Theoretical and Numerical Combustion

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Overview

Presents basic techniques and recent progress in numerical combustion while establishing important connections with the underlying combustion basics, enabling engineers and research specialists with a knowledge of fluid mechanics to move to an integrated understanding of numerical combustion. Includes classification, interactions, implications, and explorations of RANS, LES, and DNS modeling.
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Editorial Reviews

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Presenting basic techniques, this book describes the recent progress in numerical combustion while establishing important connections with the underlying combustion basics. It is intended to enable engineers and research specialists with a knowledge of fluid mechanics to move to an integrated understanding of numerical combustion. It includes information on classification, interactions, implications, and explorations of RANS, LES, and DNS modeling. Chapters focus on conservation equations, laminar premixed flames, laminar diffusion flames, turbulent combustion, turbulent premixed flames, turbulent non-premixed flames, flame/wall interactions, flame/acoustic interactions, and boundary conditions. Poinsot teaches at the Institut de M<'e>canique de Fluides de Toulouse. Veynante teaches at the Ecole Centrale Paris. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9781930217058
  • Publisher: R. T. Edwards Incorporated
  • Publication date: 3/28/2001
  • Edition description: New Edition
  • Pages: 488
  • Product dimensions: 7.56 (w) x 9.40 (h) x 1.08 (d)

Table of Contents

Preface ix
1 Conservation equations for reacting flows 1
1.1 General forms 1
1.1.1 Choice of primitive variables 1
1.1.2 Conservation of momentum 12
1.1.3 Conservation of mass and species 13
1.1.4 Diffusion velocities and Fick's law 13
1.1.5 Global mass conservation and correction velocity 14
1.1.6 Conservation of energy 16
1.2 Usual simplified forms 21
1.2.1 Constant pressure flames 21
1.2.2 Equal heat capacities for all species 22
1.2.3 Constant heat capacity for the mixture only 23
1.3 Summary of conservation equations 24
2 Laminar premixed flames 27
2.1 Introduction 27
2.2 Conservation equations and numerical solutions 28
2.3 Steady one-dimensional laminar premixed flames 30
2.3.1 One-dimensional flame codes 30
2.3.2 Sensitivity analysis 32
2.4 Theoretical solutions for laminar premixed flames 35
2.4.1 Derivation of one-step chemistry conservation equations 35
2.4.2 Thermochemistry and chemical rates 37
2.4.3 The equivalence of temperature and fuel mass fraction 40
2.4.4 The reaction rate 41
2.4.5 Analytical solutions for flame speed 44
2.4.6 Generalized expression for flame speeds 51
2.4.7 Single step chemistry limitations and stiffness of reduced schemes 54
2.4.8 Variations of flame speed with temperature and pressure 55
2.5 Premixed flame thicknesses 56
2.5.1 Simple chemistry 56
2.5.2 Complex chemistry 58
2.6 Flame stretch 59
2.6.1 Definition and expressions of stretch 59
2.6.2 Stretch of stationary flames 62
2.6.3 Examples of flames with zero stretch 62
2.6.4 Examples of stretched flames 63
2.7 Flame speeds 66
2.7.1 Flame speed definitions 66
2.7.2 Flame speeds of laminar planar unstretched flames 68
2.7.3 Flame speeds of stretched flames 70
3 Laminar diffusion flames 81
3.1 Diffusion flame configurations 81
3.2 Theoretical tools for diffusion flames 83
3.2.1 Passive scalars and mixture fraction 84
3.2.2 Flame structure in the z-space 86
3.2.3 The steady flamelet assumption 88
3.2.4 Decomposition into mixing and flame structure problems 89
3.2.5 Models for diffusion flame structures 89
3.3 Flame structure for irreversible infinitely fast chemistry 93
3.3.1 The Burke-Schumann flame structure 93
3.3.2 Maximum local flame temperature in a diffusion flame 95
3.3.3 Maximum flame temperature in diffusion and premixed flames 96
3.3.4 Maximum and mean temperatures in diffusion burners 96
3.4 Complete solutions for irreversible fast chemistry flames 99
3.4.1 Unsteady unstrained one-dimensional diffusion flame with infinitely fast chemistry and constant density 99
3.4.2 Steady strained one-dimensional diffusion flame with infinitely fast chemistry and constant density 103
3.4.3 Unsteady strained one-dimensional diffusion flame with infinitely fast chemistry and constant density 106
3.4.4 Jet flame in an uniform flow field 109
3.4.5 Extensions to variable density 111
3.5 Extensions of theory to other flame structures 112
3.5.1 Reversible equilibrium chemistry 112
3.5.2 Finite rate chemistry 112
3.5.3 Summary of flame structures 116
3.5.4 Extensions to variable Lewis numbers 116
3.6 Real laminar diffusion flames 118
3.6.1 One-dimensional codes for laminar diffusion flames 118
3.6.2 Mixture fractions in real flames 118
4 Introduction to turbulent combustion 125
4.1 Interaction between flames and turbulence 125
4.2 Elementary descriptions of turbulence 126
4.3 Influence of turbulence on combustion 129
4.3.1 One-dimensional turbulent premixed flame 130
4.3.2 Turbulent jet diffusion flame 131
4.4 Computational approaches for turbulent combustion 132
4.5 RANS simulations for turbulent combustion 141
4.5.1 Averaging the balance equations 141
4.5.2 Unclosed terms in Favre averaged balance equations 143
4.5.3 Classical turbulence models for the Reynolds stresses 144
4.5.4 A first attempt to close mean reaction rates 146
4.5.5 A challenge for turbulent combustion modeling: flame flapping and intermittency 148
4.6 Direct numerical simulations 151
4.6.1 The role of DNS in turbulent combustion studies 151
4.6.2 Numerical methods for direct simulation 152
4.6.3 Spatial resolution and physical scales 156
4.7 Large eddy simulations 160
4.7.1 LES filters 160
4.7.2 Filtered balance equations 162
4.7.3 Unresolved fluxes modeling 163
4.7.4 Simple filtered reaction rate closures 167
4.7.5 Limits of large eddy simulations 168
5 Turbulent premixed flames 171
5.1 Phenomenological description 171
5.1.1 The effect of turbulence on flame fronts: wrinkling 171
5.1.2 The effect of flame fronts on turbulence 174
5.1.3 The infinitely thin flame front limit 177
5.2 Premixed turbulent combustion regimes 184
5.2.1 A first difficulty: defining u' 184
5.2.2 Classical turbulent premixed combustion diagrams 185
5.2.3 Modified combustion diagrams 188
5.3 RANS of turbulent premixed flames 202
5.3.1 Premixed turbulent combustion with single one-step chemistry 202
5.3.2 The "no-model" or Arrhenius approach 204
5.3.3 The Eddy Break Up (EBU) model 204
5.3.4 Models based on turbulent flame speed correlations 206
5.3.5 TheBray Moss Libby (BML) model 207
5.3.6 Flame surface density models 212
5.3.7 Probability density function (pdf) models 220
5.3.8 Modeling of turbulent scalar transport terms [rho]u"[subscript i Theta]" 226
5.3.9 Modeling of the characteristic turbulent flame time 231
5.3.10 Kolmogorov-Petrovski-Piskunov analysis 232
5.3.11 Flame stabilization 235
5.4 LES of turbulent premixed flames 238
5.4.1 Introduction 238
5.4.2 Extension of RANS models 239
5.4.3 Artificially thickened flames 240
5.4.4 G-equation 241
5.4.5 Flame surface density LES formulations 243
5.4.6 Scalar fluxes modeling in LES 245
5.5 DNS of turbulent premixed flames 248
5.5.1 The role of DNS in turbulent combustion studies 249
5.5.2 DNS database analysis 249
5.5.3 Studies of local flame structures using DNS 253
5.5.4 Complex chemistry simulations 259
5.5.5 Studying the global structure of turbulent flames with DNS 262
5.5.6 Production and dissipation of flame surface area 264
5.5.7 DNS analysis for large eddy simulations 267
6 Turbulent non premixed flames 269
6.1 Introduction 269
6.2 Phenomenological description 270
6.2.1 Typical flame structure: jet flame 270
6.2.2 Specific features of turbulent non premixed flames 270
6.2.3 Turbulent non premixed flame stabilization 271
6.2.4 An example of turbulent non premixed flame stabilization 278
6.3 Turbulent non premixed combustion regimes 280
6.3.1 Flame/vortex interactions in DNS 282
6.3.2 Scales in turbulent non premixed combustion 287
6.3.3 Combustion regimes 290
6.4 RANS of turbulent non premixed flames 292
6.4.1 Assumptions and averaged equations 292
6.4.2 Models for primitive variables with infinitely fast chemistry 296
6.4.3 Mixture fraction variance and scalar dissipation rate 298
6.4.4 Models for mean reaction rate with infinitely fast chemistry 300
6.4.5 Models for primitive variables with finite rate chemistry 302
6.4.6 Models for mean reaction rate with finite rate chemistry 308
6.5 LES of turbulent non premixed flames 313
6.5.1 Linear Eddy Model 313
6.5.2 Infinitely fast chemistry 314
6.5.3 Finite rate chemistry 316
6.6 DNS of turbulent non premixed flames 317
6.6.1 Studies of local flame structure 317
6.6.2 Autoignition of a turbulent non premixed flame 321
6.6.3 Studies of global flame structure 324
7 Flame/wall interactions 327
7.1 Introduction 327
7.2 Flame-wall interaction in laminar flows 330
7.2.1 Phenomenological description 330
7.2.2 Simple chemistry flame/wall interaction 333
7.2.3 Computing complex chemistry flame/wall interaction 334
7.3 Flame/wall interaction in turbulent flows 337
7.3.1 DNS of turbulent flame/wall interaction 339
7.3.2 DNS of the influence of walls on flame stabilization 341
7.3.3 Influence of flame/wall interaction on turbulent combustion models 343
7.3.4 Influence of flame/wall interaction on wall heat transfer models 345
8 Flame/acoustics interactions 355
8.1 Introduction 355
8.2 Acoustics for non-reacting flows 356
8.2.1 Fundamental equations 356
8.2.2 Plane waves in one dimension 358
8.2.3 Harmonic waves and guided waves 360
8.2.4 Longitudinal modes in constant cross section ducts 362
8.2.5 Longitudinal modes in variable cross section ducts 363
8.2.6 Longitudinal/transverse modes in rectangular ducts 364
8.2.7 Longitudinal modes in a series of constant cross section ducts 367
8.2.8 Acoustic modes in cavities 370
8.2.9 The Helmholtz resonator 373
8.2.10 Acoustic energy density and flux 373
8.3 Acoustics for reacting flows 376
8.3.1 An equation for ln(P) in reacting flows 376
8.3.2 A wave equation in low Mach-number reacting flows 377
8.3.3 Acoustic velocity and pressure in low-speed reacting flows 378
8.3.4 Acoustic jump conditions for thin flames 379
8.3.5 Longitudinal modes in a series of ducts with combustion 382
8.3.6 The acoustic energy balance in reacting flows 384
8.4 Combustion instabilities 386
8.4.1 Stable versus unstable combustion 386
8.4.2 Interaction of longitudinal waves and thin flames 387
8.4.3 The (n - [tau] formulation for flame transfer function 389
8.4.4 Complete solution in a simplified case 390
8.4.5 Vortices in combustion instabilities 394
8.5 Large eddy simulations of combustion instabilities 400
8.5.1 Introduction 400
8.5.2 LES strategies to study combustion instabilities 400
8.5.3 LES computation of forced response 403
8.5.4 LES computation of self-excited combustion instability 406
9 Boundary conditions 409
9.1 Introduction 409
9.2 Description of characteristic boundary conditions 411
9.2.1 Theory 411
9.2.2 Reacting Navier-Stokes equations near a boundary 413
9.2.3 The Local One Dimensional Inviscid (LODI) relations 417
9.2.4 The NSCBC strategy for the Euler equations 419
9.2.5 The NSCBC strategy for Navier-Stokes equations 419
9.2.6 Edges and corners 423
9.3 Examples of implementation 424
9.3.1 A subsonic inflow with fixed velocities and temperature (SI-1) 424
9.3.2 A subsonic non-reflecting inflow (SI-4) 425
9.3.3 Subsonic non-reflecting outflows (B2 and B3) 426
9.3.4 A subsonic reflecting outflow (B4) 427
9.3.5 An isothermal no-slip wall (NSW) 428
9.3.6 An adiabatic slip wall (ASW) 428
9.4 Applications to steady non-reacting flows 429
9.5 Applications to steady reacting flows 433
9.6 Unsteady flows and numerical waves control 436
9.6.1 Physical and numerical waves 436
9.6.2 Vortex/boundary interactions 440
9.7 Applications to low Reynolds number flows 443
References 451
Index 471
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