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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
Hybrid RANS-LES, Stockholm, 14-15 July,2005
ZONAL MULTI-DOMAIN RANS/LES
Motivation / Challenge: accurate predictionof separated flows – acoustics – FSI
RANS LES
Enrichment procedure ?
RANS/LES interfaces ?
U
Hybrid RANS-LES, Stockholm, 14-15 July,2005
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
Hybrid RANS-LES, Stockholm, 14-15 July,2005
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 = ∆
+
Hybrid RANS-LES, Stockholm, 14-15 July,2005
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
Hybrid RANS-LES, Stockholm, 14-15 July,2005
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
Hybrid RANS-LES, Stockholm, 14-15 July,2005
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)
Hybrid RANS-LES, Stockholm, 14-15 July,2005
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
Hybrid RANS-LES, Stockholm, 14-15 July,2005
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
Hybrid RANS-LES, Stockholm, 14-15 July,2005
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
Hybrid RANS-LES, Stockholm, 14-15 July,2005
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
Hybrid RANS-LES, Stockholm, 14-15 July,2005
Hybrid RANS-LES, Stockholm, 14-15 July,2005
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
Random
Periodic
VMxrPeriodic 5. H VM 5.2 h Random 7.7 h
LES predictions of thereattachment point by differentmethods
Validation: Vortex Method at Inlet
Hybrid RANS-LES, Stockholm, 14-15 July,2005
Hybrid RANS-LES, Stockholm, 14-15 July,2005
Validation: Vortex Method at Inlet
Vortex Method SimulationVM Random Noise
Hybrid RANS-LES, Stockholm, 14-15 July,2005
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)
Hybrid RANS-LES, Stockholm, 14-15 July,2005
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
Hybrid RANS-LES, Stockholm, 14-15 July,2005
Ahmed Body 25°: Challenging for RANSChallenging:
Separation / reattachment above the slantUnsteady wake
Expensive with full LES (high Re case)
Full RANS (V2F)
Hybrid RANS-LES, Stockholm, 14-15 July,2005
Vortex Method & Zonal Hybrid RANS/LES
Zonal LES/RANS coupling : Ahmed Body 25°
Zonal LES/RANS: Ahmed Body
Vortex Method & Zonal Hybrid RANS/LES
Hybrid RANS-LES, Stockholm, 14-15 July,2005
Hybrid RANS-LES, Stockholm, 14-15 July,2005
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)
Hybrid RANS-LES, Stockholm, 14-15 July,2005
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
Hybrid RANS-LES, Stockholm, 14-15 July,2005
Vortex Method & Zonal Hybrid RANS/LES
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
Hybrid RANS-LES, Stockholm, 14-15 July,2005
Vortex Method & Zonal Hybrid RANS/LES
Zonal LES/RANS coupling: Ahmed Body
Hybrid RANS-LES, Stockholm, 14-15 July,2005
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
Hybrid RANS-LES, Stockholm, 14-15 July,2005
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
Hybrid RANS-LES, Stockholm, 14-15 July,2005
RANS/LES coupling
Mesh: 1.5 M cells
RANS/LES Non conformal interfaces