Velocity fluctuations are widely used to identify the behavior of developing turbulent flows. The pressure on the other hand, which is strongly coupled with the gradient of the mean velocity and fluctuations, is less explored. In this study, we report the results of wall pressure measurements for the development of pipe flow at high Reynolds numbers along the axial direction. It is found that the pressure fluctuations increase exponentially along the pipe with a self-similarity scaling. The exponential growth of the pressure fluctuations along the pipe saturates after reaching a critical position around 50 diameters from the inlet. It qualitatively agrees with the critical position usually adopted for fully developed turbulence, which was obtained from earlier velocity fluctuations at various locations along the pipe centerline. Results also show that the exponential growth of the pressure fluctuations is weakly affected by the presence of ring obstacles placed close to the pipe inlet. Finally, it is found that the pressure fluctuations decrease as a function of Reynolds number, contrary to the boundary layer flow.

References

References
1.
Tatsumi
,
T.
,
1952
, “
Stability of the Laminar Inlet-Flow Prior to the Formation of Poiseuille Regime, II
,”
J. Phys. Soc. Jpn.
,
7
(
5
), pp.
495
502
.
2.
Huang
,
L. M.
, and
Chen
,
T. S.
,
1974
, “
Stability of Developing Pipe Flow Subjected to Non-Axisymmetric Disturbances
,”
J. Fluid Mech.
,
63
(
1
), pp.
183
193
.
3.
Sarpkaya
,
T.
,
1975
, “
A Note on the Stability of Developing Laminar Pipe Flow Subjected to Axisymmetric and Non-Axisymmetric Disturbances
,”
J. Fluid Mech.
,
68
(
2
), pp.
345
351
.
4.
Gupta
,
S. C.
, and
Garg
,
V. K.
,
1981
, “
Effect of Velocity Distribution on the Stability of Developing Flow in a Pipe
,”
Phys. Fluids
,
24
(
4
), pp.
576
578
.
5.
Da Silva
,
D. F.
, and
Moss
,
E. A.
,
1994
, “
The Stability of Pipe Entrance Flows Subjected to Axisymmetric Disturbances
,”
ASME J. Fluids Eng.
,
116
(
1
), pp.
61
65
.
6.
Sahu
,
K. C.
, and
Govindarajan
,
R.
,
2007
, “
Linear Instability of Entry Flow in a Pipe
,”
ASME J. Fluids Eng.
,
129
(
10
), pp.
1277
1280
.
7.
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
.
8.
Ekman
,
V. W.
,
1910
, “
On the Change From Steady to Turbulent Motion of Liquids
,”
Ark. Mat. Astron. Fys.
,
6
, pp.
1
16
.
9.
Comolet
,
R.
,
1950
, “Recherche Sur La Genèse De La Turbulence Dans Les Conduites En Charge,” Ph.D. thesis, Public Science and Technology Ministry of Air, Paris, France.
10.
Lindgren
,
E. R.
,
1957
, “
The Transition Process and Other Phenomena in Viscous Flow
,”
Ark. Fys.
,
12
, pp. 1–169.
11.
Pfenninger
,
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 Press, New York
, pp.
961
980
.
12.
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.
,
59
(
2
), pp.
281
335
.
13.
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.
,
377
, pp.
267
312
.
14.
Durst
,
F.
,
Ray
,
S.
,
Ünsal
,
B.
, and
Bayoumi
,
O. A.
,
2005
, “
The Development Lengths of Laminar Pipe and Channel Flows
,”
ASME J. Fluids Eng.
,
127
(
6
), pp.
1154
1160
.
15.
Peixinho
,
J.
, and
Mullin
,
T.
,
2007
, “
Finite-Amplitude Thresholds for Transition in Pipe Flow
,”
J. Fluid Mech.
,
582
, pp.
169
178
.
16.
Zanoun
,
E.-S.
,
Kito
,
M.
, and
Egbers
,
C.
,
2009
, “
A Study on Flow Transition and Development in Circular and Rectangular Ducts
,”
ASME J. Fluids Eng.
,
131
(
6
), p.
061204
.
17.
Mullin
,
T.
,
2011
, “
Experimental Studies of Transition to Turbulence in a Pipe
,”
Annu. Rev. Fluid Mech.
,
43
(
1
), pp.
1
24
.
18.
Wu
,
X.
,
Moin
,
P.
,
Adrian
,
R. J.
, and
Baltzer
,
J. R.
,
2015
, “
Osborne Reynolds Pipe Flow: Direct Simulation From Laminar Through Gradual Transition to Fully Developed Turbulence
,”
Proc. Natl. Acad. Sci. U. S. A.
,
112
(
26
), pp.
7920
7924
.
19.
Ghajar
,
A. J.
, and
Tam
,
L.-M.
,
1994
, “
Heat Transfer Measurements and Correlations in the Transition Region for a Circular Tube With Three Different Inlet Configurations
,”
Exp. Therm. Fluid Sci.
,
8
(
1
), pp.
79
90
.
20.
Laufer
,
J.
,
1954
, “The Structure of Turbulence in Fully Developed Pipe Flow,” National Advisory Committee for Aeronautics, Washington, DC, Technical Report No.
1174
.
21.
Zagarola
,
M. V.
, and
Smits
,
A. J.
,
1998
, “
Mean-Flow Scaling of Turbulent Pipe Flow
,”
J. Fluid Mech.
,
373
, pp.
33
79
.
22.
Furuichi
,
N.
,
Terao
,
Y.
,
Wada
,
Y.
, and
Tsuji
,
Y.
,
2015
, “
Friction Factor and Mean Velocity Profile for Pipe Flow at High Reynolds Numbers
,”
Phys. Fluids
,
27
(
9
), p.
095108
.
23.
Habchi
,
C.
,
Russeil
,
S.
,
Bougeard
,
D.
,
Harion
,
J.-L.
,
Lemenand
,
T.
,
Della Valle
,
D.
, and
Peerhossaini
,
H.
,
2012
, “
Enhancing Heat Transfer in Vortex Generator-Type Multifunctional Heat Exchangers
,”
Appl. Therm. Eng.
,
38
, pp.
14
25
.
24.
König
,
F.
,
Zanoun
,
E.-S.
,
Öngüner
,
E.
, and
Egbers
,
C.
,
2014
, “
The CoLaPipe—the New Cottbus Large Pipe Test Facility at Brandenburg University of Technology Cottbus-Senftenberg
,”
Rev. Sci. Instrum.
,
85
(
7
), p.
075115
.
25.
König
,
F.
,
2015
, “Investigations of High Reynolds Number Pipe Flow,”
Ph.D. thesis
, Brandenburgische Technische Universität Cottbus-Senftenberg, Cottbus, Germany.
26.
Perry
,
A. E.
, and
Abell
,
C. J.
,
1975
, “
Scaling Laws for Pipe-Flow Turbulence
,”
J. Fluid Mech.
,
67
(
2
), pp.
257
271
.
27.
Shaw
,
R.
,
1960
, “
The Influence of Hole Dimensions on Static Pressure Measurements
,”
J. Fluid Mech.
,
7
(
4
), pp.
550
564
.
28.
Blasius
,
H.
,
1908
, “
Boundary Layer in Fluids With Little Friction
,”
Z. Math. Phys.
,
56
, pp.
1
37
.
29.
Nikuradse
,
J.
,
1933
, “Strömungsgesetze in Rauen Rohren,” VDI Forschungsheft, Berlin, Technical Report No. 361.
30.
Tsuji
,
Y.
,
Fransson
,
J. H. M.
,
Alfredsson
,
P. H.
, and
Johansson
,
A. V.
,
2007
, “
Pressure Statistics and Their Scaling in High-Reynolds-Number Turbulent Boundary Layers
,”
J. Fluid Mech.
,
585
, pp.
1
40
.
31.
Zanoun
,
E.-S.
, and
Egbers
,
C.
,
2016
, “
Flow Transition and Development in Pipe Facilities
,”
J. Eng. Appl. Sci.
,
63
(
2
), pp.
141
159
.
32.
Venugopal
,
A.
,
Agrawal
,
A.
, and
Prabhu
,
S. V.
,
2017
, “
Investigations on Bluff Bodies as Improved Vortex Shedders Placed Inside a Circular Pipe
,”
ASME J. Fluids Eng.
,
139
(
4
), p.
041204
.
33.
Pollard
,
A.
,
Savill
,
A. M.
, and
Thomann
,
H.
,
1989
, “
Turbulent Pipe Flow Manipulation: Some Experimental and Computational Results for Single Manipulator Rings
,”
Appl. Sci. Res.
,
46
(
3
), pp.
281
290
.
34.
Kraichnan
,
R. H.
,
1956
, “
Pressure Fluctuations in Turbulent Flow Over a Flat Plate
,”
J. Acoust. Soc. Am.
,
28
(
3
), pp.
378
390
.
35.
Corcos
,
G. M.
,
1964
, “
The Structure of the Turbulent Pressure Field in Boundary-Layer Flows
,”
J. Fluid Mech.
,
18
(
3
), pp.
353
378
.
36.
Schlatter
,
P.
, and
Örlü
,
R.
,
2012
, “
Turbulent Boundary Layers at Moderate Reynolds Numbers: Inflow Length and Tripping Effects
,”
J. Fluid Mech.
,
710
, pp.
5
34
.
37.
Naka
,
Y.
,
Stanislas
,
M.
,
Foucaut
,
J.-M.
,
Coudert
,
S.
,
Laval
,
J.-P.
, and
Obi
,
S.
,
2015
, “
Space–Time Pressure–Velocity Correlations in a Turbulent Boundary Layer
,”
J. Fluid Mech.
,
771
, pp.
624
675
.
38.
Wei
,
T.
, and
Willmarth
,
W. W.
,
1989
, “
Reynolds-Number Effects on the Structure of a Turbulent Channel Flow
,”
J. Fluid Mech.
,
204
(
1
), pp.
57
95
.
39.
Clinch
,
J. M.
,
1969
, “
Measurements of the Wall Pressure Field at the Surface of a Smooth-Walled Pipe Containing Turbulent Water Flow
,”
J. Sound Vib.
,
9
(
3
), pp.
398
419
.
40.
Farabee
,
T. M.
, and
Casarella
,
M. J.
,
1991
, “
Spectral Features of Wall Pressure Fluctuations Beneath Turbulent Boundary Layers
,”
Phys. Fluids
,
3
(
10
), pp.
2410
2420
.
41.
Agarwal
,
N. K.
,
1994
, “
The Sound Field in Fully Developed Turbulent Pipe Flow Due to Internal Flow Separation—Part I: Wall-Pressure Fluctuations
,”
J. Sound Vib.
,
169
(
1
), pp.
89
109
.
42.
Browne
,
L. W. B.
, and
Dinkelacker
,
A.
,
1995
, “
Turbulent Pipe Flow: Pressures and Velocities
,”
Fluid Dyn. Res.
,
15
(
3
), pp.
177
204
.
43.
Durant
,
C.
,
Robert
,
G.
,
Filippi
,
P. J. T.
, and
Mattei
,
P.-O.
,
2000
, “
Vibroacoustic Response of a Thin Cylindrical Shell Excited by a Turbulent Internal Flow: Comparison Between Numerical Prediction and Experimentation
,”
J. Sound Vib.
,
229
(
5
), pp.
1115
1155
.
44.
Borisyuk
,
A. O.
,
2010
, “
Experimental Study of Wall Pressure Fluctuations in Rigid and Elastic Pipes Behind an Axisymmetric Narrowing
,”
J. Fluids Struct.
,
26
(
4
), pp.
658
674
.
You do not currently have access to this content.