Intro Numerical code Results Conclusion Direct Numerical Simulations of converging-diverging channel flow J.-P. Laval (1), M. Marquillie (1) Jean-Philippe.Laval@univ-lille1.fr (1) Laboratoire de Me canique de Lille (LML), CNRS Blv Paul Langevin 59655 Vileneuve d Ascq, FRANCE
Introduction Turbulence: a long history of HPC First significant DNS in the 80 s Learn about 3D structures from DNS Increasing interest for subgrid scale modeling (90 s) DNS now available at significant Reynolds Number... but not enough to study universality of turbulence Turbulence is still a very Challenging Research Domain
DNS of Wall Turbulence DNS of Flat channel flows (J. Jimenez, 2003) Very expensive DNS, but important for modeling
Framework WALLTURB: A European Synergy for Assesment of Wall Turbulence (http://wallturb.univ-lille1.fr) FP6 EC Project (STREP) (2005-2009) 16 partners form 10 European Countries 12 Universities, 2 Research Centers 2 Industrial partners: (Airbus UK, Dassault Aviation) Physical and Numerical models of wall turbulence
Framework WALLTURB Objectives Generating and analysing new data on near wall turbulence, Extracting physical understanding from these data, Putting more physics in the near wall RANS models, Developing better LES models near the wall, Investigating models based on Low Order Dynamical Systems. WALLTURB Databases on Adverse Pressure Gradient Flows Experiments on flat wall (Poland) and curved wall (Surrey & LML) DNS of APG boundary layer on flat wall (Madrid) DNS of APG channel flow: both flat & curved wall DEISA (Performed by LML in collaboration with TU Munich (Germany), University of Rome (Italy), Chalmers University (Sueden), University of Surrey (UK))
Numerical method Incompressible Navier-Stokes equations : ū t + ( ū. ) ū = p + 1 Re ū,. ū = 0. Spatial discretisation : 4 th order finite differences for Laplacian (streamwise). Collocation-Chebyshev (normal). Fourier (spanwise) Temporal discretisation : 2nd order backward Euler. 2nd order Adams-Bashforth Projection method for incompressibility.
Complex Geometry mapping of coordinates Mesh : physical domain. y = 1 L (1 γ( x)) ȳ + γ( x), L + η( x) γ( x) = η( x) L Mesh : computation domain.
Mapped system Navier-Stokes system in the computational coordinates : u t + ( u. η ) u + ( u. G η ) u = η p G η p + 1 Re η u + 1 Re L η u η. u = G η. u Direct resolution ([N z N y ] 5 bands matrix of size N x ) Any smooth geometries in XY plane (small derivatives of η(x)) Possiblity to simulate a moving wall η(t, x) MPI Parallelization in spanwise direction (Fourier).
Parameters Computation at HLRS (DECI 2006 & 2007): 64 Processors NEC-SX8 Reynolds: Re τ = 617 at the inlet Domain: 4π 2 π Inlet: From precursor DNS of flat channel flow (same Re τ ) Resolution: 2304 384 576 (510 Millions grid points) Integration : 450 000 time steps (160000 CPU hours) Memory: 400 Gb Storage : 932 fields 3D (u,v,w,p) [NetCDF] > 7 Tb 3D fields for visualization vortices > 3 Tb 60 48 31 time evolutions > 800 Gb (every other 16 meshes in each direction)
Performances on NEC-SX8 Helmholtz and Poisson equations: 55 % (14 GFlops) FFT (VFFTPACK) : 20 % (7-8 GFlops) Communications (not overlapped with computations) : 13 % Need to optimize MPI transfer routines (rewrite version of MPI GATHER, MPI SCATTER) Performance with 64 Processors: 10 GFlops / Procs. ( > 60% of peak performance)
Spatial resolution (wall units) ( x + ) inlet = 5.1, ( z + ) inlet = 3.4 ( x + ) max = 10.7, ( z + ) max = 7.4 (resolution after dealiasing)
Spatial resolution (Kolmogorov scale) ( ) ν 3 1/4 η = : Kolomogorov scale ɛ Maximum mesh size: 4η in the region of maximum of k
Pressure coefficients
Skin-friction coefficients
Mean velocity Mean Streamwise Velocity very thin recirculation region
Vortices Isovalue (Q=300) of Q = Ω 2 S 2.
Vortices in detachment region (3D) Isovalue of Q = Ω 2 S 2 in the separation region.
Vortices in detachment region (2D) Q in the separation region.
Streaks Flat upper wall (y + = 20)
Reynolds Stresses: curved wall
Heavy Post-Processing: Reynolds Stress Budget u i u j t + u k u i u j x k = P ij + T ij + D ij + D ρ,ij + Φ ij ɛ ij Production: P ij = u j u k u i x k u i u k u j x k, Turbulent Transport: T ij = u i u j u k x k, Viscous Diffusion: D ij = ν 2 u i u j x k x k, Pressure Diffusion: D ρ,ij = 1 ρ * Pressure Strain: Φ ij = p ρ Dissipation: ɛ ij = 2ν u j! p + u i p x i x j!+ u i + u j, x j x i * u i x k u j x k +.,
Balance of turbulent kinetic energy
Balance of turbulent kinetic energy
Balance of turbulent kinetic energy
Balance of turbulent kinetic energy
Balance of turbulent kinetic energy
Balance of turbulent kinetic energy
Balance of turbulent kinetic energy
Summary Post-processing of full database still in progress... Full information available for statistical turbulence models (RANS) Full Reynolds Stress Budget Scaling of mean velocity and Reynolds stresses Database for apriori and a posteriori validation of sub-grid scales models (LES) Usefull database for preliminary investigation of flow control Stability analysis of APG turbulent flows Detection & investigation of coherent structures (vortices, streaks)
Next step Increase the Reynolds ( 10) but CPU scales as Re 3! Possibility to use DNS as a tool Parameters studies (pressure gradient,...) Basis for control strategy closed loop active control Need to adapt the code for Peta scale simulations Need for experienced people in computer science