Numerical seakeeping predictions of shallow water effect on two ship interactions in waves.

摘要

The main objective of this study is to numerically predict the shallow water effect on two ship interactions in waves. An algorithm has been developed to solve the free-surface Green function of zero forward speed in water of finite depth and in shallow water. The improper integral containing a singularity in the integral form of the Green function was solved by the Gauss-Laguerre quadrature. John's Conventional Expansion (i.e. the series form of the Green function) was found more effective than the integral form of the Green function when R/h > 1/2, where R is the horizontal distance between the source point and the field point and h is the depth of water. Therefore, a numerical scheme which combined both the integral form and the series form of the Green function was applied to compute the free-surface Green function with the water depth effect. The 1/r term in the potential function is treated by the Hess-Smith method. The interactions due to the coupled motions and hydrodynamic forces of two ships with forward speed in waves were then computed by the three-dimensional panel method based on the zero forward speed free-surface Green function with a forward speed correction. The effect of water depth on double-body flow and m-terms which have been used to compute the steady flow effect on the wave field were also considered. The m-terms, were computed by the integral equation method based on the double-body flow of two ship interactions. The viscous rolling damping coefficient had been determined by the method of Schmitke for Ship_a and Ship_b separately.; To verify this code, two numerical test cases were provided: two identical cylinders interact in water of finite depth and in shallow water. Furthermore, two ship interactions in shallow water, in water of finite depth and in deep water were carried out in regular waves with headings of 120°, 150° and 180° for forward speeds of 12 knots and 0 knots. Also a lateral separation distance of dy = 52.705m (gap distance Gy = 30.0m) and a longitudinal separation distance dx = 45m were considered in the computations.