Protecting coastlines by offshore wave farms: On optimising array configurations using a corrected far-field approximation

Abstract

A rapid-calculation method O(103)∼O(104) times faster than a typical BEM (Boundary Element Method) model is presented for optimising an array (farm) of dual-purpose wave-energy converters (WECs) that both generate electricity and protect a coast. It is known that fast semi-analytical descriptions of the wave field are available based on the far-field approach for a widely-spaced wave farm involving point-absorber-type WECs of small sizes, for which scattered waves are negligible. However, these approaches are inept at dealing with “non-small” WECs with non-simple shapes, for which scattered waves can be both complicated and non-negligible. For these devices, this paper demonstrates that a fast semi-analytical description based on a “corrected” version of the far-field approach can still be crafted for an isolated device, with the help of a BEM model. This simple description is then used in an interaction theory for an array of devices, which requires no further input from BEM, hence reducing the computation time drastically. In an example, for an array of eight WECs, 1.6×105 array configurations are calculated using a laptop computer within seven hours (this time included the time required to set up the far-field model for an isolated device), yielding an array featuring the largest “protection factor”, which quantifies wave reduction along a given line downwave of the array. The calculated wave fields around the arrays can be validated against BEM results for the same arrays. Note that the time for searching for an optimum layout can further be reduced by two orders of magnitudes when a standard optimisation routine is used, for the wave farms considered in this paper.