Exploring the Limits of Boundary Element Methods for Wave Energy Converter Hydrodynamics

Abstract

Boundary element methods (BEM) are used to calculate frequency-domain representations of hydrody-namic forces for moored and floating objects such as wave energy converters (WECs). The representations– excitation, added mass, and radiation damping in up to six degrees of freedom– define and scale the forces in the equation of motion for these devices, and can be used in time-domain modeling tools to predict the behavior of the system in response to waves. It is important for the hydrodynamic estimates to be accurate to determine the viability of a WEC design for energy capture. BEM is a computationally efficient way to calculate these values, using panel methods that only require spatial discretization on the bounding surface. BEM is based on linear potential flow theory, which has assumptions (e.g., linear, incompressible, inviscid, and irrotational flow) that may decrease the accuracy of the hydrodynamic estimates in some conditions. Despite the limitations imposed by these assumptions, results from these BEM codes are widely used in time-domain modeling with little regard for software variability or the suitability of the application. In this thesis, verification and validation procedures were performed on the two most commonly used commercial BEM packages (WAMIT and ANSYS Aqwa) and an open-source package (Capytaine) for four geometries of varying shape. We assess the impact of inter-code variations, mesh variations, and geometric variations on BEM results through grid sensitivity analyses and comparison to experimental results. Solution verification is performed through a mesh sensitivity study using both the grid convergence index and least-squares grid convergence index methods. Solution validation was performed through a comparison to published exper- imental data for the Sandia WaveBot geometry as a benchmark case. This was followed by comparison to lab-scale experiments for the scaled WaveBot and other hat-shaped geometries. The hat-shaped geometries were defined to keep specific geometric parameters constant to try to determine which parameter is most relevant for comparing results across distinctly different geometries. The eventual goal, beyond the scope of this thesis, is to classify sections of the WEC design space where BEM succeeds and fails. We show that all three BEM programs produce similar hydrodynamic estimates for all four simulated geometries, indicating that inter-program variability is minor and likely not a large source of uncertainty. The grid convergence study indicates that WAMIT is more sensitive to element size changes than Capy- taine, but has <8% change in added mass and radiation damping outputs across all oscillation frequencies and geometries, despite inconsistent convergence at higher frequencies. When compared with hydrody- namic coefficients from the two experimental geometries, BEM performs similarly for each geometry. The results align well at some frequencies, but BEM does fail to capture some behavior when viscous damping or amplitude dependence is present in the experimental data, and disagreements between BEM and experi- ments increase at higher frequencies. The comparison in BEM parameters across geometries indicates that there could be a connection between the trends in the added mass and radiation damping response with the magnitude of wetted surface area and volume. This thesis is an exploration of what matters in BEM results, and the experimental comparison provides preliminary indications at where BEM might provide sufficient accuracy for WEC modeling.