introduction to reactive gas dynamics - gbv
TRANSCRIPT
Introduction to Reactive Gas Dynamics
Raymond Brun
OXPORD UNIVERSITY PRESS
Contents
Introduction xiii
General Notations xvii
Part I Fundamental Statistical Aspects 1
Notations to Part I 3
1 Statistical Description and Evolution of Reactive Gas Systems 5 1.1 Introduction 5
1.2 Statistical description 6
1.2.1 State parameters 7
1.2.2 Transport parameters 9
1.3 Evolution of gas systems 11
1.3.1 Boltzmann equation 11
1.3.2 General properties 12
1.3.3 Macroscopic balance equations 12
1.4 General properties of collisions 14
1.4.1 Elastic collisions 14
1.4.2 Inelastic collisions 17
1.4.3 Reactive collisions 18
1.5 Properties of collisional terms 18
1.5.1 Collisional term expressions 18
1.5.2 Characteristic times: collision frequencies 21
Appendix 1.1 Elements of tensorial algebra 22
Appendix 1.2 Elements of molecular physics 25
Appendix 1.3 Mechanics of collisions 31
2 Equilibrium and Non-Equil ibrium Collisional Regimes 36
2.1 Introduction 36
2.2 Collisional regimes: generalities 37
2.3 Pure gases: equilibrium regimes 38
2.3.1 Monatomic gases 39
2.3.2 Diatomic gases 41
vi CONTENTS
2.4 Pure diatomic gases: general non-equilibrium regime 43
2.5 Pure diatomic gases: specific non-equilibrium regimes 46
2.5.1 Dominant TV collisions 47
2.5.2 Dominant VV collisions 47
2.5.3 Dominant resonant collisions 49
2.5.4 Physical applications of the results 50
2.6 Gas mixtures: equilibrium regimes 50
2.6.1 Mixtures of monatomic gases 50
2.6.2 Mixtures of diatomic gases 51
2.7 Mixtures of diatomic gases in vibrational non-equilibrium 52
2.8 Mixtures of reactive gases 53
2.8.1 Reactive gases without internal modes 53
2.8.2 Reactive gases with internal modes 55
Appendix 2.1 The H theorem 56
Appendix 2.2 Properties of the Maxwellian distribution 57
Appendix 2.3 Models for internal modes 59
Appendix 2.4 General vibrational relaxation equation 60
Appendix 2.5 Specific vibrational relaxation equations 62
Appendix 2.6 Properties of the Eulerian integrals 65
Transport and Relaxation in Quasi-Equilibrium Regimes: Pure Gases 66 3.1 Introduction 66
3.2 Expansion of the distribution function 66
3.2.1 Definition of flow regimes 66
3.2.2 Classification of flow regimes 68
3.3 First-order solutions 69
3.3.1 Pure gases with elastic collisions: monatomic gases 70
3.3.2 Pure diatomic gases with one internal mode 75
3.3.3 Pure diatomic gases with two internal modes 82
Appendix 3.1 Orthogonal bases 87
Appendix 3.2 Systems of equations for a, b, d coefficients 91
Appendix 3.3 Expressions of the collisional integrals 92
Appendix 3.4 Influence of the collisional model on the transport terms 95
Appendix 3.5 Linearization of the relaxation equation 96
Appendix 3.6 Vibrational non-equilibrium distribution 98
Transport and Relaxation in Quasi-Equilibrium Regimes: Gas Mixtures 100 4.1 Introduction 100
CONTENTS vii
4.2 Gas mixtures with elastic collisions 100
4.2.1 Chapman-Enskog method 100
4.2.2 Transport terms: Navier-Stokes equations 103
4.3 Binary mixtures of diatomic gases 106
4.3.1 One internal mode 106
4.3.2 Two internal modes 109
4.4 Mixtures of reactive gases 112
Appendix 4.1 Systems of equations for a, b, I, d coefficients 113
Appendix 4.2 Collisional integrals and simplifications 117
Appendix 4.3 Simplified transport coefficients 122
Appendix 4.4 Alternative technique: Gross-Jackson method 124
Appendix 4.5 Alternative technique: method of moments 128
Transport and Relaxation in Non-Equilibrium Regimes 131 5.1 Introduction 131
5.2 Vibrational non-equilibrium gases: SNE case 131
5.2.1 Pure diatomic gases 131
5.2.2 Mixtures of diatomic gases 135
5.2.3 Usual approximations: SNE case 137
5.3 Mixtures of reactive gases: (SNE)c case 138
5.3.1 (SNE)c + (WNE)l/case 138
5.3.2 (SNE)C+(SNEV case 144
Appendix 5.1 Pure gases in vibrational non-equilibrium 147
Appendix 5.2 First-order expression of the vibrational relaxation equation 149
Appendix 5.3 Gas mixtures in vibrational non-equilibrium 150
Appendix 5.4 Expressions of g coefficients and relaxation pressure 154
Appendix 5.5 Vibration-dissociation-recombination interaction 156
Generalized Chapman-Enskog Method 160 6.1 Introduction 160
6.2 General method 160
6.3 Vibrational^ excited pure gases 162
6.3.1 Transport terms 164
6.3.2 Approximate expressions of heat fluxes 165
6.4 Extension to mixtures of vibrational non-equilibrium gases 166
6.5 Reactive gases 167
6.6 Conclusions on non-equilibrium flows 169
Appendix 6.1 Vibrational^ excited pure gases 169
Appendix 6.2 Transport terms in non-dissociated media 171
viii CONTENTS
Appendix 6.3 Example of gases with dominant W collisions 173
Appendix 6.4 A simplified technique: BGK method 175
Appendix 6.5 Boundary conditions for the Boltzmann equation 178
Appendix 6.6 Free molecular regime 181
Appendix 6.7 Direct simulation Monte Carlo methods 183
Appendix 6.8 Hypersonic flow regimes 186
Part II Macroscopic Aspects and Applications 189
Notations to Part II 191
7 General Aspects of Gas Flows 195 7.1 Introduction 195
7.2 General equations: macroscopic aspects and review 195
7.2.1 Comments on the transport terms 196
7.2.2 Particular forms of balance equations 197
7.2.3 Entropy balance 199
7.2.4 Boundary conditions 200
7.3 Physical aspects of the general equations 201
7.3.1 Characteristic quantities 201
7.3.2 Dimensionless conservation equations 202
7.3.3 Dimensionless numbers: flow classification 204
7.4 Characteristic general flows 207
7.4.1 Steady flows 207
7.4.2 Unsteady flows 209
7.4.3 Simplified flow models 210
7.4.4 Stability of the flows: turbulent flows 211
Appendix 7.1 General equations: review 212
Appendix 7.2 Unsteady heat flux at a gas-solid interface 216
Appendix 7.3 Gas-liquid interfaces 217
Appendix 7.4 Dimensional analysis 219
Appendix 7.5 Generalities on total balances 220
Appendix 7.6 Elements of magnetohydrodynamics 221
8 Elements of Gas Dynamics 224 8.1 Introduction 224
8.2 Ideal gas model: consequences 224
8.3 Isentropic flows 226
8.3.1 One-dimensional steady flows 226
CONTENTS ix
8.3.2 Multidimensional steady flows 226
8.3.3 One-dimensional unsteady flows 227
8.4 Shock waves and flow discontinuities 229
8.4.1 Straight shock wave: Rankine-Hugoniot relations 229
8.4.2 Ideal gas model 230
8.5 Dissipative flows 231
8.5.1 Domain of influence: boundary layer 231
8.5.2 General equations: two-dimensional flows 233
Appendix 8.1 Method of characteristics 236
Appendix 8.2 Fundamentals of supersonic nozzles 237
Appendix 8.3 Shock waves: configuration and kinematics 239
Appendix 8.4 Generalities on the boundary layer 242
Appendix 8.5 Simple boundary layers: typical cases 247
Appendix 8.6 The turbulent boundary layer 252
Appendix 8.7 Flow separation and drag in MHD 255
Reactive Flows 259 9.1 Introduction 259
9.2 Generalities on chemical reactions 259
9.3 Equilibrium flows 260
9.3.1 Law of mass action: chemical equilibrium constant 260
9.3.2 Examples of reactions 261
9.3.3 Examples of equilibrium flows 264
9.4 Non-equilibrium flows 266
9.4.1 Chemical kinetics 266
9.4.2 Vibrational kinetics 268
9.4.3 General kinetics 271
9.5 Typical cases of Eulerian non-equilibrium flows 271
9.5.1 Flow behind a straight shock wave 271
9.5.2 Flow in a supersonic nozzle 278
9.5.3 Flow around a body 282
Appendix 9.1 Evolution of vibrational populations behind a shock wave 283
9.1.1 Evolution without dissociation 284
9.1.2 Evolution with dissociation 285
Appendix 9.2 Air chemistry at high temperature 286
9.2.1 Air chemistry in equilibrium conditions 286
9.2.2 Ionization phenomena 287
Appendix 9.3 Reaction-rate constants 290
Appendix 9.4 Nozzle flows 292
x CONTENTS
10 Reactive Flows in the Dissipative Regime 294 10.1 Introduction 294
10.2 Boundary layers in chemical equilibrium 295
10.2.1 The flat plate 295
10.2.2 The stagnation point 296
10.2.3 Reactive boundary layer and wall catalycity 298
10.2.4 Boundary layer along a body 300
10.3 Boundary layers in vibrational non-equilibrium 300
10.3.1 Example 1: boundary layer behind a moving shock wave 300
10.3.2 Example 2: boundary layer in a supersonic nozzle 301
10.3.3 Example 3: boundary layer behind a reflected shock wave 303
10.4 Two-dimensional flows 305
10.4.1 Hypersonic flow in a nozzle 305
10.4.2 Hypersonic flow around a body 308
10.4.3 Mixtures of supersonic reactive jets 311
Appendix 10.1 Catalycity in the vibrational non-equilibrium regime 313
Appendix 10.2 Generalized Rankine-Hugoniot relations 315
Appendix 10.3 Unsteady boundary layers 316
Appendix 10.4 CO2/N2 gas-dynamic lasers 317
Appendix 10.5 Transport terms in the non-equilibrium regime 320
Appendix 10.6 Numerical method for solving the Navier-Stokes equations 323
11 Facilities and Experimental Methods 326 11.1 Introduction 326
11.2 The shock tube 327
11.2.1 Simple shock tube theory 327
11.2.2 Disturbing effects 330
11.2.3 Reflected Shockwaves 335
11.2.4 General techniques: configurations and operation 337
11.2.5 General methods of measurement 341
11.3 The hypersonic tunnel 347
11.3.1 Generalities 347
11.3.2 The hypersonic shock tunnel 347
Appendix 11.1 Experiments in real flight 350
Appendix 11.2 Optimum flow duration in a shock tube 352
Appendix 11.3 Heat flux measurements in a shock tube 353
Appendix 11.4 Shock-interface interactions 355
Appendix 11.5 Operation of a free-piston shock tunnel 356
Appendix 11.6 Source flow in hypersonic nozzles 358
CONTENTS xi
12 Relaxation and Kinetics in Shock Tubes and Shock Tunnels 360 12.1 Introduction 360
12.2 Vibrational relaxation 361
12.2.1 Relaxation times: general methods 361
12.2.2 Vibrational populations 366
12.2.3 Vibrational catalycity 372
12.3 Chemical kinetics 374
12.3.1 Dissociation-rate constants 374
12.3.2 Time-resolved spectroscopic methods 376
12.3.3 Chemical catalycity 382
12.3.4 Hypersonic flow around bodies 383
Appendix 12.1 Generalities on IR emission 385
Appendix 12.2 Models for vibration relaxation times 386
Appendix 12.3 Simulation of emission spectra 387
Appendix 12.4 Precursor radiation in shock tubes 391
Appendix 12.5 Examples of kinetic models 394
References 397
Index 405