Nonlinear Hydrodynamic Forces and their Implications for Power Capture of Heaving Wave Energy Converters

Diffraction (incident waves on a static body), radiation (imposed body heave motions in otherwise still water), and combined (incident waves and imposed motions) tests were conducted with a spherical model in a wave flume, to investigate the implications of nonlinear forces for the power capture of heaving point absorbers. In our tests, the incident waves and the model motions were independently controlled. Specific incident wave and motion phases were chosen based on a novel phase-based harmonic decomposition method, so that almost all nonlinear terms up to third-order can be isolated in post-processing. The new decomposition method allows for detailed investigation of the complex nonlinear physics governing the hydrodynamic interaction and separates terms based on their dependence on the waves and motions, which is useful for determining, for example, linear and nonlinear terms which would be modified by different wave energy converter control strategies (terms originating from the body motions). First, as a validation of the novel method, we normalise the extracted nonlinear forces by the expected amplitude scaling behaviour assumed in the Stokes expansion, which verified that the experimental data and separation methods are consistent. We then proceed to multiply these forces by the linear velocity to obtain power contributions from each nonlinear term, and the importance of each term is discussed, especially the third-order first-harmonic forces which are found to contribute a large majority of the nonlinear power. Finally, we discuss the implications of the experimental results in the context of real wave energy converters in random sea states.