Temporal response of a flexible cantilevered plate subjected to tangentially-advecting vortex rings: Application to energy harvesting systems

Abstract

The dynamics of a cantilevered plate driven by a train of tangentially-advecting vortex rings is significantly impacted by two temporal parameters, namely the Strouhal number and the frequency ratio. The former relates the vortex ring advection time-scale to the fundamental period of the vibrating structure, while the latter relates the vortex production frequency to the structural fundamental frequency. The effect of these two parameters on the plate dynamics and the vortex-plate energy exchange process is investigated experimentally in this study. It is observed that an optimal range of Strouhal numbers exists that maximizes the plate energy. The range is centered around St=0.5, the value at which the plate dynamics and the vortex loading are in-phase. The effect of perturbations in the periodicity of the vortex production (frequency ratio) on the dynamical response of the system in off-design conditions is also explored. It is observed that the off-design response of the system, characterized by a reduction in average energy transfer to the plate, is a function of the separation distance between the advecting vortices and the flexible plate, as well as the degree of deviation of the frequency ratio from the optimal design condition, where the frequency of vortex production is the same as the fundamental frequency of the plate. The findings of this investigation can assist in the optimal design of cantilever plate-based energy harvesters, as well as providing an estimation of the energy exchange in such systems.