Active control of high-speed boundary layer flows

High-amplitude freestream disturbances, as well as surface roughness elements, trigger streamwise oriented vortices and streaks of varying amplitudes in laminar boundary layers, which can lead to secondary instabilities and ultimately to transition to turbulence. In this project we aim at deriving and testing a control algorithm based on the adjoint compressible boundary region equations, which are obtained in the assumption that the streamwise wavenumber of the disturbances is much smaller the the crossflow wavenumbers. In our control algorithm, the wall transpiration velocity represents the control variable, whereas the wall shear stress or the vortex energy designates the cost functional. We anticipate the optimal control of the streamwise vortices approach to lessen vortex energy and subsequently cause a delay of the occurrence of transition from laminar to turbulent flow. Here, we report the progress on the project.