Linear diffraction analysis for optimisation of the three-float multi-mode wave energy converter M4 in regular waves including small arrays

Abstract

A general frequency domain dynamic model based on the DIFFRACT code has been developed to predict the motion and power generation of the three-float multimode wave energy converter M4, modelled as a two-body problem. The machine has previously been shown experimentally and numerically to have broad-band high capture widths for the range of wave periods typical of offshore sites. The float sizes increase from bow to stern; 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 rotational relative motion is damped to absorb power. The floats are approximately half a wavelength apart so the float forces and motion in antiphase generate relative rotation. Here regular waves representative of swell are investigated and the model is shown to give accurate predictions of experimental results for motion and power for small wave heights and motion which are representative of operational conditions. A linear damper is used to model the power take-off. Without changing the float geometry or the hinge position, adjusting the linear damping factor for each frequency is shown to increase the power by up to three times the experimental value, with a maximum close to the theoretical value for a single float. Increasing the height of the hinge point above the mid float increases the power for the higher periods but can reduce power at lower periods. Since float motion can be quite large, this result can only be indicative of qualitative trends. The effect of small rows has been investigated, up to five machines, and it is shown in particular how the performance of wave energy devices in a row was affected by the multi-body interactions and wave directions. These results are important since the optimum damping factor is shown to be frequency dependent, and increase power generation by up to three times. Furthermore, hydrodynamic interference between M4 machines in a row may significantly increase the power generation when appropriate spacings are chosen.

State-Space Approximation of Convolution Term in Time Domain Analysis of a Raft-Type Wave Energy Converter

“…The capture width ratio is a significant parameter to evaluate the power capture ability of a WEC. In the study of the raft-type-like WEC M4, Sun et al [22,23] normalized the capture width by wavelength to obtain the capture width ratio. Here, we also adopt the same definition, since this definition of the capture width ratio enables a comparison with theoretical maxima, e.g., 3/2π in heave and pitch and/or surge for a point absorber [28] and 4/3π for a slender two-raft WEC [29].…”

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

“…The constraints between floats and beams can be categorised into two types: rigid connections (at "C1", "C2" and "C3") and a hinge (at "hinge O"). For rigid connections, the form of the constraint matrix D can be found in Sun et al (2011) and the corresponding constraint matrix for the hinge connection can be found in Sun et al (2016). When the PTO at "hinge O" in Fig.…”

“…The mid and stern floats have hemispherical and rounded bases giving negligible drag losses. This has been modelled effectively for operational conditions using linear diffraction theory in the time domain (Stansby et al 2015a(Stansby et al , 2016 and the frequency domain (Eatock Taylor et al 2015;Sun et al 2016). Eatock Taylor et al provided a general structural model based on dynamic substructuring and hydrodynamic finite element analysis assuming that the floats act in isolation giving good predictions of experimental results for response and power for longer wave periods, accounting for drag effects with flat-based floats.…”

“…An eigen analysis provided the four mode shapes and natural periods. Sun et al (2016) provided a two-body analysis with full hydrodynamic interaction using the DIFFRACT code giving response and power capture predictions in regular waves, giving good experimental prediction for smaller wave heights, with optimisation of damping coefficient and vertical hinge position for power capture. A photograph from the laboratory test is shown in Fig.…”

“…They also investigated interaction due to small rows of devices, up to five. A more general structural-hydrodynamic model is however necessary for fatigue analysis and in this paper we generalise the multi-body approach of Sun et al (2016) to allow rigid connections and hinges between bodies which now comprise three floats and two beams, following (Sun et al 2011(Sun et al , 2012. In this way, a complete structural definition is provided, though without internal dynamic behaviour arising from structural flexibility, with full hydrodynamic interaction between floats using DIFFRACT; regular, irregular and directional waves are input.…”