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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.
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©C Anil W. Date 2011
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First published 2011
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Library of Congress Cataloging in Publication data
Date, Anil W. (Anil Waman) 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)
- 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
- 1 Introduction Symbols and Acronyms xvii
- 1.1 Importance of Thermodynamics
- 1.2 Laws of Thermodynamics
- 1.3 Importance of Combustion
- 2 Thermodynamics of a Pure Substance
- 2.1 Introduction
- 2.2 Important Definitions
- 2.2.1 System, Surroundings and Boundary
- 2.2.2 Work and Heat Interactions
- 2.2.3 Closed (Constant-Mass) System
- 2.2.4 Open (Constant-Volume) System
- 2.2.5 In-Between Systems
- 2.2.6 Thermodynamic Equilibrium
- 2.2.7 Properties of a System
- 2.2.8 State of a System
- 2.3 Behavior of a Pure Substance
- 2.3.1 Pure Substance
- 2.3.2 Typical Behavior
- 2.4 Law of Corresponding States
- 2.5 Process and Its Path
- 2.5.1 Real and Quasistatic Processes
- 2.5.2 Reversible and Irreversible Processes
- 2.5.3 Cyclic Process
- 2.6 First Law of Thermodynamics
- 2.6.1 First Law for a Finite Process – Closed System
- 2.6.2 Joule’s Experiment
- 2.6.3 Specific Heats and Enthalpy
- 2.6.4 Ideal Gas Relations viii Contents
- 2.6.5 First Law for an Open System
- 2.7 Second Law of Thermodynamics
- 2.7.1 Consequence for a Finite Process – Closed System
- 2.7.2 Isolated System and Universe
- 2.7.3 First Law in Terms of Entropy and Gibbs Function
- 2.7.4 Thermal Equilibrium
- 2.7.5 Equilibrium of a General Closed System
- 2.7.6 Phase-Change Processes
- 2.7.7 Second Law for an Open System
- 3 Thermodynamics of Gaseous Mixtures
- 3.1 Introduction
- 3.2 Mixture Composition
- 3.2.1 Mass Fraction
- 3.2.2 Mole Fraction and Partial Pressure
- 3.2.3 Molar Concentration
- 3.2.4 Specifying Composition
- 3.3 Energy and Entropy Properties of Mixtures
- 3.4 Properties of Reacting Mixtures
- 3.4.1 Stoichiometric Reaction
- 3.4.2 Fuel–Air Ratio
- 3.4.3 Equivalence Ratio
- 3.4.4 Effect of on Product Composition
- 3.4.5 Heat of Combustion or Heat of Reaction
- 3.4.6 Enthalpy of Formation
- 3.4.7 Entropy of Formation
- 3.4.8 Adiabatic Flame Temperature
- 3.4.9 Constant-Volume Heat of Reaction
- 3.5 Use of Property Tables
- 4 Chemical Equilibrium
- 4.1 Progress of a Chemical Reaction
- 4.2 Dissociation Reaction
- 4.3 Conditions for Chemical Equilibrium
- 4.3.1 Condition for a Finite Change
- 4.3.2 Consequences for an Infinitesimal Change
- 4.4 Equilibrium Constant K p
- 4.4.1 Degree of Reaction
- 4.4.2 Derivation of K p
- 4.5 Problems in Chemical Equilibrium
- 4.5.1 Single Reactions
- 4.5.2 Two-Step Reactions
- 4.5.3 Multistep Reactions
- 4.5.4 Constant-Volume Combustion
- 5 Chemical Kinetics Contents ix
- 5.1 Importance of Chemical Kinetics
- 5.2 Reformed View of a Reaction
- 5.3 Reaction Rate Formula
- 5.3.1 Types of Elementary Reactions
- 5.3.2 Rate Formula for A + B → C + D
- 5.3.3 Tri- and Unimolecular Reactions
- 5.3.4 Relation between Rate Coefficient and K p
- 5.4 Construction of Global Reaction Rate
- 5.4.1 Useful Approximations
- 5.4.2 Zeldovich Mechanism of NO Formation
- 5.4.3 Quasi-Global Mechanism
- 5.5 Global Rates for Hydrocarbon Fuels
- 6 Derivation of Transport Equations
- 6.1 Introduction
- 6.2 Navier-Stokes Equations
- 6.2.1 Mass Conservation Equation
- 6.2.2 Momentum Equations ui (i = 1, 2, 3)
- 6.3 Equations of Mass Transfer
- 6.3.1 Species Conservation
- 6.3.2 Element Conservation
- 6.4 Energy Equation
- 6.4.1 Rate of Change
- 6.4.2 Convection and Conduction
- 6.4.3 Volumetric Generation
- 6.4.4 Final Form of Energy Equation
- 6.4.5 Enthalpy and Temperature Forms
- 6.5 Two-Dimensional Boundary Layer Flow Model
- 6.5.1 Governing Equations
- 6.5.2 Boundary and Initial Conditions
- 6.6 One-Dimensional Stefan Flow Model
- 6.7 Reynolds Flow Model
- 6.8 Turbulence Models
- 6.8.1 Basis of Modeling
- 6.8.2 Modeling | u ′ | and l
- 7 Thermochemical Reactors
- 7.1 Introduction
- 7.2 Plug-Flow Reactor
- 7.2.1 Governing Equations
- 7.2.2 Nonadiabatic PFTCR
- 7.3 Well-Stirred Reactor
- 7.3.1 Governing Equations
- 7.3.2 Steady-State WSTCR
- 7.3.3 Loading Parameters
- 7.4 Constant-Mass Reactor x Contents
- 7.4.1 Constant-Volume CMTCR
- 7.4.2 Variable-Volume CMTCR
- 8 Premixed Flames
- 8.1 Introduction
- 8.2 Laminar Premixed Flames
- 8.2.1 Laminar Flame Speed
- 8.2.2 Approximate Prediction of S l and δ
- 8.2.3 Refined Prediction of S l and δ
- 8.2.4 Correlations for S l and δ
- 8.3 Turbulent Premixed Flames
- 8.4 Flame Stabilization
- 8.5 Externally Aided Ignition
- 8.5.1 Spherical Propagation
- 8.5.2 Plane Propagation
- 8.6 Self- or Auto-Ignition
- 8.6.1 Ignition Delay and Fuel Rating
- 8.6.2 Estimation of Ignition Delay
- 8.7 Flammability Limits
- 8.8 Flame Quenching
- 9 Diffusion Flames
- 9.1 Introduction
- 9.2 Laminar Diffusion Flames
- 9.2.1 Velocity Prediction
- 9.2.2 Flame Length and Shape Prediction
- 9.2.3 Correlations
- 9.2.4 Solved Problems
- 9.3 Turbulent Diffusion Flames
- 9.3.1 Velocity Prediction
- 9.3.2 Flame Length and Shape Prediction
- 9.3.3 Correlations for Lf
- 9.3.4 Correlations for Liftoff and Blowout
- 9.4 Solved Problems
- 9.5 Burner Design
- 10 Combustion of Particles and Droplets - 10.1 Introduction - 10.2 Governing Equations - 10.3 Droplet Evaporation - 10.3.1 Inert Mass Transfer without Heat Transfer - 10.3.2 Inert Mass Transfer with Heat Transfer - 10.4 Droplet Combustion - 10.4.1 Droplet Burn Rate - 10.4.2 Interpretation of B - 10.4.3 Flame Front Radius and Temperature - 10.5 Solid Particle Combustion Contents xi - 10.5.1 Stages of Combustion - 10.5.2 Char Burning
- 11 Combustion Applications
- 11.1 Introduction
- 11.2 Wood-Burning Cookstove
- 11.2.1 CTARA Experimental Stove
- 11.2.2 Modeling Considerations
- 11.2.3 Zonal Modeling
- 11.2.4 Radiation Model
- 11.2.5 Output Parameters
- 11.2.6 Reference Stove Specifications
- 11.2.7 Effect of Parametric Variations
- 11.2.8 Overall Conclusions
- 11.3 Vertical Shaft Brick Kiln
- 11.3.1 VSBK Construction and Operation
- 11.3.2 Modeling Assumptions
- 11.3.3 Coal Burning
- 11.3.4 Model Equations
- 11.3.5 Inlet and Exit Conditions
- 11.3.6 Results for the Reference Case
- 11.3.7 Parametric Studies
- 11.3.8 Overall Conclusions
- 11.4 Gas Turbine Combustion Chamber
- 11.4.1 Combustor Designs
- 11.4.2 Idealization
- 11.4.3 Computed Results
- APPENDIX A: Thermochemistry Data
- APPENDIX B: Curve-Fit Coefficients for hc , T ad , K p , C p , h , and s
- APPENDIX C: Properties of Fuels
- APPENDIX D: Thermophysical and Transport Properties of Gases
- APPENDIX E: Atmospheric Data
- APPENDIX F: Binary Diffusion Coefficients at 1 atm and T = 300 K
- Bibliography
- Index
Preface
It is fair to say that a very substantial part (more than 90 percent) of the total energy used today in transportation, power production, space heating and 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), 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 chemical reaction accompanied by release of heat energy. To the extent that a change of state is involved, the laws of 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 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 com- bustion is necessary for producing useful effects as well as for fire extinction and pollution abatement. In earlier times, pollution was regarded as a very local phe- nomenon (comprising smoke and 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 combus- tion is, indeed, vast. A book that is primarily written for post-graduate students of mechanical, aeronautical and chemical engineering must therefore inevitably make compromises in coverage and emphasis. Available books on combustion, though reflecting these compromises, cannot be said to have arrived at agreement on a standard set of topics or on the manner of their presentation. Much depends on
xiii
xiv Preface
the background and familiarity of the authors with this vast and intriguing subject. Deciding on coverage for post-graduate teaching is further complicated by the fact that in a typical undergraduate program, students often have inadequate, or no, ex- posure to three subjects: mass transfer, chemical kinetics and the thermodynamics of mixtures. It is with gratitude that I acknowledge that this book draws extensively from the writings of Professor D. B. Spalding (FRS, formerly at Imperial College of 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 at iteratively, following experience teaching an Advanced Thermodynamics and Combustion course to dual-degree (BTech + MTech) and MTech students in the Thermal and Fluids Engineering stream in the Mechanical Engineering Department of IIT Bombay. The book is divided into eleven chapters. Chapter 1 establishes the links between combustion and its four neighbors men- tioned earlier. Chapter 2 deals with the thermodynamics of a pure substance, thus serving to refresh material familiar to an undergraduate student. Chapter 3 deals with the thermodynamics of inert (non-reacting) and reacting gaseous mixtures. Learning to evaluate properties of mixtures from those of the individual species that comprise them is an important preliminary. In Chapter 3, this aspect is emphasized. Stoichiometry and chemical equilibrium are idealizations that are important for defining the product states resulting from a chemical reaction. The product states are evaluated by invoking implications of the law of conservation of mass and the second law of thermodynamics. These topics are discussed in Chapter 4. Product states resulting from real combustion reactions in real equipment do not, in general, conform to those discussed in Chapter 4. This is because the real reactions proceed at a finite rate. As mentioned previously, this rate is governed by chemical kinetics, diffusion/convection mass transfer and fluid mechanics (turbulence, in par- ticular). Chapter 5 makes the first foray into the world of real chemical reactions by introducing chemical kinetics. Construction of a global reaction from postulated elemental reactions is discussed in this chapter, and the global rate constants for hydrocarbon fuels are listed. In practical equipment, the states of a reacting mixture are strongly influenced by the transport processes of heat, mass and momentum in flowing mixtures. These transport processes, in turn, are governed by fundamental equations of mass, mo- mentum (the Navier-Stokes equations) and energy transfer. Therefore, these three- dimensional equations are derived in Chapter 6, along with simplifications (such as the boundary-layer flow model, Stefan tube model and Reynolds flow model) that are commonly used in a preliminary analysis of combustion phenomena. It is import- ant to recognize that chemical kinetics, heat and mass transfer and fluid mechanics are rigorous independent subjects in their own right. Material in Chapters 4, 5, and 6, in principle, can be applied to analysis of com- bustion in practical equipment. However, to yield useful quantitative information, use of computers with elaborate programs is necessary. An introductory analysis
Symbols and Acronyms
Only major symbols are given here.
A Area (m^2 ) or pre-exponential factor B Spalding number c (^) p Constant pressure specific heat (J/kg-K) c v Constant volume specific heat (J/kg-K) D Mass diffusivity (m^2 /s) Da Damkohler number e Specific energy (J/kg) E (^) a Activation energy (J/Kmol) f Mixture fraction Fr Froude number g Specific Gibbs function (J/kg) h Enthalpy (J/kg) J Jet momentum (kg-m/s 2 ) k Thermal conductivity (W/m-K) or turbulent kinetic energy (J/kg) l Length scale (m) Le Lewis number M Molecular weight or Mach number m Mass flow or mass transfer rate (kg/s) N Mass transfer flux (kg/ m 2 -s) n Number of moles Nu Nusselt number P Perimeter (m) p Pressure (N/m^2 ) Pr Prandtl number Q ˙ Heat generation rates (W/m^3 ) q Heat flux (W/m 2 ) R Gas constant (J/kg-K ) r Radius (m) Rst Air–fuel ratio r (^) st Oxygen–fuel ratio
xvii
Symbols and Acronyms xix
stoich Stoichiometric condition surr Surroundings sys System T Transferred substance state t Turbulent u Universal w Wall or interface state xi xi , i = 1, 2, 3 directions ∞ Infinity state
Acronyms
AFT Adiabatic flame temperature BDC Bottom dead center BTK Bull’s trench kiln CFC Chlorinated flurocarbon CFD Computational fluid dynamics CMTCR Constant-mass thermochemical reactor EBU Eddy breakup model GDP Gross domestic product GHG Greenhouse gas HHV Higher heating value LHS Left-hand side LHV Lower heating value PFTCR Plug-flow thermochemical reactor RHS Right-hand side RPM Revolutions per minute SCR Simple chemical reaction STP Standard temperature and pressure TDC Top dead center UNDP United Nations Development Program VSBK Vertical shaft brick kiln WSTCR Well-stirred thermochemical reactor
