Post on 11-Jan-2016
description
Code_SaturneUser Meeting2009
School of Mechanical, Aerospace & Civil Engineering (MACE)The University of Manchester
Manchester M60 1QDwww.CFDtm.org
A robust, predictive and physically accurate eddy A robust, predictive and physically accurate eddy viscosity model for near wall effectsviscosity model for near wall effects
Code_SaturneUser Meeting2009
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)
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v 2 − f
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ϕ − f
Code_SaturneUser Meeting2009
Redistribution of Reynolds stresses due to
incompressibility / kinematic wall blocking effect
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u2
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u2€
v 2
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v 2
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w2€
w2
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u2
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u2
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w2
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w2
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v 2
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v 2
homogeneous behaviour
near-wall behaviour
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v 2 = O(y 4 )
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u2 = w2 = O(y 2)
SSG, LRR-IP, …
Code_SaturneUser Meeting2009
Elliptic equation
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Classic near wall model
ν t = fμ Cμ k T ; T = k /ε
fμ =ν t you want
ν t you have
fμ = f (y +,ν t /ν )
K-Omega
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ω =O1
y 2
⎛
⎝ ⎜
⎞
⎠ ⎟
very important
(non-local)diffusion
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Elliptic Relaxation
ν t = Cμ v 2 T
Dv 2
Dt= φ22 −ε22 +∇((ν +ν t )∇v 2)
φ22 = −2
ρv ∂p' /∂y
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φ22
k− L2Δ
φ22
k=
φ22h
k
Code_SaturneUser Meeting2009
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v 2 − f
Durbin introduced the in 1991…
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v 2 − f
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v 2 = O(y 4 )
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fw ∝v 2
k 2
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
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
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v 2realisability violatedrealisability violated
… implemented in Code_Saturne in 2005
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v 2 = O(y 3)
model less accurate !model less accurate !
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ϕ =v 2
k
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fw = 0
stable
… implemented in STAR-CD, STAR CCM+ in 2001
Code_SaturneUser Meeting2009
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ϕ −α
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ϕ
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ϕ − f
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α −L2Δα =1
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φ22 = (1−α 3)φ22WALL + α 3φ22
HOM .
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ε22 = (1−α 3)ε22WALL + α 3ε22
HOM .
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αWALL = 0
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ϕ −α 2008 BIL08
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ϕ −α 2009 BIL09
Code_SaturneUser Meeting2009
“original” Durbin, 1991
“original” Durbin, 1991
RSM versionDurbin, 1993RSM versionDurbin, 1993
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v 2 − fWizman et al. (1996)Wizman et al. (1996)Durbin, 1993Durbin, 1993
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Cε1 = f P /ε, A( )
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Cε1 = f P /ε( )
Durbin, 1995Durbin, 1995
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Cε1 = f d /L( )
code-friendly models
STANFORDLien & Durbin, 1996Lien & Kalitzin, 2001
STAR-CD, …
STANFORDLien & Durbin, 1996Lien & Kalitzin, 2001
STAR-CD, …
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fw = 0
Lien et al. 1998Lien et al. 1998
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Cε 2 = f k 2 /εν( )
Elliptic blending
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α −L2Δα =1 with α w = 0
EB-RSMManceau, 2004
CODE SATURNE
EB-RSMManceau, 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
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v 2 − f
elliptic relaxation revisited
“neutral” operator
Wizman et al, 1996Manceau &Hanjalic,
2000
“neutral” operator
Wizman et al, 1996Manceau &Hanjalic,
2000
Billard, 2008CODE
SATURNE
Billard, 2008CODE
SATURNE
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ϕ −α
Davidson et al., 2003Davidson et al., 2003
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ν t,⊥ and ν t ,//
MANCHESTERUribe, 2006
CODE SATURNE
MANCHESTERUribe, 2006
CODE SATURNE
TU DELFTHanjalic & Popovac,
2004
TU DELFTHanjalic & Popovac,
2004
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ϕ =v 2
k
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ϕ − f
Code_SaturneUser Meeting2009
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v 2 − f
Various near-wall modelling for dissipation, SSG or LRR-IP, code-friendly adaptation, time/length turbulent scale,
constants
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
Most of them calibrated on channel flow, nice profiles low/high Reynolds
number
Code_SaturneUser Meeting2009
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Y + dU +
dY +
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U +
Near wall dissipationmodelling
Near wall dissipationmodelling
Log layer, high Reynolds
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κ 2 = Cμϕ Cε 2 − Cε1( )σ ε
Defect layer:It represents
80% on a linear scale
Defect layer:It represents
80% on a linear scale
Code_SaturneUser Meeting2009
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Cε1
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Cε 2
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σε
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κ =
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 )
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Cε 2
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Y + dU +
dY +
Code_SaturneUser Meeting2009
model: instead of Near wall balance of equation not satisfied
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ϕ − f
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ϕ =O(y)
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O(y 2)
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ϕ
Lien & Durbin (1996) and Lien & Kalitzin (2001): strong overshoot in the log/central region (neglected term in equation)
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f
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ϕ =v 2
k
Code_SaturneUser Meeting2009
Need to “boost” dissipation between viscous & Log layer: usually, modification of
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Cε1
• many versions proposed
• predictions altered in other parts of the flow
• Billard et al. (2008):
• Billard et al. (2009):”E term” reconsidered€
×(1−α 3) localized influence
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2νν t
∂ 2U
∂y 2
⎛
⎝ ⎜
⎞
⎠ ⎟
2
Code_SaturneUser Meeting2009
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... + 2Cε 3νν t
∂ 2U i
∂xk∂xk
⎛
⎝ ⎜
⎞
⎠ ⎟
2
T
(re)introducing the E term(Launder & Sharma, 1974)
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ϕ −α 2009
First introduced in … 1972 in Jones Launder: laminarization in accelerating BL
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Cε1 =1.44 1+ CA1(1−α 3)1
ϕ
⎛
⎝ ⎜
⎞
⎠ ⎟
classical near-wall terms modelling
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y + dU +
dy += f (y +)
From the “Karman measure”
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ϕ −α 2008
Improved prediction of the near-wall region without deterioration of results elsewhereE term “adopted” in Manceau (2002) then abandoned for stability reasons
E term in the k equation in 2009
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ϕ −α
Code_SaturneUser Meeting2009
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Cε 2
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
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Cε 2 −1
Cε1 −1
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Cε1 =1.3+0.25
1+d
2L
⎛
⎝ ⎜
⎞
⎠ ⎟8
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Cε1
1.55 (B.L.)
1.3 (free shear)
but use of d so the idea was abandoned
Proposed: Modification of in the defect layer
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Cε 2
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ε€
Pk
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DT
Strong influence of the near wall tuning of
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Cε1
active in a wall bounded flow with no influence on the log layer
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Cε 2* = Cε 2 1−
1
2tanh
DT
ε
⎛
⎝ ⎜
⎞
⎠ ⎟
⎡
⎣ ⎢
⎤
⎦ ⎥
not active in D.I.T where
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DT = 0
log layerlog layer defect layerdefect layer
Budget of k eqn.
Code_SaturneUser Meeting2009
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ν t+
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U +
modification coefficient
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Cε 2
without
with
Code_SaturneUser Meeting2009
Channel flow: Better separation between viscous sub-layer – log layer (low/high Reynolds versatility)
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U +
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Y +
Code_SaturneUser Meeting2009
Combined natural and forced convection (Kasagi & Nishimura, 1997)Upward flow in a vertical channelRe*=150, Gr=9.6 105
Anisotropy enhancement in the buoyancy aiding sideSimple gradient hypothesis for temperature turbulent transport
Code_SaturneUser Meeting2009
HOTCOLD
Very low value of k
Very low value of k
The BETTS cavity: a difficult case for the in Code_Saturne ??
The BETTS cavity: a difficult case for the in Code_Saturne ??
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v 2 − f
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Ra = 0.86 ×106
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)€
Dω
Dt= ...− βω2
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ϕ − f
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ϕ −α
Code_SaturneUser Meeting2009
•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
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f (Re t )
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ϕ − f
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ϕ −α
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v 2 − f
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ϕ −α
•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!
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ϕ −α
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v 2 − f
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ϕ −α
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ϕ − f
•3D Diffuser (Cherrye et al.) Re=1000
Code_SaturneUser Meeting2009
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Reh ≈10600
LES(Temmerman &Leschziner, 2001)
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ϕ − fUribe, 2006
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k −ω SSTMenter, 1994
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Rij −α (EBRSM)Manceau, 2004
Billard et al., 2008
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ϕ −α
Code_SaturneUser Meeting2009
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Reh ≈ 20000
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ϕ − fUribe, 2006
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k −ω SSTMenter, 1994
Billard et al., 2009
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ϕ −α
Code_SaturneUser Meeting2009•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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ϕ − f
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ϕ − f
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ϕ − f
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ϕ −α