# Extending limits for wave power absorption by axisymmetric devices

Richard Porter, Siming Zheng, Deborah Greaves

Research output: Contribution to journalArticle (Academic Journal)peer-review

7 Citations (Scopus)

## Abstract

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 the
problem and allows strategies to be developed for setting the springs
and dampers that control the power absorption. Results demonstrate
the main result: a cylinder of fixed size can absorb as much power as
demanded 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.
Original language English A39 Journal of Fluid Mechanics 924 https://doi.org/10.1017/jfm.2021.645 Published - 16 Aug 2021

### Bibliographical note

Funding Information:
S.Z. was supported by the European Union funded Marine-I (2nd phase) project (grant no. 05R18P02816). D.G. gratefully acknowledges the EPSRC for supporting part of this work through EP/S000747/1.