Optimal reduced frequency for the power efficiency of a flat plate gliding with spanwise oscillations

Abstract

The spanwise oscillation provides an accessory or alternative to flapping motion toward high-efficiency bio-inspired flight. The power factor that measures the efficiency of a gliding wing with spanwise oscillation to support a unit weight is investigated in this work. The gliding wing model consists of a rectangular flat plate that oscillates sinusoidally along the spanwise direction in a uniform upstream flow at a post-stall angle of attack. The unsteady flows and aerodynamic forces are obtained by numerically solving the incompressible Navier-Stokes equations at a Reynolds number of 300 (based on the uniform upstream velocity and the chord length). It is found that the spanwise oscillation can effectively enhance the power factor of the rectangular wing. The power factor under the optimal spanwise oscillation is 1.97 times as large as that without spanwise oscillation. Then, we introduce an effective reduced frequency by accounting for the effect of spanwise oscillation on the velocity encountered by the wing. The results show that the optimal effective reduced frequency locates in a narrow region from 0.47 to 0.56. Finally, the analyses of the vortex structures and the Lamb vector field indicate that the enhanced power factor results from the interaction between the stable leading-edge vortex and side-edge vortices associated with the spanwise oscillation. This work is expected to be helpful in understanding the vortex dynamics and guiding the kinematic design of the high-efficiency bio-inspired flight with spanwise oscillation.