Dynamics of a wall-mounted cantilever plate under low Reynolds number transverse flow in a two-dimensional channel

Abstract

The present work numerically investigates the dynamics of an elastic two-dimensional cantilever plate fixed at the bottom wall of a channel carrying flow using an open-source multi-physics computational fluid dynamics solver, SU2. Chief non-dimensional parameters, viz., Cauchy number (Ca), channel height, and mass ratio, are explored to predict the structural response of the plate interacting with the laminar parabolic profile in the channel at relatively low Reynolds numbers (Re=20−120). For a steady inflow, we show the existence of two distinctive modes of plate flexural oscillations, namely, F1 and F2, where the plate attains self-sustained periodic oscillations close to its first and second natural frequencies, respectively, for discrete ranges of Ca and three static modes, namely, S1, S2, and S3 for the other ranges of Ca in which steady-state configuration is obtained. The physical reasons underpinning the flow-induced oscillations and static shapes are examined using scaling arguments. F1 oscillations are shown to be vortex-induced oscillations, which get suppressed at low enough channel height, owing to higher viscous dissipation. Additionally, the window of F1 zone was found to shift to lower Ca with an increase in the mass ratio. Increasing the Reynolds number was found to cause the F1 zone to diminish in size, and beyond a critical Reynolds number, F1 was completely suppressed. On the other hand, F2 oscillations, which are shown to be induced by an unsteady drag force, are found to exist throughout the range of Re considered in the study.