Large Eddy Simulation for Compressible Flows (eBook)

Pierre Saugaut is one of the leading scientists in scientific computing (Simulation, Analysis and Modeling of Compressible Turbulent Flows), and his books are considered the most important in the field of LES theory and applications (he has been given the ONERA award for the best scientific publication in 1997,1999, 2001). He is teaching at the Pierre et Marie Curie Universite Paris. The author has published several books with Springer ("Large Eddy Simulation for Incompressible Flows", ISBN 978-3-540-26344-9; "Introduction a la simulation des grandes échelles pour les écoulements de fluide incompressible", ISBN 978-3-540-64684-6; "Turbulence and Interactions", ISBN 978-3-642-00261-8; "Quality and Reliability of Large-Eddy Simulations", ISBN 978-1-4020-8577-2). He is in the Editorial/Advisory Board of the Springer Journals "Theoretical and Computational Fluid Dynamics" and "Journal of Scientific Computing".

Contents 6
Introduction 11
LES Governing Equations 15
Preliminary Discussion 15
Governing Equations 16
Fundamental Assumptions 16
Conservative Formulation 17
Alternative Formulations 19
Filtering Operator 19
Definition 20
Fundamental Properties 20
Additional Hypothesis 22
Three Classical Filters for Large Eddy Simulation 22
Differential Interpretation of the Filters 23
Discrete Representation of Filters 24
Filtering of Discontinuities 26
Filter Associated to the Numerical Method 28
Commutation Error 30
Favre Filtering 30
Summary of the Different Type of Filters 32
Formulation of the Filtered Governing Equations 32
Enthalpy Formulation 33
Temperature Formulation 34
Pressure Formulation 34
Entropy Formulation 35
Filtered Total Energy Equations 36
A System for E, p, T 37
A System for E, p, T 38
A System for E, P, T 38
A System for E, p, T 39
Momentum Equations 39
Simplifying Assumptions 40
SGS Force Terms 40
Small Scales Incompressibility 41
Additional Relations for LES of Compressible Flows 43
Preservation of Original Symmetries 43
Discontinuity Jump Relations for LES 45
Shock Modeling and Jump Relations 45
Filtered Jump Relations and Associated Constrains on Subgrid Terms 46
Second Law of Thermodynamics 47
Model Construction 48
Basic Hypothesis 48
Modeling Strategies 49
Compressible Turbulence Dynamics 50
Scope and Content of This Chapter 50
Kovasznay Decomposition of Turbulent Fluctuations 51
Kovasznay's Linear Decomposition 51
Weakly Nonlinear Kovasznay Decomposition 54
Statistical Description of Compressible Turbulence 55
Shock-Turbulence Interaction 57
Introduction to the Linear Interaction Approximation Theory 57
Vortical Turbulence-Shock Interaction 58
Mixed-Mode Turbulence-Shock Interaction 66
Influence of the Upstream Entropy Fluctuations 67
Influence of the Upstream Acoustic Fluctuations 71
Consequences for Subgrid Modeling 71
Different Regimes of Isotropic Compressible Turbulence 73
Quasi-Isentropic-Turbulence Regime 74
Nonlinear Subsonic Regime 80
Conditions for Occurrence of Shocklets 80
Energy Budget and Shocklet Influence 80
Enstrophy Budget and Shocklet Influence 81
Supersonic Regime 83
Consequences for Subgrid Modeling 84
Functional Modeling 86
Basis of Functional Modeling 86
Phenomenology of Scale Interactions 86
Basic Functional Modeling Hypothesis 88
SGS Viscosity 88
The Boussinesq Hypothesis 88
Smagorinsky Model 90
Structure Function Model 91
Mixed Scale Model 91
Isotropic Tensor Modeling 92
SGS Heat Flux 93
Modeling of the Subgrid Turbulent Dissipation Rate 94
Improvement of SGS models 94
Structural Sensors and Selective Models 94
Accentuation Technique and Filtered Models 96
High-Pass Filtered Eddy Viscosity 97
Wall-Adapting Local Eddy-Viscosity Model 97
Dynamic Procedure 98
Computation of the Deviatoric SGS Tensor 98
Computation of the Isotropic Part of the SGS Tensor 101
Computation of the Dynamic Prandtl Number 101
Implicit Diffusion and the Implicit LES Concept 102
Explicit Structural Modeling 103
Motivation of Structural Modeling 103
Models Based on Deconvolution 105
Scale-Similarity Model 108
Approximate Deconvolution Model 111
Tensor-Diffusivity Model 113
Regularization Techniques 113
Eddy-Viscosity Regularization 114
Relaxation Regularization 117
Regularization by Explicit Filtering 119
Multi-Scale Modeling of Subgrid-Scales 121
Multi-Level Approaches 121
Stretched-Vortex Model 124
Variational Multi-Scale Model 125
Relation Between SGS Model and Numerical Discretization 127
Systematic Procedures for Nonlinear Error Analysis 127
Error Sources 127
Modified Differential Equation Analysis 129
Modified Differential Equation Analysis in Spectral Space 134
Implicit LES Approaches Based on Linear and Nonlinear Discretization Schemes 137
The Volume Balance Procedure of Schumamm 137
The Kawamura-Kuwahara Scheme 138
The Piecewise-Parabolic Method 139
The Flux-Corrected-Transport Method 140
The MPDATA Method 144
The Optimum Finite-Volume Scheme 146
Implicit LES by Adaptive Local Deconvolution 148
Fundamental Concept of ALDM 148
ALDM for the Incompressible Navier-Stokes Equations 151
ALDM for the Compressible Navier-Stokes Equations 156
Boundary Conditions for Large-Eddy Simulation of Compressible Flows 162
Introduction 162
Wall Modeling for Compressible LES 163
Statement of the Problem 163
Wall Boundary Conditions in the Kovasznay Decomposition Framework: an Insight 163
Turbulent Boundary Layer: Vorticity and Temperature Fields 166
Turbulent Boundary Layer Vortical Dynamics: a Brief Reminder 166
Turbulent Boundary Layer: Mean Flow Features 167
Turbulent Boundary Layer: Acoustic Field 170
A First Insight: Surface Pressure Fluctuations 170
Production of Pressure Fluctuations by the Vorticity Field 172
Attenuation of Acoustic Modes by Vorticity and Entropy Modes 175
Consequences for the Development of Compressible Wall Models 176
Extension of Existing Wall Models for Incompressible Flows 177
Algebraic Two-Layer Wall Models 177
Thin-Boundary Layer Equations Based Models 178
Unsteady Turbulent Inflow Conditions for Compressible LES 179
Fundamentals 179
Precursor Simulation: Advantages and Drawbacks 181
Extraction-Rescaling Techniques 182
Synthetic-Turbulence-Based Models 186
Subsonic Applications with Compressibility Effects 192
Homogeneous Turbulence 192
Context 192
A Few Realizations 193
Influence of the Numerical Method 194
SGS Modeling 197
Channel Flow 198
Context 198
A Few Realizations 198
Influence of the Numerical Method 199
Influence of the SGS Model 201
Mixing Layer 202
Context 202
A Few Realizations 202
Influence of the Numerical Method 203
Influence of the SGS Model 204
Boundary-Layer Flow 205
Context 205
A Few Realizations 205
Jets 207
Context 207
A Few Realizations 208
Influence of the Numerical Method 209
Influence of the SGS Model 211
Physical Analysis 212
Flows over Cavities 213
Context 213
A Few Realizations 213
Influence of the Numerical Method 214
Influence of the SGS Model 215
Physical Analysis 215
Supersonic Applications 217
Homogeneous Turbulence 217
Channel Flow 218
Context 218
A Few Realizations 218
Influence of the Numerical Method 219
Influence of the Grid Resolution 220
Influence of the SGS Model 221
Boundary Layers 221
Context 221
A Few Realizations 222
Influence of the Numerical Method 222
Influence of the Grid Resolution 223
SGS Modeling 225
Jets 226
Context 226
A Few Realizations 226
Influence of the Numerical Method 227
Influence of the SGS Model 227
Physical Analysis 227
Supersonic Applications with Shock-Turbulence Interaction 229
Shock-Interaction with Homogeneous Turbulence 230
Phenomenology of Shock-Interaction with Homogeneous Turbulence 230
LES of Shock-Interaction with Homogeneous Turbulence 234
Shock-Turbulence Interaction in Jets 236
Phenomenology of Shock-Turbulence Interaction in Jets 236
LES of Shock-Turbulence Interaction in Jets 237
Shock-Turbulent-Boundary-Layer Interaction 239
Phenomenology of Shock-Turbulent-Boundary-Layer Interaction 239
LES of Compression-Ramp Configurations 243
Normal Shock Configurations 250
Impinging Shock Configurations 254
References 260
Index 277