Development and Application of SST-SAS Turbulence Model in the DESIDER Project
Y. Egorov, F. Menter ANSYS Germany
[email protected] © 2007 ANSYS, Inc. All rights reserved.
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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
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SAS concept • URANS: unphysical single mode unsteady behaviour • LES: too expensive • DES: – 1st 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 © 2007 ANSYS, Inc. All rights reserved.
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URANS
SAS-URANS ANSYS, Inc. Proprietary
SAS concept. Turbulence scales • Two scales required for statistical description
E(k) spectrum
L, T
• Two equations → two scales? © 2007 ANSYS, Inc. All rights reserved.
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SAS concept. 2-eq RANS models • k-ω model • One local scale: S • 2nd scale:
Dk 2 2 = ν t S − cµ ω + Diff (k ) Dt Dω 2 2 = α S − β ω + Diff (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: © 2007 ANSYS, Inc. All rights reserved.
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S 2 = cµ ω2 α S 2 = β ω2 ANSYS, Inc. Proprietary
SAS concept. v.Karman length scale • Rotta’s transport eq. for spatial correlation-based L • 2nd scale from ∂2U/∂y2 → von Karman length scale • New RANS model for k and Φ = k L
L DΦ Φ = Pk × ζ1 − ζ 2 Dt k LvK
2
Pk = ν t S 2 , LvK = κ S
− ζ 3 k + Diff (Φ ) ∇2U
• Two natural local scales: S and LvK © 2007 ANSYS, Inc. All rights reserved.
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SAS concept. SAS and RANS
π 2 ⋅ y , λ - natural scale, ignored by • U ( y ) = U 0 sin λ RANS • Two domains: δ = 4λ δ = 8λ
SAS
• RANS: L~δ
RANS
• SAS: L~λ © 2007 ANSYS, Inc. All rights reserved.
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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 LvK
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SAS concept definition • SAS: 2nd flow scale in the source terms typically via 2nd 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) © 2007 ANSYS, Inc. All rights reserved.
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No grid & time step dependence
Based on the grid spacing ∆ ANSYS, Inc. Proprietary
SST-SAS turbulence model • Experimental k-Φ model • Transformation to k-ω → SST-SAS model
Dk = ν t S 2 − cµ ω2 + Diff (k ) Standard SST Dt Dω 2 ⋅ (1 − F ) 2 2 = α S − β ω + Q SAS + Diff (ω) + ∇k∇ω Dt σ ω2 ω
(
Q SAS
)
2 L = max ζ 2 κS LvK
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2 2 ∇ ω ∇ k 2k −C ⋅ max 2 , 2 , 0 ω σΦ k 10
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SST-SAS turbulence model • Decay of isotropic turbulence
High wave number damping in SAS: - off - on - LES © 2007 ANSYS, Inc. All rights reserved.
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NACA0021 airfoil beyond stall • NACA0021 at 60°AoA, experiment by Swalwell at al., 2003 • Re = 2.7·105, low Mach number, domain span-size 4 chords • O-grid: courtesy of NTS, Russia, 1.9 million elements, y + ≈ 1
Isosurface of Q = Ω2 - S2
Contours of L / ∆ ∈ [0, 0.5] © 2007 ANSYS, Inc. All rights reserved.
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NACA0021 airfoil beyond stall • Mean values and PSD spectra of forces CL
CD
SST-SAS
0.915
1.484
Experiment
0.931
1.517
Mean pressure
2.5 2 1.5
-Cp 1 0.5 0 -0.5
SST-SAS Experiment
-1 -1.5 -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 © 2007 ANSYS, Inc. All rights reserved.
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Delta wing • Sweep angle 76°, experiment by Laschka et al., 1995 • AoA = 35°, Re = 1.07·106, low Mach number
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Delta wing • Hybrid unstructured grid, 50 million elements, y +≈ 0.5 – Courtesy of EADS Deutschland GmbH, Military Air Systems
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Delta wing • Delayed bursting of vortices predicted: numerical diffusion? Mean Cp
L/∆ Exp.
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SST-SAS
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Full aircraft configuration • Delta-canard FA-5, exp. by Laschka et al., 1995 • AoA = 15°, Re = 2.78·106, 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
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Full aircraft configuration • SAS vs. URANS
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Full aircraft configuration • Resolution details L/∆
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Full aircraft configuration • Cross planes at x/c = 0.2, 0.4, 0.6, 0.8, 1 Resolved+Modelled TKE/U02 Experiment SST-SAS
U/U0 Experiment
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SST-SAS
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3-D acoustic cavity • M219 test cavity, exp. by QinetiQ, Henshaw, 2000 • Shallow cavity: Length×Width×Depth = 5×1×1, 1=4" • ReD = 1.37·106, M∞=0.85 – local transonic zones • Coarse grid, 1.1 million elements • 90 ∆t per convective unit • 100 units run for statistics
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3-D acoustic cavity • Resolved turbulent structures • Pressure spectrum at cavity bottom near the downstream wall (K29) PSD of p 1.E+07
Experiment SST SAS
1.E+06
1.E+05
1.E+04
1.E+03 f, Hz 1.E+02 0 © 2007 ANSYS, Inc. All rights reserved.
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200
400
600
800
1000
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Other DESIDER tests simulated • Bump in a duct, experiment by ONERA
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• Generic car mirror, exp. by Höld et al., 1999
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