Energy harvesting induced by the vibration of reciprocating-piston compressor subjected to repetitive impulse

Abstract

In this study, discrete event time-variant parameter of a lumped SISO dynamical system is obtained for a novel energy harvester. The harvester utilizes the resonance vibration of a coupled fluid-mechanic system, which is comprised of a reciprocating-piston, a tunable oscillator and twin electric turbine generators. The system model is simplified by an underdamped spring-mass-damper with tunable parameters subjected to periodic or arbitrary impulse forces. We developed a method that solves general problems underlining non-homogenous ordinary second order differential equation with discrete event time-variant parameters. The method uses the superposition to compile the general solution by segmenting the problem into ODE equations with constant coefficient. Each segment corresponds to a change in system, and it is solved analytically with recursively updated initial conditions. We utilized this method to tune the system’s natural frequency such that the accumulated energy is maximum within desired time range. We obtained the general solution of the displacement response due to varying parameters and input impulse force. We obtained the displacement peaks and their time of occurrence that could help understand the structural design limitation. We showed system displacement responses (constructive and destructive) corresponding to various impulse repetition patterns. We derived the relationship between energy, volume displacement, and volumetric flow rate (or piston velocity) and provided illustrative case studies. One finding shows that for a given impulse condition the accumulative energy exhibits local maximum and minimum within a narrow band of natural frequency range. The simulations showed the feasibility of generating considerable power from electric turbine when the air flow is driven by a resonating piston.