Hydrodynamics of periodic wave energy converter arrays

Abstract

We consider the hydrodynamics of wave energy converter (WEC) arrays consisting of periodically repeated single bodies or sub-arrays. Of special interest is the array gain due to wave interactions as a function of the spatial configuration of the array. For simplicity, we assume identical WECs oscillating in heave only, although the results should extend to general motions. We find that array gains can be as high as $O(10)$ compared to the same WECs operating in isolation. We show that prominent decreases in array gain are associated with Laue resonances, involving the incident and scattered wave modes, for which we obtain an explicit condition. We also show theoretically that Bragg resonances can result in large decreases in gain with as few as two rows of strong absorbers. For general WEC geometries, we develop a multiple-scattering method of wave–body interactions applicable to generally spaced periodic arrays. For arrays of truncated vertical cylinders, we perform numerical investigations confirming our theoretical predictions for Laue and Bragg resonances. For a special class of multiple-row rectangular WEC arrays, our numerical results show that motion-trapped Rayleigh–Bloch waves can exist and be excited by an incident wave, resulting in sharp, narrow-banded spikes in the array gain.

Hydrodynamics of large wave energy converter arrays with random configuration variations

“…To evaluate the performance of a given array, we use a multiple-scattering method for fast calculation of linear wave-body interactions in arrays of bodies of arbitrary shapes and motion constraints without introducing any additional assumptions. The method is based on the approach introduced by Kagemoto & Yue (1986) and extended by Tokić & Yue (2019 b ) for periodic arrays. We express the incident, scattered and radiated wave fields (propagating and evanescent) in terms of partial wave expansions (Linton & McIver 2001), and close the linear system for the unknown amplitudes of partial waves by enforcing the boundary conditions on each body.…”

“…The scattered and radiated waves among the devices in an array can favourably interact to significantly increase the extracted energy over what the same number of devices would extract in isolation. This array gain, , is particularly pronounced in regularly spaced arrays in monochromatic seas where can readily be achieved for optimal lattice spacing (Falnes & Budal 1982; Tokić & Yue 2019 b ). The regular arrays, however, suffer from small extraction rates at particular wavenumbers, which diminishes the overall performance in irregular seas.…”

“…In § 3, we study over a broad range of and values and compare the array gains for monochromatic and irregular incident waves to those of arrays with the same . Since large uniform arrays generally exhibit significant variations in the gain with varying spacing and incident wavenumber (Tokić & Yue 2019 b ), comparisons between and arrays are particularly informative as these elucidate the importance of (in)coherent scattering within the array. In § 4, we compare optimal and arrays (optimal spacing that maximizes gain in each case) for a given incident wave spectrum within a wide range of spectrum parameters (bandwidth and peak frequency).…”

“…This question is of particular interest for irregular seas, as one can expect that for a monochromatic incident wave, the optimally spaced array that harnesses array resonances should outperform any array. We answer these questions by extensive direct computations of and arrays using a fast multiple-scattering method, which, in principle, provides an exact solution to the linear wave-multiple-body interaction problem without introducing any additional assumptions (Tokić & Yue 2019 b ). Finally, we discuss our results in § 5.…”

From Solar Cells to Ocean Buoys: Wide-Bandwidth Limits to Absorption by Metaparticle Arrays

“…1. Previous numerical-optimization work [14,[24][25][26], in particular a recent extensive computational study on large arrays [14,26], showed promising results through the design of buoy positions. The question we are trying to answer in this work is more general: given FIG.…”