Development and Application of SST-SAS Turbulence Model in the ...

Development and Application of SST-SAS 

Turbulence Model in the DESIDER Project 

Y. Egorov, F. Menter 

ANSYS Germany 

yury.egorov@ansys.com 

© 2007 ANSYS, Inc. All rights reserved. 1 ANSYS, Inc. Proprietary

Outline 

• Scale-Adaptive Simulation (SAS) concept 

• SST-SAS turbulence model 

• Aerodynamic applications 

– NACA0021 airfoil beyond stall 

– Delta wing 

– Full aircraft configuration 

– 3-D acoustic cavity 


SAS concept 

• URANS: unphysical single mode 

unsteady behaviour 

• LES: too expensive 

• DES: 

– 1 st industrial model of high Re 

flows with LES content 

– Explicit mix of RANS & LES → 

grid sensitivity 

• SAS: provides URANS with LES 

content in unsteady regions 

URANS 

SAS-URANS 


SAS concept. Turbulence scales 

• Two scales required for statistical description 

L, T 

• Two equations 

→ two scales? 

E(k) spectrum 


SAS concept. 2-eq RANS models 

• k-ω model 

• One local scale: S 

• 2 nd scale: 

Dk 

Dt 

ω 

Dt 

– Shear layer thickness via diffusion: L = κ·y , L = δ 

– Too dissipative to resolve the energy cascade 

– Homogeneous turbulence, 

frozen LES velocity field: 

No diffusion → Contradiction: 

( 2 2 

S − c ω ) + Diff ( k) 

= νt 

µ 

D 2 2 

− βω 

( ω) 

© 2007 ANSYS, Inc. All rights reserved. 5 ANSYS, Inc. Proprietary 

= 

α 

S 

S 

α S 

2 

2 

+ 

Diff 

= cµ 

ω 

2 

= βω 

2

SAS concept. v.Karman length scale 

• Rotta’s transport eq. for spatial correlation-based L 

• 2 nd scale from ∂ 2 U/∂y 2 → von Karman length scale 

• New RANS model for k and 

DΦ 

Dt 

= 

Φ 

k 

P 

⎡ 

× ⎢ζ 

⎢⎣ 

k L 

• Two natural local scales: S and L vK 

− 

ζ 

⎛ 

⎜ 

⎝ 

L 

L 


Φ 

⎞ 

⎟ 

⎠ 

⎤ 

⎥ 

⎥⎦ 

= 

− 

ζ 

k 1 2 

3 

vK 

Pk t 

vK 

2 

= ν S , L = κ S ∇ 

2 

k 

2 

U 

+ 

Diff 

( Φ)

SAS concept. SAS and RANS 

• 

⎛ 2 ⋅ ⎞ 

U ( y) 

= U ⎜ ⎟ , λ - natural scale, ignored by 

0 sin 

⎝ λ ⎠ 

RANS 

• Two 

domains: 

δ = 4λ 

δ = 8λ 

• RANS: 

L ~ δ 

• SAS: 

L ~ λ 

π y 

SAS 

RANS 


SAS concept. SAS and DES 

• DES enforces LES-behaviour via explicit grid influence 

• SAS detects resolved structures and adjusts accordingly 

DES: RANS LES based on ∆ 

SAS: RANS “LES” based on L vK 


SAS concept definition 

• SAS: 2 nd flow scale in the source terms 

typically via 2 nd velocity derivative 

• Requirements: 

– Proper RANS performance in stable 

flow region 

– Break-up of large unsteady structures 

into a turbulent spectrum 

– Proper energy dissipation at small 

scale (high wave number damping) 

No grid & 

time step 

dependence 

Based on 

the grid 

spacing ∆ 


SST-SAS turbulence model 

Q 

• Experimental k-Φ model 

• Transformation to k-ω → SST-SAS model 

Dk 

Dt 

Dω 

Dt 


= 

( 2 2 

S − c ω ) + Diff ( k) 

= νt 

µ 

= 

α 

S 

2 

− βω 

2 

+ 

Q 


+ 

Diff 

( ω) 

2⋅ 

σ 

( 1− 

F ) 

∇k∇ω 


+ 

Standard SST 

2 

2 

⎡ 

⎛ 

2⎛ 

L ⎞ 2k 

⎢ 

⎜ 

∇ω 

∇k 

max ζ κ − ⋅ 

⎢ 

⎜ 

⎟ 

2 S C max , 2 2 

σ ⎜ 

⎣ ⎝ LvK 

⎠ 

Φ ⎝ 

ω k 

ω2 

ω 

2 

⎞ ⎤ 

⎟ , 0⎥ 

⎟ 

⎠ ⎥ 

⎦

SST-SAS turbulence model 

• Decay of isotropic turbulence 

High wave number 

damping in SAS: 

- off 

- on 

- LES 


NACA0021 airfoil beyond stall 

• NACA0021 at 60°AoA, experiment by Swalwell at al., 2003 

• Re = 2.7·10 5 , low Mach number, domain span-size 4 chords 

• O-grid: courtesy of NTS, Russia, 1.9 million elements, y + ≈ 1 

Contours of L / ∆ ∈ [0, 0.5] 

Isosurface of 

Q = Ω 2 - S 2 


NACA0021 airfoil beyond stall 

• Mean values and 

PSD spectra of forces 

SST-SAS 

Experiment 

-Cp 

2.5 

2 

1.5 

1 

0.5 

0 

-0.5 

-1 

-1.5 

Mean pressure 

-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 

x/c 

C L 

0.915 

0.931 

SST-SAS 

Experiment 

C D 

1.484 

1.517 


Delta wing 

• Sweep angle 76°, 

experiment by 

Laschka et al., 1995 

• AoA = 35°, 

Re = 1.07·10 6 , 

low Mach number 



• Hybrid unstructured grid, 50 million elements, y + ≈ 0.5 

– Courtesy of EADS Deutschland GmbH, Military Air Systems 



• Delayed bursting of vortices predicted: numerical diffusion? 

L / ∆ 

Exp. SST-SAS 

Mean Cp 


Full aircraft configuration 

• Delta-canard FA-5, exp. by Laschka et al., 1995 

• AoA = 15°, Re = 2.78·10 6 , low Mach number 

• Hybrid unstructured grid, 36 million elements, y + ≈ 0.8 

– Courtesy of EADS 

Deutschland GmbH, 

Military Air Systems 

– Half of the airplane, 

symmetry BC 



• SAS vs. URANS 



• Resolution details 

L / ∆ 



• Cross planes at x/c = 0.2, 0.4, 0.6, 0.8, 1 

U/U 0 

Experiment SST-SAS 

Resolved+Modelled TKE/U 0 2 

Experiment SST-SAS 


3-D acoustic cavity 

• M219 test cavity, exp. by QinetiQ, Henshaw, 2000 

• Shallow cavity: Length×Width×Depth = 5×1×1, 1=4" 

• Re D = 1.37·10 6 , M ∞=0.85 – local transonic zones 

• Coarse grid, 

1.1 million elements 

• 90 ∆t per convective unit 

• 100 units run 

for statistics 


3-D acoustic cavity 

• Resolved turbulent structures 

• Pressure spectrum at cavity bottom near the 

downstream wall (K29) 

PSD of p 

1.E+07 

1.E+06 

1.E+05 

1.E+04 

1.E+03 

1.E+02 

0 200 400 600 800 1000 


f, Hz 

Experiment 

SST SAS

Other DESIDER tests simulated 

• Bump in a duct, 

experiment by ONERA 

• Generic car mirror, 

exp. by Höld et al., 1999

Development and Application of SST-SAS Turbulence Model in the ...

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