Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering ConferenceShanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

Numerical Simulations of Water Entry of Projectiles with Different Head Shapes
by Multiphase MPS MethodRuosi Zha1, Weiwen Zhao2, Decheng Wan2*12

School of Ocean Engineering and Technology, Sun Yat-Sen University, Zhuhai, Guangdong, China
Computational Marine Hydrodynamic Lab (CMHL), School of Naval Architecture, Ocean and Civil Engineering,
Shanghai Jiao Tong University, Shanghai, China*Corresponding author

ABSTRACTIn this paper, low-speed water entry of four projectiles with various
head types is numerically studied by using an improved multiphasemoving particle semi-implicit (MPS) method. The projectiles arecomposed of a solid circular cylinder with L/D = 4.5 and different headshapes, including hemispherical head and cone-shaped head (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. Verticalvelocities 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.

experimentally studied the trajectories, forces and cavity formation
behind spinning hydrophobic and hydrophilic spheres after water entry
in the MIT Experimental Hydrodynamics Laboratory. The splash andcavity of spheres water entry with varying spin rate and impact velocity
were compared. Yang et al. (2014) conducted a series of experiments oflow-speed water entry of different head types of projectiles. Thesnapshots of the cavity-running phase under different velocity and entry
angle conditions were recorded by high-speed photography and theinfluences of head types on the characteristics of cavity formation andclosure 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.
Over the decades, numerical simulations of water entry have been
performed based on the computational fluid dynamics (CFD) method.
Among mesh-based CFD methods, the volume of fluid (VOF) method
is one of the most popular methods to capture the free surface forsimulating the multiphase flows. For example, Song et al. (2020)
adopted the commercial software STAR-CCM+ to study the cavity ofwater entry for projectiles at an oblique speed. Overset mesh techniques
and the Dynamic Fluid Body Interaction (DFBI) method wereemployed to solve the motion of projectiles. Pressure distributions on
the nose of projectiles were analyzed at different entry angles. Jiang etal. (2021) studied couples of supersonic projectiles entering the waterin series and in parallel by solving the compressible Reynolds-averaged
Navier-Stokes (RANS) equations. In this work, different head shapes,
entry velocities, interval times and interval distances were discussed fortheir influences on drag force coefficient and the cavity evolution.

KEY WORDS: Slamming; water entry; cavity; particle method; MPSmethod; multiphase flows.

INTRODUCTION
There widely exist water-entry phenomena in the defense industry andocean engineering with 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 thehigh-speed water entry of a sphere. It was indicated that a cavity canbe characterized as a deep closure prior to closure at the surface forhigh-speed water entry and the time of deep closure was constant which
was independent of the impact velocity. Mirzaei et al. (2020) proposeda transient model to predict the shape of the oblique water entry cavity
for a cylindrical projectile in different angles. The predicted projectile
attitude and the trajectory of the projectile agreed well with theexperimental data.

However, it is still challenging to accurately simulate water splashingwith large deformation of the free surface and the motion of moving
boundaries with a large amplitude by using mesh-based methods during
water entry. The Lagrangian particle-based methods are mesh-free,which have advantages in solving water entry problems especially withhighly deformed interfaces and moving boundaries. Among theLagrangian particle methods, the smoothed particle hydrodynamics

Experimental studies on both low-speed and high-speed water entry
with cavity have also been extensively carried out by using high-speed
cameras. For example, Techet and Truscott (2009a, 2009b, 2011)

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