Open-loop control of a separated boundary layer

International audienceLinear optimal gains Gopt(!) are computed for the separated boundary-layer flow past a two-dimensional bump in the subcritical regime. Very large values are found, making it possible for small-amplitude noise to be strongly amplified and to destabilize the flow. Next, a variational technique is used to compute the sensitivity of Gopt(!) to steady control (volume force in the flow, or blowing/suction at the wall). The bump summit is identified as the region the most sensitive to wall control. Based on these (linear) sensitivity results, a simple open-loop control strategy is designed, with steady wall suction at the bump summit. Calculations on non-linear base flows confirm that optimal gains can be significantly reduced at all frequencies using this control. Finally, sensitivity analysis is applied to the length of the recirculation region lc and reveals that the above control configuration is also the most efficient to shorten the recirculation length. This suggests that lc is a relevant macroscopic parameter to characterizewall-bounded separated flows, which could be used as a proxy for energy amplification when designing steady open-loop control