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 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]

Unsteady Coanda effect and drag reduction for a turbulent wake

“…Following Shariff & Leonard (1992) and Berk et al (2017), under the local two-dimensional flow assumption, the vorticity flux per unit width can be expressed as with the notation referring to the case of the top shear layer. When further integrating over a period , the total amount of circulation created over a given time period is given by As, from the vorticity dynamics described in the previous section, we identified two main coherent structures forming during the forcing cycle, we want to link their formation to the dynamics of the shear layer and the pulsed jets.…”

“…Following Shariff & Leonard (1992) and Berk et al (2017), under the local two-dimensional flow assumption, the vorticity flux per unit width can be expressed as…”

“…To the best of the authors' knowledge, no work in the literature has extensively focused on the interaction of highly unsteady pulsed jets with small surfaces of high degree of curvature and its impact on the pressure drag generation problem for bluff blunt bodies. Recently, several studies, for instance Berk, Medjoun & Ganapathisubramani (2017) and Stella et al (2018), have focused on the fine-scale dynamic interaction between pulsed or synthetic jets and recirculating wake flows such as backward-facing steps in order to draw general scaling laws involving the formation of the pulsed jets and its influence on the recirculating wake.…”

Mass entrainment-based model for separating flows

“…non forced) flow. Anyway, Berk et al [22] show that the synthetic jets introduce an additional macroscopic scale into the instantaneous flow, which is the 1, let us approximate the shape of the vortex with an ellipse. Then, it will be:…”

High Reynolds number backward-facing step flow control

“…Due to its geometric simplicity, the BFS has also been used to examine the effectiveness of both passive and active flow control strategies for separated flows. Using periodic forcing, researchers have been able to alter the rate of flow entrainment to the re-circulatory zone and, in-turn, alter the reattachment length [6,3]. By amplifying the primary shear layer instability and increasing fluctuations in the wake, reductions in reattachment length of up to 80% have been achieved.…”