Entrainment effects in periodic forcing of the flow over a backward-facing step

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 specific frequencies present in the unforced flow. In the present study, variations with Strouhal number are explained based on a continuous variation of entrainment of momentum into the recirculation region rather than on specific frequencies. The reattachment length is shown to decrease linearly with entrainment of momentum. Vertical momentum flux is driven by vortices generated by the forcing and locally vertical momentum flux is shown to be qualitatively similar to circulation for all cases considered. Total circulation (and therewith entrainment of momentum and the effect on the reattachment length) is shown to decrease with Strouhal number whereas this is not predicted by models based on specific low- and high frequencies. 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 of momentum 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 of momentum made in this study are expected to also hold for periodic forcing of other bluff-body flows.

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Identifiers

ORCID for Takfarinas Medjnoun: orcid.org/0000-0002-8699-1305

ORCID for Bharathram Ganapathisubramani: orcid.org/0000-0001-9817-0486

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