Wake behaviour and instability of flow through a partially blocked channel

Abstract

The two-dimensional flow through a constricted channel is studied. A semi-circular bump is located on one side of the channel and the extent of blockage is varied by adjusting the radius of the bump. The blockage is varied between 0.05 and 0.9 of the channel width and the upstream Reynolds number between 25 and 3000. The geometry presents a simplified blockage specified by a single parameter, serving as a starting point for investigations of other more complex blockage geometries. For blockage ratios in excess of 0.4, the variation of reattachment length with Reynolds number collapses to within approximately 15%, while at lower ratios the behaviour differs. For the constrained two-dimensional flow, various phenomena are identified, such as multiple mini-recirculations contained within the main recirculation bubble and vortex shedding at higher Reynolds numbers. The stability of the flow to three-dimensional perturbations is analysed, revealing a transition to a three-dimensional state at a critical Reynolds number which decreases with higher blockage ratios. Separation lengths and the onset and structure of three-dimensional instability observed from the geometry of blockage ratio 0.5 resemble results taken from backward-facing step investigations. The question of the underlying mechanism behind the instability being either centrifugal or elliptic in nature and operating within the initial recirculation zone is analytically tested.