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

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


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)

€

v 2 − f

€

ϕ − f


Redistribution of Reynolds stresses due to

incompressibility / kinematic wall blocking effect

€

u2

€

u2€

v 2

€

v 2

€

w2€

w2

€

u2

€

u2

€

w2

€

w2

€

v 2

€

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, …


Elliptic equation

€

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

€

ω =O1

y 2

⎛

⎝ ⎜

⎞

⎠ ⎟

very important

(non-local)diffusion

€

Elliptic Relaxation

ν t = Cμ v 2 T

Dv 2

Dt= φ22 −ε22 +∇((ν +ν t )∇v 2)

φ22 = −2

ρv ∂p' /∂y

€

φ22

k− L2Δ

φ22

k=

φ22h

k


€

v 2 − f

Durbin introduced the in 1991…

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v 2 − f

€

v 2 = O(y 4 )

€

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

€

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

€

fw = 0

stable

… implemented in STAR-CD, STAR CCM+ in 2001


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ϕ −α

€

ϕ

€

ϕ − f

€

α −L2Δα =1

€

φ22 = (1−α 3)φ22WALL + α 3φ22

HOM .

€

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


“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

€

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

€

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

€

ϕ =v 2

k

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ϕ − f


€

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


€

Y + dU +

dY +

€

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


€

Cε1

€

Cε 2

€

σε

€

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

€

Y + dU +

dY +


model: instead of Near wall balance of equation not satisfied

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ϕ − f

€

ϕ =O(y)

€

O(y 2)

€

ϕ

Lien & Durbin (1996) and Lien & Kalitzin (2001): strong overshoot in the log/central region (neglected term in equation)

€

f

€

ϕ =v 2

k


Need to “boost” dissipation between viscous & Log layer: usually, modification of

€

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

€

2νν t

∂ 2U

∂y 2

⎛

⎝ ⎜

⎞

⎠ ⎟

2


€

... + 2Cε 3νν t

∂ 2U i

∂xk∂xk

⎛

⎝ ⎜

⎞

⎠ ⎟

2

T

(re)introducing the E term(Launder & Sharma, 1974)

€

ϕ −α 2009

First introduced in … 1972 in Jones Launder: laminarization in accelerating BL

€

Cε1 =1.44 1+ CA1(1−α 3)1

ϕ

⎛

⎝ ⎜

⎞

⎠ ⎟

classical near-wall terms modelling

€

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


€

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

€

Cε 2 −1

Cε1 −1

€

Cε1 =1.3+0.25

1+d

2L

⎛

⎝ ⎜

⎞

⎠ ⎟8

€

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

€

Cε 2

€

ε€

Pk

€

DT

Strong influence of the near wall tuning of

€

Cε1

active in a wall bounded flow with no influence on the log layer

€

Cε 2* = Cε 2 1−

1

2tanh

DT

ε

⎛

⎝ ⎜

⎞

⎠ ⎟

⎡

⎣ ⎢

⎤

⎦ ⎥

not active in D.I.T where

€

DT = 0

log layerlog layer defect layerdefect layer

Budget of k eqn.


€

ν t+

€

U +

modification coefficient

€

Cε 2

without

with


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

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U +

€

Y +


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


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

€

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

€

ϕ − f

€

ϕ −α


•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 )

€

ϕ − f

€

ϕ −α

€

v 2 − f

€

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!

€

ϕ −α

€

v 2 − f

€

ϕ −α

€

ϕ − f

•3D Diffuser (Cherrye et al.) Re=1000


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Reh ≈10600

LES(Temmerman &Leschziner, 2001)

€

ϕ − fUribe, 2006

€

k −ω SSTMenter, 1994

€

Rij −α (EBRSM)Manceau, 2004

Billard et al., 2008

€

ϕ −α


€

Reh ≈ 20000

€

ϕ − fUribe, 2006

€

k −ω SSTMenter, 1994

Billard et al., 2009

€

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

€

ϕ − f

€

ϕ − f

€

ϕ − f

€

ϕ −α

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