0
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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.

References

Lucy, L. B. , 1977, “ A Numerical Approach to the Testing of the Fission Hypothesis,” Astron. J., 82, pp. 1013–1024. [CrossRef]
Monaghan, J. J. , 1994, “ Simulating Free Surface Flows With SPH,” J. Comput. Phys., 110(2), pp. 399–406. [CrossRef]
Chaussonnet, G. , Koch, R. , Bauer, H. J. , Sanger, A. , Jakobs, T. , and Kolb, T. , 2018, “ Smoothed Particle Hydrodynamics Simulation of an Air-Assisted Atomizer Operating at High Pressure: Influence of Non-Newtonian Effects,” ASME J. Fluids Eng., 140(6), p. 061301. [CrossRef]
Farrokhpanah, A. , Samareh, B. , and Mostaghimi, J. , 2015, “ Applying Contact Angle to a Two-Dimensional Multiphase Smoothed Particle Hydrodynamics Model,” ASME J. Fluids Eng., 137(4), p. 041303. [CrossRef]
Sefid, M. , Fatehi, R. , and Shamsoddini, R. , 2014, “ A Modified Smoothed Particle Hydrodynamics Scheme to Model the Stationary and Moving Boundary Problems for Newtonian Fluid Flows,” ASME J. Fluids Eng., 137(3), p. 031201. [CrossRef]
Sadek, S. H. , and Yildiz, M. , 2013, “ Modeling Die Swell of Second-Order Fluids Using Smoothed Particle Hydrodynamics,” ASME J. Fluids Eng., 135(5), p. 051103. [CrossRef]
Cummins, S. J. , Silvester, T. B. , and Cleary, P. W. , 2012, “ Three-Dimensional Wave Impact on a Rigid Structure Using Smoothed Particle Hydrodynamics,” Int. J. Numer. Methods Fluids, 68(12), pp. 1471–1496. [CrossRef]
Khayyer, A. , and Gotoh, H. , 2012, “ A 3D Higher Order Laplacian Model for Enhancement and Stabilization of Pressure Calculation in 3D MPS-Based Simulations,” Appl. Ocean Res., 37, pp. 120–126. [CrossRef]
Crespo, A. J. C. , Domínguez, J. M. , Rogers, B. D. , Gómez-Gesteira, M. , Longshaw, S. , Canelas, R. , Vacondio, R. , Barreiro, A. , and García-Feal, O. , 2015, “ DualSPHysics: Open-Source Parallel CFD Solver Based on Smoothed Particle Hydrodynamics (SPH),” Comput. Phys. Commun., 187, pp. 204–216. [CrossRef]
Mokos, A. , Rogers, B. D. , Stansby, P. K. , and Dominguez, J. M. , 2015, “ Multi-Phase SPH Modelling of Violent Hydrodynamics on GPUs,” Comput. Phys. Commun., 196, pp. 304–316. [CrossRef]
Xu, T. , and Jin, Y. C. , 2016, “ Modeling Free-Surface Flows of Granular Column Collapses Using a Mesh-Free Method,” Powder Technol., 291, pp. 20–34. [CrossRef]
Coleman, C. S. , and Bicknell, G. V. , 1985, “ Jets With Entrained Clouds—I. Hydrodynamic Simulations and Magnetic Field Structure,” Mon. Not. R. Astron. Soc., 214(3), pp. 337–355. [CrossRef]
Stellingwerf, R. F. , 1991, “ Smooth Particle Hydrodynamics,” Advances in the Free-Lagrange Method Including Contributions on Adaptive Gridding and the Smooth Particle Hydrodynamics Method (Lecture Notes in Physics), Vol. 395, H. E. Trease , M. F. Fritts , and W. P. Crowley , eds., Springer, Berlin, pp. 239–247.
Petschek, A. G. , and Libersky, L. D. , 1993, “ Cylindrical Smoothed Particle Hydrodynamics,” J. Comput. Phys., 109(1), pp. 76–83. [CrossRef]
Omang, M. , Borve, S. , and Trulsen, J. , 2006, “ SPH in Spherical and Cylindrical Coordinates,” J. Comput. Phys., 213(1), pp. 391–412. [CrossRef]
Ming, F. R. , Sun, P. N. , and Zhang, A. M. , 2014, “ Investigation on Charge Parameters of Underwater Contact Explosion Based on Axisymmetric SPH Method,” Appl. Math. Mech., 35(4), pp. 453–468. [CrossRef]
Lee, M. , and Cho, Y. J. , 2011, “ On the Migration of Smooth Particle Hydrodynamic Formulation in Cartesian Coordinates to the Axisymmetric Formulation,” J. Strain Anal., 46(8), pp. 879–886. [CrossRef]
Yang, G. , Han, X. , and Hu, D. A. , 2015, “ Simulation of Explosively Driven Metallic Tubes by the Cylindrical Smoothed Particle Hydrodynamics Method,” Shock Waves, 25(6), pp. 573–587. [CrossRef]
Baeta-Neves, A. P. , and Ferreira, A. , 2015, “ Shaped Charge Simulation Using SPH in Cylindrical Coordinates,” Eng. Comput., 32(2), pp. 370–386. [CrossRef]
Brookshaw, L. , 2003, “ Smooth Particle Hydrodynamics in Cylindrical Coordinates,” ANZIAM J., 44(E), pp. C114–C139. [CrossRef]
Seo, S. , and Min, O. , 2006, “ Axisymmetric SPH Simulation of Elasto-Plastic Contact in the Low Velocity Impact,” Comput. Phys. Commun., 175(9), pp. 583–603. [CrossRef]
Gong, K. , and Liu, H. , 2007, “ Numerical Simulation of Circular Disk Entering Water by an Axisymmetrical SPH Model in Cylindrical Coordinates,” Fifth International Conference on Fluid Mechanics, Shanghai, China, Aug. 15–19, pp. 372–375.
Tavakkol, S. , Zarrati, A. R. , and Khanpour, M. , 2017, “ Curvilinear Smoothed Particle Hydrodynamics,” Int. J. Numer. Methods Fluids, 83(2), pp. 115–131. [CrossRef]
Colagrossi, A. , and Landrini, M. , 2003, “ Numerical Simulation of Interfacial Flows by Smoothed Particle Hydrodynamics,” J. Comput. Phys., 191(2), pp. 448–475. [CrossRef]
Monaghan, J. J. , and Kos, A. , 1999, “ Solitary Waves on a Cretan Beach,” J. Waterw. Port Coastal Ocean Eng., 125(3), pp. 145–154. [CrossRef]
Gomez-Gesteira, M. , and Dalrymple, R. A. , 2004, “ Using a Three-Dimensional Smoothed Particle Hydrodynamics Method for Wave Impact on a Tall Structure,” J. Waterw. Port Coastal Ocean Eng., 130(2), pp. 63–69. [CrossRef]
Martin, J. C. , and Moyce, W. J. , 1952, “ Part IV. An Experimental Study of the Collapse of Liquid Columns on a Rigid Horizontal Plane,” Philos. Trans. R. Soc. London, 244(882), pp. 312–324. [CrossRef]
Liu, H. , Li, J. , Shao, S. , and Tan, S. K. , 2015, “ SPH Modeling of Tidal Bore Scenarios,” Nat. Hazards, 75(2), pp. 1247–1270. [CrossRef]
Glasheen, J. W. , and McMahon, T. A. , 1996, “ Vertical Water Entry of Disks at Low Froude Numbers,” Phys. Fluids, 8(8), pp. 2078–2083. [CrossRef]
Maruzewski, P. , Le Touzé, D. , Oger, G. , and Avellan, F. , 2010, “ SPH High-Performance Computing Simulations of Rigid Solids Impacting the Free-Surface of Water,” J. Hydraul. Res., 48(Suppl. 1), pp. 126–134. [CrossRef]
Aristoff, J. M. , Truscott, T. T. , Techet, A. H. , and Bush, J. W. M. , 2010, “ The Water Entry of Decelerating Spheres,” Phys. Fluids, 22(3), p. 032102. [CrossRef]
Ahmadzadeh, M. , Saranjam, B. , Hoseini Fard, A. , and Binesh, A. R. , 2014, “ Numerical Simulation of Sphere Water Entry Problem Using Eulerian–Lagrangian Method,” Appl. Math. Modell., 38(5–6), pp. 1673–1684. [CrossRef]
Erfanian, M. R. , Anbarsooz, M. , Rahimi, N. , Zare, M. , and Moghiman, M. , 2015, “ Numerical and Experimental Investigation of a Three Dimensional Spherical-Nose Projectile Water Entry Problem,” Ocean Eng., 104, pp. 397–404. [CrossRef]
Gong, K. , Shao, S. , Liu, H. , Wang, B. , and Tan, S. , 2016, “ Two-Phase SPH Simulation of Fluid-Structure Interactions,” J. Fluids Struct., 65, pp. 155–179. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

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

Grahic Jump Location
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]

Grahic Jump Location
Fig. 3

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

Grahic Jump Location
Fig. 4

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

Grahic Jump Location
Fig. 5

Computational domain for cylindrical disk entry

Grahic Jump Location
Fig. 6

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

Grahic Jump Location
Fig. 7

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

Grahic Jump Location
Fig. 8

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

Grahic Jump Location
Fig. 9

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

Grahic Jump Location
Fig. 10

Schematic setup of computational domain for sphere entry

Grahic Jump Location
Fig. 11

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

Grahic Jump Location
Fig. 12

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

Grahic Jump Location
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).

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In