Unsteady Flow Field Downstream Of A Sudden Expansion

Abstract

Separating and reattaching flows are important in a large number of engineering configurations. The flow through a sudden expansion (backward-facing step) represents a conceptually simple case of this class of flows and hence has been the subject of numerous studies. The present study focuses on the effect of the expansion ratio (defined as the ratio of downstream channel height to upstream channel height) on the unsteady flow features in the reattachment region and further downstream. It is known that this flow demonstrates two different instabilities; the Kelvin-Helmholtz shear layer instability, which scales with the shear layer thickness, and the instability associated with the separation bubble, which scales with the step height and has similarities to K´arman vortex shedding behind a cylinder.In addition to these, there is also a possibility of the presence of the ‘preferred’ mode of the jet issuing from the inlet channel of the sudden expansion, especially at high expansion ratios, where the flow resembles a wall jet. The aim of this study is to investigate experimentally the changes in the instability of the separation bubble, as the expansion ratio is changed, and its possible interactions with the other instabilities in the flow.One might expect some changes in the flow with expansion ratio, as at low expansion ratios, the configuration represents a simple backward-facing step geometry, while at high expansion ratios, the geometry approaches that of a wall jet. A variable expansion ratio backward-facing step facility has been developed in an open circuit wind tunnel.This facility permits continuous variation of the expansion ratio from 1 to around 6. Attention is focused on the turbulent regime of the flow, where the flow structure has been found in previous studies to be relatively insensitive to the Reynolds number. The inlet conditions have been kept constant with a thin turbulent boundary layer at the step, the boundary layer thickness at separation being approximately 14 % of the inlet channel height. The Reynolds number based on the inlet channel height, H, is kept constant at Re=48,000 and the expansion ratio is varied by changing the channel height downstream of the step. Detailed hot wire measurements have been made to characterize the spatial variation of the dominant frequencies in the flow at different expansion ratios. The expansion ratio has been varied from a low value of 1.14 to a high value of 3.25, and detailed measurements are obtained for five expansion ratios of 1.14, 1.3, 1.5, 2.0 and 3.0. Further, to elucidate the dominant vortical structures in the flow, Particle Image Velocimetry measurements have been undertaken simultaneously with hot wire measurements for the case of expansion ratio 1.5, which have permitted the conditional averaging of vorticity fields.These investigations have brought forth some interesting features of the flow over a backward-facing step. Results for the time-mean properties of the flow indicate that the shear layer separating from the step deviates from a free mixing layer behaviour away from the step, possibly due to its interaction with the wall and the recirculation region underneath it. At any given streamwise location, the shear layer momentum thickness, θ, is seen to increase with the expansion ratio. Further, upto reattachment, the momentum thickness of the shear layer is seen to scale with the step height, h, independent of its initial thickness at separation, θo, as long as the boundary layer at separation is sufficiently thin as compared to the step height. Investigations for the unsteady flow features show that the frequency of the dominant peak in the velocity spectrum, supposed to represent the passage frequency (Strouhal number, S, based on the step height, h, and the inlet velocity, U) of the vortical structures, varies in the cross stream (y) direction, in addition to its expected variation in the streamwise (x) direction. The variation of the Strouhal number in the cross stream direction is seen to scale with the local momentum thickness of the shear layer, except for locations very close to the step. To characterize the development of the dominant frequency in the streamwise direction, the maximum value of the Strouhal number at a streamwise location is taken to be the representative value for that streamwise location. The Strouhal number is seen to decrease in the streamwise direction, from a very high value near the step, to a value of approximately 0.08 in the reattachment region, and remains constant further downstream. This value, supposed to represent the large scale structures shed from the reattachment region, is seen to remain very close to 0.08 for all Expansion ratios investigated. Conditional averaging of the vorticity fields in the reattachment region is done for an expansion ratio of 1.5, to get a detailed picture of the unsteady flow field. The hot wire signal at the outer edge of the shear layer in the reattachment region, which represents the non-dimensional structure passage frequency of S=0.08, is used as the conditioning signal. Results seem to indicate that the recirculation region, or the ‘bubble’ divides into two cells, and sheds the downstream cell quasi-periodically. The passage of these structures through the reattachment region seems to be concomitant With a local vertical motion of the shear layer. Further, the streamwise development of the local Strouhal number, Sθ, based on the local momentum thickness of the shear layer, and the local free stream velocity, Umax, indicates a possibility of a coupling between the shear layer and the structures shed from the reattachment region.