Controlled reattachment in separated flows: a variational approach to recirculation length reduction

A variational technique is used to derive analytical expressions for the sensitivity of recirculation length to steady forcing in separated flows. Linear sensitivity analysis is applied to the two-dimensional steady flow past a circular cylinder for Reynolds numbers $40 \leq Re \leq 120$ , in both the subcritical and supercritical regimes. Regions that are the most sensitive to volume forcing and wall blowing/suction are identified. Control configurations that reduce the recirculation length are designed based on the sensitivity information, in particular small cylinders used as control devices in the wake of the main cylinder, and fluid suction at the cylinder wall. Validation against full nonlinear Navier–Stokes calculations shows excellent agreement for small-amplitude control. The linear stability properties of the controlled flow are systematically investigated. At moderate Reynolds numbers, we observe that regions where control reduces the recirculation length correspond to regions where it has a stabilizing effect on the most unstable global mode associated with vortex shedding, while this property no longer holds at larger Reynolds numbers.