Influence of the inlet velocity profile on the flow stability in a symmetric channel expansion

In a channel flow with a sudden expansion, whether for three-dimensional (3-D) pipe and channel flows, or for two-dimensional (2-D) channel flow, it is known that increasing the Reynolds number beyond a critical value induces a symmetry breaking Pitchfork bifurcation. The linear stability analysis of the symmetric steady solution enables the Re-c to be determined efficiently and thus the influence of the expansion ratio (ER), defined as the ratio between upstream and downstream diameter regarding the expansion, to be explored. In this study, we investigate the behaviour of the flow after 2-D sudden expansions while varying the and the inlet flow profile, e.g. corresponding to a transition profile between a plug and a Poiseuille flow that could be reached for a flow after a sudden constriction upstream. Results demonstrate that imposing a plug flow at the inlet gives a higher Re-c than any other profile and that the concomitant recirculation zones are shorter. We show that these results can be rationalized using basic convection-diffusion arguments.