MULTIRESOLUTION. APPROACHES in TURBULENCE. MULHSCALf and. Applications. LES, DES and Hybrid. 2nd Edition. RANS/LES Methods and Guidelines

Size: px

Start display at page:

Download "MULTIRESOLUTION. APPROACHES in TURBULENCE. MULHSCALf and. Applications. LES, DES and Hybrid. 2nd Edition. RANS/LES Methods and Guidelines"

Nigel Kennedy
5 years ago
Views:

1 2nd Edition MULHSCALf and MULTIRESOLUTION APPROACHES in TURBULENCE LES, DES and Hybrid Applications RANS/LES Methods and Guidelines Pierre Sagaut Uniuersite Pierre et Marie Curie-Paris 6, France Sebastien Deck OJVERA, France Marc Terracol ONERA, France

2 Contents Foreword to the Second Edition vii Foreword to the First Edition ix 1. A Brief Introduction to Turbulence Common Features of Turbulent Flows Introductory concepts Randomness and coherent structure in turbulent flows Turbulent Scales and Complexity of a Turbulent Field Basic equations of turbulent flow Denning turbulent scales A glimpse at numerical simulations of turbulent flows Inter-scale Coupling in Turbulent Flows The energy cascade Inter-scale interactions Turbulence Simulation and Scale Separation Numerical Simulation of Turbulent Flows Reducing the Cost of the Simulations Scale separation Navier-Stokes-based equations for the resolved quantities Navier-Stokes-based equations for the unresolved quantities 26 xi

3 xii Multiscale and Multiresolution Approaches in Turbulence 2.3 The Averaging Approach: Reynolds-Averaged Numerical Simulation (RANS) Statistical average Reynolds-Averaged Navier-Stokes equations Phase-Averaged Navier-Stokes equations The Large-Eddy Simulation Approach (LES) Large and small scales separation Filtered Navier-Stokes equations Multilevel/Multiresolution Methods Hierarchical multilevel decomposition Practical example: the multiscale/multilevel LES decomposition Associated Navier-Stokes-based equations Classification of existing multilevel methods Multilevel methods based on resolved-only wave numbers Multilevel methods based on higher wave numbers Adaptive multilevel methods Summary Statistical Multiscale Modelling General Exact Governing Equations for the Multiscale Problem Basic equations in physical and spectral space The multiscale splitting Governing equations for band-integrated approaches Spectral Closures for Band-integrated Approaches Local versus non-local transfers Expression for the spectral fluxes Dynamic spectral splitting Turbulent diffusion terms Viscous dissipation term Pressure term A Few Multiscale Models for Band-integrated Approaches Multiscale Reynolds stress models Multiscale eddy viscosity models 70

4 Contents xiii 3.5 Spectral Closures for Local Approaches Local multiscale Reynolds stress models Closures for the linear transfer term Closures for the linear pressure term Closures for the non-linear homogeneous transfer term Closures for the non-linear non-homogeneous transfer term Local multiscale eddy viscosity models Achievements and Open Issues Multiscale Subgrid Models: Self-adaptivity Fundamentals of Subgrid Modelling Functional and structural subgrid models The Gabor-Heisenberg curse Germano-type Dynamic Subgrid Models Germano identity Two-level multiplicative Germano identity Multilevel Germano identity Generalized Germano identity Derivation of dynamic subgrid models Dynamic models and self-similarity Turbulence self-similarity Scale separation operator self-similarity Self-Similarity Based Dynamic Subgrid Models Terracol-Sagaut procedure Shao procedure Variational Multiscale Methods and Related Subgrid Viscosity Models Hughes VMS approach and extended formulations Implementation of the scale separation operator Bridging with hyperviscosity and filtered models 120

5 xiv Multiscale and Multiresolution Approaches in Turbulence 5. Structural Multiscale Subgrid Models: Small Scales Estimations Small-scale Reconstruction Methods: Deconvolution The velocity estimation model The Approximate Deconvolution Model (ADM) The original ADM approach of Stolz, Adams and Kleiser Example of application Alternative formulation by explicit filtering Alternative regularization by standard subgrid models Relaxation-based approaches Subgrid scales estimation by approximate deconvolution Small Scales Reconstruction: Multifractal Subgrid-scale Modelling General idea of the method Multifractal reconstruction of subgrid vorticity Vorticity magnitude cascade Vorticity orientation cascade Reconstruction of the subgrid velocity field Variational Multiscale Methods Multigrid-based Decomposition Global Multigrid Approaches: Cycling Methods The multimesh method of Voke The multilevel LES method of Terracol et al Cycling procedure Multilevel subgrid closures Examples of application Zonal Multigrid/Multidomain Methods Unsteady Turbulence Simulation on Self-adaptive Grids Turbulence and Self-adaptivity: Expectations and Issues Adaptive Multilevel DNS and LES Dynamic local multilevel LES 189

6 Contents xv The dynamic multilevel (DML) method of dubois, jauberteau and temam Spectral multilevel decomposition Associated Navier-Stokes-based equations Quasi-static approximation General description of the spectral multilevel method Dynamic estimation of the parameters ii, '12 and ny Dynamic global multilevel LES Adaptive Wavelet-based Methods: CVS, SCALES Wavelet decomposition: brief reminder Coherency diagram of a turbulent field Introduction to the coherency diagram Threshold value and error control Adaptive wavelet-based direct numerical simulation Coherent vortex capturing method Stochastic coherent adaptive large-eddy simulation DNS and LES with Optimal AMR Error definition: surfacic versus volumic formulation A posteriori error estimation and optimization loop Numerical results Global Hybrid RANS/LES Methods Bridging between Hybrid RANS/LES Methods and Multiscale Methods Concept: the effective filter Eddy viscosity effective filter Global hybrid RANS/LES methods as multiscale methods Motivation and Classification of RANS/LES Methods 232

7 u> xvi Multiscale and Multiresolution Approaches in Turbulence 7.3 Unsteady Statistical Modelling Approaches Unsteady RANS approach The Semi-Deterministic Method of Ha Minh The Scale Adaptive Simulation (SAS) The Turbulence-Resolving RANS approach of Travin et al Global Hybrid Approaches The Approach of Speziale Limited Numerical Scales (LNS) General idea of LNS Example of application Blending methods General idea of blending methods Applications Other approaches: PITM and PANS Partially Integrated Transport Model (PITM) Partially Averaged Navier-Stokes (PANS) Detached Eddy Simulation General idea DES based on the SA model Possible extensions of standard SA-DES Examples DES based on the k - model Extra-Large Eddy Simulation (XLES) Grey-Area Modelled-Stress-Depletion (MSD) 277 Grid and Induced Separation (GIS) Further interpretation of MSD: non-local error analysis Delayed Detached Eddy Simulation (DDES) Formulation Improved Delayed Detached Eddy Simulation (IDDES) Zonal Detached Eddy Simulation (ZDES) Formulation Implementation Interpretation and further discussion. 298

8 Mapping Contents xvii 8. Zonal RANS/LES Methods Theoretical Setting of RANS/LES Coupling Full-variables approach Enrichment procedure from RANS to LES Restriction procedure from LES to RANS Perturbation approach: NLDE Inlet Data Generation - Techniques Precursor calculation Recycling methods Main issues and possible improvements of recycling methods Synthetic Turbulence Spectral methods Inverse Fourier transform technique Random Fourier modes. synthesization Digital filtering procedure by Klein-Sadiki-Janicka The Sandham-Yao-Lawal procedure Synthetic Eddy Method (SEM) The original procedure by Jarrin et al Further improvements of the SEM method Adaptations to ZDES Forcing Methods The Spille-Kohoff-Kaltenbach controlled forcing method The dynamic forcing method by Laraufie-Deck-Sagaut The Dahlstrom and Davidson procedure Feedback from Numerical Experiments Flow Physics Classification and Modelling Strategy Suitability Illustrative Examples Practical industrial applications Wall turbulence simulation 369

9 xviii Multiscale and Multiresolution Approaches in Thirbulence Further Discussion Numerical discretization effects General statement Grid resolution requirements More detailed discussion: classical LES Zonal vs. non-zonal treatment of turbulence 391 Bibliography 397 Index 425

MULTISCALE AND MULTIRESOLUTION APPROACHES IN TURBULENCE

2nd Edition MULTISCALE AND MULTIRESOLUTION APPROACHES IN TURBULENCE LES, DES and Hybrid RANS/LES Methods: Applications and Guidelines This page intentionally left blank 2nd Edition MULTISCALE AND MULTIRESOLUTION