Abstract
Wave energy converters (WECs) are devices submerged in the ocean that move with the waves to capture wave energy. The fluid dynamics of these devices are often modeled using potential flow theory. Conventionally, to simplify the problem, WEC dynamics are approximated by solving two separate issues: a) the diffraction problem, which describes how ocean waves affect the WEC, and b) the radiation problem, which describes how the motion of the WEC influences its own dynamics. Although this approach captures the effect of the waves on the WEC, it overlooks the impact of the WEC's motion on the waves themselves. The bidirectional wave-structure interaction can be especially important for wave energy farms where wave energy is captured by successive WECs, it is expected that the WECs downstream to the waves will see waves with diminished amplitudes.
In order to fully capture the bidirectional wave-structure interaction, solving the full potential flow problem with the submerged body is needed. Panel method is one method for solving such problems. In panel method, flow singularities (sources, doublets, vortices, etc.) are placed on panels that tile the boundaries in order to generate the flow field. Panel method works well in unsteady flow field and could show the coupling effect between boundaries. Therefore, it is able to capture the bilateral fluid-structure interaction.
One issue with panel method is that the fluid domain needs to be finite while an ocean should ideally be considered an infinite domain. One can limit the study to a sufficiently large domain with finite width, but the flow and pressure conditions on the boundaries, including those for the wave surface, would need to be specified. How they should be specified seem quite arbitrary but will have significant impact on the simulation.
By imposing boundary conditions that are periodic, circular domain is a useful analysis device since the spatial domain is finite and additional assumptions of spatial boundary conditions are not necessary. To satisfy the periodical boundary conditions in a circular domain, we found that panel singularities alone are not sufficient, but a series of panel images are needed to generate a convergent, and stable dynamics. Unlike conventional panel methods on a regular domain where singularities can be sources, doublets or vortices, we found, on a circular domain, that only doublet singularities result in stable dynamics with finite number of images, and source singularities result in stable dynamics when the number of images approach infinity, and vortex singularities always result in unstable dynamics.
A case study of a point absorber WEC extracting energy in a circular domain with an initial wave profile has also been conducted. It demonstrates that as the WEC extracts energy, the wave amplitude decreases in such a way that the energy in the fluid decreases by the same amount as the energy extracted by the WEC. This case study validates the effectiveness of this approach to fully capture the bilateral WEC-wave coupling effect.