Linear sensitivity of a hypersonic boundary layer to steady wall blowing and heating

Flow control efficiency depends on the location of the actuators. Instead of performing a computational costly parametric analysis, we use and adjoint-based optimisation technique to find the optimal actuator for steady open-loop control achieved through base-flow modification. Exploiting the benefit of Algorithmic Differentiation to ease the computation of high-order state derivative operators, it relies on the sensitivity of the most predominant global modes predicted by the resolvent analysis. The method is applied on a Mach 4.5 boundary layer over an adiabatic flat plate for steady wall-blowing control and on an isothermal flat plate for steady wall-heating control. The linear gradient predicted for the second Mack mode is studied in detail. The resolvent optimal gain decreases when suction is applied upstream Fedorov's mode S/mode F synchronisation point leading to stabilisation and conversely when applied downstream. The largest suction gradient is in the region of the branch I of mode S neutral curve. For the isothermal case, strong heating at the leading edge and cooling in the unstable region of mode S stabilises the second Mack mode. Sensitivity of the streaks and the first Mack mode is also briefly discussed.