Maximum wave-power absorption by attenuating line absorbers under volume constraints

TL;DR

This paper derives an equation for the maximum wave power absorption of attenuating line absorbers with volume constraints, revealing limits and scaling behaviors relevant to wave energy converter design.

Contribution

It introduces a theoretical model linking maximum absorbed power to length and volume constraints of line absorbers, extending existing bounds.

Findings

Maximum power is limited for point absorbers regardless of volume.

Line absorbers with infinite length can absorb unlimited power proportional to volume.

Practical line absorber power limits are higher than point absorbers of similar volume.

Abstract

This work investigates the consequences of imposing a volume constraint on the maximum power that can be absorbed from progressive regular incident waves by an attenuating line absorber heaving in a travelling wave mode. Under assumptions of linear theory an equation for the maximum absorbed power is derived in terms of two dimensionless independent variables representing the length and the half-swept volume of the line absorber. The equation gives the well-known result for a point absorber wave energy converter in the limit of zero length and it gives Budal's upper bound in the limit of zero volume. The equation shows that the maximum power absorbed by a heaving point absorber is limited regardless of its volume, while for a heaving line absorber whose length tends to infinity the maximum power is proportional to its swept volume, with no limit. Power limits arise for line absorbers of practical lengths and volumes but they can be multiples of those achieved for point absorbers of similar volumes. This conclusion has profound implications for the scaling and economics of wave energy converters.