Stability of a Seagoing Vessel Contour to Capsizing by a Rogue Wave

Abstract

The topic of the article is the computational fluid dynamics method for investigation of the contour stability in the rogue waves. Sampling of the Reynolds-averaged Navier-Stokes (RANS) equations was done by the method of the control volumes. In order to solve the linear system of the scalar equations, an implicit Gauss-Seidel method was used. Pressure-velocity coupling was achieved by using the Pressure-Implicit with Splitting of Operators (PISO) algorithm. The volume of the fluid (VOF) model was used to solve a single set of the momentum equations and tracking of the volume fraction of each of the fluids throughout the domain. A geometric reconstruction scheme was implemented to represent the interface between the fluids using a piecewise-linear approach. In order to compute the translational and angular motion of the center of gravity of the vessel contour, the three degrees of freedom (3DOF) solver was used. Variable sampling in the time domain was used to ensure stability of the solution. A rogue wave with a single high central peak and two small side elevations was used in a numerical wave tank, which met most of the marine observations. The wavelength of the 30-meter high rogue waves, which can capsize marine vessels of a big displacement, was calculated. On the basis of the spatial spectrum of the rogue wave, equations of the velocity of the fluid flowing into the numerical wave tank were obtained. Due to the non-linear processes the rogue wave height reached its maximum and then collapsed to form a plunging breaker. The contour was positioned at a predetermined distance from the initial position of the rogue wave and when the contour met with the rogue wave, the heeling angle of the contour was calculated. On the basis of a series of numerical experiments, the distances and the wavelengths of the rogue waves capsizing the contours of the fishing vessels were calculated. It was discovered that the rogue waves with the length of 120-140 meters and high steepness capsize the contours of the fishing vessels with displacement up to 9260 tons.