Exciting forces for a wave energy device consisting of a pair of coaxial cylinders in water of finite depth

Abstract

Two coaxial vertical cylinders-one is a riding hollow cylinder and the other a solid cylinder of greater radius at some distance above an impermeable horizontal bottom, were considered. This problem of diffraction by these two cylinders, which were considered as idealization of a buoy and a circular plate, can be considered as a wave energy device. The wave energy that is created and transferred by this device can be appropriately used in many applications in lieu of conventional energy. Method of separation of variables was used to obtain the analytical expressions for the diffracted potentials in four clearly identified regions. By applying the appropriate matching conditions along the three virtual boundaries between the regions, a system of linear equations was obtained, which was solved for the unknown coefficients. The potentials allowed us to obtain the exciting forces acting on both cylinders. Sets of exciting forces were obtained for different radii of the cylinders and for different gaps between the cylinders. It was observed that changes in radius and the gap had significant effect on the forces. It was found that mostly the exciting forces were significant only at lower frequencies. The exciting forces almost vanished at higher frequencies. The problem was also investigated for the base case of no plate arrangement, i.e., the case having only the floating cylinder tethered to the sea-bed. Comparison of forces for both arrangements was carried out. In order to take care of the radiation of the cylinders due to surge motion, the corresponding added mass and the damping coefficients for both cylinders were also computed. All the results were depicted graphically and compared with available results.