Investigation of the Damping Moment Induced by a Forced Rolling Cylinder with Bilge Keels

Abstract

In this paper, 2D nonlinear viscous flow caused by rolling motion of submerged cylinder with and without bilge keels are simulated using the finite-volume method in order to investigate the relationship between the damping moment induced by the bilge keel and the width of the bilge keel. The cylinder is submerged far away from the free surface to eliminate the interaction of the cylinder and the surface wave induced by the motion of it, and in this way, the damping moments obtained are caused by the cylinder and the bilge keels only. Verification and validation of the numerical results are performed in the conditions of different rolling periods and maximal rolling angles. Three parameters such as the width of the bilge keel, the rolling period and the maximal rolling angle are taken into account, and the effect of the width of the bilge keel is discussed. The analysis of the numerical result shows that there is a minimum effective width of the bilge keel, so the further research is performed, in which a result that the damping moment of the cylinder with the given bilge keels is less than the one without bilge keels is discovered. The calculation data is analyzed in detail, and the reason is discussed by the investigation of the damping moment components in the different conditions. After that, the damping moments of the cylinder with different bilge keel width in different conditions are calculated and compared. The result of the systematic research shows that the damping moment of the submerged cylinder with bilge keels increases nonlinearly while the width of the bilge keel increases linearly when the width of bilge keel is larger than the minimum effective width.