Theoretical Evaluation of the Hydrodynamic Characteristics of Arrays of Vertical Axisymmetric Floaters of Arbitrary Shape in front of a Vertical Breakwater

Abstract

The present paper deals with the analytical evaluation of the hydrodynamic characteristics of an array of vertical axisymmetric bodies of arbitrary shape, placed in front of a reflecting vertical breakwater, which can be conceived as floaters for wave power absorption. At the first part of the paper, the hydrodynamic interactions between the floaters and the adjacent breakwater are exactly taken into account using the method of images, whereas, the interaction phenomena between the floaters of the array are estimated using the multiple scattering approach. For the solution of the problem, the flow field around each floater of the array is subdivided into ring-shaped fluid regions, in each of which axisymmetric eigenfunction expansions for the velocity potential are made. In the second part of the paper, extensive theoretical results are presented concerning the exciting wave forces and the hydrodynamic coefficients for various arrays’ arrangements of axisymmetric floaters. The aim of the study is to show parametrically the effect that the vertical breakwater has on the hydrodynamic characteristics of each particular floater.

Hydrodynamic Efficiency of a Wave Energy Converter in Front of an Orthogonal Breakwater

“…Additionally, a linear breakwater with parabolic openings, as a parabolic reflector, has been studied to converge propagating waves toward a focus point, in which the wave height is further amplified compared to the wave height in front of a vane-type vertical wall [20]. Furthermore, the efficiency of an array of heaving WECs located in front of a linear breakwater has been studied recently in [21][22][23]. In these investigations, the method of images [24,25] was utilized to simulate the presence of the vertical wall, thus a fully reflecting, bottom seated, surface piercing breakwater of infinite length was considered.…”

Mean Drift Forces on Vertical Cylindrical Bodies Placed in Front of a Breakwater

“…. , N, taking into consideration the presence of the N image devices, for two wave heading angles θ and 180-θ [41]. This is, however, not the case for the mean drift forces.…”

“…Indicative theoretical and experimental studies concerning the effect of a vertical wall on the hydrodynamic characteristics of an array of five floating cylindrical bodies are studied in References [33,34], whereas, in Reference [35], the resonances of a freely floating half immersed cylinder in front of a vertical rigid breakwater have been investigated. Additionally, in References [36][37][38][39][40][41], the corresponding wave diffraction problem, as well as the motionand pressure-radiation problems of a single truncated cylinder and of an oscillating water column wave energy converter (WEC), placed in front of a vertical wall, was examined.…”

“…Having determined the velocity potential around each body of the array, either with the matched axisymmetric eigenfunctions expansions (see Section 2.1) or the sink source technique, the exciting forces and the hydrodynamic coefficients of the bodies, as well as their motions and rotations can be evaluated. This analysis has been thoroughly described in References [41,53], thus, no further elaboration is provided here. An indicative representation of the motion equation system of an array of N bodies placed in front of a breakwater is presented in the Appendix A.…”

“…An array of N cylindrical bodies placed in front of a vertical breakwater is assumed to float independently in 6 degrees of freedom. The system of motion equations in the frequency domain can be written as: The exciting forces on the q body, denoted as f q k , when the latter is part of an array of bodies placed in front of a breakwater can be determined by summing properly the exciting forces on the examined body q for two wave trains of angles θ and 180-θ [41]. In addition, the q body's hydrodynamic mass and damping matrices, denoted as a qp kj and b qp kj , can be derived by summing the corresponding hydrodynamic characteristics of the q body due to the motions of the p body with the corresponding characteristics of the q body due to the motions of the p body's image solid [41].…”