Quality and Reliability of Large-Eddy Simulations II (eBook)

Preface 6
Contents 9
List of Contributors 13
SGS modeling and discretization errors 19
Error-landscape assessment of large-eddy simulations: a review 20
Introduction 20
Error landscapes and multi-objective refinement trajectories 21
The basic principles 21
Error balancing and error definitions 24
A comparison of numerical methods 25
Error-landscape results for a high-Reynolds-number boundary layer 26
Summary 29
References 30
Numerical and physical instabilities in massively parallel LES of reacting flows 32
Introduction 32
Numerical waves in LES of reacting flows 34
The growth of rounding errors in LES 36
Effects of the number of processors on LES 37
Sensitivity of LES in laminar and turbulent flows 39
Mesh effects in LES of gas turbine chamber 42
Objectives 42
Target configuration 43
Instantaneous flow topology and flame structure 44
Mean flow results 44
Conclusions 45
References 47
Quality Issues of Combustion LES 50
Introduction 50
Modes of Combustion 51
Combustion LES 51
Modelling in the limit of very fine grids 52
Quantifying Errors 54
Quality Estimators and Error Estimators 54
The Error Landscape 56
Conclusions 58
References 61
Energy cascade and spatial fluxes of filtered wall-turbulent flows 64
Introduction 64
Analysis of the Direct Numerical Simulation data base 65
The Kolmogorov equation for filtered velocity field 67
Assessment of the LES models 72
Conclusions 73
References 73
A computational study of turbulent flow separation for a circular cylinder using skin friction boundary conditions 74
Introduction 74
Computational model 75
Turbulent boundary layers 76
Experimental results 77
Computational results 77
Discussion and summary 78
Acknowledgements 84
References 84
LES-SSAM for a high Reynolds number turbulent channel flow 86
Introduction 86
LES-SSAM approach and model formulation 87
Numerical Results and discussion 90
Conclusion 94
References 94
A new development of the dynamic procedure for the integral-based implicit filtering in large-eddy simulation 96
Introduction 96
Integral versus differential-based filtered equations in continuous form 98
Integral versus differential-based discrete filtered equations. Analysis of the implicit filtering 100
Further tasks and conclusions 104
References 106
Reduced interaction between numerical and model errors through anisotropic filtering 108
Introduction 108
Theoretical LES 109
The filtering operation 109
LES Models 109
UAED Approach 110
Applications and results 111
Concluding Remarks 116
References 117
Analysis of the subgrid models in the flow between rotating discs 118
Introduction 118
Computational domain and numerical method 121
Parameters of HPF subgrid model 121
Results and discussion 122
Conclusions 125
References 126
A priori analysis of an Isothermal, Turbulent Two-Phase Flow 128
Introduction 128
Governing equations 129
Numerical method for DNS 130
DNS results 131
A priori analysis of the interfacial subgrid terms 133
Conclusions 136
References 137
A Posteriori Analysis of Numerical Errors in Computing Scalar Variance 138
Introduction 138
Details of LES Computations 139
Results 140
Patterns of spatial correlation 141
Evolution of subfilter variance distributions 142
Conclusions 144
References 147
Quality of classical and variational multiscale LES simulations of the flow around a circular cylinder 148
Introduction 148
Methodology 150
Application and results 152
References 156
LES model intercomparisons for the stable atmospheric boundary layer 158
Model intercomparison as a means of quality assurance 158
GABLS intercomparisons 159
Setup and results from GABLS-1 159
Setup and results of GABLS-3 160
How to deal with complex forcings 162
More realistic, more complex forcings 162
Ensemble and composite cases 162
Conclusion 164
Acknowledgement 164
References 164
Evaluating Subgrid-Scale Models for Large-Eddy Simulation of Turbulent Katabatic Flow 166
Introduction 166
Governing Equations and Closures 167
Model setup and flow characteristics 170
A Posteriori Testing 172
Conclusions 176
References 176
Large-eddy simulation of pyroclastic density currents 178
Introduction 178
Overview of the physical and numerical model 179
3D simulation of a stratified PDC 180
Flow-building interaction 183
Conclusions 185
References 186
Analysis of SGS effects on dispersed particles in LES of heated channel flow 188
Introduction 188
Physical problem statement and closure relationships 189
Numerical solution 191
Computation results and discussion 192
Concluding remarks 196
References 196
Relevance of approximate deconvolution for one-way coupled motion of inertial particles in LES of turbulent channel flow 198
Introduction 198
Mathematical model 200
Turbulent statistics and deconvolution 202
Conclusion 204
References 206
Inertial particle segregation and deposition in large-eddy simulation of turbulent wall-bounded flows 208
Introduction 208
Problem Formulation and Numerical Methodology 209
Particle tracking in LES flow fields at Re=300 211
Discussion 215
References 217
Scalar sub-grid energy in large-eddy simulation of turbulent flames: mesh quality criterion 218
Introduction 218
Scalar energy decomposition 219
Scalar scaling 221
Method of Manufactured Solution (MMS) for SGS scalar energy scaling 222
Time averaged scalar variance signal and mesh optimization 224
DNS minimum Reynolds number for Rv to vanish 224
Summary 226
References 226
Accuracy, Reliability and Performance of Spray Combustion Models in LES 228
Introduction 228
Formulation 229
Results and Discussions 230
Isotropic Turbulence 231
Temporal Mixing Layer 232
Lean Direct Injection Combustor 235
Conclusions 236
References 237
LES of Triangular-stabilized Lean Premixed Turbulent Flames with an algebraic reaction closure: Quality and Error Assessment 238
Introduction 238
Governing equations and modelling 239
Premixed turbulent combustion model 239
LES quality assessment 240
Geometry, grids and boundary conditions 240
Results and discussion 241
Non-reacting flow: subgrid scale closures 241
Non-reacting flow: Influence of mesh resolution 242
Non-reacting flow: Effect of poor grid resolution 243
Reacting flows 243
LES quality assessment based on Celik et al. approach 244
LES error assessment based on the Klein approach 245
Conclusion 246
References 247
Grid Effects on LES Thermo-Acoustic Limit-Cycle of a Full Annular Aeronautical Engine 248
Introduction 248
Numerical tools 249
Target configuration 249
Results and discussion 250
Mesh dependency in terms of mean flow 252
Mesh dependency of the thermo-acoustic instabilities 254
Conclusion 255
References 256
Extension of LES approaches to conductive fluids and plasmas 258
Introduction 258
Extension of LES approaches to MHD 259
Extension of LES approaches to kinetic equations 261
Conservation laws in Gyrokinetic equations 262
Filtered Gyrokinetic simulation 263
Conclusions 265
References 266
Assessment and reduction of computational errors 267
Grid Design and the Fate of Eddies in External Flows 268
Introduction 268
Grid Regions in DES, LES, and DNS 270
Requirements for a Simulation to be a DNS 272
Sub-Grid-Scale Modelling in Coarsening Resolution 273
Explicit Determination of Grid Regions: an Exercise 277
Outlook 281
References 282
How to estimate the resolution of an LES of recirculating flow 283
Introduction 283
Equations 284
The momentum equations 284
The turbulence model 284
The Numerical Method 285
Inlet boundary conditions 285
Results 285
Diffuser 285
Decaying isotropic grid turbulence 297
Concluding remarks 298
References 299
Quality assessment of Dynamic Finite Difference schemes on the Taylor-Green Vortex 301
Dynamic Finite Difference Approximations 301
Construction 301
High-Reynolds Calibration. 303
Taylor-Green Vortex Setup 304
Quality-Assessment 306
Error definitions 306
Modeling errors, numerical errors and their interactions 307
Conclusions 309
References 310
Stochastic Coherent Adaptive Large-Eddy Simulation with explicit filtering 311
Introduction 311
Explicit wavelet-filtering approach 312
Wavelet-filtered velocity 312
Wavelet-filtered equations 313
Subfilter-scale model 315
Numerical experiments 317
Concluding remarks 321
References 322
Error reduction in LES via adaptive moving grids 323
Introduction 323
Numerical framework and LES modelling 324
Moving Mesh PDE 324
Choice of the monitor function 325
Application to the flow over periodic hills 327
Conclusions 331
References 331
Influence of Reynolds number and grid resolution on large-eddy simulations of self-similar jets based on relaxation filtering 333
Introduction 333
Methods and parameters 334
LES methodology 334
Numerical algorithm 335
Simulation definition 335
Results 336
Vorticity snapshots 336
Energy dissipation and filtering activity 336
Mean and turbulent jet development 338
Concluding remarks 341
References 341
An Examination of the Spatial Resolution Requirements for LES of a Compressible Jet 343
Introduction 343
Numerical Method 344
Estimating Spatial Resolution 345
Modeling the Mach 0.9 Jet 346
Results 348
Prediction of the Flowfield 348
Resolution of the Turbulent Structures 349
Summary and Conclusions 351
References 352
A Computational Uncertainty Analysis of LES/DNS: towards building a reliable engineering turbulence prediction capability 353
Introduction 353
Model Error Analysis for RANS, LES 354
Analysis of Discretisation Errors 356
Analysis of Solution Errors 358
Importance of the initial and boundary conditions in LES/DNS 360
Conclusions 362
References 363
Computational error-minimization for LES of non-premixed turbulent combustion 364
Introduction 364
Simulation of a turbulent bluff-body flame 365
Error landscape analysis of a turbulent combustion 368
Computational error optimization using SIPI 371
Concluding remarks 371
References 372
Assessment of eddy resolving techniques for the flow over periodically arranged hills up to Re=37,000 374
Introduction 374
Test case 375
Numerical details 377
Results 377
Conclusions 379
References 382
Mathematical analysis and foundation for SGS modeling 384
From suitable weak solutions to entropy viscosity 385
Introduction 385
Suitable weak solutions 386
The Navier-Stokes problem 386
Suitable weak solutions 387
Direct Numerical Simulations (DNS) 387
More open questions for DNS 389
Proposal for a LES model based on suitability 390
Practical interpretation of the notion of suitable solution 390
What happens in under-resolved simulations? 391
A LES model based on suitability 392
Numerical illustrations for scalar conservation laws 392
Scalar conservation equations 392
The algorithm 393
Inviscid Burgers equation 394
KPP rotating wave 395
Numerical illustration for the Euler equations 396
The Euler equations 396
Description of the algorithm for finite elements 397
Mach 3 step 398
Double Mach reflection 399
A Riemann problem with Fourier approximation 400
Conclusions 400
References 401
A new deconvolution approach 403
Introduction 403
Application of the new deconvolution method to LES 404
Application of the new deconvolution method to the differential filters 407
The new deconvolution approach applied to the low-pass filter 407
The new deconvolution approach applied to the parabolic filter 408
The new deconvolution approach applied to the convective filter 409
Conclusions 410
References 410
Horizontal Approximate Deconvolution for Stratified Flows: Analysis and Computations 411
Introduction 411
An anisotropic Large Eddy Simulation model 412
Some properties of the horizontal Rational/Clark model 414
On the Boussinesq system 416
Perspectives for future studies 417
Numerical Results 418
References 422
The effect of subfilter-scale physics on regularization models 423
Introduction 423
Navier-Stokes 424
LANS- and rigid body formation 424
Clark-, Leray-, and influence of circulation on rigid bodies 426
MHD: circulation and outlook for LES 427
LAMHD- and absence of rigid bodies 428
LAMHD- as a SFS model 428
Summary 430
References 431
When does eddy viscosity damp subfilter scales sufficiently? 433
Problem setting 433
When does eddy viscosity damp any subfilter-scale disturbances? 435
When does eddy viscosity stop vortex stretching from continuing at subfilter scales? 438
Eddy viscosity revisited 440
References 442