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 Rec induces a symmetry breaking Pitchfork bifurcation. The linear stability analysis of the symmetric steady solution enables the Rec 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 $ER$ 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 Rec 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.