A single-degree-of-freedom mathematical model for energy harvesting from cavity flow oscillations

Abstract

Flow-induced vibrations have proven to be a valuable power source for wireless sensors and MEMS devices. In this study, the energy harvesting aspects of an open cavity flow is explored and modelled as a single-degree-of-freedom system. Experiments with flow over a cavity of length-to-depth ratio of 3, with an incoming velocity of 30 m/s was taken as a case study to validate the model. It was observed in experiments that three distinct flow oscillation frequencies of significant amplitudes, corresponding to the different modes of oscillation were generated. To harvest this oscillatory power, a piezoelectric cantilever beam, mounted on the aft wall was subjected to unsteady pressure forces. To harvest efficiently, the natural frequency of the cantilever beam was tuned to lock in with the flow oscillation frequencies. The frequencies of cavity oscillations agreed well with Rossiter’s model in the experiments. A single-degree-of-freedom system assuming lumped parameters was used for modelling. The forcing term was described using a periodic function that uses empirical values for amplitude. The model was able to predict the overall trend and values of the average power and RMS voltage generated across a resistor load with reasonable accuracy. Using the model, the effects of cavity length, incoming velocity and resonant frequency were also studied.