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

TL;DR

This paper uses adjoint-based optimization to identify the optimal pitching and rolling motions of a 3D ellipsoidal plate to maximize thrust, revealing key kinematic parameters and flow structures that enhance propulsion.

Contribution

It introduces a continuous adjoint method with non-cylindrical calculus for efficient optimization of complex morphing domains in flapping propulsion.

Findings

Optimal phase delay of 122.6° enhances thrust.

Increasing rolling amplitude significantly improves thrust.

Stronger leading-edge vortex correlates with higher propulsion efficiency.

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 large control space including the pitching amplitude, the rolling amplitude, and the phase delay between the pitching and rolling motion. A continuous adjoint approach with boundary motion being handled by non-cylindrical calculous is developed as a computationally efficient optimization algorithm to deal with the large control space with morphing domain. The comparison between the optimal motion and other reference motions shows a significant improvement of thrust from the increase of rolling amplitude and an optimal phase delay of $122.6^\circ$ between the pitching and the rolling motion. The combination of these two factors impacts the overall thrust performance through their strong effects on the angle of attack, circulation, and the pressure distribution on the plate. Further wake structure analysis suggests that the optimal control improves its propulsive performance by generating a stronger leading-edge vortex (LEV) and straightening the wake deflection.