Extending limits for wave power absorption by axisymmetric devices

Abstract

The theoretical limit for absorption of energy in monochromatic water waves of wavelength 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 length of an incident wave crest. For devices absorbing through surge and/or pitch motions the so-called capture width doubles to. For devices absorbing in both heave and surge/pitch the capture width increases further to. In this paper it is demonstrated that 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 is 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 the problem and allows strategies to be developed for setting the springs and dampers that control the power absorption. Results demonstrate that a cylinder of fixed size can absorb as much power as demanded from a plane incident wave although the practical limitations of linear theory are rapidly breached as that demand increases unless the size of the cylinder increases in proportion. In this paper we do not explore these limits in detail or further practical design considerations, such as imposing motion constraints. The continuum approximation is tested against a discrete paddle simulation for accuracy.