Research Papers: Multiphase Flows

Cylindrical Smoothed Particle Hydrodynamics Simulations of Water Entry

[+] Author and Article Information
Kai Gong

Department of Mechanical Engineering,
National University of Singapore,
1 Engineering Drive 2,
Singapore 117576
e-mail: mpegk@nus.edu.sg

Songdong Shao

Department of Civil and Structural Engineering,
University of Sheffield,
Sheffield, S1 3JD, UK;
College of Shipbuilding Engineering,
Harbin Engineering University,
Harbin 150001, China
e-mail: s.shao@sheffield.ac.uk

Hua Liu

Department of Engineering Mechanics,
MOE Key Laboratory of Hydrodynamics,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: hliu@sjtu.edu.cn

Pengzhi Lin

State Key Laboratory of Hydraulics and
Mountain River Engineering,
Sichuan University,
Chengdu 610065, China
e-mail: cvelinpz@scu.edu.cn

Qinqin Gui

Faculty of Maritime and Transportation,
Ningbo University,
Ningbo 315211, China
e-mail: guiqinqin@nbu.edu.cn

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received February 10, 2018; final manuscript received December 17, 2018; published online January 30, 2019. Assoc. Editor: Oleg Schilling.

J. Fluids Eng 141(7), 071303 (Jan 30, 2019) (12 pages) Paper No: FE-18-1095; doi: 10.1115/1.4042369 History: Received February 10, 2018; Revised December 17, 2018

This paper presents a smoothed particle hydrodynamics (SPH) modeling technique based on the cylindrical coordinates for axisymmetrical hydrodynamic applications, thus to avoid a full three-dimensional (3D) numerical scheme as required in the Cartesian coordinates. In this model, the governing equations are solved in an axisymmetric form and the SPH approximations are modified into a two-dimensional cylindrical space. The proposed SPH model is first validated by a dam-break flow induced by the collapse of a cylindrical column of water with different water height to semi-base ratios. Then, the model is used to two benchmark water entry problems, i.e., cylindrical disk and circular sphere entry. In both cases, the model results are favorably compared with the experimental data. The convergence of model is demonstrated by comparing with the different particle resolutions. Besides, the accuracy and efficiency of the present cylindrical SPH are also compared with a fully 3D SPH computation. Extensive discussions are made on the water surface, velocity, and pressure fields to demonstrate the robust modeling results of the cylindrical SPH.

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Fig. 1

Cylindrical 2D (left), 3D side (middle), and 3D top (right) views of initial particle configuration in SPH setup

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Fig. 2

Relative distance of surge front to the axis of symmetry versus normalized time, compared between 2D cylindrical SPH, 3D Cartesian SPH, and experimental data [26]

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Fig. 3

Particle snapshots of water column collapse computed by 2D cylindrical SPH model

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Fig. 4

Particle pressure field of dam-break flow computed by 2D cylindrical SPH with (left) and without (right) density re-initialization

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Fig. 5

Computational domain for cylindrical disk entry

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Fig. 6

Computed air cavity region just prior to closure for different disk radius R and Fr numbers

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Fig. 7

Computed time evolution of cavity region behind the entry disk (Fr = 20 and R = 0.02 m)

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Fig. 8

Comparisons between SPH results and experimental data [27] on cavity closure depth hseal/R against square-root of Fr number

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Fig. 9

Particle pressure field of disk entry computed by 2D cylindrical SPH with (left) and without (right) density re-initialization

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Fig. 10

Schematic setup of computational domain for sphere entry

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Fig. 11

Comparison between experimental photos [29] and SPH simulations on sphere entry for different sphere densities

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Fig. 12

The time history of sphere entry depth for the different sphere densities

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Fig. 13

The characteristics of water entry cavity for different sphere densities. The symbols denote the dependence on Fr1/2 of the normalized (a) pinch-off depth zpinch, (b) pinch-off time tpinch, (c) sphere depth at the pinch-off Z(tpinch), and (d) ratio of the pinch-off depth to depth at the pinch-off zpinch/Z(tpinch).



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