Hydrodynamic loads during initial stage of floating body impact

Hydrodynamic loads acting on a floating flared body, which starts suddenly to move, are investigated by using both asymptotic and numerical methods. The initial stage of the body motion is of main concern in this paper. Analysis is performed within the approximation of two-dimensional potential flow of an ideal and incompressible liquid with negligible surface tension effects. Initially the body is in contact with liquid, the liquid free surface is horizontal and the body displacement during the initial stage is assumed prescribed as a function of time. The body is symmetric with respect to the vertical axis and can move only in the vertical direction. Initial asymptotics of the hydrodynamic loads acting on the moving body are derived. Nondimensional body displacement plays the role of the small parameter of the problem. It is shown that the force asymptotics are strongly dependent on the flow details close to the intersection points between the body surface and the liquid free boundary. In particular, the standard small time expansion procedure, which provides correct initial asymptotics of loads in the case of a fully submerged body, is not applicable to the problem of a partly submerged (floating) body. This is because, for floating bodies, noninteger powers of body displacement appear in the initial asymptotics of the loads. For bodies with deadrise angles at the water level smaller than 45, negative powers have been discovered in the initial asymptotics. Fully nonlinear unsteady numerical simulations are carried out for a floating wedge, which starts suddenly to penetrate the water. A careful verification of the numerical results is performed aimed at identifying the initial part of the time history of the hydrodynamic loads which, due to the simplifying assumptions of the numerical approach, is not reliable. Asymptotic analysis is used for interpretation of the numerical results. A fairly good agreement between the theoretical and numerical predictions of the hydrodynamic loads just after the impact has been found. A practical method to derive the initial hydrodynamic loads, by using the results of direct numerical simulations of the floating body impact, is suggested.