Numerical simulations of an inverted flexible plate in linear shear flows

Abstract

In this paper, the interaction between an elastic plate and viscous fluids is numerically studied through a coupling lattice Boltzmann method with a finite element method. In simulations, the plate, which has a clamped trailing edge, is immersed in a linear shear flow of relatively low Reynolds numbers (Re). The dynamical analysis has been conducted in terms of aspect ratio (H), Reynolds number (Re), stiffness coefficient (K), and attack angle (β). Four generic modes for the plate motion or deformation are identified, and the respective characteristics are shown. Three maps of mode distributions depending on K, H, Re, and β are given definitely. Three routes for the plate to reach the deflected mode have been found. The elastic potential energy under different K numbers and aspect ratios H is compared. It is indicated that the larger aspect ratio would result in larger efficiency of energy transformation. It is also found that the flapping mode can only occur when the attack angle β ≥ 0°, i.e., if β < 0°, the plate merely remains in the deflected or straight mode. The vortex structures and the pressure distributions are shown clearly for flapping and deflected modes of the plate. The present results can provide useful information to the physical understanding of the dynamics for the plate motion in shear flows and can also offer additional knowledge about a flexible plate using energy from ambient fluids.