A high-fidelity numerical study on the propulsive performance of pitching flexible plates

TL;DR

This study numerically analyzes how the flexibility and trailing edge shape of pitching plates influence their propulsive efficiency and thrust, revealing optimal conditions near resonance and specific shape-flexibility combinations for enhanced performance.

Contribution

It provides new insights into the effects of trailing edge shape and flexibility on propulsion, identifying optimal parameters and mechanisms for improved thrust and efficiency in flexible pitching plates.

Findings

Maximum thrust near resonance at f*=1

Optimal efficiency around f*=1.54

Convex plates with low/high stiffness perform best

Abstract

In this paper, we numerically investigate the propulsive performance of three-dimensional pitching flexible plates with varying flexibility and trailing edge shapes. To eliminate the effect of other geometric parameters, only the trailing edge angle is varied from 45{\deg} (concave), 90{\deg} (rectangular) to 135{\deg} (convex) while maintaining the constant area of the flexible plate. We examine the impact of the frequency ratio f* defined as the ratio of the natural frequency of the flexible plate to the actuated pitching frequency. Through our numerical simulations, we find that the global maximum mean thrust occurs near f*=1 corresponding to the resonance condition. However, the optimal propulsive efficiency is achieved around f*=1.54 instead of the resonance condition. While the convex plate with low and high bending stiffness values shows the best performance, the rectangular plate with moderate bending stiffness is the most efficient propulsion configuration. Through dynamic mode decomposition, we find that the passive deformation can help in redistributing the pressure gradient thus improving the efficiency and thrust production. A momentum-based thrust evaluation approach is adopted to link the instantaneous vortical structures with the time-dependent thrust. When the vortices detach from the trailing edge, the instantaneous thrust shows the largest values due to the strong momentum change and convection process. Moderate flexibility and convex shape help transfer momentum to the fluid, thereby improving thrust generation and promoting the transition from drag to thrust. The increase of the trailing edge angle can broaden the range of flexibility that produces positive mean thrust.