COMBUSTION SCIENCE AND ENGINEERING

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CRC Series in

COMPUTATIONAL MECHANICS and APPLIED ANALYSIS

COMBUSTION SCIENCE

AND ENGINEERING

Kalyan Annamalai

Ishwar K. Puri

(rflP) CRC Press

> ^ J Taylor & Francis Group

Boca Raton London New York CRC Press is an imprint of the

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Preface xxxi

The Authors xxxv

Relations/Accounting Equations xxxvii

Nomenclature xliii

1 Introduction and Review of Thermodynamics 1

1.1 Introduction 1

1.2 Combustion Terminology 4 1.3 Matter and Its Properties 7 1.3.1 Matter 8 1.3.2 Mixture 8 1.3.3 Property 10 1.3.4 State 11 1.3-5 Equation of State 11 1.3.6 Standard Temperature and Pressure 12 1.3.7 Partial Pressure 13 1.3.8 Phase Equilibrium 13 1.4 Microscopic Overview of Thermodynamics 15 1.4.1 Matter 15 1.4.2 Intermolecular Forces and Potential Energy 16 1.4.3 Molecular Motion 18 1.4.3.1 Collision Number and Mean Free Path 18 1.4.3.2 Molecular Velocity Distribution 19 1.4.3-3 Average, RMS, and Most Probable Molecular

Speeds 20 1.4.4 Temperature 21 1.4.5 Knudsen Number 21 1.4.6 Chemical Potential and Diffusion 22 1.4.7 Entropy (S) 22 1.4.7.1 Overview 22 1.4.7.2 Entropy S = S (U, V) 23 vii

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1.5 Conservation of Mass and Energy and the First

Law of Thermodynamics 23 1.5.1 Closed System 23 1.5.1.1 Mass Conservation 23 1.5.1.2 Energy Conservation 23 1.5.2 Open Systems 28 1.5.2.1 Mass 29 1.5.2.2 First Law of Thermodynamics or Energy

Conservation Equation 30 1.6 The Second Law of Thermodynamics 34 1.6.1 Introduction 34 1.6.2 Entropy and Second Law 35 1.6.2.1 Mathematical Definition 35 1.6.2.2 Relation between dS, Q, and T during an

Irreversible Process 35 1.6.2.3 Entropy Balance Equation for a Closed

System 36

1.6.2.4 Entropy Balance Equation for an Open

System 41 1.6.3 Entropy Balance in Integral and Differential Form 42 1.6.3-1 Integral Form 42 1.6.3.2 Differential Form 43 1.6.4 Combined First and Second Laws 43 1.6.4.1 Fixed-Mass System 43 1.7 Summary 45

Stoichiometry and Thermochemistry

of Reacting Systems 47

2.1 Introduction 47 2.2 Overall Reactions 47 2.2.1 Stoichiometric Equation with O2 47

2.2.2 Stoichiometric Equation with Air „ 49 2.2.3 Reaction with Excess Air (Lean Combustion) 51 2.2.4 Reaction with Excess Fuel (Rich Combustion)

or Deficient Air 52 2.2.5 Equivalence Ratio § and Stoichiometric Ratio (SR) 52 2.3 Gas Analyses 55 2.3-1 Dew Point Temperature of Product Streams 55 2.3.2 Generalized Dry Gas Analysis for Air with Ar 58 2.3.2.1 Excess Air % from Measured CO2% and O2% ...58

2.3.2.2 Generalized Analysis for Fuel CHhOoNn Ss 59

2.3-3 Emissions of NOX and Other Pollutants 6l

2.4 Global Conservation Equations for Reacting Systems 61 2.4.1 Mass Conservation and Mole Balance Equations 6l 2.4.1.1 Closed System 6l 2.4.1.2 Open System 62

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2.4.2 Energy Conservation Equation in Molar Form 63

2.4.2.1 Open System 63

2.4.2.2 Differential Form 64

2.4.2.3 Unit Fuel-Flow Basis , 64

2.5 Thermochemistry 65

2.5.1 Enthalpy of Formation 65

2.5.1.1 Enthalpy of Formation from Measurements 66

2.5.1.2 Bond Energy and Enthalpy of Formation 66

2.5.2 Thermal or Sensible Enthalpy 67

2.5.3 Total Enthalpy 67

2.5.4 Enthalpy of Reaction and Combustion 69

2.5.5 Heating Value (HV), Higher HV (HHV) or Gross HV

(GHV), and Lower HV (LHV) 70

2.5.5.1 Heating Values 70

2.5.6 Heating Value Based on Stoichiometric Oxygen 72

2.5.7 Applications of Thermochemistry 77

2.5.7.1 First Law Analysis of Reacting Systems 77

2.5.7.2 Adiabatic Flame Temperature 78

2.5.8 Second Law Analysis of Chemically Reacting Systems ....83

2.5.8.1 Entropy 83

2.5.8.2 Entropy Generated during Any Chemical

Reaction 83

2.5.8.3 Entropy Balance Equation 84

2.5.8.4 Gibbs Function, and Gibbs Function of

Formation 89

2.6 Summary 91

2.7 Appendix 92

2.7.1 Determination of h

f

from Bond Energies 92

Reaction Direction and Equilibrium 97

3.1 Introduction 97

3.2 Reaction Direction and Chemical Equilibrium 97

3.2.1 Direction of Heat Transfer 97

3.2.2 Direction of Reaction 98

3.2.3 Mathematical Criteria for a Closed System 100

3.2.3.1 Specified Values of U, V, and m 100

3.2.3.2 Specified Values of S, V, and m 100

3.2.3.3 Specified Values of S, P, and m 100

3.2.3.4 Specified Values of H, P, and m 100

3.2.3.5 Specified Values of T, V, and m 101

3.2.3.6 Specified Values of T, P, and m 101

3.2.4 Evaluation of Properties during Irreversible

Reactions 101

3.2.4.1 Nonreacting Closed System 102

3.2.4.2 Reacting Closed System 102

3.2.4.3 Reacting Open System 104

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3.2.5 Criteria in Terms of Chemical Force

Potential 104 3.2.5.1 Single Reaction 104 3.2.5.2 Multiple Reactions 108 3.2.6 Generalized Relation for the Chemical Potential 108 3.2.7 Approximate Method for Determining Direction

of Reaction, AG°, and Gibbs Function of Formation 112 3-3 Chemical Equilibrium Relations 115 3-3.1 Real Mix of Substances 115 3.3.2 Ideal Mix of Liquids and Solids 116 3-3.3 Ideal Gases 116

3.3.3.1 Equilibrium Constant and Gibbs Free

Energy 116 3.3.3-2 Criteria for Direction of Reaction and

Chemical Equilibrium in Various Forms 117 3.3.4 Gas, Liquid, and Solid Mixtures 124 3.3.5 Dissociation Temperatures 126 3.3.6 Equilibrium for Multiple Reactions 127 3.4 Vant Hoff Equation 130 3.4.1 Effect of Temperature on K°(T) 131 3.4.2 Effect of Pressure 133 3-5 Adiabatic Flame Temperature with Chemical Equilibrium 135 3.5.1 Steady-State, Steady-Flow (SSSF) Process 135 3-5.2 Closed Systems 135 3.6 Gibbs Minimization Method 137 3.6.1 General Criteria for Equilibrium 137 3.6.2 G Minimization Using Lagrange Multiplier

Method 138 3-7 Summary 142 3.8 Appendix 142 3.8.1 Equilibrium Constant in Terms of Elements 142 Fuels 145 4.1 Introduction 145 4.2 Gaseous Fuels ,/. 146 4.2.1 Low- and High-BTU Gas 147 4.2.2 Wobbe Number 147 4.3 Liquid Fuels 149 4.3.1 Oil Fuel Composition 149 4.3.2 Paraffins 150 4.3.3 Olefins 151 4.3.4 Diolefins 152 4.3.5 Naphthenes or Cycloparaffin 152 4.3.6 Aromatics 152 4.3.7 Alcohols 153 4.3.8 Common Liquid Fuels 154 4.3.9 API Gravity, Chemical Formulae, Soot,

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4.3.9.1 API Gravity 154 4.3.9.2 Empirical Formulae and Formulae Unit for

Complex Fuels 155 4.3.9.3 Soot 155 4.3.9.4 Flash, Fire, Pour, and Cloud Points 156 4.4 Solid Fuels 156 4.4.1 Coal 156 4.4.2 Solid Fuel Analyses 158 4.4.2.1 Proximate Analysis (ASTM D3172) 158 4.4.2.2 Ultimate or Elemental Analysis

(ASTM D3176) 160 4.4.2.3 Coal Classification, Composition, and

Rank l 6 l 4.4.3 Coal Pyrolysis 166 4.4.3.1 Chemical Formulae for Volatiles 167 4.4.4 Ash and Loss on Ignition (LOI) 167

A A A.I Physical Properties 168

4.4.5 Heating Value (ASTM D5865) 168 4.5 Other Fuels 173 4.5.1 Industrial Gaseous Fuels 173 4.5.2 Synthetic Liquids 174 4.5.3 Biomass 174 4.5.4 Municipal Solid Waste (MSW) 179 4.6 Size Distributions of Liquid and Solid Fuels 180 4.6.1 Size Distribution 182 4.6.1.1 Lognormal Distribution 182 4.6.1.2 Rosin-Rammler Relation 185 4.6.2 Some Empirical Relations 187 4.7 Summary 188 4.8 Appendix 188 4.8.1 Ash Tracer Method for Coal Analysis 188 4.8.1.1 Ash Fraction 188 4.8.1.2 Burned or Gasification Fraction 189 4.8.1.3 Fraction of S or Element Conversion 189 4.8.1.4 Ideal Conversion 190 C h e m i c a l K i n e t i c s 191 5.1 Introduction 191 5.2 Reaction Rates: Closed and Open Systems 191 5.2.1 Law of Stoichiometry 194 5.2.2 Reaction Rate Expression, Law of Mass Action,

and the Arrhenius Law 195 5.3 Elementary Reactions and Molecularity 195 5.3.1 Unimolecular Reaction 196 5.3.1.1 Characteristic Reaction Times (tchar) 197

5.3.2 Bimolecular Reaction 199 5.3.2.1 Characteristic Reaction Times (tchar) 199

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5.3.3 Trimolecular Reactions 200 5.3.3.1 Characteristic Reaction Times (tchar) 201

5.4 Multiple Reaction Types 201 5.4.1 Consecutive or Series Reactions 201 5.4.2 Competitive Parallel Reactions 201 5.4.3 Opposing or Backward Reactions 201 5.4.4 Exchange or Shuffle Reactions 202 5.4.5 Synthesis 204 5.4.6 Decomposition 204 5.5 Chain Reactions and Reaction Mechanisms 204 5.5.1 Chain Initiation Reactions 205 5.5.2 Chain Propagating Reactions 205 5.5.3 Chain Branching Reactions 205 5.5.4 Chain Breaking Reactions 206 5.5.5 Chain Terminating Reactions 206 5.5.6 Overall Reaction Rate Expression 206 5.5.7 Steady-State Radical Hypothesis 207 5.5.8 Catalytic Reactions 208 5.6 Global Mechanisms for Reactions 209 5.6.1 Zeldovich Mechanism for NOx from N2 209

5.6.2 NO2 Conversion to NO 210

5.6.3 Hydrocarbon Global Reactions 211 5.6.3.1 Generic Approaches 211 5.6.3-2 Reduced Kinetics 211

5.6.4 The H2-O2 System 213

5.6.5 Carbon Monoxide Oxidation 214 5.7 Reaction Rate Theory and the Arrhenius Law 215 5.7.1 Collision Theory 215

5.7.1.1 Collision Number and Mean Free

Path — Simple Theory 215 5.7.1.2 Collision Number, Reaction Rate,

and Arrhenius Law 216 5.7.2 An Application ...219 5.7.3 Determination of Kinetics Constants in

Arrhenius Law 221 5.8 Second Law and Global and Backward Reactions 224 5.8.1 Backward Reaction Rate and Second Law 224 5.8.2 Equilibrium Constants and Estimation

of Backward Reaction Rate Constants 225 5.8.2.1 Equimolecularity of Products and Reactants....225 5.8.2.2 General Reaction of Any Molecularity 229 5.9 The Partial Equilibrium and Reaction Rate Expression 230 5.9.1 Partial Equilibrium 230 5.9.2 Reaction Rate 231 5.10 Timescales for Reaction 234 5.10.1 Physical Delay 234 5.10.2 Induction Time "(tind) 234

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5.10.3 Ignition Time (tign) 234

5.10.4 Characteristic Reaction or Chemical/Combustion

Times 235 5.10.5 Half-Life Time and Time Constants (t1/2) 235

5.10.6 Total Combustion Time 237 5.11 Solid-Gas (Heterogeneous) Reactions

and Pyrolysis of Solid Fuels 237 5.11.1 Solid-Gas (Heterogeneous) Reactions 237 5.11.2 Heterogeneous Reactions 237 5.11.2.1 Desorption Control 239 5.11.2.2 Absorption Control 239 5.11.2.3 Global Reaction 240 5.11.3 Forward and Backward Reaction Rates 240 5.11.4 Pyrolysis of Solids 242

5.11.4.1 Single Reaction Model (at Any Instant

of Time) 243 5.11.4.2 Competing Reaction Model 244 5.11.4.3 Parallel Reaction Model 247 5.12 Summary 249 5.13 Appendix 249 5.13.1 Multistep Reactions 249 5.13.2 Simplified CH4 Reactions 250

5.13-3 Conversion of Reaction Rate Expressions 251 5.13-3.1 Conversion of Law of Mass Action

from Molar Form (kmol/m3) to Mass Form

(Concentration in kg/m3) 251

5.13-3.2 Conversion of Law of Mass Action

from Mass Form to Molar Form 252 5.13.3.3 Summary on Conversions 252 5.13.4 Some Approximations in Kinetics Integrals 253

Mass Transfer 255

6.1 Introduction 255 6.2 Heat Transfer and the Fourier Law 255 6.3 Mass Transfer and Fick's Law 257 6.3.1 Fick's Law 257 6.3.2 Definitions 258 6.4 Molecular Theory 267

6.4.1 Approximate Method for Transport Properties

of Single Component 267 6.4.1.1 Absolute Viscosity 267 6.4.1.2 Any Property a 268 6.4.2 Rigorous Method for Transport Properties

of Single Component 269 6.4.2.1 Absolute Viscosity 269 6.4.2.2 Thermal Conductivity 269 6.4.2.3 Self-Diffusion Coefficient 270

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6.4.3 Transport Properties of Multiple Components 270 6.4.3.1 Absolute Viscosity 270 6.4.3.2 Thermal Conductivity 271 6.4.3.3 Diffusion in Multicomponent Systems 272 6.5 Generalized Form of Fourier's and Fick's Laws

for a Mixture, with Simplifications 274 6.5.1 Generalized Law: Multicomponent Heat

Flux Vector 274 6.5.2 Generalized Law: Multicomponent Diffusion 275

6.6 Summary 279

6.7 Appendix: Rigorous Derivation for Multicomponent

Diffusion 279

First Law A p p l i c a t i o n s 2 8 3 7.1 Introduction 283 7.2 Generalized Relations in Molar Form 283 7.2.1 Mass Conservation and Molar Balance 283 7.2.2 First Law 284 7.3 Closed-System Combustion 284 7.3.1 Simple Treatment 284 7.3.1.1 Constant-Volume Reactor 285 7.3.1.2 Constant-Pressure Reactor 289 7.3.2 Rigorous Formulation 290 7.3-3 Applications of Rigorous Treatment 294 7.3.3.1 Constant Pressure 294 7.3.3.2 Isobaric and Isothermal 294 7.3.3-3 Constant Volume 294 7.3.3.4 Constant Volume and Isothermal 295 7.4 Open Systems 297 7.4.1 Damkohler Numbers 298 7.4.2 Plug Flow Reactor (PFR) 298 7.4.3 Nonisothermal Reactor and Ignition 305 7.4.4 Perfectly Stirred Reactor (PSR) I..306 7.4.4.1 What Is a PSR? 306 7.4.4.2 Simplified Method 309 7.4.4.3 Rigorous Formulation from Mass and

Energy Equations 310 7.5 Solid Carbon Combustion 319 7.5.1 Diffusion Rate of Oxygen 320 7.5.2 Burn Rate 321 7.5.3 Sherwood Number Relations for Mass

Transfer 329 7.5.4 Carbon Temperature during

Combustion 331 7.6 Droplet Burning 332 7.7 Summary , 335

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8 Conservation Relations 337

8.1 Introduction 337 8.2 Simple Diffusive Transport Constitutive Relations 337 8.2.1 Diffusive Momentum Transfer (Newton's Law) 337 8.2.2 Diffusive Heat Transfer (Fourier's Law) 338 8.2.3 Diffusive Species Transfer (Fick's Law) 338 8.3 Conservation Equations 338 8.3.1 Overall Mass 338 8.3.2 Species Conservation 340 8.4 Generalized Transport 343 8.4.1 Energy 344 8.4.1.1 Total Enthalpy Form 344 8.4.1.2 Thermal Enthalpy Form 346 8.4.2 Species 347 8.4.3 Momentum 347 8.4.4 Element 347 8.5 Simplified Boundary-Layer-Type Problems 349 8.5.1 Governing Equations 350 8.5.2 General Solution 351 8.5.3 Mixture Fraction 351 8.5.3-1 Definition 351 8.5.3.2 Local Equivalence Ratio 353 8.5.3-3 Relation between Mixture Fraction, Element

Fraction, and Total Enthalpy 353 8.6 Shvab-Zeldovich Formulation 355 8.6.1 Boundary-Layer Problems 355 8.6.1.1 Single-Step Reaction 355 8.6.1.2 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) 362 8.6.4 Combustion of Liquids and Solids 364 8.6.4.1 Interface Conservation Equations 364 8.6.4.2 Numerical Solution 369 8.6.4.3 ThnvFlame or Flame Surface

Approximation 370

8.6 A A Burn Rate, Analogy to Heat Transfer

and Resistance Concept 372 8.7 Turbulent Flows 377 8.8 Summary 378 8.9 Appendix 379 8.9.1 Vector and Tensors 379 8.9.2 Modified Constitutive Equations 381

8.9.2.1 Diffusive Momentum Fluxes and Pressure

Tensor 381 8.9.2.2 Generalized Relation for Heat Transfer 384

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8.9-3 Rigorous Formulation of the Conservation

Relations 385 8.9.3.1 Momentum 385 8.9.3.2 Kinetic Energy (v2/2) 385

8.9.3.3 Internal and Kinetic Energies 386 8.9-4 Enthalpy 386 8.9.5 Stagnation Enthalpy 386 8.9-6 Film Theory and Mass Transfer 386 C o m b u s t i o n o f Solid Fuels, Carbon, a n d Char 3 8 9 9.1 Introduction 389 9.2 Carbon Reactions 390 9.2.1 Reactions 390 9.2.2 Identities Involving Carbon

Reactions 391 9.3 Conservation Equations for a Spherical Particle 391 9.3.1 Physical Processes 391 9.3.2 Dimensional Form and Boundary Conditions 392 9.4 Nondimensional Conservation Equations

and Boundary Conditions 393 9.4.1 Gas-Phase Profiles 396 9.5 Interfacial Conservation Equations or BCs 396 9.5.1 General System with Arbitrary Surface 396 9.5.1.1 Mass and Species 396 9.5.1.2 Energy 399 9.5.2 Spherical Particle 400 9.6 Solutions for Carbon Particle Combustion 401 9.6.1 Reaction I along with Gas Phase Reaction V 401

9.6.1.1 Finite Kinetics Gas Phase and

Heterogeneous Kinetics 401 9.6.1.2 Finite Kinetics Heterogeneous Chemistry

and Frozen Gas Phase (i.e., SFM) 403 9.6.1.3 Fast Heterogeneous Kinetics and Frozen

Gas Phase (i.e., SFM) 405 9.6.2 Other Carbon Reactions 406 9.6.3 Boudouard and Surface Oxidation Reactions

with Frozen Gas Phase (i.e., SFM) 408 9.6.3.1 Burn Rate 408 9.6.3.2 CO Mass Fraction 409 9.6.3.3 Carbon Surface Temperature Tw 410

9.6.4 Boudouard and Surface Oxidation Reactions

along with Gas Phase Oxidation (i.e., DFM) 411 9.6.4.1 Finite Chemistry 411 9.6.5 Fast Chemistry.... 413 9.6.5.1 CO Mass Fraction 413 9.6.5.2 Surface Temperature 413 9.6.5.3 Flame Location 414

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9.6.5.4 Flame Temperature — DFM 417 9.6.5.5 CO2 Mass Fraction in Flame 417

9.7 Thermal NOX from Burning Carbon Particles 419

9.8 Non-Quasi-Steady Nature of Combustion of Particle 421 9-9 Element Conservation and Carbon Combustion 422 9.10 Porous Char 424 9.11 Summary 432 9.12 Appendix: d Law and Stefan Flow

Approximation 432 9.12.1 d Law for Kinetic-Controlled Combustion (i.e., SFM)....432 9.12.2 Stefan Flow Approximation 433

10 D i f f u s i o n F l a m e s — Liquid Fuels 4 3 5 10.1 Introduction 435 10.2 Evaporation, Combustion, and d2 Law 436

10.3 Model/Physical Processes 436 10.3.1 Model 436 10.3.2 Diffusion-Controlled Combustion 438 10.4 Governing Equations 438 10.4.1 Assumptions 438 10.4.2 Conservation Equations: Dimensional Form 439 10.4.2.1 Energy 440 10.4.3 Conservation Equations Nondimensional Form 440 10.4.4 Boundary Conditions 441 10.4.5 Solutions 441 10.4.5.1 SZ Variable 441 10.4.5.2 Interface Boundary Conditions 442 10.5 Solutions 444 10.5.1 Burn Rate 444 10.5.1.1 Thick Flames 444 10.5.1.2 Thin Flames 445 10.5.1.3 Physical Meaning of Transfer Number B 446

10.5.2 D2 Law ! 447

10.5.3 Burning Time. 448 10.5.4 Exact Solution for Tw 450

10.5.4.1 Species: Fuel (F) 450 10.5.4.2 Thin-Flame Results 452 10.5.4.3 Mass Fractions of CO2 and H20 454

10.5.4.4 Exact Procedure for Drop Temperature

and Burn Rate 455 10.5.5 Flame Structure and Flame Location, rf 455

10.5.5.1 Flame Temperature 457 10.5.5.2 Relation between Flame and Adiabatic Flame

Temperatures 457 10.5.6 Extension to Combustion of Plastics 461 10.5.7 Extension to Combustion of Coal and Biomass 461

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10.5.8 Extension of Combustion Analyses to Pure

Vaporization/Gasification 46l

10.5.9 Mass Transfer Correction 462

10.5.10 Evaporation and Combustion inside a Shell

of Radius b and the Diameter Law 463

10.6 Convection Effects 463

10.6.1 Drag Coefficient C

D

, Nu and Sh Numbers 463

10.6.2 Burn Rates 464

10.6.3 Wake Flames 465

10.7 Transient and Steady-Combustion Results 465

10.8 Multicomponent-Isolated-Drop Evaporation and Combustion ...466

10.8.1 Evaporation 467

10.8.1.1 Governing Equations 467

10.8.1.2 Interface Conservation Equations 467

10.8.1.3 Solutions 468

10.8.2 Combustion of Multicomponent Drop 472

10.8.2.1 Nonvolatile (B) and Volatile (A)

Components 472

10.8.2.2 Combustible Volatile Components 472

10.8.2.3 Combustible and Noncombustible

Components 476

10.9 Summary 478

11 Combustion in Boundary Layers 479

11.1 Introduction 479

11.2 Phenomenological Analyses 481

11.2.1 Momentum 481

11.2.2 Energy 483

11.2.3 Mass 483

11.2 A Growths of BLs and Dimensionless Numbers 484

11.2.5 Combustion 484

11.3 Generalized Conservation Equations

and Boundary Conditions ^....484

11.3.1 Conservation Equations in Compressible Form 485

11.3.1.1 Mass 485

11.3.1.2 Momentum Conservation 485

11.3.1.3 Species Conservation 486

11.3.1.4 Energy Conservation (Thermal Enthalpy

Form) 486

11.3.1.5 Energy (Total Enthalpy Form) 486

11.3.1.6 General Property 487

11.3.1.7 SZ Formulation 487

11.3.2 Boundary Conditions 487

11.3.3 Transformation Variables for Conversion

to "Incompressible" Form 488

11.3 A Conservation Equations in Incompressible Form 489

11.3.4.1 Mass'. 489

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XIX 11.3.4.2 Momentum 489 11.3.4.3 Species 489 11.3.4.4 Thermal Enthalpy 489 11.3.4.5 Total Enthalpy 489 11.3.4.6 General Property "b" 490 11.3.4.7 SZ Variable 490 11.3-4.8 Normalized SZ (NSZ) Variable 490 11.3.4.9 Boundary Conditions (BCs) 490 11.4 Interface Boundary Conditions 491 11.4.1 Species and Energy 491 11.5 Generalized Numerical Solution Procedure for

BL Equations in Partial Differential Form 492 11.6 Normalized Variables and Conservation Equations 492 11.6.1 Normalized Variables 492 11.6.2 Normalized Conservation Equations 493 11.6.2.1 Mass 493 11.6.2.2 Momentum (x Direction) 493 11.6.2.3 Species 494 11.6.2.4 Thermal Enthalpy 494 11.6.2.5 Generic Property "b" 495 11.6.2.6 Normalized SZ Variable 495 11.6.2.7 Reference Conditions 495 11.7 Similarity Solutions-BL Equations 495 11.7.1 Stream Functions and Similarity Variable 495 11.7.2 Conservation Equations in Terms

of Similarity Variable 496 11.7.2.1 Momentum 496 11.7.2.2 Species and SZ 496 11.7.2.3 Finite Chemistry 498 11.7.3 Boundary and Interface Conditions in Terms

of Similarity Variable 498 11.8 Applications of Generalized Similarity Equations

to Various Flow Systems 499 11.8.1 Forced Convection over Flat Plate, Inclined Plate,

and Curved Surfaces 499 11.8.2 2-D Stagnation Flow Systems (k = 0) 501 11.8.2.1 Infinite Chemistry 501 11.8.2.2 Finite Chemistry 501 11.8.3 Axisymmetric Stagnation Flow Systems (k = 1) 501

11.8.3.1 Species and Energy for Axisymmetric Jet

with Finite Chemistry 501 11.8.3-2 Infinite Chemistry or SZ 501 11.8.4 Free Convection 502 11.8.4.1 Finite Chemistry 502 11.8.4.2 Infinite Chemistry or SZ 502 11.9 Solutions for Boundary Layer Combustion

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11.9.1 Exact Numerical Solution Procedure for Various

Flow Systems 502 11.9.1.1 Flame Location 503 11.9.1.2 Forced Convection...: 504 11.9.1.3 Free Convection 504 11.9.1.4 Stagnation Flows 506 11.9.2 Approximate Results 507

11.9.2.1 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 Burning

under Convection 513 11.10.1 Chemical Reactions Involving Nonpyrolyzing

Solids 515 11.10.1.1 Chemical Vapor Deposition 515 11.10.1.2 Boundary Layer Combustion of Carbon...518 11.10.1.3 Double-Film Layer 520 11.10.2 Free Convection 526 11.10.2.1 Physics of Free Convection 526 11.10.2.2 Simplified Solutions from Fluid Mechanics

and Heat Transfer 527 11.10.2.3 Integral Solutions for Free-Convective

Burning 527 11.10.2.4 Combustion of Liquids and Pyrolyzing

Solids over Vertical Walls 530 11.10.3 Stagnation Flows 530 11.11 Excess Fuel and Excess Air under Convection 531 11.11.1 Closed (Enveloped) and Open Flames 531 11.11.2 Excess Fuel 532 11.12 Summary 535

12 Combustion of Gas Jets 537

12.1 Introduction 537 12.2 Burke-Schumann (B-S) Flame 537 12.2.1 Overview 537 12.2.2 Assumptions 538 12.2.3 Governing Equations 539 12.2.3.1 Mass 539 12.2.3.2 Species and Energy Conservation

Equation 539 12.2.3.3 Boundary Conditions 540 12.2.4 Normalized Conservation Equations 541 12.2.5 Solution 542 12.2.5.1 Normalized SZ Variable 542 12.2.5.2 Flame Structure 542

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12.2.5.3 Flame Profile 542 12.2.5.4 Over- and Underventilated Flames —

Criteria 542 12.2.5.5 Flame Heights 543 12.3 Modification to B-S Analyses 545

12.3.1 Flames in Infinite Surroundings with Equal

Fuel and Air Velocity 545 12.3.2 Mass Flux as Function of Axial Distance 545 12.4 Laminar Jets 546 12.4.1 Introduction 546 12.4.2 Terminology of Jets 547 12.4.2.1 Potential Core 547 12.4.2.2 Mixing Layer 548 12.4.2.3 Global Chemical Reaction and

Thin Flames 549 12.5 Planar Laminar Jets 549 12.5.1 Overview 549 12.5.2 Simplified Analysis of 2-D Laminar Jets 550 12.5.3 Governing Differential Equations for Planar Jets 551 12.5.4 Normalized Conservation Equations 551 12.5.5 Boundary Conditions for Planar Jets 552 12.5.6 Normalized Boundary Condition 553 12.5.7 Similarity Variables for Planar Jets 553 12.5.8 Momentum Equation in Similarity Coordinates 554 12.5.9 Momentum Solutions for Planar Jets 555 12.5.9.1 Velocities (Momentum Equation) 555 12.5.9.2 Jet Half Width (y*1/2) 556

12.5.10 Species, Temperature, and O Equations in

Similarity Coordinates 556 12.5.11 Solutions for Normalized SZ and Scalar Properties ...556 12.5.12 Mass Flow of Gas and Air and A:F at Any x 557 12.5.13 Solutions for Pure Mixing Problems

(Chemically Frozen Flow) , 558 12.5.14 Solutions for Combustion 558 12.5.14.1 Normalized SZ Variable 558 12.5.14.2 Flame Profile and Structure 558 12.5.14.3 Flame Heights 559 12.5.14.4 Mass Flow of Gas, Air and

A:F at Any x 560 12.6 Circular Jets 562 12.6.1 Simplified Relations for Circular Laminar Jets 562 12.6.2 Governing Differential Equations for Circular Jets 562 12.6.3 Boundary Conditions for Circular Jets 563

12.6 A Normalization 563

12.6.5 Normalization of Governing Differential

Equations 564 12.6.6 Similarity Variables for Circular Jets 565

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XXII

12.6.7 Momentum Equation in Similarity Coordinates 565 12.6.8 Solution to Momentum Equation 565 12.6.8.1 Velocities 565 12.6.9 NSZ Equation in Similarity Coordinates 566 12.6.10 Solutions for Species, Temperature, and <D 567 12.6.11 Solutions for Combustion and Pure Mixing 567 12.6.11.1 Solutions for Combustion 567 12.6.11.2 Solutions for Mixing 568 12.6.12 Mass Flow of Gas, Air, and A:F at Any x 571 12.7 Summary of Solutions for 2-D and Circular Jets 574 12.8 Stoichiometric Contours for 2-D and Circular Jets,

Liftoff, and Blow-Off 574 12.8.1 A:F Contours 574 12.8.2 Stoichiometric Contours 576 12.8.3 Liftoff Distance 576 12.8.4 Anchoring of Flames 579 12.9 Jets in Coflowing Air: Jet Flame Structure in

Strongly Coflowing Air for 2-D and Circular Jets 581 12.9.1 Governing Equations 581 12.9.2 Boundary Conditions 582 12.9.3 Solutions 582 12.9.3.1 Planar Jet in Coflowing Air 582 12.9.3.2 Cylindrical System 583 12.10 Turbulent Diffusion Flames 583 12.10.1 Turbulent Planar Jets 584 12.10.1.1 Empirical Viscosity 584 12.10.1.2 Conservation Equations 584 12.10.1.3 Normalized Conservation Equations 585 12.10.1.4 Solutions for Turbulent Planar Jets 586 12.10.2 Turbulent Circular Jets 588 12.10.2.1 Solutions 588 12.11 Partially Premixed Flame 589 12.12 Summary ,....590

13 Ignition and Extinction 591

13.1 Introduction..,. 591 13.2 Modes of Ignition 591 13-3 Ignition of Gas Mixtures in Rigid Systems:

Uniform System 593 13.3.1 Solution for Ignition 594 13.3.1.1 Numerical Solution 594 13-3.1.2 Steady-State Approximate Solution 598 13.3.2 Ignition Energy 603 13.4 Constant-Pressure Systems 604 13.4.1 Analysis 604 13.4.2 Ignition of Combustible Gas Mixture

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XXIII

13.5 Ignition of Solid Particle 608 13.5.1 Carbon/Char Particle 608 13.5.1.1 Numerical Method 609 13-5.1.2 Explicit Solutions When YO2 at Char

Surface is the Same as Free-Stream

Mass Fraction 610 13.5.1.3 Implicit Steady-State Solutions When

YO2,w * YO2>~ 614

13.5.1.4 Approximate Explicit Solution with

Radiation Heat Loss 6l6 13.5.2 Coal Ignition 619 13.5.2.1 Heterogeneous Ignition of Coal 620 13.5.3 Ignition of Plastics 620 13.6 Ignition of Nonuniform Temperature

Systems — Steady-State Solutions 621 13.6.1 Slab 621 13.6.1.1 Physical Processes 622 13-6.1.2 Normalized Governing Equations 624 13.6.1.3 Solution for Ignition 625 13.6.2 Generalized Geometry 628 13.6.3 Some Applications 630 13.6.4 Biological Systems 630 13.7 Summary 631 14 Deflagration a n d D e t o n a t i o n 6 3 3 14.1 Introduction 633 14.2 Conservation Equations 635 14.2.1 Mass 635 14.2.2 Momentum 635 14.2.3 Energy 635 14.2.4 The Equation of State 637 14.3 Solutions for Rayleigh and Hugoniot Curves 637 14.3.1 Rayleigh Lines 637 14.3.2 Hugoniot Curves 638 14.3.3 Entropy 640 14.4 Flame Propagation into Unburned Mixture 641

14A.I General Remarks 641

14.4.2 Detonation Branch 641 14.4.3 Physical Explanation for Detonation 642 14.4.4 Deflagration Branch 643 14.4.5 CJ Waves 644 14.4.5.1 Explicit Results for CJ Waves 644 14.5 Summary 646 14.6 Appendix I: Spreadsheet Program for CJ Waves 646 14.7 Appendix II: The Solutions for vTO

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XXIV

15 Flame Propagation and Flammability Limits 649

15.1 Introduction 649

15.2 Phemenological Analysis 651 15.2.1 Homogeneous Mixtures 651 15.2.1.1 Space Heating Rate (SHR) 654 15.2.1.2 Effect of Various Parameters on

v0 or S 654

15.2.2 Heterogeneous Liquid Mixtures 655 15.2.2.1 Micronized Drops 655 15.2.2.2 Medium-Sized Drops 655 15.2.3 Heterogeneous Pulverized Coal: Air

Mixtures 655 15.2.3.1 Micronized Particles 655 15.2.3.2 Medium-Sized Particles 655 15.3 Rigorous Analysis 656 15.3-1 Conservation Equations 656 15.3.1.1 Mass 656 15.3.1.2 Momentum 656 15.3.1.3 Species 656 15.3.1.4 Energy 657 15.3.2 General Solution 657 15.3.3 Explicit Solutions 657 15.3.3.1 SZ Variable 658 15.3.3-2 Product Temperature for Lean Mixture 658 15.3.3-3 Relation between YF and T Profiles

for Lean Mixtures 658 15.3.3.4 Product Temperature for Rich Mixture 659 15.3.3.5 Relation between YO2 and T Profiles

for Rich Mixtures 659 15.3.4 Relation between Flux Ratio and Temperature 659 15.3.5 Solution for Flame Velocity for

Lean Mixtures 660 15.3.6 Effects of Thermophysical and Chemical

Properties of Mixture on Flame Velocity 661 15.3.6.1 Transport Properties.. 661 15.3.6.2 Order of Reaction 662 15.3.7 Numerical Simulation 662 15.4 Flame Stretching 664 15.5 Determination of Flame Velocity 665 15.6 Flammability Limits 666 15.6.1 Simplified Analyses 667 15.6.2 Rigorous Analyses 669

15.6.2.1 Species B or O2 in Excess for Lean

Flammability Limit (LFL) 670 15.6.2.2 Fuel (A) in Excess for Rich Flammability

Limit (RFL) 674 15.6.2.3 Spalding's Explicit Results 675

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XXV

15.6.3 Empirical Methods 675

15.6.4 Temperature and Pressure Dependencies 676

15.6.5 Flammability Limit of Multiple Fuel and

Inert Mixtures 676

15.7 Quenching Diameter 677

15.7.1 Definition 677

15.7.2 Simplified Analyses 677

15.7.3 Effect of Physical and Chemical

Properties 679

15.8 Minimum Ignition Energy for Spark Ignition 679

15.9 Stability of Flame in a Premixed Gas Burner 683

15.9.1 Flash-Back Criteria 684

15.9-2 Blow-Off 686

15.10 Turbulent Flame Propagation 691

15.11 Summary 692

16 Interactive Evaporation and Combustion 693

16.1 Introduction 693

16.2 Simplified Analyses 694

16.2.1 Interactive Processes 694

16.2.2 Combustion 695

16.2.3 Evaporation 697

16.2.4 Correction Factor 698

16.3 Arrays and Point Source Method 698

16.3.1 Evaporation of Arrays 698

16.3.1.1 Non-Stefan Flow (NSF) Problems 698

16.3.1.2 Stefan Flow (SF) Problems 701

16.3.1.3 Diameter Law and Evaporation

Time 705

16.3.2 Combustion of Arrays 706

16.3.2.1 Combustion under NSF 707

16.3-2.2 SF in Combustion 707

16.4 Combustion of Clouds of Drops and Carbon

Particles 710

16.4.1 Conservation Equations 710

16.4.1.1 Overall Mass 710

16.4.1.2 Group Combustion for Simple

Geometries 713

16.5 Terminology 713

16.5.1 Isolated-Drop Combustion (ISOC) 713

16.5.2 Individual Flame Combustion (IFC) 713

16.5.3 Incipient Group Combustion (IGC) 715

16.5.4 Partial Group Combustion (PGC) 715

16.5.5 Critical Group Combustion (CGC) 716

16.5.6 Total Group Combustion or Group

Combustion (GC) 716

1(5.5.7 Sheath Combustion (SC) 716

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XXVI

16.6 Governing Equations for Spherical Cloud 716 16.6.1 Mass 718 16.6.2 Fuel Species 718 16.6.3 Modified SZ Variable 718 16.7 Results 721 16.7.1 G Number 721 16.7.2 Nondimensional Mass Flow Rate 722 16.7.3 NSZ Variable 722 16.7.4 Cloud Mass-Loss Rate and Correction Factor 722 16.7.5 NSZ Variable at Cloud Center 724 16.7.6 Flame Radius 725 16.7.7 Spray Classification 726 16.8 Relation between Group Combustion

and Drop Array Studies 727 16.9 Interactive Char/Carbon Combustion 728 16.9.1 Terminology 728 16.9.1.1 SFM 729 16.9-1.2 ISOC 729 16.9.1.3 IFC 729 16.9.1.4 IGC 729 16.9.1.5 PGC/CGC/GC 729 16.9.1.6 SC 729 16.9.2 Model 730 16.9-3 Results 730 16.9.4 Analogy between Porous Char Particle

Combustion and Cloud Combustion of

Char Particles 730 16.10 Multicomponent Array Evaporation 731 16.10.1 Array of Arbitrary Composition 731 16.10.2 Array of Drops of Volatile (A) and Nonvolatile

(B) Components 733 16.10.3 Binary Array of Drops of Volatile Components 735

16.10.3.1 Binary Array of Drops of Volatile

and Nonvolatile Components 735 16.10.3.2 Experimental Data Binary Array 735 16.11 Summary.... 737

17 Pollutants Formation and Destruction 739

17.1 Introduction 739 17.2 Emission-Level Expressions and Reporting 740 17.2.1 Reporting as ppm 740 17.2.2 O2 Normalization or Corrected ppm

Concentrations 741 17.2.3 Emission Index (g/kg of Fuel) 742 17.2.4 Emissions in Mass Units per Unit Heat

Value (g/GJ) 743 17.2.5 Reporting as kg per Million m3 of Gas 744

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XXVII

17.2.6 Conversion of NO to mg of NO2/m3 744

17.2.7 Fuel N Conversion Efficiency 745 17.3 Effects of Pollutants on Environment

and Biological Systems 745 17.3.1 Health Effects 745 17.3.2 NO and Ozone Destruction 746 17.3-3 Photochemical Smog 748 17.3.4 Acid Rain 749 17.3-5 CO2 Greenhouse Effect 750

17.3.6 Paniculate Matter 750 17.4 Pollution Regulations 752 17.5 NOX Sources and Production Mechanisms 755

17.5.1 Nitrogen Oxide Compounds 755

17.5.2 Sources of NOX 755 17.5.2.1 Mechanisms of Production of NOX 755 17.5.2.2 Fuel NOX 759 17.5.2.3 Prompt NOX 763 17.6 NOX Formation Parameters 764 17.6.1 Type of Facility 764 17.6.2 Operational Conditions 765 17.6.3 Fuel 765 17.7 Stationary Source NOX Control 766

17.7.1 Combustion Modifications 766 17.7.2 Postcombustion Exhaust Gas Treatment

or Flue Gas Denitrification 771 17.7.2.1 Selective Non-Catalytic Reduction

(SNCR) 771 17.7.2.2 Selective Catalytic Reduction

(SCR) 774 17.7.2.3 Reburn Methodology 774

17.8 CO2 Sequestration 777

17.9 Carbon Monoxide: CO 778 17.10 SOX Formation and Destruction 779

17.10.1 Elements of SOX Formation from Coal 779

17.10.1.1 Simplified Schemes 781 17.10.2 SOX Reduction Methods 782

17.11 Soot 784 17.12 Mercury Emissions 786 17.12.1 Mercury Sources 786 17.12.2 Mercury Forms and Effect

of Cl 787 17.12.3 Determination of Hg 788 17.12.4 Reactions with Hg 788 17.13 Summary 789

COMBUSTION SCIENCE AND ENGINEERING

CRC Series in

COMPUTATIONAL MECHANICS and APPLIED ANALYSIS