Adjoint-Based Optimization of Three-Dimensional Flapping-Wing Flows

Abstract

Optimization of the three-dimensional unsteady viscous flow near a flapping wing in hover is performed using a time-dependent adjoint-based methodology. The sensitivities of a penalized lift coefficient to wing shape and kinematic parameters are computed using a time-dependent discrete-adjoint formulation. The unsteady discrete-adjoint equations required for the calculation of the sensitivity derivatives are integrated backward in time over the entire interval of interest. The gradient of the objective functional obtained using the adjoint formulation is then used to update the values of shape and kinematic design variables. The efficiency of this adjoint-based methodology is demonstrated by optimizing the shape and kinematics of a hovering wing. The numerical results show that the highest improvement in the wing performance is obtained by using combined optimization of the wing shape and kinematics.