Wall-based feedback control of a compressible laminar boundary layer subjected to free-stream vortical disturbances

This thesis presents theoretical and numerical results on the penetration of small amplitude free-stream vortical disturbances into a compressible laminar boundary layer, the formation and evolution of streamwise-elongated, low-frequency fluctuations inside the boundary layer and the wall-based feedback control of such disturbances.
The theoretical formulation of the low-frequency disturbances, also called laminar streaks or Klebanoff modes, builds upon the works of Leib, Wundrow & Goldstein [43], Ricco & Wu [58] and Ricco [56], and it is based on the compressible linearised unsteady boundary region equations. For the first time, the incompressible framework by Ricco [56] is extended to the compressible case. The initial and outer boundary conditions for the outer layer compressible disturbances are therefore derived and put into context of the compressible Klebanoff modes analysis by Ricco & Wu [58]. Numerical results on the boundary region equations for the compressible and incompressible cases are presented.
The general adjoint theory is presented and applied to the compressible linear unsteady boundary region equations for the first time. The theoretical formulation
considers blowing and suction and wall thermal actuation to attenuate the Klebanoff modes. This further develops the works of Cathalifaud & Luchini [13] on spatial control for the incompressible linear boundary region equations and of Zuccher, Luchini & Bottaro [72] for the incompressible nonlinear boundary region equations. However, the previous studies were limited to the incompressible cases and neglected the free-stream turbulent forcing. Numerical solutions of the attenuated Klebanoff modes via an iterative feedback algorithm are presented, focusing on optimal wall-normal blowing suction.