Investigating interaction effects in an array of multi-mode wave energy converters

A number of wave energy device developers have now successfully tank-tested scale-model prototypes and several are attempting full-scale deployment at sea [1]. Many believe the superior survivability of simple, buoy-like designs make them the most economically viable solutions [2, 3]. Developers of so called ‘point-absorbers’ hope to install multiple devices in arrays, offering considerable savings in terms of moorings, grid connections and maintenance. It is recognised that the additional hydrodynamic interactions between devices, from scattered and radiated waves within the array, can significantly alter the surface elevation and enhance the interaction factor, q, defined as the ratio of power from the array to that from the same number of isolated devices [4-6]. In contrast to traditional offshore structures, like floating platforms [7], enhancements due to these interactions could have practical benefit in the effective design of wave energy converter (WEC) arrays [8]. However, these interactions depend on numerous system variables leading to a complex array transfer function, referred to here as the Configuration Response Amplitude Operator (CRAO). There exists a CRAO specific to each possible configuration, consisting of a set of q-factors which describe the output of the array, compared to isolated devices, as a function of incident wave frequency and direction. Research directly concerning WEC arrays has focussed primarily on optimal response; however, there has been limited success in designing optimal array configurations over a range of incident wave conditions. Some novel control methods have been suggested [9, 10] and this work considers combining multiple oscillatory modes as one possible method, differing from the majority of the literature which considers single mode oscillation only (usually heave). Numerical modelling has become increasingly important in the assessment of a given concept before going to the expense of full scale deployment. There exist a number of complex numerical methods for solving the case by case diffraction and radiation problem for floating offshore structures like tension-leg platforms (TLPs). However, when designing WEC arrays, precise computation of the interactions between multiple floating bodies is widely considered too expensive to investigate the effects of various parameters efficiently [6, 11]. Therefore, there is still a need for simplified design tools which capture the essential hydrodynamic features without the need for computationally expensive simulations. As shown here, progress can be made towards such a tool using superposition of analytical solutions, linear wave theory and various simplifications and approximations [4, 6]. In this work, the direct matrix method of Siddorn and Eatock Taylor [8] is utilised to find the surface elevation around a single, floating, ‘point-absorber’ WEC when subject to incident waves of different frequencies and directions. These results are then used to extend the heuristic ‘Parabolic Intersection’ method of Child and Venugopal [4] to enable fast array designs that include the diffraction and radiation interactions arising from floating devices. Superposition of the free surface behaviour around an isolated device is used to estimate the CRAOs for simple staggered arrays and assess the potential for improved frequency response through combined oscillation in heave and pitch.