Flow over 2D periodic hills

Authors: Temmerman and Leschziner

Type: Numerical

Status: stargold



Flow Parameters

Reference Publications



Flow over 2D periodic hills consisting in polynomial-shaped obstacles mounted on a flat plate with recirculation region in their wake.

The test case is relevant for studying near-wall or/and subgrid-scale modelling in LES in the presence of separation and reattachement.

The geometry retains the shape of the hill defined by Almeida (See below). As the true periodicity of the experiment was in question during the 1995 ERCOFTAC/IAHR workshop, no reliable experimental data is available. So, the rest of the configuration has been modified for computing cost reasons.

The geometrical parameters are:

  • Hill height: h = 28 mm
  • Hill crests are separated by: Lx = 9h
  • Channel height: Ly = 3.035 h


Flow Parameters

  • Reynolds number: Ubh/ nu = 10 595. The Reynolds number is based on the bulk velocity, Ub, taken at the crest of the first hill, the hill height h and laminar viscosity nu.
  • The flow is periodic in the streamwise direction.
  • The spanwise width of the LES computation is 4.5 h .

Additional information (links, pictures, etc.)

Simulation Details:

The simulation was performed over a grid of approximately 5M nodes, covering a spanwise direction of 4.5 hill heights. The mesh was close to orthogonal, of low aspect ratio and mesh-expansion ratio below 1.05. The $y^+$ value at the nodes closest to the wall was around 0.5, allowing the no-slip condition to be used directly. Statistical data was assembled over a period of 55 flow-through times, at a cost of approximately 50 000 processor hours on the Manchester CSAR Cray T3E computer.

The reference data can be found at:

Case 81, Ercoftac databse

Shape of the hill:

Almeida et al. 1993 Wake flows behind two-dimensional model hills Accurate geometry specification, x ranges from 0. to 54. (spline going through the following measured points:

0. 28.0

9.0 27.0

14.0 24.0

20.0 19.0

30.0 11.0

40.0 4.0

54.0 0.0)

Between x=0. and x=9. h(x)=min(28., 2.800000000000E+01 +0.000000000000E+00*x +6.775070969851E-03*x^2 -2.124527775800E-03*x^3 ) Between x=9. and x=14. h(x)= 2.507355893131E+01 +9.754803562315E-01*x -1.016116352781E-01*x^2 +1.889794677828E-03*x^3

Between x=14. and x=20. h(x)= 2.579601052357E+01 +8.206693007457E-01*x -9.055370274339E-02*x^2 +1.626510569859E-03*x^3

Between x=20. and x=30. h(x)= 4.046435022819E+01 -1.379581654948E+00*x +1.945884504128E-02*x^2 -2.070318932190E-04*x^3

Between x=30. and x=40. h(x)= 1.792461334664E+01 +8.743920332081E-01*x -5.567361123058E-02*x^2 +6.277731764683E-04*x^3

Between x=40. and x=54. h(x)=max(0., 5.639011190988E+01 -2.010520359035E+00*x 1.644919857549E-02*x^2 +2.674976141766E-05*x^3 )

  • LES Streamlines:

Reference Publications

  1. Mellen, Frohlich, Rodi , 2000, Large Eddy Simulation of the flow over periodic hills, 16th IMACS World Congress , Lausanne.
  2. Temmerman, Leschziner , 2001, Large Eddy Simulation of separated flow in a streamwise periodic channel construction, Int. Symp. on Turbulence and Shear Flow Phenomena, Stockholm, June 27-29.
  3. Jang, Temmerman, Leschziner, 2001, Investigation of anisotropy-resolving turbulence models by reference to highly resolved LES data for separated flow, ECCOMAS Computational Fluid Dynamics Conference, Swansea, September 4-7.
  4. Froehlich, Mellen, Rodi, Temmerman and Leschziner (2005) Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions . Journal of Fluid Mechanics, Vol. 526, pp. 19-66
  5. Breuer, Peller, Rapp and Manhart (2009) Flow over periodic hills Numerical and experimental study in a wide range of Reynolds numbers . Computers and Fluids, Vol. 38, pp. 433-457


Simulation results available for this case:
Code Version Author Restrictions
Code_Saturne 1.3.2 Juan Uribe Main.None
Number of topics: 1


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Topic attachments
I Attachment Action Size Date Who Comment
jpgjpg hilloutlined.jpg manage 4.7 K 2008-11-20 - 12:23 JuanUribe Outline
jpgjpg hillstreamlines.jpg manage 18.5 K 2008-11-20 - 12:23 JuanUribe LES Streamlines
Topic revision: r12 - 2010-07-02 - 15:21:17 - DominiqueLaurence

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