Direct numerical simulation of the flow around a wall-mounted square cylinder under various inflow conditions

Abstract

The flow around a wall-mounted square cylinder of side d is investigated by means of direct numerical simulation (DNS). The effect of inflow conditions is assessed by considering two different cases with matching momentum-thickness Reynolds numbers Re_θ ≃ 1000 at the obstacle: the first case is a fullyturbulent zero pressure gradient boundary layer, and the second one is a laminar boundary layer with prescribed Blasius inflow profile further upstream. An auxiliary simulation carried out with the pseudo-spectral Fourier–Chebyshev code SIMSON is used to obtain the turbulent time-dependent inflow conditions which are then fed into the main simulation where the actual flow around the cylinder is computed. This main simulation is performed, for both laminar and turbulent-inflows, with the spectral-element method code Nek5000. In both cases the wake is completely turbulent, and we find the same Strouhal number St ≃ 0.1, although the two wakes exhibit structural differences for x > 3d downstream of the cylinder. Transition to turbulence is observed in the laminar-inflow case, induced by the recirculation bubble produced upstream of the obstacle, and in the turbulent-inflow simulation the streamwise fluctuations modulate the horseshoe vortex. The wake obtained in our laminar-inflow case is in closer agreement with reference particle image velocimetry measurements of the same geometry, revealing that the experimental boundary layer was not fully turbulent in that dataset, and highlighting the usefulness of DNS to assess the quality of experimental inflow conditions.

Keywords:

• wall turbulence
• direct numerical simulation
• three-dimensional flows
• separated flows
• square-cylinder flow

Acknowledgements

This research article is based on a presentation by the last author (D.S. Henningson) during the Wall Turbulence Colloquium under the Midnight Sun held at Trondheim in June 2014. The authors would like to thank Lars-Uve Schrader for his assistance with mesh generation, and gratefully acknowledge funding by VR (The Swedish Research Council) and NSERC (Natural Sciences and Engineering Research Council of Canada). Computer time was provided by SNIC (Swedish National Infrastructure for Computing) with a generous grant by the Knut and Alice Wallenberg (KAW) Foundation.