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An adjoint-based optimization is applied to study the thrust performance of apitching-rolling ellipsoidal plate in a uniform stream at Reynolds number 100.To achieve the highest thrust, the optimal kinematics of pitching-rollingmotion is sought in a large control space including the pitching amplitude, therolling amplitude, and the phase delay between the pitching and rolling motion.A continuous adjoint approach with boundary motion being handled bynon-cylindrical calculous is developed as a computationally efficientoptimization algorithm to deal with the large control space with morphingdomain. The comparison between the optimal motion and other reference motionsshows a significant improvement of thrust from the increase of rollingamplitude and an optimal phase delay of $122.6^\circ$ between the pitching andthe rolling motion. The combination of these two factors impacts the overallthrust performance through their strong effects on the angle of attack,circulation, and the pressure distribution on the plate. Further wake structureanalysis suggests that the optimal control improves its propulsive performanceby generating a stronger leading-edge vortex (LEV) and straightening the wakedeflection.

Adjoint-based optimization for thrust performance of a three-dimensional pitching-rolling plate