Response of U-Oscillating Water Column arrays: semi-analytical approach and numerical results

Nowadays, sea waves are recognized as an energy source that may contribute in the future to the global electricity demand. This fact manifests itself with the quite relevant number of proposed devices aimed at converting wave energy to electrical energy. In this context, the Oscillating Water Column (OWC) system plays a leading role, as it demonstrated flexibility, in the sense that it can work in conjunction with other marine systems, and effectiveness from a strict energy harvesting perspective. As a subclass, the U-Oscillating Water Column (U-OWC) was developed for further improving the OWC performance in mild-seas, where the natural resource is not abundant, such as in the Mediterranean Sea. This wave energy converter is composed by a water column in the lower part, an air pocket over the water column which is connected to a Power Take-Off device, and an external vertical duct connecting the water column to the open wave field. This paper deals with the problem of determining the response of a plant composed by an array of U-OWCs. This problem is relevant to the design of upright breakwaters embodying U-OWC chambers, where the interaction between contiguous U-OWCs influences the dynamics of each water column and, thus, the energy-wise performance of the whole plant. The models proposed currently in the literature are based on two-dimensional approaches neglecting three-dimensional effects and the mutual interference among the chambers. Therefore, firstly, the system of integro-differential equations describing the array dynamics is derived. Then, a semi-analytical approach is proposed for determining infinite frequency added mass and retardation function matrices. For this purpose, the wave field is described by the linear water wave theory and the boundary value problems pertaining to the determination of these hydrodynamic parameters are solved by combining Fourier transform and domain decomposition techniques. Next, numerical results are shown under the assumption of regular and irregular incident waves. It is seen that the individual U-OWC response is affected by the surrounding U-OWCs. Specifically, it is observed that the power available to the turbines decreases of about 9% with respect to the power associated with an isolated U-OWC in regular wave conditions. Although the reduction occurs over a wide range of incident wave frequencies, the numerical studies undertaken herein do not show the occurrence of frequencies leading to the sudden drop or magnification of the power output. This observation is confirmed by numerical simulations in case of irregular incident waves.