Refrigerators, Heat Pumps and Reverse Cycle Engines E-Book

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Serie: ISTE Consignment
• Sprache: Englisch

Seitenzahl: 371

Veröffentlichungsjahr: 2023

Beschreibung

In the context of global warming and the energy transition, two essential questions arise: how to cool environments without major environmental impact and how to produce heat efficiently without combustion. These questions reveal a reversal of the energy paradigm that has prevailed since the Industrial Revolution, when the challenge was to produce work from heat. Reverse cycle thermal machines (refrigeration systems, heat pumps and thermofridges), operating in reverse of the thermomechanical conversion motor cycle, have a major role to play in answering these questions, which are at the heart of the energy challenges that humanity will have to face in the coming decades. This book first presents a state of the art on these systems, whose operating principle is sometimes old, but whose performance analysis and optimization have sometimes been neglected. Emerging technologies, which will certainly find their place in the future energy panorama, are also discussed.

Leseprobe

Table of Contents

Cover

Title Page

Copyright Page

Foreword

Preface

Chapter 1. Heating and Cooling by Reverse Cycle Engines: State of the Art

1.1. Vapor compression refrigerators and heat pumps

1.2. Systems driven by thermal energy

1.3. References

Chapter 2. Entropy and Exergy Analyses Applied to Reverse Cycles

2.1. Definition of the study system and objectives

2.2. Energy analysis

2.3. Entropy analysis

2.4. Exergy analysis

2.5. Case study for exergy analysis

2.6. References

Chapter 3. Thermodynamics and Optimization of Reverse Cycle Engines

3.1. Reverse cycle engines according to equilibrium thermodynamics: reminders of the concepts

3.2. Receiving engines in the presence of internal irreversibilities

3.3. The Carnot refrigerator according to finite-time thermodynamics

3.4. The reverse cycle Carnot engine model according to finite physical dimensions thermodynamics (FPDT)

3.5. Generalization of the reverse cycle Carnot engine model according to FPDT .

3.6. Latest advances in a reverse cycle Carnot engine model

3.7. Extension of finite physical dimensions thermodynamics to two complex systems

3.8. Some conclusions and perspectives

3.9. References

Chapter 4. Scientific and Technological Challenges of Thermal Compression Refrigerating Systems

4.1. Introduction

4.2. Kinetics and dynamics – heat and mass transfers in thermal compression engines

4.3. Technological challenges in component design

4.4. Risks associated with liquid–solid phase transition phenomena

4.5. Conclusion

4.6. References

Chapter 5. Magnetocaloric Refrigeration: Principle and Applications

5.1. Introduction

5.2. Magnetic refrigeration

5.3. Numerical models

5.4. Applications

5.5. Conclusion

5.6. References

Chapter 6. Thermoelectric Systems as an Alternative to Reverse Cycle Engines

6.1. Thermoelectricity fundamentals

6.2. Implementation and performance analysis

6.3. Applications

6.4. References

List of Authors

Index

Wiley End User License Agreement

List of Tables

Chapter 1

Table 1.1. Thermodynamic properties at different cycle points for propane

Table 1.2. Thermodynamic properties of fluids at different points in the cycle

Chapter 2

Table 2.1. Properties of the fluid at the characteristic points of the cycle (levels 1 and 2 of complexity)

Table 2.2. Properties of the fluid at the characteristic points of the cycle designed at level 3 of complexity

Table 2.3. Properties of the fluid at the characteristic points of the cycle designed at level 4 of complexity

Table 2.4. Properties of the fluid at the characteristic points of the cycle (levels 1 and 2 of complexity)

Table 2.5. Properties of the fluid at the characteristic points of the cycle designed at level 3 of complexity

Table 2.6. Carnot COP and cooling efficiency according to the analyst choice in terms of the level of complexity and source temperatures

Table 2.7. Distribution of the entropy generation in the different components and circulation lines of the refrigeration system studied

Table 2.8. Main quantities relating to the analysis in terms of entropy generation number for the reverse cycle engine studied, operating as a refrigeration system or as a heat pump

Chapter 4

Table 4.1. Some values of the parameters of the calculation of the global kinetic coefficient (Sharafian and Bahrami 2015)

Table 4.2. Example of the diameter range of adsorbents studied in the scientific literature and, if known, the diameter range recommended by the authors

Table 4.3. Example of coating thickness studied in the scientific literature and, if known, exchanger/adsorbent mass ratio or thickness recommended by the authors

Chapter 5

Table 5.1. Numerical models of magnetocaloric regenerators

Table 5.2. Geometric quantities of the Lionte model (Lionte 2015)

Table 5.3. Features of the Lionte operation (Lionte 2015)

Table 5.4. Prototypes at ambient temperature

Chapter 6

Table 6.1. Optimal operating conditions (maximum thermal power and maximum conversion efficiency) of a thermoelectric module (with )

List of Illustrations

Chapter 1

Figure 1.1. Thermal generator

Figure 1.2. Carnot engine

Figure 1.3. Classic cycle of a vapor compression refrigerator or heat pump. a) Schematic of the installation. b) Cycle in an enthalpy diagram

Figure 1.4. Example of transcritical cycle (case of CO

2

)

Figure 1.5. Two-stage compression: heat exchange with an external source. a) Diagram of the installation. b) Cycle in an enthalpy diagram

Figure 1.6. Two-stage compression: heat exchange with the evaporating fluid. a) Diagram of the installation. b) Evolution cycle of the fluid in an enthalpy diagram. Note that in this case h

1

≈ h

1′

≈ h

1″

and h

4

≈ h

4′

Figure 1.7. Two-stage compression: injection into an intermediate reservoir. a) Diagram of the installation. b) Evolution cycle of the fluid in enthalpy diagram

Figure 1.8. Diagram of a two-stage compression and expansion refrigerating machine and cycles of evolution of the refrigerant. a) Diagram of the installation. b) Evolution cycle of the fluid in an enthalpy diagram

Figure 1.9. Principle of a two-stage cascade

Figure 1.10. Diagram of an ejector. 1, convergent; 2, divergent; 3, secondary fluid inlet; 4, mixing zone; and 5, nozzle for recompression (Bouziane 2014)

Figure 1.11. Example of an ejection vapor compression refrigerating machine. a) Diagram of the installation. b) Evolution cycle of the fluid in an enthalpy diagram with the 40°C isotherm as an example

Figure 1.12. Principle of operation of a machine driven by thermal energy. Example of an absorption machine

Figure 1.13. Diagram of an absorption machine

Figure 1.14. Oldham diagram of the ammonia–water pair. Diagram inspired by Duminil (2002)

Figure 1.15. Merkel diagram of the ammonia–water pair. Diagram inspired by Duminil (2002)

Figure 1.16. Oldham diagram (enthalpy-concentration) of the ammonia–water pair: operating limits. Diagram inspired by Duminil (2002)

Figure 1.17. Diagram of the installation of an absorption chiller with intermediate heat recovery exchanger

Figure 1.18. Operating diagram of an ejection refrigerating system (Bouzrara 2018)

Figure 1.19. Schematic view of an ejector and changes in pressure and speed as a function of position (Chunnanond and Aphornratana 2004)

Figure 1.20. Enthalpy diagram of an ejection refrigerating system

Figure 1.21. Influence of the ejector outlet pressure (counter-pressure) on the entrainment ratio at a constant reduced low pressure

Figure 1.22. Characteristic field of an ejector. Figure inspired by Zegenhagen and Ziegler (2015)

Chapter 2

Figure 2.1. Conceptual diagram of a reverse cycle engine

Figure 2.2. Circuit of a vapor compression reverse cycle engine

Figure 2.3. Circuit of an absorption reverse cycle engine

Figure 2.4. Thermodynamic cycle of complexity of level 1 or level 2

Figure 2.5. Thermodynamic cycle of level 3 complexity

Figure 2.6. Thermodynamic cycle of the complexity of level 4

Figure 2.7. Schematic representation of the temperatures of equivalent external or internal sources and temperature profiles in the exchangers

Figure 2.8. Influence of analysis choices on Carnot COP and refrigeration efficiency

Figure 2.9. Contribution of components and circulation lines to the total entropy generation of the studied system

Figure 2.10. Carnot engine

Figure 2.11. Diagram of an ejection heat pump

Chapter 3

Figure 3.1. Reverse endoreversible or endo-irreversible Carnot cycle (reference to the cold end)

Figure 3.2. Real reverse Carnot cycle

Figure 3.3. Block diagram of a reverse cycle engine

Figure 3.4. Carnot endo-irreversible refrigerator

Figure 3.5. Representation of the modified Chambadal refrigeration cycle

Figure 3.7. LT and HT cycles of a two-stage endoreversible engine

Figure 3.8. Double-function heat pump model with internal irreversibility

Figure 3.9. Block diagram of a geothermal sorption engine

Chapter 4

Figure 4.1. Diagram of the modeled falling film specifying the temperature and LiBr concentration profiles proposed by Zinet et al. (2012)

Figure 4.2. Schematic representation of a set of adsorption isotherms

Figure 4.3. Adsorption and desorption curves of water by silica gel for different conditions representative of the conditions obtained in adsorption engines (Glaznev and Aristov 2010). For a color version of this figure, see www.iste.co.uk/bonjour/refrigerators.zip

Figure 4.4. Count of experimental points in the literature specifying the main sorbents used with ammonia (left) and with water (right)) (Wang et al. 2015). For a color version of this figure, see www.iste.co.uk/bonjour/refrigerators.zip

Figure 4.5. Schematic representation of a horizontal tube absorber. For a color version of this figure, see www.iste.co.uk/bonjour/refrigerators.zip

Figure 4.6. Example of an adsorber made from a finned tube heat exchanger in the process of being filled. For a color version of this figure, see www.iste.co.uk/bonjour/refrigerators.zip

Figure 4.7. Example of coated surface heat exchanger presented in a) Bendix et al. (2017), b) Restuccia et al. (2004)

Figure 4.8. Example of evolution of power and COP versus thickness of adsorbent coating observed in the scientific literature (Bendix et al. 2017; Duong et al. 2020)

Figure 4.9. Comparison of the impact of the weight of the water column (hydrostatic pressure) on the saturation pressure between water and ammonia for a fluid at equilibrium with vapor at 10°C. For a color version of this figure, see www.iste.co.uk/bonjour/refrigerators.zip

Figure 4.10. Schematic evolution of the heat transfer coefficient obtained (secondary fluid temperature 15°C, pressure 1.2 kPa) (from Seiler et al. 2020). For a color version of this figure, see www.iste.co.uk/bonjour/refrigerators.zip

Figure 4.11. Example a) of two-phase flow observed in a flat plate evaporator and b) of evolution of the heat transfer coefficient (secondary fluid temperature 21°C, pressure 1.4 kPa, Giraud et al. (2016)). For a color version of this figure, see www.iste.co.uk/bonjour/refrigerators.zip

Figure 4.12. Diagram of the absorption chiller modeled by Zinet et al. (2012)

Figure 4.13. Principle of operation of the evapo-absorber proposed by Zinet et al. (2012)

Figure 4.14. Description of how the evapo-absorber works: (a) Perspective view of three plates, (b) 2D view of a 5-plate prototype. (Obame Mve 2014). For a color version of this figure, see www.iste.co.uk/bonjour/refrigerators.zip

Figure 4.15. Oldham diagram of the water/lithium bromide pair. For a color version of this figure, see www.iste.co.uk/bonjour/refrigerators.zip

Chapter 5

Figure 5.1. Tesla’s thermomagnetic motor (Tesla 1889)

Figure 5.2. Principle of the MCE. Left: magnetic material, the magnetic moments are in random directions. Right: magnetic material under magnetic field, the magnetic moments are aligned

Figure 5.3. Principle of a magnetic refrigerator

Figure 5.4. Comparison between magnetic refrigeration and conventional refrigeration

Figure 5.5. Magnetic refrigeration cycle

Figure 5.6. Magnetic Carnot cycle

Figure 5.7. Magnetic Ericsson cycle

Figure 5.8. Magnetic Brayton cycle

Figure 5.9. Magnetic AMR cycle

Figure 5.10. Gadolinium regenerator (Legait et al. 2014)

Figure 5.11. Heat exchanger made up of magnetocaloric composite materials based on La(Fe1-xSix)13 (Skokov et al. 2014)

Figure 5.12. Performance of different magnetocaloric materials as a function of a) the number of transfer units (NTU), b) thermal conductivity and c) frequency (Legait et al. 2014)

Figure 5.13. Properties of magnetocaloric materials (Mayer et al. 2017)

Figure 5.14. Amount of CO

2

emitted and water used per kg of material produced per transformation of global annual production (Mayer et al. 2017)

Figure 5.15. Different geometries of magnetic regenerators

Figure 5.16. Performance for different configurations of magnetic regenerators according to the NTU (Trevizoli et al. 2017)

Figure 5.17. Series and parallel magnetic regenerators

Figure 5.18. Geometry of the Lionte model (Lionte 2015). For a color version of this figure, see www.iste.co.uk/bonjour/refrigerators.zip

Figure 5.19. Boundary conditions of the numerical model (Lionte 2015)

Figure 5.20. Regenerator temperature during a cycle (Lionte et al. 2014a, 2014b, 2014c)

Figure 5.21. Evolution of the temperature for an AMR (Lionte et al. 2014a, 2014b, 2014c). For a color version of this figure, see www.iste.co.uk/bonjour/refrigerators.zip

Figure 5.22. The 2D distribution of temperatures during a cycle (Lionte 2015). For a color version of this figure, see www.iste.co.uk/bonjour/refrigerators.zip

Figure 5.23. Cooling power as a function of temperature difference (Lionte 2015). For a color version of this figure, see www.iste.co.uk/bonjour/refrigerators.zip

Figure 5.24. Coefficient of performance (Lionte 2015). For a color version of this figure, see www.iste.co.uk/bonjour/refrigerators.zip

Figure 5.25. Linear prototype

Figure 5.26. Rotary prototype

Figure 5.27. Brown’s (1976) prototype

Figure 5.28. Zimm’s (1998) prototype

Figure 5.29. Arnold’s (2014) prototype. For a color version of this figure, see www.iste.co.uk/bonjour/refrigerators.zip

Figure 5.30. Jacobs’ (2014) prototype

Figure 5.31. Cooling power – Jacobs’ (2014) prototype

Figure 5.32. Johra’s (2019) prototype

Figure 5.33. Nakashima’s (2021) prototype

Figure 5.34. Exergy-equivalent cooling power as a function of the temperature difference for the prototypes developed by the University of Victoria (UVic) in Canada (Tura and Rowe 2011) and by the Technical University of Denmark (DTU) (Lozano et al. 2014)

Figure 5.35. Principle of a GeoThermag geothermal magnetic refrigerator (Aprea et al. 2015)

Figure 5.36. Integration of a magnetocaloric heat pump in a geothermal system composed of a geothermal heat exchanger and floor heating (Johra et al. 2019)

Figure 5.37. COP of the magnetocaloric heat pump in a geothermal system (Johra 2018)

Chapter 6

Figure 6.1. The two ways of using a thermoelectric (TE) module

Figure 6.2. Simple thermoelectric (TE) system {Reservoir(R

1

)–TE Material–Reservoir (R

2

)} in its two operating modes. The semiconductor “n”-type TE material is held between two reservoirs (R

1

and R

2

)

Figure 6.3. Electronic and vibrational (phonons) quasi-particle states in phase space in wave vectors and in energy

Figure 6.4. Charge and energy transfer phenomena in the system {Reservoir (R

1

)–type-n thermoelectric material (TE)–Reservoir (R

2

)}. The orange vertical rectangles represent the electronic filling in R

1

and R

2

up to electrochemical potentials μ

R1

and μ

R2

respectively. The simplified band structure of the TE material is “n” type (see Figure 6.3(c))

Figure 6.5. Adapted from L.-D. Zhao et al. (2014). Examples of thermoelectric (TE) temperature measurements in the oxychalcogenide BiCuSeO TE material. a) Crystallographic structure consisting of an alternation of Bi

2

O

2

and Cu

2

Se

2

planes. Temperature dependences between 300 and 900 K of b) electrical conductivity (σ), c) Seebeck coefficient (S), d) thermal conductivity (λ) total (solid squares) and lattice (open squares) and e) of the figure of merit TE (ZT)

Figure 6.6. Qualitative evolutions of the Seebeck coefficient (α), electrical conductivity (σ), thermoelectric power factor (α

2

σ), thermal conductivity of electronic origin (κ

e

) and lattice thermal conductivity (κ

L

)

Figure 6.7. Thermoelectric figure of merit (zT) as a function of temperature for the families of materials (Adapted from Freer et al.2022)

Figure 6.8. Adapted from Benyahia et al. (2018). (a) Electron microscopy images of a surface obtained after fracture of a solid nanostructured sample of the material In

0.25

Co

4

Sb

12

at two magnifications allowing the scales indicated in the figures to be reached. The average distribution of grain diameters (D) is represented by the red bar graph. (b) Lattice thermal conductivity (λ

L

) and (c) thermoelectric figure of merit (ZT) measured for three different average grain sizes in the compound In

0.25

Co

4

Sb

12

Figure 6.9. Complex crystallographic meshes at the nanometric scale

Figure 6.10. Representation of a TE module in the so-called “vertical” architecture as shown in the scheme of Figure 6.1 a) The segments of the “p” (blue pads)- and “n” (red pads)-type TE materials are interconnected by metal electrodes, supported by ceramic insulating substrates. b) Illustration of the heat pump operating mode of a TE leg made up of a “p” and “n” segment and powered electrically. The isothermal electrical current flow induces cooling and heating of the opposite surfaces due to energy transfers at the TE material/metal electrode junctions (Peltier effect)

Figure 6.11. Schematic representation of the energy flows exchanged between the thermoelectric system and its heat reservoirs (cold and hot) in heat pump mode. a) Ideal thermal couplings and b) with thermal resistances

Figure 6.12. Cooling capacity Q

c

and conversion efficiency η

HP

of a Bi

2

Te

3

thermoelectric module (S = 230 10

-6

V.K

-1

; λ = 1.6 W.m

-1

.K

-1

; ρ = 1.4 10

-5

Ω.m; L = 5 10

-3

m; A = 1 10

-6

m

2

), for electrical currents varying between 0 and 1.6 A (in increments of 0.2 A) and junction temperature ratios between 0.8 and 1 (in increments of 0.1), with a constant average temperature of 350 K. The solid lines are drawn for constant junction temperature ratios, and the dotted lines for constant electrical currents

Figure 6.13. Optimal cooling COP values of thermoelectric systems, as a function of material figure of merit ZT and cold junction temperature T

c

for a hot junction temperature of T

h

= 300 K

Figure 6.14. Proposal for an innovative design of thermoelectric modules in order to improve their performance, in the case of low space constraints

Figure 6.15. Cooling thermal power Q

c

and conversion efficiency η

HP

of a Bi

2

Te

3

thermoelectric module (S = 230 10

-6

V.K

-1

; λ = 1.6 W.m

-1

.K

-1

; ρ = 1.4 10

-5

Ω.m; L = 5 10

-3

m; A = 1 10

-6

m

2

), for electrical currents I varying between 0.5 and 1.7 A (in steps of 0.1 A) and thermal resistances between 0 and 1,000 K.W

-1

(in steps of 200 K.W

-1

), for reservoir temperatures and . Solid lines are drawn for constant thermal resistances, and dotted lines for constant electrical currents

Figure 6.16. Equivalent representation of a thermoelectric system by electrical analogy (intensity: energy flux; potential: temperature)

Figure 6.17. Thermal association of thermoelectric modules a) in parallel, b) in cascade. c) Recommended association configuration and d) resulting COP as a function of the useful effect temperature T

h

and thermal power Q

h

, for a low temperature of T

c

= 283 K

Guide

Cover Page

Title Page

Copyright Page

Foreword

Preface

Table of Contents

Begin Reading

List of Authors

Index

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SCIENCES

Energy, Field Directors – Alain Dollet and Pascal Brault

Physics of Energy and Energy Efficiency,Subject Head – Michel Feidt

Refrigerators, Heat Pumps and Reverse Cycle Engines

Principles, State of the Art and Trends

Coordinated by

Jocelyn Bonjour

First published 2023 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

ISTE Ltd27-37 St George’s RoadLondon SW19 4EUUKwww.iste.co.uk

John Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USAwww.wiley.com

© ISTE Ltd 2023The rights of Jocelyn Bonjour to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s), contributor(s) or editor(s) and do not necessarily reflect the views of ISTE Group.

Library of Congress Control Number: 2022947623

British Library Cataloguing-in-Publication DataA CIP record for this book is available from the British LibraryISBN 978-1-78945-123-8

ERC code:PE8 Products and Processes Engineering PE8_6 Energy processes engineering

Foreword

Michel FEIDT

Université de Lorraine, LEMTA, CNRS, Nancy, France

The book you have in your hands is one of the books from the “Physics of Energy and Energy Efficiency” subject in the Engineering and Systems department.

The subject of “Physics of Energy and Energy Efficiency”, albeit recent, is not new. It is particularly underpinned by a thermodynamic approach, whatever the scale.

The selected aspect will be phenomenological and characterized explicitly in order to emphasize the key concept of “efficiency”, essential for any system or process.

The characterization chosen for the development of this subject has been arranged into four successive books, each strongly correlated with each other, and also with other series within the department:

–

Fundamental Physics of Energy

;

–

Thermodynamics of Heat Engines

;

–

Heat Engines with Inverse Cycles

;

–

Efficiency in Practice

.

I would like to thank ISTE, the various coordinators, and the authors for their contributions and effective actions, despite the very particular conditions of the moment. We are awaiting and would like to encourage comments, suggestions and questions from readers.

Preface

Jocelyn BONJOUR

CETHIL, INSA Lyon, Villeurbanne, France

For thousands of years, the quest for energy has been focused on a single purpose: the production of heat (thermal energy), mainly for domestic heating and cooking. Combustion, which practically used to be the only energy conversion technology, was gradually mastered and improved.

Combustion was still at the heart of the Industrial Revolution, which was triggered when heat could be used to produce mechanical work. The title of Sadi Carnot’s book is unambiguous: the founder of thermodynamics shared in 1824 his Reflections on the Motive Power of Fire and on Machines Fitted to Develop that Power. It was during this period that many thermo-mechanical energy conversion systems were developed. These systems had in common that they were based on cyclic transformations of fluids, then called “engine cycles” or “direct cycles”. Thermodynamicists then considered reversing the engine cycle: reverse cycle engines were born, used as refrigerators, heat pumps or even double-function heat pumps.

Climate change and the energy crisis have undoubtedly called for real changes in energy paradigms. Engine cycles will still be widely used to produce mechanical and electrical work, provided that the thermal energy sources are powered less and less by the combustion of fossil fuels. Similarly, the share of thermal energy production derived directly from combustion is bound to decrease over time. Finally, due to global warming, the need for cooling is bound to increase, whether for refrigeration for food safety and sanitary purposes, or for the cooling of premises. It is therefore clear that, more than ever, reverse cycle thermal engines will play an important role in the energy landscape of the coming decades.

The objective of this book is to offer readers (graduate students, PhD students, engineers, researchers) a state of the art on reverse cycle engines, in order to prepare them for their future positions, as well as to outline the research trends on still emerging technologies.

Thus, Chapter 1 presents a scientific and technical state of the art concerning heating and cooling by the most common reverse cycle engines: vapor compression, ejection, absorption or adsorption engines.

The energy crisis invites us to improve the energy efficiency of systems, whose performances must be evaluated with rigor and precision. This is the purpose of Chapter 2, which develops entropy and exergy analysis methods applied to reverse cycle engines and to the scale of their components. Chapter 3 completes the approach by proposing optimization methods of systems, by way of finite time/finite speed thermodynamics.

The development of mechanical compression engines during the 20th century has made this technology very mature, so that the margins for progress are less than for thermal compression engines (absorption, adsorption), which are therefore the subject of various research projects. There are still some scientific and technical obstacles which are discussed in Chapter 4, as well as the avenues envisaged to overcome them.

Magnetic refrigeration is an emerging technology. It is based on a reverse cycle like the systems mentioned above, but it is a magnetic material (and not a fluid) that undergoes a set of cyclic transformations. Chapter 5 presents the principle of this technology and different current or future applications.

Finally, Chapter 6 presents the thermoelectric effect as an alternative to reverse cycle engines. A good understanding of this physical phenomenon allows us to analyze the performance of thermoelectric refrigeration systems and to identify some applications for which they could be particularly relevant.

We hope that this book will enlighten the reader on the operation and future evolution of all the reverse cycle engines used for heating and cooling, as well as on their essential role in the decades to come.

Lyon

March 2023

1Heating and Cooling by Reverse Cycle Engines: State of the Art

Philippe HABERSCHILL and Rémi REVELLIN

CETHIL, INSA Lyon, Villeurbanne, France

Heat pumps are, from a thermodynamic point of view, no different from refrigerators: in both cases, they are a thermal generator which, thanks to energy consumption, passes heat from a cold source to a hot source (heat sink). On the one hand, the purpose of heat pumps is to provide heat to the hot source (air of a building, domestic hot water, swimming pool, etc.). On the other hand, refrigerating machines make it possible to obtain and maintain a system at a temperature lower than the ambient temperature. To do this, it is necessary to remove heat from this system or even “produce cold”. There are two main types of reverse cycle thermal generators: vapor compression systems (two-heat-source systems) and systems driven by thermal energy (three-heat-source systems). This chapter presents different configurations of vapor compression systems to describe two common systems driven by thermal energy: absorption systems and ejection systems.

1.1. Vapor compression refrigerators and heat pumps

Air refrigeration systems were the first compression refrigerators used. They are increasingly being abandoned (except in particular in the field of very low temperatures: cryogenics) in favor of vapor compression systems, and therefore of condensable fluids under the conditions of use. Such machines, thanks to the use of the refrigerant latent heat of change of state, make it possible to obtain refrigerating effects per unit mass of fluid that are clearly superior to those of gas systems. The systems are thus smaller in size.

1.1.1. Operation principle of closed-circuit refrigeration installation: definitions

As in heat engines, the system considered is a fluid in cyclic evolution. This fluid, which is intended to exchange heat with the sources, is called the refrigerant.

If the fluid absorbs the amount of heat Qf from the cold source (CS), it therefore releases Qc to the hot source (HS) (Figure 1.1):

[1.1]

where W is the mechanical (or other) energy received.

Figure 1.1.Thermal generator

NOTE.– The purpose of a refrigerator is to extract Qf from the cold source, whereas the purpose of a heat pump is to deliver |Qc| to the hot source. Essentially, these two systems are no different.

The amount of heat Qf taken at the cold source is called the refrigeration effect or cooling capacity.

The ratio is called the energy efficiency ratio or coefficient of performance.

Let us look for the expression of ε in two different cases: reversible operation and irreversible operation.

1.1.1.1. Reversible operation

Like a heat engine, a thermodynamic generator can operate reversibly (internal and external reversibilities) between two thermal sources only if the evolution cycle of the refrigerant is a Carnot cycle. Tc is the maximum temperature and Tf is the minimum temperature (Figure 1.2).

Figure 1.2.Carnot engine

Heat and work per unit mass of fluid will be denoted by q and w, respectively, expressed in J/kg

[1.2]

and

[1.3]

Therefore:

[1.4]

with s being the specific entropy of the fluid expressed in J/kg.K. Moreover, εCarnot is the Carnot energy efficiency ratio. Thus, εCarnot can be greater than 1 depending on the value of Tf with respect to Tc − Tf:

εCarnot > 1 if is the most frequent case

εCarnot < 1 if; this is the case for the liquefaction of certain gases.

1.1.1.2. Irreversible operation

For any vapor compression refrigerating machine, the quantities of heat are given by:

where s′ represents the entropy generation.

The mechanical energy exchanged is therefore: w = (Tc − Tf) |Δsf| + Tcs′

So

[1.5]

For refrigeration machines, as for engines, the Carnot cycle leads to the highest energy efficiency ratio. The difference between any machine and a Carnot machine is measured by the cooling efficiency ηf, which by definition is:

[1.6]

ηf also corresponds to the exergy efficiency ηex of the refrigeration cycle if the reference temperature Tref is considered equal to that of the hot source Tc . The exergy efficiency is therefore a better indicator of the quality of the thermodynamic cycle than the energy efficiency ratio, in that it is immediately interpreted as a ratio of the actual performance to the ideal performance.

A heat pump is, from a thermodynamic point of view, no different from a refrigerator: in both cases, it is a thermal generator which, thanks to energy consumption, transports heat from a cold source to a hot source. Thus, the previous systems, qualified as “refrigerators”, can all be used as a heat pump. The difference between these two types of machines lies in how they are used. What is interesting about a heat pump is the quantity of heat qc which will be supplied to the hot source. This difference of interest gives the definition of the coefficient of performance (COP):

[1.7]

This relation is, according to the first law (|qc| = qf + w), always greater than 1, meaning that these systems are of great theoretical and practical interest. Indeed, unlike other heating processes, this one makes it possible to obtain thermal energy greater than the energy expended to obtain it. The difference of course comes from the energy “pumped” into the cold source.

With the theoretical and technological development of heat pumps being modeled on that of refrigerating systems, there is no need to repeat it here. Emphasis will simply be placed on the difference between the definitions of the energy efficiency ratio ε, on the one hand, and of the COP, on the other hand, which of course leads to differences in expressions. For example, the COP of a heat pump operating according to the Carnot cycle is:

[1.8]

The relative coefficient of performance corresponds to the exergy efficiency ηex (if the reference temperature is equal to the temperature of the cold source) of a heat pump and is given by:

[1.9]

1.1.2. Actual cycle with superheating and subcooling

Figure 1.3 shows a diagram of a refrigerator (or heat pump), as well as the evolution cycle of the associated refrigerant. At state 1, the vapor, at low pressure, is either saturated (vapor quality of 1) or superheated (as in the example). The vapor is then compressed in a compressor where its pressure and temperature are increased (point 2). The superheated vapor is then condensed in a condenser at the outlet of which the fluid is in a liquid state, either saturated (vapor quality equal to 0) or subcooled (point 3). The liquid is then expanded in an expansion valve and partial vaporization is observed (vapor quality of around 0.2–0.3 at point 4). This two-phase fluid is then vaporized in an evaporator to reach state 1.

It should be noted that for a domestic refrigerator, the cold source corresponds to the refrigerated enclosure, while the hot source is represented by the air in the kitchen. Conversely, for a residential heat pump, the cold source and the hot source correspond respectively to the outside air and to the fluid to be heated (air, domestic hot water (DHW), etc.) inside the building.

Figure 1.3.Classic cycle of a vapor compression refrigerator or heat pump. a) Schematic of the installation. b) Cycle in an enthalpy diagram

1.1.3. Special cycles

1.1.3.1. Transcritical cycles

A pressure higher than the critical pressure of the fluid in the high-temperature exchanger can be a particularity encountered in certain vapor compression cycles. Such cycles are called transcritical. Refrigeration machines using CO2 as a refrigerant are often transcritical when the ambient temperature is higher than the critical temperature of the fluid. There is then no more condensation in the “hot” exchanger, but a cooling of the gas. An example of a transcritical cycle is shown in Figure 1.4, which represents a refrigeration cycle. In this figure, there is a strong change in temperature in the high-pressure exchanger: from approximately 120°C to 30°C. There are strong thermal differences between the source, whose temperature varies little, and the refrigerant in the exchanger, which leads to strong transfer irreversibility and contributes to a deterioration in the efficiency in this type of system.

Nevertheless, this strong temperature gradient on the refrigerant can become an advantage in the case of strong variations in the temperature of the hot source, such as in heat pumps intended to produce DHW. In this case, the “hot source”, which is the water to be heated, has a temperature which must change from the network temperature (generally below 20°C) to a temperature above 60°C. The temperature glide of the refrigerant is then partly compensated by the source temperature glide, which reduces irreversibility.

Figure 1.4.Example of transcritical cycle (case of CO2)

Note that the HP (high pressure) is no longer conditioned by the condensing temperature, but is left to the discretion of the designer. However, at a constant outlet temperature, there is an optimum pressure:

– below the critical pressure, the refrigeration production is zero because the entire cycle is in the vapor phase;

– at the critical pressure, the cooling capacity is low due to a minimum enthalpy variation in the evaporator;

– for pressures above the critical pressure, the cooling production increases;

– if the pressure is too high, the gain in cooling production is less than the additional cost of compression and the coefficient of performance deteriorates.

The optimum pressure depends on the operating conditions, but is approximately 90 bar for an air-cooled gas cooler with an outlet temperature of 35°C and an evaporation temperature of 0°C.

1.1.3.2. Multistage cycles

In certain thermal situations, or for certain refrigerants, the overall compression ratio requires compression to be carried out in two stages, or even more. The fluid passes from one stage to another to cool it in an intermediate exchanger (direct contact or mixer).

Several machine construction schemes are then possible. In all these examples, the compressions will be considered adiabatic. As a result, the compression works will be expressed simply from a difference in enthalpy.

1.1.3.2.1. Heat exchanges with an external source

This system is represented in Figure 1.5(a) with its associated cycle (Figure 1.5(b)). The fluid leaving the LP stage passes through an exchanger connected to the external source at temperature TM before entering the HP stage. The sum of the specific work of both stages is clearly lower than the specific work for a single stage. The energy efficiency ratio is expressed by:

[1.10]

The COP of the installation, meanwhile, is written as:

[1.11]

Figure 1.5.Two-stage compression: heat exchange with an external source. a) Diagram of the installation. b) Cycle in an enthalpy diagram

1.1.3.2.2. Heat exchanges with the evaporating fluid

In Figure 1.6(a), the fluid leaving the LP stage is cooled by the cold fluid coming from the expansion of a fraction (f) of the fluid leaving the condenser. The energy efficiency ratio is expressed by:

[1.12]

with the fraction f of fluid removed, which can be determined thanks to an enthalpy balance on the exchanger:

[1.13]

Note that in this case h1 ≈ h1′ ≈ h1″ and that h4 ≈ h4′.

The COP of the installation, meanwhile, is written as:

[1.14]

Figure 1.6.Two-stage compression: heat exchange with the evaporating fluid. a) Diagram of the installation. b) Evolution cycle of the fluid in anenthalpy diagram. Note that in this caseh1 ≈ h1′ ≈ h1″and h4 ≈ h4′

1.1.3.2.3. Injection into an intermediate reservoir

In Figure 1.7(a), the fluid leaving the LP stage is cooled by the evaporation (endothermic reaction) of the fraction of the fluid (f) leaving 4’. At point b, the fluid is in the form of saturated vapor because it is removed from the upper part of the reservoir containing the two-phase refrigerant in the liquid-vapor state. The evolution cycle in the enthalpy diagram is given in Figure 1.7(b). The energy efficiency ratio is expressed by:

[1.15]

The fraction f of fluid removed can be determined thanks to an enthalpy balance on the intermediate reservoir:

[1.16]

The COP of the installation, meanwhile, is written as:

[1.17]

Figure 1.7.Two-stage compression: injection into an intermediate reservoir.a) Diagram of the installation. b) Evolution cycle of the fluid in enthalpy diagram

1.1.3.2.4. Injection into an intermediate reservoir with staged expansion

An intermediate mixer-type heat exchanger (Figure 1.8(a)) at intermediate pressure Pi receives the superheated vapor, which leaves the low-pressure (LP) stage of the compressor in state a (Figures 1.8(b)), and the fluid from the high-pressure (HP) expansion device in a two-phase state c. The dry saturated vapor (state b) leaves the mixer to enter the HP stage of the compressor. The saturated liquid, which leaves the bottom of the mixer in state d, feeds the LP expansion valve which supplies the evaporator with a fluid in state 4.

For such a refrigerating system, the energy efficiency ratio is given by:

[1.18]

with the fraction f of fluid removed, which can be determined thanks to an enthalpy balance on the mixer:

[1.19]

The COP of the installation, meanwhile, is written as:

[1.20]

A possible improvement of this system in terms of energy consists of precooling the fluid, leaving the LP stage (state a) by the hot fluid.

Figure 1.8.Diagram of a two-stage compression and expansion refrigerating machine and cycles of evolution of the refrigerant. a) Diagram of the installation. b) Evolution cycle of the fluid in an enthalpy diagram

1.1.3.2.5. Cascade cycles

The use of a pure phase change refrigerant remains limited to the temperature interval between the critical point temperature, at which the latent heat of transformation is canceled out, and the triple point temperature, below which any simple mechanical cycling disappears. Moreover, this same temperature difference would cause excessive technical constraints to appear, mainly linked to the volume of the fluid at low pressure, to the difference between high and low pressures, hence correlatively amplified irreversibility.

A judiciously chosen cascade of fluids is then naturally used to ensure lower and lower temperature levels under reasonable pressures. Figure 1.9 shows the block diagram of such an installation in the case of a two-stage cascade. The extension to a higher number of stages is done by iteration.

Currently, two-stage cascade machines are used with CO2 in commercial refrigeration, especially in supermarkets as units that can be combined in two different ways:

– CO

2

for both stages (low and high temperatures). In this case, the high-temperature stage is very often transcritical;

– CO

2

for the low-temperature stage combined with propane or ammonia or even a low GWP HFO for the high-temperature stage.

Figure 1.9.Principle of a two-stage cascade

1.1.3.2.6. Ejection cycles

An ejector can be used in vapor compression systems, as well as in systems driven by thermal energy (section 1.2.3). The former is a component that allows part of the expansion energy to be recovered in order to suck up the fluid coming from the evaporator. This has the effect of reducing the compression ratio at the terminals of the compressor and reducing the energy required for compression.

The ejector is depicted in Figure 1.10. It uses the Venturi effect of a convergent– divergent nozzle (if sonic at the throat), or simply a convergent nozzle (if subsonic at the convergent outlet): the high-pressure working fluid is accelerated in the nozzle, which induces a drop in pressure allowing, at the nozzle outlet, suction of the secondary fluid. Mixing occurs in the mixing zone before the mixture is recompressed in the nozzle outlet to the intermediate pressure.

Figure 1.10.Diagram of an ejector. 1, convergent; 2, divergent; 3, secondary fluid inlet; 4, mixing zone; and 5, nozzle for recompression (Bouziane 2014)

There are various solutions for using an ejector to improve the operation of refrigerators, air conditioners or heat pumps.

Figure 1.11(a) shows an example of a refrigeration system operating on CO2 according to a transcritical cycle with an intermediate exchanger. The evolution cycle of the corresponding fluid is shown in Figure 1.11(b).

The increase in the energy efficiency ratio can be as much as 20%. These ejection systems are increasingly widespread, especially for CO2 and for various ranges of flow rates.

Figure 1.11.Example of an ejection vapor compression refrigerating machine. a) Diagram of the installation. b) Evolution cycle of the fluid in an enthalpy diagram with the 40°C isotherm as an example

1.1.3.3. Application example

We propose comparing three cases for the intermediate cooling of a refrigeration installation using propane as a refrigerant. The evaporation temperature is -40°C. There is a slight superheating, down to -37°C, before the compression is carried out in two stages. The outlet pressure of the LP body is 3.5 bar, and the isentropic efficiency (ηs) of each compression is 0.7. Condensation of propane ends, without subcooling, at 35°C. For these three cases, the fraction (f) is calculated and the energy efficiency ratio is compared.

Case no. 1. Surface exchanger between a fraction (f) of the fluid removed from the condenser outlet and the fluid leaving the LP body (Figure 1.6(a)). For the points numbered b and 1’, the vapor quality is equal to 1.

Case no. 2. Injection into the intermediate reservoir of part (f) of the fluid taken from the condenser outlet (Figure 1.7(a)). For point b, the vapor quality is equal to 1.

Case no. 3. Staged reduction in pressure (Figure 1.8(a)).

Table 1.1.