Curved pipes are essential components of nearly all the industrial process equipments, ranging from power production, chemical and food industries, heat exchangers, nuclear reactors, or exhaust gas ducts of engines. During the last two decades, an interest on turbulent flows in such conduits has revived, probably due to their connection to technical applications such as cooling systems of nuclear reactors (e.g., safety issues due to flow-induced fatigue) and reciprocating engines (e.g., efficiency optimization through exhaust gas treatment in pulsatile turbulent flows). The present review paper, therefore, is an account on the state-of-the-art research concerning turbulent flow in curved pipes, naturally covering mostly experimental work, while also analytical and numerical works are reviewed. This paper starts with a historical review on pipe flows in general and specifically on flows through curved conduits. In particular, research dealing with the effect of curvature on transition to turbulence, work dealing with pressure losses in curved pipes, as well as turbulence statistics are summarized. The swirl-switching phenomenon, a specific structural phenomenon occurring in turbulent curved pipe flows, which has interesting fundamental as well as practical implications, is reviewed. Additional complications, with respect to flow through bends, namely, entering swirling flow and pulsating flow, are reviewed as well. This review closes with a summary on the main literature body as well as an outlook on future work that should be performed in order to tackle open questions remaining in the field.

References

References
1.
Bradshaw
,
P.
,
1973
, “
Effects of Streamline Curvature on Turbulent Flow
,”
AGARDograph No. 169
.http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=AD0768316
2.
Goldstein
,
S.
,
1938
,
Modern Developments in Fluid Mechanics
,
Oxford University Press
,
Oxford, UK
.
3.
Schlichting
,
H.
,
1979
,
Boundary-Layer Theory
,
McGraw–Hill
,
New York
.
4.
Ward-Smith
,
A. J.
,
1980
,
Internal Fluid Flow. The Fluid Dynamics of Flow in Pipes and Ducts
,
Clarendon Press
,
Oxford, UK
.
5.
Pedley
,
T. J.
,
1980
,
The Fluid Mechanics of Large Blood Vessels
,
Cambridge University Press
,
Cambridge, UK
.
6.
Berger
,
S. A.
,
Talbot
,
L.
, and
Yao
,
L. S.
,
1983
, “
Flow in Curved Pipes
,”
Annu. Rev. Fluid Mech.
,
15
(
1
), pp.
461
512
.
7.
Ito
,
H.
,
1987
, “
Flow in Curved Pipes
,”
Bull. JSME
,
30
(262), pp.
543
552
.https://www.jstage.jst.go.jp/article/jsme1987/30/262/30_262_543/_article
8.
Spedding
,
P. L.
, and
Benard
,
E.
,
2004
, “
Fluid Flow Through 90 Degree Bends
,”
Dev. Chem. Eng. Miner. Process.
,
12
(1–2), pp.
107
128
.
9.
Naphon
,
P.
, and
Wongwises
,
S.
,
2006
, “
A Review of Flow and Heat Transfer Characteristics in Curved Tubes
,”
Renewable Sustainable Energy Rev.
,
10
(
5
), pp.
463
490
.
10.
Vashisth
,
S.
,
Kumar
,
V.
, and
Nigam
,
K. D. P.
,
2008
, “
A Review on the Potential Applications of Curved Geometries in Process Industry
,”
Ind. Eng. Chem. Res.
,
47
(
10
), pp.
3291
3337
.
11.
Kundu
,
K. P.
,
Cohen
,
M. I.
, and
Dowling
,
R. D.
,
2012
,
Fluid Mechanics
,
5th ed.
,
Elsevier
, Oxford, UK.
12.
Dean
,
W. R.
,
1927
, “
Note on the Motion of Fluid in a Curved Pipe
,”
Philos. Mag.
,
4
(
20
), pp.
208
223
.
13.
Dean
,
W. R.
,
1928
, “
The Stream-Line Motion of Fluid in a Curved Pipe
,”
Philos. Mag.
,
5
(30), pp.
671
695
.
14.
McConalogue
,
D. J.
, and
Srivastava
,
R. S.
,
1968
, “
Motion of a Fluid in a Curved Tube
,”
Proc. R. Soc.
,
307
(
1488
), pp.
37
53
.
15.
Taylor
,
G. I.
,
1929
, “
The Criterion for Turbulence in Curved Pipes
,”
Proc. R. Soc.
,
124
(
794
), pp.
243
249
.
16.
White
,
C. M.
,
1929
, “
Streamline Flow Through Curved Pipes
,”
Proc. R. Soc.
,
123
(
792
), pp.
645
663
.
17.
Anwer
,
M.
, and
So
,
R. M. C.
,
1993
, “
Swirling Turbulent Flow Through a Curved Pipe—Part 1: Effect of Swirl and Bend Curvature
,”
Exp. Fluids
,
14
(1), pp.
85
96
.
18.
Rütten
,
F.
,
Meinke
,
M.
, and
Schröder
,
W.
,
2001
, “
Large-Eddy Simulations of 90 deg Pipe Bend Flows
,”
J. Turbul.
,
2
, p.
N3
.
19.
Canton
,
J.
,
Schlatter
,
P.
, and
Örlü
,
R.
,
2016
, “
Modal Instability of the Flow in a Toroidal Pipe
,”
J. Fluid Mech.
,
792
, pp.
894
909
.
20.
Cieślicki
,
K.
, and
Piechna
,
A.
,
2012
, “
Can the Dean Number Alone Characterize Flow Similarity in Differently Bent Tubes?
,”
ASME J. Fluids Eng.
,
134
(
5
), p.
051205
.
21.
Hagen
,
G.
,
1839
, “
Über die Bewegung des Wassers in engen zylindrischen Röhr
,”
Poggendorff's Ann. Phys.
,
46
, pp.
423
442
.
22.
Poiseuille
,
J. L. M.
,
1842
, “
Recherches expérimentales sur le mouvement des liquides dans les tubes de trés-petits diameters
,”
C. R. Chim.
,
11
, pp.
961
967
.
23.
Darcy
,
H.
,
1857
,
Recherches expérimentales relatives au mouvement de l'eau dans les tuyaux
, Mallet-Bachelier, Paris.
24.
Darcy
,
H.
,
1856
,
Les fontaines publiques de la ville de Dijon
,
Dalmont
,
Paris
.
25.
Reynolds
,
O.
,
1883
, “
An Experimental Investigation of the Circumstances Which Determine Whether the Motion of Water Shall Be Direct or Sinuous, and of the Law of Resistance in Parallel Channels
,”
Proc. R. Soc. London
,
35
(224–226), pp.
84
99
.
26.
Boussinesq
,
M. J.
,
1868
, “
Mémoire sur l'influence des frottements dans les mouvements réguliers des fluids
,”
J. Math. Pures Appl.
,
13
(2), pp.
377
424
.
27.
Thomson
,
J.
,
1876
, “
On the Origin of Windings of Rivers in Alluvial Plains With Remarks on the Flow of Water Round Bends in Pipes
,”
Proc. R. Soc.
,
25
, pp.
5
8
.http://rspl.royalsocietypublishing.org/content/25/171-178/5.full.pdf
28.
Thomson
,
J.
,
1877
, “
Experimental Demonstration in Respect to the Origin of Windings of Rivers in Alluvial Plains, and to the Mode of Flow of Water Round Bends of Pipes
,”
Proc. R. Soc.
,
26
(179–184), pp.
356
357
.
29.
Thomson
,
J.
,
1912
,
Collected Papers in Physics and Engineering
,
Cambridge University Press
,
Cambridge, UK
.
30.
Weisbach
,
J.
,
1855
,
Experimentelle Hydraulik
,
Engelhardt
,
Freiberg, Germany
.
31.
Williams
,
G. S.
,
Hubbell
,
C. W.
, and
Fenkell
,
G. H.
,
1902
, “
Experiments at Detroit, MI, on the Effect of Curvature Upon the Flow of Water in Pipes
,”
Am. Soc. Civ. Eng.
,
47
, pp.
1
196
.
32.
Eustice
,
J.
,
1910
, “
Flow of Water in Curved Pipes
,”
Proc. R. Soc.
,
84
(
568
), pp.
107
118
.
33.
Eustice
,
J.
,
1911
, “
Experiments on Stream-Line Motion in Curved Pipes
,”
Proc. R. Soc.
,
85
(
576
), pp.
119
131
.
34.
Dean
,
W. R.
,
1928
, “
Fluid Motion in a Curved Channel
,”
Proc. R. Soc.
,
121
(
787
), pp.
402
420
.
35.
Nature,
1952
, “
Mathematics at University College, London: Prof. W. R. Dean
,”
Nature
,
169
(4306), p.
779
.
36.
Faculty of Mathematics, University of Cambridge, Centre for Mathematical Sciences (personal communication), 2016.
37.
Dean
,
W. R.
, and
Hurst
,
J. M.
,
1959
, “
Note on the Motion of Fluid in a Curved Pipe
,”
Mathematika
,
6
(
1
), pp.
77
85
.
38.
Binnie
,
A. M.
,
1978
, “
Some Notes on the Study of Fluid Mechanics in Cambridge, England
,”
Annu. Rev. Fluid Mech.
,
10
(
1
), pp.
1
11
.
39.
Finlay
,
W. H.
,
Keller
,
J. B.
, and
Ferziger
,
J. H.
,
1988
, “
Instability and Transition in Curved Channel Flow
,”
J. Fluid Mech.
,
194
, pp.
417
456
.
40.
Matsson
,
O. J. E.
, and
Alfredsson
,
P. H.
,
1992
, “
Experiments on Instabilities in Curved Channel Flow
,”
Phys. Fluids A
,
4
(
8
), p.
1666
.
41.
Cohen
,
M.
,
2010
, “
My Dear Eve...: The Remaining Letters From Eve's Rutherford File
,”
Fontanus
,
12
, pp.
1
10
.http://fontanus.mcgill.ca/article/view/188
42.
Batcheloris
,
M.
,
2006
, “
Rutherford and the Trinity Golf Circus
,”
Phys. World
,
19
(1), p.
48
.
43.
Einstein
,
H. A.
,
1926
, “
Die Ursache der Mäanderbildung der Flußläufe und des sogenannten Baerschen Gesetzes
,”
Naturwissenschaften
,
14
(11), pp.
223
224
.
44.
Adler
,
M.
,
1934
, “
Strömung in gekrümmten Rohren
,”
Z. Angew. Math. Mech.
,
14
(
5
), pp.
257
275
.
45.
Wattendorf
,
F. L.
,
1935
, “
A Study of the Effect of Curvature on Fully Developed Turbulent Flow
,”
Proc. R. Soc.
,
148
(
865
), pp.
565
598
.
46.
Greenspan
,
D.
,
1973
, “
Secondary Flow in a Curved Tube
,”
J. Fluid Mech.
,
57
(
1
), pp.
167
176
.
47.
Collins
,
W. M.
, and
Dennis
,
S. C. R.
,
1975
, “
The Steady Motion of a Viscous Fluid in a Curved Tube
,”
Q. J. Mech. Appl. Math.
,
28
(
2
), pp.
133
156
.
48.
Van Dyke
,
M.
,
1978
, “
Extended Stokes Series: Laminar Flow Through a Loosely Coiled Pipe
,”
J. Fluid Mech.
,
86
(
1
), pp.
129
145
.
49.
Smith
,
F. T.
,
1976
, “
Fluid Flow Into a Curved Pipe
,”
Proc. R. Soc.
,
351
(
1664
), pp.
71
87
.
50.
Dennis
,
S. C. R.
, and
Ng
,
M.
,
1982
, “
Dual Solutions for Steady Laminar Flow Through a Curved Tube
,”
Q. J. Mech. Appl. Math.
,
35
(
3
), pp.
305
324
.
51.
Dennis
,
S. C. R.
, and
Riley
,
N.
,
1991
, “
On the Fully Developed Flow in a Curved Pipe at Large Dean Number
,”
Proc. R. Soc.
,
434
(
1891
), pp.
473
478
.
52.
Ito
,
H.
,
1959
, “
Friction Factors for Turbulent Flow in Curved Pipes
,”
ASME J. Basic Eng.
,
81
(2), pp.
123
134
.
53.
Keulegan
,
G. H.
, and
Beij
,
K. H.
,
1937
, “
Pressure Losses for Fluid Flow in Curved Pipes
,”
J. Res. Natl. Bur. Stand.
,
18
(
1
), pp.
89
114
.
54.
Srinivasan
,
P. S.
,
Nandapurkar
,
S. S.
, and
Holland
,
F. A.
,
1970
, “
Friction Factors for Coils
,”
Trans. Inst. Chem. Eng.
,
48
(4–6), pp.
156
161
.
55.
Sreenivasan
,
K. R.
, and
Strykowski
,
P. J.
,
1983
, “
Stabilization Effects in Flow Through Helically Coiled Pipes
,”
Exp. Fluids
,
1
(
1
), pp.
31
36
.
56.
Viswanath
,
P. R.
, and
Narasimha
,
R.
,
1978
, “
Visualisation of Relaminarizing Flows
,”
J. Indian Sci.
,
60
, pp.
159
165
.
57.
Narasimha
,
R.
, and
Sreenivasan
,
K. R.
,
1979
, “
Relaminarization of Fluid Flows
,”
Adv. Appl. Mech.
,
19
, pp.
221
308
.
58.
Kurokawa
,
M.
,
Cheng
,
K. C.
, and
Shi
,
L.
,
1998
, “
Flow Visualization of Relaminarization Phenomena in Curved Pipes and Related Measurements
,”
J. Visualization
,
1
(
1
), pp.
9
28
.
59.
Webster
,
D. R.
, and
Humphrey
,
J. A. C.
,
1993
, “
Experimental Observations of Flow Instability in a Helical Coil (Data Bank Contribution)
,”
ASME J. Fluids Eng.
,
115
(
3
), pp.
436
443
.
60.
Webster
,
D. R.
, and
Humphrey
,
J. A. C.
,
1997
, “
Traveling Wave Instability in Helical Coil Flow
,”
Phys. Fluids
,
9
(
2
), p.
407
.
61.
Di Piazza
,
I.
, and
Ciofalo
,
M.
,
2011
, “
Transition to Turbulence in Toroidal Pipes
,”
J. Fluid Mech.
,
687
, pp.
72
117
.
62.
Kühnen
,
J.
,
Braunshier
,
P.
,
Schwegel
,
M.
,
Kuhlmann
,
H. C.
, and
Hof
,
B.
,
2015
, “
Subcritical Versus Supercritical Transition to Turbulence in Curved Pipes
,”
J. Fluid Mech.
,
770
, p.
R3
.
63.
Kühnen
,
J.
,
2012
, “
Experimental Investigation of Transition to Turbulence in a Torus
,”
Ph.D. thesis
, Technical University Wien, Wien, Austria.http://pub.ist.ac.at/~jkuehnen/files/Kuehnen12_Thesis.pdf
64.
Kühnen
,
J.
,
Holzner
,
M.
,
Hof
,
B.
, and
Kuhlmann
,
H.
,
2014
, “
Experimental Investigation of Transitional Flow in a Toroidal Pipe
,”
J. Fluid Mech.
,
738
, pp.
463
491
.
65.
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
.
66.
Kubair
,
V.
, and
Varrier
,
C. B. S.
,
1961
, “
Pressure Drop for Liquid Flow in Helical Coils
,”
Trans. Indian Inst. Chem. Eng.
,
14
, p.
93
.
67.
Noorani
,
A.
, and
Schlatter
,
P.
,
2015
, “
Evidence of Sublaminar Drag Naturally Occurring in a Curved Pipe
,”
Phys. Fluids
,
27
(
3
), p.
035105
.
68.
Alexander
,
C. W. L.
,
1905
, “
The Resistance Offered to the Flow of Water in Pipes by Bends and Elbows
,”
Minutes Proc. Inst. Civ, Eng.
,
159
, pp.
341
364
.
69.
Grindley
,
J. H.
, and
Gibson
,
A. H.
,
1908
, “
On the Frictional Resistances to the Flow of Air Through a Pipe
,”
Proc. R. Soc.
,
80
(
536
), pp.
114
139
.
70.
Nippert
,
H.
,
1929
, “
Über den strömungsverlust in gekrümmten kanälen
,” Ph.D. thesis, Technischen Hochschule der Freien Stadt Danzig, Danzig, Germany.
71.
Richter
,
H.
,
1930
, “
Der Druckabfall in gekrümmten glatten Rohrleitungen
,”
VDI Forschungsh.
,
338
.
72.
Jeschke
,
H.
,
1925
, “
Wärmeübergang und Druckverlust in Rohrschlangen
,”
VDI Z.
,
506
, pp.
24
28
.
73.
Schmidt
,
E. F.
,
1967
, “
Wärmeübergang und Druckverlust in Rohrschlangen
,”
Chem. Ing. Tech.
,
39
(
13
), pp.
781
789
.
74.
Wasielewski
,
R.
,
1932
, “
Verluste in glatten Rohrkrülmmern mit kreisrundem Querschnitt bei weniger als 90∘ Ablenkung
,”
Mitt. Hydraul. Inst. Techn. Hochsch. München
,
5
, pp.
53
67
.
75.
Barua
,
S. N.
,
1963
, “
On Secondary Flow in Stationary Curved Pipes
,”
Q. J. Mech. Appl. Math.
,
16
(
1
), pp.
61
77
.
76.
Ito
,
H.
,
1960
, “
Pressure Losses in Smooth Pipe Bends
,”
ASME J. Basic Eng.
,
82
(1), pp.
131
140
.
77.
Beck
,
C.
,
1960
, “
Discussion: Pressure Losses in Smooth Pipe Bends
,”
ASME J. Basic Eng.
,
82
(
1
), pp.
140
142
.
78.
Pigott
,
R. J. S.
,
1957
, “
Losses in Pipe and Fittings
,”
Trans. ASME
,
79
, pp.
1767
1783
.
79.
Ward-Smith
,
A. J.
,
1971
,
Pressure Losses in Ducted Flows
,
Butterworth
,
London
.
80.
Ali
,
S.
,
2001
, “
Pressure Drop Correlations for Flow Through Regular Helical Coil Tubes
,”
Fluid Dyn. Res.
,
28
(
4
), pp.
295
310
.
81.
Noorani
,
A.
,
El Khoury
,
G. K.
, and
Schlatter
,
P.
,
2013
, “
Evolution of Turbulence Characteristics From Straight to Curved Pipes
,”
Int. J. Heat Fluid Flow
,
41
(ETMM9), pp.
16
26
.
82.
Weske
,
J. R.
,
1948
, “
Experimental Investigation of Velocity Distributions Downstream of Single Duct Bends
,”
Report No. NACA-TN-1471
.http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA381178
83.
Detra
,
R. W.
,
1953
, “
The Secondary Flow in Curved Pipes
,”
Ph.D. thesis
, The Swiss Federal Institute of Technology, Zurich, Switzerland.
84.
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
.
85.
Enayet
,
M. M.
,
Gibson
,
M. M.
,
Taylor
,
A.
, 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
.
86.
Azzola
,
J.
,
Humprey
,
J. A. C.
,
Iacovides
,
H.
, and
Launder
,
B. E.
,
1986
, “
Developing Turbulent Flow in a U-Bend of Circular Cross-Section: Measurement and Computation
,”
ASME J. Fluids Eng.
,
108
(
2
), pp.
214
221
.
87.
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
.
88.
Anwer
,
M.
,
So
,
R. M. C.
, and
Lai
,
Y. G.
,
1989
, “
Perturbation by and Recovery From Bend Curvature of a Fully Developed Turbulent Pipe Flow
,”
Phys. Fluids A
,
1
(
8
), p.
1387
.
89.
Hellström
,
L. H. O.
,
Zlatinov
,
M.
, and
Smits
,
A. J.
,
2011
, “
Turbulent Pipe Flow Through a 90 deg Bend
,”
7th International Symposium on Turbulence and Shear Flow Phenomena
, Ottawa, Canada, July 28–31.
90.
Rowe
,
M.
,
1970
, “
Measurements and Computations of Flow in Pipe Bends
,”
J. Fluid Mech.
,
43
(
4
), pp.
771
783
.
91.
Lee
,
G. H.
,
Choi
,
Y. D.
, and
Han
,
S. H.
,
2007
, “
Measurement of Developing Turbulent Flow in a U-Bend of Circular Cross-Section
,”
J. Mech. Sci. Technol.
,
21
(
2
), pp.
348
359
.
92.
Anwer
,
M.
, and
So
,
R. M. C.
,
1990
, “
Frequency of Sublayer Bursting in a Curved Bend
,”
J. Fluid Mech.
,
210
, pp.
415
435
.
93.
Alfredsson
,
P. H.
, and
Johansson
,
A. V.
,
1984
, “
On the Detection of Turbulence-Generating Events
,”
J. Fluid Mech.
,
139
, p.
325
.
94.
Pruvost
,
J.
,
Legrand
,
J.
, and
Legentilhomme
,
P.
,
2004
, “
Numerical Investigation of Bend and Torus Flows—Part I: Effect of Swirl Motion on Flow Structure in U-Bend
,”
Chem. Eng. Sci.
,
59
(
16
), pp.
3345
3357
.
95.
Hellström
,
F.
, and
Fuchs
,
L.
,
2007
, “
Numerical Computations of Steady and Unsteady Flow in Bended Pipes
,”
AIAA
Paper No. 2007-4350.
96.
Wilcox
,
D. C.
,
1994
, “
Turbulence Modeling for CFD
,”
DCW Industries
,
La Cañada Flintridge, CA
.
97.
Durbin
,
P. A.
, and
Pettersson-Reif
,
B. A.
,
2011
,
Statistical Theory and Modeling for Turbulent Flows
,
2nd ed.
,
Wiley
,
Chichester, UK
.
98.
Wallin
,
S.
, and
Johansson
,
A. V.
,
2002
, “
Modelling Streamline Curvature Effects in Explicit Algebraic Reynolds Stress Turbulence Models
,”
Int. J. Heat Fluid Flow
,
23
(
5
), pp.
721
730
.
99.
Noorani
,
A.
,
2015
, “
Particle-Laden Turbulent Wall-Bounded Flows in Moderately Complex Geometries
,”
Ph.D. thesis
, KTH Mechanics, Stockholm, Sweden.http://www.diva-portal.org/smash/record.jsf?pid=diva2%3A872194&dswid=218
100.
Röhrig
,
R.
,
Jakirlic
,
S.
, and
Tropea
,
C.
,
2015
, “
Comparative Computational Study of Turbulent Flow in a 90 deg Pipe Elbow
,”
Int. J. Heat Fluid Flow
,
55
(ETMM10), pp.
102
111
.
101.
Patankar
,
S. V.
,
Pratap
,
V. S.
, and
Spalding
,
D. B.
,
1975
, “
Prediction of Turbulent Flow in Curved Pipes
,”
J. Fluid Mech.
,
67
(
3
), pp.
583
595
.
102.
Mori
,
Y.
, and
Nakayama
,
W.
,
1967
, “
Study of Forced Convective Heat Transfer in Curved Pipes (2nd Report, Turbulent Region)
,”
Int. J. Heat Mass Transfer
,
10
(
1
), pp.
37
59
.
103.
Al-Rafai
,
W. N.
,
Tridimas
,
Y. D.
, and
Woolley
,
N. H.
,
1990
, “
A Study of Turbulent Flows in Pipe Bends
,”
Proc. Inst. Mech. Eng., Part C
,
204
(
6
), pp.
399
408
.
104.
Hilgenstock
,
A.
, and
Ernst
,
R.
,
1996
, “
Analysis of Installation Effects by Means of Computational Fluid Dynamics—CFD Versus Experiments?
,”
Flow Meas. Instrum.
,
7
(
3–4
), pp.
161
171
.
105.
Sugiyama
,
H.
, and
Hitomi
,
D.
,
2005
, “
Numerical Analysis of Developing Turbulent Flow in a 180 deg Bend Tube by an Algebraic Reynolds Stress Model
,”
Int. J. Numer. Methods Fluids
,
47
(
12
), pp.
1431
1449
.
106.
Pellegrini
,
M.
,
Endo
,
H.
, and
Ninokata
,
H.
,
2011
, “
Numerical Investigation of Bent Pipe Flows at Transitional Reynolds Number
,”
Prog. Nucl. Energy
,
53
(
7
), pp.
916
920
.
107.
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
.
108.
Bradshaw
,
P.
,
1987
, “
Turbulent Secondary Flows
,”
Annu. Rev. Fluid Mech.
,
19
(
1
), pp.
53
74
.
109.
Lai
,
Y.
,
So
,
R. M. C.
, and
Zhang
,
H. S.
,
1991
, “
Turbulence-Driven Secondary Flows in a Curved Pipe
,”
Theor. Comput. Fluid Dyn.
,
3
(
3
), pp.
163
180
.
110.
Kalpakli
,
A.
, and
Örlü
,
R.
,
2013
, “
Turbulent Pipe Flow Downstream a 90 deg Pipe Bend With and Without Superimposed Swirl
,”
Int. J. Heat Fluid Flow
,
41
(ETMM9), pp.
103
111
.
111.
Boersma
,
B. J.
, and
Nieuwstadt
,
F. T. M.
,
1996
, “
Direct Numerical Simulation of the Flow in a Bend
,”
3rd International Symposium on Engineering Turbulence Modelling and Measurement
, Heraklion, Greece, May 27–29.
112.
Boersma
,
B. J.
, and
Nieuwstadt
,
F. T. M.
,
1996
, “
Large-Eddy Simulation of Turbulent Flow in a Curved Pipe
,”
ASME J. Fluids Eng.
,
118
(
2
), p.
248
.
113.
Rütten
,
F.
,
Schröder
,
W.
, and
Meinke
,
M.
,
2005
, “
Large-Eddy Simulation of Low Frequency Oscillations of the Dean Vortices in Turbulent Pipe Bend Flows
,”
Phys. Fluids
,
17
(
3
), p.
035107
.
114.
Tan
,
L.
,
Zhu
,
B.
,
Wang
,
Y.
,
Cao
,
S.
, and
Liang
,
K.
,
2014
, “
Turbulent Flow Simulation Using Large Eddy Simulation Combined With Characteristic-Based Split Scheme
,”
Comput. Fluids
,
94
, pp.
161
172
.
115.
Wang
,
Y.
,
Dong
,
Q.
, and
Wang
,
P.
,
2015
, “
Numerical Investigation on Fluid Flow in a 90-Degree Curved Pipe With Large Curvature Ratio
,”
Math. Probl. Eng.
,
2015
, p.
548262
.
116.
Boersma
,
B. J.
, and
Nieuwstadt
,
F. T. M.
,
1997
, “
Non-Unique Solutions in Turbulent Curved Pipe Flow
,”
Direct and Large-Eddy Simulation II
,
Springer
,
Dordrecht, The Netherlands
, pp.
257
266
.
117.
Hüttl
,
T. J.
, and
Friedrich
,
R.
,
2000
, “
Influence of Curvature and Torsion on Turbulent Flow in Helically Coiled Pipes
,”
Int. J. Heat Fluid Flow
,
21
(
3
), pp.
345
353
.
118.
Germano
,
M.
,
1982
, “
On the Effect of Torsion on a Helical Pipe Flow
,”
J. Fluid Mech.
,
125
, pp.
1
8
.
119.
Germano
,
M.
,
1989
, “
The Dean Equations Extended to a Helical Pipe Flow
,”
J. Fluid Mech.
,
203
, pp.
289
305
.
120.
Yamamoto
,
K.
,
Akita
,
T.
,
Ikeuchi
,
H.
, and
Kita
,
Y.
,
1995
, “
Experimental Study of the Flow in a Helical Circular Tube
,”
Fluid Dyn. Res.
,
16
(
4
), pp.
237
249
.
121.
Noorani
,
A.
, and
Schlatter
,
P.
,
2015
, “
Swirl-Switching Phenomenon in Turbulent Flow Through Toroidal Pipes
,”
9th International Symposium on Turbulence and Shear Flow Phenomena
, TSFP9, Melbourne, Australia, June 30–July 3.
122.
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
.
123.
Di Liberto
,
M.
,
Di Piazza
,
I.
, and
Ciofalo
,
M.
,
2013
, “
Turbulence Structure and Budgets in Curved Pipes
,”
Comput. Fluids
,
88
, pp.
452
472
.
124.
Carlsson
,
C.
,
Alenius
,
E.
, and
Fuchs
,
L.
,
2015
, “
Swirl Switching in Turbulent Flow Through 90 deg Pipe Bends
,”
Phys. Fluids
,
27
(
8
), p.
085112
.
125.
Kalpakli Vester
,
A.
,
Örlü
,
R.
, and
Alfredsson
,
P. H.
,
2015
, “
POD Analysis of the Turbulent Flow Downstream a Mild and Sharp Bend
,”
Exp. Fluids
,
56
(
3
), pp.
57
15
.
126.
Hellström
,
L. H. O.
,
Zlatinov
,
M.
,
Cao
,
G.
, and
Smits
,
A. J.
,
2013
, “
Turbulent Pipe Flow Downstream of a 90 deg Bend
,”
J. Fluid Mech.
,
735
, p.
R7
.
127.
Ono
,
A.
,
Kimura
,
N.
,
Kamide
,
H.
, and
Tobita
,
A.
,
2010
, “
Influence of Elbow Curvature on Flow Structure at Elbow Outlet Under High Reynolds Number Condition
,”
Nucl. Eng. Des.
,
241
(NURETH-13), pp.
4409
4419
.
128.
Sakakibara
,
J.
, and
Machida
,
N.
,
2012
, “
Measurement of Turbulent Flow Upstream and Downstream of a Circular Pipe Bend
,”
Phys. Fluids
,
24
(
4
), p.
041702
.
129.
Tunstall
,
M. J.
, and
Harvey
,
J. K.
,
1968
, “
On the Effect of a Sharp Bend in a Fully Developed Turbulent Pipe-Flow
,”
J. Fluid Mech.
,
34
(
3
), pp.
595
608
.
130.
Brücker
,
C.
,
1998
, “
A Time-Recording DPIV-Study of the Swirl Switching Effect in a 90 Bend Flow
,”
8th International Symposium on Flow Visualization
, Sorrento, Italy, Sept. 1–4, p. 171.https://www.researchgate.net/profile/Christoph_Bruecker/publication/234138907_A_time-recording_DPIV-study_of_the_swirl-switching_effect_in_a_90_bend_flow/links/0fcfd50f845c9f1665050802.pdf
131.
Kalpakli
,
A.
,
Örlü
,
R.
, and
Alfredsson
,
P. H.
,
2012
, “
Dean Vortices in Turbulent Flows: Rocking or Rolling?
,”
J. Visualization
,
15
(
1
), pp.
37
38
.
132.
Sakakibara
,
J.
,
Sonobe
,
R.
,
Goto
,
H.
,
Tezuka
,
H.
,
Tada
,
H.
, and
Tezuka
,
K.
,
2010
, “
Stereo-PIV Study of Turbulent Flow Downstream of a Bend in a Round Pipe
,”
14th International Symposium on Flow Visualization
, EXCO, Daegu, South Korea, June 21–24.
133.
Berkooz
,
G.
,
Holmes
,
P.
, and
Lumley
,
J. L.
,
1993
, “
The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows
,”
Annu. Rev. Fluid Mech.
,
25
(
1
), pp.
539
575
.
134.
Raiola
,
M.
,
Discetti
,
S.
, and
Ianiro
,
A.
,
2015
, “
On PIV Random Error Minimization With Optimal POD-Based Low-Order Reconstruction
,”
Exp. Fluids
,
56
(
4
), p.
75
.
135.
Guala
,
M.
,
Hommema
,
S. E.
, and
Adrian
,
R. J.
,
2006
, “
Large-Scale and Very-Large-Scale Motions in Turbulent Pipe Flow
,”
J. Fluid Mech.
,
554
, pp.
521
542
.
136.
Shiraishi
,
T.
,
Watakabe
,
H.
,
Sago
,
H.
, and
Yamano
,
H.
,
2009
. “
Pressure Fluctuation Characteristics of the Short-Radius Elbow Pipe for FBR in the Postcritical Reynolds Regime
,”
J. Fluid Sci. Technol.
,
4
(
2
), pp.
430
441
.
137.
Takamura
,
H.
,
Konno
,
H.
,
Hashizume
,
H.
,
Aizawa
,
K.
, and
Yamano
,
H.
,
2011
. “
PIV Measurements of a Complex Turbulent Flow in a Short Elbow Piping Under a High Reynolds Number Condition
,”
9th International Symposium on PIV
, PIV’11, Tsukuba, Japan, July 21–23.
138.
Yamano
,
H.
,
Tanaka
,
M.
,
Murakami
,
T.
,
Iwamoto
,
Y.
,
Yuki
,
K.
,
Sago
,
H.
, and
Hayakawa
,
S.
,
2011
. “
Unsteady Elbow Pipe Flow to Develop a Flow-Induced Vibration Evaluation Methodology for Japan Sodium-Cooled Fast Reactor
,”
J. Nucl. Sci. Technol.
,
48
(
4
), pp.
677
687
.
139.
Fjällman
,
J.
,
Mihaescu
,
M.
, and
Fuchs
,
L.
,
2013
, “
Analysis of Secondary Flow Induced by a 90 deg Bend in a Pipe Using Mode Decomposition Techniques
,”
4th International Conference on Jets, Wakes, and Separated Flows
, Nagoya, Japan, Sept. 17–21.http://www.diva-portal.org/smash/record.jsf?pid=diva2%3A748453&dswid=-4873
140.
Yuki
,
K.
,
Hasegawa
,
S.
,
Sato
,
T.
,
Hashizume
,
H.
,
Aizawa
,
K.
, and
Yamano
,
H.
,
2011
, “
Matched Refractive-Index PIV Visualization of Complex Flow Structure in a Three-Dimensionally Connected Dual Elbow
,”
Nucl. Eng. Des.
,
241
(
11
), pp.
4544
4550
.
141.
Kalpakli Vester
,
A.
,
Sattarzadeh
,
S. S.
, and
Örlü
,
R.
,
2016
, “
Combined Hot-Wire and PIV Measurements of a Swirling Turbulent Flow at the Exit of a 90 deg Pipe Bend
,”
J. Visualization
,
19
(
2
), pp.
261
273
.
142.
Örlü
,
R.
,
2009
, “
Experimental Studies in Jet Flows and Zero Pressure-Gradient Turbulent Boundary Layers
,”
Ph.D. thesis
, KTH Mechanics, Stockholm, Sweden.http://www.diva-portal.org/smash/record.jsf?pid=diva2%3A217489&dswid=9476
143.
Gupta
,
A. K.
,
Lilley
,
D. G.
, and
Syred
,
N.
,
1985
,
Swirl Flows
,
ABACUS Press
,
Cambridge, MA
.
144.
Facciolo
,
L.
,
Tillmark
,
N.
,
Talamelli
,
A.
, and
Alfredsson
,
P. H.
,
2007
, “
A Study of Swirling Turbulent Pipe and Jet Flows
,”
Phys. Fluids
,
19
(
3
), p.
035105
.
145.
White
,
A.
,
1964
, “
Flow of a Fluid in an Axially Rotating Pipe
,”
J. Mech. Eng. Sci.
,
6
(
1
), pp.
47
52
.
146.
Murakami
,
M.
, and
Kikuyama
,
K.
,
1980
, “
Turbulent Flow in Axially Rotating Pipes
,”
ASME J. Fluids Eng.
,
102
(
1
), pp.
97
103
.
147.
Reich
,
G.
, and
Beer
,
H.
,
1989
, “
Fluid Flow and Heat Transfer in an Axially Rotating Pipe—I: Effect of Rotation on Turbulent Pipe Flow
,”
Int. J. Heat Mass Transfer
,
32
(
3
), pp.
551
562
.
148.
Kikuyama
,
K.
,
Murakami
,
M.
,
Nishibori
,
K.
, and
Maeda
,
K.
,
1983
, “
Flow in an Axially Rotating Pipe: A Calculation of Flow in the Saturated Region
,”
Bull. JSME
,
26
(
214
), pp.
506
513
.
149.
Imao
,
S.
,
Itoh
,
M.
, and
Harada
,
T.
,
1996
, “
Turbulent Characteristics of the Flow in an Axially Rotating Pipe
,”
Int. J. Heat Fluid Flow
,
17
(
5
), pp.
444
451
.
150.
Kikuyama
,
K.
,
Murakami
,
M.
, and
Nishibori
,
K.
,
1983
, “
Development of Three-Dimensional Turbulent Boundary Layer in an Axially Rotating Pipe
,”
ASME J. Fluids Eng.
,
105
(2), pp.
154
160
.
151.
Rocklage-Marliani
,
G.
,
Schmidts
,
M.
, and
Vasanta Ram
,
V.
,
2003
, “
Three-Dimensional Laser-Doppler Velocimetry Measurements in Swirling Turbulent Pipe Flow
,”
Flow Turbul. Combust.
,
70
(
1
), pp.
43
67
.
152.
Eggels
,
J.
,
1994
, “
Direct and Large Eddy Simulation of Turbulent Flow in a Cylindrical Geometry
,” Ph.D. thesis, Delft University of Technology, Delft, The Netherlands.
153.
Orlandi
,
P.
, and
Fatica
,
M.
,
1997
, “
Direct Simulations of Turbulent Flow in a Pipe Rotating About Its Axis
,”
J. Fluid Mech.
,
343
, pp.
43
72
.
154.
Feiz
,
A. A.
,
Ould-Rouis
,
M.
, and
Lauriat
,
G.
,
2003
, “
Large Eddy Simulation of Turbulent Flow in a Rotating Pipe
,”
Int. J. Heat Fluid Flow
,
24
(
3
), pp.
412
420
.
155.
Speziale
,
C. G.
,
Younis
,
B. A.
, and
Berger
,
S. A.
,
2000
, “
Analysis and Modelling of Turbulent Flow in an Axially Rotating Pipe
,”
J. Fluid Mech.
,
407
, pp.
1
26
.
156.
Nygård
,
F.
, and
Andersson
,
H. I.
,
2009
, “
DNS of Swirling Turbulent Pipe Flow
,”
Int. J. Numer. Methods. Fluids
,
64
(9), pp.
945
972
.
157.
So
,
R.
, and
Anwer
,
M.
,
1993
, “
Fully-Developed Turbulent Flow Through a Curved Pipe With and Without Swirl
,”
ASME Publ. FED
,
146
, pp.
29
43
.https://www.researchgate.net/profile/RMC_So/publication/257311327_Fully-developed_turbulent_flow_through_a_curved_pipe_with_and_without_swirl/links/02e7e524e806e8c05a050802.pdf
158.
So
,
R. M. C.
, and
Anwer
,
M.
,
1993
, “
Swirling Turbulent Flow Through a Curved Pipe—Part 2: Recovery From Swirl and Bend Curvature
,”
Exp. Fluids
,
14
(3), pp.
169
177
.
159.
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
.
160.
Binnie
,
A. M.
,
1962
, “
Experiments on the Swirling Flow of Water in a Vertical Pipe and a Bend
,”
Proc. R. Soc.
,
270
(
1343
), pp.
452
466
.
161.
Shimizu
,
Y.
, and
Sugino
,
K.
,
1980
, “
Hydraulic Losses and Flow Patterns of a Swirling Flow in U-Bends
,”
Bull. JSME
,
23
(
183
), pp.
1443
1450
.
162.
Kitoh
,
O.
,
1987
, “
Swirling Flow Through a Bend
,”
J. Fluid Mech.
,
175
, pp.
429
446
.
163.
Chang
,
T. H.
, and
Lee
,
H. S.
,
2003
, “
An Experimental Study on Swirling Flow in a 90 Degree Circular Tube by Using Particle Image Velocimetry
,”
J. Visualization
,
6
(
4
), pp.
343
352
.
164.
McDonald
,
D. A.
,
1955
, “
The Relation of Pulsatile Pressure to Flow in Arteries
,”
J. Physiol.
,
127
(
3
), p.
533
.
165.
Chandran
,
K. B.
, and
Yearwood
,
T. L.
,
1981
, “
Experimental Study of Physiological Pulsatile Flow in a Curved Tube
,”
J. Fluid Mech.
,
111
, pp.
59
85
.
166.
Glenn
,
A. L.
,
Bulusu
,
K.
,
Shu
,
F.
, and
Plesniak
,
M. W.
,
2012
, “
Secondary Flow Structures Under Stent-Induced Perturbations for Cardiovascular Flow in a Curved Artery Model
,”
Int. J. Heat Fluid Flow
,
35
(TSFP-7), pp.
76
83
.
167.
Stokes
,
G. G.
,
1851
, “
On the Effect of the Internal Friction of Fluids on the Motion of Pendulums
,”
Trans. Cambridge Philos. Soc.
,
9
, p.
8
.http://www.nawcc-index.net/Articles/Stokes-InternalFriction.pdf
168.
He
,
S.
, and
Jackson
,
J. D.
,
2009
, “
An Experimental Study of Pulsating Turbulent Flow in a Pipe
,”
Eur. J. Mech. B/Fluids
,
28
(
2
), pp.
309
320
.
169.
Womersley
,
J.
,
1957
, “
Oscillatory Flow in Arteries: The Constrained Elastic Tube as a Model of Arterial Flow and Pulse Transmission
,”
Phys. Med. Biol.
,
2
(
2
), pp.
178
187
.
170.
Scotti
,
A.
, and
Piomelli
,
U.
,
2001
, “
Numerical Simulation of Pulsating Turbulent Channel Flow
,”
Phys. Fluids
,
13
(
5
), pp.
1367
1384
.
171.
Carpinlioğlu
,
M. Ö.
, and
Gündoğdu
,
M. Y.
,
2001
, “
A Critical Review on Pulsatile Pipe Flow Studies Directing Towards Future Research Topics
,”
Flow Meas. Instrum.
,
12
(
3
), pp.
163
174
.
172.
Zohir
,
A. E.
,
Abdel Aziz
,
A. A.
, and
Habib
,
M. A.
,
2015
, “
Heat Transfer Characteristics and Pressure Drop of the Concentric Tube Equipped With Coiled Wires for Pulsating Turbulent Flow
,”
Exp. Therm. Fluid Sci.
,
65
, pp.
41
51
.
173.
Guo
,
L.
,
Chen
,
X.
,
Feng
,
Z.
, and
Bai
,
B.
,
1998
, “
Transient Convective Heat Transfer in a Helical Coiled Tube With Pulsatile Fully Developed Turbulent Flow
,”
Int. J. Heat Mass Transfer
,
41
(
19
), pp.
2867
2875
.
174.
Ramezani Kharvani
,
H.
,
Ilami Doshmanziari
,
F.
,
Zohir
,
A. E.
, and
Jalali-Vahid
,
D.
,
2016
, “
An Experimental Investigation of Heat Transfer in a Spiral-Coil Tube With Pulsating Turbulent Water Flow
,”
Heat Mass Transfer
,
52
(9), pp. 1779–1789.
175.
Timité
,
B.
,
Castelain
,
C.
, and
Peerhossaini
,
H.
,
2010
, “
Pulsatile Viscous Flow in a Curved Pipe: Effects of Pulsation on the Development of Secondary Flow
,”
Int. J. Heat Fluid Flow
,
31
(
5
), pp.
879
896
.
176.
Jarrahi
,
M.
,
Castelain
,
C.
, and
Peerhossaini
,
H.
,
2010
, “
Secondary Flow Patterns and Mixing in Laminar Pulsating Flow Through a Curved Pipe
,”
Exp. Fluids
,
50
(6), pp.
1539
1558
.
177.
Kalpakli
,
A.
,
Örlü
,
R.
,
Tillmark
,
N.
, and
Alfredsson
,
P. H.
,
2012
, “
Experimental Investigation on the Effect of Pulsations on Exhaust Manifold-Related Flows Aiming at Improved Efficiency
,”
10th International Conference on Turbochargers and Turbocharging
(
IMechE
), London, May 15–16, pp.
377
387
.http://www.diva-portal.org/smash/record.jsf?pid=diva2%3A498748&dswid=3133
178.
Laurantzon
,
F.
,
Tillmark
,
N.
,
Örlü
,
R.
, and
Alfredsson
,
P. H.
,
2012
, “
A Flow Facility for the Characterization of Pulsatile Flows
,”
Flow Meas. Instrum.
,
26
, pp.
10
17
.
179.
Laurantzon
,
F.
,
Örlü
,
R.
,
Segalini
,
A.
,
Tillmark
,
N.
, and
Alfredsson
,
P. H.
,
2012
, “
Experimental Analysis of Turbocharger Interaction With a Pulsatile Flow Through Time-Resolved Flow Measurements Upstream and Downstream the Turbine
,”
10th International Conference on Turbochargers and Turbocharging
(
IMechE
), London, May 15–16, pp.
405
415
.https://books.google.com/books?hl=en&lr=&id=8n9wAgAAQBAJ&oi=fnd&pg=PA405&dq=Experimental+Analysis+of+Turbocharger+Interaction+With+a+Pul-+2072+satile+Flow+Through+Time-Resolved+Flow+Measurements+Upstream+and+2073+Downstream+the+Turbine&ots=IbDl5lfjdP&sig=49GgR0QYx6PZY3srFB7zBBKRSxc#v=onepage&q&f=false
180.
Kalpakli
,
A.
,
Örlü
,
R.
, and
Alfredsson
,
P. H.
,
2013
, “
Vortical Patterns in Turbulent Flow Downstream a 90 deg Curved Pipe at High Womersley Numbers
,”
Int. J. Heat Fluid Flow
,
44
, pp.
692
699
.
181.
Kalpakli Vester
,
A.
,
Örlü
,
R.
, and
Alfredsson
,
P. H.
,
2015
, “
Pulsatile Turbulent Flow in Straight and Curved Pipes—Interpretation and Decomposition of Hot-Wire Signals
,”
Flow Turbul. Combust.
,
94
(
2
), pp.
305
321
.
182.
Noorani
,
A.
, and
Schlatter
,
P.
,
2016
, “
Swirl-Switching Phenomenon in Turbulent Flow Through Toroidal Pipes
,”
Int. J. Heat Fluid Flow
(in press).
183.
Yongmann
,
C.
,
2015
, University of Warwick, Coventry, UK (personal communication).
184.
Hufnagel
,
L.
,
2016
, “
On the Swirl-Switching in Developing Bent Pipe Flow With Direct Numerical Simulation
,” MSc. thesis, KTH Mechanics, Stockholm, Sweden.
185.
Kalpakli Vester
,
A.
,
2014
, “
Vortices in Turbulent Curved Pipe Flow—Rocking, Rolling and Pulsating Motions
,”
Ph.D. thesis
, KTH Mechanics, Stockholm, Sweden.http://www.diva-portal.org/smash/record.jsf?pid=diva2%3A717536&dswid=1707
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