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Advancements in 2D Hill Flow Research: Geometry, LES, and Flow Analysis

This presentation discusses Test Case 9.2 from the .IAHR./.ERCOFTAC Workshop on Refined Turbulence Modelling in Darmstadt, 2001, focusing on flow over a series of hills. Motivated by the EU-Project LESFOIL, the requirements include massive turbulent separation, realistic Reynolds number, and cost-efficient computation with reference data. The geometry and flow aspects are vital, with an emphasis on the 2D character and the role of hill shape in flow dynamics. Insights from previous studies and new test case developments are presented, highlighting LES modeling, reattachment points, and flow structures like vortices and pressure fluctuations. Attention is given to grid resolution, boundary conditions, Reynolds stresses, and flow visualization techniques. Experiences and recommendations for improving streamwise discretization near the hill crest and understanding flow features near the separation regions are shared.

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Advancements in 2D Hill Flow Research: Geometry, LES, and Flow Analysis

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  1. IAHR / ERCOFTAC Workshop on Refined Turbulence Modelling, Darmstadt, 2001 Test Case 9.2: Flow over a Series of Hills Presentation of Geometry and Flow Jochen Fröhlich Institut für Hydromechanik, Universität Karlsruhe Germany Joint work: C.P. Mellen, W.Rodi

  2. I Motivation Geometry

  3. EU-Project LESFOIL: LES of flow around the A - airfoil turbulent boundary layer transition turbulent separation recirculation • Desire for test case - just this feature - cheaper than airfoil (LES)

  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

  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

  6. 2D Hill Flow: [Almeida et al.93] • Both: • Almost square channel => secondary flow !? • Sidewalls expensive to include • Channel quite high => expensive = 60000 Consecutive hills are close Back view hill

  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

  8. II Flow

  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]

  10. Reference simulations < u > < uu > x/h = 2

  11. Steamwise velocity

  12. Average flow | < v > | and Streamlines Resolved kinetic energy

  13. Reynolds stresses < uu > < vv > < ww > < uv >

  14. Pressure < p > p - < p >

  15. Flow structure K.–H. vortices Görtler vortices Helical pairing

  16. Pressure surface

  17. Pressure fluctuation

  18. Near – wall u-velocity

  19. Experiences • good streamwise discretization near crest of hill required • Hill is flat near crest t < > < y+ > w

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