Analytical Solutions Of Wave-structure Interaction With Dissipation Introduction

There are many kinds of offshore structures with different geometric forms of which the cylindrical structures are basic and widely used such as the SEVEN-FPSO,SPAR platform,TLP platform,Wind mills installed at sea.In coastal engineering,cylindrical or arc-shaped breakwaters have been often constructed.In order to reduce wave reflection and induced wave load on structures,some attention has been paid to the porous cylindrical structures.Therefore,the hydrodynamic characteristics of vertical cylindrical structures,such as a single cylinder,a combined cylinder with different diameters,a cylinder with moonpool and an array of cylinders,are of great significance for the design of offshore structures.Based on the traditional potential flow theory and following the geometric properties of cylindrical structures,the fluid domain is subdivided into several subdomains of cylindrical form.In each subdomain,the eigenfunction expansion is chosen to satisfy the associated boundary conditions.The unknown coefficients in the expansion are determined by the linear system obtained by Galerkin procedure to satisfy the continuous conditions of velocity potential and it normal derivative though the coupling surface between two subdomains.After having obtained the velocity potential,the first and second order wave force,and elevation on the free surface for the diffraction problem,and the added-mass and damping for the radiation problem have been computed.Obtained results are in excellent agreement with those of the literature or the HydroStar,the hydrodynamic software of BV based on Boundary Element Method of the three-dimensional linear frequency domain potential flow theory.Following the variation of parameters such as weterdepth,cylinders' diameter and draft,a series of non-dimensional wave forces,free-surface elevation,added-mass and damping are collected and tabulated.Peculiar attention has been paid for the cylinders with moonpool.At some wave frequencies,the water elevation in the moonpool can be highly exaggerated in classical potential methods.This is due to the missing of dissipation which plays an essential role to reduce the resonant amplitude.In order to introduce the dissipation,two approaches have been implemented in the present analytical method.One consists of adding a term of dissipation in the boundary condition on the free surface and another by introducing a dissipative surface(vertical cylindrical surface,or horizontal disc)through which a pressure drop is defined.Applications to zero-thickness cylinder with moonpool and MONOBR show the effectiveness of the dissipation and these conclusions have certain instructional significance to engineering design.