Optimal control integrated immersed boundary multiphase flow framework for simulating wave energy converter (WEC) devices

In this presentation, we present a novel computational fluid dynamics (CFD) framework that couples the fictitious domain Brinkman penalization (FD/BP) method, a robust multiphase flow solver, and a model predictive control (MPC)-based optimal controller to simulate and maximize the energy conversion of WEC devices. Our framework is capable of accurately resolving the complex wave structure interactions (WSI) involved in the wave energy conversion process, wherein the nonlinear Navier-Stokes equations and the dynamics of the converter are solved on locally refined Cartesian grids. The MPC controller solves an optimization problem over a time horizon of one to two wave periods into the future, given the current state of the device and the past wave elevation data; the latter information is obtained from the CFD framework. In particular, the past wave elevation data collected by a sensor located at a pre-calculated distance in front of the WEC is used to predict the future wave elevations using an auto-regressive (AR) model. Future wave excitation forces required by the MPC are estimated using the predicted wave elevations. Path constraint on displacement, velocity and control input is also implemented. Various penalty terms are added to the objective function to: (i) smooth the actuator forces; and to (ii) restrict the flow of power flow from the device to the electric grid. Our results show that the conventional linear potential theory-based solvers overpredict the WEC dynamics and the power absorbed by the device, whereas the CFD framework provides realistic estimates of the power.