In the paper, the hydrodynamic problem of a cone entering the water through the free fall motion has been analyzed based on three dimensional (3D) velocity potential theory. The fluid is assumed to be inviscid and incompressible, the flow to be irroatational and the gravity effect has been considered. The physical problem is solved by the boundary element method in the stretched coordinate system. The fully nonlinear boundary conditions are satisfied on the instantaneous free surface and the moving body surface. The auxiliary function method is used to decouple the body motion and the fluid force. The velocity and acceleration of the body is analyzed,


Fluid-structure impact is a very common phenomenon in nature (e.g. violent wave impact on offshore or coastal structures, ship slamming in rough seas, the landing of seaplanes and so on) and has a wide range of practical application. Extremely large fluid loading can be created during the impact. In some cases, consequences can be catastrophic, causing wrecking of structures and loss of lives. Impact usually occurs in a very short period of time, over which both the fluid velocity and the fluid pressure change rapidly with time and location. This is accompanied by large and rapid deformation of the liquid surface. Such behavior poses great challenges in fluid mechanics.

There are many methods computing that body enters into water at a constant speed. Based on the function obtained by Wagner, Dobrovol'skaya (1969) presented self-similar solutions that compute water entry of wedges at a constant speed by solving an implicit integral equation. Zhao and Faltinsen (1993) also solved the problem. But they used a more accurate method and gave a nonlinear boundary element method to study water entry of arbitrary 2D bodies. Except for these constant speed water entry, varying speed water entry problems are also investigated by many people. Xu, Duan and Wu (2011) studied a circular cone falling into water freely by reducing the problem virtually to a two dimensional one. Sun and Wu (2013) studied the self- similar problem of the varying speed water entry. Wu and Sun (2014) also obtained that water entry of curved bodies (e.g. paraboloid curved cones) can be self-similar if the body enters into water and simultaneously expands in a given speed. Sun, Sun and Wu (2015) studied the interaction between a vertical falling cone and an incident wave.

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