te and the refrigerant isotherm temperature in the evaporator T1 = T5

Fig. 4.5 Variation or air and refrigerant temperatures, Carnot factors, and coenthalpies between the two ventilation air flows in the heat pump transferring air at constant-temperature isotherms in the evaporator and the condenser (alternative C)

4.3 Heat Recovery Processes Between the Two Cooling Air Flows …

103

Fig. 4.6 Variation or air and refrigerant temperatures, Carnot factors, and coenthalpies between the two ventilation air flows in the heat pump transferring air at variable-temperature isotherms in the evaporator and the condenser (alternative V)

= −30 °C overlap in the column on the left. As a result, the Carnot factor amounts to 0 along the evaporator, and coenthalpy does not change. The fact that in the case of Te = 10 °C the evaporator’s Carnot factor departs from the Carnot factor of the air speaks about an increase in the amount of exergy destroyed. The same is evident from the massive change in the refrigerant coenthalpies k5 − k1 compared to the insignificant change in the air coenthalpies during the heat transfer process taking place in the evaporator. These comments are fragmented yet they show that, if one were to understand their thermodynamic significance, these diagrams would reveal the specifics of the process. In alternative V (Fig. 4.5), the Carnot factors are drawing closer to one another from left to right. The differences in the coenthalpies of the air and the refrigerant are closer to each other. This speaks about a drop in the amount of exergy destroyed in the evaporator.

104

4 Analysis of the Modes of Operation of the Heat Pump …

The typical results of exergy analysis for alternatives C and V are presented in more detail in the following chapters.

4.4 Results of Parametric Analysis of the Heat Pump as an Air Handling Unit The processes of energy transformation in the AHU and its HP are represented by a substantial number of different parameters. On the other hand, optimisation done by way of parametric analysis involves juggling between knowledge of thermodynamic process limitations and intuition, investigative skills, and engineering practice. Whenever possible, the two alternatives will be discussed in parallel. The beacon and the original graphical expression of optimisation in this monograph would be the variation of the temperatures of the heat transfer media (air and refrigerant) between the two air flows in the heat-transferring heat pump (Fig. 4.1). Figure 4.7 shows both alternatives: alternative C above, and alternative V below. The following temperatures are visualised: Te = Tc , the outdoor air temperature that also amounts to the temperature upstream of the condenser; TR , the room temperature that amounts to the temperatures downstream of the condenser and upstream of the evaporator; TE , the temperature of exhaust air downstream of the evaporator. The refrigerant temperatures are marked with solid lines in Fig. 4.7 and the nature of their variation is the key factor differentiating alternative C from alternative V. When alternative C is adopted as the starting point of parametric analysis, the air temperatures have been observed to tend to shift towards the room air temperature TR (which, in the case at hand, is 22 °C) as the outdoor air temperature and Te increases. The parametric analysis reached alternative V, where the variation of the temperatures of the isotherms of the heat exchangers (the evaporator and the condenser) would follow the same pattern. This is shown in the figure on the right. The air temperatures in the room downstream of the condenser and upstream of the evaporator are steady in all cases; they are equal to one another and do not depend on Te . Figure 4.8 shows and compares other modal parameters of the same alternatives. These are the compressor power, the refrigerant flowrate, the specific CN and EV heat flows (AU )C N and (AU ) E V , and the differences between the air and refrigerant temperatures, TC N and TE V in these heat exchangers. The refrigerant temperatures are reiterated as well. In case C, significant variation of the specific heat flows required for the heat exchangers, AU , is observable first and foremost. Within the Te in question, it decreases by half for the condenser, and by nearly ten-fold for the evaporator. With variable AU values obtained in the calculations, the values that are the highest would need to be selected for a real-life unit. Going outside of the scope of thermodynamic analysis, this can be said to make the unit larger and more expensive. The temperature difference between the refrigerant and the air changes in both of the heat exchangers, decreasing for the CN and increasing for the EV.

4.4 Results of Parametric Analysis of the Heat Pump …

105

Fig. 4.7 The dependency of the air and the refrigerant temperatures on the air (environment) temperature Te at constant (alternative C above) and variable (alternative V below) refrigerant isotherms TC N i zot and TE V i zot

In case V, the refrigerant and the air temperatures (their continuations) intersect at the room temperature marker TR (22 °C). The temperatures varied but the variation was limited to the task of heating the air supplied to the adequate temperature, i.e. TC N i zot > TR . In case V, the temperatures of these isotherms move in the direction of one another (with the EV isotherm demonstrating a higher degree of variation). One result of the parametric analysis of the modes of variation of one of the required temperatures would be case V in Fig. 4.7, where the specific heat flows of the CN and the EV, (AU )C N and (AU ) E V vary to a small extent. In case V, the temperature differences are TE V = TC N . The variation of the compressor power and the refrigerant flowrate is similar in both cases, their absolute values are quite comparable. Their differences are more pronounced in the discussion and comparison of the efficiency indicators of the alternatives below. All these indicators were obtained with the equations presented in Tables 4.1 and 4.2. In case V, the HP variable rotation rate compressor CM must have the right ‘flowrate–pressure’ characteristic and, together with the throttle valve TV, should operate under the control algorithm aligned with

106

4 Analysis of the Modes of Operation of the Heat Pump …

Fig. 4.8 The dependency of the modal parameters of the heat pump with constant (C) and variable (V) evaporator and condenser isotherms on the temperature of the outdoor air, Te

the defined modes. Combinations of interim modal indicators between alternatives C and V are possible and merit evaluation.

4.5 Results of the Analysis of the Exergy Parameters of the Heat Pump as an Air Handling Unit Figure 4.9 shows the variation of the coefficient of performance (COPHP , formula 4.3) and the universal and the functional exergy efficiencies of the HP alternatives. The absolute value of all these indicators is higher across most of the range. Besides, they are higher at the heating season’s prevalent, duration-wise, RET. The advantage of this circumstance comes into light during the analysis of the AHU seasonal efficiency indicators in Chap. 6. In case C, when the difference of temperatures between the isotherms at 60 °C is stable, the COP is steady across the Te range. In alternative V, the rather stable exergy efficiency values increase at higher Te . These characteristics depend on the amounts and directions of exergy flows and the values of exergy destroyed in the components of the heat pump. This is shown in Figs. 4.10 and 4.11.

4.5 Results of the Analysis of the Exergy Parameters of the Heat …

107

Fig. 4.9 The dependency of the coefficient of performance of the alternatives of the HP transferring heat between the ventilation air flows (COPHP ) and the universal and the functional exergy efficiencies on the outdoor air temperature Te

The key finding is that the absolute values of the variation of exergy destroyed in the components and the nature of the variation (Fig. 4.10) as well as the proportions of distribution between the components (Fig. 4.11) can be influenced by altering the numeric values of the refrigerant isotherms. Of course, this has a direct connection with the values of exergy efficiency and COP indicators. The examples show only two numeric cases of C and V. On the other hand, the reciprocal positions of the absolute values of the COP and exergy destroyed can be altered by choosing different modes between the C and V alternatives that are presented here, or by choosing a smaller original temperature difference between the refrigerant’s isotherms at the minimum Te value in alternative V. In case V, it is chosen to be 85 °C, and in C, 60 °C. This temperature difference equalises at roughly Te ≈ −15 °C. Importantly, the indicators of exergy efficiency in case V are more stable throughout the range, and the COP has a tendency to increase as Te rises. The distribution of the percentage of exergy destroyed in the components is more gradual at the values of the refrigerant’s isotherms in the evaporator and the condenser that are altered using a method of choice.

4.6 Summary of This Chapter The chapter presents a parametric analysis of the power outputs and energy amount combinations of the components of the heat pump used for handling air for room

108

4 Analysis of the Modes of Operation of the Heat Pump …

Fig. 4.10 The dependency of exergy destroyed in HP components with constant (C, on the top) and variable (V, on the bottom) isotherms of the evaporator and the condenser on the environment air temperature Te

4.6 Summary of This Chapter

109

Fig. 4.11 Distribution of exergy destroyed in HP components

ventilation by way of heat recovery. The characteristic indicators are the states of the heat pump (HP) refrigerant in the condenser (CN), the evaporator (EV), the compressor (CM), and the throttle valve (TV). They are defined as temperatures and other ancillary or derivative parameters. The ventilation task is defined by the amount of air for ventilation, outdoor and room temperatures, and the resulting heat flows, their values shifting as the outdoor air temperature varies. The optional, variable or constant parameters would be the temperatures (isotherms) at which the evaporation or condensation of the refrigerant takes place, and the differences between the air and the refrigerant. The derivative parameters would be the specific heat flows of the evaporator and the condenser, the refrigerant flowrate, the compressor power output, the coefficient of performance of the heat pump. A framework of equations is presented, in which these parameters are interconnected for the purposes of the task of ventilation air heat recovery problem.

110

4 Analysis of the Modes of Operation of the Heat Pump …

Controlling said isotherms with throttling (hence, simplicity) negatively affects exergy indicators, while so otherwise could create technological difficulties (hence, complexity). A parametric analysis was performed to reveal the parameters that affect the development of a proper control algorithm, investigate the impact of variation of several thermodynamic, reference environment, and technical parameters on an exergy-efficient solution. The findings were that isotherms that vary in a defined manner point to a possibility to have high and stable heat pump efficiency indicators as the environment temperature varies. The results obtained included the variation of the values of exergy destroyed in the components, the universal and the functional exergy efficiencies and the coefficient of performance (COP) of the heat pump in a wide range of variation of the environment air temperature. The search algorithm that has been designed is expected to open up new possibilities to optimise the cycle of the heat pump involved in the task of ventilation further, and address technological tasks of controlling this cycle.

Chapter 5

Comparative Exergy Analysis of Cases of the Air Handling Unit

It is common knowledge that the operation of a HVAC system depends on the climatic conditions and on the environment temperature in particular. The results scrutinised here confirm that, when it comes to thermodynamic analysis, the consumption of exergy is very much dependant on the environment temperature. On the other hand, an emphasis was made in the introduction that, for the purposes of that analysis, the reference temperature (RET) currently is considered constant as often as not, and any attempts to use it as a variable are not without flaw. The methodology developed by the authors and presented in this study shows that all exergy-based parameters, such as the universal and the functional exergy efficiencies and destruction of exergy are highly sensitive to changes in the reference temperature. The results do not contradict the underlying axioms of thermodynamic (exergy) analysis. Therefore, the methodology proposed can be applied for the purposes of analysing and improving heating, ventilation, and air conditioning systems that as a rule operate at varying environment temperatures, as well as developing dynamic models of such systems and their control algorithms based on exergy. The results of the numeric case of four technological AHU diagrams that were obtained with the newly developed methodology for determining exergy efficiency and were introduced in Chap. 2 will be presented here. It is worth reminding that, apart from the direct exergy efficiency, exergy analysis also includes the amount of exergy destroyed, its structure by components and processes taking place therein. As it was already mentioned in Chap. 3, when it comes to analysing exergy efficiency, two cases are on the table: • universal exergy efficiency: the ratio of all exergy flows leaving and entering the system; • functional exergy efficiency: the ratio of exergy flows generated (produced) and supplied (consumed) for that purpose in the system. Due to the universal and the functional efficiencies being inherently different, this difference should be reflected in the equations for the calculation of the two efficiencies, considering the variable reference conditions. The efficiencies can be © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 V. Martinaitis et al., Exergy Analysis of the Air Handling Unit at Variable Reference Temperature, https://doi.org/10.1007/978-3-030-97841-9_5

111

112

5 Comparative Exergy Analysis of Cases of the Air Handling Unit

+ + expressed with exergy flows entering the system ein (input) or consumed econsum . On the other hand, thermodynamically speaking, exergy destroyed during the process l AHU in any event cannot depend on the specifics of the evaluation of exergy efficiency in determining those flows. The results of the exergy analysis of the heat recovery exchanger (Chap. 3) and the heat pump (Chap. 4) are integrated in this chapter and may overlap, because the heat recovery exchanger and the heat pump are the main components for energy transformation in the AHU. This chapter presents additional equations, complete with brief commentary, that are necessary exclusively for the exergy analysis of the AHU. Most of other applicable analytical expressions were presented in the previous chapters.

5.1 General Input Data of the Cases of the Air Handling Unit Figures 2.6 and 2.7 visualised AHU diagrams, showing the parameters of values of the heat transfer media involved in the process. These are the ventilation air flowrate M˙ V , the room air coenthalpy k R , the exhaust air coenthalpy k E , and the outdoor air coenthalpy ke . They share their indices with enthalpies or temperatures. The common value e± is used in the below equations to measure the exergy flows that are necessary for the purposes of air handling processes and transcend the limits of the system, including those that are not directly tied to M˙ V . It is demonstrated that the system does not generate (e− = 0) any exergy flows that are not tied to M˙ V , and no such flows leave the system; however, such flows can be used by the system (e+ = 0). For the entire AHU: • the energy balance equation is M˙ V h e + M˙ V h R + E˙ C M + 2 E˙ F N = M˙ V h R + M˙ V h E ,

(5.1)

• the exergy balance equation is M˙ V ke + M˙ V k Ro + E˙ C M + 2 E˙ F N = M˙ V k Ri + M˙ V k E + L˙ AHU .

(5.2)

The cases involve the supply of exergy (work, electricity) to the heat pump compressor E˙ C M in diagram c and d. In diagrams a and b it can be replaced with exergy supplied to the water-to-air heat exchanger E˙ W AH or the electric water heat exchanger E˙ E AH . The air handling processes that go beyond the limits of the systems require ‘external’ flows of exergy between the cases of a, b and c, d. In technological diagrams (Fig. 1.7) a and b, the relative exergy supplied is

5.1 General Input Data of the Cases of the Air Handling Unit

e+ =

M˙ W (k W in − k W out ) + e Fs + e Fe , M˙ V

113

(5.3)

where M˙ W is the heat transfer medium flowrate in the water-to-air heat exchanger, kg/s; k W in k W out is the heat transfer medium coenthalpies going in or out of said heat exchanger, kJ/kg; e Fs , e Fe is the relative amount of exergy for the supply and exhaust fans, kJ/kg. With the electric water-to-air heat exchanger, the first term of the equation can be simply replaced with a comparative flow of electricity. In technological diagrams c and d, the relative exergy supplied is obtained by the power outputs needed for the compressor and the fans: e+ = eC M + e Fs + e Fe ,

(5.4)

where eC M is the relative amount of exergy for the heat pump compressor, kJ/kg. The study was based on the following assumptions: 1. 2.

3. 4.

The room and the outdoor air is dry, the quantity of supply air equals the quantity of exhaust air. The AHU is insulated for heat (adiabatic); in addition to the heat exchangers shown in the diagrams, the air also received heat from the supply and exhaust fans. The fan power output is selected based on the indicator recommended for ventilation system design, expressed in W/m3 /s. The room does not have any heat affluxes or other heat sources that can be attributed to ventilation.

In these AHU cases, relative amounts of exergy are expressed with coenthalpy as a state parameter using the equations obtained from the thermodynamic analysis and presented in Table 5.1. In the numeric analysis of the AHU, the ventilation air flow M˙ V and the room temperature TR are constant across all diagrams. The total amount of heat to be provided to the supply air is proportionate to Te (under Eq. 2.40) and is identical for all diagrams. As it was already mentioned, the chosen efficiency indicators of the technological diagrams are their coefficient of performance (COP), the universal and the functional exergy efficiencies, and the amount of exergy destroyed. Across all alternatives, numeric analysis involves the case when the amount of air is 560 m3 /h, and the fan electric output is 2 × 77 W. The room does not have any heat gains, and the temperature of air inside it is 22 °C. The calculations are done within the reference temperature range of Te = −30 to +10 °C. These absolute indicators do not have a lot of direct influence on the relative indicators such as the COP or exergy efficiency that are addressed below. With the HRE (b, d), its temperature efficiency εT , % (60, 70, 80) is specified as defined by Eqs. (2.55) or (2.56). When necessary, an abbreviation HRE70 or the like is used in the legend. The efficiency of the compressor εiC = 0.80 or the fans ε F = 0.82. A slightly heavier focus is placed on a comparison of the exergy indicators of the AHU diagrams under comparable or

l AHU e+ − (k E − ke ) + = 1 − e+ + (k − k ) ein R e (5.10) (k R − ke ) + (k E − ke ) = , e+ + (k R − ke )

ηU AHU = 1 −

(5.9)

+ econsum = e+ + (k R − k E ), (5.6)

+ ein = e+ + (k R − ke ), (5.5) − eout = (k R − ke ) + (k E − ke ) + e− , (e− = 0), (5.7) + − + + l AHU = ein − eout = econsum − e− pr od = e − (k E − ke ),

l AHU e+ − (k E − ke ) =1− + + e + (k R − k E ) econsum (5.11) (k R − ke ) = + , e + (k R − k E )

η FAHU = 1 −

− − e− pr od = (k R − ke ) + e , (e = 0), (5.8)

Functional AHU exergy efficiency

Universal AHU exergy efficiency

Table 5.1 Equations for the calculation of the AHU’s exergy efficiency (based on Fig. 2.7)

114 5 Comparative Exergy Analysis of Cases of the Air Handling Unit

5.1 General Input Data of the Cases of the Air Handling Unit

115

similar conditions. That is why the temperatures of the supplied and returning water in the WAH (a, b) match the heat transfer medium temperatures in the HP condenser (c, d), when it is at 75 °C downstream of the condenser, and at 30 °C in the isothermal phase of the condensation process. The HP uses refrigerant R410A, its p–h diagram in Fig. 4.4 showing the boundaries of the HP processes under consideration. In the diagrams (c, d), the HP is calculated at constant condenser isotherms TC N i zot = 30 °C and evaporator isotherms TE V i zot = −30 °C. This corresponds to the red lines in Fig. 4.4 and alternative C that was covered in Chap. 4. There is also the case (d, HP.V ) when we have variable levels of refrigerant isotherms, i.e. when one of the HVAC system HP controlling algorithms that were revealed in this study with the help of exergy analysis applies. In this case, the adjustable HP cycle refrigerant parameters shift from the values marked with red lines to the ones highlighted with blue lines. The option of overcooling the refrigerant in the condenser or overheating it in the evaporator is not on the table. This case is in line with alternative V that was covered in Chap. 4. The following numeric results of case analysis will be used to demonstrate that the right approach to the directions of heat exergy flows and the identification of their values with the coordinated application of methods devised on the basis of the Carnot factor and coenthalpies allows formulating HVAC system dynamic modelling algorithms and reflecting the specifics of the energy transformation processes in HVAC units with a high degree of thermodynamic validity.

5.2 Graphic Interpretation of Exergy Analysis with Methods Based on the Carnot Factor and Coenthalpies An integral diagram of variation of AHU (HP-HRE70) heat transfer medium (the air and the refrigerant) temperatures is shown in Fig. 5.1. The temperatures are displayed within the range that is typical to real-life ventilation processes and to the HP used for that purpose. To the right of the 0.0 x-axis, there is the thermal power consumed by the AHU, which is generated by the HRE and the condenser. To the left of 0.0, there is the thermal power of the evaporator that it receives from the exhaust air. Methodologically speaking, the choice of the AHU value, Te = −20 °C and the specific numeric values of the heat flow do not affect the problems of exergy analysis concerned. The heating of air in the fans was factored in the calculations, but does not have a direct reflection in the diagram owing to its relatively small numeric value. Figure 5.2 shows the temperature values of the same AHU within the heat exchangers at the outdoor air temperature Te = −30 and 10 °C. Changes are observed both in the reciprocal positions of the heat transfer medium temperatures and in the heat flow transferred through them, as shown on the abscise axis of varying scale. Said methods (based on the Carnot factor and coenthalpies) are also used here in the same numeric case of a fully-kitted AHU (HP, HRE, FN). The cases of variation

116

5 Comparative Exergy Analysis of Cases of the Air Handling Unit

Fig. 5.1 The diagram of air and refrigerant temperature variation in AHU heat exchangers at Te = −20 °C

of the Carnot factors of these cases of three temperatures (Te = −30, −20 and 10 °C) are shown in Fig. 5.3. We can see that the Carnot factor of the outdoor air entering the HRE is always 0. It also amounts to 0 for the evaporator when TE V i zot = Te = −30 °C. The area between the Carnot lines within the limits of the power output of the heat exchanger and other shared power outputs indicates the amount of exergy destroyed, as was shown in Fig. 2.5. The case of +10 °C stands out in its relatively large area and leads to the problem of reducing the amount of exergy destroyed in the evaporator first, when the outdoor air temperature is higher. Figure 5.4 shows the same three cases of outdoor air temperatures, with the states of the heat transfer media expressed as coenthalpies. Notably, in the exergy analysis of the HRE (Chap. 3), the hot and cold heat transfer media of the heat exchanger are air that has the same flowrate—therefore, the results of the analysis are interpreted directly on the basis of the variation of the heat transfer medium coenthalpies. As we evaluate the HRE, the EV, and the CN in an integral manner, this advantage disappears. We have (by choice) the air handling unit with the constant flowrate of M˙ V , but the flowrate of the heat pump’s refrigerant (which is the same for the evaporator and the condenser) depends on Te . Furthermore, the reference numeric values of the parameters of the state of these parameters (enthalpy and entropy) of the thermodynamic state of heat transfer media, which are different in nature, are autonomous. At this stage, the chosen graphical representation shows air coenthalpies, while the coenthalpies of the refrigerant are ˙ reduced at a rate ofM˙ f / M  case, the condenser exergy balance Eq. (4.22)  V . In that ˙ ˙ would be M f / MV k2 − M˙ f / M˙ V k4 = (k K − kc ) + lC N .

5.2 Graphic Interpretation of Exergy Analysis with Methods …

117

Fig. 5.2 Temperatures and heat flows within heat exchangers at an outdoor air temperature of −30 and + 10 °C

So reduced, the coenthalpies of the refrigerant allow for a graphical comparison of the values of exergy flows for the HRE, the EV, and the CN. Notably, the area between the coenthalpies, k = f (Q), does not have any physical, thermodynamic match, like the match between the area and the amount of exergy destroyed in the Carnot case. The key quantitative indicator is the difference between the starting and the final coenthalpies of the process for the specific heat transfer medium, which corresponds

118 Fig. 5.3 Carnot factors and heat flows within heat exchangers at an outdoor air temperature of −30, −20 and +10 °C

5 Comparative Exergy Analysis of Cases of the Air Handling Unit

5.2 Graphic Interpretation of Exergy Analysis with Methods … Fig. 5.4 Coenthalpies and heat flows in heat exchangers at an outdoor air temperature of −30, −20, and +10 °C

119

120

5 Comparative Exergy Analysis of Cases of the Air Handling Unit

to the flow of exergy that it received from and released to the system. It is worth remembering that the value of the coenthalpy that decreases in the direction of the heat transfer medium’s flow in the process (for instance, a particular heat exchanger) indicates that it provides a flow of exergy to the system. If the coenthalpy increases in the direction of the heat transfer medium flow, it is the system that provides the heat transfer medium with an exergy flow. Cases when the coenthalpy increases and decreases in the same unit are covered in Chap. 3, Figs. 3.14 and 3.15. One characteristic case is that of the evaporator at −30 °C, when the coenthalpy does not change due to the refrigerant temperature amounting to the outdoor air temperature throughout the process: RET equal to TE V i zot = Te . In the cases shown in Figs. 5.1, 5.2, 5.3 and 5.4, the isotherms of the evaporator and the condenser do not vary across the entire range of outdoor air temperatures. This would be in line with alternative C covered in Chap. 4. Only then no HRE was used. To determine and optimise the operation of the energy transformation system, analysis of these systems includes an assessment of the amount of entropy and the possibilities to minimise it in the process. Of course, this kind of optimisation does not always benefit the value of the purpose of system design. Combining entropy and the concept of exergy reveals that generating entropy correlates with the destruction of exergy. Furthermore, exergy analysis does not always necessarily aim to minimise the destruction of exergy; instead, the desired outcome may be to achieve a reduction of input and/or output exergy and the maximum exergy efficiency of the system. In this context of AHU exergy analysis, Fig. 5.5 shows the variation of entropy produced within the boundaries of Te = −30 to +10 °C. These results were obtained with Eqs. (2.12) and (2.13). The first equation is attributed to this work’ calculation of coenthalpies that are connected to them on the grounds of entropies, the second one, on the grounds of the Carnot factor. The comparison of the results for the condenser (CN) and the evaporator (EV) in Fig. 5.5b reveals that there is no significant difference between the heat flow measured with the Carnot factor (2.13) or the results obtained with process flow entropies (2.12) within the range of the specific HVAC temperatures. Similar findings are obtained for other AHU components as well. This proves that, when it comes to dynamic modelling algorithms, the method of choice could be one that benefits the available data more. This assumption should be verified for units with a broader range of process temperatures than those that are addressed in this monograph, which are typical to HVAC units. Again, it is worth remembering that the outdoor air temperature in the diagrams always equals the reference environment temperature (RET). Figure 5.6 shows the amounts of exergy destroyed in several AHU components. Considering AHU operation in real-life conditions (within a broad range of outdoor air temperatures), one thing to note is the decreasing values of exergy destroyed in the HRE and the CN, while the amounts of exergy destroyed in the EV and the FNs that do not decrease as the outdoor temperature rises. Therein lies the potential for improving the thermodynamic efficiency ratios of the AHU. In reliance on the above methodological foundation, we can obtain AHU indicators that are relevant for the purposes of HVAC design and are the target of dynamic

5.2 Graphic Interpretation of Exergy Analysis with Methods …

121

h produced in the components of the AHU (HP-HRE70) at different enviFig. 5.5 Entropy  S˙c,irr ronment temperatures (a). Diagram (b) contains an extract from the bottom part of diagram (a), with the EV and the CN calculated with formulas (2.12) and (2.13)

modelling, such as C O PAHU (Eq. 2.42) or exergy efficiency ηex (Eq. 2.43). The dependency of these indicators on the outdoor air temperature (hence, the RET) is shown in Fig. 5.7. Besides, this also demonstrates that, as it was already mentioned before, the HRE efficiency (Eqs. 2.55 and 2.56) plays an important role in terms of the AHU’s coefficients of performance. To that end, two cases of εT amounting to 70–80% are shown. A higher εT allows achieving higher AHU coefficients of performance, especially

122

5 Comparative Exergy Analysis of Cases of the Air Handling Unit

˙ in the AHU components—HRE, EV, CN, and FNs—at different Fig. 5.6 Exergies destroyed, L, environment (outdoor air) temperatures

Fig. 5.7 The dependency of the AHU’s exergy efficiency and COP on the reference temperature

at lower values of the reference temperature. We can see that the HRE exergy efficiency remains nearly constant (in both cases of εT ) because of the air supplied to it at environment temperature. The exergy efficiency of the entire unit is more responsive to the reference environment temperature, seeing how it decreases by as much as several times within the range in question (between −30 and +10 °C). And this can be achieved primarily because the amount of exergy destroyed in the components of the evaporator and the fans is basically independent of the RET (see Fig. 5.6).

5.2 Graphic Interpretation of Exergy Analysis with Methods …

123

Additional calculations show that without the HRE, the AHU’s coefficient of performance C O PAHU would virtually become identical to the HP and in this numeric case would be close to 3. It is worth remembering the specifics of the processes taking place in HVAC units that were already mentioned before. First of all, heat transfer media parameters shift and depend on the highly varying outdoor air temperature Te , which for the purposes of exergy analysis is the reference environment temperature, RET. The pattern of variation of outdoor air temperatures at a particular location is exclusive to that location only. Evaluating and choosing solutions from the engineering and the economic point of view depends on extended, seasonal processes, the efficiency indicators of the units that can only be revealed through dynamic process modelling, exergy analysis being one of its key elements. The results of the case analysis and modelling presented here show that every unit component has its own unique nature of entropy generated, differences in exergy destroyed and exergy efficiency at different reference temperatures. The characteristics of the processes taking place in the AHU that are laid down and demonstrated here, as well as their reflection in dynamic modelling algorithms makes the application of exergy analysis in evaluating and choosing HVAC systems all the more important. This is displayed with a higher degree of clarity through analysis and comparison of the four technological AHU diagrams that were mentioned in Chap. 2.

5.3 Comparison of the Mode Characteristics of the Four Diagrams of the Components of the Air Handling Unit The results of operation and efficiency indicators of the AHU are presented and covered in the illustrations in the following sequence. Each curve in the illustrations is tied to one of the technological diagrams (a, b, c, d) and this is specified in brackets. The abbreviation indicates the method of heating the air: WAH for the water-toair heater (a, b), HP for the heat pump (c, d). When the unit is equipped with a heat recovery exchanger, the abbreviation reads HRE (b, d), with the heat recovery exchanger’s temperature efficiency as a percentage specified next to it (Eq. 2.55). Here, mode characteristics are indicators like heat transfer medium state parameters, flowrates, power outputs, and so on. In other words, these are values that do not carry any direct indication of the results of exergy analysis. The fact that some of the mode characteristics have a straight-line dependency on the reference temperature is not something new, yet the proportions of those indicators and the impact they have in different technological diagrams when they serve the same function—ventilation at a steady flowrate—merit some attention. The examples provided here are part of the potential cases of a future parametric analysis that are opened by the methodology showcased here. First of all, Fig. 5.8 presents variation of the power output of heat exchangers [the water-to-air heat exchanger (WAH) and the condenser (CN)]. In diagrams a and

124

5 Comparative Exergy Analysis of Cases of the Air Handling Unit

Fig. 5.8 Power outputs of heat exchangers of technologically different AHUs

c, these outputs match, because the heat flow required for the direct heating of the outside air does not depend on the unit. The indicators of diagrams b and d match as well when the heat exchangers used have the same level of temperature efficiency (HRE70). These indicators clearly show the role of the HRE and its temperature efficiency. This was highlighted in the process of developing the methodology of their thermodynamic analysis presented in Chap. 3. Figure 5.9 presents the flowrates of the heat transfer media (water for diagrams a, b; refrigerant for diagrams c, d) and the HP compressor output (diagrams c, d). A larger flowrate itself does not have any direct significance, and the amount of energy required for its circulation is proportionate to it. In diagrams c and d, the compressor output is directly proportionate to the flowrate when the same cycle applies in both cases. Therefore, as far as efficiency is concerned, diagram c Only HP has no appeal

Fig. 5.9 Heat transfer medium (water, refrigerant) flowrates and HP compressor power

5.3 Comparison of the Mode Characteristics of the Four Diagrams …

125

Fig. 5.10 Specific heat flows of heat exchangers, differences in temperatures between the heat transfer media

and one of the reasons here is the relatively large refrigerant flowrate. This solution (only without the fans) was analysed in Chap. 4. Figure 5.10 shows the indicators of the heat exchange process in HP heat exchangers—the evaporator and the condenser. Their specific heat flows (AU )C N and (AU ) E V are expressed with the equations presented in Table 4.1. They drop as the environment temperatures increase, and not on a straight-line basis at that, and following a different variation pattern for the condenser and the evaporator. This is evident from numeric solutions, however, physically speaking, indicator A is the size of the heat exchangers that does not change in a real-life unit, while the variation of the heat transfer coefficient is rather limited. This reveals a problem for the parametric analysis: parametric combinations should attempt to achieve an indicator that is more stable and less variable in terms of the reference temperature. Technologically speaking, the temperature difference between the heat transfer media (Fig. 4.3) can be more flexible, yet solving the problem of controlling the AHU processes calls for the correlations shown in Table 4.1 to be maintained. Figure 5.11 shows the variation of the temperature of the air exhausted from the AHU for the diagrams under analysis. In case a, air at temperature T R is simply exhausted from the room (and is even heated to a small degree in the fan). Informal logic dictates that a solution when the temperature of the exhaust air is as low as possible (until it drops below the environment temperature) holds more value. This we have in diagram d: HP-HRE70. A more reliable assessment is obtained in the process of investigating the COP and exergy efficiencies; however, these assessments often overlap with this simplified one. The restriction resulting from parametric analysis that the right-hand extensions of most temperatures intersect at the TR value merits some attention.

126

5 Comparative Exergy Analysis of Cases of the Air Handling Unit

Fig. 5.11 Temperatures of air exhausted from the AHU

Figure 5.12 shows the dependency of COP variation. Solid lines mark cases where a HP is present (c, d). A COP of slightly less than 1 only exists in the case where there is no HP and HRE, i.e. AHU OnlyWAH (a), because a small amount of energy consumed by fans is simply not transferred to the ventilation air. In other cases that do not have a HP as shown here, COPs are above 1, because the HRE recovers heat

Fig. 5.12 The dependency of the AHU’s COP on the reference temperature

5.3 Comparison of the Mode Characteristics of the Four Diagrams …

127

from the exhaust air for heating, which does not even cross the boundaries of the system concerned. In the case where εT = 80% WAH-HRE80 (b), the COP value is close to 5 across the RET range under analysis. This value is much higher than that of the system OnlyHP (c) that only has a HP, which is around 3. Therefore, ignoring the HRE in the AHU that has a HP (for instance, due to the small-form factor) has its own price. Systems with a HP and a HRE (d) are represented by two curves. First of all, they are different in nature from the ones presented above by virtue of interaction of the processes in the HP and the HRE. Even in case b, when the HRE is assumed to have εT = 70%, the COP values for both cases are significantly higher than in case c, which only has a HP. The d cases have the two highest COP values. They differ from one another in a way that the lower values exist in the case where the level of the isotherms of the condenser and the evaporator remains the same across the entire range of outdoor temperatures (alternative C). The highest values exist in alternative V, which was presented and discussed in more detail within the framework of the heat pump exergy analysis in Chap. 4. The method discussed therein was used to modify the isotherm temperatures for the CN and the EV, depending on Te and on TR to some extent first and foremost. The data in the figure show that the coefficient of performance of the AHU can be greatly improved by controlling the heat pump cycle in a way that befits the ventilation task. The idea of the proposed HP cycle control algorithm was shown in Fig. 4.4. It is equally important that the maximum value of the coefficient of performance is located close to the outdoor air temperatures that last the longest in regions with a colder climate. This matter is discussed at length in Chap. 6, where seasonal efficiency indicators of the AHU are presented.

5.4 Comparison of the Exergy Indicators of the Four Diagrams of the Components of the Air Handling Unit This subchapter presents and compares the indicators of the exergy analysis of the selected AHU technological diagrams. These indicators are the amount of exergy destroyed and exergy efficiency. The shared indicators of the whole AHU and its components are discussed, their interaction in terms of these indicators commented upon.

5.4.1 Exergy Destroyed in Air Handling Units Figure 5.13 shows the dynamics of exergy destroyed for the 4 AHU diagrams within the RET range of −30 to 10 °C. We can see that the largest amount of exergy is destroyed in AHU setups without a HRE (diagrams a and c). AHU diagrams with a HRE, especially one that has a high temperature efficiency rating, demonstrate the

128

5 Comparative Exergy Analysis of Cases of the Air Handling Unit

Fig. 5.13 Exergy destroyed for different AHU cases

smallest losses of exergy. Therefore, the importance of the HRE, both in terms of analysis and the usage of the device, merits special attention. Figure 5.13 shows that a combination of a HRE with a high temperature efficiency rating and a HP control algorithm allows boosting the performance results of the AHU. Notably, there has to be some cohesion between the methodologies of thermodynamic calculation of both the operation of the entire AHU diagram and its individual components, especially at a variable RET. Even though Fig. 5.13 showcases a summary of the results of exergy destroyed for each AHU diagram and allows to compare all cases, each combination may be subjected to closer scrutiny. This allows revealing the effect that the components have on the efficiency of the entire unit. Follows a detailed distribution of exergy destroyed in the AHU diagrams under consideration. Figure 5.14 shows the amount of exergy destroyed in the system’s components in the AHU case of Only WAH (a) (in terms of quantity and as a percentage). The WAH here is the main energy transformer here. The temperatures of the water supplied and replaced are constant and independent of Te ; therefore, the amount of exergy destroyed at low outdoor air temperature is relatively large. This can be observed in the distribution of percentages. Of course, this indicator can be brought down by adjusting the temperature of the water used based on Te . Figure 5.15 shows the amount of exergy destroyed in the system’s components in the AHU case of WAH-HRE (b). The system consists of a WAH, a HRE, and two fans. First of all, this should be compared with the previous diagram. In addition to the fans, exergy in diagram b is destroyed in two other components that nonetheless have absolute values way below those of case a. We can compare the amounts in Fig. 5.13. In case b, the amount of smaller. The amount of exergy destroyed in the

5.4 Comparison of the Exergy Indicators of the Four Diagrams …

129

a

b

Fig. 5.14 Exergy destroyed (a) and its distribution (b) in the AHU components in the case of Only WAH (a)

WAH varies on a straight-line basis. Just like in case a, the water temperatures are constant; however, the required water flowrate here is lower. The HRE covers a significant part of the demand for heat, and the amount of exergy destroyed by it decreases consistently (albeit not in a straight line, as the environment temperature rises. The fans have the same value of exergy destroyed across all diagrams, yet their relative impact increased and reached over 50% at 10 °C. We will get back to the fans after all of the diagrams have been presented. The distribution of exergy destroyed in the components for diagrams Only HP (c) and HP-HRE70 (d) is visualised in Figs. 5.16 and 5.17. As the RET rises, the amounts of exergy destroyed in the main HP components decrease drastically. The largest amounts of exergy are destroyed in the condenser (RET = −30 to −18 °C) and in the evaporator (when the RET varies between −

130

5 Comparative Exergy Analysis of Cases of the Air Handling Unit

Fig. 5.15 Exergy destroyed (a) and its distribution (b) in the AHU components in the case of WAH-HRE (b)

18 and 10 °C). Whereas the amount of exergy destroyed in the fans remains almost stead within the entire RET range under consideration. In the relative investigation of the distribution of exergy destroyed in the AHU (c) (Fig. 5.16, above), the portion of exergy destroyed remains constant in the compressor (14%) and in the throttle valve (16–17%) across the RET range. However, as the RET increases, we can observe the inevitably growing impact of the fans in this system. The portion of exergy destroyed in the fans changed from 4.5 to 18.1% of the total amount of exergy destroyed in the AHU. The data of exergy destroyed and its distribution in the components for the case of HP-HRE70 (d) are shown in Fig. 5.17. We can see from this figure that HRE operation is sensitive to the variation of the RET, and the amount of exergy destroyed in this component shows the highest degree of variation [from 0.36 kW (RET = −30 °C) to 0.02 kW (RET = 10 °C)] compared to other AHU components. A special focus on HRE exergy analysis (efficiency and exergy destroyed) at a variable RET is placed

5.4 Comparison of the Exergy Indicators of the Four Diagrams …

131

Fig. 5.16 Exergy destroyed (a) and its distribution (b) in the AHU components in the case of Only HP (c)

in Chap. 3 of this monograph, including the methodology and the results of numeric examples. The percentages of exergy destroyed in the AHU components in the case of HPHRE70 (d) show that 50–59% of exergy destroyed is borne by the HP regardless of the RET. Exergy destroyed in the compressor, the condenser, and the throttle valve decreases directly as the RET rises. The percentage of exergy destroyed in these three HP components decreased from 42 to 28%. The fans used in the AHU diagrams use power that does not depend on the outdoor temperature (as well as RET) and generate clearly increasing values of exergy destroyed as the RET rises (from 13.4% when the RET = −30 °C to 44.5%, when the RET = 10 °C). Whereas the HRE component in a way offsets the impact of the fans that is so far difficult to prevent.

132

5 Comparative Exergy Analysis of Cases of the Air Handling Unit

Fig. 5.17 Exergy destroyed (a) and its distribution (b) in the AHU components in the case of HP HRE70 (d)

5.4.2 Exergy Efficiency of Air Handling Units A comparison of the exergy efficiencies of the diagrams in question is presented in this subchapter, and the exergy efficiencies of their components are discussed below. The analysis begins with universal and functional exergy efficiencies in the absence of a heat pump (diagrams a and b) at different HRE (diagram b) temperature efficiencies. It is shown in Fig. 5.18. Universal efficiency ηU is shown as solid lines, functional efficiency η F , as dotted lines. The two efficiencies have the lowest values in diagram a, when the WAH is the only source of heat. The best indicators are in diagram b with a HRE present and possessed of the highest temperature efficiency. These reciprocal positions of exergy efficiency indicators were to be expected.

5.4 Comparison of the Exergy Indicators of the Four Diagrams …

133

Fig. 5.18 The universal and the functional exergy efficiencies of AHU technological diagrams a and b

Another noteworthy fact that is relevant for exergy analysis purposes is that functional efficiency is much more sensitive to the technological and HRE temperature efficiency characteristics. For instance, at RET = −10 °C, the universal exergy efficiency of the AHU diagrams concerned (AHU a and all AHU b) shifts from 38 to 48%, and functional exergy efficiency, from 23 to 47%. Which makes functional exergy efficiency more sensitive to changes in the ongoing processes. At the same time, it can provide more information for the purposes of assessing those changes and improving the processes. Figure 5.19 shows the dependency of ηU on the variable reference temperature for all AHUs (diagrams a and b). Besides, diagram b has three cases of HRE temperature efficiency: 60, 70, and 80%. It is evident that with a low εT , the ηU difference in diagrams a and b is small. With the temperatures of the heat transfer medium supplied

Fig. 5.19 The universal exergy efficiency of the AHU (for diagrams a, b, c, d)

134

5 Comparative Exergy Analysis of Cases of the Air Handling Unit

Fig. 5.20 The functional exergy efficiency of the AHU (for diagrams a, b, c, d)

by the WAH reduced, diagram a can be expected to be more efficient than b as far as ηU is concerned. It means that the amount of exergy supplied will reduce while the demand for heat will remain the same. The ηU indicators in diagrams c and d (in which a heat pump is present) are clearly below those in diagrams a and b. Therefore, the use of a HP does not have any benefit here in terms of thermodynamic (exergy) efficiency. At the same time, the exergy analysis conducted under the method showcased in the monograph showed that this benefit would become apparent if the HP cycle were controlled in a manner that is tailored to the functional operation of the AHU. Figure 5.20 shows the extent to which η F depends on the varying reference temperature for the same diagrams that have their ηU presented in Fig. 5.19. To begin with, it is clear that the diagrams without a HP (a and b) have the biggest gap between their η F value compared to ηU . This is something that was already observed in the discussion of the results in Fig. 5.18. Besides, every diagram has η F < ηU , although this difference is slightly dependent on the reference temperature. The difference is smaller for diagrams where a HP is present (c, d). However, at temperatures of about −7 °C and higher, ηU drops below the efficiency of HPV-HRE70. This is because a variable temperature (and pressure) is applied in the HPV-HRE70 evaporator and condenser (in line with alternative V with variable isotherms in the evaporator and the condenser, see Chap. 4). The change in the universal exergy efficiency, ηU of case HPV-HRE70 is less sensitive to variation of the reference temperature, and thermodynamically speaking, HPV-HRE70 is superior to WAH-HRE70. The values of AHU c and AHU d COPAHU (Fig. 5.12) and exergy efficiency (Fig. 5.19) depend on the operation of the HP. Even though the COP of the HP in both AHUs is above 1, the exergy efficiency of these systems is always below 1. This is because of the limited thermal exergy supplied, and the large amount of exergy supplied in the HP as electrical energy. Thermal exergy is calculated based on a rate

5.4 Comparison of the Exergy Indicators of the Four Diagrams …

135

of conversion (Carnot efficiency), which depends on the environment temperature (1 − Te /Ti ). The functional exergy efficiency of the AHU is shown in Fig. 5.19. It is obvious that the values of the universal and the functional exergy efficiencies of AHU a differ by a lot. The functional exergy efficiency of this system drops from 32 to 9%, and the universal exergy efficiency shifts from 49 to 18%, when the reference temperature rises from −30 to +10 °C. A similar trend (η F < ηU ) can be observed across all diagrams, and the difference between the universal and the functional efficiencies depends on the reference temperature. For AHU c and AHU d systems equipped with a HP, this difference is smaller. Moreover, a comparison of WAH-HRE70, HP-HRE70 and HPV-HRE70 shows that the change in the functional exergy efficiency follows the pattern of variation of the universal exergy efficiency. The functional exergy efficiency of HP-HRE70 remains significantly lower at any reference temperature compared to WAH-HRE70 and HPV-HRE70, and the functional exergy efficiency of HPV-HRE70 exceeds the exergy efficiency of WAH-HRE70 at a reference temperature in excess of −14 °C. In the discussion of Figs. 5.18, 5.19 and 5.20, the exergy efficiencies of all AHU systems were presented, their characteristics addressed. Integral values of the exergy efficiency of the entire AHU were presented there as well. When it comes to analysing the exergy efficiency of these AHUs, one should know and see the exergy efficiencies of their components. In combination with the amount of exergy destroyed by these components as addressed above, this allows arranging the components by their impact on the exergy efficiency of the entire AHU and revealing the components that need to be focused upon when it comes to improving their efficiency. These figures show AHU exergy efficiencies with fans running and with the impact of the fans disregarded (no Fans). It is another way of showing their effect on the thermodynamic performance of the AHU. Figure 5.21 shows data for diagrams Only WAH (a) and WAH-HRE (b) with no heat pump present. In case b, the system is equipped with a HRE. It is clear that the nature of variation of the universal and the functional exergy efficiencies of the whole system is similar and is affected by the use of the WAH in both diagrams. In diagram a, there is a pronounced difference between the universal and the functional efficiencies. This is − (Eq. 5.7) that occurs with this combination of temperatures due to the exergy flow E˙ out in the case of universal efficiency, compared to E˙ − pr od (Eq. 5.8), when the amount of exergy destroyed is the same for both of these cases (Eq. 5.9). The functional exergy efficiency of the WAH and the AHU (with no fans) are virtually the same, because in that case the WAH is the only unit transforming energy in this diagram. Compared to other diagrams on the basis of the AHU functional exergy efficiency at −5 °C alone, in figure above we have η FAHU = 20.51%. In this case, −5 °C is chosen as the longest predominant temperature during the heating season. In the assessment of case WAH-HRE, we have diagram a, to which a HRE with a 70% temperature efficiency rating was added. In this case, the thermal capacity of and the amount of exergy destroyed by WAH decreases substantially, and we have a different structure of component efficiency. The WAH functional efficiency (at −

136

5 Comparative Exergy Analysis of Cases of the Air Handling Unit

Fig. 5.21 The overall and component universal and functional exergy efficiency of Only WAH (a) and WAH-HRE (b)

5 °C) increased from 23.12 to 38.87%. Thanks to the rather stable exergy efficiency of the HRE, η FH R E ≈ 55%, we have η FAHU = 36.12%. That is 1.8 times more than in diagram a. It is worth remembering that diagram a was chosen first of all to showcase the suggested methodology rather than as a case that has a broad application in engineering, even though it does occur in practice from time to time. Figure 5.22 shows diagrams of Only HP, where the heat pump is the only heat generator, and the same system with a HRE added, HP-HRE. The commentary on the results expands the above commentary on exergy destroyed for these diagrams and compare these diagrams. The analysis results for the Only HP diagram are similar to the results of the heat pump analysis in Chap. 4. Technologically speaking, the processes of energy transformation taking place here are very similar or overlapping. Exergy efficiency is a parameter with high thermodynamic requirements. The heat pump uses electricity to work and thus increases the denominator in the formula to calculate this efficiency. The agreed efficiency for diagram Only HP η FAHU = 12.44%. Lowest among all four diagrams, this value is nearly 1.6 times smaller than the same indicator of the AHU diagram. The thermodynamic quality of the HP-HRE diagram is much higher.

5.4 Comparison of the Exergy Indicators of the Four Diagrams …

137

Fig. 5.22 The overall and component universal and functional exergy efficiency of Only HP (a) and HP-HRE (b)

A HRE with a 70% temperature efficiency rating allows reducing the power output of the HP compressor greatly (by nearly 3.5 times), and the HRE itself has a high and stable η FH R E ≈ 55%. The heat pump’s exergy efficiency η FH P within the range of outdoor air temperatures (between −30 and +10 °C) shifts from 69.43 to 51.03%; the value used for comparison purposes (at −5 °C) is 58.11%. That is more than 4.5 times higher than in the case of Only HP.

5.5 Summary of This Chapter Energy transformation processes usually take place inside HVAC systems all year round. These are processes that facilitate the circulation of heat transfer and power usage heat transfer media. As a rule, the quantitative and qualitative parameters of these processes shift depending on the environment temperature, which varies constantly. Considering the extent of the demand for energy and the continuous

138

5 Comparative Exergy Analysis of Cases of the Air Handling Unit

operation, HVAC systems have to achieve a level of energy efficiency, which in turn faces the challenge of application thermodynamic (exergy) analysis for its evaluation. The conventional exergy analysis used for energy conversion system assessment purposes has some limitations, because the reference temperature (and pressure) is fixed. The demand for energy in HVAC systems depends on the environment temperature, which varies during the season and can be lower, higher than, or equal to the working temperature of the working fluids. After we had exhausted the possibilities of thermodynamic (exergy) analysis (Chaps. 2, 3 and 4) and added new options to its toolkit, we managed to analytically describe the processes taking place in the AHU (avoiding tools of empiric investigation). This allowed us to perform a parametric analysis of technological AHU diagrams at varying environment temperatures. Parameters such as the power outputs of the components, heat flows, and their combinations are bound analytically in our methodology. Other parameters of the state, such as heat transfer medium temperatures and flowrates, can be altered but they remain connected to one another through their indicators. This creates a possibility to reveal the specific efficiency indicators of the unit and its components and to look for their most efficient combinations. Our goal was to compare four AHUs on the basis of a set of thermodynamic parameters, including the COP, the universal exergy efficiency, the functional exergy efficiency, exergy destroyed when the variable reference environment temperature is within the range of −30 and +10 °C. In other words, using the variable RET method when that temperature equals the temperature of the outside air used for ventilation purposes. The COP, universal and functional exergy efficiency, destroyed exergy ratings clearly indicate which of the AHU systems under consideration is the more efficient at different environment temperatures. This information facilitates further development of calculation algorithms for determining and measuring the seasonal operation of HVAC systems. On the other hand, the methodology proposed here can be readily expanded with the exergoeconomic assessments of the heat exchangers or the whole AHU that allow obtaining explicit values of the original T and TE V i zot . The efficiency of the HRE has the biggest effect on the COP, the universal and the functional exergy efficiencies. Ergo, the choice of the right HRE should be based on exergy analysis and adjusted in the light of the other AHU components, considering the variation of the reference environment temperature at the specific locations. The exergy analysis showed that the AHU that was equipped with a HP only (Only HP, c) had a lower COP compared to the AHU with a WAH and a HRE installed (WAH-HRE, b), and is significantly lower than that of the AHU that had a HP and a HRE (HP-HRE, d). The AHU with only a HP has the lowest universal and functional exergy efficiency rating. This system should only be used when the small-form factor of the air conditioner is the number one priority in terms of thermodynamic efficiency. The differences between the values of the universal and the functional exergy efficiencies of the AHU are small. Compared to the universal exergy efficiency, functional exergy efficiency provides more details and has a higher degree of sensitivity to the variation of the thermal efficiency of the HRE. The difference between these indicators is less pronounced for units that are equipped with a HP.

5.5 Summary of This Chapter

139

The application of a variable environment temperature shows that fans that have a constant speed (power) rating are one of the factors that negatively affect the AHU’s COP or exergy efficiency. The parameters of the processes taking place in the AHU and its HP components and the indicators of performance shift within the range of RET variation. The prevailing tendency is that as the RET increases, most of the indicators go down. Still, the nature of variation of entropy produced, exergy destroyed, and exergy efficiency is specific for each of the components. Despite not being an indicator for the purposes of comparing the AHU’s coefficient of performance, entropy generation highlights the distribution of process irreversibility in the components and the characteristics of its variation. Besides, it allows verifying the interim results of the process of exergy analysis. When the temperatures inside the heat exchangers vary on a nearly straightline basis, meaning that when temperature variation is insignificant, for the purposes of exergy analysis, we can use methods that are grounded both on the Carnot factors and coenthalpies. The choice depends on the information available.

Chapter 6

Seasonal Thermodynamic Efficiency of the Air Handling Unit

With AHU methodology of how thermodynamic analysis should be performed at a chosen temperature available and once the trends of variation of exergy flows, exergy destroyed, and exergy efficiency at variable RET have been investigated, the next step would be to move to calculating the chosen seasonal indicators. This matter usually concerns researchers and designers and users of equipment alike. Only while some of them may be more interested in individual indicators of the process and the effects different parameters have on an indicator, others are concerned with, and find practical relevance in the overall operating efficiency of the entire solution or unit at a particular location. The goal thus is to determine the ηex of a component or the entire unit for a season or any other chosen period. As it was mentioned in previous chapters, the thermodynamic efficiency of ventilation and other technical systems in a building is closely related to the local climate, one of its parameters being that the environment air temperature remains relevant at basically all times. For instance, the amounts of energy consumed and their proportions in buildings depend on the climatic conditions of a particular location, construction and consumer behaviour, economic level, and prevalent customs. Review of studies shows that if a system runs in a chosen mode for a whole season, a temperature that ensures the highest degree of consumption and destruction of exergy can be fixed (Streckien˙e et al. 2017). At the same time, this leads to a discussion on the calculation of seasonal indicators (Januševiˇcius et al. 2017). This additional qualitative information about the full operation of hardware during a season also has practical relevance in terms to transitioning to economic indicators, because, as a rule, seasonal indicators are proportional to the costs of maintaining a microclimate as well as those of natural resources.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 V. Martinaitis et al., Exergy Analysis of the Air Handling Unit at Variable Reference Temperature, https://doi.org/10.1007/978-3-030-97841-9_6

141

142

6 Seasonal Thermodynamic Efficiency of the Air Handling Unit

6.1 Determining Seasonal Indicators The application of seasonal operating indicators is particularly relevant for designing a system and comparing it with other alternatives. For instance, for heat pumps, the seasonal coefficient of performance (SCOP) is very popular. Its application is also regulated by international standards, such as ISO 21978:2021. Besides, as we already saw, the outputs and amounts of BTS energy and exergy, contrary to those of the conventional energy or industrial transformers, greatly depend on the local climatic conditions. These latter have their annual cycle, which can be further divided into shorter periods of time based on their characteristic temperatures (such as winter, summer, or a transitional period). Such cases call for the identification of seasonal indicators, which become just as important as the rest of the indicators (nominal, short-term, peak, instant, optimal, and so on). These indicators have a particular degree of relevance for practitioners—decision-makers, economists, end-users— because the seasonal operating efficiency of equipment directly correlates with the economic costs incurred in an energy system under investigation. We could also speak about the general political, environmental, social goals when the inclusion of exergy goes hand in hand with sustainable development (Bilgen and Sarikaya 2015).

6.1.1 Determining Local Climatic Conditions The local climate, which is defined on the basis of its key parameters, such as, among other things, the outdoor air temperature, wind speed, atmospheric pressure, relative air humidity, solar radiation, is often classed as boundary conditions as far as energy systems are concerned. Besides, understanding climatic design conditions is one of the first steps towards ensuring an energy-efficient operation of the system or the whole building. Each climatic parameter usually has its own specific trends in terms of variation or even consistency during the day, a season, or the whole year, and also depends on the location. In the case of the AHU presented in the thermodynamic analysis, the parameter of the outdoor air temperature has to be identified as well; this parameter, too, has the above tendencies towards variation during the day or a season. However, in the above design and scientific case, the key matter of concern is connecting the seasonal indicators of the equipment and the local climate, and in this case, the pattern of temperature variation. The development of local temperatures and the seasonal indicators of system operation can be estimated on an analytical function of temperature distribution by days, z(T ) and the function of the frequency of cumulative distribution of the temperature directly needed for the BTS as derived on its basis, Z (T ). The function of temperature distribution, z(T ) as the decisive factor that defines temperature variation, is calculated as follows (Streckiene et al. 2009; Martinaitis et al. 2010): z(T ) = N

a , cosh (a(Tm − T ))2

(6.1)

6.1 Determining Seasonal Indicators

143

where a = c/Sd ; c is the region-specific constant value, which often amounts to 1; Sd is the standard deviation of the average daily temperature; N is the duration of the period in question in days (e.g., one year’s N = 365); Tm is the average monthly temperature. This function of the frequency of the cumulative distribution of temperature expressed in days, Z (T ) and its inverted function, T (Z ) are calculated as follows: Z (T ) = N

1 + tanh(a(T − Tm )) , 2

(6.2a)

and T (Z ) = Tm −

  N 1 ln −1 . 2a Z

(6.2b)

These can be expanded to analytical expressions that can be used in an exergy analysis. The temperature functions presented here approximate the long-term statistical temperature data. The compatibility of the temperatures obtained and the statistical data facilitates the integration of climatic data by describing the specific location in the algorithm. The availability of the analytical functions of temperature distribution, z(T ) and Z (T ) or T (Z ), and the methodology for the assessment of exergy flows and exergy efficiency opens up a possibility to obtain the indicators for the chosen durations (season) of the AHU’s energy-transforming components: the HRE, the HP, or the entire unit or system.

6.1.2 Determining Seasonal Indicators of the Air Handling Unit The seasonal indicators of the chosen AHU and its seasonal exergy efficiency are determined in the following 4 steps: (1)

(2)

(3)

AHU energy and exergy balances are drawn by performing energy and exergy analysis. The power outputs and the amounts of energy and exergy are determined for individual components and the entire unit within the Te range used in the calculations, i.e. with variable Te , the necessary data are determined in the chosen increment of Te variation (detailed calculation of these data is presented in Chap. 5). Local climatic data are collected and prepared and the functions of temperature distribution are formulated. This can be done both in reliance on historical data and synthetic data formats, such as tmy, epw. With spot data (data determined at specific Te ) of the AHU and its components as obtained in step one available, these values are translated into seasonal

144

6 Seasonal Thermodynamic Efficiency of the Air Handling Unit

(4)

indicators. Thus, distribution frequencies of the chosen values depending on the Te are obtained. This allows determining the Te , at which the amount of exergy destroyed is the largest and the demand for exergy and energy, the highest. The seasonal exergy efficiency of the AHU or its components is calculated under the formula:  (Z (T ) · ηex )  . (6.3) ηex,sez = Z (T )

The seasonal COP based on temperature durations can be calculated in the same way:  SC O P =

(Z (T ) · C O P)  Z (T )

(6.4)

Accordingly, seasonal η F,sez and ηU,sez can be determined for the chosen duration of the unit’s operation. When necessary, more complex cases of AHU operation, such as the HP evaporator freezing over, can be scrutinised. With the right data on hand, steps 2–4 are recapped to determine the seasonal efficiency of the equipment for the chosen period of time. A detailed sequence of calculations when the analysis begins with original data is shown in Fig. 6.1. There are two large blocks that can be singled out in this figure: one of the choice of the AHU component combination, and one of the calculations. This algorithm can be applied to draw various AHU diagrams that were analysed above. Any energy and exergy calculations are done only once the combination of AHU components under consideration is made.

6.2 Analysis of Individual Cases of Air Handling Units 6.2.1 Air Handling Unit Where the Heat Recovery Exchanger Is the Main Component The case chosen for an initial demonstration of the methodology involves an AHU consisting of supply and exhaust fans, a heater and a heat recovery exchanger (Fig. 2.7, diagram b). To reveal the positive impact of the HRE, the same system is contrasted with a system without a HRE, when the AHU is only equipped with two fans and a heater (Fig. 2.7, diagram a). A visualisation of these systems with their underlying exergy flows and limits is presented in Sect. 2.5.1. At the same time, to showcase the benefits of thermodynamic analysis for the purposes of measuring

6.2 Analysis of Individual Cases of Air Handling Units

145

Fig. 6.1 The algorithm of the thermodynamic assessment of the modes of AHU operation and its seasonal efficiency

146

6 Seasonal Thermodynamic Efficiency of the Air Handling Unit

the quality of energy a possibility to use an electric or water-to-air heat exchanger is highlighted. These cases will also be compared. Based on the methodologies presented in prior chapters (based on the Carnot factor or coenthalpies), exergy flows and the amount of exergy destroyed at appropriate environment air temperature, such as from −30 and 22 °C, which is the temperature inside the room, are calculated. Typically, in each individual case we are concerned with how the specific equipment or system works at a particular location or property, which has its own respective characteristics. In this case, the thermodynamic analysis trains the spotlight on the environment conditions, with particular emphasis on the environment temperature as a parameter. The subject AHU case with and without the HRE and a possibility to use an electric or water-to-air heater is further analysed under Lithuanian climatic conditions (the city of Vilnius, heating degree days HDD = 4660). At the chosen location, the heating season normally lasts from early October to late April. Spot data about the flows within each component and the unit in general are estimated in 0.5 °C increments. T e is assumed to be a fringe condition, also assuming it to be at 22 °C inside the room during the heating season. The applicable average HRE temperature efficiency is 70%, the amount of air for ventilation, 560 m3 /h. In line with the sequence of calculations presented in Sect. 6.1.2, energy and exergy analysis is performed first by making the relevant balances as analysed in the previous chapters. Step two involves location analysis, for instance, in the case of Vilnius city (Lithuania), historical data (Fig. 6.2a) are used to generate a temperature distribution density function z(T ) (Fig. 6.2b). The factual climatic data of the outdoor air temperature in the chosen Lithuanian city were obtained using information from Statistic Lithuania and an international data base at https://www.wunderground.com/history/monthly/lt/vilnius/ and https:// osp.stat.gov.lt/statistiniu-rodikliu-analize?indicator=S2R003#/. For the purposes of formulating a temperature distribution frequency function in the case at hand, data were filtered for the heating season only and for environment air temperatures of below 10 °C, because that is when the heating process is on. The function of temperature distribution density can be generated both in reliance on factual data and on software-generated climate data. For that purpose, Meteonorm or other databases offer a convenient source of data. With local meteorological data from a specific weather station, the data must first be meticulously checked for erroneous or missing sequences. Therefore, any data of real-life measurements may need to be processed, corrected, sometimes filling in gaps by using linear or cubic interpolation. In individual cases, when the chosen building with the necessary BTS does not fit in a particular type but rather has its own unique architectural qualities and so on, the function of temperature distribution density based on long-term data observations or typical meteorological year can be employed to generate an extreme—very hot or very cold—heating season. Furthermore, for long-term prognostic assessments covering a period of 2–50 years or more, the climate change effect may need to be factored in.

6.2 Analysis of Individual Cases of Air Handling Units

147

Fig. 6.2 Variation of factual air temperature in the city of Vilnius (a) and the function of temperature distribution density for the heating season (b)

In the subject case of Vilnius (Fig. 6.2), we can see that temperatures are usually recorded at around 0 °C. It is therefore worth noting observing, in further calculations, what happens with energy and exergy flows when temperature recurrence is at its highest. At step three, the relevant instant flows and power outputs are obtained for the following unit configurations: • • • •

AHU with only an electric heater, a—only EAH, AHU with only a water-to-air heat exchanger, a—only WAH, AHU with an electric heater and a HRE, b—EAH-HRE, AHU with a water-to-air heat exchanger and an HRE, b—WAH-HRE.

In the case at hand, they are presented in Fig. 6.3, with the exergy flow for the AHU in general and its individual components estimated at a temperature range between −30 and 22 °C. This comparison clearly shows that the application of an electric heater increases the amount of exergy consumed, and this difference can be manifold: for instance, at an outdoor air temperature of 0 °C, the flow of exergy consumed between the systems only equipped with a heat exchanger and fans amounts to 4.22, and 0.79 kW when there is an electric and a water-to-air heat exchanger in place, marking a difference of

148 Fig. 6.3 Exergy consumed in the air handling units and its components: a AHU with an electric air heater; b AHU with a water-to-air heat exchanger; c AHU with a HRE and an electric air heater; d AHU with a HRE and a water-to-air heat exchanger

6 Seasonal Thermodynamic Efficiency of the Air Handling Unit

6.2 Analysis of Individual Cases of Air Handling Units

149

5.3 times. Meanwhile, the necessary flow of exergy consumed is 7.96 and 1.86 kW, accordingly, which amounts to 4.3 times the exergy flow. This also highlights the advantage of the system equipped with a HRE, which allows using smaller amounts of exergy. The fan component remains constant across all systems, because the fans supply and exhaust a stable amount of air within the temperature range concerned. The trends of exergy destroyed in all 4 cases in question are shown in Fig. 6.4. This also clearly reflects the components where the amount of exergy destroyed is the largest, such as the heat exchangers and the electric air heater (EAH) in particular. The presence of a HRE allows this situation to be improved. For instance, if we take an environment temperature of 0 °C as the reference environment temperature, the amount of exergy destroyed in an AHU system with an electric heater and a HRE and in one that does not have a HRE increases from 1.29 to 4.06 kW—i.e., it nearly triples. With an AHU with water-to-air heat exchangers, the difference in the flow of exergy destroyed between the variants at 0 °C is 0.32 and 1.29 kW, marking a quadruple increase. Another important indicator that is covered at length here is exergy efficiency in its own right, as well as its variation at the appropriate RET. With the flows of exergy destroyed and exergy consumed as calculated above available, exergy efficiency can be calculated as ηex =

·

E− · E+

= 1−

·

L ·

E+

. The obtained results of the exergy efficiencies

of these diagrams are shown in Fig. 6.5. Therefore, the calculation of exergy efficiency for each of the components and for the whole system provides the most visual representation of which system has the biggest advantage: in this case, it is the AHU with a heat recovery exchanger and a water-to-air heat exchanger. The exergy efficiency of the heat recovery exchanger varied within a very narrow range of 0.55–0.54 across the entire AAT range (−30 to 22 °C). The next step involves calculating the seasonal exergy efficiency of the entire unit or its individual components (formula 6.3). Figure 6.6 shows the separate results of the calculations for the whole AHU and for the electric heater and for the water-to-air heat exchanger. Calculating seasonal exergy efficiency describes the factual or expected value of this indicator at a particular location, with the highest value (0.32) recorded for the system with a HRE and a water-to-air heat exchanger. Whereas the poorest result is that of the system with an electric heater, its estimated seasonal efficiency only amounting to 0.04. That can be easily explained, because the high-quality input— electricity—is used for the low-temperature purposes of heating the room. It can further be seen that the presence of the HRE component reduces the demand for the heater exchange output, which has its own energy-related and economic benefits both over the short and the long term of operation of the equipment.

150 Fig. 6.4 Exergy destroyed in the air handling unit and its components: a AHU with an electric air heater; b AHU with a water-to-air heat exchanger; c AHU with a HRE and an electric air heater; d AHU with a HRE and a water-to-air heat exchanger

6 Seasonal Thermodynamic Efficiency of the Air Handling Unit

6.2 Analysis of Individual Cases of Air Handling Units Fig. 6.5 Exergy efficiency in the air handling unit and its components: a AHU with an electric air heater; b AHU with a water-to-air heat exchanger; c AHU with a HRE and an electric air heater; d AHU with a HRE and a water-to-air heat exchanger

151

152

6 Seasonal Thermodynamic Efficiency of the Air Handling Unit

Fig. 6.6 Seasonal exergy efficiency in the air handling unit and its heat exchangers

6.2.2 Assessing the Impact of Climatic Conditions: The Results of the Parametric Analysis Choosing the system with the best performance indicators out of the four systems as per above (an AHU with and without a HRE and a relevant heat exchanger) and performing similar calculations for a different location, such as Paris, would produce relevant amounts of exergy at new environment temperatures. A comparison of outdoor air temperatures in these two cities is presented in Fig. 6.7, showing data of a typical meteorological year as obtained using the EC interactive tool (EU Science Hub 2021).

Fig. 6.7 Development of the environment air temperature in Vilnius and Paris during a year

6.2 Analysis of Individual Cases of Air Handling Units

153

Fig. 6.8 Temperature distribution density functions for Vilnius and Paris

After we process the climatic year, we can obtain handy analytical expressions and temperature durations, which are shown in Fig. 6.8. Since the comparison will concern the same duration of the season, it was assumed that the calculations would be done at outdoor air temperatures of up to 10 °C. These two cities can be seen to have different conditions temperature-wise, which will naturally affect the seasonal calculations of exergy. Analysis of the local environment air temperature is followed by calculations of other indicators and the drawing of Fig. 6.9, which shows the amounts of exergy consumed and destroyed, considering the RET and its duration during the heating season. For the Paris case, only the variation of the indicators of the whole AHU

Fig. 6.9 Exergy consumed and destroyed in the air handling unit with a heat recovery exchanger and a water-to-air heat exchanger, comparing the RET durations in Vilnius and in Paris. E+ is exergy supplied; L exergy destroyed

154

6 Seasonal Thermodynamic Efficiency of the Air Handling Unit

and the HRE is presented. Unless designated as belonging to Paris, this indicator is attributed to the case of Vilnius. This seasonal picture sheds more light on the situation when the values of exergy destroyed and, as a consequence, the demand for exergy supply are at their highest. In the case of Vilnius, this RET is −2.5 °C. Assuming that the RET is within the range of −10 and 8 °C, it follows that this is where 82% of the season’s total demand for exergy is consumed. Using the same AHU configuration in Paris, where the climate is warmer, the highest demand for exergy occurs at a RET of 6.0 °C. The estimated seasonal exergy efficiency at the same potential RETs in the case of Paris stands at 0.16. Which makes the original fringe climatic conditions particularly relevant both for the purposes of spot and seasonal calculations in order to evaluate the quality of one’s choice.

6.2.3 Air Handling Unit with a Heat Recovery Exchanger and a Heat Pump The diagram analysed here was already covered in previous chapters (Sect. 2.5.1, Fig. 2.7. Only HP option d). The same four-step sequence applies here as well. The calculations were based on the coenthalpy method. All of the above assumptions and calculation results for the city of Vilnius continue to apply. This case is further illustrated with cumulative values that represent the total values of the indicators of the heating season concerned. The amounts of energy obtained under the FLT in the case of the system with a HRE and a HP, considering the duration of the environment air temperature, are presented in Fig. 6.10, which shows the amounts of heat in the relevant system components. We can see that the largest amounts of heat are obtained when the environment temperature varies between −5 and 0 °C (Fig. 6.10a), and the highest values are achieved at −2.5 °C. The main reasons for that are the values of the heat flows that occur in the appropriate components and the relatively long duration of the recurrence of this value during the season, for instance, at an environment temperature of − 2.5 °C, the total heat flow needed for heating the air amounts to 4.58 kW, yet in this case the duration of this flow needs to be factored in as well. Analysis of the energy flows generated depending on temperature has been dissected at length. The amount of heat supplied to the air during the season (Fig. 6.10b) is 20.4 MWh, the amount received by the HRE 14.4 MWh; at the same time, the HP compressor consumes 1.78 MWh, and the two fans, 0.37 MWh of electricity. The exergy analysis put the amount of exergy destroyed and produced under a microscope (Figs. 6.11 and 6.12), which allowed to further calculate the seasonal exergy efficiency of the unit. Analysis of exergy destroyed shows that most of it gets destroyed in the HP components (Fig. 6.11a). A breakdown of the HP components (Fig. 6.11b), shows that the seasonal values of exergy destroyed in the condenser and in the compressor are more or less the

6.2 Analysis of Individual Cases of Air Handling Units

155

Fig. 6.10 The amount of energy in the components of the air handling unit (a) and its total value (b) during the heating season

same and are higher in the throttle valve. However, the largest amount of exergy is destroyed in the HP evaporator. This kind of analysis of individual AHU components based on the RET and its duration during the season in question allows taking the specific critical components that require improvement into consideration. Analysis of the total amount of exergy consumed in the AHU components and the amounts of exergy destroyed produces the highest values for the same moment as in the case of energy analysis: between ~−5 and ~0 °C. In this specific case, too, the

156

6 Seasonal Thermodynamic Efficiency of the Air Handling Unit

Fig. 6.11 Principal amounts of exergy destroyed in the air handling unit (a) and its detailed distribution in the components (b)

amount of exergy consumed is the largest at −2.5 °C, while the amount destroyed, at −2.0 °C, and the amount produced, at −4.0 °C (Fig. 6.12). During the period in question, the lowest value of the C O PAHU (Eq. 2.42) was 6.64, the highest 9.41. With the climatic parameters, such as the environment air temperature and its duration, factored in, the AHU seasonal coefficient of performance, or SCOP, is obtained (Eq. 6.4), amounting to 8.0. With seasonal exergy data at specific environment air temperatures and their durations available, seasonal exergy efficiency can be calculated. In this case, the duration of this efficiency under specific conditions is taken into consideration. In the case of the chosen AHU (Vilnius air temperature data), seasonal exergy efficiency amounts to 24.0%. During the season under consideration, it is the lowest (12.1%) when the environment air temperature

6.2 Analysis of Individual Cases of Air Handling Units

157

Fig. 6.12 Seasonal amounts of exergy consumed, produced, and destroyed (a) and their cumulative diagram (b)

(Te ) is 10 °C, and is the highest (47.1%) when the Te = −30 °C, when the differences in potentials are the greatest, but this Te is short-lived. This analysis proves that the operation of HVAC systems and their components depends on the climatic conditions, with temperature identified as one of the key parameters. The applied method of exergy analysis that takes the variable environment air temperature and its duration into consideration may be used for the purposes of developing dynamic energy system models that cover amounts and quality of energy.

158

6 Seasonal Thermodynamic Efficiency of the Air Handling Unit

6.2.4 Air Handling Unit with a Heat Recovery Exchanger and a Heat Pump at Variable Refrigerant Isotherms Considering the variants of TC N i zot and TE V i zot , two alternatives—C and V, which were investigated above through the seasonal prism, are chosen. Their detailed description is presented in Sect. 4.2.2, , i.e.: • for alternative C, TC N i zot = const ≈ 30 °C, TE V i zot = const ≈ −30 °C. • for alternative V, TC N i zot = var, TE V i zot = var. As was the case in prior investigations, only the heating season is addressed, stretching for the purposes of calculations from early October (1/10) to the end of April (30/4). All calculations in the analysis of seasonal indicators are done for an air flowrate of 1 kg/s. The results are presented for the city of Vilnius. The distribution of the outdoor air temperature (its duration in hours) and exergy flows, or rather their frequencies (considering the duration of these values at a particular RET) are presented in Fig. 6.13. Evidently, the prevalent Te in Vilnius during the period under consideration is between −2 and 1 °C (with −0.5 °C racking up the largest number of hours), totalling a massive 1010 h. It can be seen that both for alternative C and alternative V, the principal exergy flows (exergy consumed, destroyed in the unit and the entire exergy flow entering the unit) reach their maximum values at the following environment temperatures: • for alternative C, the maximum amount of exergy destroyed is at −2 °C; alternative V, at −3 °C; • the largest amount of exergy consumed and the total amount of exergy entering the AHU is at −3 °C for alternative C, and at −3.5 °C for alternative V.

Fig. 6.13 The duration of outdoor air temperature in October–April and the distribution frequencies of the principal exergy flows of alternative C and V

6.2 Analysis of Individual Cases of Air Handling Units

159

We can see from Fig. 6.13 that alternative V demonstrates better exergy performance compared to alternative C: smaller amounts of exergy consumed and destroyed at the same flow of air supplied to the room, thus assuring the same level of service. The figure below breaks down the amounts of exergy destroyed for both of these alternatives in the main components of the AHU, considering the durations of Te (Fig. 6.14). As we can see, the amounts of exergy destroyed in the fans and in the HRE and the same for both alternatives. The highest value of exergy destroyed in the fans can be observed at the longest-lasting temperature of the heating season (−0.5 °C), as their efficiency does not depend on the RET. The amount of exergy destroyed in the fans at this temperature is 115 kJ/kg. The highest value of exergy destroyed in the HRE is 63 kJ/kg, when the environment air temperature is −4.0 °C. However, a significant drop in the amount of exergy destroyed can be observed in the HP components of alternative V, and in EV in particular. The largest amount of exergy destroyed in the evaporator is achieved at Te −5 °C and totals 17 kJ/kg for alternative V, and at −1.5 °C, totalling 90 kJ/kg for alternative C; at −5 °C, this value is 77 kJ/kg. Fig. 6.14 The frequency of exergy destroyed in AHU components for C and V alternatives

160

6 Seasonal Thermodynamic Efficiency of the Air Handling Unit

Fig. 6.15 Frequencies of AHU exergy efficiency distribution of alternative C and V (Vilnius)

The distribution (by duration in hours) of the universal, ηU AHU and the functional, η FAHU exergy efficiencies that depend on the varying Te during the heating season is shown for alternative C and V in Fig. 6.15. Figure 6.15 shows that ηU AHU and η FAHU nearly overlap for both of the alternatives. However, for alternative V, the highest values of these efficiencies move to the right, pointing to a longer duration. It was estimated that within the Te range of −30 and +22 °C (in October–April), the average seasonal exergy AHU efficiency would be as follows: • alternative C: functional η FAHU 23.5%, universal ηU AHU 23.7%. • alternative V: functional η FAHU 33.3%, universal ηU AHU 33.4%. The results obtained show that, in terms of exergy and with the seasonal temperature variation factored in, alternative V is superior to alternative C.

6.2.5 Comparison of the Results for Different Climate Zones The key seasonal calculations for alternative C and V as presented above only apply to Vilnius. To determine the impact the local Te has on those two alternatives, the following calculations for the two alternatives concern the city of Paris and the variation of its Te , as presented above. The calculations are based on the outdoor air temperature for the same period of October–April. All assumptions, methodologies, technological conditions are the same as in the case of AHU analysis in Vilnius. The goal here is to highlight how exergy analysis can reveal the characteristics of climate and the degree of cohesion that systems have with it at the same time. The distribution frequencies of the amounts of exergy destroyed, consumed, and the total amounts of exergy entering the AHU for alternative C and V are shown in Fig. 6.16.

6.2 Analysis of Individual Cases of Air Handling Units

161

Fig. 6.16 The duration of Te in Paris in October to April and the distribution frequencies of the principal exergy flows for alternative C and V

All principal exergy flows followed the highest value of the Paris Te frequency as it shifted towards higher temperatures, since the average temperature of the October– April season is 6.5 °C (253 h). As a result: • in case C and case V, the highest value of exergy destroyed in the AHU occurs at 6 °C (amounting to 535 kJ/kg for the alternative C AHU, and to 291 kJ/kg for the alternative V AHU); • the amount of exergy destroyed and the total amount of exergy entering the AHU is the largest at 6 °C for alternative C and at 5.5 °C for alternative V. A comparison of Figs. 6.13 and 6.16 also shows that when the heating season is narrower (as it is in the case of Paris), the highest values of the principal exergy flows are higher. The AHU exergy efficiency as calculated for alternative C and V and its duration in hours are shown in Fig. 6.17.

Fig. 6.17 The durations of AHU exergy efficiencies for alternative C and V (Paris)

162

6 Seasonal Thermodynamic Efficiency of the Air Handling Unit

Fig. 6.18 A comparison of the seasonal exergy efficiencies of the AHU and the HRE for different cities

A comparison of the AHU’s FEE and UEE under different climatic conditions shows that both η FAHU and ηU AHU are lower for both of the alternatives in the case of Paris. Thus, when the same AHU with a HP is used for heating purposes under milder climatic conditions, the differences in temperatures within the unit will be smaller and its exergy efficiency lower. In the case of Vilnius, the AHU operates with higher efficiency for a longer period of time. A detailed comparison of average seasonal ηex for the whole AHU and for the HRE alone is shown in Fig. 6.18. The figure shows that the functional and the universal average seasonal exergy efficiencies of the AHU are nearly the same for the same alternative and climatic conditions. With alternative V, the AHU has an even higher ηex compared to alternative C. One characteristic of the HRE component is that its η FAHU has a higher degree of sensitivity than ηU AHU . However, the variations between the results obtained for the HRE component in Vilnius and in Paris were not significant.

6.2.6 Investigation of the Impact of the Temperature Efficiency of the Heat Recovery Exchanger Under Different Climatic Conditions This investigation is performed on two technological diagrams from Sect. 2.5.1, which are equipped with a HRE component—diagrams b and d. Additionally, the following sequence of temperature efficiency values is analysed: 60, 70, and 80%. The technological diagrams will be labelled in figures below as follows: • WAH-HRE (60, 70, 80) for a water-to-air heat exchanger and a heat recovery exchanger with an appropriate efficiency rating;

6.2 Analysis of Individual Cases of Air Handling Units

163

Fig. 6.19 A map of Europe showing cities in relevant climate zones (ASHRAE Standard 169-2013)

• HP-HRE (60, 70, 80) for a heat pump and a heat recovery exchanger with an appropriate efficiency rating. Also, because we saw how exceptionally important the RET is, the analysis covers several different climates, based on a choice of appropriate cities that could represent different climatic conditions, from warm humid to very cold. The location of the cities on the map and their climatic allocation is presented in Fig. 6.19. A brief introduction thereof is presented in Table 6.1. A Koppen ¨ climate classification is presented sideby-side with ASHRAE standard 169 labelling. These two classifications are some of the commonly used climate classification systems, especially when it comes to dealing with buildings and their energy systems. The energy and exergy analysis as described above is applied to instant indicators to calculate the relevant amounts of energy, the, C O PAHU , followed by exergy values and exergy efficiency, with a summary of the results of seasonal calculations (SCOP and seasonal exergy efficiency) presented in the end. A detailed comparison of the two diagrams that have a HRE component with varying efficiency ratings is presented for the climatic case of the city of Vilnius; the same calculations apply for other cities and, to avoid duplication, only their key indicators, COP and efficiency are presented. Figure 6.20 shows the amounts of energy in an AHU equipped with a water-to-air heat exchanger and HRE with different efficiency ratings: the amount of heat supplied to air, the power output to the fans, the amounts of heat in the appropriate HRE and water-to-air heat exchangers

164

6 Seasonal Thermodynamic Efficiency of the Air Handling Unit

Table 6.1 Different European cities representing different climate zones under ASHRAE and Koppen ¨ classification Climate Climate Degree daysa zone description

Koppen ¨ class

City

Country

Average annual temp., °C

3A

Warm humid

Caf

Rome

Italy

15.22

3B

Warm dry

Cyprus

19.95

4A

Mixed humid

1500 < CDD10 °C < 3500 Caf/Daf 2000 < HDD18 °C ≤ 3000

Paris

France

11.20

5A

Cool humid

1000 < CDD10 °C < 3500 Daf 3000 < HDD18 °C ≤ 4000

Berlin

Germany

9.42

6A

Cold humid

4000 < HDD18 °C ≤ 5000 Daf/Dbf

Vilnius

Lithuania

6.70

7

Very cold

5000 < HDD18 °C ≤ 7000 Dbf

Sodankyla Finland

2500 < CDD10 °C < 3500 HDD18 °C ≤ 2000

BSk/BWh/H Larnaca

−0.98

The table shows criteria based on ASHRAE standard 169, where CDD are cooling degree days, and HDD are heating degree days

Fig. 6.20 The AHU WAH-HRE case: seasonal energy amounts, the city of Vilnius

of the relevant systems. The values in the diagram are shown with the relevant local outdoor air temperatures already factored in. The energy picture of the other system equipped with a heat pump and HRE with a different temperature efficiency rating is painted by the same analogy (Fig. 6.21). Both cases are concerned with values from −30 to 10 °C, when indoor heating becomes relevant. It can furthermore be observed that, regardless of the technological diagram, the amount of heat supplied into the room is the same and reaches its peak value at −2.5 °C during the season, only the components that provide it differ. Since both diagrams use the same air supply and exhaust fans and heat recovery exchangers, the amounts of energy attributable to

6.2 Analysis of Individual Cases of Air Handling Units

165

Fig. 6.21 The AHU HP-HRE case: seasonal energy amounts, the city of Vilnius

these system components are the same for both systems. Consequently, Fig. 6.20 shows that there is a dependency on the temperature efficiency of the HRE and the amount of energy consumed by the water-to-air heat exchanger (WAH), and that the amounts of energy and exergy decrease with equipment that has a higher efficiency rating. Such tendencies are observed for the HP-HRE system as well. With the amounts of energy consumed and produced available, the unit’s COP is calculated under the FLT. This calculation is performed within the temperature range of −30 and 10 °C, highlighting the lowest and highest values observed and estimating the seasonal COP, considering the durations of the relevant temperatures. The results of this calculation are shown in Fig. 6.22. The calculations show that the AHU’s seasonal COP is not the average of its lowest and highest values and that the duration of the relevant outdoor air temperature needs to be factored in or weighted ratios applied. According to the FLT, the AHU HP-HRE diagram is superior to the AHU WAH-HRE configuration, with higher COP obtained at all times. Consequently, a HRE component with a higher efficiency rating allows obtaining higher efficiency indicators, with the SCOP going up from 6.39 to 10.70 (1.7 times) when he HRE used as an 80% temperature efficiency rating, compared to 60% for the AHU HP-HRE in diagram d. Exergy analysis identifies the amounts of exergy destroyed, which allows approaching the processes taking place in the system’s components from a qualitative point of view. A comparison of seasonal values—the amounts of exergy destroyed— of both cases is presented in Figs. 6.23 and 6.24. The prior quantitative comparison (Fig. 6.22) showed the system with a heat pump to be superior, however, as we move on to the assessment of exergy destroyed, the system with this component appears to experience a higher rate of exergy destruction. The largest amounts of exergy destroyed in the entire AHU with a HRE and a WAH also occur at −2.5 °C, as this temperature has a relatively high rate of recurrence during the season. The case of the AHU with a HRE and a HP shows larger amounts of exergy destroyed, peaking out at −2 °C, which is specifically linked with the heat pump, or rather its components,

166

6 Seasonal Thermodynamic Efficiency of the Air Handling Unit

Fig. 6.22 A comparison of the lowest, highest, and seasonal COP of the cases considering the temperature efficiency of the HRE

Fig. 6.23 HRE WAH-HRE: seasonal amounts of exergy destroyed, Vilnius

particularly the evaporator, where the amount of exergy destroyed is the largest (also see Fig. 6.11). As we can see, the HRE efficiency is directly related to the amount of exergy destroyed in the other main AHU components in all cases; the lower the temperature efficiency, the larger the amounts of exergy destroyed in the heat exchanger or the heat pump.

6.2 Analysis of Individual Cases of Air Handling Units

167

Fig. 6.24 AHU HP-HRE, seasonal amounts of exergy destroyed, Vilnius

Considering the duration of the value at relevant temperatures, the amount of exergy consumed, produced, and destroyed in the entire AHU and individual cumulative graphs of these values are presented in Fig. 6.25. An exergy cross-section of both system variants shows that all AHU variants with a heat pump installed carry higher cumulative values of exergy consumed and destroyed. The amount of exergy produced stays similar for both cases, and remains identical for the same system that nonetheless has a HRE component with a different efficiency rating, because the final product to be produced by the system is the same. A relative analysis of cumulative values showed that even though the system with the heat pump consumes more exergy, with a HRE component that has a better efficiency rating, this difference decreases: at 60% temperature efficiency, the cumulative value of exergy consumed in the HP system is 34% higher compared to the WAH-AHU, whereas if the temperature efficiency of the HRE is 70 and 80%, the difference between the systems (one with a HP and one with a WAH) becomes 27 and 19%. Furthermore, as the temperature efficiency of the HRE increases, the amount of exergy destroyed in the two systems drops from 48 to 32%. This shows that with a modification or improvement of the heat pump control cycle and the employment of a more efficient HRE component, the diagram with the HP, as far as exergy is concerned, may excel the system equipped with a water-to-air heat exchanger. The duration of the functional exergy efficiency of the six variants concerned, as calculated at the relevant outdoor air temperature, is shown in Fig. 6.26. It is evident that in the case of the AHU HP-HRE70, the exergy efficiency is between 0.22 and 0.26 most of the time, standing at 0.29–0.33 for the AHU WAH-HRE70 system. As a result, the duration of this efficiency can be determined for other variants, too. It can also be observed that the highest values of exergy efficiency recorded at lower temperatures (