Dynamics of a wall-mounted flexible plate in oscillatory flows

The present work numerically studies the dynamics of a two-dimensional wall-mounted flexible plate in an oscillatory flow, aiming to assess the effect of structure bending stiffness and wave orbital excursion on the plate deflection, reconfiguration, and drag reduction. Different modes of dynamic responding behaviors are identified such as quasi-linear, linear, non-linear, and irregular modes with varied studying parameters. The plates of the quasi-linear mode show a fully reconfigured state in oscillatory flow with different wave excursions, of which the tip deflection and effective length for the reconfiguration effect are analyzed and the scaling laws are derived based on force and energy balances. With decreasing elasticity, the plates through linear motion show the limitation of reconfiguration and move passively and rigorously following along oscillatory flow with zero phase lag, wherein the tip deflections saturate to the same order as wave excursions and the effective lengths change slightly where the bending stiffness effect is insignificant. A critical Cauchy number, C a cri, which separates the fully reconfigured state and passive movement state, is proposed using the scaling arguments based on the time scales of flow oscillation frequency and time for plates to reach full reconfiguration for different wave orbital excursions. To account for the non-linear motion effect on drag reduction, we derive a scaling model based on the spatially and temporally averaged relative velocity and the prediction performs well. Furthermore, a rich phenomenology of fluid-structure interaction including phase lag, fluid loading distribution, internal elastic energy, vibration resonance, and vortex structure is presented.