| Introduction |
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xiii | |
| General Notations |
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xvii | |
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Part I Fundamental Statistical Aspects |
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1 | (188) |
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3 | (2) |
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Statistical Description and Evolution of Reactive Gas Systems |
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5 | (31) |
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5 | (1) |
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6 | (5) |
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7 | (2) |
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9 | (2) |
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11 | (3) |
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11 | (1) |
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12 | (1) |
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Macroscopic balance equations |
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12 | (2) |
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General properties of collisions |
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14 | (4) |
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14 | (3) |
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17 | (1) |
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18 | (1) |
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Properties of collisional terms |
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18 | (18) |
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Collisional term expressions |
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18 | (3) |
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Characteristic times: collision frequencies |
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21 | (1) |
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Appendix 1.1 Elements of tensorial algebra |
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22 | (3) |
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Appendix 1.2 Elements of molecular physics |
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25 | (6) |
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Appendix 1.3 Mechanics of collisions |
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31 | (5) |
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Equilibrium and Non-Equilibrium Collisional Regimes |
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36 | (30) |
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36 | (1) |
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Collisional regimes: generalities |
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37 | (1) |
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Pure gases: equilibrium regimes |
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38 | (5) |
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39 | (2) |
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41 | (2) |
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Pure diatomic gases: general non-equilibrium regime |
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43 | (3) |
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Pure diatomic gases: specific non-equilibrium regimes |
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46 | (4) |
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47 | (1) |
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47 | (2) |
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Dominant resonant collisions |
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49 | (1) |
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Physical applications of the results |
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50 | (1) |
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Gas mixtures: equilibrium regimes |
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50 | (2) |
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Mixtures of monatomic gases |
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50 | (1) |
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Mixtures of diatomic gases |
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51 | (1) |
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Mixtures of diatomic gases in vibrational non-equilibrium |
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52 | (1) |
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Mixtures of reactive gases |
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53 | (13) |
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Reactive gases without internal modes |
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53 | (2) |
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Reactive gases with internal modes |
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55 | (1) |
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Appendix 2.1 The H theorem |
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56 | (1) |
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Appendix 2.2 Properties of the Maxwellian distribution |
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57 | (2) |
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Appendix 2.3 Models for internal modes |
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59 | (1) |
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Appendix 2.4 General vibrational relaxation equation |
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60 | (2) |
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Appendix 2.5 Specific vibrational relaxation equations |
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62 | (3) |
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Appendix 2.6 Properties of the Eulerian integrals |
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65 | (1) |
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Transport and Relaxation in Quasi-Equilibrium Regimes: Pure Gases |
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66 | (34) |
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66 | (1) |
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Expansion of the distribution function |
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66 | (3) |
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Definition of flow regimes |
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66 | (2) |
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Classification of flow regimes |
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68 | (1) |
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69 | (31) |
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Pure gases with elastic collisions: monatomic gases |
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70 | (5) |
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Pure diatomic gases with one internal mode |
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75 | (7) |
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Pure diatomic gases with two internal modes |
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82 | (5) |
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Appendix 3.1 Orthogonal bases |
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87 | (4) |
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Appendix 3.2 Systems of equations for a, b, d coefficients |
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91 | (1) |
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Appendix 3.3 Expressions of the collisional integrals |
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92 | (3) |
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Appendix 3.4 Influence of the collisional model on the transport terms |
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95 | (1) |
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Appendix 3.5 Linearization of the relaxation equation |
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96 | (2) |
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Appendix 3.6 Vibrational non-equilibrium distribution |
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98 | (2) |
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Transport and Relaxation in Quasi-Equilibrium Regimes: Gas Mixtures |
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100 | (31) |
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100 | (1) |
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Gas mixtures with elastic collisions |
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100 | (6) |
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100 | (3) |
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Transport terms: Navier-Stokes equations |
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103 | (3) |
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Binary mixtures of diatomic gases |
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106 | (6) |
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106 | (3) |
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109 | (3) |
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Mixtures of reactive gases |
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112 | (19) |
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Appendix 4.1 Systems of equations for a, b, I, d coefficients |
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113 | (4) |
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Appendix 4.2 Collisional integrals and simplifications |
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117 | (5) |
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Appendix 4.3 Simplified transport coefficients |
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122 | (2) |
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Appendix 4.4 Alternative technique: Gross-Jackson method |
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124 | (4) |
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Appendix 4.5 Alternative technique: method of moments |
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128 | (3) |
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Transport and Relaxation in Non-Equilibrium Regimes |
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131 | (29) |
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131 | (1) |
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Vibrational non-equilibrium gases: SNE case |
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131 | (7) |
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131 | (4) |
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Mixtures of diatomic gases |
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135 | (2) |
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Usual approximations: SNE case |
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137 | (1) |
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Mixtures of reactive gases: (SNE)C case |
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138 | (22) |
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138 | (6) |
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144 | (3) |
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Appendix 5.1 Pure gases in vibrational non-equilibrium |
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147 | (2) |
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Appendix 5.2 First-order expression of the vibrational relaxation equation |
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149 | (1) |
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Appendix 5.3 Gas mixtures in vibrational non-equilibrium |
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150 | (4) |
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Appendix 5.4 Expressions of g coefficients and relaxation pressure |
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154 | (2) |
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Appendix 5.5 Vibration-dissociation-recombination interaction |
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156 | (4) |
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Generalized Chapman-Enskog Method |
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160 | (29) |
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160 | (1) |
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160 | (2) |
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Vibrationally excited pure gases |
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162 | (4) |
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164 | (1) |
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Approximate expressions of heat fluxes |
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165 | (1) |
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Extension to mixtures of vibrational non-equilibrium gases |
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166 | (1) |
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167 | (2) |
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Conclusions on non-equilibrium flows |
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169 | (20) |
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Appendix 6.1 Vibrationally excited pure gases |
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169 | (2) |
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Appendix 6.2 Transport terms in non-dissociated media |
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171 | (2) |
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Appendix 6.3 Example of gases with dominant VV collisions |
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173 | (2) |
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Appendix 6.4 A simplified technique: BGK method |
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175 | (3) |
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Appendix 6.5 Boundary conditions for the Boltzmann equation |
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178 | (3) |
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Appendix 6.6 Free molecular regime |
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181 | (2) |
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Appendix 6.7 Direct simulation Monte Carlo methods |
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183 | (3) |
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Appendix 6.8 Hypersonic flow regimes |
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186 | (3) |
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Part II Macroscopic Aspects and Applications |
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189 | (208) |
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191 | (4) |
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General Aspects of Gas Flows |
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195 | (29) |
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195 | (1) |
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General equations: macroscopic aspects and review |
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195 | (6) |
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Comments on the transport terms |
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196 | (1) |
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Particular forms of balance equations |
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197 | (2) |
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199 | (1) |
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200 | (1) |
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Physical aspects of the general equations |
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201 | (6) |
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Characteristic quantities |
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201 | (1) |
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Dimensionless conservation equations |
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202 | (2) |
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Dimensionless numbers: flow classification |
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204 | (3) |
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Characteristic general flows |
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207 | (17) |
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207 | (2) |
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209 | (1) |
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210 | (1) |
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Stability of the flows: turbulent flows |
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211 | (1) |
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Appendix 7.1 General equations: review |
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212 | (4) |
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Appendix 7.2 Unsteady heat flux at a gas-solid interface |
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216 | (1) |
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Appendix 7.3 Gas-liquid interfaces |
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217 | (2) |
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Appendix 7.4 Dimensional analysis |
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219 | (1) |
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Appendix 7.5 Generalities on total balances |
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220 | (1) |
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Appendix 7.6 Elements of magnetohydrodynamics |
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221 | (3) |
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224 | (35) |
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224 | (1) |
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Ideal gas model: consequences |
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224 | (2) |
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226 | (3) |
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One-dimensional steady flows |
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226 | (1) |
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Multidimensional steady flows |
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226 | (1) |
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One-dimensional unsteady flows |
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227 | (2) |
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Shock waves and flow discontinuities |
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229 | (2) |
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Straight shock wave: Rankine-Hugoniot relations |
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229 | (1) |
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230 | (1) |
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231 | (28) |
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Domain of influence: boundary layer |
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231 | (2) |
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General equations: two-dimensional flows |
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233 | (3) |
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Appendix 8.1 Method of characteristics |
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236 | (1) |
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Appendix 8.2 Fundamentals of supersonic nozzles |
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237 | (2) |
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Appendix 8.3 Shock waves: configuration and kinematics |
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239 | (3) |
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Appendix 8.4 Generalities on the boundary layer |
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242 | (5) |
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Appendix 8.5 Simple boundary layers: typical cases |
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247 | (5) |
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Appendix 8.6 The turbulent boundary layer |
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252 | (3) |
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Appendix 8.7 Flow separation and drag in MHD |
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255 | (4) |
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259 | (35) |
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259 | (1) |
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Generalities on chemical reactions |
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259 | (1) |
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260 | (6) |
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Law of mass action: chemical equilibrium constant |
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260 | (1) |
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261 | (3) |
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Examples of equilibrium flows |
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264 | (2) |
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266 | (5) |
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266 | (2) |
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268 | (3) |
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271 | (1) |
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Typical cases of Eulerian non-equilibrium flows |
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271 | (23) |
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Flow behind a straight shock wave |
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271 | (7) |
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Flow in a supersonic nozzle |
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278 | (4) |
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282 | (1) |
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Appendix 9.1 Evolution of vibrational populations behind a shock wave |
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283 | (1) |
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9.1.1 Evolution without dissociation |
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284 | (1) |
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9.1.2 Evolution with dissociation |
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285 | (1) |
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Appendix 9.2 Air chemistry at high temperature |
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286 | (1) |
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9.2.1 Air chemistry in equilibrium conditions |
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286 | (1) |
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9.2.2 lonization phenomena |
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287 | (3) |
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Appendix 9.3 Reaction-rate constants |
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290 | (2) |
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Appendix 9.4 Nozzle flows |
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292 | (2) |
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Reactive Flows in the Dissipative Regime |
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294 | (32) |
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294 | (1) |
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Boundary layers in chemical equilibrium |
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295 | (5) |
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295 | (1) |
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296 | (2) |
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Reactive boundary layer and wall catalycity |
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298 | (2) |
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Boundary layer along a body |
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300 | (1) |
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Boundary layers in vibrational non-equilibrium |
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300 | (5) |
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Example 1: boundary layer behind a moving shock wave |
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300 | (1) |
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Example 2: boundary layer in a supersonic nozzle |
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301 | (2) |
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Example 3: boundary layer behind a reflected shock wave |
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303 | (2) |
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305 | (21) |
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Hypersonic flow in a nozzle |
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305 | (3) |
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Hypersonic flow around a body |
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308 | (3) |
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Mixtures of supersonic reactive jets |
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311 | (2) |
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Appendix 10.1 Catalycity in the vibrational non-equilibrium regime |
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313 | (2) |
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Appendix 10.2 Generalized Rankine-Hugoniot relations |
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315 | (1) |
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Appendix 10.3 Unsteady boundary layers |
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316 | (1) |
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Appendix 10.4 CO2/N2 gas-dynamic lasers |
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317 | (3) |
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Appendix 10.5 Transport terms in the non-equilibrium regime |
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320 | (3) |
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Appendix 10.6 Numerical method for solving the Navier-Stokes equations |
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323 | (3) |
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Facilities and Experimental Methods |
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326 | (34) |
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326 | (1) |
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327 | (20) |
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327 | (3) |
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330 | (5) |
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335 | (2) |
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General techniques: configurations and operation |
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337 | (4) |
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General methods of measurement |
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341 | (6) |
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347 | (13) |
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347 | (1) |
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The hypersonic shock tunnel |
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347 | (3) |
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Appendix 11.1 Experiments in real flight |
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350 | (2) |
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Appendix 11.2 Optimum flow duration in a shock tube |
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352 | (1) |
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Appendix 11.3 Heat flux measurements in a shock tube |
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353 | (2) |
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Appendix 11.4 Shock-interface interactions |
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355 | (1) |
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Appendix 11.5 Operation of a free-piston shock tunnel |
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356 | (2) |
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Appendix 11.6 Source flow in hypersonic nozzles |
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358 | (2) |
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Relaxation and Kinetics in Shock Tubes and Shock Tunnels |
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360 | (37) |
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360 | (1) |
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361 | (13) |
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Relaxation times: general methods |
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361 | (5) |
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366 | (6) |
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372 | (2) |
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374 | (23) |
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Dissociation-rate constants |
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374 | (2) |
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Time-resolved spectroscopic methods |
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376 | (6) |
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382 | (1) |
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Hypersonic flow around bodies |
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383 | (2) |
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Appendix 12.1 Generalities on IR emission |
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385 | (1) |
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Appendix 12.2 Models for vibration relaxation times |
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386 | (1) |
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Appendix 12.3 Simulation of emission spectra |
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387 | (4) |
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Appendix 12.4 Precursor radiation in shock tubes |
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391 | (3) |
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Appendix 12.5 Examples of kinetic models |
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394 | (3) |
| References |
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397 | (8) |
| Index |
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405 | |