Interaction(s) fluide-structure & modélisation de la turbulence

Transcription

1 Interaction(s) fluide-structure & modélisation de la turbulence Pierre Sagaut Institut Jean Le Rond d Alembert Université Pierre et Marie Curie- Paris 6, France GDR Turbulence & GDR IFS 3-5 Novembre 2010

2 Fil conducteur IFS instationnarité (Cond. Lim.) modification écoulement Effets sur la turbulence? Conséquence pour la validité des modèles de turbulence? Prévision des efforts exercés sur la structure? Choix pour l exposé: couche limite turbulente 2

3 Motivations Unsteady simulations are now of common use for theoretical studies for engineering purposes All scales of turbulent flows cannot be directly captured because of required computing ressources Number of grid points : O(Re 9/4 ) Number of time steps : O(Re 1/2 ) Courtesy of ONERA, France some scales must be modeled many available approaches Courtesy of C. Kato, Tokyo

4 The LES concept (linear filtering) Computed filtered solution Exact solution

5 LBM-LES schematic view NS-LES Filtered macroscopic (ū, p) LBM-LES Filtered microscopic ( f, ρ, ũ) Non-linear terms inherited macroscopic (u, p) advection (quadratic) microscopic f microscopic f collision (exponential form/ Nth-order Hermite)

6 Hierarchy of CFD methods «Multiscale & Multiresolution approaches for turbulence» Sagaut, Deck & Terracol, Imperial College Press, 2006

7 RANS mean flow equations Material derivative associated with mean velocity field

8 RANS mean flow kinetic energy Mean flow kinetic energy Mean flow advection Pressure diff. Viscous diff. dissipation external force power Turbulent diff. transfer

9 RANS fluctuating momentum eqs. Mean field advection Reynolds stress Fluctuating field advection

10 RANS fluctuating kinetic energy Mean flow advection production Turbulent diff. dissipation External force power pressure diff. viscous diff.

11 Quasi-steady approximation (RANS) Quasi-steady approximation: unsteady forcing of turbulence doesn t induce significant modifications in turbulence dynamics usual models can be used Flow can be described using sequential steady RANS simulations t φ 0 11

12 Quasi-steady approximation (RANS) Validity? E.g.: turbulent boundary layer submitted to periodic forcing f/fburst 0.8 f burst U 5δ unsteady TBL (Rao, 1971) Unsteady effects restricted to viscous sublayer if 2ν ω u τ ν < 8 (Cousteix, 1985) 0 0 quasi-steady U forcing /U 0.6

13 RANS eddy-viscosity model sensitivity R ij = 2 3 Kδ ij 2ν t Sij Jones Launder (1972)

14 Logarithmic layer recovery «production = dissipation» equilibrium hypothesis Corresponding eddy-viscosity distribution Equalization with model prediction

15 Cont d Dissipation equation (accounting for the equilibrium condition) From which

16 RANS reconstruction of wall-pressure spectrum Prediction of wall-pressure induced loads on structure 16

17 Semi-empirical formula (Peltier et al., 2007) 17

18 Cont d Full exact expression 18

19 Cont d Quasi-Normal approximation Assumptions: 19

20 Cont d (Peltier et al., 2007) 20

21 Hierarchy of CFD methods «Multiscale & Multiresolution approaches for turbulence» Sagaut, Deck & Terracol, Imperial College Press, 2006

22 Schematic view at LES dynamics Net drain of resolved kinetic energy Origin of eddy-viscosity concept

23 LES grid resolution Most subgrid models are eddy-viscosity models Turbulence production mechanisms must be directly captured very fine grid resolution in TBL most unsteady effects directly captured in fine-grid LES x , y + 12, δz + = 1(min)

24 LES wall models

25 Cont d

26 Subgrid dissipation splitting (Härtel & Kleiser)

27 Main approaches Find an empirical explicit relation between the skin friction and the velocity at the first off-wall point (Schumann, Grötzbach, Wengle 1970s) Algebraic model Based on equilibrium boundary layer mean flow Solve a boundary layer equation within the first grid cell (Balaras et al., CTR group 1990s) Gain: pressure assumed to be constant in the wallnormal direction More general

28 TBL approach Basis: streamwise momentum TBL equation

29 Cont d

30 Cont d

31 31