Abstract

The swirling secondary flow in curved pipes is studied in three-space dimensions using a weakly compressible smoothed particle hydrodynamics (WCSPH) formulation coupled to new nonreflecting outflow boundary conditions. A large eddy simulation (LES) model for turbulence is benchmarked with existing experimental data. After validation of the present model against experimental results for a 90deg pipe bend, a detailed numerical study aimed at reproducing experimental flow measurements for a wide range of Reynolds numbers has been performed for different pipe geometries, including U pipe bends, S-shaped pipes, and helically coiled pipes. In all cases, the SPH calculated behavior shows reasonably good agreement with the measurements across and downstream the bend in terms of streamwise velocity profiles and cross-sectional contours. Maximum mean-root-square deviations from the experimentally obtained profiles are always less than 1.8%. This combined with the very good matching between the SPH and the experimental cross-sectional contours shows the uprising capabilities of the present scheme for handling engineering applications with streamline curvature, such as flows in bends and manifolds.

References

1.
Humphrey
,
J. A. C.
,
Whitelaw
,
J. H.
, and
Yee
,
G.
,
1981
, “
Turbulent Flow in a Square Duct With Strong Curvature
,”
J. Fluid Mech.
,
103
(
1
), pp.
443
463
.10.1017/S0022112081001419
2.
Taylor
,
A. M. K. P.
,
Whitelaw
,
J. H.
, and
Yianneskis
,
M.
,
1982
, “
Curved Ducts With Strong Secondary Motion: Velocity Measurements of Developing Laminar and Turbulent Flow
,”
ASME J. Fluids Eng.
,
104
(
3
), pp.
350
359
.10.1115/1.3241850
3.
Enayet
,
M. M.
,
Gibson
,
M. M.
,
Taylor
,
A. M. K. P.
, and
Yianneskis
,
M.
,
1982
, “
Laser-Doppler Measurements of Laminar and Turbulent Flow in a Pipe Bend
,”
Int. J. Heat Fluid Flow
,
3
(
4
), pp.
213
219
.10.1016/0142-727X(82)90024-8
4.
Chang
,
S. M.
,
Humphrey
,
J. A. C.
, and
Modavi
,
A.
,
1983
, “
Turbulent Flow in a Strongly Curved U-Bend and Downstream Tangent of Square Cross-Sections
,”
Physicochem. Hydrodyn.
,
4
(
3
), pp.
243
269
.
5.
Sreenivasan
,
K. R.
, and
Strykowski
,
P. J.
,
1983
, “
Stabilization Effects in Flow Through Helically Coiled Pipes
,”
Exp. Fluids
,
1
(
1
), pp.
31
36
.10.1007/BF00282264
6.
Azzola
,
J.
,
Humphrey
,
J. A. C.
,
Iacovides
,
H.
, and
Launder
,
B. E.
,
1986
, “
Developing Turbulent Flow in a U-Bend of Circular Cross-Section: Measurements and Computation
,”
ASME J. Fluids Eng.
,
108
(
2
), pp.
214
221
.10.1115/1.3242565
7.
Fiedler
,
H. E.
,
1997
, “
A Note on Secondary Flow in Bends and Bend Combinations
,”
Exp. Fluids
,
23
(
3
), pp.
262
264
.10.1007/s003480050109
8.
Sudo
,
K.
,
Sumida
,
M.
, and
Hibara
,
H.
,
1998
, “
Experimental Investigation on Turbulent Flow in a Circular-Sectioned 90-Degree Bend
,”
Exp. Fluids
,
25
(
1
), pp.
42
49
.10.1007/s003480050206
9.
Sudo
,
K.
,
Sumida
,
M.
, and
Hibara
,
H.
,
2000
, “
Experimental Investigation on Turbulent Flow Through a Circular-Sectioned 180° Bend
,”
Exp. Fluids
,
28
(
1
), pp.
51
57
.10.1007/s003480050007
10.
Sudo
,
K.
,
Sumida
,
M.
, and
Hibara
,
H.
,
2001
, “
Experimental Investigation on Turbulent Flow Through a Square-Sectioned 180° Bend
,”
Exp. Fluids
,
30
(
3
), pp.
246
252
.10.1007/s003480000157
11.
El-Gammal
,
M.
,
Mazhar
,
H.
,
Cotton
,
J. S.
,
Shefski
,
C.
,
Pietralik
,
J.
, and
Ching
,
C. Y.
,
2010
, “
The Hydrodynamics Effects of Single-Phase Flow on Flow Accelerated Corrosion in a 90-Degree Elbow
,”
Nucl. Eng. Des.
,
240
(
6
), pp.
1589
1598
.10.1016/j.nucengdes.2009.12.005
12.
Hellström
,
L. H. O.
,
Sinha
,
A.
, and
Smits
,
A. J.
,
2011
, “
Visualizing the Very-Large-Scale Motions in Turbulent Pipe Flow
,”
Phys. Fluids
,
23
(
1
), p.
011703
.10.1063/1.3533016
13.
Amicis
,
J. D.
,
Cammi
,
A.
,
Colombo
,
L. P. M.
,
Colombo
,
M.
, and
Ricotti
,
M. E.
,
2014
, “
Experimental and Numerical Study of the Laminar Flow in Helically Coiled Pipes
,”
Prog. Nucl. Energy
,
76
, pp.
206
215
.10.1016/j.pnucene.2014.05.019
14.
Mazhar
,
H.
,
Ewing
,
D.
,
Cotton
,
J. S.
, and
Ching
,
C. Y.
,
2016
, “
Measurement of the Flow Field Characteristics in Single and Dual S-Shape 90° Bends Using Matched Refractive Index PIV
,”
Exp. Therm. Fluid Sci.
,
79
, pp.
65
73
.10.1016/j.expthermflusci.2016.06.025
15.
Oki
,
J.
,
Ikeguchi
,
M.
,
Ogata
,
Y.
,
Nishida
,
K.
,
Yamamoto
,
R.
,
Nakamura
,
K.
,
Yanagida
,
H.
, and
Yokohata
,
H.
,
2017
, “
Experimental and Numerical Investigation of a Pulsatile Flow Field in an S-Shaped Exhaust Pipe of an Automotive Engine
,”
J. Fluid Sci. Technol.
,
12
(
2
), p.
JFST0014
.10.1299/jfst.2017jfst0014
16.
Kalpakli
,
A.
, and
Örlü
,
R.
,
2013
, “
Turbulent Pipe Flow Downstream a 90° Pipe Bend With and Without Superimposed Swirl
,”
Int. J. Heat Fluid Flow
,
41
, pp.
103
111
.10.1016/j.ijheatfluidflow.2013.01.003
17.
Vester
,
A. K.
,
Sattarzadeh
,
S. S.
, and
Örlü
,
R.
,
2016
, “
Combined Hot-Wire and PIV Measurements of a Swirling Turbulent Flow at the Exit of a 90° Pipe Bend
,”
J. Visualization
,
19
(
2
), pp.
261
273
.10.1007/s12650-015-0310-1
18.
Cioncolini
,
A.
, and
Santini
,
L.
,
2006
, “
An Experimental Investigation Regarding the Laminar to Turbulent Flow Transition in Helically Coiled Pipes
,”
Exp. Therm. Fluid Sci.
,
30
(
4
), pp.
367
380
.10.1016/j.expthermflusci.2005.08.005
19.
Hayamizu
,
Y.
,
Yamamoto
,
K.
,
Yanase
,
S.
,
Hyakutake
,
T.
,
Shinohara
,
T.
, and
Morita
,
S.
,
2008
, “
Experimental Study of the Flow in Helical Circular Pipes: Torsion Effect on the Flow Velocity and Turbulence
,”
J. Therm. Sci.
,
17
(
3
), pp.
193
198
.10.1007/s11630-008-0193-8
20.
Gupta
,
R.
,
Wanchoo
,
R. K.
, and
Ali
,
T. R. M. J.
,
2011
, “
Laminar Flow in Helical Coils: A Parameter Study
,”
Ind. Eng. Chem. Res.
,
50
(
2
), pp.
1150
1157
.10.1021/ie101752z
21.
Pimenta
,
T. A.
, and
Campos
,
J. B. L. M.
,
2012
, “
Friction Losses of Newtonian and Non-Newtonian Fluids Flowing in Laminar Regime in a Helical Coil
,”
Exp. Therm. Fluid Sci.
,
36
, pp.
194
204
.10.1016/j.expthermflusci.2011.09.013
22.
Dean
,
W. R.
,
1927
, “
XVI. Note on the Motion of Fluid in a Curved Pipe
,”
London, Edinburgh Dublin Philos. Mag. J. Sci.
,
4
(
20
), pp.
208
223
.10.1080/14786440708564324
23.
Homicz
,
G. F.
,
2004
, “
Computational Fluid Dynamic Simulations of Pipe Elbow Flow
,” Sandia National Laboratories, Albuquerque, NM, Report No. 3467.
24.
Tanaka
,
M.
,
Ohshima
,
H.
, and
Monji
,
H.
,
2009
, “
Numerical Investigation of Elbow Structure in Pipe Flow With Large Eddy Simulation Approach
,”
ASME Paper No. PVP-77598.
25.
Hüttl
,
T. J.
, and
Friedrich
,
R.
,
2001
, “
Direct Numerical Simulation of Turbulent Flows in Curved and Helically Coiled Pipes
,”
Comput. Fluids
,
30
(
5
), pp.
591
605
.10.1016/S0045-7930(01)00008-1
26.
Noorani
,
A.
,
Khoury
,
G. K. E.
, and
Schlatter
,
P.
,
2013
, “
Evolution of Turbulence Characteristics From Straight to Curved Pipes
,”
Int. J. Heat Fluid Flow
,
41
, pp.
16
26
.10.1016/j.ijheatfluidflow.2013.03.005
27.
Kim
,
J.
,
Yadav
,
M.
, and
Kim
,
S.
,
2014
, “
Characteristics of Secondary Flow Induced by 90-Degree Elbow in Turbulent Pipe Flow
,”
Eng. Appl. Comput. Fluid Mech.
,
8
(
2
), pp.
229
239
.10.1080/19942060.2014.11015509
28.
Röhrig
,
R.
,
Jakirlić
,
S.
, and
Tropea
,
C.
,
2015
, “
Comparative Computational Study of Turbulent Flow in a 90° Pipe Elbow
,”
Int. J. Heat Fluid Flow
,
55
, pp.
120
131
.10.1016/j.ijheatfluidflow.2015.07.011
29.
Dutta
,
P.
,
Saha
,
S. K.
,
Nandi
,
N.
, and
Pal
,
N.
,
2016
, “
Numerical Study on Flow Separation in 90° Pipe Bend Under High Reynolds Number by k-ϵ Modelling
,”
Eng. Sci. Technol., Int. J.
,
19
(
2
), pp.
904
910
.
30.
Wang
,
S.
,
Ren
,
C.
,
Sun
,
Y.
,
Yang
,
X.
, and
Tu
,
J.
,
2016
, “
A Study of the Instantaneous Turbulent Flow Field in a 90-Degree Elbow Pipe With Circular Section
,”
Sci. Technol. Nucl. Install.
,
2016
, pp.
1
8
.10.1155/2016/5265748
31.
Di Piazza
,
I.
, and
Ciofalo
,
M.
,
2010
, “
Numerical Prediction of Turbulent Flow and Heat Transfer in Helically Coiled Pipes
,”
Int. J. Therm. Sci.
,
49
(
4
), pp.
653
663
.10.1016/j.ijthermalsci.2009.10.001
32.
Jayakumar
,
J. S.
,
Mahajani
,
S. M.
,
Mandal
,
J. C.
,
Iyer
,
K. N.
, and
Vijayan
,
P. K.
,
2010
, “
Cfd Analysis of Single-Phase Flows Inside Helically Coiled Pipes
,”
Comput. Chem. Eng.
,
34
(
4
), pp.
430
446
.10.1016/j.compchemeng.2009.11.008
33.
Tang
,
L.
,
Tang
,
Y.
, and
Parameswaran
,
S.
,
2016
, “
A Numerical Study of Flow Characteristics in a Helical Pipe
,”
Adv. Mech. Eng.
,
8
(
7
), pp. 1–8.10.1177/1687814016660242
34.
Glenn
,
A. L.
,
Bulusu
,
K. V.
,
Shu
,
F.
, and
Plesniak
,
M. W.
,
2012
, “
Secondary Flow Structures Under Stent-Induced Perturbations for Cardiovascular Flow in a Curve Artery Model
,”
Int. J. Heat Fluid Flow
,
35
, pp.
76
83
.10.1016/j.ijheatfluidflow.2012.02.005
35.
van Wyk
,
S.
,
Wittberg
,
L. P.
,
Bulusu
,
K. V.
,
Fuchs
,
L.
, and
Plesniak
,
M. W.
,
2015
, “
Non-Newtonian Perspectives on Pulsatile Blood-Analog Flows in a 180° Curved Artery Model
,”
Phys. Fluids
,
27
, p.
071901
.10.1063/1.4923311
36.
Vester
,
A. K.
,
Örlü
,
R.
, and
Alfredsson
,
P. H.
,
2016
, “
Turbulent Flows in Curved Pipes: Recent Advances in Experiments and Simulations
,”
ASME Appl. Mech. Rev.
,
68
(
5
), p.
050802
.10.1115/1.4034135
37.
Morris
,
J. P.
,
Fox
,
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
38.
Sigalotti
,
L. D. G.
,
Klapp
,
J.
,
Sira
,
E.
,
Meleán
,
Y.
, and
Hasmy
,
A.
,
2003
, “
SPH Simulations of Time-Dependent Poiseuille Flow at Low Reynolds Numbers
,”
J. Comput. Phys.
,
191
(
2
), pp.
622
638
.10.1016/S0021-9991(03)00343-7
39.
Basa
,
M.
,
Quinlan
,
N.
, and
Lastiwka
,
M.
,
2009
, “
Robustness and Accuracy of SPH Formulations for Viscous Flow
,”
Int. J. Numer. Methods Fluids
,
60
(
10
), pp.
1127
1148
.10.1002/fld.1927
40.
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
7075
.10.1016/j.jcp.2012.05.005
41.
Ferrand
,
M.
,
Laurence
,
D.
,
Rogers
,
B.
,
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. Methods Fluids
,
71
(
4
), pp.
446
472
.10.1002/fld.3666
42.
Meister
,
M.
,
Burger
,
G.
, and
Rauch
,
W.
,
2014
, “
On the Reynolds Number Sensitivity of Smoothed Particle Hydrodynamics
,”
J. Hydraulic Res.
,
52
(
6
), pp.
824
835
.10.1080/00221686.2014.932855
43.
Federico
,
I.
,
Marrone
,
S.
,
Colagrossi
,
A.
,
Aristodemo
,
F.
, and
Antuono
,
M.
,
2012
, “
Simulating 2D Open-Channel Flows Through an SPH Model
,”
Eur. J. Mech.-B
,
34
, pp.
35
46
.10.1016/j.euromechflu.2012.02.002
44.
Liang
,
C.
,
Huang
,
J.
, and
Shi
,
W.
,
2014
, “
A New Treatment for Boundary of Laminar Flow Inlet or Outlet in SPH
,”
J. Software Eng.
,
8
(
4
), pp.
321
327
.10.3923/jse.2014.321.327
45.
Shi
,
Y.
,
Wei
,
J.
,
Li
,
S.
,
Song
,
P.
, and
Zhang
,
B.
,
2019
, “
A Meshless WCSPH Boundary Treatment for Open-Channel Flow Over Small-Scale Rough Bed
,”
Math. Probl. Eng.
,
2019
, pp.
1
17
.10.1155/2019/1573049
46.
Hou
,
Q.
,
Kruisbrink
,
A. C. H.
,
Pearce
,
F. R.
,
Tijsseling
,
A. S.
, and
Yue
,
T.
,
2014
, “
Smoothed Particle Hydrodynamics Simulations of Flow Separation at Bends
,”
Comput. Fluids
,
90
, pp.
138
146
.10.1016/j.compfluid.2013.11.019
47.
Alvarado-Rodríguez
,
C. E.
,
Klapp
,
J.
,
Sigalotti
,
L. D. G.
,
Domínguez
,
J. M.
, and
de la Cruz Sánchez
,
E.
,
2017
, “
Nonreflecting Outlet Boundary Conditions for Incompressible Flows Using SPH
,”
Comput. Fluids
,
159
, pp.
177
188
.10.1016/j.compfluid.2017.09.020
48.
Rup
,
K.
,
Malinowski
,
L.
, and
Sarna
,
P.
,
2011
, “
Measurement of Flow Rate in Square-Sectioned Duct Bend
,”
J. Theor. Appl. Mech.
,
49
, pp.
301
311
.
49.
Rosić
,
N. M.
,
Kolarević
,
M. B.
,
Savić
,
L. M.
,
Đorđević
,
D. M.
, and
Kapor
,
R. S.
,
2017
, “
Numerical Modelling of Supercritical Flow in Circular Conduit Bends Using SPH Method
,”
J. Hydrodyn., Ser. B
,
29
(
2
), pp.
344
352
.10.1016/S1001-6058(16)60744-8
50.
Becker
,
M.
, and
Teschner
,
M.
,
2007
, “
Weakly Compressible SPH for Free Surface Flows
,”
Proceedings of the ACM SIGGRAPH/Europhysics Symposium on Computer Animation, ACM SIGGRAPH/Europhysics
, San Diego, CA, pp.
209
217
.
51.
Antuono
,
M.
,
Colagrossi
,
A.
,
Marrone
,
S.
, and
Molteni
,
D.
,
2010
, “
Free-Surface Flows Solved by Means of SPH Schemes With Numerical Diffusive Terms
,”
Comput. Phys. Commun.
,
181
(
3
), pp.
532
549
.10.1016/j.cpc.2009.11.002
52.
Yoshizawa
,
A.
,
1986
, “
Statistical Theory for Compressible Turbulent Shear Flows, With the Application to Subgrid Modeling
,”
Phys. Fluids
,
29
(
7
), pp.
2152
2164
.10.1063/1.865552
53.
Gomez-Gesteira
,
M.
,
Rogers
,
B. D.
,
Crespo
,
A. J. C.
,
Dalrymple
,
R. A.
,
Narayanaswamy
,
M.
, and
Dominguez
,
J. M.
,
2012
, “
Sphysics—Development of a Free-Surface Fluid Solver—Part 1: Theory and Formulations
,”
Comput. Geosci.
,
48
, pp.
289
299
.10.1016/j.cageo.2012.02.029
54.
Monaghan
,
J. J.
,
1992
, “
Smoothed Particle Hydrodynamics
,”
Annu. Rev. Astron. Astrophys.
,
30
(
1
), pp.
543
574
.10.1146/annurev.aa.30.090192.002551
55.
Liu
,
M. B.
, and
Liu
,
G. R.
,
2010
, “
Smoothed Particle Hydrodynamics (SPH): An Overview and Recent Developments
,”
Arch. Comput. Methods Eng.
,
17
(
1
), pp.
25
76
.10.1007/s11831-010-9040-7
56.
Colagrossi
,
A.
, and
Landrini
,
M.
,
2003
, “
Numerical Simulation of Interfacial Flows by Smoothed Particle Hydrodynamics
,”
J. Comput. Phys.
,
191
(
2
), pp.
448
475
.10.1016/S0021-9991(03)00324-3
57.
Lo
,
E. Y. M.
, and
Shao
,
S.
,
2002
, “
Simulation of Near-Shore Solitary Wave Mechanics by an Incompressible SPH Method
,”
Appl. Ocean Res.
,
24
(
5
), pp.
275
286
.
58.
Hernquist
,
L.
, and
Katz
,
N.
,
1989
, “
Treesph: A Unification of SPH With the Hierarchical Tree Method
,”
Astrophys. J. Suppl. Ser.
,
70
, pp.
419
446
.10.1086/191344
59.
Vacondio
,
R.
,
Rogers
,
B. D.
,
Stansby
,
P. K.
,
Mignosa
,
P.
, and
Feldman
,
J.
,
2013
, “
Variable Resolution for SPH: A Dynamic Particle Coalescing and Splitting Scheme
,”
Comput. Methods Appl. Mech. Eng.
,
256
, pp.
132
148
.10.1016/j.cma.2012.12.014
60.
Wendland
,
H.
,
1995
, “
Piecewise Polynomial, Positive Definite and Compactly Supported Radial Functions of Minimal Degree
,”
Adv. Comput. Math.
,
4
(
1
), pp.
389
396
.10.1007/BF02123482
61.
Dehnen
,
W.
, and
Aly
,
H.
,
2012
, “
Improving Convergence in Smoothed Particle Hydrodynamics Simulations Without Pairing Instability
,”
Mon. Not. R. Astron. Soc.
,
425
(
2
), pp.
1068
1082
.10.1111/j.1365-2966.2012.21439.x
62.
Crespo
,
A. J. C.
,
Gómez-Gesteira
,
M.
, and
Dalrymple
,
R. A.
,
2007
, “
Boundary Conditions Generated by Dynamic Particles in SPH Methods
,”
Comput., Mater. Continua
,
5
, pp.
173
184
.10.3970/cmc.2007.005.173
63.
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
.10.1016/j.cpc.2014.10.004
64.
MacDonald
,
J. R.
,
1966
, “
Some Simple Isothermal Equations of State
,”
Rev. Mod. Phys.
,
38
(
4
), pp.
669
679
.10.1103/RevModPhys.38.669
65.
Li
,
Y.-H.
,
1967
, “
Equation of State of Water and Sea Water
,”
J. Geophys. Res.
,
72
(
10
), pp.
2665
2678
.
66.
Zagarola
,
M. V.
, and
Smits
,
A. J.
,
1997
, “
Scaling of the Mean Velocity Profile for Turbulent Pipe Flow
,”
Phys. Rev. Lett.
,
78
(
2
), pp.
239
242
.10.1103/PhysRevLett.78.239
67.
Ito
,
H.
,
1959
, “
Friction Factors for Turbulent Flow in Curved Pipes
,”
ASME J. Fluids Eng.
,
81
(
2
), pp.
123
132
.10.1115/1.4008390
68.
Murakami
,
M.
,
Mori
,
K.
, and
Sano
,
K.
,
1971
, “
A Study on the Hydraulic Loss of Tubular Coils
,”
Bull. Jpn. Soc. Mech. Eng.
,
14
(
78
), pp.
1296
1303
.10.1299/jsme1958.14.1296
69.
Jeong
,
S.-J.
,
2014
, “
A Full Transient Three-Dimensional Study on the Effect of Pulsating Exhaust Flow Under Real Running Condition on the Thermal and Chemical Behavior of Closed-Coupled Catalyst
,”
Chem. Eng. Sci.
,
117
, pp.
18
30
.10.1016/j.ces.2014.06.011
70.
Womersley
,
J. R.
,
1955
, “
Method for the Calculation of Velocity, Rate of Flow and Viscous Drag in Arteries When the Pressure Gradient is Known
,”
J. Physiol.
,
127
(
3
), pp.
553
563
.10.1113/jphysiol.1955.sp005276
You do not currently have access to this content.