Non-sinusoidal Trajectory Optimization of Flapping Airfoil using Unsteady Adjoint Approach

Presented in this paper is the gradient-based optimization of trajectory of motion of a flapping airfoil, in which the trajectory is parameterized using NURBS functions. Besides harmonic motions, such parameterization also allows to account for periodic but nonharmonic trajectories, which are observed in nature and might be beneficial to flapping flight performances. The adopted solver is an unsteady incompressible Navier-Stokes code, and the sensitivities required by the optimizer are obtained from the time-averaged unsteady adjoint equations and are formulated for periodic flow. Several optimization studies are performed to investigate the impact of the parameterization on the effectiveness of the optimization. The capability of the proposed non-sinusoidal parameterization is successfully demonstrated for a one degree of freedom (DOF) motion, i.e., pure plunging. For a multiDOF motion, which includes pitching and aft-forward motions, synchronization among participating DOFs is necessary to achieve an optimal trajectory.

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