Theoretical and Numerical Combustion

Theoretical and Numerical Combustion

by Thierry Poinsot, Denis Veynante

ISBN-10: 1930217056

ISBN-13: 9781930217058

Pub. Date: 03/28/2001

Publisher: R. T. Edwards Incorporated

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


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.

Product Details

R. T. Edwards Incorporated
Publication date:
Edition description:
New Edition
Product dimensions:
7.56(w) x 9.40(h) x 1.08(d)

Table of Contents

1Conservation equations for reacting flows1
1.1General forms1
1.1.1Choice of primitive variables1
1.1.2Conservation of momentum12
1.1.3Conservation of mass and species13
1.1.4Diffusion velocities and Fick's law13
1.1.5Global mass conservation and correction velocity14
1.1.6Conservation of energy16
1.2Usual simplified forms21
1.2.1Constant pressure flames21
1.2.2Equal heat capacities for all species22
1.2.3Constant heat capacity for the mixture only23
1.3Summary of conservation equations24
2Laminar premixed flames27
2.2Conservation equations and numerical solutions28
2.3Steady one-dimensional laminar premixed flames30
2.3.1One-dimensional flame codes30
2.3.2Sensitivity analysis32
2.4Theoretical solutions for laminar premixed flames35
2.4.1Derivation of one-step chemistry conservation equations35
2.4.2Thermochemistry and chemical rates37
2.4.3The equivalence of temperature and fuel mass fraction40
2.4.4The reaction rate41
2.4.5Analytical solutions for flame speed44
2.4.6Generalized expression for flame speeds51
2.4.7Single step chemistry limitations and stiffness of reduced schemes54
2.4.8Variations of flame speed with temperature and pressure55
2.5Premixed flame thicknesses56
2.5.1Simple chemistry56
2.5.2Complex chemistry58
2.6Flame stretch59
2.6.1Definition and expressions of stretch59
2.6.2Stretch of stationary flames62
2.6.3Examples of flames with zero stretch62
2.6.4Examples of stretched flames63
2.7Flame speeds66
2.7.1Flame speed definitions66
2.7.2Flame speeds of laminar planar unstretched flames68
2.7.3Flame speeds of stretched flames70
3Laminar diffusion flames81
3.1Diffusion flame configurations81
3.2Theoretical tools for diffusion flames83
3.2.1Passive scalars and mixture fraction84
3.2.2Flame structure in the z-space86
3.2.3The steady flamelet assumption88
3.2.4Decomposition into mixing and flame structure problems89
3.2.5Models for diffusion flame structures89
3.3Flame structure for irreversible infinitely fast chemistry93
3.3.1The Burke-Schumann flame structure93
3.3.2Maximum local flame temperature in a diffusion flame95
3.3.3Maximum flame temperature in diffusion and premixed flames96
3.3.4Maximum and mean temperatures in diffusion burners96
3.4Complete solutions for irreversible fast chemistry flames99
3.4.1Unsteady unstrained one-dimensional diffusion flame with infinitely fast chemistry and constant density99
3.4.2Steady strained one-dimensional diffusion flame with infinitely fast chemistry and constant density103
3.4.3Unsteady strained one-dimensional diffusion flame with infinitely fast chemistry and constant density106
3.4.4Jet flame in an uniform flow field109
3.4.5Extensions to variable density111
3.5Extensions of theory to other flame structures112
3.5.1Reversible equilibrium chemistry112
3.5.2Finite rate chemistry112
3.5.3Summary of flame structures116
3.5.4Extensions to variable Lewis numbers116
3.6Real laminar diffusion flames118
3.6.1One-dimensional codes for laminar diffusion flames118
3.6.2Mixture fractions in real flames118
4Introduction to turbulent combustion125
4.1Interaction between flames and turbulence125
4.2Elementary descriptions of turbulence126
4.3Influence of turbulence on combustion129
4.3.1One-dimensional turbulent premixed flame130
4.3.2Turbulent jet diffusion flame131
4.4Computational approaches for turbulent combustion132
4.5RANS simulations for turbulent combustion141
4.5.1Averaging the balance equations141
4.5.2Unclosed terms in Favre averaged balance equations143
4.5.3Classical turbulence models for the Reynolds stresses144
4.5.4A first attempt to close mean reaction rates146
4.5.5A challenge for turbulent combustion modeling: flame flapping and intermittency148
4.6Direct numerical simulations151
4.6.1The role of DNS in turbulent combustion studies151
4.6.2Numerical methods for direct simulation152
4.6.3Spatial resolution and physical scales156
4.7Large eddy simulations160
4.7.1LES filters160
4.7.2Filtered balance equations162
4.7.3Unresolved fluxes modeling163
4.7.4Simple filtered reaction rate closures167
4.7.5Limits of large eddy simulations168
5Turbulent premixed flames171
5.1Phenomenological description171
5.1.1The effect of turbulence on flame fronts: wrinkling171
5.1.2The effect of flame fronts on turbulence174
5.1.3The infinitely thin flame front limit177
5.2Premixed turbulent combustion regimes184
5.2.1A first difficulty: defining u'184
5.2.2Classical turbulent premixed combustion diagrams185
5.2.3Modified combustion diagrams188
5.3RANS of turbulent premixed flames202
5.3.1Premixed turbulent combustion with single one-step chemistry202
5.3.2The "no-model" or Arrhenius approach204
5.3.3The Eddy Break Up (EBU) model204
5.3.4Models based on turbulent flame speed correlations206
5.3.5TheBray Moss Libby (BML) model207
5.3.6Flame surface density models212
5.3.7Probability density function (pdf) models220
5.3.8Modeling of turbulent scalar transport terms [rho]u"[subscript i Theta]"226
5.3.9Modeling of the characteristic turbulent flame time231
5.3.10Kolmogorov-Petrovski-Piskunov analysis232
5.3.11Flame stabilization235
5.4LES of turbulent premixed flames238
5.4.2Extension of RANS models239
5.4.3Artificially thickened flames240
5.4.5Flame surface density LES formulations243
5.4.6Scalar fluxes modeling in LES245
5.5DNS of turbulent premixed flames248
5.5.1The role of DNS in turbulent combustion studies249
5.5.2DNS database analysis249
5.5.3Studies of local flame structures using DNS253
5.5.4Complex chemistry simulations259
5.5.5Studying the global structure of turbulent flames with DNS262
5.5.6Production and dissipation of flame surface area264
5.5.7DNS analysis for large eddy simulations267
6Turbulent non premixed flames269
6.2Phenomenological description270
6.2.1Typical flame structure: jet flame270
6.2.2Specific features of turbulent non premixed flames270
6.2.3Turbulent non premixed flame stabilization271
6.2.4An example of turbulent non premixed flame stabilization278
6.3Turbulent non premixed combustion regimes280
6.3.1Flame/vortex interactions in DNS282
6.3.2Scales in turbulent non premixed combustion287
6.3.3Combustion regimes290
6.4RANS of turbulent non premixed flames292
6.4.1Assumptions and averaged equations292
6.4.2Models for primitive variables with infinitely fast chemistry296
6.4.3Mixture fraction variance and scalar dissipation rate298
6.4.4Models for mean reaction rate with infinitely fast chemistry300
6.4.5Models for primitive variables with finite rate chemistry302
6.4.6Models for mean reaction rate with finite rate chemistry308
6.5LES of turbulent non premixed flames313
6.5.1Linear Eddy Model313
6.5.2Infinitely fast chemistry314
6.5.3Finite rate chemistry316
6.6DNS of turbulent non premixed flames317
6.6.1Studies of local flame structure317
6.6.2Autoignition of a turbulent non premixed flame321
6.6.3Studies of global flame structure324
7Flame/wall interactions327
7.2Flame-wall interaction in laminar flows330
7.2.1Phenomenological description330
7.2.2Simple chemistry flame/wall interaction333
7.2.3Computing complex chemistry flame/wall interaction334
7.3Flame/wall interaction in turbulent flows337
7.3.1DNS of turbulent flame/wall interaction339
7.3.2DNS of the influence of walls on flame stabilization341
7.3.3Influence of flame/wall interaction on turbulent combustion models343
7.3.4Influence of flame/wall interaction on wall heat transfer models345
8Flame/acoustics interactions355
8.2Acoustics for non-reacting flows356
8.2.1Fundamental equations356
8.2.2Plane waves in one dimension358
8.2.3Harmonic waves and guided waves360
8.2.4Longitudinal modes in constant cross section ducts362
8.2.5Longitudinal modes in variable cross section ducts363
8.2.6Longitudinal/transverse modes in rectangular ducts364
8.2.7Longitudinal modes in a series of constant cross section ducts367
8.2.8Acoustic modes in cavities370
8.2.9The Helmholtz resonator373
8.2.10Acoustic energy density and flux373
8.3Acoustics for reacting flows376
8.3.1An equation for ln(P) in reacting flows376
8.3.2A wave equation in low Mach-number reacting flows377
8.3.3Acoustic velocity and pressure in low-speed reacting flows378
8.3.4Acoustic jump conditions for thin flames379
8.3.5Longitudinal modes in a series of ducts with combustion382
8.3.6The acoustic energy balance in reacting flows384
8.4Combustion instabilities386
8.4.1Stable versus unstable combustion386
8.4.2Interaction of longitudinal waves and thin flames387
8.4.3The (n - [tau] formulation for flame transfer function389
8.4.4Complete solution in a simplified case390
8.4.5Vortices in combustion instabilities394
8.5Large eddy simulations of combustion instabilities400
8.5.2LES strategies to study combustion instabilities400
8.5.3LES computation of forced response403
8.5.4LES computation of self-excited combustion instability406
9Boundary conditions409
9.2Description of characteristic boundary conditions411
9.2.2Reacting Navier-Stokes equations near a boundary413
9.2.3The Local One Dimensional Inviscid (LODI) relations417
9.2.4The NSCBC strategy for the Euler equations419
9.2.5The NSCBC strategy for Navier-Stokes equations419
9.2.6Edges and corners423
9.3Examples of implementation424
9.3.1A subsonic inflow with fixed velocities and temperature (SI-1)424
9.3.2A subsonic non-reflecting inflow (SI-4)425
9.3.3Subsonic non-reflecting outflows (B2 and B3)426
9.3.4A subsonic reflecting outflow (B4)427
9.3.5An isothermal no-slip wall (NSW)428
9.3.6An adiabatic slip wall (ASW)428
9.4Applications to steady non-reacting flows429
9.5Applications to steady reacting flows433
9.6Unsteady flows and numerical waves control436
9.6.1Physical and numerical waves436
9.6.2Vortex/boundary interactions440
9.7Applications to low Reynolds number flows443

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