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.
Issue Section:
Multiphase Flows
Keywords:
SPH,
axisymmetric,
cylindrical coordinates,
water entry,
dam break,
cylindrical disk,
circular sphere
Topics:
Disks,
Hydrodynamics,
Particulate matter,
Water,
Simulation,
Computation,
Flow (Dynamics),
Dams,
Pressure,
Density
References
1.
Lucy
, L. B.
, 1977
, “A Numerical Approach to the Testing of the Fission Hypothesis
,” Astron. J.
, 82
, pp. 1013
–1024
.2.
Monaghan
, J. J.
, 1994
, “Simulating Free Surface Flows With SPH
,” J. Comput. Phys.
, 110
(2
), pp. 399
–406
.3.
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
.4.
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
.5.
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
.6.
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
.7.
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
.8.
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
.9.
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
.10.
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
.11.
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
.12.
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
.13.
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
.14.
Petschek
, A. G.
, and Libersky
, L. D.
, 1993
, “Cylindrical Smoothed Particle Hydrodynamics
,” J. Comput. Phys.
, 109
(1
), pp. 76
–83
.15.
Omang
, M.
, Borve
, S.
, and Trulsen
, J.
, 2006
, “SPH in Spherical and Cylindrical Coordinates
,” J. Comput. Phys.
, 213
(1
), pp. 391
–412
.16.
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
.17.
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
.18.
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
.19.
Baeta-Neves
, A. P.
, and Ferreira
, A.
, 2015
, “Shaped Charge Simulation Using SPH in Cylindrical Coordinates
,” Eng. Comput.
, 32
(2
), pp. 370
–386
.20.
Brookshaw
, L.
, 2003
, “Smooth Particle Hydrodynamics in Cylindrical Coordinates
,” ANZIAM J.
, 44
(E
), pp. C114
–C139
.21.
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
.22.
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.
23.
Tavakkol
, S.
, Zarrati
, A. R.
, and Khanpour
, M.
, 2017
, “Curvilinear Smoothed Particle Hydrodynamics
,” Int. J. Numer. Methods Fluids
, 83
(2
), pp. 115
–131
.24.
Colagrossi
, A.
, and Landrini
, M.
, 2003
, “Numerical Simulation of Interfacial Flows by Smoothed Particle Hydrodynamics
,” J. Comput. Phys.
, 191
(2
), pp. 448
–475
.25.
Monaghan
, J. J.
, and Kos
, A.
, 1999
, “Solitary Waves on a Cretan Beach
,” J. Waterw. Port Coastal Ocean Eng.
, 125
(3
), pp. 145
–154
.26.
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
.27.
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
.28.
Liu
, H.
, Li
, J.
, Shao
, S.
, and Tan
, S. K.
, 2015
, “SPH Modeling of Tidal Bore Scenarios
,” Nat. Hazards
, 75
(2
), pp. 1247
–1270
.29.
Glasheen
, J. W.
, and McMahon
, T. A.
, 1996
, “Vertical Water Entry of Disks at Low Froude Numbers
,” Phys. Fluids
, 8
(8
), pp. 2078
–2083
.30.
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
.31.
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
.32.
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
.33.
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
.34.
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
.Copyright © 2019 by ASME
You do not currently have access to this content.
