Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering Conference
Shanghai, 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 study on water exit of the axisymmetric vehicle with the cavity
Zhongyu Zhang, 1 Longquan Sun, 2 Jiayang Gu, 1 Yanwu Tao, 1 Jishun Qu 1
1Marine Equipment and Technology Institute, Jiangsu University of Science and Technology,
Zhenjiang, Jiangsu Province, PR China
2College of Ship building Engineering, Harbin Engineering University,Harbin, Heilongjiang Province, PR China

If the flow field contains a sharp interface, the Eulerian-based or
Lagrangian-based method can be used to track the interface.
Additionally, the Arbitrary Lagrangian Eulerian (ALE) method is also a
popular way of capturing multiphase problems, in which the interface isdefined by a sequence of grids. The Lagrangian approach is used toupdate grid information, which is then utilized to capture the movementof interface. This avoids the need for interface reconstruction at eachtime step during the process of capturing the interface using the Euler
approach, resulting in a relatively small calculation amount.
Simultaneously, the grid moves arbitrarily, eliminating the grid
distortion generated by the Lagrangian approach. Pishevar and Amirifar(2010) numerically simulated the motion of underwater explosive
bubbles and the resultant cavitation near a wall using the ALE method.
Although the remeshing technique is still used in the numericalcalculation, the number of remeshed meshes is significantly less than
the number used in the Lagrangian-based interface tracking method.
Nguyen (2010a) suggested a high-precision two-phase flow numericalsimulation approach by combining the discontinuous Galerkin (DG)
method and the ALE method. Numerical examples demonstrate that
this method is capable of tracking the interface created by contact
discontinuity successfully. Lomtev et al. (1999) numerically simulatedcompressible viscous flow in a moving domain using ALEDG method.
The mathematical derivation demonstrates that, unlike the finite
volume technique, which requires additional equations to ensure
conservation, this method naturally meets the geometric conservationlaw (GCL). However, due to the error of numerical discretization,
Persson et al. (2009) transformed the grid into a fixed reference gridthrough isoparametric transformation, and discretized the additional
equations on the reference grid to strictly ensure the GCL. The
numerical solution of the GCL equation is carried out using the timespace DG method, which will greatly increase the amount of numericalcalculation. Mavriplis and Nastase (2011) enhanced a higher-order
discrete scheme for the GCL problem. Naturally, Nguyen et al. (2010b)
demonstrated through numerical experiments that the error associatedwith numerical discretization of the GCL equation is negligible andmay be ignored.

ABSTRACTThe cavity may be attached to the surface of an axisymmetric vehicle toreduce the resistance effectively. Thus, the interactions between thefree surface and the cavity during the water exit process are ofimportance. Based on the advantages of ALEDG method, a numericalapproach for multiphase flow is developed. Then the cavity movement
during water exit is numerically simulated, and the mechanism ofcavity collapse is investigated. The numerical results show that thepressure difference between the cavity and the free surface makes thecavity collapsed along the axial and radial directions of the vehicle,
resulting in a large collapse load acting on the vehicle. However, theincrease in the initial internal pressure can reduce the collapse load as it
can reduce the cavity collapse speed.

KEY WORDS: Discontinuous Galerkin method; cavity collapse;
Arbitrary Lagrangian Eulerian method; axisymmetric vehicle.

INTRODUCTION
Ventilation is a common approach for underwater vehicles to reduce
resistance, but when the vehicle passes through the free surface, thecavity is compressed and eventually breaks up, impeding the movementof the vehicle. As a result, it is critical to investigate the vehicle withthe cavity emerging from water. Based on the mixture two-phase flow
model, Wang et al. (2014) explained the evolution process of cavity
collapse, and proposed a straightforward formula for collapse load. Youet al. (2011) analyzed the load characteristics of the flow field during
the water exit process. When the vehicle leaves the water at an obliqueangle, the cavity collapse will produce a large torque and promote thedeflection of the vehicle. Base on the Potential flow theory, Zhao et al.
(2014) pointed out that the gas would also cause high pressure due toits compressibility, which affected collapse load. Meanwhile, Xue et al.
(2014) investigated bubble shape and jet direction while the vehicle
was at a variable speed.

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