Global destabilization of flow over a backward-facing step

Abstract

Global destabilization of two-dimensional flow over a backward-facing step embedded in a channel, i.e., flow in a plane channel with a sudden expansion, is investigated by numerical simulations using a spectral element method. In the low Reynolds number regime where the two-dimensional flow is steady without manipulation, self-excited oscillations of the entire flow are induced by appropriate simultaneous suction at the step face and blowing at the wall adjacent to the step. The boundary between steady and time-dependent (destabilized) flow is determined as a function of the streamwise extent of the blowing region and its position relative to the step, for an expansion ratio of approximately two, a Reynolds number fixed at Re=1000, and equal suction and blowing mass flow rates. The computed periodic, globally synchronized flow regimes are characterized using instantaneous streamline patterns, time traces of physical quantities, and proper orthogonal decomposition of the velocity fields. The global flow behavior is also related to the absolute instability properties of the local streamwise velocity profiles. Preliminary three-dimensional simulations finally suggest that the 2-D unsteady flows obtained in the present study are, in general, susceptible to three-dimensional secondary instabilities. Nevertheless, the first experiments suggest that the 2-D analysis provides a qualitatively correct description of the flow transitions and that practical applications of this wall-blowing and -suction scheme, such as mixing enhancement, may be feasible.