1. 1 Q-LES 2007, 24-26 October, Leuven, Belgium. Optimal Unstructured Meshing for Large Eddy Simulation Y Addad, U Gaitonde, D Laurence Speaker: S. Rolfo The University of Manchester, M60 1QD, UK School of Mechanical, Aerospace & Civil Engineering. CFD group The University of Manchester

2. 2 L.E.S. on unstructured grids Unstructured FV industrial codes  Geometry complexity imposes unstructured grids (Even pipe flow requires unstr. grid. (no channel flows in industry !)  Indust. Pbs often Multiscale L.E.S  Principle = grid that captures larger eddies + some of the energy cascade  Integral Length-scale is highly variable in any real application  Most LES today still on structured grids. PWR lower Plenum ( EDF Code Saturne) Why not use flexibility of unstructured FV to fix the cell size to LES criteria LOCALLY?

3. 3 Channel Flow LES on structured grid at Re*=395 (Re*=y + at centre ) % error on friction Under-Resolved LES Under-resolved LES => more dangerous than coarse RANS ! => Q-LES very much needed now that Industry is into LES

4. 4 Empirical Guidelines for “hand made mesh”: Guidelines for channel flow unstructured grids - Much experience for channel flow, -but what about new applications (and real prediction) ? - “hand made mesh” is tedious ! - Ideal would be to feed precursor RANS results into automatic mesh generator

5. 5 Again “hand made mesh”. Can we make it automatic? Zonal mesh adaptation to integral scale

6. 6 Kolmogorov lengthscale Taylor microscale Von Karman Lengthscale Turbulent energy lengthscale Integral lengthscale Length scales

7. 7 Integral length scales in channel flow Turbulent energy scale is easy RANS “ model ” but does not represent true (2 point correlation) integral scale for channel flow streaks 1- x : streamwise 2- y : wall normal 3 – z : spanwise Solid: stream-wise separation Dashed: span-wise separation Nb: longitudinal lenghtscales are divided by 2

8. 8 Taylor micro scales in HIT Available from RANS Nb: Integral and Kolmororov scales can be combined to form the Taylor scale

9. 9 Taylor length scales in channel flow Lines = “ home ” fine LES Symbols = only points available DNS data (THT lab Tokyo U., N Kasagi)

10. 10 Comparison between different length-scales for the channel flow test case at Re  =720. 10 Kolmogorov Taylor spanwise Tayor streamwise Integral /10

11. 11 NxNyNz LES68 to 2004642 to 100 DNS256193192 Re=395 Domain 2   2    LES Ncells= 443,272 DNS Ncells = 9,486,336 (Ref: Moser et al. 1999) Grid generation following Taylor scale

12. 12 Channel Re=395 with different grid topology O DNS (10 Million cells) Structured Grid (0.3M) Bloc refinement 2-3 2h=Taylor continuous fit (0.44M)

13. 13 Bloc refinement 1-2 (Benhamadouche Thesis) Channel Re=395 with different grid topology O DNS (10 Million cells) LES (0.5 Million cells) : - Structured Grid - Bloc refinement 2-3 - Taylor/2 continuous fit Present LES (Addad)

14. 14 Span = 1 cell to 64 cells on body) Embedded refinement strategy 1 to 2 refinement with central differencing leads to spurious oscillations 2 to 3 refinement now systematically used

15. 15 Energy conservation: Taylor-Green vortices test case.

16. 16 Energy conservation: Taylor-Green vortices test case.

17. Mesh smoothing for LES see also Iaccarino & Ham, CTR briefs 05

18. Energy conservation: Taylor-Green vortices test case. Error map for the U velocity component for the Cartesian mesh 60x60 Error map of U for the Cartesian mesh 60x60 + 5-8 refinement Error map of U for the Cartesian mesh 60x60 + 1-2 refinement. Max error where the velocity is min and the V component is max. Max error in the middle

19. Energy conservation: Taylor-Green vortices test case. Velocity components are pointing in the wrong directions.

20. 20 Conclusions  Lenghtscales from precursor RANS simulations can be used to estimate LES grid requirements.  Mesh following span-wise Taylor micro-scales in stream-wise, and span- wise directions is close to “empirical knowledge” and gives good agreement of the LES results with DNS  Less trivial test cases are necessary to define criteria 2h=f (Integral s., Taylor s., Kolmogorov) and demonstrate real benefits (jets, separated flows…)  Use of non conformal meshes can introduce spurious oscillations in the solutions. More investigations, in particular focussing on the interpolation of flow quantities at the cell faces, are studied in order to avoid the problem.Acknowledgements This work was carried out as part of the TSEC programme KNOO and as such we are grateful to the EPSRC for funding under grant EP/C549465/1, and to N Jarrin for Saturne code results

21. 21 Arbitrary unstructured grids Control of cell size essential in LES Refinements: Bloc structured (+ non-conform refin ’ t) or Distributed refinement? Note: “ hanging node ” = 5 sided cell, no special treatment

22. 22 Colocated unstructured Finite Volumes - Ferziger & Peric: Computational Fluid Dynamics, 3rd edt. Springer 2002. -“Face based” data-structure => simple - Fine for convection terms - Approximations come from interpolations and Taylor expansions from cell centres to cell faces

23. 23 Interpretation: - an LES instantaneous field is NOT an instance of a filtered DNS field (S. Pope) - but it should give the same statistics as a filtered DNS field - means eliminate all statistical bias in numerical scheme - preserve symmetries of NS rather that solve it (as lattice Boltzmann or SPH give NS solution “statistically”) = “phase error not so important as amplitude error” = “position of vortex not important, but magnitude should be conserved” - MILES ? LES and low order schemes

24. 24 Energy conservation ? Ex. Scalar convection mass flux across face between cells I and J interpolation on IJ face contains the non-orthogonality correction interpolation weighing. If regular grid convection term for cell I is cancel locally if is constant cancel 2x2 if and FV conserves mass & momentum, Energy can only be conserved? Conservation of convective flux of “energy” between cells I and J ? Requirements: - centered in space and time, - regular mesh spacing, and no non-orthogonality corrections - mass flux may be explicit

25. 25 L.E.S. of H.I.T. Code_Saturne Classic test for LES: Homogeneous Isotropic Turbulence (decay of turbulence downstream of a grid) Viscosity = Smagorinsky (classical LES model) Viscosity = 0 E(K)= a K 2 Total energy = constant

26. 26 Inviscid H.I.T test (viscosity =0, Euler eq.) S. Berrouk, STAR-CD V4 Viscosity = 0 K 2 distribution as expected STAR-CD V4: Similar to Saturne but 3 time level scheme (2nd order in space & time)