Adjoint-Based Optimization for Thrust Performance of Three-Dimensional Pitching–Rolling Plate

Abstract

An adjoint-based optimization is applied to study the thrust performance of a pitching–rolling ellipsoidal plate in a uniform stream at Reynolds number 100. To achieve the highest thrust, the optimal kinematics of pitching–rolling motion is sought in a control space including the pitching amplitude, the rolling amplitude, and the phase delay between the pitching and rolling motions. A continuous adjoint approach with boundary motion being handled by noncylindrical calculus is developed as a computationally efficient optimization algorithm to deal with large control space with a morphing domain. The comparison between the optimal motion and other reference motions shows a significant improvement of thrust from the increase of the rolling amplitude and an optimal phase delay of 122.6 deg between the pitching and rolling motions. The combination of these two factors impacts the overall thrust performance through their strong effects on the angle of attack, the leading-edge vortex circulation, and the pressure distribution on the plate. Further wake structure analysis suggests that the optimal motion improves its propulsive performance by generating a stronger leading-edge vortex and straightening the wake deflection.