Immersed Boundary Method and Chimera Method applied to Fluid-
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1 The numericsacademy Fixed Colloquium IBM on Moving Immersed IBM Boundary Applications Methods : Conclusion Current Status and Future Research Directions June 2009, Academy Building, Amsterdam, the Netherlands Immersed Boundary Method and Chimera Method applied to Fluid- Structure Interactions Y. Hoarau, V. Novacek, T. Deloze, A. Makradi Institut de Mécanique des Fluides et des Solides, Université de Strasbourg / CNRS Groupe Instabilité, Turbulence, Diphasique 2 rue Boussingault Strasbourg France hoarau@imfs.u-strasbg.fr
2 Motivations «Complex» geometries, FSI and structured grids?
3 NSMB solver (Navier-Stokes MultiBloc) - Navier-Stokes compressible and incompressible solver - Finite volumes, structured grids, multi-blocks and parallel (MPI) - Turbulence modelling : algebraic models, Spalart-Allmaras, two equations models, EARSM, NLEVM, RSM, OES, DES, DDES, WMLES, LES - ALE : moving grid, deforming grid (remeshing) - Chimera method (overlapping grid) - Immersed Boundary Method Compressible Version - Spatial schemes : centered with artificial dissipation (Jameson, Martinelli, Matrix), upwind (Roe, AUSM, AUSMP, AUSMDV), Harten, Van Leer, Riemman - Temporal scheme : Runge-Kutta, LU-SGS semi implicit, dual time stepping - Multi-grid - Preconditioning (Weiss Smith, Choi/Merkle, artificial compressibility) - Chemistry : Equilibrium/Non-Equilibrium i E i Air, Argon and N2 Chemistry for hypersonic and plasma flows application, diffusion flame combustion model, coupling with Chemkin II - Patch and sliding grids, AMR 3
4 NSMB solver (Navier-Stokes MultiBloc) Incompressible version - Pressure-velocity coupling : SIMPLE, SIMPLEC, PISO, Braza - Rhie & Chow stabilisation - Spatial schemes : centered (2 nd et 4 th order), upwind (1 st, 2 nd and 3 rd order) - Temporal scheme : 1 st,2 nd and 3 rd order backward Euler, Cranck-Nicolson - (Multi-grid) - Thermal convection - SPARSKIT library to solve sparse matrix 4
5 NSMB solver (Navier-Stokes MultiBloc) The Immersed Boundary Method in NSMB - Discrete forcing : Ghost-cell method - 2 layers of ghost-cells are interpolated - Interpolation based on inverse distance - Fully parallelised - No correction at the IB for the incompressibility constraint (for the moment!) Fluid domain Solid domain 5
6 NSMB solver (Navier-Stokes MultiBloc) The Chimera Method in NSMB + = 6
7 NSMB solver (Navier-Stokes MultiBloc) Limit of the sphere mesh Buffer layer cells Buffer layer cells Interpolated cells Interpolated cells ignored cells ignored cells Limit of the wall dominant layer near the tube wall mesh near wall dominant layer Couche dominante proche paroi 7
8 Validation of fixed IBM Trans-sonic/Supersonic sonic/supersonic flows around a NACA0012 2D steady cylinder Sphere 2D unsteady cylinder NACA0012 at 20 of incidence, Re=800 8
9 Validation of fixed IBM NACA0012, M=0.85, α=2, Re=100 Cx Cx IBM 4 th order Central 0, , rd order Roe 0, , rd order AUSM+ 0, , rd order Van Leer 0, ,
10 Validation of fixed IBM NACA0012, M=2, α=5, Re=500 3 rd order Roe scheme IBM : Cx = Cz = Body fitted grid Cx = 0.33 Cz =
11 Validation of fixed IBM 2D steady cylinder SIMPLE, 4 th order central scheme Re=20 Re=30 11
12 Validation of fixed IBM 2D steady cylinder SIMPLE, 4 th order central scheme 12
13 Validation of fixed IBM Steady sphere SIMPLE, 4 th order central scheme 13
14 Validation of fixed IBM Steady sphere SIMPLE, 4 th order central scheme 14
15 Validation of fixed IBM Steady sphere with thermal convection SIMPLE, 4 th order central scheme 15
16 Validation of fixed IBM Unsteady 2D cylinder 4 th order Braza central scheme Re=300 16
17 Validation of fixed IBM Unsteady 2D cylinder 4 th order Braza central scheme 17
18 Validation of fixed IBM NACA0012, α =20, Re=800 4 th order Braza central scheme Nombre de Strouhal NSMB IBM Icare 0.55 Ventikos 0.52 Pulliam 0.5 Bouhadji
19 Validation of moving IBM Unsteady oscillating 2D cylinder 4 th order Braza central scheme, Re=100 Forced oscillation motion : z=z z 0 +Asin( A.sin(ω t) F = f osc / f 0 Lock-in zone by Koopman, JFM 1967 Comparison with Placzek & al, Comp. & Flds
20 Validation of moving IBM Unsteady oscillating 2D cylinder 4 th order Braza central scheme, Re=100 (A,F)=(0.25,1) (A,F)=(0.25,0.9) 20
21 Validation of moving IBM Unsteady oscillating 2D cylinder 4 th order Braza central scheme, Re=100 (A,F)=(0.25,1.5) 21
22 Validation of moving IBM Unsteady oscillating 2D cylinder 4 th order Braza central scheme, Re=100 22
23 Validation of moving IBM Unsteady oscillating 2D cylinder 4 th order Braza central scheme, Re=100 (A,F)=(1,0.9) Mode 2P 23
24 Validation of moving IBM Unsteady oscillating 2D cylinder 4 th order Braza central scheme, Re=100 (A,F)=(1.25,1.5) Mode P+S 24
25 Validation of moving IBM Z = z d Unsteady free oscillating 2D cylinder 4 th order Braza central scheme, Re=100 2 d Z dz * * * * m. + b. + k. Z = C ( t ) 2 Z dt dt U m b * * * *, t = t, m =, b =, k = 1 1 d 2 ρ U d 2 ρ U d 1 2 k ρ U 2 k* m* A f* Cx Shiels & al NSMB Shiels & al NSMB Shiels & al NSMB
26 Laminar tube array 26
27 Icicle melting. Q dt = λ ds dn dm = dt. Q L 27
28 Turek FSI test-case 28
29 Conclusion - Chimera and Immersed boundary methods successfully implemented in NSMB - Very powerful tools to handle complex geometries and FSI - IBM : need to check convergence order and incompressibility correction - Physical applications : add free movement of the sphere, add a solid solver Thank You for your attention ti 29
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