Open-loop control of a separated boundary layer

Linear optimal gains $G_{opt}(\omega)$ 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 $G_{opt}(\omega)$ 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 $l_c$ and reveals that the above control configuration is also the most efficient to shorten the recirculation region. This suggests that $l_c$ is a relevant macroscopic parameter to characterize wall-bounded separated flows, which could be used as a proxy for energy amplification when designing steady open-loop control.