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Thermodynamics and Propulsion

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Krishnendu Sinha
Department of Aerospace Engineering
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Indian Institute of Technology Bombay,
Mumbai 400076, India.
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Prepared for AE223 course at IIT Bombay

Copyright Krishnendu Sinha, 2018

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 Preface

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Thermodynamics is a basic ingredient for engineering and the natural sciences. As
the study of energy and its conversion, thermodynamics forms the basis of almost

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everything that we see around us ? from boiling water to rocket engines. It is gov-
erned by a set of empirical laws that are built upon abstract concepts like system,
surrounding, enthalpy and entropy. A student of thermodynamics is required to mas-
ter these concepts and their development to tackle a variety of engineering problems.
Engines form an important class of application, both in terms of historical develop-
ment of thermodynamics as well as present- day challenges of energy and emission
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control. Thermodynamics and propulsion thus forms an integral part of Mechanical
and Aerospace Engineering curriculum.

The objective of the book is to present classical thermodynamics in a way that is

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oriented towards and directly useful to the propulsion field. The majority of en-
gines are either of piston-cylinder type or based on gas turbine. Gas turbine engines
are flow-through devices with components, like compressor, combustor and turbine,
arranged in series. The laws of thermodynamics are therefore cast in the control vol-
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ume framework using total enthalpy and shaft work that are crucial for gas turbine
analysis. The ideas are applied extensively to the engine components, and how the
components together lead to thrust generation at different operating conditions. Fi-
nally, we present full engine analysis for turbojet, turbofan and ramjet engines, and
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end with an advanced application to scramjet propulsion.

The book is targeted towards undergraduate students in Aerospace and Mechan-

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ical engineering. It covers the basic concepts and principles of thermodynamics,

followed by their application to idealized engine cycles. Analysis of real engines
includes component efficiencies, fuel consumption, heat transfer and thermal limits.
Each section starts with a list of main points to be covered in the text, a detailed
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development of the key ideas and extensively solved examples. A set of conceptual
and numerical problems in realistic scenario is provided at the end of each chapter.
In addition, the book has several interactive features in the form of dialog boxes,

v
 vi Preface

to bring out important take-away points, interesting facts and additional resources.
These are aimed at developing strong methodological skills in a student-friendly
way.

A key feature of the book is the emphasis on concepts and underlying principles.
Each idea is first explained in layman language, followed by examples and analo-
gies, and then a physical and mathematical development to firm up the idea. The
discussion also goes over the different nuances that need to be understood for a

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successful application to different scenarios. The text is dotted with simple thinking
questions (points to ponder), which lead the reader to advanced conceptual questions

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at the end of the chapter. Also, the solutions to example problems are systematically
developed in a way to provide detailed understanding of the assumptions and their
limitations, as well as the implication of the results.

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The book attempts to develop intuitive understanding of the subject by connecting
the abstract concepts of thermodynamics to practical examples. For instance, total
enthalpy is explained in terms of power generation in a turbine, whereas total pres-

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sure is related to the friction losses in a nozzle. When placed in the perspective of
engine application, these analogies can breathe life into some of the dry concepts
of thermodynamics and make the subject much more exciting to study. In my opin-
ion, a physical feel along with the mathematical developments is essential to build
a strong foundation, and it goes a long way in retaining the comprehension gained
in the subject.
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Finally, the book is written for a sample user base of Aerospace Engineering under-
graduate students at IIT Bombay, where the course has been taught at the sophomore
level for a number of years. Many of the pedagogical features are based on student
feedback on a draft version of the current manuscript.
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Mumbai, July 2018 Krishnendu Sinha

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 Contents

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1 Introduction

2 Basic Concepts

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2.1 System and surroundings
2.2 Thermodynamic state, properties, process and cycle
2.3 Steady state vs. Equilibrium

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2.4 Control volume
2.5 Quasi-static and reversible process

Work and heat interactions

3.1 Displacement work (pdV work)
3.2 Flow work
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3.3 Shaft work
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3.4 Heat Transfer
3.5 Energy and enthalpy
3.6 Specific heat
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3.7 Zeroth law of thermodynamics

4 First law of thermodynamics

4.1 First law applied to flow processes
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4.2 Heat exchanger application

4.3 First law applied to unsteady processes

5 Second law of thermodynamics

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5.1 Heat engine

5.1.1 Reservoir
5.1.2 Heat pump
5.2 Statement of Second law
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5.3 Reversibility of a process

5.3.1 Heat transfer through a finite temperature difference
5.3.2 Flow caused by finite pressure difference
5.4 Carnot Cycle
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5.5 Ideal gas in a piston-cylinder configuration

5.6 Flow process refrigeration cycle
5.7 Carnot theorem

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 viii CONTENTS

5.7.1 Historical development leading to Carnots theorem

5.7.2 Proof of Carnot theorem
5.7.3 Efficiencies of reversible engines operating between the
same source and sink
5.8 Absolute temperature scale
5.8.1 The Kelvin and Rankine scales
5.8.2 Creating the absolute temperature scale
5.8.3 Absolute zero temperature

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5.8.4 Ideal gas temperature vs. Absolute temperature

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6 Entropy
6.1 Analogy between first and second law of thermodynamics
6.2 Carnot cycle applied to a general reversible cycle
6.2.1 Carnot cycle

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6.2.2 Any reversible process
6.2.3 Any reversible cycle
6.3 Definition of Entropy
6.3.1 dQ/T is path independent
6.3.2 What is entropy?
6.4 T S diagram
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6.4.1 Carnot cycle on T S diagram
6.5 Irreversible cycles
6.5.1 Comparison with Carnot cycle
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6.5.2 Any irreversible process and irreversible cycle
6.5.3 Entropy inequality
6.6 Entropy principle
6.6.1 Heat transfer through a finite temperature difference
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6.6.2 Maximum work extracted from heat flow between two finite
bodies
6.7 Entropy generation
6.7.1 System approach
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6.7.2 Control volume approach

6.8 Gibbs equation
6.8.1 Application to a piston-cylinder arrangement
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7 Exergy or Availability
7.1 Reservoir at fixed temperature
7.2 Finite body at temperature T
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7.3 Exergy of steady state flow system

8 Cycle Analysis
8.1 Four – stroke Internal Combustion Engine
8.2 Otto cycle
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8.3 Diesel cycle

8.4 Gas-turbine engine
 CONTENTS ix

8.5 Brayton cycle

9 Aircraft Propulsion
9.1 Aircraft engine performance parameters
9.2 Turbojet, Turbofan, Turboprop engines
9.3 Ramjet and scramjet engines
9.4 Stagnation vs. static state
9.5 Thermodynamic analysis of turbojet components

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9.5.1 Axial compressor
9.5.2 Engine intake

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9.5.3 Axial turbine
9.5.4 Exhaust nozzle

10 Heat Transfer

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10.1 Modes of heat transfer
10.2 Conduction
10.2.1 Conductivity, diffusivity and Prandtl number
10.2.2 Heat diffusion equation
10.2.3 Boundary conditions

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10.2.4 One dimensional applications
10.3 Convection
10.3.1 Natural and force convection
10.3.2 Governing equations
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10.3.3 Boundary layer equations
10.3.4 Similarity parameters
10.3.5 Convection correlations
10.4 Radiation
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10.4.1 Black body radiation

10.4.2 Emmissivity and absorbtivity
10.4.3 Stephan-Boltzmann law
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11 Analysis of Scramjet engine

11.1 Engine configuration and schematic
11.2 Shock wave analysis for intake
11.2.1 Shock on lip for design point
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11.2.2 Off-design mass capture

11.3 Rayleigh and Fanno flow analysis for combustor
11.3.1 Constant area analysis
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11.3.2 Diverging duct analysis

11.4 Method of characteristics for nozzle design
11.4.1 Nozzle thrust calculation
11.5 Range and fuel requirement
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 List of Figures

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1.1 Schematic of gas turbine engine . . . . . . . . . . . . . . . . . . . 3

2.1 System and its boundaries. (a). Irregular system and (b). piston-
cylinder arrangement . . . . . . . . . . . . . . . . . . . . . . . . . 6

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2.2 p V diagram of cycle . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 T vs x to steady state . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4 T vs x to equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3

2.4
2.5
2.6
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Systems in different types of non-equilibrium. (a) Thermal, (b)
chemical, and (c) Mechanical equilibrium . . . . . . . . . . . . . .
T vs x to equilibrium. (a) Compressor, and (b) Control volume . . .
Expansion of a gas in a piston-cylinder arrangement . . . . . . . . .
A quasi-static process in a compressor . . . . . . . . . . . . . . . .
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13
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3.1 Air flow in a axial turbine that drives the compressor . . . . . . . . 19
3.2 Electric motor powered by a battery . . . . . . . . . . . . . . . . . 20
3.3 piston cylinder arrangement . . . . . . . . . . . . . . . . . . . . . 21
3.4 p V diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
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3.5 Flow-through a converging duct . . . . . . . . . . . . . . . . . . . 23

3.6 Flow-through a converging duct like nozzle . . . . . . . . . . . . . 25
3.7 Axial compressor in a gas turbine engine . . . . . . . . . . . . . . . 30
3.8 Schematic of system and shaft work . . . . . . . . . . . . . . . . . 31
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3.9 Different internal energy modes: (a) translational, (b) rotational, (c)
vibrational, (d) nuclear, (e) electronic and (f) chemical. . . . . . . . 35
3.10 A schematic illustrates of Zeroth law of thermodynamics . . . . . . 37
3.11 p V diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
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4.1 control volume form of the first law of thermodynamics . . . . . . . 44

4.2 Joules paddle wheel experiment . . . . . . . . . . . . . . . . . . . 45
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4.3 a. Control volume b. Mass of fluid at time t and t + dt . . . . . . . 46

4.4 a. Converging nozzle, b. Bell-shaped converging-diverging nozzle . 51
4.5 A schematic of heat exchanger . . . . . . . . . . . . . . . . . . . . 58
4.6 A schematic of system defined with the bottle, the pipe and the con-
necting tube. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
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4.7 A schematic of system defined with the bottle. . . . . . . . . . . . . 63

4.8 Schematic of the model problem . . . . . . . . . . . . . . . . . . . 66

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 LIST OF FIGURES xi

4.9 Schematic of the model problem . . . . . . . . . . . . . . . . . . . 68

5.1 Piston-cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.2 Gas turbine engine . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.3 a. A schematic of a heat engine, b. Thermodynamic cycle . . . . . . 75
5.4 A schematic of a heat pump . . . . . . . . . . . . . . . . . . . . . . 76
5.5 A schematic of a heat pump of refrigerator . . . . . . . . . . . . . . 77
5.6 A schematic of a perpetual motion machine(PMM1) . . . . . . . . . 79

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5.7 Piston-cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.8 Heat transfer through a finite temperature difference . . . . . . . . . 81

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5.9 Flow caused by finite pressure difference . . . . . . . . . . . . . . . 82
5.10 Carnot cycle operating with an ideal gas as the working fluid on a
p V diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.11 Ideal gas filled inside a cylinder . . . . . . . . . . . . . . . . . . . 85

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5.12 Carnot cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.13 A sketch of Newcomen first engine . . . . . . . . . . . . . . . . . . 91
5.14 A sketch of mill race . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.15
5.16
5.17
5.18
5.19
5.20
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Steam engine of Watt’s . . . . . . . . . . . . . . . . . . . . . . . . 93
Fire engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
Irreversible engine Ei and the reversed heat pump Pr . . . . . . . . . 95
Reversible heat engines . . . . . . . . . . . . . . . . . . . . . . . . 97
Carnot engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Absolute temperature scale . . . . . . . . . . . . . . . . . . . . . . 102
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5.21 p V diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

6.1 p n diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

6.2 Thermodynamic cycle divided into small segments . . . . . . . . . 115
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6.3 Thermodynamic cycle divided into small segments . . . . . . . . . 116

6.4 Carnot cycle splitted in two parts R1 and R2 . . . . . . . . . . . . . 117
6.5 Carnot cycle splitted in two parts R1 and R2 . . . . . . . . . . . . . 118
6.6 T S diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
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6.7 Carnot cycle on the T S diagram . . . . . . . . . . . . . . . . . . 121

6.8 Two engines operating between the same reservoirs . . . . . . . . . 123
6.9 p V diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.10 p V diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
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6.11 p V diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

6.12 p V diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.13 p V diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
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6.14 p V diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

6.15 p V diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
6.16 p V diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
6.17 p V diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
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8.1 Four-stroke Internal Combustion Engine . . . . . . . . . . . . . . . 152

 xii LIST OF FIGURES

8.2 Four strokes: the intake stroke, the compression stroke, the power
stroke and the exhaust stroke . . . . . . . . . . . . . . . . . . . . . 153
8.3 p V diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
8.4 p V diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
8.5 p V diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
8.6 T S diagram of Otto cycle . . . . . . . . . . . . . . . . . . . . . 157
8.7 Cycle efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
8.8 The p V plot of an idealized compression-ignited engine . . . . . 161

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8.9 The four steps of a Diesel cycle showing the heat and work interac-
tions through p V diagram. . . . . . . . . . . . . . . . . . . . . . 162

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8.10 The four steps of a Diesel cycle showing the heat and work interac-
tions through T S diagram. . . . . . . . . . . . . . . . . . . . . . 162
8.11 Otto and Diesel cycles with identical compression and heat rejection
steps through T S diagram. . . . . . . . . . . . . . . . . . . . . . 165

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8.12 Otto and Diesel cycles with identical compression and heat rejection
steps through T S diagram. . . . . . . . . . . . . . . . . . . . . . 165
8.13 Schematic of multiple stages of compressor and turbine. . . . . . . 166
8.14
8.15
8.16
8.17
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Schematic of Brayton cycle. . . . . . . . . . . . . . . . . . . . . .
p V and T S diagrams of Brayton cycle. . . . . . . . . . . . . .
Cycle efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
T S diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
168
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Chapter 1

Introduction

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Let us begin with a brief introduction to ‘Thermodynamics and Propulsion’ that is
the subject of this book. In simple term, thermodynamics is the science of energy.

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The study of different kinds of energy forms a central part of many disciplines
in engineering and natural sciences. The subject of thermodynamics dates back
centuries and, even in current times, it applies to almost everything we see around
us. Section 1.1 presents several examples from different applications. It also in-
troduces the key ideas of thermodynamics that help us understand and analyse
energy in its different forms. Section 1.2 takes us into the field of propulsion –
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the science and engineering of driving machines. Energy is essential for driving
machines, and thus thermodynamics forms an integral ingredient for propulsion.
We look into different kinds of engines, their working and a variety of applica-
tions, where engines are used. Most important, we discuss how thermodynamics
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can be used to understand the working of engines and answer important questions
about their performance. Finally, section 1.3 delineates the content of the book in
terms of its chapters and how they tie together to make a comprehensive study of
thermodynamics and propulsion.
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1.1 Thermodynamics as a subject

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Thermodynamics in simple terms, is related to the pressure, temperature and vol-

ume of a gas. In fact, these are nothing but different ways of quantifying the energy
contained in the gas. By definition, thermodynamics is the study of energy trans-
fer, energy conversion or energy transformation. Energy is contained in any form
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of matter, not just gas, and it can be in different forms. These include internal
energy in the form of the heat contained in the matter, the energy stored in the
chemical bonds, nuclear energy or the energy of the nuclear particles, and so on.
Thermodynamics is the science of conversion of one form of energy into another,

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2 1 Introduction

and more often, to convert the energy stored in a material into mechanical work.
Work in the form of mechanical force is useful in driving machines.

The energy conversion takes place either in engineering devices or in nature. The
material that undergoes energy conversion in these devices is usually called the
working medium, or the working fluid. Most engines have air or a gas as the
working fluid, with a smaller number of engine applications involving liquids or
water. More general applications in nature can have other forms of matter as well.

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The energy contained in a working medium determines the physical properties
of the material. For gases and liquids, these properties are often in the form of

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pressure, temperature and volume.

The Laws of thermodynamics are the principles that govern energy conversion
from one form to another. They are used to characterize the properties of a material

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and how they change during energy conversion. Thermodynamic laws decide how
much energy is contained in a given mass of the material and how much of that
energy can be converted into other forms or into mechanical work.

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Energy conversion devices are the main focus of thermodynamics, where the laws
of thermodynamics are to be applied to understand how these devices work and
how to make them work better. Here are a few examples of energy conversion
devices; some are very common and others are not so trivial.
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1. All kinds of engines, including automobile engines, aircraft engines, rockets
and steam engines. Here, the chemical energy stored in fuel is converted into
mechanical work.
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2. Power generation machinery, like steam and nuclear power plants, hydraulic
power plants and even the tiny solar cells on rooftops.
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3. Household appliances, like air conditioner and refrigerator are common exam-
ples in thermodynamics. They use electric energy to cool a body by pumping
heat out of it. On the other hand, a microwave oven or a steam iron converts
electrical energy in to heat.
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4. Fluid flow in and around aerospace vehicles, especially high-speed (compress-

ible) flows encountered in supersonic and hypersonic flight. Here, the kinetic
energy of air is converted to internal energy or heat, which then can lead to se-
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vere heating of the vehicle. The reverse effect happens in a rocket nozzle where
a hot gas is converted into a high-speed jet.

5. Esoteric examples like the human body, Earth’s eco system and its associated
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global warming problem, astrophysical entities like black holes, and so on.

Thermodynamics is all pervasive, as is apparent from the list above. It is appli-

cable to simple daily examples like boiling of water to advanced technology like
rocket engines. The principles of thermodynamics have to be general enough to
1.2 Propulsion application 3

encompass all these applications and many more. As a result, they are often cast
in terms of abstract ideas like systems and surroundings (to be defined in the next
chapter), enthalpy (chapter 3), entropy (chapter 6) and others. Traditionally, the
subject of thermodynamics develops these concepts without any specific physical
shape or form, so that they can be tailored to a wide range of applications. For ex-
ample, the system can be defined as the water boiling in a kettle or it can represent
the combustion chamber inside a rocket engine.

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In this book, we take a slightly different approach. We develop the same ideas of
thermodynamics (system, surrounding, work, enthalpy, entropy and others), but

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they are introduced in the context of engines and its components. For example,
work is often related to force or thrust generated by the engine and enthalpy is
defined in the context of fluid flowing through engine components. That way the
thermodynamic concepts are directly related to realistic examples. Connecting ab-

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stract ideas to particular geometry and application helps to gain physical insight
into the principles governing the subject. This can develop an intuitive understand-
ing that is crucial in retaining the comprehension gained in the subject.

1.2 Propulsion application

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Engines form an important class of application for thermodynamics. Historically,
the development of the steam engine was the main driving force behind the indus-
trial revolution. The steam engine also played a major role in the development of
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thermodynamics as a subject of study [1]. The piston-cylinder arrangement used

in the early steam engines still forms the core of the internal combustion (IC) en-
gine in modern day automobiles. Here, a piston compresses air in a cylinder; fuel
is then injected and burned inside the cylinder, followed by expanding the gas and
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moving the piston out (Fig. 1.1). The process repeats, such that each expansion
stroke of the piston generates power from the engine. The power is transmitted to
a crank shaft connected to the wheels. There are also a number of valves, which
open and close from time to time to let fresh air into the cylinder or let out fuel-
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burnt air out of the engine. IC engines often use more than one cylinder, and the
pistons of these cylinders are synchronised in a way to generate continuous power
for the vehicle. Engines of various shapes and sizes are used in a wide variety of
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applications. See Refs. [2, 3] for a detailed description of how an IC engine works.

The other commonly used engine is the gas turbine engine. Almost all commer-
cial and military aircrafts use turbojet, turboprop and turbofan engines that are
based on the gas turbine. Such engines are also used in several land and sea based
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applications, including power generation. A gas turbine engine follows the same
steps (compression, combustion and expansion) to generate power, as in an IC en-
gine. The main difference is that the different steps are accomplished in different
parts of the engine. The three main parts or components of the engine are com-
4 1 Introduction

Fuel
Valves

Burnt gas
Air Piston

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cylinder

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crank
shaft

+ + +

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Compression Combustion

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Fig. 1.1: Schematic of an internal combustion engine, showing its main parts and
the key steps of operation.
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pressor, combustor and turbine, and they are arranged sequentially one after the
other; see Fig. 1.2. The working fluid (usually air) flows from one component to
other, unlike the IC engine, where compression, combustion and expansion are all
done sequentially (one after the other) in a single unit – the piston-cylinder. Air-
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craft applications usually have an additional part, called the nozzle, placed after
the turbine, to generate a high-speed jet exhaust. An intake duct is also provided
at the front of the compressor. Further details of the gas turbine and its internal
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components can be found in [4, 5]. Several video links and other useful material
on gas turbine engines are available on the internet.

An aircraft engine simply works on Newton’s third law of motion, i.e. if you can
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propel air fast enough backward, the equal and opposite reaction is the thrust that
will move the aircraft forward. Consider an engine attached under the wing of a
commercial transport aircraft, for example, flying at an altitude of 35,000 ft. The
engine takes in ambient air at a temperature of 50 C and a pressure of about
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quarter of the atmospheric pressure we feel at sea level. The speed of the air going
into the engine is equal and opposite to the aircraft velocity, roughly around 860
km/hr. The air entering the engine is first compressed to high pressure (making it
slower in this process). This occurs in a rotating machinery called an axial com-
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pressor shown in Fig. 1.2. Fuel is then injected into the air stream in a combustor
and the burning of the fuel adds energy to the gas, which is then propelled into
a high-speed jet in a nozzle. Before the air gets to the nozzle, some of its energy
is extracted by another rotating machine called the turbine. It is connected to the
1.2 Propulsion application 5

Fuel

Air jet

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Combustor
Intake
Nozzle
Compressor Turbine

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Fig. 1.2: A schematic of a turbojet engine based on gas turbine, showing the flow
of air through its main components.

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compressor by a common shaft and it provides the necessary power to compress
the gas in the first place.

The thrust generated by an engine is equal and opposite to the change in momen-
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tum of the air (or the gas) between the nozzle exhaust and the engine entry. The
change in momentum is the product of the mass of air flowing through the engine
and the change in its velocity. An increase in velocity or kinetic energy of the air
is achieved by the extra energy added to it by burning fuel. The natural question
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is how much thrust is generated by a given engine and how to maximise it? We
can get higher thrust by accelerating a larger mass of air through the engine. That
would require a bigger engine or more number of engines, which will add to the
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weight and drag of the aircraft. A heavier aircraft will in turn require even more
thrust to fly!

A higher thrust can also be generated by making the exhaust jet faster, i.e. increas-
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ing the kinetic energy of the exhaust gas. It will require higher input of chemical
energy, by burning more fuel. The heat released by burning fuel in the combustor
also raises the temperature of the gas, so that the high-speed jet exhaust coming
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out of the nozzle is also very hot. It turns out that a lot of the energy input in the
combustor is lost in the form of the hot gas, ejected into the atmosphere and hence
rendered useless. Can we not minimise, or altogether eliminate this wastage of en-
ergy and utilize all the chemical energy input only to increase the kinetic energy
of the gas? That way, we should be able to generate higher exhaust jet velocity and
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higher thrust for the same amount of fuel burnt in the combustor. After all, any
additional fuel consumption directly reflects on the price of tickets for passengers.

Now, here is the trick with thermodynamics. Not all the chemical energy input
from the fuel burnt or the heat added in the combustor can be converted into the
6 1 Introduction

thrust power generated by the engine. Some of the energy has to be rejected or
thrown away. Why? Because that is what second law of thermodynamics tells us.
It is an empirical law that is based purely on observations, and cannot be derived.
The second law seems to be valid always, and no case to the contrary has been
reported. So, we believe it, learn it, apply it and trust its results. One of the key
question to answer then is: out of the heat added by burning fuel in the engine,
what is the maximum part of it, if not all, that can be actually be converted to thrust
power? What is the minimum heat rejection in the best possible situation? Second

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law of thermodynamics lets us calculate exactly this quantity, i.e. the fraction of
heat input that can be converted into work output in a hypothetical engine without

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any friction losses or heat leakage.

A real engine will obviously encounter many different kinds of losses. These could
be due to friction in the bearings or viscous losses associated with fuel-air mixing.

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There can be heat leakage from the hot combustion chamber to the cooler ambient
atmosphere. Such losses will bring down the performance of an engine, and the
losses have to be quantified in order to estimate the thrust of a real engine. Several

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good references are dedicated entirely to gas turbine engine analysis [4, 5].

The objective of this book is to learn the concepts and principles of thermody-
namics, so as to apply them directly to the propulsion field. The thermodynamic
laws are used to compute the thrust and power generated by an engine. The laws
are also used to formulate the best possible scenario of an ideal engine that serves
IT
as a benchmark to compare the performance of real engines. The two main appli-
cations are the internal combustion engine and the gas turbine engine. Because of
its complexity, the gas turbine engine and its components are given higher atten-
tion in the chapters. Additional topics relevant to gas turbine engines, namely, the
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thermodynamics of compressible flows and different modes of heat transfer, are

also presented. These are complimentary to the traditional thermodynamic anal-
ysis, and they allow us to take up advanced applications like scramjet propulsion
for hypersonic fight.
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There are many books on engineering thermodynamics; see for example, Refs. [6,
7] and others. The majority of them have a wide scope and encompass all differ-
ent engineering applications of thermodynamics. Engines form a small subset of
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the study and get limited coverage. By comparison, a study of thermodynamics

focused on the propulsion field allows us to go deeper into the thermodynamic
analysis of engines. We can look into the details of the processes occurring in the
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engine and its different components. Studying the working of the engine compo-
nents give us a better understanding of how to analyse them thermodynamically. In
particular, we can critically assess the assumptions involved and their limitations
under realistic conditions. We are also able to combine the component level calcu-
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lations to the scale of a full engines operating under realistic conditions. Different
variants of the engines are considered, so as to understand why one is preferred
over the other depending on the operational requirements.
1.3 Overview of chapters 7

A key feature of the book is the emphasis on concepts and underlying princi-
ples. The concepts are developed in detail, using physical examples and analo-
gies, wherever possible, along with the mathematical derivation. We also go over
the finer nuances that need to be understood for a successful application of the
governing principles. The text is dotted with small thinking questions to check
comprehension, and they lead to more advanced conceptual questions at the end
of each chapter. Applying the concepts to example problems is also described in
detail, including the physical configuration, the assumptions involved and their

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limitations, as well as the implication of the numerical results obtained.

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The book takes a physical approach to the study of thermodynamics. This is in
contrast to a mathematical or a problem-solving approach, which is mostly fo-
cused on deriving equations and using them to get numerical solution to engi-
neering problems. We attempt to develop intuitive understanding of the subject

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by connecting abstract concepts to practical examples. Examples drawn from en-
gine applications are used to elucidate difficult thermodynamic concepts. See, for
example, the part relating to chapter 6 in the following section. These physical

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analogies can breathe life into some of the dry topics in thermodynamics and
make the subject far more exciting to study. A physical appreciation of the ideas
and concepts go a long way in building a strong foundation in the subject.
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1.3 Overview of chapters
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The book is divided into two parts: basic thermodynamics and applied thermody-
namics. The first part consists of chapters 2 through 7. It develops the necessary
background in the subject, the laws of thermodynamics and the associated con-
cepts of enthalpy, entropy and exergy. These are applied to propulsion application
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in the second part of the book, which consists of chapters 8 through 13. Addi-
tional topics relevant to engine analysis, namely, heat transfer, combustion and
compressible flows are also included in the later chapters.
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1.3.1 Basic thermodynamics

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Chapter 2 sets the foundation of thermodynamics in terms of the building-block

ideas of system and surrounding, equilibrium vs. non-equilibrium, and reversible
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vs. irreversible processes. Many of these concepts are explained in terms of exam-
ples drawn from the propulsion field. This helps the reader to get familiarised by
the working of engines and their components. Chapter 3 describes macroscopic
and microscopic energy, specific heat, enthalpy and the different kinds of work
8 1 Introduction

and heat interactions. Once again, the focus is on the energy conversions that are
encountered in engine application.

Chapter 4 formulates the first law of thermodynamics. It is presented in two paral-

lel frameworks – one suited to the internal combustion engine (systems approach)
and the other for the gas turbine (control volume approach). The development
takes a physical approach and focuses on engine components. Also, the majority
of the development assumes air as the working fluid and uses ideal gas law to

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compute its properties. This is found to be sufficient to elucidate and understand
the working of the IC engine and the gas turbine. Additional topics, including

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van der Waals’ gas, vapor and liquid tables, and psychrometry, are not covered.
There are excellent books with a wider scope and the reader is referred to Refs.
[6, 7, 8, 9] for topics outside the purview of the current text.

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The second law of thermodynamics is developed in Chapter 5 in terms of the
two building blocks – heat engine and heat pump. It is then used to differentiate
between reversible and irreversible processes commonly encountered in engines.

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Next, we present the Carnot cycle and the absolute temperature scale. The Carnot
engine is the very best engine among the most ideal engines that can be con-
structed, and it plays a pivotal role in assessing the performance of different types
of engines. The Carnot cycle is then used to develop a mathematical form of the
second law, and it allows us to quantify the performance of engines under varying
operating conditions.
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Chapter 6 introduces the important concept of entropy. Instead of starting with
the mathematical form for entropy, we go through a series of conceptual devel-
opments. We see how the idea of a Carnot engine can be systematically extended
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to any thermodynamic process and thus used to define the entropy of a substance.
We also derive the entropy inequality and the entropy principle. Going through
the derivations is important because they tell us how all the ideas of second law of
thermodynamics, including heat engine, heat pump, reversibility and irreversibil-
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ity, can be converted into a single quantity called entropy. Next, we bring in the
T-s diagram to represent a thermodynamic process. The T-s diagram is both om-
nipresent and omnipotent in engine analysis, because of the central role played by
entropy in quantifying the performance of compressor and turbine.
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Chapter 7 develops the ideas of second law and entropy to define the term exergy.
It represents the amount of energy available in a material that can be converted into
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useful work. As expected, exergy is important in energy conversion devices like

engines, whose sole objective is to convert heat into useful work. Thus we have
the main quantities of thermodynamics: energy, entropy and exergy. The reader is
expected to understand these concepts well, so as to use them effectively in the
analysis of engines presented subsequently.
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1.3 Overview of chapters 9

1.3.2 Applied thermodynamics

The second part of the book is oriented towards propulsion applications. In chap-
ter 8, we take a closer look at the functioning of the IC engine and the gas turbine.
The engine operations are idealised in terms of known thermodynamic processes,
and the energy input and output are computed using the thermodynamic principles
presented in earlier chapters. A key objective is to identify the critical parameters

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of the engine that determine its output and efficiency. We focus on the thermody-
namics of IC engines and the gas turbine. Others applications, like refrigeration

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cycle, can be found in Refs. [6, 7].

Chapter 9 extends the analysis to real engines used in aircraft propulsion. The
majority of the development is for a turbojet engine; turbofan and turboprop en-

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gines are also taken up, along with ramjet and scramjet engines for hypersonic
propulsion. The objective is to bring in the effect of friction and other losses en-
countered in the engine components. The analysis goes into the functioning of the

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different components, so as to quantify their losses, and then combine them to
evaluate the performance of a real turbojet engine. We also develop the concepts
of total and static states of a gas in motion, and use them extensively in the engine
calculations.

Heat transfer and thermal considerations plays a pivotal role in propulsion appli-
IT
cations. Heat transfer is often in terms of heat losses from the engine to cooler
ambient, or due to active cooling of engine components. Chapter 10 presents the
different modes of heat transfer in terms of their basic concepts and the govern-
ing equations. A few key empirical relations useful for engine calculation are also
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presented. Additional details can be found in Refs. [12, 13]. Of particular interest
is the cooling of turbine blades, a practical example that combines different modes
of heat transfer into a single problem. The maximum allowable blade temperature
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determines the critical operating thermal limit of the engine.

Two additional topics – combustion and compressible flows – are essential for
gas turbine analysis. Combustion is the process of heat addition by burning fuel
in air, and the thermodynamic aspects of combustion are presented in chapter 11.
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We study the chemical reactions involved in fuel burning and the stoichiometric
ratios. This is followed by heat of reaction and heat of formation, which enable
us to compute the amount of heat released by burning fuel in an engine. Finally,
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combustion products and pollutants are discussed in the context of fuel-lean burn-
ing in aircraft engines. More detailed description of combustion can be found in
Refs. [14, 15].
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The flow in gas turbine engines is inherently compressible. Chapter 12 introduces

the basic ideas of compressible flows, including sound waves, Mach number and
some preliminary analysis of shocks and expansion waves. These are useful in
understanding the flow encountered in the engine components. Thermodynamic
principles applied to one-dimensional compressible flow in a variable area duct
10 1 Introduction

is a key building block for engine inlets and nozzles. Additionally, the thermo-
dynamics of heat addition in a flow through a constant area duct is taken up as a
model problem for gas turbine combustor. These can be effectively used to com-
plement the thermodynamic analysis of engine components, and to explore off-
design operating conditions. Once again, the material in this chapter can be taken
as a beginning for compressible flows. More detailed study of the subject can be
found in Refs. [16, 17, 18].

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Finally, the thermodynamic principles and the analysis tools studied in the book
are applied to a realistic scramjet engine. A scramjet, or supersonic combustion

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ramjet, engine is an air-breathing engine used for hypersonic flight. It is based
on the same working principles as a turbojet engine described in section 1.2. We
study the compression, combustion and expansion processes occurring in a real-
istic scramjet configuration. Practically relevant flight parameters are considered;

m
both at design point and off-design conditions. These are used as input to the en-
gine calculation, which in turn is used to quantify fuel requirement for a specified
flight operation. The material follows the development in Ref. [19, 20], where
additional details of scramjet propulsion can be found.

References
Bo
IT
1. Heat and thermodynamics: a historical perspective by C. J. T. Lewis, Greenwood Press, Westport,
Conn. USA, 2007.
2. Internal Combustion Engines: Applied Thermosciences by A. T. Kirkpatrick and C. R. Ferguson,
,I

Wiley, 2nd edition, 2011

3. Internal Combustion Engine in Theory and Practice: Thermodynamics, Fluid Flow, Performance v.1
by C. F. Taylor, MIT Press, 2nd edition, 1977
4. Gas turbine theory by H. I. H. Saravanamuttoo, H. Cohen, and G. F. C. Rogers, Pearson Education,
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Ltd., 7th edition, 2017.

5. Gas turbines by V. Ganesan, Tata McGraw-Hill Education, 3rd edition, 2010
6. Thermodynamics: An engineering approach by Y. Cengel and M. Boles, McGraw-Hill Education,
8th edition, 2015.
7. Fundamentals of Engineering Thermodynamics by M.J. Moran, H. N. Shapiro, D. D. Boettner and
in

M. B. Bailey, John Wiley & Sons, Inc., 8th edition, 2014.

8. Elements of engineering thermodynamics by R. H. Sabersky, McGraw-Hill, 1957.
9. Thermodynamics and Heat Power by K. C. Rolle, Pearson, 6th edition, 2004.
10. Aircraft Propulsion by Saeed Farokhi, Wiley-Blackwell, 2nd edition, 2014.
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11. Mechanics and Thermodynamics of Propulsion by P. Hill, and C. Peterson, Addison-Wesley Pub-
lishing Company, Inc., 2nd edition, 2009.
12. Fundamentals of Heat and Mass Transfer by F. P. Incropera, D. P. DeWitt, L. Bergman and A. S.
Lavine, Wiley; 6th edition, 2006.
13. Heat transfer by J. P. Holman, McGraw Hill Education, 10th edition, 2009.
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14. Combustion Thermodynamics and Dynamics by J. M. Powers, Cambridge University Press, 2016
15. Combustion by I. Glassman, Academic Press, 4th edition, 2008.
16. Modern compressible flow by J. Anderson, McGraw Hill Education, 3rd edition, 2017.
17. Fundamental mechanics of fluids by I. G. Currie, CRC Press, 3rd edition, 2002.
18. Fundamentals of Gas Dynamics by R. D. Zucker and O. Biblarz, Wiley, 2nd Edition, 2002.
19. Hypersonic airbreathing propulsion by W. Heiser and D. Pratt, AIAA, 1994.
References 11

20. Scramjet Propulsion by E. T. Curran and S. N. B. Murthy, AIAA, 2001.

21. Video link for IC engine (Link: https://www.youtube.com/watch?v=O9tfIfwlmz8).
22. Video link for Gas turbine engine (Link: https://www.youtube.com/watch?v=zy4A-z2WKhw).

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