Introduction to Reactive Gas Dynamics

Contents......Page 6
Introduction......Page 14
General Notations......Page 18
Part I: Fundamental Statistical Aspects......Page 22
Notations to Part I......Page 24
1.1 Introduction......Page 26
1.2 Statistical description......Page 27
1.3 Evolution of gas systems......Page 32
1.4 General properties of collisions......Page 35
1.5 Properties of collisional terms......Page 39
Appendix 1.1 Elements of tensorial algebra......Page 43
Appendix 1.2 Elements of molecular physics......Page 46
Appendix 1.3 Mechanics of collisions......Page 52
2.1 Introduction......Page 57
2.2 Collisional regimes: generalities......Page 58
2.3 Pure gases: equilibrium regimes......Page 59
2.4 Pure diatomic gases: general non-equilibrium regime......Page 64
2.5 Pure diatomic gases: specific non-equilibrium regimes......Page 67
2.6 Gas mixtures: equilibrium regimes......Page 71
2.7 Mixtures of diatomic gases in vibrational non-equilibrium......Page 73
2.8 Mixtures of reactive gases......Page 74
Appendix 2.1 The H theorem......Page 77
Appendix 2.2 Properties of the Maxwellian distribution......Page 78
Appendix 2.3 Models for internal modes......Page 80
Appendix 2.4 General vibrational relaxation equation......Page 81
Appendix 2.5 Specific vibrational relaxation equations......Page 83
Appendix 2.6 Properties of the Eulerian integrals......Page 86
3.2 Expansion of the distribution function......Page 87
3.3 First-order solutions......Page 90
Appendix 3.1 Orthogonal bases......Page 108
Appendix 3.2 Systems of equations for a, b, d coefficients......Page 112
Appendix 3.3 Expressions of the collisional integrals......Page 113
Appendix 3.4 Influence of the collisional model on the transport terms......Page 116
Appendix 3.5 Linearization of the relaxation equation......Page 117
Appendix 3.6 Vibrational non-equilibrium distribution......Page 119
4.2 Gas mixtures with elastic collisions......Page 121
4.3 Binary mixtures of diatomic gases......Page 127
4.4 Mixtures of reactive gases......Page 133
Appendix 4.1 Systems of equations for a, b, l, d coefficients......Page 134
Appendix 4.2 Collisional integrals and simplifications......Page 138
Appendix 4.3 Simplified transport coefficients......Page 143
Appendix 4.4 Alternative technique: Gross–Jackson method......Page 145
Appendix 4.5 Alternative technique: method of moments......Page 149
5.2 Vibrational non-equilibrium gases: SNE case......Page 152
5.3 Mixtures of reactive gases: (SNE)[sub(c)] case......Page 159
Appendix 5.1 Pure gases in vibrational non-equilibrium......Page 168
Appendix 5.2 First-order expression of the vibrational relaxation equation......Page 170
Appendix 5.3 Gas mixtures in vibrational non-equilibrium......Page 171
Appendix 5.4 Expressions of g coefficients and relaxation pressure......Page 175
Appendix 5.5 Vibration–dissociation–recombination interaction......Page 177
6.2 General method......Page 181
6.3 Vibrationally excited pure gases......Page 183
6.4 Extension to mixtures of vibrational non-equilibrium gases......Page 187
6.5 Reactive gases......Page 188
Appendix 6.1 Vibrationally excited pure gases......Page 190
Appendix 6.2 Transport terms in non-dissociated media......Page 192
Appendix 6.3 Example of gases with dominant VV collisions......Page 194
Appendix 6.4 A simplified technique: BGK method......Page 196
Appendix 6.5 Boundary conditions for the Boltzmann equation......Page 199
Appendix 6.6 Free molecular regime......Page 202
Appendix 6.7 Direct simulation Monte Carlo methods......Page 204
Appendix 6.8 Hypersonic flow regimes......Page 207
Part II: Macroscopic Aspects and Applications......Page 210
Notations to Part II......Page 212
7.2 General equations: macroscopic aspects and review......Page 216
7.3 Physical aspects of the general equations......Page 222
7.4 Characteristic general flows......Page 228
Appendix 7.1 General equations: review......Page 233
Appendix 7.2 Unsteady heat flux at a gas–solid interface......Page 237
Appendix 7.3 Gas–liquid interfaces......Page 238
Appendix 7.4 Dimensional analysis......Page 240
Appendix 7.5 Generalities on total balances......Page 241
Appendix 7.6 Elements of magnetohydrodynamics......Page 242
8.2 Ideal gas model: consequences......Page 245
8.3 Isentropic flows......Page 247
8.4 Shock waves and flow discontinuities......Page 250
8.5 Dissipative flows......Page 252
Appendix 8.1 Method of characteristics......Page 257
Appendix 8.2 Fundamentals of supersonic nozzles......Page 258
Appendix 8.3 Shock waves: configuration and kinematics......Page 260
Appendix 8.4 Generalities on the boundary layer......Page 263
Appendix 8.5 Simple boundary layers: typical cases......Page 268
Appendix 8.6 The turbulent boundary layer......Page 273
Appendix 8.7 Flow separation and drag in MHD......Page 276
9.2 Generalities on chemical reactions......Page 280
9.3 Equilibrium flows......Page 281
9.4 Non-equilibrium flows......Page 287
9.5 Typical cases of Eulerian non-equilibrium flows......Page 292
Appendix 9.1 Evolution of vibrational populations behind a shock wave......Page 304
Appendix 9.2 Air chemistry at high temperature......Page 307
Appendix 9.3 Reaction-rate constants......Page 311
Appendix 9.4 Nozzle flows......Page 313
10.1 Introduction......Page 315
10.2 Boundary layers in chemical equilibrium......Page 316
10.3 Boundary layers in vibrational non-equilibrium......Page 321
10.4 Two-dimensional flows......Page 326
Appendix 10.1 Catalycity in the vibrational non-equilibrium regime......Page 334
Appendix 10.2 Generalized Rankine–Hugoniot relations......Page 336
Appendix 10.3 Unsteady boundary layers......Page 337
Appendix 10.4 CO[sub(2)]/N[sub(2)] gas-dynamic lasers......Page 338
Appendix 10.5 Transport terms in the non-equilibrium regime......Page 341
Appendix 10.6 Numerical method for solving the Navier–Stokes equations......Page 344
11.1 Introduction......Page 347
11.2 The shock tube......Page 348
11.3 The hypersonic tunnel......Page 368
Appendix 11.1 Experiments in real flight......Page 371
Appendix 11.2 Optimum flow duration in a shock tube......Page 373
Appendix 11.3 Heat flux measurements in a shock tube......Page 374
Appendix 11.4 Shock–interface interactions......Page 376
Appendix 11.5 Operation of a free-piston shock tunnel......Page 377
Appendix 11.6 Source flow in hypersonic nozzles......Page 379
12.1 Introduction......Page 381
12.2 Vibrational relaxation......Page 382
12.3 Chemical kinetics......Page 395
Appendix 12.1 Generalities on IR emission......Page 406
Appendix 12.2 Models for vibration relaxation times......Page 407
Appendix 12.3 Simulation of emission spectra......Page 408
Appendix 12.4 Precursor radiation in shock tubes......Page 412
Appendix 12.5 Examples of kinetic models......Page 415
References......Page 418
D......Page 426
M......Page 427
T......Page 428
V......Page 429