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.

References

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
.
You do not currently have access to this content.