Effects of aspect ratio on the hydrodynamics of a self-propelled flexible plate near the ground

Abstract

The hydrodynamics of a three-dimensional self-propelled flexible plate near the ground was explored using the penalty immersed boundary method. A self-propelled flexible plate was realized by enforcing a prescribed harmonic oscillation in the vertical direction but allowing the plate to move freely in the horizontal direction. The gap distance ( g) from the ground is a key parameter governing the propulsive performance. A strong vortex is generated by interaction of the plate with the ground, which leads to an increase in the cruising speed. For comparison, two-dimensional simulations near the ground were also performed. The aspect ratio ( A R = L / W) affects the cruising performance, where L and W are the length and width of the plate, respectively. Vortical structures ( omega x and omega z) were visualized to characterize the effects of the A R and g on the performance of a self-propelled flexible plate. The cruising speed near the ground was 49.4% greater than the cruising speed far from the ground for A R = 2.0. A scaling relation was formulated to represent the effects of the A R and g on the locomotion of a self-propelled flexible plate.