In this paper, the low-speed water entry of four projectiles with various head types is numerically studied by using an improved multiphase moving particle semi-implicit (MPS) method. The projectiles are composed of a solid circular cylinder with L/D=4.5 and different head shapes, including a hemispherical head and three cone-shaped heads (90°~150°). During the water entry of these free-falling projectiles, splashing water, the deformed free surface, and the cavity evolution behind the cylinder are presented, which show agreement with experimental data. The vertical velocities and forces obtained by the multiphase MPS method are given. The influences of varying head shapes on the motion of the projectiles and the generation and closure of cavities are analyzed.


There widely exist water entry phenomena in the defense industry and ocean engineering with a fluid-structure interaction and multiphase flow. Water entry by a projectile involving cavity formation and collapse has been investigated theoretically. For example, Lee et al. (1997) developed an analytical model for the cavity dynamics to study the high-speed water entry of a sphere. It was indicated that a cavity can be characterized as a deep closure prior to closure at the surface for high-speed water entry, and the time of deep closure was constant, which was independent of the impact velocity. Mirzaei et al. (2020) proposed a transient model to predict the shape of the oblique water entry cavity for a cylindrical projectile at different angles. The predicted projectile attitude and the trajectory of the projectile agreed well with the experimental data.

Experimental studies on both low-speed and high-speed water entry with cavities have also been extensively carried out by using high-speed cameras. For example, Truscott and Techet (2009a, 2009b) and Techet and Truscott (2011) experimentally studied the trajectories, forces, and cavity formation behind spinning hydrophobic and hydrophilic spheres after water entry in the MIT Experimental Hydrodynamics Laboratory at the Massachusetts Institute of Technology. The splash and cavity of spheres’ water entry with varying spin rates and impact velocities were compared. Yang et al. (2014) conducted a series of experiments of low-speed water entry of projectiles with different head types. The snapshots of the cavity-running phase under different velocity and entry angle conditions were recorded by high-speed photography, and the influences of head types on the characteristics of cavity formation and closure were analyzed. The oblique high-speed water entry of projectiles was investigated by Song et al. (2020). The deflection of trajectories and the evolution of supercavities were analyzed.

This content is only available via PDF.
You can access this article if you purchase or spend a download.