Modeling and Numerical Simulation of Non-Linear FSI Systems for Energy Harvesting Based on Ocean Waves and Beams with Piezoelectric Patches

In this work, a numerical approach is adopted to solve the fluid-structure interaction (FSI) model for energy harvesting from ocean wave motion. A mathematical model is presented based on the nonlinear Navier-Stokes equations for the ocean water flow and the large deformation model of beam vibration based on the Euler-Bernoulli theory with piezoelectric patches. The FSI model is solved by coupling the mixed finite element method with the differential quadrature method (DQM) for the spatial discretization of the fluid and structure equations. An implicit time scheme and the Newton-Raphson method are used to solve the flow equations, while an adaptive nonlinear Newmark scheme is implemented to obtain the non-linear dynamic response of the beam deflections. In order to evaluate the root mean square (RMS) of the generated electric power from the piezoelectric patches, the obtained numerical results are coupled with the mathematical expressions of the generated charge and the voltage. The RMS values are investigated with respect to the ratio of cantilever length H to the ocean depth Ly, the ratio of distance d of the cantilever from the entrance to the distance of the flow channel Lx and the ratio of the width b to the thickness h of the cantilever. Also, the effect of the Reynolds number and the number of the attached piezoelectric patches are discussed. The obtained results show that the RMS increases when H/ Ly and b/h increase, while it decreases when d/ Lx increases. As a result, an increase in the RMS values by more than 4 Watt when increasing the Reylonds number from 100 to 300. Also, the RMS reaches a fixed value when we use more than 3 piezoelectric patches in the cantilver. The presence work is of a great importance in term of design and optimization of new method for energy harvesting from ocean wave via piezoelectric structures. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.