An experimental investigation of a turbulent boundary-layer flow over a heterogeneous surface is carried out to examine the mean flow and turbulence characteristics, and to document the variation of skin friction that might affect the applicability of traditional scaling and similarity laws. The heterogeneity is imposed along the spanwise direction and consists of streamwise-aligned smooth raised strips whose spanwise spacing $S$ is comparable to the boundary-layer thickness ($S/\unicode[STIX]{x1D6FF}=O(1)$). Single-point velocity measurements alongside direct skin-friction measurements are used to examine the validity of Townsend’s similarity hypothesis. The skin-friction coefficients reveal that the drag of the heterogeneous surface increased up to 35 % compared to a smooth wall, while velocity measurements reveal the existence of a log layer but with a zero-plane displacement and a roughness function that vary across the spanwise direction. Lack of collapse in the outer region of the mean velocity and variance profiles is attributed to the secondary flows induced by the heterogeneous surfaces. Additionally, the lack of similarity also extends to the spectra across all scales in the near-wall region with a gradual collapse at small wavelengths for increasing $S$. This suggests that the effect of surface heterogeneity is not necessarily felt at the smaller scales other than to reorganise their presence through turbulent transport.

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Abstract

The effect of the Strouhal number on periodic forcing of the flow over a backward-facing step (height, H) is investigated experimentally. Forcing is applied by a synthetic jet at the edge of the step at Strouhal numbers ranging from 0.21 < StH < 1.98 (StH = f H/U∞) at a Reynolds number of ReH = HU∞/ν = 41000. In the literature, the effect of Strouhal number on the reattachment length is often divided into low-and high frequency actuation, referring to different frequency modes in the unforced flow. In the present paper, variations with Strouhal number are explained based on entrainment rather than frequency modes. The reattachment length is shown to decrease linearly with entrainment. Entrainment is driven by vortices generated by the forcing and locally entrainment is shown to be qualitatively similar to circulation for all cases considered. Total circulation (and therewith entrainment and the effect on the reattachment length) is shown to decrease with Strouhal number whereas this is not predicted by models based on frequency modes. An empirical model for the (decay of) circulation is derived by tracking vortices in phase-locked data. This model is used to decipher relevant scaling parameters that explain the variations in circulation, entrainment and reattachment length. Three regimes of Strouhal number are identified. A low-Strouhal-number regime is observed for which vortices are formed at a late stage relative to the recirculation region, causing a decrease in effectiveness. For high Strouhal numbers vortices are being re-ingested into the actuator or are packed so close together that they cancel each other, both decreasing the effectiveness of forcing. In the intermediate regime a vortex train is formed of which the decay of circulation increases for increasing Strouhal number. The scaling of this decay fully explains the observed variation in reattachment length. The observations on entrainment made in this study are expected to also hold for periodic forcing of other bluff-body flows. * G.Bharath@southampton.ac.uk arXiv:1702.06895v1 [physics.flu-dyn]

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