The Effect Of Corners On Diffraction/Radiation Forces And Wave Drift Damping

Abstract

ABSTRACT A high order panel method has been developed for the calculation of wave diffraction and radiation by a moving body with a small steady forward speed. This has been used to compute results for a series of truncated cylinders with the same radius and draft but different comer radii. The results show that the most important hydrodynamic forces and amplitudes of body motion do not change significantly when the radius of the comer approaches zero. This suggests that even though in theory the potential flow solution is singular when the radius of the comer approaches zero, it is still possible to describe the body surface by a sharp comer in practical calculations, and to use the same method as for smooth bodies. INTRODUCTION Many moored and compliant offshore systems in deep water have low natural frequencies in their horizontal modes, which can be excited in random waves. As the low frequency response is a resonant phenomenon, it may only be predicted if adequate knowledge is available concerning low frequency damping. During low frequency excitation, wave drift forces are varying with the change of speed of the floating body, and this variation of the mean drift force can be considered as causing a form of damping. At any instant the action between the body and the fluid can be approximated as the problem of the body moving with a steady forward speed. Wichers1 defined the rate of change of the mean wave drift force with forward speed as the wave drift damping. Research has shown that the drift damping plays a role similar to that of viscous damping in the low frequency behaviour of a floating body. The prediction of wave drift damping depends on accurate calculation of velocity potentials diffracted and radiated by advancing bodies. In this respect, significant progress has recently been made2–6. For the calculation of the potential flow problem around floating bodies with steady forward speeds, the integral equation method is widely used. Using a Green function which satisfies the free surface and the far field conditions, the integration domain can be limited to the body surface and a small area on the free surface. Recently a higher order method has been applied to this Problem7. Higher order methods can provide accurate descriptions of body surfaces, and it is believed that they can also give accurate and continuous results along a discretised body surface. The difficulty in applying higher order panel methods lies in having to specify the solid angle of the body surface, and calculation of some singular integrals which exist only in a Cauchy principal value (CPV) sense. For the zero speed problem this can be avoided by indirect methods; for example, Noblesse8 and Chau and Eatock Taylor9 used another companion boundary integral equation inside the body, combined with the original integral equation, to cancel the solid angle and CPV integrals. For the radiation problem of a moving floating body with steady forward speed there are however other CPV integrals in the boundary integral.