Locomotion of a self-propulsive pitching plate in a quiescent viscous fluid

Abstract

The locomotion of a flexible plate pitching in a quiescent viscous fluid is numerically studied by using the lattice Boltzmann method (LBM) for the fluid and a finite element method (FEM) for the plate, with an immersed boundary (IB) method for the fluid–structure interaction (FSI). In the simulation, the leading edge of the plate undergoes a prescribed pitching motion, and the entire plate moves freely due to the fluid–plate interaction. The effects of the pitching amplitude, bending rigidity, plate-to-fluid mass ratio and Reynolds number on the propulsive performance of the flexible plate are examined in a range of parameters. The numerical results show that a certain flexibility can remarkably improve the propulsive speed and efficiency. The optimal parameters for the pitching plate are obtained, i.e. $0.4\le {\omega }^{*}\le 0.6$ ( ${\omega }^{*}$ is a non-dimensional frequency, with ${\omega }^{*}=0$ means rigid plate and larger ${\omega }^{*}$ means more flexible) and 20° ≤ α₀ ≤ 25° (α₀ is the pitching amplitude). The comparisons of three plate-to-fluid mass ratios (1.0, 2.5 and 5.0) show that the mass of the plate decreases the propulsive speed, but contrarily increases the efficiency. The results obtained in the present study provide an insight into the understanding of the performance of self-propulsive plate in pitching motion and can further guide the engineering design of micro aerial vehicles.