Large-Eddy Simulation for Acoustics (2007)(en)(441s)

Cover......Page 1
Half-title......Page 3
Series-title......Page 5
Title......Page 7
Copyright......Page 8
Contents......Page 9
List of Figures and Tables......Page 15
Contributors......Page 23
Preface......Page 27
1.1.1 Health effects......Page 31
1.1.3 Annoyance......Page 32
1.1.4 Technical noise sources......Page 33
1.1.5 Political and social reactions to noise......Page 34
1.1.7 Research on acoustics by LES......Page 35
1.2.2 History......Page 37
1.2.3 Aeroacoustics......Page 38
1.2.4 Conceptual approaches......Page 39
1.2.5.1 Discretization......Page 43
1.2.5.4 Conclusions......Page 44
1.3.1 Broadband noise prediction in general......Page 45
1.3.2.1 Decaying and forced isotropic turbulence......Page 47
1.3.2.2 Jet flows......Page 48
1.3.2.3 Flow around airfoils and cylinders......Page 49
1.3.2.5 Applied flow problems......Page 51
2.1 Introduction to aeroacoustics......Page 54
2.2.1 Mass, momentum, and energy equations......Page 55
2.2.2 Constitutive equations......Page 58
2.2.3 Approximations and alternative forms of the basic equations......Page 60
2.3.1 Orders of magnitude......Page 63
2.3.2 Wave equation and sources of sound......Page 65
2.3.3 Green’s function and integral formulation......Page 66
2.3.4 Inverse problem and uniqueness of source......Page 68
2.3.5 Elementary solutions of the wave equation......Page 69
2.3.6 Acoustic energy and impedance......Page 74
2.3.8 Multipole expansion......Page 77
2.3.9 Doppler effect......Page 79
2.3.10.1 Lorentz or Prandtl–Glauert transformation......Page 82
2.3.10.2 Plane waves......Page 83
2.3.10.3 Half-plane diffraction problem......Page 84
2.4.1 Lighthill’s analogy......Page 85
2.4.2 Curle’s formulation......Page 89
2.4.3 Ffowcs Williams–Hawkings formulation......Page 90
2.4.4 Choice of aeroacoustic variable......Page 92
2.4.5 Vortex sound......Page 95
2.5.1 Wave propagation in a duct......Page 98
2.5.2 Low-frequency Green’s function in an infinitely long uniform duct......Page 102
2.5.3 Low-frequency Green’s function in a duct with a discontinuity......Page 104
2.5.4.1 Introduction to open pipe termination acoustics......Page 106
2.5.4.2 Low-frequency linear behavior without main flow......Page 107
2.5.4.4 Influence of main flow on linear behavior at low frequencies......Page 109
2.5.4.5 Influence of main flow on linear behavior at high frequencies......Page 112
2.5.4.6 Frequency dependence of the effect of flow on the radiation impedance......Page 113
2.5.4.7 Whistling......Page 114
3.1.1 General issues......Page 119
3.1.2 Large-eddy simulation: Underlying assumptions......Page 120
3.2.1 The Navier–Stokes equations......Page 121
3.2.2.1 Definition......Page 122
3.2.2.2 Properties......Page 123
3.2.2.3 Other filtering procedures......Page 124
3.2.3.1 First example: Generic conservation law......Page 125
3.2.3.3 Leonard’s decomposition......Page 126
3.2.3.4 Germano’s consistent decomposition......Page 127
3.2.4.1 De.nition of the filtered variables......Page 128
3.2.4.2 Example of filtered equations......Page 129
3.2.5 Filtering on real-life computational grids......Page 130
3.2.5.1 Filtering the equations in Cartesian coordinates......Page 131
3.2.5.2 Filtering the equations in general coordinates......Page 132
3.2.5.3 What is the filtering length scale on general meshes?......Page 133
3.2.5.4 Discrete test filters......Page 134
3.3.1.1 Homogeneous and free-shear flows......Page 135
3.3.1.2 Wall-bounded flows......Page 136
3.3.1.3 Sound waves......Page 137
3.3.1.4 Shock waves......Page 138
3.3.2.1 Direct numerical simulation......Page 139
3.3.2.2 Large-eddy simulation......Page 140
3.4.1 The closure problem......Page 142
3.4.2 Functional modeling......Page 143
3.4.2.1 Smagorinsky model......Page 145
3.4.2.3 Mixed-scale model......Page 146
3.4.2.4 Estimation of the subgrid-scale kinetic energy......Page 147
3.4.3 Structural modeling......Page 148
3.4.4 Linear combination models, full deconvolution, and Leray’s regularization......Page 149
3.4.5 Extended deconvolution approach for arbitrary nonlinear terms......Page 150
3.4.7 The dynamic procedure......Page 151
3.4.7.2 Computation of the subgrid model constant......Page 152
3.4.7.3 Extension to multiparameter models......Page 153
3.4.7.4 Accounting for numerical errors......Page 154
3.5.2 Extension of functional models......Page 155
3.5.4 The MILES concept for compressible flows......Page 156
4.1 Introduction to hybrid RANS–LES methods......Page 158
4.2.1 The approach of Speziale......Page 160
4.2.2 Detached-eddy simulation......Page 161
4.2.3 LNS......Page 163
4.2.4 The approach of Menter, Kunz, and Bender......Page 168
4.2.5 Defining the filter width......Page 170
4.2.6 Modeling the noise from unresolved scales......Page 172
4.2.7 Synthetic reconstruction of turbulence......Page 173
4.2.8 The NLAS approach of Batten, Goldberg, and Chakravarthy......Page 175
4.3 Zonal hybrid approaches......Page 178
4.3.2 The approach of Labourasse and Sagaut......Page 180
4.3.3 Zonal-interface boundary coupling......Page 182
4.4.1 Flow in the wake of a car wing mirror......Page 184
4.4.2 Unsteady flow in the slat cove of a high-lift airfoil......Page 188
4.5 Summary of hybrid RANS–LES methods......Page 193
5.1.1 Introduction to discretization schemes......Page 197
5.1.2.1 Dispersion and dissipation errors of the spatial scheme......Page 198
5.1.3 Spatial discretization schemes......Page 200
5.1.3.1 Classical central- and upwind-type schemes......Page 201
Upwind schemes......Page 202
Symmetric DRP schemes......Page 203
Asymmetric DRP schemes......Page 205
1D formulation......Page 206
Extension to multidimensions and Navier–Stokes......Page 212
Stabilization using filters or artificial dissipation......Page 217
1D formulation......Page 219
Extension to multidimensions and Navier–Stokes......Page 224
5.1.3.6 Discontinuous Galerkin methods......Page 225
5.1.4.1 Runge–Kutta schemes......Page 227
Classical Runge–Kutta schemes......Page 228
5.1.4.2 Optimized schemes......Page 229
5.2 Boundary conditions for LES......Page 231
5.2.1 Outflow boundary conditions......Page 233
5.2.2 Inflow boundary conditions......Page 234
5.2.3.1 Introduction to solid-wall boundary conditions......Page 238
5.2.3.2 Classical wall models......Page 240
5.2.3.3 Zonal and nonzonal approaches......Page 242
5.2.4 Far-field boundary conditions for compressible flows......Page 244
5.2.5 Final remark for discretization schemes......Page 245
5.3 Boundary conditions: Acoustics......Page 246
5.3.1 Characteristic nonreflecting boundary condition......Page 247
5.3.3 Absorbing-zone techniques......Page 248
5.3.3.2 Grid stretching and numerical filtering......Page 249
5.3.4 Perfectly matched layers......Page 250
5.4 Some concepts of LES–CAA coupling......Page 252
5.4.1 LES inflow boundary......Page 255
5.4.2 Silent embedded boundaries......Page 262
6.1 Plane and axisymmetric mixing layers......Page 268
6.1.1 Plane mixing layer......Page 269
6.1.2.1 Moderate-Reynolds-number jet......Page 271
6.1.2.2 High-Reynolds-number jet......Page 272
6.1.3 Concluding remarks for mixing-layer simulations......Page 274
6.2.1 Introduction to jet acoustics......Page 275
6.2.2.1 Near-field discretization......Page 277
6.2.2.2 Boundary conditions......Page 278
6.2.2.3 Far-field sound extrapolation......Page 281
6.2.3.1 Brief literature survey......Page 282
6.2.3.2 Discussion of LES acoustic results......Page 284
6.2.4.1 Resolution effects on the near and far fields......Page 289
6.2.4.2 Subgrid-scale noise model......Page 291
6.3.1 Introduction to cavity noise......Page 292
Use of URANS approaches......Page 293
Direct noise computations......Page 294
6.3.3.1 A challenging test case......Page 296
6.3.3.2 LES of a deep cavity in a channel......Page 297
6.3.3.3 Influence of the incoming-flow turbulence......Page 298
6.3.3.4 Switching between competitive modes......Page 301
6.4.1 Introduction to aeroelastic noise......Page 302
6.4.2 Fluid–structure interaction......Page 304
6.4.3 Numerical simulation......Page 306
6.4.4.1 Test case description......Page 308
Mesh sizes and general dimensions......Page 309
The plate and the cavity......Page 310
Mesh description......Page 311
Analysis......Page 312
Mean flow......Page 313
Mean pressure and rms levels......Page 314
6.4.6.2 Wall-pressure fluctuations......Page 315
Cross-spectral densities (CSD)......Page 316
6.4.6.3 Vibroacoustics response......Page 319
6.4.7 Mesh influence......Page 320
6.5.1 Introduction to trailing-edge noise simulation using LES......Page 323
6.5.2.1 Hybrid simulation approach......Page 326
Acoustic perturbation equations (APE)......Page 327
APE-based acoustic analogy......Page 329
Computational methods......Page 330
Determination of volume sources......Page 331
Large-eddy simulation I: Flat plate......Page 335
Large-eddy simulation II: Airfoil......Page 336
Acoustic simulation I: Flat plate......Page 337
Acoustic simulation II: Airfoil......Page 342
6.5.3.1 Objective......Page 345
Filtered Navier–Stokes equations......Page 346
Geometry, computational grid, and numerical procedure......Page 347
Aerodynamic results......Page 348
Power spectral densities......Page 350
Comparison with experimental data......Page 351
Wave-number–frequency spectra......Page 353
Instantaneous maps of pressure fluctuations......Page 355
Low-pass filtering by the CFD grid......Page 356
6.5.4.3 Spanwise coherences......Page 357
Propagation code......Page 358
Data injection process......Page 359
LES–Euler coupling result......Page 360
Kirchhoff formulation......Page 361
Final result......Page 362
6.6.1 Overview of blunt-body simulations......Page 363
6.6.2.1 Etkin test case......Page 365
6.6.2.2 ECL test case......Page 366
6.6.3 Car......Page 375
6.7.2.1 Source modeling......Page 379
6.7.2.3 Results in the case of a diaphragm in a duct......Page 380
Fluid–acoustic coupling......Page 381
Results in the case of a ducted cavity......Page 383
6.7.4.1 Presentation of the test case......Page 384
6.7.5 Conclusions for internal flow prediction......Page 385
6.8.1 Introduction to industrial aeroacoustics analyses......Page 386
6.8.2.1 Hybrid nature of flow-noise generation and propagation mechanisms......Page 387
6.8.3.1 Steady-state calculations......Page 388
6.8.3.2 Steady-state postprocessing......Page 389
Mesh frequency cutoff (MFC) measure of Mendonça......Page 390
6.8.3.3 Transient calculations......Page 393
Turbulence modeling......Page 394
Inlet perturbations......Page 395
Boundary mapping – global to local domain interfacing......Page 396
Transient data sampling and spectral postprocessing......Page 398
6.8.4 Postprocessing through acoustic coupling......Page 400
Surface and volume sources......Page 401
Fan sources......Page 403
6.8.6 Acknowledgments......Page 406
7.1 Governing equations and acoustic analogies......Page 408
7.2 Numerical errors......Page 414
7.3 Initial and boundary conditions......Page 415
7.4 Examples......Page 416
A.1 Symbols......Page 419
A.3 Mathematical operators......Page 420
APPENDIX B Abbreviations......Page 421
References......Page 425
Index......Page 459