Adjoint-based optimal actuation for separated flow past an airfoil

This study determines the normal actuation on the surface of a NACA (National Advisory Committee for Aeronautics) 0012 airfoil for lift and drag benefits using numerical optimization. The airfoil is at an angle of attack of alpha=15 degrees and a Reynolds number of Re=1000 and actuation is permissible on both the suction and pressure surfaces. This approach of optimal actuation along the full airfoil surface augments most other studies that have focused on parametrically varying control on the suction surface. The gradient-based optimization procedure requires the gradient of the cost functional with respect to the design variables, which is determined using the adjoint of the governing equations. The optimal actuation profiles for the two performance aims are compared. Where possible, similarities with commonly considered open-loop actuation in the form of backward traveling waves on the suction surface have been highlighted. In addition, the key spatial locations on the airfoil surface for the two control strategies have been compared to earlier works where actuation has been limited to a sub-domain of the airfoil surface. The flow features emerging from the optimal actuation variations and their consequent influence on the instantaneous aerodynamic coefficients have been analyzed. To complement our findings with normal actuation, we also provide in the Appendixes: results for a more general form of actuation with independent x and y components and for a different optimization window to assess the effect of this window parameter on the actuation profile and the flow features.