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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
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EDF-Manchester meeting18-19th May 2009
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
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EDF-Manchester meeting18-19th May 2009
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)
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EDF-Manchester meeting18-19th May 2009
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
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EDF-Manchester meeting18-19th May 2009
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
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EDF-Manchester meeting18-19th 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
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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.
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EDF-Manchester meeting18-19th May 2009
Results on the T3A flat plate
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EDF-Manchester meeting18-19th May 2009
Improvement for High/Low REVariables like U, or YdUdY are in
fact weakly Reynolds dependant
But near wall extra terms are generally Re-
dependant
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EDF-Manchester meeting18-19th May 2009
Improvement for High/Low Re
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EDF-Manchester meeting18-19th May 2009
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
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EDF-Manchester meeting18-19th May 2009
Improvement for High/Low Re
channel flow
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EDF-Manchester meeting18-19th 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.
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•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
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EDF-Manchester meeting18-19th May 2009
Results, Cp, case 9 (attached)
COURTESY OF AIRBUS
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EDF-Manchester meeting18-19th May 2009
Results, Cf, upper surface, case 9
COURTESY OF AIRBUS
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EDF-Manchester meeting18-19th May 2009
Results, Cp, case 10 (separated)
COURTESY OF AIRBUS
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EDF-Manchester meeting18-19th May 2009
Results, Cf, upper surface, case 10
COURTESY OF AIRBUS