Extending limits for wave power absorption by axisymmetric devices

The theoretical limit for absorption of energy in monochomatic water waves of wavelength $\lambda$ by axisymmetric wave energy converters operating in rigid-body motion was established in the 1970s. The maximum mean power generated by a device absorbing due to heave motion is equivalent to that contained in $\lambda/2\upi$ length of incident wave crest. For devices absorbing through surge and/or pitch motions the so-called capture width doubles to $\lambda/\upi$. For devices absorbing in both heave and surge/pitch the capture width increases further to $3\lambda/2\upi$. In this paper it is demonstrated it is theoretically possible to extend the capture width for axisymmetric wave energy converters without bound through the use of generalised (non-rigid body) modes of motion. This concept will be applied to vertical cylinders whose surface is surrounded by an array of narrow vertical absorbing paddles.A continuum approximation is made to the paddle motion which simplifies theproblem and allows strategies to be developed for setting the springs and dampers that control the power absorption. Results demonstratethe main result: a cylinder of fixed size can absorb as much power asdemanded from a plane incident wave although there are practical considerations which are also discussed. The continuum approximation is tested against a discrete paddle simulation for accuracy.