1. Code_Saturne User Meeting 2009 School of Mechanical, Aerospace & Civil Engineering (MACE) The University of Manchester Manchester M60 1QD www.CFDtm.org A robust, predictive and physically accurate eddy viscosity model for near wall effects

2. Code_Saturne User Meeting 2009 WHY still review and develop Near-Wall RANS models in 2009? BECAUSE: HPC now allows industrial CFD with meshes down to y + =1 Robust N-W models are based on ad-hoc correlations (k-omega SST) OK for cold flow Aerodynamics, but poor for complex physics (relaminarization...) Physically accurate (vs DNS databases) models hard to converge (need for code friendly models!) Robustness required for RANS-LES coupling or industrial grids PhD topic: Improvement of the ( ) in Code_Saturne (Near wall eddy viscosity RANS model) PhD topic: Improvement of the ( ) in Code_Saturne (Near wall eddy viscosity RANS model)

3. Code_Saturne User Meeting 2009 Non linear (Pettersson Rief, 2006) Secondary flows (Pecnik and Iaccarino, 2008) Hybrid RANS/LES coupling  “Seamless hybrid” based on EB-RSM and PITM (Poitiers)  Manchester: based on Schumann’s decomposition Uribe et al. 2007 based on model … Stress-Strain Lag turbulence model (Revell et al., 2006) Synthetic eddy method (Jarrin et al., 2008) Recent extensions of further adaptations

4. Code_Saturne User Meeting 2009 Redistribution of Reynolds stresses due to incompressibility / kinematic wall blocking effect homogeneous behaviour near-wall behaviour SSG, LRR-IP, …

5. Code_Saturne User Meeting 2009 Elliptic equation K-Omega very important (non-local) diffusion

6. Code_Saturne User Meeting 2009 Durbin introduced the in 1991… In (industrial) segregated solvers: estimated at the first off- wall cell unstable In (industrial) segregated solvers: estimated at the first off- wall cell unstable robust… but strong overprediction of realisability violated … implemented in Code_Saturne in 2005 model less accurate ! stable … implemented in STAR-CD, STAR CCM+ in 2001

7. Code_Saturne User Meeting 2009 Use of the reduced variable for increased numerical robustness (as done for the ) Use of the elliptic blending (Manceau, 2002) for a non-dimensional coefficient Code friendly model Further work on the dissipation rate equation modelling BIL08 BIL09

8. Code_Saturne User Meeting 2009 “original” Durbin, 1991 “original” Durbin, 1991 RSM version Durbin, 1993 RSM version Durbin, 1993 Wizman et al. (1996) Durbin, 1993 Durbin, 1995 code-friendly models STANFORD Lien & Durbin, 1996 Lien & Kalitzin, 2001 STAR-CD, … STANFORD Lien & Durbin, 1996 Lien & Kalitzin, 2001 STAR-CD, … Lien et al. 1998 Elliptic blending EB-RSM Manceau, 2004 CODE SATURNE EB-RSM Manceau, 2004 CODE SATURNE rescaled Manceau et al., 2002 rescaled Manceau et al., 2002 rescaled RSM Manceau et al., 2002 rescaled RSM Manceau et al., 2002 elliptic relaxation revisited “neutral” operator Wizman et al, 1996 Manceau &Hanjalic, 2000 “neutral” operator Wizman et al, 1996 Manceau &Hanjalic, 2000 Billard, 2008 CODE SATURNE Billard, 2008 CODE SATURNE Davidson et al., 2003 MANCHESTER Uribe, 2006 CODE SATURNE MANCHESTER Uribe, 2006 CODE SATURNE TU DELFT Hanjalic & Popovac, 2004 TU DELFT Hanjalic & Popovac, 2004

9. Code_Saturne User Meeting 2009 Various near-wall modelling for dissipation, SSG or LRR- IP, code-friendly adaptation, time/length turbulent scale, constants Most of them calibrated on channel flow, nice profiles low/high Reynolds number

10. Code_Saturne User Meeting 2009 Near wall dissipation modelling Near wall dissipation modelling Log layer, high Reynolds Defect layer: It represents 80% on a linear scale Defect layer: It represents 80% on a linear scale

11. Code_Saturne User Meeting 2009 Durbin (1991), Durbin (1993) and Durbin (1996): non-conventional values for,, 0.33 – 0.36 Lien & Durbin (1996) and Billard (2009) correct representation of viscous/log layer separation (but damping function in Lien & Durbin (1996) ) Billard (2009): defect layer prediction (variable )

12. Code_Saturne User Meeting 2009 model: instead of Near wall balance of equation not satisfied Lien & Durbin (1996) and Lien & Kalitzin (2001): strong overshoot in the log/central region (neglected term in equation)

13. Code_Saturne User Meeting 2009 Need to “boost” dissipation between viscous & Log layer: usually, modification of many versions proposed predictions altered in other parts of the flow Billard et al. (2008): Billard et al. (2009): ”E term” reconsidered localized influence

14. Code_Saturne User Meeting 2009 (re)introducing the E term (Launder & Sharma, 1974) 2009 First introduced in … 1972 in Jones Launder: laminarization in accelerating BL classical near-wall terms modelling From the “Karman measure” 2008 Improved prediction of the near-wall region without deterioration of results elsewhere E term “adopted” in Manceau (2002) then abandoned for stability reasons E term in the k equation in 2009

15. Code_Saturne User Meeting 2009 Durbin (1995): The spreading rate of a shear layer is different in a free shear flow and in a wall bounded flow. It is a function of 1.55 (B.L.) 1.3 (free shear) but use of d so the idea was abandoned Proposed: Modification of in the defect layer Strong influence of the near wall tuning of active in a wall bounded flow with no influence on the log layer not active in D.I.T where log layer defect layer Budget of k eqn.

16. Code_Saturne User Meeting 2009 modification coefficient without with

17. Code_Saturne User Meeting 2009 Channel flow: Better separation between viscous sub-layer – log layer (low/high Reynolds versatility)

18. Code_Saturne User Meeting 2009 Combined natural and forced convection (Kasagi & Nishimura, 1997) Upward flow in a vertical channel Re*=150, Gr=9.6 10 5 Anisotropy enhancement in the buoyancy aiding side Simple gradient hypothesis for temperature turbulent transport

19. Code_Saturne User Meeting 2009 HOT COLD Very low value of k Very low value of k The BETTS cavity: a difficult case for the in Code_Saturne ?? Robustness = Near wall balance handled carefully (if possible implicitly) SST: (Fixed in 2008) (OK) Robustness = Near wall balance handled carefully (if possible implicitly) SST: (Fixed in 2008) (OK)

20. Code_Saturne User Meeting 2009 Forced, mixed and natural convection in a heated pipe (You, 2003) Turbulence impairment (relaminarization) k-omega SST: relaminarization missed (insensitive to low Reynolds effects needed?),, Lien & Durbin OK, but best convergence noticed with the model Collaboration with AIRBUS (Jeremy Benton). Validation of the on a turbulent flat plate Transonic RAE 2822 airfoil, better numerical properties reported with the compared with (95), or even k-omega SST! 3D Diffuser (Cherrye et al.) Re=1000

21. Code_Saturne User Meeting 2009 Forced, mixed and natural convection in a heated pipe (You, 2003) =0.63 (forced/mixed conv.),=0.87 (relaminarization), =2.41 (recovery) Near wall balance of small terms in,,, equation required

22. Code_Saturne User Meeting 2009 LES (Temmerman & Leschziner, 2001) Uribe, 2006 Menter, 1994 Manceau, 2004 Billard et al., 2008

23. Code_Saturne User Meeting 2009 Uribe, 2006 Menter, 1994 Billard et al., 2009

24. Code_Saturne User Meeting 2009 Improvement of the existing of Code_Saturne Old ideas (1972, …) adapted in a code friendly way Added modification are “localized” in regions of interest easier tuning No regression compared with the existing Elliptic blending: improved robustness + near wall term balance Applications of the Extensive validation (shared with ) Buoyancy induced relaminarization Industrial aeronautics applications (with AIRBUS) European Project ADVerse pressure gradient ANd Turbulence for the new AGE Aknowledgements: University of Manchester (School of MACE) British Energy