In this paper, water entry of a cone into calm water in 3DOFs free fall motion is simulated by fully nonlinear boundary element method based on velocity potential theory. Auxiliary function method is used to decouple the body motion and the fluid force. The equation of motion is set up in which the fully nonlinear added matrix is incorporated into the body mass matrix to give more accurate motion results. A stretched coordinate system is adopted to make the computational domain adapting to the rapid change of wetted surface during the water entry. The cases with different initial horizontal velocities are simulated. The velocity, acceleration as well as the pressure distribution are presented.


The fluid-structure impact is a common phenomenon which poses a great threat to the hull safety of ships and offshore structures. While the impact occurs, strong fluid-structure interaction may cause great slamming load leading to structural damage. Study on the water entry is essential for the prediction of slamming load and ship design and this problem has been extensively investigated by various methods.

In the early stage of water entry study, Von Karman (1929) studied a simplified method for predicting the slamming load of a seaplane landing. Wagner (1932) considered the uplift effect of the free surface on the basis of Von Karman's research. Based on Wagner's function, Dobrovol' Skaya (1969) presented self-similar solutions of wedges at constant speed. Machie (1962) linearized the wetted surface, free surface and Bernoulli equation, and studied water entry of wegde and cone with large deadrise angle.

After computer technology got developed, nonlinear problem can be solved by numerical method more conveniently. Zhao and Faltinsen (1993) used boundary element method to solve water entry problem of wedge at constant speed into calm water in the time domain. Lu ,He and Wu (2000) expanded Zhao and Faltinsen‘s method and studied elastic wedge at constant velocity. In this research, they discussed the effect of structural elasticity on the water entry process. Battistin and Iafrati (2003) used panel method to obtain the numerical solution of water entry of wedge, cylinder and cone with nonlinear free surface boundary and wetted surface condition. Xu, Duan and Wu (2010) investigated the problem of a wedge entering water freely in 3DOFs. They got the pressure distribution on the wetted surface and impact load. Cheng, Ji, Oleg and Bai (2018) studied water entry of wedge into waves through free fall motion by high order boundary element method. Sun, Liu and Zhang (2019) simulated cones falling into waves with constant velocity. Xu, Duan and Wu (2011) used boundary element method to study the 1DOF free fall motion of cone into calm water. Although water entry of a cone in free fall motion has been studied previously, only vertical entry of a cone in 1DOF was considered due to axial symmetry. In fact, most of engineering related problems are 3DOFs. Thus 3DOFs free fall motion is investigated in present paper. As the cone is axisymmetric. To realize the 3DOFs free fall, the initial horizontal velocity is imposed to give translational motion and rotary motion. This problem is solved by boundary element method and the influence of initial horizontal velocity on hydrodynamic behaviors is discussed, which can provide a reference for actual situations such as water entry of a ship bow with horizontal speed.

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