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Flow over periodic hills: an experimental study

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Abstract

Two-dimensional flow over periodically arranged hills was investigated experimentally in a water channel. Two-dimensional particle image velocimetry (PIV) and one-dimensional laser Doppler anemometry (LDA) measurements were undertaken at four Reynolds numbers (\(\text{5,600} \le Re \le \text{37,000}\)). Two-dimensional PIV field measurements were thoroughly validated by means of point-by-point 1D LDA measurements at certain positions of the flow. A detailed study of the periodicity and the homogeneity was undertaken, which demonstrates that the flow can be regarded as two-dimensional and periodic for \(Re \ge \text{10,000}\). We found a decreasing reattachment length with increasing Reynolds number. This is connected to a higher momentum in the near-wall zone close to flow separation which comes from the velocity speed up above the obstacle. This leads to a velocity overshoot directly above the hill crest which increases with Reynolds number as the inner layer depth decreases. The flow speed up above that layer is independent of the Reynolds number which supports the assumption of inviscid flow disturbance in the outer layer usually made in asymptotic theory for flow over small hills.

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Notes

  1. Earlier works of Prandtl (1926), von Kármán (1930), Nikuradse (1932) and Nikuradse (1933) dealt with smooth and rough surfaces rather than the definition of wavy walls by Fromm (1923) and Hopf (1923).

  2. Denoted as ‘periodicity’ is the periodic behavior in the streamwise direction, whereas ‘homogeneity’ refers to the spanwise direction.

  3. \( \nu={\frac{1.78 \times 10^{-6}} {1+3.37 \times 10^{-2} T + 2.21 \times 10^{-4} T^2}} \left[{\frac{\hbox{m}^2}{{\rm s}}}\right], \hbox{with}\,T\, [^{\circ}\hbox{C}] .\)

  4. However, the discharge was continuously recorded by a magneto-inductive device. The signal was analyzed but fluctuations were not detected in the spectra.

  5. The method of determining the point of reattachment will be explained in Sect. 4.7.

  6. Temmerman (2004) compared LES with one and two periods and found differences in the point of reattachment of 0.05 hill heights.

  7. The measurements were only conducted at the left channel half such that genuine symmetry about the centerline has not been demonstrated.

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Acknowledgments

We would like to thank the Deutsche Forschungsgemeinschaft (DFG) for the generous support of the PIV system and the funding of the research position (MA-2062-6).

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  1. Fachgebiet Hydromechanik, Technische Universität München, Arcisstraße 21, 80333, München, Germany

    Ch. Rapp & M. Manhart

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Correspondence to Ch. Rapp.

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Rapp, C., Manhart, M. Flow over periodic hills: an experimental study. Exp Fluids 51, 247–269 (2011). https://doi.org/10.1007/s00348-011-1045-y

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