ANALYTIC COMBUSTION Combustion involves change in the chemical state of a substance from a fuel state to a product state via a chemical reaction accompanied by release of heat energy. Design or performance evaluation of equipment also requires knowledge of the rate of change of state. This rate is governed by the laws of thermodynamics and by the empirical sciences of heat and mass transfer, chemical kinetics and fluid dynamics. Theoretical treatment of combustion requires integrated knowledge of these subjects and strong mathematical and numerical skills. Analytic Combustion is written for advanced undergraduates, graduate students and professionals in mechanical, aeronautical and chemical engineering. Topics were carefully selected and are presented to facilitate learning, with emphasis on effective mathematical formulations and solution strategies. The book features more than 60 solved numerical problems and analytical derivations and nearly 145 end-of-chapter exercise problems. The presentation is gradual, starting with thermodynamics of pure and mixture substances and chemical equilibrium and building to a uniquely strong chapter on application case studies. Professor Anil W. Date received his PhD in Heat Transfer from the Imperial College, London. He has been a member of the Thermal & Fluids Group of the Mechanical Engin- eering Department at the Indian Institute of Technology Bombay since 1973. Professor Date has taught both undergraduate and post-graduate courses in thermodynamics, en- ergy conversion, heat and mass transfer and combustion. He actively engaged in research and consulting in enhanced convective heat/mass transfer, stability and phase-change in nuclear thermo-hydraulics loops, numerical methods applied to computational fluid dy- namics, solidification and melting and interfacial flows. Professor Date has published in the International Journal of Heat and Mass Transfer, Journal of Enhanced Heat Trans- fer, Journal of Numerical Heat Transfer, and American Society of Mechanical Engineers Journal of Heat Transfer and has carried out important sponsored and consultancy pro- jects for national agencies. He has been Editor for India of the Journal of Enhanced Heat Transfer. Professor Date has held visiting professorships at the University of Karlsruhe, Germany, and City University of Hong Kong, and has been visiting scientist at Cornell University and UIUC, USA. He has delivered lectures/seminars in Australia, UK, USA, Germany, Sweden, Switzerland, Hong Kong and China. Professor Date founded the Center for Technology Alternatives for Rural Areas (CTARA) in IIT Bombay in 1985 and has been its leader again since 2005. He derives great satisfaction from applying thermo-fluids and mechanical science to rural technology problems and has inspired sev- eral generations of students to work on such problems. He has taught courses in science, technology and society and appropriate technology. Professor Date was elected Fellow of the Indian National Academy of Engineering (2001), received the Excellence in Teaching Award of IIT Bombay in 2006 and was chosen as the first Rahul Bajaj Chair-Professor of Mechanical Engineering by IIT Bombay in 2009. Professor Date is the author of Introduction to Computational Fluid Dynamics, published by Cambridge University Press, in 2005. Analytic Combustion WITH THERMODYNAMICS, CHEMICAL KINETICS, AND MASS TRANSFER Anil W. Date Indian Institute of Technology, Bombay cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, S ˜ ao Paulo, Delhi, Tokyo, Mexico City Cambridge University Press 32 Avenue of the Americas, New York, NY 10013-2473, USA www.cambridge.org Information on this title: www.cambridge.org/9781107002869 C Anil W. Date 2011 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2011 Printed in the United States of America A catalog record for this publication is available from the British Library. Library of Congress Cataloging in Publication data Date,AnilW.(AnilWaman) Analytic Combustion : With Thermodynamics, Chemical Kinetics, and Mass Transfer / A.W. Date. p. cm Includes bibliographical references and index. ISBN 978-1-107-00286-9 (hardback) 1. Combustion – Mathematical models. 2. Thermodynamics – Mathematical models. I. Title. QD516D26 2011 541  .361015118–dc22 2010049634 ISBN 978-1-107-00286-9 Hardback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party Internet Web sites referred to in this publication and does not guarantee that any content on such Web sites is, or will remain, accurate or appropriate. To the MTech and PhD students of the Thermal and Fluids Engineering Specialization in the Mechanical Engineering Department, IIT Bombay for their appreciative evaluations of my teaching and To my wife Suranga, son Kartikeya, and daughter Pankaja for their patience and support, and for caring to call me home from my office, howling, “It is well past dinner time!” Contents Preface page xiii Symbols and Acronyms xvii 1 Introduction 1 1.1 Importance of Thermodynamics 1 1.2 Laws of Thermodynamics 5 1.3 Importance of Combustion 7 2 Thermodynamics of a Pure Substance 12 2.1 Introduction 12 2.2 Important Definitions 12 2.2.1 System, Surroundings and Boundary 12 2.2.2 Work and Heat Interactions 13 2.2.3 Closed (Constant-Mass) System 13 2.2.4 Open (Constant-Volume) System 14 2.2.5 In-Between Systems 14 2.2.6 Thermodynamic Equilibrium 15 2.2.7 Properties of a System 16 2.2.8 State of a System 17 2.3 Behavior of a Pure Substance 18 2.3.1 Pure Substance 18 2.3.2 Typical Behavior 18 2.4 Law of Corresponding States 21 2.5 Process and Its Path 23 2.5.1 Real and Quasistatic Processes 24 2.5.2 Reversible and Irreversible Processes 25 2.5.3 Cyclic Process 27 2.6 First Law of Thermodynamics 27 2.6.1 First Law for a Finite Process – Closed System 28 2.6.2 Joule’s Experiment 30 2.6.3 Specific Heats and Enthalpy 31 vii viii Contents 2.6.4 Ideal Gas Relations 32 2.6.5 First Law for an Open System 32 2.7 Second Law of Thermodynamics 35 2.7.1 Consequence for a Finite Process – Closed System 36 2.7.2 Isolated System and Universe 38 2.7.3 First Law in Terms of Entropy and Gibbs Function 40 2.7.4 Thermal Equilibrium 40 2.7.5 Equilibrium of a General Closed System 42 2.7.6 Phase-Change Processes 43 2.7.7 Second Law for an Open System 44 3 Thermodynamics of Gaseous Mixtures 48 3.1 Introduction 48 3.2 Mixture Composition 49 3.2.1 Mass Fraction 49 3.2.2 Mole Fraction and Partial Pressure 50 3.2.3 Molar Concentration 51 3.2.4 Specifying Composition 51 3.3 Energy and Entropy Properties of Mixtures 51 3.4 Properties of Reacting Mixtures 54 3.4.1 Stoichiometric Reaction 54 3.4.2 Fuel–Air Ratio 56 3.4.3 Equivalence Ratio  57 3.4.4 Effect of  on Product Composition 57 3.4.5 Heat of Combustion or Heat of Reaction 60 3.4.6 Enthalpy of Formation 62 3.4.7 Entropy of Formation 63 3.4.8 Adiabatic Flame Temperature 63 3.4.9 Constant-Volume Heat of Reaction 64 3.5 Use of Property Tables 64 4 Chemical Equilibrium 70 4.1 Progress of a Chemical Reaction 70 4.2 Dissociation Reaction 71 4.3 Conditions for Chemical Equilibrium 72 4.3.1 Condition for a Finite Change 72 4.3.2 Consequences for an Infinitesimal Change 72 4.4 Equilibrium Constant K p 74 4.4.1 Degree of Reaction 74 4.4.2 Derivation of K p 75 4.5 Problems in Chemical Equilibrium 78 4.5.1 Single Reactions 78 4.5.2 Two-Step Reactions 80 4.5.3 Multistep Reactions 82 4.5.4 Constant-Volume Combustion 86 Contents ix 5 Chemical Kinetics 90 5.1 Importance of Chemical Kinetics 90 5.2 Reformed View of a Reaction 91 5.3 Reaction Rate Formula 92 5.3.1 Types of Elementary Reactions 92 5.3.2 Rate Formula for A +B → C +D 94 5.3.3 Tri- and Unimolecular Reactions 98 5.3.4 Relation between Rate Coefficient and K p 98 5.4 Construction of Global Reaction Rate 101 5.4.1 Useful Approximations 101 5.4.2 Zeldovich Mechanism of NO Formation 104 5.4.3 Quasi-Global Mechanism 108 5.5 Global Rates for Hydrocarbon Fuels 109 6 Derivation of Transport Equations 112 6.1 Introduction 112 6.2 Navier-Stokes Equations 113 6.2.1 Mass Conservation Equation 113 6.2.2 Momentum Equations u i (i=1,2,3) 113 6.3 Equations of Mass Transfer 115 6.3.1 Species Conservation 115 6.3.2 Element Conservation 116 6.4 Energy Equation 117 6.4.1 Rate of Change 117 6.4.2 Convection and Conduction 117 6.4.3 Volumetric Generation 118 6.4.4 Final Form of Energy Equation 120 6.4.5 Enthalpy and Temperature Forms 120 6.5 Two-Dimensional Boundary Layer Flow Model 121 6.5.1 Governing Equations 122 6.5.2 Boundary and Initial Conditions 123 6.6 One-Dimensional Stefan Flow Model 125 6.7 Reynolds Flow Model 126 6.8 Turbulence Models 128 6.8.1 Basis of Modeling 128 6.8.2 Modeling |u  | and l 128 7 Thermochemical Reactors 134 7.1 Introduction 134 7.2 Plug-Flow Reactor 135 7.2.1 Governing Equations 135 7.2.2 Nonadiabatic PFTCR 144 7.3 Well-Stirred Reactor 146 7.3.1 Governing Equations 146 7.3.2 Steady-State WSTCR 148 7.3.3 Loading Parameters 152 x Contents 7.4 Constant-Mass Reactor 155 7.4.1 Constant-Volume CMTCR 156 7.4.2 Variable-Volume CMTCR 159 8 Premixed Flames 164 8.1 Introduction 164 8.2 Laminar Premixed Flames 165 8.2.1 Laminar Flame Speed 165 8.2.2 Approximate Prediction of S l and δ 166 8.2.3 Refined Prediction of S l and δ 169 8.2.4 Correlations for S l and δ 173 8.3 Turbulent Premixed Flames 176 8.4 Flame Stabilization 178 8.5 Externally Aided Ignition 182 8.5.1 Spherical Propagation 182 8.5.2 Plane Propagation 184 8.6 Self- or Auto-Ignition 188 8.6.1 Ignition Delay and Fuel Rating 188 8.6.2 Estimation of Ignition Delay 189 8.7 Flammability Limits 192 8.8 Flame Quenching 194 9 Diffusion Flames 198 9.1 Introduction 198 9.2 Laminar Diffusion Flames 200 9.2.1 Velocity Prediction 200 9.2.2 Flame Length and Shape Prediction 203 9.2.3 Correlations 207 9.2.4 Solved Problems 208 9.3 Turbulent Diffusion Flames 210 9.3.1 Velocity Prediction 210 9.3.2 Flame Length and Shape Prediction 212 9.3.3 Correlations for L f 216 9.3.4 Correlations for Liftoff and Blowout 217 9.4 Solved Problems 218 9.5 Burner Design 220 10 Combustion of Particles and Droplets 223 10.1 Introduction 223 10.2 Governing Equations 226 10.3 Droplet Evaporation 228 10.3.1 Inert Mass Transfer without Heat Transfer 228 10.3.2 Inert Mass Transfer with Heat Transfer 234 10.4 Droplet Combustion 239 10.4.1 Droplet Burn Rate 240 10.4.2 Interpretation of B 240 10.4.3 Flame Front Radius and Temperature 242 [...]... fixed-bed combustion, biomass gasifiers and combustion in internal combustion engines When fuels burn, they do so with a visible-to-the-eye zone called a flame A closer examination of combustion in practical equipment, of course, requires study of the properties of flames Chapter 8 thus deals with premixed flames because in many combustion devices, gaseous fuel is premixed with air before entering the combustion. .. assumptions In combustion engineering, these idealizations of practical equipment are called thermo-chemical reactors Chapter 7 presents analysis of three types of reactors, namely the plug-flow reactor, the well-stirred reactor and the constant-mass reactor Mathematical models of such reactors can be applied to several combustion devices, such as gas-turbine combustion chambers, fluidized-bed combustion, ... Science and Technology, London) on the subjects of combustion, heat and mass transfer In particular, I have drawn inspiration from Spalding’s Combustion and Mass Transfer That book, in my reckoning, provides a good mix of the essentials of the theory of combustion and their use in understanding the principles guiding design of practical equipment involving combustion The topics in this book have been arrived... thermodynamics provide the backbone to the study of combustion Design of practical combustion equipment, however, requires further information in the form of the rate of change of state This information is provided by the empirical sciences of heat and mass transfer, coupled with chemical kinetics The rate of change is also governed by fluid mechanics The heat released by combustion is principally used to produce... used to produce mechanical work in engines and power plants, or is used directly in applications such as space-heating or cooking Combustion can also produce adverse impacts, however, as in a fire or in causing pollution from the products of combustion Thus, understanding combustion is necessary for producing useful effects as well as for fire extinction and pollution abatement In earlier times, pollution... particulates, for example) However, recognition of the so-called greenhouse gases (which are essentially products of combustion) and their effect on global climate change has given added impetus to the study of combustion The foregoing will inform the reader that the scope for the study of combustion is, indeed, vast A book that is primarily written for post-graduate students of mechanical, aeronautical...Contents xi 10.5 Solid Particle Combustion 10.5.1 Stages of Combustion 10.5.2 Char Burning 246 246 249 11 Combustion Applications 261 11.1 Introduction 11.2 Wood-Burning Cookstove 11.2.1 CTARA Experimental Stove 11.2.2 Modeling Considerations... domestic cooking is produced by combustion (burning) of solid, liquid and gaseous fuels Although the phenomenon of combustion was known to the earliest man, and although great strides have been made through painstaking experimental and theoretical research to understand this phenomenon and to use this understanding in designs of practical equipment (principally, burners and combustion chambers or furnaces),... understanding in designs of practical equipment (principally, burners and combustion chambers or furnaces), any claim to a perfect science of combustion remains as elusive as ever Designers of combustion equipment thus rely greatly on experimental data and empirical correlations Combustion is a phenomenon that involves the change in the chemical state of a substance from a fuel state to a product state via a... Schematic of Newcomen engine The steam engine, however, was an external combustion engine By 1768, Street had proposed an internal combustion (IC) engine, in which vaporized turpentine was exploded in the presence of air.3 Commercial use of the gas engine was delayed by almost a century The gas (H2 + CO) was derived from partial combustion of coal Then, in 1870, Otto invented the gasoline (or Petrol) . to several combustion devices, such as gas-turbine combustion chambers, fluidized-bed combustion, fixed-bed com- bustion, biomass gasifiers and combustion. Theoretical treatment of combustion requires integrated knowledge of these subjects and strong mathematical and numerical skills. Analytic Combustion is written