Abstract

A three-dimensional full-scale centrifugal pump is simulated using the moving particle semi-implicit (MPS) method. The generic smoothed wall (GSW) boundary is used and extended to three dimensions to address complicated wall shapes and thin-walled structures such as blades in turbomachines. The nonsurface detection technique (NSD) based on conceptual particles is introduced to avoid the loss of the particle-number-density near wall boundaries. A generic approach that can transfer arbitrary CAD models to wall-particle models is established by utilizing the nodal information of the shell mesh. An adaptative resolution technique is proposed by using fine and coarse particles to model the wall boundary with complex geometry. Fine and coarse particles are applied to curved and flat surfaces, respectively, to reduce the computational cost while maintaining high discretizing precision. A criterion based on the normal smooth angle (NSA) is defined to evaluate the local or global precision of established models and provide instructions for refinement. A fully-developed velocity inflow boundary based on 3D inlet rings and pressure outflow boundary based on the moving virtual wall is implemented. Three typical cases including hydrostatic cases with a typical geometry, flow over a two-dimensional backward-facing step, and flow over a three-dimensional tube are tested to verify the proposed models. A particle-based framework to simulate incompressible fluid machines, in which flow fields can be integrally discretized and solved within a single coordinate system, is established. The results are compared with those of the fine volume method and satisfactory agreements are observed.

References

1.
Chaussonnet
,
G.
,
Koch
,
R.
, and
Koch
,
R.
,
2018
, “
Smoothed Particle Hydrodynamics Simulation of an Air-Assisted Atomizer Operating at High Pressure: Influence of Non-Newtonian Effects
,”
ASME J. Fluids Eng.
,
140
(
1
), p. 061301.10.1115/1.4038753
2.
Sun
,
Z. G.
,
Liang
,
Y. Y.
, and
Xi
,
G.
,
2011
, “
Numerical Simulation of the flow in Straight Blade Agitator With the MPS Method
,”
Int. J. Numer. Methods Fluids
,
67
(
12
), pp.
1960
1972
.10.1002/fld.2474
3.
Wang
,
F.
,
Sun
,
Z. G.
, and
Liu
,
Q. X.
,
2021
, “
Numerical Analysis of Flow Field in the Y-Type Micromixer Using MPS Method
,”
J. Xi'an Jiaotong Univ.
,
55
(
5
), pp.
5
14
.107652/xjtuxb202105018
4.
Rahim
,
S.
,
2018
, “
Incompressible SPH Modeling of Rotary Micropump Mixers
,”
Int. J. Comput. Methods
,
15
(
1
), pp.
191
207
.10.1142/S0219876218500196
5.
Marongiu
,
J.-C.
,
Leboeuf
,
F.
,
Caro
,
JËlle.
, and
Parkinson
,
E.
,
2010
, “
Free Surface flows Simulations in Pelton Turbines Using a Hybrid SPH-ALE Method
,”
J. Hydraulic Res.
,
48
(
sup1
), pp.
40
49
.10.1080/00221686.2010.9641244
6.
Kakuda
,
K.
,
Ushiyama
,
Y.
, and
Obara
,
S.
,
2010
, “
Flow Simulations in a Liquid Ring Pump Using a Particle Method
,”
Comput. Model. Eng. Sci.
,
66
(
3
), pp.
215
226
.10.3970/cmes.2010.066.215
7.
Kakuda
,
K.
,
Nagashima
,
T.
, and
Hayashi
,
Y.
,
2013
, “
Three-Dimensional Fluid Flow Simulations Using GPU-Based Particle Method
,”
Comput. Model. Eng. Sci.
,
93
(
5
), pp.
363
376
.10.3970/cmes.2013.093.363
8.
Samir
,
H. S.
, and
Yildiz
,
M.
,
2013
, “
Modeling Die Swell of Second-Order Fluids Using Smoothed Particle Hydrodynamics
,”
ASME J. Fluids Eng.
,
135
(
5
), p. 051103.10.1115/1.4023645
9.
Zhe
,
J.
,
Milos
,
S.
, and
Erwin
,
A. H.
,
2018
, “
Numerical Simulations of Oil flow Inside a Gearbox by Smoothed Particle Hydrodynamics (SPH) Method
,”
Tribol. Int.
,
127
(
5
), pp.
47
58
.10.1016/j.triboint.2018.05.034
10.
Deng
,
X.
,
Wang
,
S.
,
Wang
,
S.
,
Wang
,
J.
,
Liu
,
Y.
,
Dou
,
Y.
,
He
,
G.
, and
Qian
,
L.
,
2020
, “
Lubrication Mechanism in Gearbox of High-Speed Railway Trains
,”
J. Adv. Mech. Des., Syst., Manuf.
,
14
(
4
), p.
JAMDSM0054
.10.1299/jamdsm.2020jamdsm0054
11.
Guo
,
D.
,
Chen
,
F.
,
Liu
,
J.
,
Wang
,
Y.
, and
Wang
,
X.
,
2020
, “
Numerical Modeling of Churning Power Loss of Gear System Based on Moving Particle Method
,”
Tribol. Trans.
,
63
(
1
), pp.
182
193
.10.1080/10402004.2019.1682212
12.
Adami
,
S.
,
Hu
,
X. Y.
, and
Adams
,
N. A.
,
2012
, “
A Generalized Wall Boundary Condition for Smoothed Particle Hydrodynamics
,”
J. Comput. Phys.
,
231
(
21
), pp.
7057
7575
.10.1016/j.jcp.2012.05.005
13.
Cummins
,
S. J.
, and
Murray
,
R.
,
1999
, “
An SPH Projection Method
,”
J. Comput. Phys.
,
152
(
2
), pp.
584
607
.10.1006/jcph.1999.6246
14.
Gómez-Gesteira
,
M.
,
Cerqueiro
,
D.
,
Crespo
,
C.
, and
Dalrymple
,
R. A.
,
2005
, “
Green Water Overtopping Analyzed With a SPH Model
,”
Ocean Eng.
,
32
(
2
), pp.
223
238
.10.1016/j.oceaneng.2004.08.003
15.
Georgios
,
F.
,
Renato
,
V.
, and
Benedict
,
D. R.
,
2015
, “
On the Approximate Zeroth and first-Order Consistency in the Presence of 2-D Irregular Boundaries in SPH Obtained by the Virtual Boundary Particle Methods
,”
Int. J. Numer. Meth. Fluids
,
78
(
2
), pp.
475
501
.10.1002/fld.4026
16.
Joseph
,
P.
,
Morris
,
P. J.
, and
Zhu
,
Y.
,
1997
, “
Modeling Low Reynolds Number Incompressible Flows Using SPH
,”
J. Comput. Phys.
,
136
(
1
), pp.
214
226
.10.1006/jcph.1997.5776
17.
Zhang
,
T.
,
Koshizuka
,
S.
,
Murotani
,
K.
,
Shibata
,
K.
,
Ishii
,
E.
, and
Ishikawa
,
M.
,
2016
, “
Improvement of Boundary Conditions for Non-Planar Boundaries Represented by Polygons With an Initial Particle Arrangement Technique
,”
Int. J. Comput. Fluid Dyn.
,
30
(
2
), pp.
155
175
.10.1080/10618562.2016.1167194
18.
Zhang
,
T.
,
Koshizuka
,
S.
,
Murotani
,
K.
,
Shibata
,
K.
, and
Ishii
,
E.
,
2017
, “
Improvement of Pressure Distribution to Arbitrary Geometry With Boundary Condition Represented by Polygons in Particle Method
,”
Int. J. Numer. Meth. Eng.
,
112
(
7
), pp.
685
710
.10.1002/nme.5520
19.
Zhang
,
T.
,
Koshizuka
,
S.
,
Xuan
,
P.
,
Li
,
J.
, and
Gong
,
C.
,
2019
, “
Enhancement of Stabilization of MPS to Arbitrary Geometries With a Generic Wall Boundary Condition
,”
Comput. Fluids
,
178
(
3
), pp.
88
112
.10.1016/j.compfluid.2018.09.008
20.
Matsunaga
,
T.
,
Södersten
,
A.
, and
Shibata
,
K.
,
2020
, “
Improved Treatment of Wall Boundary Conditions for a Particle Method With Consistent Spatial Discretization
,”
Comput. Methods Appl. Mech. Eng.
,
358
(
1
), pp.
112
140
.10.1016/j.cma.2019.112624
21.
Wang
,
Z.
,
Duan
,
G.
,
Matsunaga
,
T.
, and
Sugiyama
,
T.
,
2020
, “
Consistent Robin Boundary Enforcement of Particle Method for Heat Transfer Problem With Arbitrary Geometry
,”
Int. J. Heat Mass Transfer
,
157
(
2
), pp.
119919
139
.10.1016/j.ijheatmasstransfer.2020.119919
22.
Shibata
,
K.
,
Masaie
,
I.
,
Kondo
,
M.
,
Murotani
,
K.
, and
Koshizuka
,
S.
,
2015
, “
Improved Pressure Calculation for the Moving Particle Semi-Implicit Method
,”
Comp. Part. Mech.
,
2
(
1
), pp.
91
108
.10.1007/s40571-015-0039-6
23.
Mitsume
,
N.
,
Yoshimura
,
S.
, and
Murotani
,
K.
,
2014
, “
Improved MPS-FE Fluid-Structure Interaction Coupled Method With MPS Polygon Wall Boundary Model
,”
Comput. Model. Eng. Sci.
,
101
(
4
), pp.
229
247
.10.3970/cmes.2014.101.229
24.
Long
,
T.
,
Hu
,
D.
,
Wan
,
D.
,
Zhuang
,
C.
, and
Yang
,
G.
,
2017
, “
An Arbitrary Boundary With Ghost Particles Incorporated in Coupled FEM–SPH Model for FSI Problems
,”
J. Comput. Phys.
,
350
(
4
), pp.
166
183
.10.1016/j.jcp.2017.08.044
25.
Nguyen
,
M. T.
,
Abdelraheem
,
M. A.
, and
Lee
,
S. W.
,
2018
, “
Improved Wall Boundary Conditions in the Incompressible Smoothed Particle Hydrodynamics Method
,”
Int. J. Numer. Methods Heat Fluid Flow
,
28
(
3
), pp.
704
725
.10.1108/HFF-02-2017-0056
26.
Nasar
,
A. M. A.
,
Fourtakas
,
G.
,
Lind
,
S. J.
,
Rogers
,
B. D.
,
Stansby
,
P. K.
, and
King
,
J. R. C.
,
2021
, “
High-Order Velocity and Pressure Wall Boundary Conditions in Eulerian Incompressible SPH
,”
J. Comput. Phys.
,
434
(
3
), pp.
109
138
.10.1016/j.jcp.2020.109793
27.
Ferrand
,
M.
,
Laurence
,
D. R.
,
Rogers
,
B. D.
,
Violeau
,
D.
, and
Kassiotis
,
C.
,
2013
, “
Unified Semi-Analytical Wall Boundary Conditions for Inviscid Laminar or Turbulent flows in the Meshless SPH Method
,”
Int. J. Numer. Meth. Fluids
,
71
(
4
), pp.
446
472
.10.1002/fld.3666
28.
Leroy
,
A.
,
Violeau
,
D.
,
Ferrand
,
M.
, and
Kassiotis
,
C.
,
2014
, “
Unified Semi-Analytical Wall Boundary Conditions Applied to 2-D Incompressible SPH
,”
J. Comput. Phys.
,
261
(
3
), pp.
106
129
.10.1016/j.jcp.2013.12.035
29.
Mayrhofer
,
A.
,
Ferrand
,
M.
,
Kassiotis
,
C.
,
Violeau
,
D.
, and
Morel
,
F.-X.
,
2015
, “
Unified Semi-Analytical Wall Boundary Conditions in SPH: Analytical Extension to 3-D
,”
Numer. Algorithms
,
68
(
1
), pp.
15
34
.10.1007/s11075-014-9835-y
30.
Aristodemo
,
F.
,
Marrone
,
S.
, and
Federico
,
I.
,
2015
, “
SPH Modeling of Plane Jets Into Water Bodies Through an inflow/Outflow Algorithm
,”
Ocean Eng.
,
105
(
2
), pp.
160
175
.10.1016/j.oceaneng.2015.06.018
31.
Marrone
,
S.
,
Antuono
,
M.
,
Colagrossi
,
A.
,
Colicchio
,
G.
,
Le Touzé
,
D.
, and
Graziani
,
G.
,
2011
, “
θ-SPH Model for Simulating Violent Impact flows
,”
Comput. Methods Appl. Mech. Eng.
,
200
(
13–16
), pp.
1526
1542
.10.1016/j.cma.2010.12.016
32.
He
,
Y.
,
Zhou
,
Z-y.
,
Cao
,
W-J.
, and
Chen
,
W-P.
,
2011
, “
Simulation of Mould Filling Process Using Smoothed Particle Hydrodynamics
,”
Trans. Nonferrous Met. Soc. China
,
21
(
12
), pp.
2684
2692
.10.1016/S1003-6326(11)61111-4
33.
Shahriari
,
S.
,
Kadem
,
L.
,
Rogers
,
B. D.
, and
Hassan
,
I.
,
2012
, “
Smoothed Particle Hydrodynamics Method Applied to Pulsatile flow Inside a Rigid Two-Dimensional Model of Left Heart Cavity
,”
Int. J. Numer. Meth. Fluids
,
28
(
11
), pp.
1121
1143
.10.1002/cnm.2482
34.
Alvarado
,
R. C. E.
,
Sigalotti
,
L. D. G.
, and
Klapp
,
J.
,
2021
, “
Smoothed Particle Hydrodynamics Simulations of Turbulent Flow in Curved Pipes With Different Geometries: A Comparison With Experiments
,”
ASME J. Fluids Eng.
,
143
(
9
), p. 091503.10.1115/1.4050514
35.
Liu
,
Z. G.
, and
Liu
,
Z. X.
,
2017
, “
The Comparison of Viscous Force Approximations of SPH in Poiseuille Flow Simulation
,”
ASME J. Fluids Eng.
,
139
(
5
), p. 051302.10.1115/1.4035635
36.
Kunz
,
P.
,
Hirschler
,
M.
,
Huber
,
M.
, and
Nieken
,
U.
,
2016
, “
Inflow/Outflow With Dirichlet Boundary Conditions for Pressure in ISPH
,”
J. Comput. Phys.
,
326
(
1
), pp.
171
187
.10.1016/j.jcp.2016.08.046
37.
Kazemi
,
E.
,
Nichols
,
A.
,
Tait
,
S.
, and
Shao
,
S. D.
,
2017
, “
SPH Modelling of Depth-Limited Turbulent Open Channel flows Over Rough Boundaries
,”
Int. J. Numer. Methods Fluids
,
83
(
1
), pp.
3
27
.10.1002/fld.4248
38.
Monteleone
,
A.
,
Montefort
,
M.
, and
Napoli
,
E.
,
2017
, “
Inflow/Outflow Pressure Boundary Conditions for Smoothed Particle Hydrodynamics Simulations of Incompressible flows
,”
Comput. Fluids
,
159
(
2
), pp.
9
22
.10.1016/j.compfluid.2017.09.011
39.
Tafuni
,
A.
,
Domínguez
,
J. M.
,
Vacondio
,
R.
, and
Crespo
,
A. J. C.
,
2018
, “
A Versatile Algorithm for the Treatment of Open Boundary Conditions in Smoothed Particle Hydrodynamics GPU Models
,”
Comput. Methods Appl. Mech. Eng.
,
342
(
1
), pp.
604
624
.10.1016/j.cma.2018.08.004
40.
Thomas
,
D. G.
,
Florian
,
D. V.
,
Henri
,
C.
, and
Philippe
,
R.
,
2018
, “
Simulations of Intermittent Two-Phase flows in Pipes Using Smoothed Particle Hydrodynamics
,”
Comput. Fluids
,
177
(
4
), pp.
101
122
.10.1016/j.compfluid.2018.10.004
41.
Verbrugghe
,
T.
,
Domínguez
,
J. M.
,
Altomare
,
C.
,
Tafuni
,
A.
,
Vacondio
,
R.
,
Troch
,
P.
, and
Kortenhaus
,
A.
,
2019
, “
Non-Linear Wave Generation and Absorption Using Open Boundaries Within DualSPHysics
,”
Comput. Phys. Commun.
,
240
(
3
), pp.
46
59
.10.1016/j.cpc.2019.02.003
42.
Ferrand
,
M.
,
Joly
,
A.
,
Kassiotis
,
C.
,
Violeau
,
D.
,
Leroy
,
A.
,
Morel
,
F.-X.
, and
Rogers
,
B. D.
,
2017
, “
Unsteady Open Boundaries for SPH Using Semi-Analytical Conditions and Riemann Solver in 2D
,”
Comput. Phys. Commun.
,
210
(
9
), pp.
29
44
.10.1016/j.cpc.2016.09.009
43.
Shakibaeinia
,
A.
, and
Jin
,
Y. C.
,
2011
, “
MPS-Based Mesh-Free Particle Method for Modeling Open-Channel Flows
,”
J. Hydraul. Eng.
,
137
(
11
), pp.
1375
1384
.10.1061/(ASCE)HY.1943-7900.0000394
44.
Shakibaeinia
,
A.
, and
Jin
,
Y. C.
,
2010
, “
A Weakly Compressible MPS Method for Modeling of Open-Boundary Free-Surface flow
,”
Int. J. Numer. Methods Fluids
,
63
(
2
), pp.
1208
1232
.10.1002/fld.2132
45.
Xiang
,
H.
, and
Chen
,
B.
,
2015
, “
Simulating non-Newtonian Flows With the Moving Particle Semi-Implicit Method With an SPH Kernel
,”
Fluid Dyn. Res.
,
47
(
1
), pp.
015511
42
.10.1088/0169-5983/47/1/015511
46.
Liu
,
Q. X.
,
Sun
,
Z. G.
,
Sun
,
Y. J.
,
Chen
,
X.
, and
Xi
,
G.
,
2019
, “
Numerical Investigation of Liquid Dispersion by Hydrophobic/Hydrophilic Mesh Packing Using Particle Method
,”
Chem. Eng. Sci.
,
202
(
2
), pp.
447
461
.10.1016/j.ces.2019.03.046
47.
Jafari-Nodoushan
,
E.
,
Hosseini
,
K.
,
Shakibaeinia
,
A.
, and
Mousavi
,
S.-F.
,
2016
, “
Meshless Particle Modelling of Free Surface Flow Over Spillways
,”
J. Hydroinfo.
,
18
(
2
), pp.
354
370
.10.2166/hydro.2015.096
48.
Shibata
,
K.
,
Koshizuka
,
S.
,
Matsunaga
,
T.
, and
Masaie
,
I.
,
2017
, “
The Overlapping Particle Technique for Multi-Resolution Simulation of Particle Methods
,”
Comput. Methods Appl. Mech. Eng.
,
325
(
1
), pp.
434
462
.10.1016/j.cma.2017.06.030
49.
Shibata
,
K.
,
Koshizuka
,
S.
,
Murotani
,
K.
,
Sakai
,
M.
, and
Masaie
,
I.
,
2015
, “
Boundary Conditions for Simulating Karman Vortices Using the MPS Method
,”
Jpn. Soc. Simul. Technol.
,
2
(
2
), pp.
235
254
.10.15748/jasse.2.235
50.
Tanaka
,
M.
,
Cardoso
,
R.
, and
Bahai
,
H.
,
2018
, “
Multi-Resolution MPS Method
,”
J. Comput. Phys.
,
359
(
4
), pp.
106
136
.10.1016/j.jcp.2017.12.042
51.
Sun
,
Y. J.
,
Xi
,
G.
, and
Sun
,
Z. G.
,
2021
, “
A Generic Smoothed Wall Boundary in Multi-Resolution Particle Method for Fluid–Structure Interaction Problem
,”
Comput. Methods Appl. Mech. Eng.
,
378
(
1
), pp.
113
726
.10.1016/j.cma.2021.113726
52.
Chen
,
X.
,
Xi
,
G.
, and
Sun
,
Z. G.
,
2014
, “
Improving Stability of MPS Method by a Computational Scheme Based on Conceptual Particles
,”
Comput. Methods Appl. Mech. Eng.
,
278
(
5
), pp.
254
271
.10.1016/j.cma.2014.05.023
53.
Abbas
,
K.
, and
Hitoshi
,
G.
,
2013
, “
Enhancement of Performance and Stability of MPS Mesh-Free Particle Method for Multiphase flows Characterized by High Density Ratios
,”
J. Comput. Phys.
,
242
(
2
), pp.
211
233
.10.1016/j.jcp.2013.02.002
54.
Tanaka
,
M.
, and
Masunaga
,
T.
,
2010
, “
Stabilization and Smoothing of Pressure in MPS Method by Quasi-Compressibility
,”
J. Comput. Phys.
,
229
(
11
), pp.
4279
4290
.10.1016/j.jcp.2010.02.011
55.
Armaly
,
B. F.
,
Durst
,
F.
,
Pereira
,
J. C. F.
, and
Schönung
,
B.
,
1983
, “
Experimental and Theoretical Investigation of Backward-Facing Step Flow
,”
J. Fluid Mech
,
127
(
1
), pp.
473
496
.10.1017/S0022112083002839
56.
Hu
,
F. Y.
,
Wang
,
Z. D.
,
Tamai
,
T.
, and
Koshizuka
,
S.
,
2020
, “
Consistent Inlet and Outlet Boundary Conditions for Particle Methods
,”
Int. J. Numer. Methods Fluids
,
92
(
1
), pp.
1
19
.10.1002/fld.4768
57.
Vacondio
,
R.
,
Altomare
,
C.
,
De Leffe
,
M.
,
Hu
,
X.
,
Le Touzé
,
D.
,
Lind
,
S.
,
Marongiu
,
J.-C.
,
Marrone
,
S.
,
Rogers
,
B. D.
, and
Souto-Iglesias
,
A.
,
2021
, “
Grand Challenges for Smoothed Particle Hydrodynamics Numerical Schemes
,”
Comput. Particle Mech.
,
8
(
3
), pp.
575
588
.10.1007/s40571-020-00354-1
You do not currently have access to this content.