rans-les inlet boundary condition for aerodynamic...

Hybrid RANS-LES, Stockholm, 14-15 July,2005

RANSRANS--LES inlet boundary condition for LES inlet boundary condition for aerodynamic and aeroaerodynamic and aero--acoustic acoustic

applicationsapplications

Fabrice Mathey – Davor Cokljat

Fluent Inc.

Presented byFredrik CarlssonFluent Sweden


ZONAL MULTI-DOMAIN RANS/LES

Motivation / Challenge: accurate predictionof separated flows – acoustics – FSI

RANS LES

Enrichment procedure ?

RANS/LES interfaces ?

U


ZONAL MULTI-DOMAIN RANS/LES

Fluent 6.2: general purpose CFD solver

Enrichment procedure: LES Turbulent Inlet boundaryconditions: Vortex Method (Sergent 2002)

LES

Enrichment procedure


WALE Model (Nicoud, Ducros, 1999)

Wall-Adapting Local Eddy-Viscosity modelAlgebraic (0-equation) model – retains the simplicity of Smagorinsky’s model

The WALE SGS model adapts to local near-wall flow structure.• Wall damping effects are accounted for without using the

damping function explicitly.• Correct asymptotic behavior of νt

( ) ( )( ) ( )

3/ 22

5/ 45/ 2

d dij ij

SGS s d dij ij ij ij

S SC

S S S Sν = ∆

+


Numerics

• 2nd (O) Implicit time advancement scheme

• Non-Iterative Time-Advancement (NITA) schemesFractional-step method

Kim et al. (2002, Int. J. Numer. Meth. Fluids., 38)PISO (Non Iterative PISO)

• Spatial discretization: Momentum 2nd CD or BCD for complex geometriesEnergy, Species, Scalars: QUICK


Bounded Central DifferencingMotivation

Central differencing (CD) is an ideal (non-dissipative) scheme for LES due to its non-dissipative nature.Yet, CD often produces unphysical wiggles.• Aggravated by small physical

diffusivity with LES and coarse meshes

Unphysical wiggles from CD


Bounded Central DifferencingIdea of “Bounding”

Normalized variableFOU

fφ~

Cφ~1

1

SOU

CD

?=β

?

UD

U

φφφφ

φ−

−=

~

1−i i 1+i1+i

U C D

21

+i

f

( )* *1CD SOUf f fφ φ φ= Γ + − Γ% % %

Normalized-Variable Diagram (NVD)

Bounded Central Differencing (cont’d)

CD BCD



LES Inlet Boundary Conditions Turbulent Inlet Boundary conditions :

( ) ( ){

( )mean velcocity field turbulent fluctuations

, ,i i iu t U u t′= +x x x123

Precursor domain, recycling (Lund et al. 1998)

Realistic inlet turbulence

Cpu cost – not universal

Vortex Method (Sergent at al. 2002)

Spatial correlation – simple implementation


VORTEX METHOD

Based on Sergent (2003)

Consider the 2D vorticity transport equation:

A particle discretization (“vortex point” transported by the flow) is considered :

With Γ(k,ε) given by:

and η(k,ε):

With k,ε in the inlet plan, σ vortex size and S the inlet surface.

2( . )utω ω ν ω∂

+ ∇ = ∇∂

r

N

ii=1

ω( ,t)= ( )η( , )ix t x x tΓ −∑r r r

( )( , )( , ) 4

3 2ln(3) 3ln(2)iSk x yx y

NπΓ =

−

( )

2 2

2 22 22

1 2 12

x x

x e eσ σηπσ

− −⎛ ⎞⎜ ⎟= −⎜ ⎟⎜ ⎟⎝ ⎠

r r

r


VORTEX METHOD

Use Biot-Savart law for velocity field:

Local vortex size:

Characteristic time scale: τ ~ k / ε

Typical vortex number (200-300)

( ) ( )''

2'

( ) .12

x x x zu x dx

x x

ω

π

− ×= −

−∫∫

r r r rr r

r r

( )2 2

2 22 22

1

( )1 12

i ix x x xN

ii

i i

x x zu x e ex x

σ σ

π

− −− −

=

⎛ ⎞− × ⎜ ⎟= Γ −⎜ ⎟− ⎜ ⎟⎝ ⎠

∑r r r r

r r rr r

r r

3/ 2~ /kσ ε


Vortex Method:

U

for unstructured grid in fluent 6.2 (Mathey et al. 2003)

Periodic ref. Case Mellen et al. 2000Change periodic condition with VM and outflow

U

Computational Domain

Inlet + Vortex Method

Re=10595

Outflow

Validation: Vortex Method at Inlet




Random

Periodic

VMxrPeriodic 5. H VM 5.2 h Random 7.7 h

LES predictions of thereattachment point by differentmethods



Vortex Method SimulationVM Random Noise


25° Ahmed Body : challenging caseRANS simulation:• RANS predicted Fully attached/separated flow• Unsteady wake

LES simulation: • Hinterberger at al. 2004 :Fully separated flows - use of wall

functions - need to resolve boundary layers ?• Krajnovic et al. 2005: low RE

DES: (Kapadia & Roy, 2004)• Fully separated flow

Scattering in experimental results• Ahmed et al. (1984) / Lienhart & Becker (2003)


Zonal LES/RANS coupling: Ahmed Body

• RANS/LES: Two separate simulations Full RANS (V2F) 4 M cells(prism+tetra)Slant and Wake: LES (WALE) 1.6 M cells (hexa) + Vortex Method

RANS/LES interface:RANS profiles +VM

LES: WALE

RANS: V2F

Y+ ~1 to 5

Y+ ~1 to 5

Vortex Method & Two Steps Zonal Hybrid RANS/LES: Ahmed Body


Ahmed Body 25°: Challenging for RANSChallenging:

Separation / reattachment above the slantUnsteady wake

Expensive with full LES (high Re case)

Full RANS (V2F)


Vortex Method & Zonal Hybrid RANS/LES

Zonal LES/RANS coupling : Ahmed Body 25°

Zonal LES/RANS: Ahmed Body




Ahmed Body Slant

250

270

290

310

330

350

370

390

410

430

450

U

y (m

m)

250

270

290

310

330

350

370

390

410

430

450

U rms

y (m

m)


0,00E+00

5,00E+01

1,00E+02

1,50E+02

2,00E+02

2,50E+02

3,00E+02

3,50E+02

4,00E+02

4,50E+02

5,00E+02

u-rms

y (m

m)

0

50

100

150

200

250

300

350

400

450

500

U

y (m

m)

Ahmed Body Wake


Ahmed Body Slant

RANS

RANS/LES

RANSLES



TABLE 1: DRAG FORCE AND FORCE COMPONENT

RANS LES/RANS Exp(Ahmed)

Exp(Lienhart et al.)

Cs 0.144 0.16 0.145 0.158

Cb 0.12 0.098 0.077 0.116

Cf 0.01 0.02

Cd 0.364 0.285



Zonal LES/RANS coupling: Ahmed Body


Conclusion & future work: Embedded LES

• RANS/LES interface conditions:

Virtual body force in Filtered NS equations to drive the velocityField to perturbed velocity fieldwith the VM enrichmentprocedure

• LES/RANS interface:

• k,ε boundary conditions basedon correlations ?• Quéméré & sagaut (2004)

« LES box »

« RANS domain»

Airfoil

RANS/LES

LES/RANS


Embedded LES: Trailing Edge Acoustics Prediction

RANS: attached boundary layers

LES box: acoustics sourceTrailing Edge Noise Prediction - ReC =1.85 106

Exp. Data from C. Kunze (2004) University of Notre Dame

U Ffowcs Williams: radiated sound

δs


RANS/LES coupling

Mesh: 1.5 M cells

RANS/LES Non conformal interfaces


RANS/LES coupling

LESRANS/LES coupling

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-5 -3 -1 1 3 5

0

0.05

0.1

0.15

0.2

0.25

-5 -4 -3 -2 -1 0 1 2 3 4 5

RANS

-7

-5

-3

-1

1

3

5

7

0 0.2 0.4 0.6 0.8 1 1.2

Um

urmsUm


rans-les inlet boundary condition for aerodynamic...

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