Adjoint-based optimal control of an airfoil in gusting flows

In this study, we apply optimal control to an airfoil in gusting flow to investigate the possibility of extracting energy. The gradients~of an objective function are obtained via the adjoint method and used to minimize the cost. The immersed boundary~projection method~is used for our forward solver, and the~relevant~adjoint equations are derived by the discrete-then-differentiate approach. Translational~gusts are generated by a body force in the computational domain upstream to the body, and the method finds the optimal angles of the airfoil that exploits~the greatest amount of energy. The influence of a vortex traversing an airfoil is also investigated and optimized to reduce the fluctuating lift.