A coupled formulation of fluid-structure interaction and piezoelectricity for modeling a multi-body energy harvester from vortex-induced vibrations

Abstract

In this work, a coupled formulation for modeling multiple piezoelectric energy harvesters based on vortex-induced vibrations phenomenon at arbitrary locations was presented and experimentally validated. The mathematical formulation was performed by coupling the Navier-Stokes equations for incompressible fluid-flow, the Gauss law for piezoelectric equations and, a mass-spring-damper system for representing the oscillating rigid body. Piezoelectricity was described by a mixed formulation coupling mechanical and electrical variables. The coupled formulation was numerically implemented into a new OpenFOAM library. The library could be configured to add various piezoelectric materials for both types of wire connection, in series and in parallel. The numerical simulations for selected test cases were validated by experiments. After validating the numerical results, several working scenarios of three piezoelectric energy harvesters in tandem were simulated in order to evaluate the applicability of the proposed numerical formulation. The obtained results showed the synchronization state of the three harvesters operating in tandem was 500% wider than that of an isolated harvester. The interaction between cylinders played an important role in demonstrating that the output voltage of the three harvesters in tandem for a bimorph configuration connected in parallel (series) was approximately 128% (262%) higher than the unimorph one.