 | Gatski T.B. Compressibility, turbulence and high speed flow / T.B.Gatski, J.-P.Bonnet. - Oxford; Amsterdam: Elsevier, 2009. - xii, 283 p.: ill. - Ref.: p.247-273. - Ind.: p.275-283. - ISBN 978-0-08-044565-6
|
Preface ........................................................ xi
1 Kinematics, thermodynamics and fluid transport properties .... 1
1.1 Kinematic preliminaries ................................. 3
1.1.1 Motion of material elements ...................... 4
1.1.2 Deformation ...................................... 5
1.1.3 Reynolds transport theorem ....................... 8
1.2 Equilibrium thermodynamics .............................. 9
1.3 Compressible subsonic and supersonic flows ............. 12
1.4 Turbulent flows and compressible turbulence ............ 16
2 The dynamics of compressible flows .......................... 21
2.1 Mass conservation ...................................... 21
2.2 Momentum conservation .................................. 22
2.2.1 Surface forces: the stress tensor ............... 24
2.2.2 Body forces ..................................... 26
2.3 Energy conservation .................................... 26
2.4 Solenoidal velocity fields and density changes ......... 30
2.5 Two-dimensional flow and a Reynolds analogy ............ 35
3 Compressible turbulent flow ................................. 39
3.1 Averaged and filtered variables ........................ 39
3.1.1 Reynolds average ................................ 40
3.1.2 Average over fixed phase ........................ 41
3.1.3 Temporal LES filters ............................ 42
3.1.4 Spatial LES filters ............................. 43
3.2 Density-weighted variables ............................. 44
3.3 Transport equations for the mean/resolved field ........ 51
3.4 Fluctuation transport equations ........................ 59
3.5 Momentum and thermal flux relationships ................ 64
3.5.1 Strong Reynolds analogy ......................... 64
3.5.2 Morkovin's hypothesis ........................... 75
4 Measurement and analysis strategies ......................... 79
4.1 Experimental constraints for supersonic flows .......... 79
4.1.1 Constraints on wind tunnel testing .............. 80
4.1.2 Constraints on data collection and measurement
apparatus ....................................... 83
4.2 Measurement methods .................................... 88
4.2.1 Intrusive method: hot-wire anemometry ........... 88
Anemometers and probes .......................... 89
Data reduction .................................. 92
4.2.2 Non-intrusive methods ........................... 95
With particles: LDV, PIV and DGV ................ 95
Without particles: Rayleigh-scattering
methods ........................................ 100
4.3 Analysis using modal representations .................. 105
4.4 Reynolds-and Favre-averaged correlations .............. 113
5 Prediction strategies and closure models ................... 117
5.1 Direct numerical simulations .......................... 117
5.2 Large eddy simulations and hybrid methods ............. 121
5.3 Closure of the Reynolds-averaged Navier-Stokes
equations ............................................. 127
5.3.1 Differential turbulent stress transport
equations ...................................... 128
Turbulent stress and kinetic energy transport
equations ...................................... 128
Turbulent stress anisotropy transport
equation ....................................... 131
5.3.2 Turbulent energy dissipation rate .............. 135
Solenoidal dissipation rate transport
equation ....................................... 137
Dilatation dissipation rate .................... 144
5.3.3 Pressure-strain rate correlation ............... 147
5.3.4 Scalar flux modelling .......................... 153
Heat flux ...................................... 154
Mass flux ...................................... 156
5.3.5 Other closure issues ........................... 158
Polynomial representations for second-moments
and scalar fluxes .............................. 159
Wall proximity effects ......................... 160
6 Compressible shear layers .................................. 161
6.1 Free shear flows ...................................... 161
6.1.1 Jets ........................................... 162
6.1.2 Mixing-layers .................................. 165
Flow structure ................................. 166
Spreading rate ................................. 170
6.1.3 Wakes .......................................... 185
Base flows ..................................... 185
Flat plate wakes ............................... 188
6.2 Wall-bounded flows .................................... 190
6.2.1 Thermal and velocity fields .................... 191
Mean thermal field ............................. 193
Mean velocity field ............................ 196
Turbulent field ................................ 202
6.2.2 Skin-friction and shape factor ................. 205
7 Shock and turbulence interactions .......................... 211
7.1 Homogeneous turbulence interactions ................... 211
7.1.1 Application of linear theory ................... 211
7.1.2 Numerical simulations .......................... 218
7.1.3 Comparison with experimental results ........... 225
7.2 Inhomogeneous turbulence interaction .................. 232
7.2.1 Free shear flows ............................... 232
Jet/shock wave interactions .................... 233
Mixing-layer/shock wave interactions ........... 235
Wake/shock wave interactions ................... 236
7.2.2 Wall-bounded flows ............................. 238
References .................................................... 247
Index ......................................................... 275
|
|
