Three-dimensional fluid-structure-electrical interaction modeling of piezoelectric plates

Abstract

Fully coupled fluid-structure-electrical interaction of piezoelectric plates plays a key role in many aero- and hydro-piezoelectric applications, such as energy harvesting from ambient fluid flows and direct actuation of flexible plates for biomimetic propulsion. Many of these applications involve complex three-dimensional flow dynamics and structure dynamics. Yet, a three-dimensional high-fidelity modeling framework for simulating these multi-physical problems is still scarce. In this study, we present a numerical framework of this kind. Using the Hamilton's principle and the reduced constitutive law of piezoelectric plates, the governing equations and boundary conditions of an electromechanical system are formulated. These equations are then coupled with the incompressible Navier-Stokes equations using the continuous forcing immersed boundary method, forming a set of governing equations describing multi-physics phenomena involving strong three-dimensional fluid-structure-electrical interactions. The accuracy of the numerical model is verified by three test cases through comparisons with benchmark results. We then demonstrate the full capacity of this framework through two representative case studies: one is flow energy harvesting using a piezoelectric plate undergoing flow-induced fluttering and the other is thrust generation using a flapping plate driven through inverse piezoelectricity. This numerical framework also has great potentials in modeling many other applications involving strong piezoelectricity-related fluid-structure-electrical interactions, such as piezoelectric-actuated active flow/vibration/noise control.