Manipulating flow separation: sensitivity of stagnation points, separatrix angles and recirculation area to steady actuation

A variational technique is used to derive analytical expressions for the sensitivity of several geometric indicators of flow separation to steady actuation. Considering the boundary layer flow above a wall-mounted bump, the six following representative quantities are considered: the locations of the separation point and reattachment point connected by the separatrix, the separation angles at these stagnation points, the backflow area and the recirculation area. For each geometric quantity, linear sensitivity analysis allows us to identify regions which are the most sensitive to volume forcing and wall blowing/suction. Validations against full non-linear Navier-Stokes calculations show excellent agreement for small-amplitude control for all considered indicators. With very resemblant sensitivity maps, the reattachment point, the backflow and recirculation areas are seen to be easily manipulated. In contrast, the upstream separation point and the separatrix angles are seen to remain extremely robust with respect to external steady actuation.