Adjoint-optimal surface actuation for an airfoil at a stalled angle of attack

Flow control in the form of surface actuation has previously been used for modifying the flow field and deriving aerodynamic performance benefits. For the flow past an airfoil at a Reynolds number of 1000 and practical angles of attack, where separation is inevitable, such an actuation strategy has utility in altering the inherent vortex-shedding process. In our earlier work, normal actuation on the suction surface of an airfoil was prescribed in an open-loop setting. A backward traveling wave was considered, with a parametric sweep used to explore the effect of wave parameters on the aerodynamic flow and associated lift. Lift improvements were observed for a subset of the wave parameters considered. In the current work, we use numerical optimization to compute performance-beneficial actuation profiles, for actuation profiles not restricted to be sinusoidal in space or time. Rooted in our earlier (open-loop) observation that lift benefits were accompanied by a penalty in drag, we optimize for lift and drag separately. We discuss the effect of actuation for the two separate performance goals, connecting the actuation profiles to their effects on key vortex-shedding processes and aerodynamic performance. The computed optimal actuation is allowed to be nonzero over both the suction and pressure sides , and we discuss the non-intuitive role of pressure-side actuation near the leading and trailing edges where the suction and pressure surfaces meet. We compare our optimally computed profiles to open-loop actuation strategies considered, and explore extrapolation of the optimal profile to time windows longer than the optimization horizon.