Frhlich 9th IAHR / ERCOFTAC Workshop on Refined Turbulence Modelling, Darmstadt 2001 1 Test Case...
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![Page 1: Frhlich 9th IAHR / ERCOFTAC Workshop on Refined Turbulence Modelling, Darmstadt 2001 1 Test Case 9.2: Flow over a Series of Hills Presentation of Geometry.](https://reader035.fdocument.pub/reader035/viewer/2022062413/5a4d1b8d7f8b9ab0599bf90f/html5/thumbnails/1.jpg)
Fröhlich 9th IAHR / ERCOFTAC Workshop on Refined Turbulence Modelling, Darmstadt 2001 1
Test Case 9.2: Flow over a Series of HillsPresentation of Geometry and Flow
Jochen Fröhlich
Institut für Hydromechanik, Universität Karlsruhe
Germany
Joint work: C.P. Mellen, W.Rodi
IAHR / ERCOFTAC Workshop on Refined Turbulence Modelling, Darmstadt, 2001
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Fröhlich 9th IAHR / ERCOFTAC Workshop on Refined Turbulence Modelling, Darmstadt 2001 2
I
Motivation
Geometry
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Fröhlich 9th IAHR / ERCOFTAC Workshop on Refined Turbulence Modelling, Darmstadt 2001 3
EU-Project LESFOIL: LES of flow around the A - airfoil
transitionturbulent boundary layer
turbulent separation
0 613.3 Re 2.1 10
Desire for test case - just this feature- cheaper than airfoil (LES)
recirculation
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Fröhlich 9th IAHR / ERCOFTAC Workshop on Refined Turbulence Modelling, Darmstadt 2001 4
Test case requirements
• Massive, turbulent separation
• Separation not fixed by geometry (smooth surface)
• 2d geometry
• Realistic Reynolds number
• Cheap to compute
• Reference data available
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Fröhlich 9th IAHR / ERCOFTAC Workshop on Refined Turbulence Modelling, Darmstadt 2001 5
2D Hill Flow: [Almeida et al.93] 4th ERCOFTAC/IAHR ’95
• Single hill: Inflow condition required
yields long domain (unsteady signal for LES)
• Series of hills: Periodicity not fully achieved in experiments
Exp. data can not be used
#7
…
…
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Fröhlich 9th IAHR / ERCOFTAC Workshop on Refined Turbulence Modelling, Darmstadt 2001 6
2D Hill Flow: [Almeida et al.93]
• Both:
- Almost square channel => secondary flow !?
- Sidewalls expensive to include
- Channel quite high => expensive
= 60000 Reh
hill
Back view
Consecutive hills are close
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Fröhlich 9th IAHR / ERCOFTAC Workshop on Refined Turbulence Modelling, Darmstadt 2001 7
New Test Case Geometry [MFR00]
• lower Re=> fine-grid LES is feasible, Re-indep.• Re with bulk velocity => easier to impose & to compare
• Conserve shape of hill => experience, easily accessible
• Streamwise periodicity => no doubt about inflow conditions
• Larger distance between hills => Reattachment point is sensitive=> more Relaxation before next separ.=> Lx/Ly ~ 3 as in plane channel
• Spanwise homogeneity => periodic conditions in LES=> truly 2D for RANS
• No experimental data => use fine-grid LES as reference
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Fröhlich 9th IAHR / ERCOFTAC Workshop on Refined Turbulence Modelling, Darmstadt 2001 8
II
Flow
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Fröhlich 9th IAHR / ERCOFTAC Workshop on Refined Turbulence Modelling, Darmstadt 2001 9
Highly – resolved LES [MFR00]• Grid Ni x Nj x Nk = 196 x 128 x 186 (inner cells) by elliptic eq.
• Lz =4.5h
• Re_h = 10595
• Bottom: no-slip top: wall function
• SGS: Dynamic Smagorinsky
• Averaging in span & time (T=55 Lx/Ub)
• 96 Proc. on IBM-SP, 60000 h
Similar computation by [Temmerman, Leschziner 01]
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Fröhlich 9th IAHR / ERCOFTAC Workshop on Refined Turbulence Modelling, Darmstadt 2001 10
Reference simulations
< u > < uu >
x/h = 2
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Steamwise velocity
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Fröhlich 9th IAHR / ERCOFTAC Workshop on Refined Turbulence Modelling, Darmstadt 2001 12
Average flow
| < v > | and Streamlines
Resolved kinetic energy
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Fröhlich 9th IAHR / ERCOFTAC Workshop on Refined Turbulence Modelling, Darmstadt 2001 13
Reynolds stresses
< uu > < vv >
< ww > < uv >
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Fröhlich 9th IAHR / ERCOFTAC Workshop on Refined Turbulence Modelling, Darmstadt 2001 14
Pressure
< p >
p - < p >
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Fröhlich 9th IAHR / ERCOFTAC Workshop on Refined Turbulence Modelling, Darmstadt 2001 15
Flow structure
K.–H. vortices
Helical pairingGörtler vortices
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Fröhlich 9th IAHR / ERCOFTAC Workshop on Refined Turbulence Modelling, Darmstadt 2001 16
Pressure surface
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Fröhlich 9th IAHR / ERCOFTAC Workshop on Refined Turbulence Modelling, Darmstadt 2001 17
Pressure fluctuation
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Fröhlich 9th IAHR / ERCOFTAC Workshop on Refined Turbulence Modelling, Darmstadt 2001 18
Near – wall u-velocity
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Fröhlich 9th IAHR / ERCOFTAC Workshop on Refined Turbulence Modelling, Darmstadt 2001 19
Experiences
• good streamwise discretization near crest of hill required
• Hill is flat near crest
< y+ > < >w