UFR 3-30 Test Case

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2D Periodic Hill

Underlying Flow Regime 3-30


Test Case

Brief Description of the Test Case Studied

The measures of the geometry introduced by Mellen et al. (2000) relate to the hill height h. The hill constricts the channel height of 3.036h by about one third, whereas the inter hill distance is 9h. The contour of the 3.857h long two-dimensional hill is described by the following six polynomials.

At x/h=0 the hill height is maximal, whereas the boundary is flat in the range between x/h=1.929 and x/h=7.071. Between x/h=7.071 and x/h=9 the contour follows the above equations but the hill geometry is mirrored at x/h = 4.5. Besides the geometry, the following figure shows streamlines at a Reynolds number, that is based on the hill height h and the bulk velocity above the crest, of 5,600 [Rapp 2009)].

Streamlines from PIV measurements at Re=5,600

The mean flow separates at the curved hill crown. In the wake of the hill the fluid recirculates before it attaches naturally at about x/h=4.5.

Experimental Setup

A water channel has been set up in the Laboratory for Hydromechanics of the Technische Universität München to investigate the flow experimentally. In total 10 hills with a height of 50 mm were built into the rectangular channel to accomplish periodicity whilst the measurement range lies between hills seven and eight. To achieve homogeneity in the spanwise direction an extent of 18 hill heights was appointed. The following figure sketches the experimental setup.

Sketch of the experimental setup.

The 2D PIV measurements were undertaken between hills seven and eight - and to investigate the periodicity of the flow - between the hill pair six and seven through vertical laser light sheets. The homogeneity in the spanwise direction was controlled by 2D PIV measurements in horizontal planes. The PIV field data was thoroughly validated through 1D LDA measurements. Experiments were done at four Reynolds numbers: Re=5,600; Re=10,600; Re=19,000 and Re=37,000.

CFD Methods

The numerical part of the present study relies on two completely independent codes based on either curvilinear body-fitted grids with a colocated variable arrangement or Cartesian non-uniform grids using a staggered configuration. The objective is to present highly reliable results obtained by carefully cross-checking between the outcome of both numerical schemes and additional experimental data. Afterwards the investigations concentrate on the physical aspects of the flow considered.


Front Page

Description

Test Case Studies

Evaluation

Best Practice Advice

References


Contributed by: (*) Christoph Rapp, (**) Michael Breuer — (*) Technische Universitat München, (**) Helmut-Schmidt Universität Hamburg

© copyright ERCOFTAC 2009