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School of Mechanical, Aerospace & Civil Engineering (MACE) The University of Manchester

CODE_SATURNE USER MEETING DECEMBER 7-8, 2009. A robust, predictive and physically accurate eddy viscosity model for near wall effects. Flavien Billard. School of Mechanical, Aerospace & Civil Engineering (MACE) The University of Manchester Manchester M60 1QD www.CFDtm.org. Introduction.

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School of Mechanical, Aerospace & Civil Engineering (MACE) The University of Manchester

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  1. CODE_SATURNE USER MEETING DECEMBER 7-8, 2009 A robust, predictive and physically accurate eddy viscosity model for near wall effects FlavienBillard School of Mechanical, Aerospace & Civil Engineering (MACE) The University of Manchester Manchester M60 1QD www.CFDtm.org

  2. Introduction PhD topic: Improvement of the ( ) in Code_Saturne (Near wall eddy viscosity RANS model) • 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

  3. The non-local effects Redistribution of Reynolds stresses due to incompressibility / kinematic wall blocking effect W A L L near-wall behaviour homogeneous behaviour SSG, LRR-IP, …

  4. Modelling near-wall damping K-Omega very important (non-local) diffusion Elliptic equation

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

  6. The model • 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

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

  8. 1991-2008 : 13+ versions of the 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

  9. Universal Log layer view (1/2) (velocity gradient) Near wall dissipation modelling Log layer, high Reynolds Defect layer: It represents 80% on a linear scale

  10. Universal Log layer view (2/2) Billard (2009): defect layer prediction (variable ) Lien & Durbin (1996) and Billard (2009) correct representation of viscous/log layer separation (but damping function in Lien & Durbin (1996) ) Durbin (1991), Durbin (1993) and Durbin (1996): non-conventional values for , , 0.33 – 0.36

  11. Predictions of v2 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)

  12. Near-wall adaptation of the dissipation equation 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

  13. Why the E term? First introduced in … 1972 in Jones Launder: laminarization in accelerating BL From the “Karman measure” 2009 2008 (re)introducing the E term (Launder & Sharma, 1974) classical near-wall terms modelling 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

  14. Modification of the coefficient 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.) but use of d so the idea was abandoned 1.3 (free shear) Budget of k eqn. Strong influence of the near wall tuning of Proposed: Modification of in the defect layer log layer defect layer active in a wall bounded flow with no influence on the log layer not active in D.I.T where

  15. Illustration on channel flow without modification coefficient with

  16. Preliminary validation Channel flow: Better separation between viscous sub-layer – log layer (low/high Reynolds versatility)

  17. Vertical heated channel • Combined natural and forced convection (Kasagi & Nishimura, 1997) • Upward flow in a vertical channel • Re*=150, Gr=9.6 105 • Anisotropy enhancement in the buoyancy aiding side • Simple gradient hypothesis for temperature turbulent transport

  18. Improved robustness (1/2) The BETTS cavity: a difficult case for the in Code_Saturne ?? Very low value of k HOT COLD • Robustness = Near wall balance handled carefully (if possible implicitly) • SST: • (Fixed in 2008) • (OK) Very low value of k

  19. Improved robustness (2/2) • 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

  20. Pressure induced separation (1/2) 2D periodic hill LES (Temmerman & Leschziner, 2001) Manceau, 2004 Billard et al., 2008 Uribe, 2006 Menter, 1994

  21. Pressure induced separation (2/2) Asymmetric plane diffuser Billard et al., 2009 Uribe, 2006 Menter, 1994

  22. Conclusion • 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

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