Abstract
Attenuator-type wave energy converters (WECs) such as the M4 are tuned to respond and absorb wave power in a frequency range matching prevailing conditions at a given deployment site. This resonant behaviour in the wave frequency range makes the response remarkably linear, and they are therefore straightforward to study in the context of Design Waves, i.e. a short wave sequence conditioned to induce the average maximum response of a structure.
Ocean scale trials with an M4 WEC are planned for 2024 in King George Sound near Albany, Western Australia. In preparation, a model scale experimental campaign was conducted in a wave basin. The M4 WEC consists of three rows of cylindrical floats with rounded bottoms, attached to two beams, which are connected by a hinge (see figure 1). The float diameter and draft increase from the bow to the stern to ensure alignment with the mean wave direction and the variants are labelled by the number of floats in each row; here the 1-2-1 M4 is studied.
On the basis of NewWave theory (Tromans et al. 1991), Santo et al. (2017) conducted a Design Wave analysis for the 1-1-1 M4 using experimentally derived response transfer functions and determined that the wave that induces the averaged largest hinge motion response is distinct from the incident NewWave in both amplitude and phase. A similar analysis was carried out experimentally in a recent work (Hansen et al. 2023), where further Design Wave analysis was presented. The Design Wave signal was found by averaging the incident wave signals occurring around the time of the maximum hinge angles in a severe irregular sea state. Reproducing the Design Wave as as isolated wave packet in the basin showed a good match between the averaged maximum hinge angle instances in the random waves run and the measured response to the Design Wave group. We note that the primarily linear hinge angle response of M4 is affected by dunking - a full submergence of the centre floats, which represents an abrupt change of the system’s properties.
The M4 is designed to the wave period of the most commonly occurring sea-states. For storm sea states, this means that the hinge natural frequency f0 will be located out on the high tail of the wave spectrum. We will show that for a band-limited resonant response mode (like the hinge angle of the M4) in the high tail of a severe sea state, a Design Wave analysis for a given spectral shape and steepness is independent of the peak period. The analysis is conducted with the WEC in survival mode - i.e. with the power take off disconnected.