The present paper reports observations on some aspects regarding the dependence of the transition Reynolds number and flow development on the inlet flow conditions and the entrance length in circular and rectangular ducts for Rem106×103, where Rem is the Reynolds number based on the bulk flow velocity (U¯b) and the duct integral length scale (D). The hot-wire anemometer was used to carry out measurements close to the circular duct exit; however, the laser-Doppler anemometry was utilized for the rectangular duct measurements. Particular considerations were given to the bulk flow velocity, the mean-velocity profile, the centerline-average-velocity, and the centerline turbulence statistics to the fourth order. Transition criteria in both ducts were discussed, reflecting effects of flow geometry, entrance flow conditions, and entrance length on the transition Reynolds number. A laminar behavior was maintained up to Rem15.4×103 and Rem2×103 in the circular and rectangular ducts, respectively, and the transition was observed to take place at different downstream positions as the inlet flow velocity varied.

1.
Draad
,
A. A.
,
Kuiken
,
G. D. C.
, and
Nieuwstadt
,
F. T. M.
, 1998, “
Laminar-Turbulent Transition in Pipe Flow for Newtonian and Non-Newtonian Fluids
,”
J. Fluid Mech.
0022-1120,
377
, pp.
267
312
.
2.
Monin
,
A. S.
, and
Yaglom
,
A. M.
, 1999,
Statistical Fluid Mechanics: The Mechanics of Turbulence
,
Center for Turbulence Research-CTR Monograph
Vol.
I
, English edition, revised, and augmented by A. M. Yaglom, Chap. 4,
Stanford University
,
Stanford
/
NASA Ames Research Center
,
Moffett Field, CA
.
3.
Faisst
,
H.
, and
Eckhardt
,
B.
, 2003, “
Traveling Waves in Pipe Flow
,”
Phys. Rev. Lett.
0031-9007,
91
, p.
224502
.
4.
Wedin
,
H.
, and
Kerswell
,
R. R.
, 2004, “
Exact Coherent Structures in Pipe Flow: Traveling Wave Solutions
,”
J. Fluid Mech.
0022-1120,
508
, pp.
333
371
.
5.
Hof
,
B.
,
Juel
,
A.
, and
Mullin
,
T.
, 2003, “
Scaling of the Turbulence Transition Threshold in a Pipe
,”
Phys. Rev. Lett.
0031-9007,
91
(
24
), pp.
244502
.
6.
Eckhardt
,
B.
,
Schneider
,
T. M.
,
Hof
,
B.
, and
Westerweel
,
J.
, 2007, “
Turbulence Transition in Pipe Flow
,”
Annu. Rev. Fluid Mech.
0066-4189,
39
, pp.
447
468
.
7.
Kerswell
,
R. R.
, 2005, “
Recent Progress in Understanding the Transition to Turbulence in a Pipe
,” Institute of Physics Publishing,
Nonlinearity
0951-7715,
18
, pp.
R17
R44
.
8.
Willis
,
A. P.
,
Peixinhoy
,
J.
,
Kerswell
,
R. R.
, and
Mullin
,
T.
, 2008, “
Experimental and Theoretical Progress in Pipe Flow Transition
,”
Philos. Trans. R. Soc. London, Ser. A
0962-8428,
366
(
1876
), pp.
2671
2684
.
9.
Trefethen
,
L. N.
,
Trefethen
,
A. E.
,
Reddy
,
S. C.
, and
Driscoll
,
T. A.
, 1993, “
Hydrodynamic Stability Without Eigenvalues
,”
Science
0036-8075,
261
, pp.
578
584
.
10.
Waleffe
,
F.
, 1997, “
On the Self-Sustaining Process in Shear Flows
,”
Phys. Fluids
1070-6631,
9
, pp.
883
900
.
11.
Wygnanski
,
I. J.
, and
Champagne
,
F. H.
, 1973, “
On Transition in a Pipe. Part 1. The Origin of Puffs and Slugs and the Flow in a Turbulent Slug
,”
J. Fluid Mech.
0022-1120,
59
, pp.
281
335
.
12.
Wygnanski
,
I. J.
,
Sokolov
,
M.
, and
Friedman
,
D.
, 1975, “
On Transition in a Pipe. Part 2. The Equilibrium Puff
,”
J. Fluid Mech.
0022-1120,
69
, pp.
283
304
.
13.
Zagarola
,
M. V.
, and
Smits
,
A. J.
, 1998, “
Mean-Flow Scaling of Turbulent Pipe Flow
,”
J. Fluid Mech.
0022-1120,
373
, pp.
33
79
.
14.
Nikuradse
,
J.
, 1932, “
Gesetzmässigkeiten der turbulenten Strömung in glatten Rohren
,”
Forschg. Arb. Ing.-Wes. Heft
,
356
, pp.
1
36
. 0022-1120
15.
Sarpkaya
,
T.
, 1975, “
A Note on the Stability of Developing Laminar Flow Subjected to Axisymmetric and Non-Axisymmetric Disturbances
,”
J. Fluid Mech.
0022-1120,
68
, pp.
345
351
.
16.
Huang
,
L. M.
, and
Chen
,
T. S.
, 1974, “
Stability of Developing Pipe Flow Subjected to Non-Axisymmetric Disturbances
,”
J. Fluid Mech.
0022-1120,
63
, pp.
183
193
.
17.
Huang
,
L. M.
, and
Chen
,
T. S.
, 1974, “
Stability of the Developing Laminar Pipe Flow
,”
Phys. Fluids
1070-6631,
17
, pp.
245
247
.
18.
Perry
,
A. E.
, and
Abel
,
C. J.
, 1975, “
Scaling Laws for Pipe-Flow Turbulence
,”
J. Fluid Mech.
0022-1120,
67
, pp.
257
271
.
19.
Lien
,
K.
,
Monty
,
J. P.
,
Chong
,
M. S.
, and
Ooi
,
A.
, 2004, “
The Entrance Length for Fully Developed Turbulent Channel Flow
,”
15th Australian Fluid Mechanics Conference
, Dec. 13–17,
University of Sydney
,
Sydney, Australia
.
20.
Laufer
,
J.
, 1953, “
The Structure of Turbulence in Fully Developed Pipe Flow
,” NACA, Report No. 1174.
21.
Patel
,
V. C.
, and
Head
,
M. R.
, 1969, “
Some Observations on Skin Friction and Velocity Profiles in Fully Developed Pipe and Channel Flows
,”
J. Fluid Mech.
0022-1120,
38
, pp.
181
201
.
22.
Doherty
,
J.
,
Ngan
,
P.
,
Monty
,
J.
, and
Chong
,
M.
, 2007, “
The Developments of Turbulent Pipe Flow
,”
16th Australian Fluid Mechanics Conference
, Crown Plaza, Gold Coast, Australia, Dec. 2–7, pp.
266
270
.
23.
Zanoun
,
E. -S.
,
Durst
,
F.
,
Bayoumi
,
O.
, and
Al-Salaymeh
,
A.
, 2007, “
Wall Skin Friction and Mean Velocity Profiles of Fully Developed Turbulent Pipe Flows
,”
Exp. Therm. Fluid Sci.
0894-1777,
32
(
1
), pp.
249
261
.
24.
Fischer
,
M.
, 1999, “
Turbulente wandgebundene Strömungen bei kleinen Reynoldszahlen
,” Ph.D., thesis, Universität Erlangen Nürnberg, Germany.
25.
Sarradj
,
E.
,
Schulze
,
C.
, and
Zeibig
,
A.
, 2005, “
Identification of Noise Source Mechanisms Using Orthogonal Beam Forming
,” Nov., St. Raphael.
26.
Hof
,
B.
, 2004, “
Transition to Turbulence in Pipe Flow
,”
Laminar-Turbulent Transition and Finite Amplitude Solutions
,
T.
Mullin
and
R. R.
Kerswell
, eds.,
Springer
,
Dordrecht
, pp.
221
231
.
27.
Grossmann
,
S.
, 2000, “
The Onset of Shear Flow Turbulence
,”
Rev. Mod. Phys.
0034-6861,
72
(
2
), pp.
603
618
.
28.
Schiller
,
L.
, 1922, “
Die Entwicklung der laminaren Geschwindigkeitsverteilung und ihre Bedeutung für Zähigkeitsmessungen
,”
Z. Angew. Math. Mech.
0044-2267,
2
, pp.
96
106
.
29.
Pfeninger
,
W.
, 1961, “
Boundary Layer Suction Experiments With Laminar Flow at High Reynolds Numbers in the Inlet Length of a Tube by Various Suction Methods
,”
Boundary Layer and Flow Control
,
G. V.
Lachman
, ed.,
Pergamon
,
Oxford
, pp.
961
980
.
30.
Blasius
,
H.
, 1913, “
Das Ähnlichkeitsgesetz bei Reibungsvorgängen in Flüssikeiten
,”
Forsch. Arb. Ing.-Wes
, pp.
131
137
.
31.
Zanoun
,
E. -S.
,
Durst
,
F.
, and
Nagib
,
H.
, 2003, “
Evaluating the Law of the Wall in Two-Dimensional Fully Developed Turbulent Channel Flows
,”
Phys. Fluids
1070-6631,
15
(
10
), pp.
3079
3089
.
32.
Bhatia
,
J. C.
,
Durst
,
F.
, and
Jovanovic
,
J.
, 1982, “
Corrections of Hot-Wire Measurements Near Walls
,”
J. Fluid Mech.
0022-1120,
122
, pp.
411
431
.
33.
Durst
,
F.
,
Zanoun
,
E. -S.
, and
Pashtrapanska
,
M.
, 2001, “
In Situ Calibration of Hot Wires Close to Highly Heat-Conducting Walls
,”
Exp. Fluids
0723-4864,
31
, pp.
103
110
.
34.
Hinze
,
J. O.
, 1975,
Turbulence
,
2nd ed.
,
McGraw-Hill
,
New York
.
35.
McKeon
,
B. J.
,
Swanson
,
C. J.
,
Zagarola
,
M. V.
,
Donnelly
,
R. J.
, and
Smits
,
A. J.
, 2004, “
Friction Factors for Smooth Pipe Flow
,”
J. Fluid Mech.
0022-1120,
511
, pp.
41
44
.
36.
Perry
,
A. E.
,
Hafez
,
S.
, and
Chong
,
M. S.
, 2001, “
A Possible Reinterpretation of the Princeton Superpipe Data
,”
J. Fluid Mech.
0022-1120,
49
, pp.
395
401
.
37.
Nagib
,
H. M.
,
Chauhan
,
K. A.
, and
Monkewitz
,
P. A.
, 2007, “
Approach to an Asymptotic State for ZPG Turbulent Boundary Layers
,”
Philos. Trans. R. Soc. London, Ser. A
0962-8428,
95
, pp.
755
770
.
38.
Nagib
,
M. H.
, and
Kapil
,
A. C.
, 2008, “
Variations of von Kàrmàn Coefficient in Canonical Flows
,”
Phys. Fluids
1070-6631,
20
, p.
101518
.
39.
Reynolds
,
O.
, 1883, “
On the Dynamical Theory of Incompressible Viscous Fluids and Determination of the Criterion
,”
Philos. Trans. R. Soc. London
0370-2316,
186
, pp.
123
164
.
40.
Nishi
,
M.
,
Ünsal
,
B.
, and
Durst
,
F.
, 2008, “
Laminar-to-Turbulent Transition of Pipe Flows Through Slugs and Puffs
,”
J. Fluid Mech.
0022-1120,
614
, pp.
425
446
.
41.
Durst
,
F.
, and
Ünsal
,
B.
, 2006, “
Forced Laminar to Turbulent Transition of Pipe Flows
,”
J. Fluid Mech.
0022-1120,
560
, pp.
449
464
.
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