Linear diffraction analysis of the three-float multi-mode wave energy converter M4 for power capture and structural analysis in irregular waves with experimental validation

L. Sun, J. Zang, Peter Stansby, E. Carpintero Moreno, P. H. Taylor, R. Eatock Taylor

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35 Citations (SciVal)


A frequency domain dynamic model based on the DIFFRACT code has previously been applied to the moored, three-float, multi-mode wave energy converter M4 in regular waves, modelled as a two-body problem, showing good agreement of relative rotation and power capture with experiments for small wave height (Sun et al., 2016 J Ocean Eng Mar Energy 2(4):429–438). The machine has both a broad-banded and relatively high capture width for the range of wave periods typical of offshore sites. The float sizes increase from bow to stern facilitating alignment with the local wave direction; the bow and mid float are rigidly connected by a beam and the stern float is connected by a beam to a hinge above the mid float where the relative rotation is damped to absorb power. The floats are approximately half a representative wavelength apart so the float forces and motion in anti-phase generate relative rotation. The mid and stern floats have hemispherical and rounded bases giving negligible drag losses. Here the multi-body model is generalised to enable bending moment prediction in the beams and by including excitation by irregular wave fields with and without directional spreading. Responses are compared with experiments with input wave spectra of JONSWAP type. In uni-directional waves, the measured spectra were a close approximation to the target JONSWAP spectra and were input into the model giving excellent predictions of relative rotation and bending moment in all cases and slight overprediction of power. Predictions of bending moment in regular waves were surprisingly somewhat less accurate. With multi-directional waves the measured wave spectra did not match the target JONSWAP spectra as well, particularly for smaller periods, and the directional spreading was not measured. However with the target spreading function and the measured spectra input to the model the predictions were again excellent. Since the model is validated for uni-directional waves it seems likely that it will also be valid in multi-directional waves and the accurate predictions thus suggest that the actual spreading was indeed close to the target. The model indicates that realistic directional spreading can reduce power capture by up to about 30%. However, optimising the damping coefficient in the linear damper can increase power capture by a similar amount, and optimising the vertical hinge position can increase this further although this cannot be varied in situ. Power optimisation is inevitably less marked than with regular waves. Good agreement with experiment is thus achieved for small to moderate wave heights (about twice average) at typical full scales, indicating that this efficient frequency domain method is valuable for fatigue analysis and energy yield assessment. Accurate prediction based on linear diffraction theory in steep or extreme waves is however not expected.

Original languageEnglish
Pages (from-to)51-68
Number of pages18
JournalJournal of Ocean Engineering and Marine Energy
Issue number1
Early online date8 Dec 2016
Publication statusPublished - 1 Feb 2017


  • Beam bending moment
  • Capture width ratio
  • Directional spreading
  • Irregular waves
  • Optimisation
  • Wave energy converter

ASJC Scopus subject areas

  • Renewable Energy, Sustainability and the Environment
  • Water Science and Technology
  • Energy Engineering and Power Technology
  • Ocean Engineering


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