1 Progress on the v2f model with Code_Saturne EDF - Manchester meeting 18-19th May 2009

EDF-Manchester meeting 18-19th May The model and Code_Saturne A low-Reynolds (near-wall integration) eddy viscosity model derived from second moment closure models No damping functions, no wall functions, less empirical assumptions Best results on range of test cases, heat transfer and natural convection in particular. The original model is stiff (requires coupled solver or very small time-step) Degraded version available in StarCD, Fluent, NUMECA.. Long collaboration Stanford, Delft, Chatou, Manchester (Durbin, Parneix, Hanjalic, Manceau, Uribe) => “several code friendly” versions since Present: Reconsider all historical choices with numerical stability and known asymptotic states as principal objectives Accuracy Robustness Stanford 1991 TU-Delft 2004 Manchester 2004 Stanford 1996 (Fluent, STAR-CD)

EDF-Manchester meeting 18-19th May 2009 Starting from the model Uribe (2006), Laurence et al. (2004), available in CS ( ITURB=50 ) Same overall good perfomances as the original But lack of compliance with asymptotic behaviour requirement. No - diffusion for (does not « feel » its B.C.) instead of Problems reported: Near wall overshooting of HOT COLD Very low value of k Betts Cavity

EDF-Manchester meeting 18-19th May 2009 Improved code friendly version Elliptic blending Unlike, correct near wall behaviour of, hence No over prediction of the in the core region, unlike Lien and Durbin model with Only a few sub-iterations needed to converge More robust (B.C. 0)

EDF-Manchester meeting 18-19th May 2009 Prediction of weak turbulence Case 1: Forced, mixed and natural convection in a heated pipe (You et al. (2003)). Re*= : Forced/mixed convection 0.241: Relaminarisation 0.400: Recovery

EDF-Manchester meeting 18-19th May 2009 Prediction of weak turbulence Case 2: Combined natural and forced convection (Kasagi and Nishimura (1997)) Re*=150, Gr= Upward flow in a vertical channel Turbulent anisotropy enhancement in the buoyancy aiding side

EDF-Manchester meeting 18-19th May 2009 Improved prediction of by-pass transition Near wall adaptation of the equation (near wall terms) Usual modelling (also used in the ): Launder Sharma model (1974). E term: models the term P3 of the exact equation. Howard (2004), application to a skewed channel Latest version of the : E term in the equation : more robust could be added as well.

EDF-Manchester meeting 18-19th May 2009 Results on the T3A flat plate

EDF-Manchester meeting 18-19th May 2009 Improvement for High/Low RE Variables like U, or YdUdY are in fact weakly Reynolds dependant But near wall extra terms are generally Re- dependant

EDF-Manchester meeting 18-19th May 2009 Improvement for High/Low Re

EDF-Manchester meeting 18-19th May 2009 Improvement for High/Low Re 2008 version : near wall tem in the Ep. equation 2008 version : near wall tem in the K equation

EDF-Manchester meeting 18-19th May 2009 Improvement for High/Low Re channel flow

EDF-Manchester meeting 18-19th May 2009 Application on RAE2822 aerofoil Collaboration with Jeremy Benton (AIRBUS). Prelimiary tests on a turbulent boundary layer ( up to 5368): Cf overprediction reported with the 2008 and the, problem cured with the latest version. Two cases: case 9 (attached) and case 10 (separated). model tested with a non-linear stress-strain relationship (Pettersson-Reif, 2006) and in an Algebraic Structure based model (Kassinos) Numerical stability reported to be better than the SST model and the

EDF-Manchester meeting 18-19th May 2009 Results, Cp, case 9 (attached) COURTESY OF AIRBUS

EDF-Manchester meeting 18-19th May 2009 Results, Cf, upper surface, case 9 COURTESY OF AIRBUS

EDF-Manchester meeting 18-19th May 2009 Results, Cp, case 10 (separated) COURTESY OF AIRBUS

EDF-Manchester meeting 18-19th May 2009 Results, Cf, upper surface, case 10 COURTESY OF AIRBUS