Modeling and simulation of thin-walled piezoelectric energy harvesters immersed in flow using monolithic fluid–structure interaction

Highlights

• A fully monolithic model tailored to flow-driven thin-walled piezoelectric energy harvesters (PEHs).

• A novel method to tackle the strongly discontinuous pressure field of the fluid field.

• The computational framework is validated against classical FSI benchmark problems.

• The importance of optimized PEH electrode coverage is revealed by two new benchmarks.

• Reference implementation using the open-source finite element framework FEniCS.

Abstract

A monolithic numerical scheme for fluid–structure interaction with special interest in thin-walled piezoelectric energy harvesters driven by fluid is proposed. Employing a beam/shell model for the thin-walled structure in this particular application creates a FSI problem in which an $(n-1)$-dimensional structure is embedded in an $n$-dimensional fluid flow. This choice induces a strongly discontinuous pressure field along the moving fluid–solid interface. We overcome this challenge within a continuous finite element framework by a splitting-fluid-domain approach. The governing equations of the multiphysics problem are solved in a simultaneous fashion in order to reliably capture the main dynamic characteristics of the strongly-coupled system that involves a large deformation piezoelectric composite structure, an integrated electric circuit and an incompressible viscous fluid. The monolithic solution scheme is based on the weighted residuals method, with the boundary-fitted finite element method used for the discretization in space, and the generalized-$\alpha$ method for discretization in time. The proposed framework is evaluated against reference data of two popular FSI benchmark problems. Two additional numerical examples of flow-driven thin-walled piezoelectric energy harvesters demonstrate the feasibility of the framework to predict controlled cyclic response and limit-cycle oscillations and thus the power output in typical operational states of this class of energy harvesting devices.