Finite Physical Dimensions Optimal Thermodynamics 1: Fundamentals

By Michel Feidt

Energy and the environment are inextricably linked to the economy. Thermodynamics therefore seems to be a privileged tool in overcoming the constraints associated with optimization.This first volume reports on an original, contemporary approach leading to optimal solutions in the form of trend models, proving the existence of solutions which can then be refined in a more complete and sophisticated manner.The validation of the proposed methodology is realized through real-life examples (engines, heat pumps, refrigeration systems, etc.). However, the more fundamental aspects linked to the dynamics of the transfer and conversion of energy and matter are also explored, as well as the evolution which characterizes the second law of thermodynamics.This book presents recent advances, often still undergoing research, as well as structured exercises, and is therefore aimed at both students and researchers in the field of energetics.

• It proposes a view of the evolution of knowledge regarding the thermodynamics modeling of systems and processes
• It shows results and also the existence of optimum all and along the development
• It focuses on multidisciplinary approach that characterizes thermodynamics

• Language: English
• Publisher: Elsevier Science
• Release date: Aug 28, 2017
• ISBN: 9780081023495

Michel Feidt

Michel Feidt is Professor in the Department of Physics and Mechanics at the University of Lorraine, France.

Book preview

Finite Physical Dimensions Optimal Thermodynamics 1

Fundamentals

Michel Feidt

Table of Contents

Cover

Title page

Copyright

Preface

Acknowledgements

List of Notations and Acronyms

1: From Thermostatics to Non-equilibrium Thermodynamics

Abstract

1.1 Equilibrium thermodynamics, a brief history

1.2 Essentials of thermostatics

1.3 Further additions: analytical thermodynamics

1.4 Major branches of thermodynamics

1.5 Second and third laws of thermodynamics

1.6 First conclusions and perspectives

2: Heat Exchangers

Abstract

2.1 Heat exchangers – essential component of systems and processes

2.2 Thermodynamic models of heat exchangers

2.3 Heat exchanger optimization: a generic compromise

2.4 Transient of heat exchangers

2.5 Conclusions of this chapter

3: From Carnot Cycle to Carnot Heat Engine: A Case Study

Abstract

3.1 Thermomechanical engine – a model

3.2 Thermomechanical engine: first power optimization

3.3 Thermomechanical engine: constrained optimizations

3.4 Reverse cycle Carnot machine

3.5 Generalization of the Carnot machine model

3.6 Conclusions and perspectives

4: Internal Combustion Engines Revisited

Abstract

4.1 A brief review of internal combustion engines

4.2 From technique to the first models

4.3 Models revisited

4.4 Other variants

4.5 Conclusions and extensions

5: Combustion Turbines and Other Heat Engines

Abstract

5.1 Introduction

5.2 The combustion turbine

5.3 From CT to GT

5.4 External combustion engines

5.5 Other engines

6: Reverse Cycle Machines

Abstract

6.1 Introduction

6.2 Classical thermodynamics of machines with steam compression

6.3 New thermodynamics contributions to machines with one source and one heat sink

6.4 Machines with three or four heat reservoirs

6.5 Other machines

6.6 Conclusion and extensions

6.7 Illustrative exercises

Conclusion and Perspectives

Main conclusions

Perspectives

Appendix 1: Fluids

Appendix 2: Mathematics

A2.1 Legendre transformation

A2.2 Calculus of variations

Bibliography

Index

Copyright

First published 2017 in Great Britain and the United States by ISTE Press Ltd and Elsevier Ltd

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 Press Ltd

27–37 St George’s Road

London SW19 4EU

UK

www.iste.co.uk

Elsevier Ltd

The Boulevard, Langford Lane

Kidlington, Oxford, OX5 1GB

UK

www.elsevier.com

Notices

Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary.

Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility.

To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein.

For information on all our publications visit our website at http://store.elsevier.com/

© ISTE Press Ltd 2017

The rights of Michel Feidt to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.

British Library Cataloguing-in-Publication Data

A CIP record for this book is available from the British Library

Library of Congress Cataloging in Publication Data

A catalog record for this book is available from the Library of Congress

ISBN 978-1-78548-232-8

Printed and bound in the UK and US

Preface

Michel Feidt May 2017

This work is the result of over half a century of thought, teaching and research in the field of thermodynamics of systems and processes.

The starting point is a new trend in thermodynamics, called finite-time thermodynamics, which originated in the article [CUR 75] by Curzon and Ahlborn. The ongoing development in France of this by thermodynamics started in 1957, with P. Chambadal, although it draws on much earlier developments, and in particular on the approaches taken by S. Carnot, obviously, and also by L. Onsager.

The aim of this book is to show that thermodynamics is a multidisciplinary and federative umbrella science, which takes into account the phenomena of transfer and conversion of energy and matter simultaneously.

The gradual unfolding of the book will prove useful both from a didactic perspective (introduction to modern phenomenological thermodynamics: Volume 1) and from the research perspective, as it touches upon recent advances still undergoing and (or) in the phase of research (Volume 2). Therefore, the target audience of this book comprises students as well as engineers and researchers in the energetics field.

The content of Volume 1 is divided into 6 chapters.

Chapter 1 reviews equilibrium thermodynamics (ET) or thermostatics and places it in context in the realm of sciences, leading to a new challenge: finite physical dimensions thermodynamics (FPDT or FDT).

Chapter 2 focuses on heat exchangers, which are key components of energy systems and consequently of thermomechanical systems. Dynamic steady-state and transient state modeling is discussed in this chapter. In steady state there is strong coupling between heat transfer and mass transfer leading, for example, to optimization by minimizing the production of internal entropy relative to exchanger (a key example of entropic analysis). On the other hand, transient state modeling introduces the notions of time constant and delay time. The generality of the presented results arises from the equivalence between any heat exchanger and a double tube exchanger. Examples of optimization in time of these exchangers are also provided.

Chapter 3 is dedicated to the passage from Carnot cycle to Carnot heat engine, which is an emblematic example of the new thermodynamics (finite physical dimensions optimal thermodynamics (FDOT)).

, are far more original (two finite dimensions). Likewise, the constrained optimization approach evidences new optima that have been scarcely developed in the literature. From a methodological perspective, the results span from prime mover to receiver or reverse machine (field in which the author was a precursor).

Chapter 4 revisits internal combustion engines (ICEs). As part of everyday life (transportation), their main practical implementations will be illustrated in this chapter. This will make it easier to go back from technical applications to thermodynamic models.

Theoretical cycles are described and compared to Watt’s diagram. Unlike most of the works in the field, this chapter proposes genuine thermodynamic models of controlled ignition or autoignition engines. These models come in two variants: with imposed heat flux input or with imposed maximum temperature. But most importantly, they evidence the influence of irreversibilities and non-adiabaticity. This results in original optimizations and a generalization of approach in the form of dual cycle.

Chapter 5 focuses on combustion turbines (CT) and other heat engines (like ICE). It presents CT such as jet engines, which are key to air transportation. Modeling according to ET leads to optimization. This modeling is, nevertheless, completed according to FPDT, mainly for the gas turbine, whose characteristic is to bring about an input of external heat, similar to steam engines. Two main cases are presented: a first one, with imposed heat flux input, and a second with imposed maximum temperature, the latter corresponding to current limitations of engines.

In terms of low mechanical power, Organic Rankine Cycles, as well as External Combustion Engines (Stirling, Ericsson), are promising applications. The main optimizations associated with these configurations are reported in Volume 1.

Chapter 6 approaches the field of reverse cycle machines, whose important role in daily life (cooling, freezing, air conditioning, and heat pumps for heating) is well known.

Current problems of these machines, essentially those with mechanical compression of steam, are taking into consideration environmental criteria (ODP, global warming potential (GWP)), and this has led to successively developing several generations of refrigerants (CFC, HCFC, HFC, HC and natural fluids). Therefore, there is ongoing research in this field, and with high technological impact.

Constrained thermodynamic optimization in finite dimensions provides a tool and interesting results for the machines with mechanical compression of steam. The future may, nevertheless, bring fundamental changes, and even disruptions in the current landscape due to the emergence of machines with three or four heat reservoirs or other (thermoelectric, thermomagnetic or with permanent gas) machines. The approach to studying these machines is the same. A complete example referring to Ranque–Hilsch tube is provided.

Volume 1 of this book is dedicated to thermomechanical machines (Chapters 3–6). Chapters 2–6 provide results and perspectives that will be completed in Volume 2 by successive examination of machines other than thermomechanical, such as multistage machines, cascade and hybrid machines.

FPDT appears as a privileged tool, showing the existence of performance optima and optima optimorum that can serve as realistic references for the qualification of real systems.

This book shows that finiteness is a ubiquitous condition for any approach considered in this book. Moreover, it sheds light on how these optimizations, as consequences of this finiteness, are subjected to many new criteria, including economic and environmental ones. Besides physical constraints, this opening evidences technical or usage constraints.

Analysis and optimization are therefore imperative, and the current conjecture being proposed here based on this phenomenological approach is the existence, from a fundamental perspective, of an FDOT.

At the end of this book, FDOT appears as a well-established challenge, as far as applications are concerned. The next step will be to enhance its potential from the level of simple (didactic) cases to real and necessarily sophisticated usages, which constitute the subject of Volume 2 of this book.

Hoping that his convictions will be shared by the reader, the author wishes to thank the many colleagues he came in contact with throughout the world, and also the editor for their reception and patience.

Finally, the author is open to any remark on this work, which is by necessity imperfect and extendable.

Acknowledgements

The English edition of this book would have never seen the light if it were not so favorably received by C. Menasce several months ago. Given the scale of the task, the decision was made to publish it in two volumes.

Furthermore, the editor’s patience has greatly facilitated the completion of this project. I am deeply grateful to the many colleagues and students who have, either from afar or have more actively participated in the elaboration of this work, offering their insight and proposals for improved readability (particularly to Angéline C., Jean B., Monica C., including my all-time secretary, Françoise H.).

A special thought goes to my family: Renaud, who has been very receptive to my efforts, Marie José and Aude for their encouragements in the accomplishment of this task and their renewed support, and my granddaughter Jade, very mindful of her grandparents.

This book is also dedicated to the future that awaits us.

List of Notations and Acronyms

Notations

A area, m²; constant

a(intermediate variable); absorber

An anergy, J

B(b) magnetic induction, T; constant; (boiler)

C(c) Curie constant or other constant; heat capacity, J/K; (specific heat capacity, J/(kg. K); condenser); torque or consumption

d constant; number; desorber

e electron charge; constant; evaporator

E(e) total energy, J (thickness, m)

Em Emergy, J

En Entransy, JK

Ex Exergy, J

 Faraday constant, 36500 C

F(f) force, N; function; free energy, J; (specific free energy); factor

g gravity acceleration (conventionally considered 9.81 m/s²)

G(g) free enthalpy, J; (specific free enthalpy, J/kg)

H(h) enthalpy, J; (specific enthalpy J/kg); heat exchange coefficient W/m²K; constant; compression ratio; (Planck constant)

I current intensity, A

J generalized flux

k polytropic exponent

K(k) conductance, various units; (transfer coefficient);

L length, m; phenomenological coefficient; Lagrangian

M(m) mass, kg; molar mass, kg/mol; magnetic moment, A. m²

N rotational speed, tr/min; NTU abbreviation; number of years

n(N) normal; number of moles; (number)

P(p) pressure, N/m²; point (perimeter)

Q(q) quantity of heat, J; (dimensionless quantity of heat)

R ideal gas constant, 8.32 J/mol; ratio of heat rates; refrigerant, ratio

 irreversibility ratio or factor

R(r) resistance, various units; (radius, m

S(s) entropy, /K; entropy parameter; (specific entropy)

T temperature, °C (reduced); time, s

T temperature, K; service life (s or years)

U(u) internal energy, J; (specific internal energy, J/kg)

V(v) volume, m³; (specific volume, m³/kg); speed, m/s; Peltier coefficient; economic value, Euros; Valve

W(w) work, J; (dimensionless work); speed

X(x) generalized force; temperature difference; (reduced NTU); variable

Y(y) variable; function

z altitude (conventionally considered with respect to sea level)

Z(z) intermediate variable; (efficiency of thermoelement)

Indices

→ vector

- average value

* quantity associated with optimum

.)

|| norm of a quantity

≈ approximately equal to

≠ not equal

~ entropic average (temperature)

a ambient environment; (at rest, vacuum); coefficient; air; (aspire); absorber

A(a) relative to surface A; (apparent)

ad adiabatic

aux auxiliary

B(b) low; (coefficient; boiler)

C(c) cold; control; kinetic; compression; combustible; condenser; Carnot

ch chemical

comb combustion

cond conduction

cycle cycle

D(d) expansion; desorber; (total differential; degraded; expansion); expense

e entry; evaporator

eff effective

elec electric

eq equivalent

ex external; relative to Exergy

F(f) cold; final; flue gas; functioning

g gravitational potential; generator; (boiler)

G global; generalized

H hot; high; hydraulic; isenthalpic

i index; initial; internal

I investment; intermediate; irreversible; relative to the first law

II relative to the second law

Irrev irreversible

is isentropic

j summation index

k summation index

I summation index

L longitudinal; loss; liquid; low

lim limit

λ Lagrange parameter

m relative to mass transfer; engine; minimum; mechanical

M engine; machine; maximum

ma arithmetic mean

RM refrigerating machine

MAX maximum

ml logarithmic mean

n index of transfer law

opt optimum

P(p) constant pressure; pump; (wall; heat loss; propulsion)

HP heat pump

Ph physical

Q(q) under imposed heat; (quality)

R(r) reaction; (chemical or real); discharge; (delay; reduced discharge); recuperative heat exchanger

ref reference

rev reversible

S source or heat sink

S(s) system; (outlet; specific); stagnation

sol solar

T(t) constant temperature; transformation; (total or transverse); imposed temperature; decantation

Th thermal

tot total

u useful

V(v) constant volume; (volumetric); vapor

X arbitrary physical quantity

Greek letters

‘ derivative with respect to one space variable (linear derivative)

‘’ derivative with respect to two space variables (surface area derivative)

‘" derivative with respect to three space variables (volume derivative)

α coefficient of cubic expansion (intermediate variable); absorptivity; Seebeck coefficient

β coefficient of increase of pressure (intermediate variable); temperature coefficient K− 1

γ surface tension, J/m²; Cp/Cv, isentropic coefficient

δ differential form

Δ finite increment of a quantity (discriminant of second degree equations)

ε effectiveness of heat exchanger; surface emissivity; infinitely small

ζ coefficient

η efficiency

| parameter; Carnot factor

λ heat conductivity; Lagrange parameter; conductive losses (index)

μ chemical potential, J/kg (or J/mol; fraction of cold mass flow rate

ν dynamic viscosity; frequency, S− 1

ρ density, kg/m³

σ(Σ) Stefan constant, 5.67.10− 8W/m²K⁴ (discrete summation)

τ time constant, s; dimensionless temperature (or other); transformity

φ(Π) coefficient or index (dissipation function)

χ coefficient of compressibility

ψ(ψ) coefficient

ω angular speed, rad/s

 continuous summation (bound summation)

Acronyms

An anergy

AP average pressure

BDC Bottom Dead Center

C constraint; condenser

CC combined cycles

CC Capital Cost

CFC ChloroFluoroCarbon

CHP (CHHP; CCHP) combined heat and power