Flow-induced reconfiguration and cross-flow vibrations of an elastic plate and implications to energy harvesting

Abstract

We numerically study flow-induced vibrations (FIV) of an elastic cantilevered plate in a cross-flow configuration. The plate is kept upright in an open domain with a fixed bottom end. Such a configuration eliminates energy losses in the wall boundary. Due to allowed vortex shedding from its bottom end, the resulting novel dynamics of the fluid-structure interaction (FSI) system is explored. An in-house sharp-interface immersed boundary method-based flow solver, coupled with a Saint-Venant Kirchhoff material model-based open-source finite element solver, is employed. Two sets of simulations were carried out in two-dimensional Cartesian coordinates at Reynolds number of 100 for a wide range of reduced velocity (UR), by performing a parametric sweep of dimensionless Young’s modulus (E) and mass ratio (M). In general, FIV characteristics of the plate are similar to the transverse vortex-induced vibration of an elastically-mounted cylinder. The plate deforms to a curved mean position depending on E and M and exhibits angular oscillations. In particular, the following FIV regimes are obtained with increasing UR: initial excitation, lock-in with the first mode, desynchronization after the first lock-in, lock-in with the second mode, and desynchronization after the second lock-in. During lock-in, the plate oscillation and vortex shedding frequency are closer to the first or second mode natural frequency of plate. A larger angular amplitude and increased energy exchange between the structure and fluid characterize the lock-in. We quantify the modal contributions of Euler-Bernoulli modes in the plate’s vibration response with a curved mean position. The spatiotemporal variation of energy exchange between the fluid and plate is analyzed to understand the observed plate dynamics. The flow physics of the wake is discussed using wake patterns, vortex formation length, and vortex strength. Drag over the plate reduces due to flow-induced reconfiguration and strongly correlates with these parameters. Lastly, based on the spatial distribution of strain energy density over the plate, we present a potential design for an ambient fluid energy harvester to harness the plate’s vibration energy with optimized piezoelectric patching. The optimum location and height of a piezoelectric patch on the plate for different cases are reported.