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

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Progress on the v2f model with Code_Saturne

EDF - Manchester meeting

18-19th May 2009

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EDF-Manchester meeting18-19th May 2009

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 1995.

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)

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v 2 − f




Starting from the model

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ϕ − f

•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:

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v 2 − f

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ν

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ϕ

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ϕ SATURNE = O(y)

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O(y 2)

Near wall overshooting of

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ϕHOT COLD

Very low value of k

Very low value of k

Betts Cavity

ϕνϕν 22∇+∇∇+= k

kff




Improved code friendly version

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ϕ −αElliptic blending

•Unlike , correct near wall behaviour of , hence

•No over prediction of the in the core region, unlike Lien and Durbin model

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ϕ − f

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v 2

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ν t

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v 2€

α =1+ L2Δα with

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αw = 0•Only a few sub-iterations needed to converge

•More robust (B.C. 0)




Prediction of weak turbulence

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Gr /Re2

Case 1: Forced, mixed and natural convection in a heated pipe (You et al. (2003)). Re*=180.

•0.087: Forced/mixed convection

•0.241: Relaminarisation

•0.400: Recovery




Prediction of weak turbulenceCase 2: Combined natural and forced convection (Kasagi

and Nishimura (1997)) Re*=150, Gr=9.6 105

•Upward flow in a vertical channel

•Turbulent anisotropy enhancement in the buoyancy aiding side




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

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ε

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Cε1 =1.4 1+1

30

1

ϕ

⎛

⎝ ⎜

⎞

⎠ ⎟

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ϕ − f

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ϕ −α

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k

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ε

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∂v 2

∂y

∂U

∂y

∂ 2U

∂y 2 could be added as well.




Results on the T3A flat plate




Improvement for High/Low REVariables like U, or YdUdY are in

fact weakly Reynolds dependant

But near wall extra terms are generally Re-

dependant




Improvement for High/Low Re





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Dε

Dt=

Cε1P − Cε 2ε

T+ Diffν +ν t

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Cε1 =1.4 1+ CA1

1

ϕ

⎛

⎝ ⎜

⎞

⎠ ⎟

2008 version : near wall tem in the Ep. equation

2008 version : near wall tem in the K equation





channel flow




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)

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ϕ −α

•Numerical stability reported to be better than the SST model and the

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ϕ − f

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Reτ ,δ

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ϕ − f

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ϕ −α




Results, Cp, case 9 (attached)

COURTESY OF AIRBUS




Results, Cf, upper surface, case 9

COURTESY OF AIRBUS




Results, Cp, case 10 (separated)

COURTESY OF AIRBUS




Results, Cf, upper surface, case 10

COURTESY OF AIRBUS

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

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