Linear hydrodynamic model of rotating lift-based wave energy converters

A linear potential flow model of a rotating lift-based wave energy converter is developed by assuming that the lift is generated by a pair of equal and opposite circulations and that the amplitude of motion is small. The linearisation of the hydrodynamics means that the forces can decomposed and expressions for the wave excitation force and radiation damping force are derived independently and shown to be related to each other through the Haskind Relations. The expressions for the forces are used to show that there is an optimum phase and product of circulation and radius of rotation to maximise the wave power extracted, which is equivalent to the optimum phase and amplitude of motion from ‘conventional’ wave energy converter theory. It is also shown that at this optimum condition 100% of the incident wave energy can be extracted. It is shown that the forces are directly proportional to the velocities due to the motion of the vortices, the water particle velocities due to the incident wave, and the water particle velocities induced by the vortices. The effect of the vortex-induced water particle velocities is considered and the importance of including these velocities on the passive generation of circulation, e.g. by hydrofoils, is highlighted. The impact of a sub-optimum product of circulation and radius of rotation is also investigated and shown that the power capture is not highly sensitive to the optimal conditions in the same way as ‘conventional’ wave energy converters