CRC Series inCOMPUTATIONAL MECHANICS and APPLIED ANALYSIS

COMBUSTION SCIENCEAND ENGINEERING

Kalyan AnnamalaiIshwar K. Puri

(rflP) CRC Press> ^ J Taylor & Francis Group

Boca Raton London New York

CRC Press is an imprint of theTaylor & Francis Group, an informa business

Table of Contents

Preface xxxi

The Authors xxxv

Relations/Accounting Equations xxxvii

Nomenclature xliii

1 Introduction and Review of Thermodynamics 11.1 Introduction 11.2 Combustion Terminology 41.3 Matter and Its Properties 7

1.3.1 Matter 81.3.2 Mixture 81.3.3 Property 101.3.4 State 111.3-5 Equation of State 111.3.6 Standard Temperature and Pressure 121.3.7 Partial Pressure 131.3.8 Phase Equilibrium 13

1.4 Microscopic Overview of Thermodynamics 151.4.1 Matter 151.4.2 Intermolecular Forces and Potential Energy 161.4.3 Molecular Motion 18

1.4.3.1 Collision Number and Mean Free Path 181.4.3.2 Molecular Velocity Distribution 191.4.3-3 Average, RMS, and Most Probable Molecular

Speeds 201.4.4 Temperature 211.4.5 Knudsen Number 211.4.6 Chemical Potential and Diffusion 221.4.7 Entropy (S) 22

1.4.7.1 Overview 221.4.7.2 Entropy S = S (U, V) 23

vii

VIII

1.5 Conservation of Mass and Energy and the FirstLaw of Thermodynamics 231.5.1 Closed System 23

1.5.1.1 Mass Conservation 231.5.1.2 Energy Conservation 23

1.5.2 Open Systems 281.5.2.1 Mass 291.5.2.2 First Law of Thermodynamics or Energy

Conservation Equation 301.6 The Second Law of Thermodynamics 34

1.6.1 Introduction 341.6.2 Entropy and Second Law 35

1.6.2.1 Mathematical Definition 351.6.2.2 Relation between dS, Q, and T during an

Irreversible Process 351.6.2.3 Entropy Balance Equation for a Closed

System 361.6.2.4 Entropy Balance Equation for an Open

System 411.6.3 Entropy Balance in Integral and Differential Form 42

1.6.3-1 Integral Form 421.6.3.2 Differential Form 43

1.6.4 Combined First and Second Laws 431.6.4.1 Fixed-Mass System 43

1.7 Summary 45

Stoichiometry and Thermochemistryof Reacting Systems 472.1 Introduction 472.2 Overall Reactions 47

2.2.1 Stoichiometric Equation with O2 472.2.2 Stoichiometric Equation with Air „ 492.2.3 Reaction with Excess Air (Lean Combustion) 512.2.4 Reaction with Excess Fuel (Rich Combustion)

or Deficient Air 522.2.5 Equivalence Ratio § and Stoichiometric Ratio (SR) 52

2.3 Gas Analyses 552.3-1 Dew Point Temperature of Product Streams 552.3.2 Generalized Dry Gas Analysis for Air with Ar 58

2.3.2.1 Excess Air % from Measured CO2% and O2% ...582.3.2.2 Generalized Analysis for Fuel CHhOoNn Ss 59

2.3-3 Emissions of NOX and Other Pollutants 6l2.4 Global Conservation Equations for Reacting Systems 61

2.4.1 Mass Conservation and Mole Balance Equations 6l2.4.1.1 Closed System 6l2.4.1.2 Open System 62

IX

2.4.2 Energy Conservation Equation in Molar Form 632.4.2.1 Open System 632.4.2.2 Differential Form 642.4.2.3 Unit Fuel-Flow Basis , 64

2.5 Thermochemistry 652.5.1 Enthalpy of Formation 65

2.5.1.1 Enthalpy of Formation from Measurements 662.5.1.2 Bond Energy and Enthalpy of Formation 66

2.5.2 Thermal or Sensible Enthalpy 672.5.3 Total Enthalpy 672.5.4 Enthalpy of Reaction and Combustion 692.5.5 Heating Value (HV), Higher HV (HHV) or Gross HV

(GHV), and Lower HV (LHV) 702.5.5.1 Heating Values 70

2.5.6 Heating Value Based on Stoichiometric Oxygen 722.5.7 Applications of Thermochemistry 77

2.5.7.1 First Law Analysis of Reacting Systems 772.5.7.2 Adiabatic Flame Temperature 78

2.5.8 Second Law Analysis of Chemically Reacting Systems ....832.5.8.1 Entropy 832.5.8.2 Entropy Generated during Any Chemical

Reaction 832.5.8.3 Entropy Balance Equation 842.5.8.4 Gibbs Function, and Gibbs Function of

Formation 892.6 Summary 912.7 Appendix 92

2.7.1 Determination of hf from Bond Energies 92

Reaction Direction and Equilibrium 973.1 Introduction 973.2 Reaction Direction and Chemical Equilibrium 97

3.2.1 Direction of Heat Transfer 973.2.2 Direction of Reaction 983.2.3 Mathematical Criteria for a Closed System 100

3.2.3.1 Specified Values of U, V, and m 1003.2.3.2 Specified Values of S, V, and m 1003.2.3.3 Specified Values of S, P, and m 1003.2.3.4 Specified Values of H, P, and m 1003.2.3.5 Specified Values of T, V, and m 1013.2.3.6 Specified Values of T, P, and m 101

3.2.4 Evaluation of Properties during IrreversibleReactions 1013.2.4.1 Nonreacting Closed System 1023.2.4.2 Reacting Closed System 1023.2.4.3 Reacting Open System 104

3.2.5 Criteria in Terms of Chemical ForcePotential 1043.2.5.1 Single Reaction 1043.2.5.2 Multiple Reactions 108

3.2.6 Generalized Relation for the Chemical Potential 1083.2.7 Approximate Method for Determining Direction

of Reaction, AG°, and Gibbs Function of Formation 1123-3 Chemical Equilibrium Relations 115

3-3.1 Real Mix of Substances 1153.3.2 Ideal Mix of Liquids and Solids 1163-3.3 Ideal Gases 116

3.3.3.1 Equilibrium Constant and Gibbs FreeEnergy 116

3.3.3-2 Criteria for Direction of Reaction andChemical Equilibrium in Various Forms 117

3.3.4 Gas, Liquid, and Solid Mixtures 1243.3.5 Dissociation Temperatures 1263.3.6 Equilibrium for Multiple Reactions 127

3.4 Vant Hoff Equation 1303.4.1 Effect of Temperature on K°(T) 1313.4.2 Effect of Pressure 133

3-5 Adiabatic Flame Temperature with Chemical Equilibrium 1353.5.1 Steady-State, Steady-Flow (SSSF) Process 1353-5.2 Closed Systems 135

3.6 Gibbs Minimization Method 1373.6.1 General Criteria for Equilibrium 1373.6.2 G Minimization Using Lagrange Multiplier

Method 1383-7 Summary 1423.8 Appendix 142

3.8.1 Equilibrium Constant in Terms of Elements 142

Fuels 1454.1 Introduction 1454.2 Gaseous Fuels ,/. 146

4.2.1 Low- and High-BTU Gas 1474.2.2 Wobbe Number 147

4.3 Liquid Fuels 1494.3.1 Oil Fuel Composition 1494.3.2 Paraffins 1504.3.3 Olefins 1514.3.4 Diolefins 1524.3.5 Naphthenes or Cycloparaffin 1524.3.6 Aromatics 1524.3.7 Alcohols 1534.3.8 Common Liquid Fuels 1544.3.9 API Gravity, Chemical Formulae, Soot,

and Flash and Fire Points 154

XI

4.3.9.1 API Gravity 1544.3.9.2 Empirical Formulae and Formulae Unit for

Complex Fuels 1554.3.9.3 Soot 1554.3.9.4 Flash, Fire, Pour, and Cloud Points 156

4.4 Solid Fuels 1564.4.1 Coal 1564.4.2 Solid Fuel Analyses 158

4.4.2.1 Proximate Analysis (ASTM D3172) 1584.4.2.2 Ultimate or Elemental Analysis

(ASTM D3176) 1604.4.2.3 Coal Classification, Composition, and

Rank l6l4.4.3 Coal Pyrolysis 166

4.4.3.1 Chemical Formulae for Volatiles 1674.4.4 Ash and Loss on Ignition (LOI) 167

A A A.I Physical Properties 1684.4.5 Heating Value (ASTM D5865) 168

4.5 Other Fuels 1734.5.1 Industrial Gaseous Fuels 1734.5.2 Synthetic Liquids 1744.5.3 Biomass 1744.5.4 Municipal Solid Waste (MSW) 179

4.6 Size Distributions of Liquid and Solid Fuels 1804.6.1 Size Distribution 182

4.6.1.1 Lognormal Distribution 1824.6.1.2 Rosin-Rammler Relation 185

4.6.2 Some Empirical Relations 1874.7 Summary 1884.8 Appendix 188

4.8.1 Ash Tracer Method for Coal Analysis 1884.8.1.1 Ash Fraction 1884.8.1.2 Burned or Gasification Fraction 1894.8.1.3 Fraction of S or Element Conversion 1894.8.1.4 Ideal Conversion 190

Chemical Kinetics 1915.1 Introduction 1915.2 Reaction Rates: Closed and Open Systems 191

5.2.1 Law of Stoichiometry 1945.2.2 Reaction Rate Expression, Law of Mass Action,

and the Arrhenius Law 1955.3 Elementary Reactions and Molecularity 195

5.3.1 Unimolecular Reaction 1965.3.1.1 Characteristic Reaction Times (tchar) 197

5.3.2 Bimolecular Reaction 1995.3.2.1 Characteristic Reaction Times (tchar) 199

XII

5.3.3 Trimolecular Reactions 2005.3.3.1 Characteristic Reaction Times (tchar) 201

5.4 Multiple Reaction Types 2015.4.1 Consecutive or Series Reactions 2015.4.2 Competitive Parallel Reactions 2015.4.3 Opposing or Backward Reactions 2015.4.4 Exchange or Shuffle Reactions 2025.4.5 Synthesis 2045.4.6 Decomposition 204

5.5 Chain Reactions and Reaction Mechanisms 2045.5.1 Chain Initiation Reactions 2055.5.2 Chain Propagating Reactions 2055.5.3 Chain Branching Reactions 2055.5.4 Chain Breaking Reactions 2065.5.5 Chain Terminating Reactions 2065.5.6 Overall Reaction Rate Expression 2065.5.7 Steady-State Radical Hypothesis 2075.5.8 Catalytic Reactions 208

5.6 Global Mechanisms for Reactions 2095.6.1 Zeldovich Mechanism for NOx from N2 2095.6.2 NO2 Conversion to NO 2105.6.3 Hydrocarbon Global Reactions 211

5.6.3.1 Generic Approaches 2115.6.3-2 Reduced Kinetics 211

5.6.4 The H2-O2 System 2135.6.5 Carbon Monoxide Oxidation 214

5.7 Reaction Rate Theory and the Arrhenius Law 2155.7.1 Collision Theory 215

5.7.1.1 Collision Number and Mean FreePath — Simple Theory 215

5.7.1.2 Collision Number, Reaction Rate,and Arrhenius Law 216

5.7.2 An Application .....2195.7.3 Determination of Kinetics Constants in

Arrhenius Law 2215.8 Second Law and Global and Backward Reactions 224

5.8.1 Backward Reaction Rate and Second Law 2245.8.2 Equilibrium Constants and Estimation

of Backward Reaction Rate Constants 2255.8.2.1 Equimolecularity of Products and Reactants....2255.8.2.2 General Reaction of Any Molecularity 229

5.9 The Partial Equilibrium and Reaction Rate Expression 2305.9.1 Partial Equilibrium 2305.9.2 Reaction Rate 231

5.10 Timescales for Reaction 2345.10.1 Physical Delay 2345.10.2 Induction Time "(tind) 234

XIII

5.10.3 Ignition Time (tign) 2345.10.4 Characteristic Reaction or Chemical/Combustion

Times 2355.10.5 Half-Life Time and Time Constants (t1/2) 2355.10.6 Total Combustion Time 237

5.11 Solid-Gas (Heterogeneous) Reactionsand Pyrolysis of Solid Fuels 2375.11.1 Solid-Gas (Heterogeneous) Reactions 2375.11.2 Heterogeneous Reactions 237

5.11.2.1 Desorption Control 2395.11.2.2 Absorption Control 2395.11.2.3 Global Reaction 240

5.11.3 Forward and Backward Reaction Rates 2405.11.4 Pyrolysis of Solids 242

5.11.4.1 Single Reaction Model (at Any Instantof Time) 243

5.11.4.2 Competing Reaction Model 2445.11.4.3 Parallel Reaction Model 247

5.12 Summary 2495.13 Appendix 249

5.13.1 Multistep Reactions 2495.13.2 Simplified CH4 Reactions 2505.13-3 Conversion of Reaction Rate Expressions 251

5.13-3.1 Conversion of Law of Mass Actionfrom Molar Form (kmol/m3) to Mass Form(Concentration in kg/m3) 251

5.13-3.2 Conversion of Law of Mass Actionfrom Mass Form to Molar Form 252

5.13.3.3 Summary on Conversions 2525.13.4 Some Approximations in Kinetics Integrals 253

Mass Transfer 2556.1 Introduction 2556.2 Heat Transfer and the Fourier Law 2556.3 Mass Transfer and Fick's Law 257

6.3.1 Fick's Law 2576.3.2 Definitions 258

6.4 Molecular Theory 2676.4.1 Approximate Method for Transport Properties

of Single Component 2676.4.1.1 Absolute Viscosity 2676.4.1.2 Any Property a 268

6.4.2 Rigorous Method for Transport Propertiesof Single Component 2696.4.2.1 Absolute Viscosity 2696.4.2.2 Thermal Conductivity 2696.4.2.3 Self-Diffusion Coefficient 270

XIV

6.4.3 Transport Properties of Multiple Components 2706.4.3.1 Absolute Viscosity 2706.4.3.2 Thermal Conductivity 2716.4.3.3 Diffusion in Multicomponent Systems 272

6.5 Generalized Form of Fourier's and Fick's Lawsfor a Mixture, with Simplifications 2746.5.1 Generalized Law: Multicomponent Heat

Flux Vector 2746.5.2 Generalized Law: Multicomponent Diffusion 275

6.6 Summary 2796.7 Appendix: Rigorous Derivation for Multicomponent

Diffusion 279

First Law Applicat ions 2837.1 Introduction 2837.2 Generalized Relations in Molar Form 283

7.2.1 Mass Conservation and Molar Balance 2837.2.2 First Law 284

7.3 Closed-System Combustion 2847.3.1 Simple Treatment 284

7.3.1.1 Constant-Volume Reactor 2857.3.1.2 Constant-Pressure Reactor 289

7.3.2 Rigorous Formulation 2907.3-3 Applications of Rigorous Treatment 294

7.3.3.1 Constant Pressure 2947.3.3.2 Isobaric and Isothermal 2947.3.3-3 Constant Volume 2947.3.3.4 Constant Volume and Isothermal 295

7.4 Open Systems 2977.4.1 Damkohler Numbers 2987.4.2 Plug Flow Reactor (PFR) 2987.4.3 Nonisothermal Reactor and Ignition 3057.4.4 Perfectly Stirred Reactor (PSR) I..306

7.4.4.1 What Is a PSR? 3067.4.4.2 Simplified Method 3097.4.4.3 Rigorous Formulation from Mass and

Energy Equations 3107.5 Solid Carbon Combustion 319

7.5.1 Diffusion Rate of Oxygen 3207.5.2 Burn Rate 3217.5.3 Sherwood Number Relations for Mass

Transfer 3297.5.4 Carbon Temperature during

Combustion 3317.6 Droplet Burning 3327.7 Summary , 335

XV

8 Conservation Relations 3378.1 Introduction 3378.2 Simple Diffusive Transport Constitutive Relations 337

8.2.1 Diffusive Momentum Transfer (Newton's Law) 3378.2.2 Diffusive Heat Transfer (Fourier's Law) 3388.2.3 Diffusive Species Transfer (Fick's Law) 338

8.3 Conservation Equations 3388.3.1 Overall Mass 3388.3.2 Species Conservation 340

8.4 Generalized Transport 3438.4.1 Energy 344

8.4.1.1 Total Enthalpy Form 3448.4.1.2 Thermal Enthalpy Form 346

8.4.2 Species 3478.4.3 Momentum 3478.4.4 Element 347

8.5 Simplified Boundary-Layer-Type Problems 3498.5.1 Governing Equations 3508.5.2 General Solution 3518.5.3 Mixture Fraction 351

8.5.3-1 Definition 3518.5.3.2 Local Equivalence Ratio 3538.5.3-3 Relation between Mixture Fraction, Element

Fraction, and Total Enthalpy 3538.6 Shvab-Zeldovich Formulation 355

8.6.1 Boundary-Layer Problems 3558.6.1.1 Single-Step Reaction 3558.6.1.2 Fuel Having Two Components 359

8.6.2 Relation between Mixture Fraction (fM)and an SZ Variable 362

8.6.3 Plug Flow Reactor (PFR) 3628.6.4 Combustion of Liquids and Solids 364

8.6.4.1 Interface Conservation Equations 3648.6.4.2 Numerical Solution 3698.6.4.3 ThnvFlame or Flame Surface

Approximation 3708.6 A A Burn Rate, Analogy to Heat Transfer

and Resistance Concept 3728.7 Turbulent Flows 3778.8 Summary 3788.9 Appendix 379

8.9.1 Vector and Tensors 3798.9.2 Modified Constitutive Equations 381

8.9.2.1 Diffusive Momentum Fluxes and PressureTensor 381

8.9.2.2 Generalized Relation for Heat Transfer 384

XVI

8.9-3 Rigorous Formulation of the ConservationRelations 3858.9.3.1 Momentum 3858.9.3.2 Kinetic Energy (v2/2) 3858.9.3.3 Internal and Kinetic Energies 386

8.9-4 Enthalpy 3868.9.5 Stagnation Enthalpy 3868.9-6 Film Theory and Mass Transfer 386

Combust ion of Solid Fuels, Carbon, and Char 3899.1 Introduction 3899.2 Carbon Reactions 390

9.2.1 Reactions 3909.2.2 Identities Involving Carbon

Reactions 3919.3 Conservation Equations for a Spherical Particle 391

9.3.1 Physical Processes 3919.3.2 Dimensional Form and Boundary Conditions 392

9.4 Nondimensional Conservation Equationsand Boundary Conditions 3939.4.1 Gas-Phase Profiles 396

9.5 Interfacial Conservation Equations or BCs 3969.5.1 General System with Arbitrary Surface 396

9.5.1.1 Mass and Species 3969.5.1.2 Energy 399

9.5.2 Spherical Particle 4009.6 Solutions for Carbon Particle Combustion 401

9.6.1 Reaction I along with Gas Phase Reaction V 4019.6.1.1 Finite Kinetics Gas Phase and

Heterogeneous Kinetics 4019.6.1.2 Finite Kinetics Heterogeneous Chemistry

and Frozen Gas Phase (i.e., SFM) 4039.6.1.3 Fast Heterogeneous Kinetics and Frozen

Gas Phase (i.e., SFM) 4059.6.2 Other Carbon Reactions 4069.6.3 Boudouard and Surface Oxidation Reactions

with Frozen Gas Phase (i.e., SFM) 4089.6.3.1 Burn Rate 4089.6.3.2 CO Mass Fraction 4099.6.3.3 Carbon Surface Temperature Tw 410

9.6.4 Boudouard and Surface Oxidation Reactionsalong with Gas Phase Oxidation (i.e., DFM) 4119.6.4.1 Finite Chemistry 411

9.6.5 Fast Chemistry.... 4139.6.5.1 CO Mass Fraction 4139.6.5.2 Surface Temperature 4139.6.5.3 Flame Location 414

XVII

9.6.5.4 Flame Temperature — DFM 4179.6.5.5 CO2 Mass Fraction in Flame 417

9.7 Thermal NOX from Burning Carbon Particles 4199.8 Non-Quasi-Steady Nature of Combustion of Particle 4219-9 Element Conservation and Carbon Combustion 4229.10 Porous Char 4249.11 Summary 4329.12 Appendix: d Law and Stefan Flow

Approximation 4329.12.1 d Law for Kinetic-Controlled Combustion (i.e., SFM)....4329.12.2 Stefan Flow Approximation 433

10 Diffusion Flames — Liquid Fuels 43510.1 Introduction 43510.2 Evaporation, Combustion, and d2 Law 43610.3 Model/Physical Processes 436

10.3.1 Model 43610.3.2 Diffusion-Controlled Combustion 438

10.4 Governing Equations 43810.4.1 Assumptions 43810.4.2 Conservation Equations: Dimensional Form 439

10.4.2.1 Energy 44010.4.3 Conservation Equations Nondimensional Form 44010.4.4 Boundary Conditions 44110.4.5 Solutions 441

10.4.5.1 SZ Variable 44110.4.5.2 Interface Boundary Conditions 442

10.5 Solutions 44410.5.1 Burn Rate 444

10.5.1.1 Thick Flames 44410.5.1.2 Thin Flames 44510.5.1.3 Physical Meaning of Transfer Number B 446

10.5.2 D2 Law ! 44710.5.3 Burning Time. 44810.5.4 Exact Solution for Tw 450

10.5.4.1 Species: Fuel (F) 45010.5.4.2 Thin-Flame Results 45210.5.4.3 Mass Fractions of CO2 and H20 45410.5.4.4 Exact Procedure for Drop Temperature

and Burn Rate 45510.5.5 Flame Structure and Flame Location, rf 455

10.5.5.1 Flame Temperature 45710.5.5.2 Relation between Flame and Adiabatic Flame

Temperatures 45710.5.6 Extension to Combustion of Plastics 46110.5.7 Extension to Combustion of Coal and Biomass 461

iviii

10.5.8 Extension of Combustion Analyses to PureVaporization/Gasification 46l

10.5.9 Mass Transfer Correction 46210.5.10 Evaporation and Combustion inside a Shell

of Radius b and the Diameter Law 46310.6 Convection Effects 463

10.6.1 Drag Coefficient CD, Nu and Sh Numbers 46310.6.2 Burn Rates 46410.6.3 Wake Flames 465

10.7 Transient and Steady-Combustion Results 46510.8 Multicomponent-Isolated-Drop Evaporation and Combustion ...466

10.8.1 Evaporation 46710.8.1.1 Governing Equations 46710.8.1.2 Interface Conservation Equations 46710.8.1.3 Solutions 468

10.8.2 Combustion of Multicomponent Drop 47210.8.2.1 Nonvolatile (B) and Volatile (A)

Components 47210.8.2.2 Combustible Volatile Components 47210.8.2.3 Combustible and Noncombustible

Components 47610.9 Summary 478

11 Combustion in Boundary Layers 47911.1 Introduction 47911.2 Phenomenological Analyses 481

11.2.1 Momentum 48111.2.2 Energy 48311.2.3 Mass 48311.2 A Growths of BLs and Dimensionless Numbers 48411.2.5 Combustion 484

11.3 Generalized Conservation Equationsand Boundary Conditions ^....48411.3.1 Conservation Equations in Compressible Form 485

11.3.1.1 Mass 48511.3.1.2 Momentum Conservation 48511.3.1.3 Species Conservation 48611.3.1.4 Energy Conservation (Thermal Enthalpy

Form) 48611.3.1.5 Energy (Total Enthalpy Form) 48611.3.1.6 General Property 48711.3.1.7 SZ Formulation 487

11.3.2 Boundary Conditions 48711.3.3 Transformation Variables for Conversion

to "Incompressible" Form 48811.3 A Conservation Equations in Incompressible Form 489

11.3.4.1 Mass'. 489

XIX

11.3.4.2 Momentum 48911.3.4.3 Species 48911.3.4.4 Thermal Enthalpy 48911.3.4.5 Total Enthalpy 48911.3.4.6 General Property "b" 49011.3.4.7 SZ Variable 49011.3-4.8 Normalized SZ (NSZ) Variable 49011.3.4.9 Boundary Conditions (BCs) 490

11.4 Interface Boundary Conditions 49111.4.1 Species and Energy 491

11.5 Generalized Numerical Solution Procedure forBL Equations in Partial Differential Form 492

11.6 Normalized Variables and Conservation Equations 49211.6.1 Normalized Variables 49211.6.2 Normalized Conservation Equations 493

11.6.2.1 Mass 49311.6.2.2 Momentum (x Direction) 49311.6.2.3 Species 49411.6.2.4 Thermal Enthalpy 49411.6.2.5 Generic Property "b" 49511.6.2.6 Normalized SZ Variable 49511.6.2.7 Reference Conditions 495

11.7 Similarity Solutions-BL Equations 49511.7.1 Stream Functions and Similarity Variable 49511.7.2 Conservation Equations in Terms

of Similarity Variable 49611.7.2.1 Momentum 49611.7.2.2 Species and SZ 49611.7.2.3 Finite Chemistry 498

11.7.3 Boundary and Interface Conditions in Termsof Similarity Variable 498

11.8 Applications of Generalized Similarity Equationsto Various Flow Systems 49911.8.1 Forced Convection over Flat Plate, Inclined Plate,

and Curved Surfaces 49911.8.2 2-D Stagnation Flow Systems (k = 0) 501

11.8.2.1 Infinite Chemistry 50111.8.2.2 Finite Chemistry 501

11.8.3 Axisymmetric Stagnation Flow Systems (k = 1) 50111.8.3.1 Species and Energy for Axisymmetric Jet

with Finite Chemistry 50111.8.3-2 Infinite Chemistry or SZ 501

11.8.4 Free Convection 50211.8.4.1 Finite Chemistry 50211.8.4.2 Infinite Chemistry or SZ 502

11.9 Solutions for Boundary Layer Combustionof Totally Gasifying Fuels 502

XX

11.9.1 Exact Numerical Solution Procedure for VariousFlow Systems 50211.9.1.1 Flame Location 50311.9.1.2 Forced Convection...: 50411.9.1.3 Free Convection 50411.9.1.4 Stagnation Flows 506

11.9.2 Approximate Results 50711.9.2.1 Simplified Solutions from Fluid Mechanics

and Heat Transfer for Liquids, Solids,and Plastics 507

11.9.2.2 "Conventional" and "Nonconventional"Integral Technique 509

11.10 Combustion Results for Fuels Burningunder Convection 51311.10.1 Chemical Reactions Involving Nonpyrolyzing

Solids 51511.10.1.1 Chemical Vapor Deposition 51511.10.1.2 Boundary Layer Combustion of Carbon...51811.10.1.3 Double-Film Layer 520

11.10.2 Free Convection 52611.10.2.1 Physics of Free Convection 52611.10.2.2 Simplified Solutions from Fluid Mechanics

and Heat Transfer 52711.10.2.3 Integral Solutions for Free-Convective

Burning 52711.10.2.4 Combustion of Liquids and Pyrolyzing

Solids over Vertical Walls 53011.10.3 Stagnation Flows 530

11.11 Excess Fuel and Excess Air under Convection 53111.11.1 Closed (Enveloped) and Open Flames 53111.11.2 Excess Fuel 532

11.12 Summary 535

12 Combustion of Gas Jets 53712.1 Introduction 53712.2 Burke-Schumann (B-S) Flame 537

12.2.1 Overview 53712.2.2 Assumptions 53812.2.3 Governing Equations 539

12.2.3.1 Mass 53912.2.3.2 Species and Energy Conservation

Equation 53912.2.3.3 Boundary Conditions 540

12.2.4 Normalized Conservation Equations 54112.2.5 Solution 542

12.2.5.1 Normalized SZ Variable 54212.2.5.2 Flame Structure 542

XXI

12.2.5.3 Flame Profile 54212.2.5.4 Over- and Underventilated Flames —

Criteria 54212.2.5.5 Flame Heights 543

12.3 Modification to B-S Analyses 54512.3.1 Flames in Infinite Surroundings with Equal

Fuel and Air Velocity 54512.3.2 Mass Flux as Function of Axial Distance 545

12.4 Laminar Jets 54612.4.1 Introduction 54612.4.2 Terminology of Jets 547

12.4.2.1 Potential Core 54712.4.2.2 Mixing Layer 54812.4.2.3 Global Chemical Reaction and

Thin Flames 54912.5 Planar Laminar Jets 549

12.5.1 Overview 54912.5.2 Simplified Analysis of 2-D Laminar Jets 55012.5.3 Governing Differential Equations for Planar Jets 55112.5.4 Normalized Conservation Equations 55112.5.5 Boundary Conditions for Planar Jets 55212.5.6 Normalized Boundary Condition 55312.5.7 Similarity Variables for Planar Jets 55312.5.8 Momentum Equation in Similarity Coordinates 55412.5.9 Momentum Solutions for Planar Jets 555

12.5.9.1 Velocities (Momentum Equation) 55512.5.9.2 Jet Half Width (y*1/2) 556

12.5.10 Species, Temperature, and O Equations inSimilarity Coordinates 556

12.5.11 Solutions for Normalized SZ and Scalar Properties ...55612.5.12 Mass Flow of Gas and Air and A:F at Any x 55712.5.13 Solutions for Pure Mixing Problems

(Chemically Frozen Flow) , 55812.5.14 Solutions for Combustion 558

12.5.14.1 Normalized SZ Variable 55812.5.14.2 Flame Profile and Structure 55812.5.14.3 Flame Heights 55912.5.14.4 Mass Flow of Gas, Air and

A:F at Any x 56012.6 Circular Jets 562

12.6.1 Simplified Relations for Circular Laminar Jets 56212.6.2 Governing Differential Equations for Circular Jets 56212.6.3 Boundary Conditions for Circular Jets 56312.6 A Normalization 56312.6.5 Normalization of Governing Differential

Equations 56412.6.6 Similarity Variables for Circular Jets 565

XXII

12.6.7 Momentum Equation in Similarity Coordinates 56512.6.8 Solution to Momentum Equation 565

12.6.8.1 Velocities 56512.6.9 NSZ Equation in Similarity Coordinates 56612.6.10 Solutions for Species, Temperature, and

XXIII

13.5 Ignition of Solid Particle 60813.5.1 Carbon/Char Particle 608

13.5.1.1 Numerical Method 60913-5.1.2 Explicit Solutions When YO2 at Char

Surface is the Same as Free-StreamMass Fraction 610

13.5.1.3 Implicit Steady-State Solutions WhenYO2,w * YO2>~ 614

13.5.1.4 Approximate Explicit Solution withRadiation Heat Loss 6l6

13.5.2 Coal Ignition 61913.5.2.1 Heterogeneous Ignition of Coal 620

13.5.3 Ignition of Plastics 62013.6 Ignition of Nonuniform Temperature

Systems — Steady-State Solutions 62113.6.1 Slab 621

13.6.1.1 Physical Processes 62213-6.1.2 Normalized Governing Equations 62413.6.1.3 Solution for Ignition 625

13.6.2 Generalized Geometry 62813.6.3 Some Applications 63013.6.4 Biological Systems 630

13.7 Summary 631

14 Deflagration and Detonat ion 63314.1 Introduction 63314.2 Conservation Equations 635

14.2.1 Mass 63514.2.2 Momentum 63514.2.3 Energy 63514.2.4 The Equation of State 637

14.3 Solutions for Rayleigh and Hugoniot Curves 63714.3.1 Rayleigh Lines 63714.3.2 Hugoniot Curves 63814.3.3 Entropy 640

14.4 Flame Propagation into Unburned Mixture 64114A.I General Remarks 64114.4.2 Detonation Branch 64114.4.3 Physical Explanation for Detonation 64214.4.4 Deflagration Branch 64314.4.5 CJ Waves 644

14.4.5.1 Explicit Results for CJ Waves 64414.5 Summary 64614.6 Appendix I: Spreadsheet Program for CJ Waves 64614.7 Appendix II: The Solutions for vTO

at a Given v0 or m"or m* 647

XXIV

15 Flame Propagation and Flammability Limits 64915.1 Introduction 64915.2 Phemenological Analysis 651

15.2.1 Homogeneous Mixtures 65115.2.1.1 Space Heating Rate (SHR) 65415.2.1.2 Effect of Various Parameters on

v0 or S 65415.2.2 Heterogeneous Liquid Mixtures 655

15.2.2.1 Micronized Drops 65515.2.2.2 Medium-Sized Drops 655

15.2.3 Heterogeneous Pulverized Coal: AirMixtures 65515.2.3.1 Micronized Particles 65515.2.3.2 Medium-Sized Particles 655

15.3 Rigorous Analysis 65615.3-1 Conservation Equations 656

15.3.1.1 Mass 65615.3.1.2 Momentum 65615.3.1.3 Species 65615.3.1.4 Energy 657

15.3.2 General Solution 65715.3.3 Explicit Solutions 657

15.3.3.1 SZ Variable 65815.3.3-2 Product Temperature for Lean Mixture 65815.3.3-3 Relation between YF and T Profiles

for Lean Mixtures 65815.3.3.4 Product Temperature for Rich Mixture 65915.3.3.5 Relation between YO2 and T Profiles

for Rich Mixtures 65915.3.4 Relation between Flux Ratio and Temperature 65915.3.5 Solution for Flame Velocity for

Lean Mixtures 66015.3.6 Effects of Thermophysical and Chemical

Properties of Mixture on Flame Velocity 66115.3.6.1 Transport Properties.. 66115.3.6.2 Order of Reaction 662

15.3.7 Numerical Simulation 66215.4 Flame Stretching 66415.5 Determination of Flame Velocity 66515.6 Flammability Limits 666

15.6.1 Simplified Analyses 66715.6.2 Rigorous Analyses 669

15.6.2.1 Species B or O2 in Excess for LeanFlammability Limit (LFL) 670

15.6.2.2 Fuel (A) in Excess for Rich FlammabilityLimit (RFL) 674

15.6.2.3 Spalding's Explicit Results 675

XXV

15.6.3 Empirical Methods 67515.6.4 Temperature and Pressure Dependencies 67615.6.5 Flammability Limit of Multiple Fuel and

Inert Mixtures 67615.7 Quenching Diameter 677

15.7.1 Definition 67715.7.2 Simplified Analyses 67715.7.3 Effect of Physical and Chemical

Properties 67915.8 Minimum Ignition Energy for Spark Ignition 67915.9 Stability of Flame in a Premixed Gas Burner 683

15.9.1 Flash-Back Criteria 68415.9-2 Blow-Off 686

15.10 Turbulent Flame Propagation 69115.11 Summary 692

16 Interactive Evaporation and Combustion 69316.1 Introduction 69316.2 Simplified Analyses 694

16.2.1 Interactive Processes 69416.2.2 Combustion 69516.2.3 Evaporation 69716.2.4 Correction Factor 698

16.3 Arrays and Point Source Method 69816.3.1 Evaporation of Arrays 698

16.3.1.1 Non-Stefan Flow (NSF) Problems 69816.3.1.2 Stefan Flow (SF) Problems 70116.3.1.3 Diameter Law and Evaporation

Time 70516.3.2 Combustion of Arrays 706

16.3.2.1 Combustion under NSF 70716.3-2.2 SF in Combustion 707

16.4 Combustion of Clouds of Drops and CarbonParticles 71016.4.1 Conservation Equations 710

16.4.1.1 Overall Mass 71016.4.1.2 Group Combustion for Simple

Geometries 71316.5 Terminology 713

16.5.1 Isolated-Drop Combustion (ISOC) 71316.5.2 Individual Flame Combustion (IFC) 71316.5.3 Incipient Group Combustion (IGC) 71516.5.4 Partial Group Combustion (PGC) 71516.5.5 Critical Group Combustion (CGC) 71616.5.6 Total Group Combustion or Group

Combustion (GC) 7161(5.5.7 Sheath Combustion (SC) 716

XXVI

16.6 Governing Equations for Spherical Cloud 71616.6.1 Mass 71816.6.2 Fuel Species 71816.6.3 Modified SZ Variable 718

16.7 Results 72116.7.1 G Number 72116.7.2 Nondimensional Mass Flow Rate 72216.7.3 NSZ Variable 72216.7.4 Cloud Mass-Loss Rate and Correction Factor 72216.7.5 NSZ Variable at Cloud Center 72416.7.6 Flame Radius 72516.7.7 Spray Classification 726

16.8 Relation between Group Combustionand Drop Array Studies 727

16.9 Interactive Char/Carbon Combustion 72816.9.1 Terminology 728

16.9.1.1 SFM 72916.9-1.2 ISOC 72916.9.1.3 IFC 72916.9.1.4 IGC 72916.9.1.5 PGC/CGC/GC 72916.9.1.6 SC 729

16.9.2 Model 73016.9-3 Results 73016.9.4 Analogy between Porous Char Particle

Combustion and Cloud Combustion ofChar Particles 730

16.10 Multicomponent Array Evaporation 73116.10.1 Array of Arbitrary Composition 73116.10.2 Array of Drops of Volatile (A) and Nonvolatile

(B) Components 73316.10.3 Binary Array of Drops of Volatile Components 735

16.10.3.1 Binary Array of Drops of Volatileand Nonvolatile Components 735

16.10.3.2 Experimental Data Binary Array 73516.11 Summary.... 737

17 Pollutants Formation and Destruction 73917.1 Introduction 73917.2 Emission-Level Expressions and Reporting 740

17.2.1 Reporting as ppm 74017.2.2 O2 Normalization or Corrected ppm

Concentrations 74117.2.3 Emission Index (g/kg of Fuel) 74217.2.4 Emissions in Mass Units per Unit Heat

Value (g/GJ) 74317.2.5 Reporting as kg per Million m3 of Gas 744

XXVII

17.2.6 Conversion of NO to mg of NO2/m3 744

17.2.7 Fuel N Conversion Efficiency 74517.3 Effects of Pollutants on Environment

and Biological Systems 74517.3.1 Health Effects 74517.3.2 NO and Ozone Destruction 74617.3-3 Photochemical Smog 74817.3.4 Acid Rain 74917.3-5 CO2 Greenhouse Effect 75017.3.6 Paniculate Matter 750

17.4 Pollution Regulations 75217.5 NOX Sources and Production Mechanisms 755

17.5.1 Nitrogen Oxide Compounds 75517.5.2 Sources of NOX 755

17.5.2.1 Mechanisms of Productionof NOX 755

17.5.2.2 Fuel NOX 75917.5.2.3 Prompt NOX 763

17.6 NOX Formation Parameters 76417.6.1 Type of Facility 76417.6.2 Operational Conditions 76517.6.3 Fuel 765

17.7 Stationary Source NOX Control 76617.7.1 Combustion Modifications 76617.7.2 Postcombustion Exhaust Gas Treatment

or Flue Gas Denitrification 77117.7.2.1 Selective Non-Catalytic Reduction

(SNCR) 77117.7.2.2 Selective Catalytic Reduction

(SCR) 77417.7.2.3 Reburn Methodology 774

17.8 CO2 Sequestration 77717.9 Carbon Monoxide: CO 77817.10 SOX Formation and Destruction 779

17.10.1 Elements of SOX Formation from Coal 77917.10.1.1 Simplified Schemes 781

17.10.2 SOX Reduction Methods 78217.11 Soot 78417.12 Mercury Emissions 786

17.12.1 Mercury Sources 78617.12.2 Mercury Forms and Effect

of Cl 78717.12.3 Determination of Hg 78817.12.4 Reactions with Hg 788

17.13 Summary 789

XXVIII

18 An Introduction to Turbulent Combustion 79118.1 Introduction 79118.2 Turbulence Characteristics 79118.3 Averaging Techniques 792

18.3.1 Relation between Favre Averaging and ReynoldsAveraging 795

18.3.2 A Few Rules of Averaging 79518.4 Instantaneous and Average Governing Equations 795

18.4.1 Mass 79618.4.2 Momentum 79618.4.3 Enthalpy, Kinetic Energy, and Stagnation

Enthalpy 79718.4.3.1 Kinetic Energy 79818.4.3.2 Stagnation Enthalpy 800

18.4.4 Reynolds Stress Transport 800

18.4.5 Turbulent Kinetic Energy (k = (1 /2 )^ . " ) 80318.4.6 Species 80418.4.7 Turbulence Models 804

18.4.7.1 Algebraic Models 80418.4.7.2 Higher-Order Models 80518.4.7.3 The (k-e) Model 805

18.5 Governing Differential Equations: AxisymmetricCase and Mixture-Fraction PDF Combustion Model 80618.5.1 Chemical Kinetics in Turbulent Flames 80818.5.2 Kinetics in Low Turbulence 808

18.5.2.1 Slow Kinetics 80818.5.2.2 Fast Kinetics 80918.5.2.3 Intermediate Kinetics 809

18.6 Turbulent Combustion Modeling (Diffusion Flames) 81018.7 Probability Density Function 812

18.7.1 Property q and Average q 81318.7.2 Reaction Rate Expression 81518.7.3 Qualitative PDFs for a Few Problems 81518.7.4 Mixture Fraction Governing Equations 816

18.7.4.1 Single Mixture Fraction 81618.7.4.2 Mixture Fraction with Source Terms 81718.7.4.3 Favre Averaging 819

18.7.5 Equilibrium Chemistry 81918.7.6 Two-Mixture Fraction Model 82118.7.7 Three-Mixture Fraction: Calculation of

Time-Mean Reaction Rates 82218.8 Premixed and Partially Premixed Turbulent

Flames: Modeling Approaches 82618.8.1 Fast Kinetics 82618.8.2 Finite-Rate Kinetics 827

XXIX

18.9 Summary 82818.10 Appendix I: Cylindrical Coordinate System with

Particle-Laden Flow 82818.10.1 Favre-Averaged Governing Equations 82918.10.2 k-e Turbulence Model 830

Problems 833Formulae 929Appendix A 981Appendix B 1063References 1069Index 1085