A semi-analytical solution for the three-dimensional Wagner steep wave impact on a vertical circular cylinder

Abstract

This study investigates the hydrodynamic problem of the steep wave impact on a vertical cylinder. The problem is considered in the three-dimensional space (3D) using linear potential theory. The formulation is idealized assuming that the volume of liquid is rectangular (extending transversely to infinity), resembling the geometry of a steep wave that propagates toward a vertical cylinder with constant velocity. The equivalent linearized boundary value problem of the 3D Wagner liquid impact is treated using a semi-analytical solution methodology. A fundamental assumption is made that the instantaneous contact line between the cylinder and the liquid is weakly dependent upon the vertical coordinate. The validity of this assumption is verified through the numerical results obtained from the theoretical model and through dedicated CFD computations. Several calculations are presented which concern the hydrodynamic loads, the evolution of the position of the contact line and the total impulse exerted on the solid. The main outcome of this study is that it shows that the actual 3D solution of Wagner steep wave impact falls between the simplified 2D von Karman and the 2D Wagner approximations.