Wall treatment in Large Eddy Simulation

Transcription

1 Wall treatment in arge Edd Simlation David Monfort Sofiane Benhamadoche (ED R&D) Pierre Sagat (Université Pierre et Marie Crie) 9 novembre 007 Code_Satrne User Meeting Wall treatment in arge Edd Simlation

2 Overview. Context. Qick review of existing approaches 3. Extending the classical wall-model 4. Reslts on a heated channel flow 5. Conclsion and perspectives 9 novembre 007 Code_Satrne User Meeting Wall treatment in arge Edd Simlation

3 Context : Trblence and arge-edd Simlation 3 9 novembre 007 Code_Satrne User Meeting Wall treatment in arge Edd Simlation

4 . Context. Wall fnctions 3. Extended law 4. Channel flow 5. Conclsions arge Edd Simlation Ideal to solve nstead flows Usefl for areas like lid Strctre Interaction, thermal fatige Resolve large scales while modelling smallest ones Bt, need for a ver fine mesh for trblent flows to resolve small scales next to the walls Spalart (000): compters not efficient enogh before novembre 007 Code_Satrne User Meeting Wall treatment in arge Edd Simlation

5 . Context. Wall fnctions 3. Extended law 4. Channel flow 5. Conclsions Wh a model for the wall bondar laer Estimation of the nmber of points needed for a comptation in the different laers Oter laer, nb of nodes ~ Re 0.5 Inner laer, nb of nodes ~ Re novembre 007 Code_Satrne User Meeting Wall treatment in arge Edd Simlation

6 . Context. Wall fnctions 3. Extended law 4. Channel flow 5. Conclsions Code_Satrne and its wall treatment Code developped in ED and originall designed for nclear vessels comptation inite volme method on polhedron nstrctred meshes Collocated cell-centered variables Incompressible or weakl compressible Navier-Stokes eqations Two kind of wall-bondar conditions for the velocit ocal coordinates defined b cell-centered velocit Comptation of the diffsive terms at the wall * Shear stress τ ( ) w ρ Comptation of edd viscosit Cell-centered velocit gradient I, nmerical I, theoretial n I novembre 007 Code_Satrne User Meeting Wall treatment in arge Edd Simlation

7 rom Schmann s law to zonal models : a qick review of classical methods 7 9 novembre 007 Code_Satrne User Meeting Wall treatment in arge Edd Simlation

8 . Context. Wall fnctions 3. Extended law 4. Channel flow 5. Conclsions Differents available approaches Classical «instantaneos» methods Taking into accont the «driving» terms (pressre gradient, time derivative, ) 8 9 novembre 007 Code_Satrne User Meeting Wall treatment in arge Edd Simlation

9 9 novembre 007 Code_Satrne User Meeting Wall treatment in arge Edd Simlation 9 Some classical wall-fnctions Werner & Wengle power law (shear stress directl available) lim, A B n I ν τ τ Reichardt law (blended law) ( ) ( ) b D D C n I, exp exp ln κ κ τ lim, ln B n I ν κ τ τ Instantaneos logarithmic law. Context. Wall fnctions 3. Extended law 4. Channel flow 5. Conclsions

10 . Context. Wall fnctions 3. Extended law 4. Channel flow 5. Conclsions Thin Bondar aer Approach (TBE) ramework Keep a coarse mesh for the ES Solve a simplified set of eqations on a D-mesh in the first cell next to the wall Balaras et al, Wang, Moin Drawbacks Rather difficlt to implement on nstrctred meshes rom Piomelli et al 0 9 novembre 007 Code_Satrne User Meeting Wall treatment in arge Edd Simlation

11 3 An extension of the classical wall model 9 novembre 007 Code_Satrne User Meeting Wall treatment in arge Edd Simlation

12 . Context. Wall fnctions 3. Extended law 4. Channel flow 5. Conclsions Dimensionless bondar laer eqations All the terms are made dimensionless b the friction velocit. τ τ w ρ We se classical hpothesis b neglecting the following terms (in a first attempt): Diffsion along streamwise and spanwise directions Convection Time derivative This leads to the following eqation where stands for the pressre gradient, time derivative, ν t ( ) Which model for the edd viscosit? 9 novembre 007 Code_Satrne User Meeting Wall treatment in arge Edd Simlation

13 9 novembre 007 Code_Satrne User Meeting Wall treatment in arge Edd Simlation 3 Mixing-lenght hpothesis A exp κ U U t ν with ( ) t ν and ( ) ν t ( ) w τ Ths we can now obtain an eqation on the velocit in the first cell off-wall.. Context. Wall fnctions 3. Extended law 4. Channel flow 5. Conclsions

14 . Context. Wall fnctions 3. Extended law 4. Channel flow 5. Conclsions Velocit profiles The std of the eqation (on the right) gives the following profiles for the velocit in the first cell off-wall. ( ) ( X X X τ ) 0 w ( ) ( f, τ ) 0, w d Don t forget that : The velocit is positive in local coordinates The redced shear stress is /- 4 9 novembre 007 Code_Satrne User Meeting Wall treatment in arge Edd Simlation

15 9 novembre 007 Code_Satrne User Meeting Wall treatment in arge Edd Simlation 5 Soltions of the nd order eqation X X ( ) ( ) 0 X X ( ) ( )( ) 4 X ( ) ( )( ) ) ( 4 a d b a. irst, X X ( ) ( ) 0 X X ( ) ( )( ) 4 X ( ) ( )( ) ) ( 4 a d b a. Second,. Context. Wall fnctions 3. Extended law 4. Channel flow 5. Conclsions

16 9 novembre 007 Code_Satrne User Meeting Wall treatment in arge Edd Simlation 6 Velocit profiles, following the datas Impossible, de to the constraint that the velocit mst be positive at the first-cell off wall 0 < 0 0 < w τ 0 > w τ ( ) ( )( ) * 0 4 d ( ) ( )( ) * 0 4 d ( ) ( )( ) d 0 4 ( ) ( )( ) d * 4 ) ( * ( ) ( )( ) d * 4 ) ( *. Context. Wall fnctions 3. Extended law 4. Channel flow 5. Conclsions

17 . Context. Wall fnctions 3. Extended law 4. Channel flow 5. Conclsions Getting the velocit friction After having obtained the dimensionless velocit profiles, one compte the velocit friction b a Newton-Raphson method. rom the velocit profile ( ) f ( ) one can obtain an eqation on the friction velocit n I * f * h ν * f h ν * n I 0 or h f ( h ) Re 0 loc 7 9 novembre 007 Code_Satrne User Meeting Wall treatment in arge Edd Simlation

18 . Context. Wall fnctions 3. Extended law 4. Channel flow 5. Conclsions Some velocit profiles.. for positive shear stress and a given local Renolds nmber 8 9 novembre 007 Code_Satrne User Meeting Wall treatment in arge Edd Simlation

19 . Context. Wall fnctions 3. Extended law 4. Channel flow 5. Conclsions Nmerical sensitivit The algorithm depends onl on the nmber of intervals and reaches an asmptote 9 9 novembre 007 Code_Satrne User Meeting Wall treatment in arge Edd Simlation

20 . Context. Wall fnctions 3. Extended law 4. Channel flow 5. Conclsions Extension to a generic scalar case et s consider a convection-diffsion eqation for a scalar : φ ( α αt ) φ where stands for the nstead, convective and sorce terms. The same approach leads to compte a friction scalar at the wall φ sch as : ρ * φ * φ α novembre 007 Code_Satrne User Meeting Wall treatment in arge Edd Simlation

21 . Context. Wall fnctions 3. Extended law 4. Channel flow 5. Conclsions Prandtl nmber sensitivit Rather good agreement between the predicted profiles for the extended wall-fnction in the generic scalar case (e.g. the temperatre) and the Kader correlations. 9 novembre 007 Code_Satrne User Meeting Wall treatment in arge Edd Simlation

22 4 A test case : The heated channel flow 9 novembre 007 Code_Satrne User Meeting Wall treatment in arge Edd Simlation

23 . Context. Wall fnctions 3. Extended law 4. Channel flow 5. Conclsions Test case: Heated channel flow Periodic channel: π x x π Mesh: 3x6x3 cells Uniform in all directions h 30 at the wall dx 80, dz 40 Case parameters: Re* 640 Pr 0.7 DNS from Kawamra et al 3 9 novembre 007 Code_Satrne User Meeting Wall treatment in arge Edd Simlation

24 . Context. Wall fnctions 3. Extended law 4. Channel flow 5. Conclsions Reslts for a heated channel flow () 4 9 novembre 007 Code_Satrne User Meeting Wall treatment in arge Edd Simlation

25 . Context. Wall fnctions 3. Extended law 4. Channel flow 5. Conclsions Reslts for a heated channel flow () 5 9 novembre 007 Code_Satrne User Meeting Wall treatment in arge Edd Simlation

26 . Context. Wall fnctions 3. Extended law 4. Channel flow 5. Conclsions Extended law response Distance to the center of the first cell off-wall: h 0, 40 and 00 Scalabilit against the Renolds nmber: Smbols: Re*000 (DNS from Jimenez) Plain: Re*4000 Dashed: Re* novembre 007 Code_Satrne User Meeting Wall treatment in arge Edd Simlation

27 5 Conclsions 7 9 novembre 007 Code_Satrne User Meeting Wall treatment in arge Edd Simlation

28 . Context. Wall fnctions 3. Extended law 4. Channel flow 5. Conclsions Conclsions and perspectives Conclsions Qite accrate in the core of the flow and in the prediction of the shear stress near the wall Meshless approach: no need to solve a sstem of D eqations Pressre gradient and nstead term can be proposed b defalt Perspectives Appl this approach to RANS and nstead RANS models (kepsilon, )? Extend to boanc-driven flows Extensive testing for the scalar case 8 9 novembre 007 Code_Satrne User Meeting Wall treatment in arge Edd Simlation