In this work, turbulent drag reduction in a pipe is investigated by using laser Doppler velocimetry. The effect of decreasing the friction factor of the flow is obtained by addition of high molecular weight polymers. The mechanism of drag reduction is explained in terms of a stress anisotropy that inhibits the transversal transport of momentum by turbulent fluctuations. Semi-theoretical models based on a nonlinear constitutive equation, which takes into account an extra extensional rate of strain in the flow produced by the local additive orientation, are presented. The semi-theoretical models used to predict the friction factor of the flow in the presence of the polymer have successfully described the experimental measurements. The results have revealed a reduction in the friction factor of 65% for a concentration of 350ppm in volume of polyacrylamide (PAMA) in an aqueous solution. In addition, the flow statistics, such as the axial and radial velocity fluctuations, the normalized autocorrelation functions as well as the power spectra for both velocity fluctuation components, are examined for the Newtonian flow of pure water and the flow of a 120ppm solution of PAMA at the same friction velocity. Next, the results are compared in order to characterize the effect of the additive on the turbulent flow.

1.
Toms
,
B. A.
, 1948, “
Some Observations on the Flow of Linear Polymer Solutions Through Strait Tubes at Large Reynolds Numbers
,”
Proc. of 1st Intern. Congress on Rheology
,
North Holland, Amsterdam
, Vol.
2
pp.
135
141
.
2.
Bark
,
F. H.
,
Hinch
,
E. J.
, and
Landahl
,
M. T.
, 1975, “
Drag Reduction in Turbulent Flow Due to Additives: A Report on Euromech 52
,”
J. Fluid Mech.
0022-1120,
68
, pp.
129
138
.
3.
Pinho
,
F. T.
, and
Whitelaw
,
J. H.
, 1990, “
Flow of Non-Newtonian Fluids in a Pipe
,”
J. Non-Newtonian Fluid Mech.
0377-0257,
34
, pp.
129
144
.
4.
Gyr
,
A.
, and
Bewersdorff
,
H. W.
, 1995,
Drag Reduction of Turbulent Flow by Additives
,
Kluwer Academic Publishers
,
Dordrecht
.
5.
Blick
,
E. F.
,
Walters
,
R. R.
,
Smith
,
R.
, and
Chu
,
H.
, 1969, “
Compliant Coating Skin Friction Experiments
,”
AIAA J.
0001-1452,
69
, p.
165
.
6.
Fraim
,
F. W.
, and
Heiser
,
W. H.
, 1967, “
The Effect of a Strong Longitudinal Magnetic Field on the Flow of Mercury in a Circular Pipe
,”
J. Fluid Mech.
0022-1120,
33
, pp.
397
413
.
7.
Cunha
,
F. R.
, and
Sobral
,
Y. D.
, 2005, “
Asymptotic Solution for Pressure Driven Flow of Magnetic Fluids in Pipes
,”
J. Magn. Magn. Mater.
0304-8853,
289
, pp.
314
317
.
8.
Lumley
,
J. L.
, 1969, “
Drag Reduction in Turbulent Flow by Polymer Additives
,”
J. Polym. Sci., Part A-1
0449-296X,
7
, pp.
263
290
.
9.
Ryskin
,
G.
, 1991, “
Turbulent Drag Reduction by Polymers: A Quantitative Theory
,”
Phys. Rev. Lett.
0031-9007,
59
, pp.
2059
2062
(see also Erratum: 1991,
Phys. Rev. Lett.
0031-9007,
66
, p.
968
).
10.
L’vov
,
V. S.
,
Pomyalov
,
A.
,
Procaccia
,
I.
, and
Toberkevich
,
V.
, 2004, “
Drag Reduction by Polymers in Wall Bounded Turbulence
,”
Phys. Rev. Lett.
0031-9007,
92
(
24
), pp.
244503
.
11.
De Gennes
,
P. G.
, 1990,
Introduction to Polymer Dynamics
,
Cambridge University Press
,
Cambridge, England
.
12.
Joseph
,
D. D.
, 1990,
Fluid Dynamics of Viscoelastic Liquids
,
Springer-Verlag
,
Berlin
.
13.
Min
,
T.
,
Yoo
,
Y. J.
,
Choi
,
H.
, and
Joseph
,
D. D.
, 2003, “
Drag Reduction by Polymer Additives in a Turbulent Channel Flow
,”
J. Fluid Mech.
0022-1120,
486
, pp.
213
238
.
14.
Massah
,
H.
, and
Hanratty
,
T. J.
, 1997, “
Added Stress Because of the Presence of FENE-P Bead-Spring Chains in a Random Velocity Field
,”
J. Fluid Mech.
0022-1120,
337
, pp.
67
101
.
15.
Landhal
,
M. T.
, 1973, “
Drag Reduction by Polymer Addition
,”
Theoretical and Applied Mechanics, Proc. 13th Intl. Congr. Theor. and Appl. Mech.
,
E.
Becher
, and
G. K.
Mikhailov
, eds.,
Springer
,
New York
, Vol.
1
, pp.
177
199
.
16.
Hinch
,
E. J.
, 1977, “
Mechanical Models of Dilute Polymer Solutions in Strong Flows
,”
Phys. Fluids
0031-9171,
20
, pp.
22
30
.
17.
Hinch
,
E. J.
, 1994, “
Uncoiling a Polymer Molecule in a Strong Extensional Flow
,”
J. Non-Newtonian Fluid Mech.
0377-0257,
54
, pp.
209
230
.
18.
Draaad
,
A. A.
, and
Hulsen
,
M. A.
, 1995, “
Transition From Laminar to Turbulent Flow for Non-Newtonian Fluids
,”
Advances in Turbulence V, Proc. of European Turbulence Conference V
,
R.
Benzi
, ed., Siena, Italy, Vol.
1
, pp.
105
110
.
19.
Den Toonder
,
J. M. J.
,
Hulsen
,
M. A.
,
Kuiken
,
G. D. C.
, and
Nieuwstadt
,
F. T. M.
, 1997, “
Drag Reduction by Polymer Additives in a Turbulent Pipe Flow: Numerical and Laboratory Experiments
,”
J. Fluid Mech.
0022-1120,
337
, pp.
193
231
.
20.
Andreotti
,
M.
,
Cunha
,
F. R.
, and
Sousa
,
A. J.
, 2003, “
Investigation of Friction Affected by Additives in Turbulent Flows in Pipelines
,”
Bol. Tec. Petrobras
,
46
, pp.
55
77
.
21.
Sasaki
,
S.
, 1992, “
Drag Reduction Effect of Rod-Like Polymer Solution, 3. Molecular Weight Dependence
,”
J. Phys. Soc. Jpn.
0031-9015,
61
(
6
), pp.
1960
1963
.
22.
Azaiez
,
J.
, 2000, “
Linear Stability of Free Shear Flows of Fiber Suspensions
,”
J. Fluid Mech.
0022-1120,
404
, pp.
179
209
.
23.
Handler
,
R. A.
, and
Levich
,
E.
, 1993, “
Drag Reduction in Turbulent Channel Flow by Phase Randomization
,”
Phys. Fluids A
0899-8213,
5
(
3
), pp.
686
694
.
24.
Dimitropoulos
,
C. D.
,
Sureshkumar
,
R.
, and
Beris
,
A. N.
, 1998, “
Direct Numerical Simulation of Viscoelastic Turbulent Channel Flow Exhibiting Drag Reduction: Effect of the Variation of Rheological Parameters
,”
J. Non-Newtonian Fluid Mech.
0377-0257,
79
, pp.
433
468
.
25.
Orlandi
,
P.
, 1995, “
A Tentative Approach to the Direct Simulation of Drag Reduction by Polymers
,”
J. Non-Newtonian Fluid Mech.
0377-0257,
60
, pp.
277
301
.
26.
Benzi
,
R.
,
De Angelis
,
E.
,
Govindarajan
,
R.
, and
Procaccia
,
I.
, 2003, “
Shell Model for Drag Reduction With Polymer Additives in Homogeneous Turbulence
,”
Phys. Rev. E
1063-651X,
68
, pp.
016308
.
27.
Salas
,
F. A.
,
Oliveira
,
T. F.
, and
Cunha
,
F. R.
, 2006, “
A Note on the Extensional Viscosity of Elastic Liquids Under Strong Flows
,”
Mech. Res. Commun.
0093-6413,
33
(
3
), pp.
401
414
.
28.
Cunha
,
F. R.
, 1995, “
Hydrodynamic Dispersion in Suspensions
,” Ph.D thesis, DAMTP-University of Cambridge, Cambridge.
29.
Kuhn
,
W.
, and
Kuhn
,
H.
, 1945, “
Bedeutung Beschrnkt Freier Drehbarkeit fr die Viskositt und Strmungsdoppelbrechung von Fadenmolekellsungen
,”
Helv. Chim. Acta
0018-019X,
28
, pp.
1533
1579
.
30.
Einstein
,
A.
, 1956,
Investigations on the Theory of the Brownian Movement
,
Dover Publications
,
New York
.
31.
Batchelor
,
G. K.
, 1970, “
Slender-Body Theory for Particle of Arbitrary Cross Section in Stokes Flow
,”
J. Fluid Mech.
0022-1120,
44
, pp.
419
440
.
32.
Hinch
,
E. J.
, and
Leal
,
L. G.
, 1976, “
Constitutive Equations in Suspension Mechanics, Part 2. Approximate Forms for a Suspension of Rigid Particles Affected by Brownian Rotations
,”
J. Fluid Mech.
0022-1120,
76
(
1
), pp.
187
208
.
33.
Ericksen
,
J. L.
, 1960, “
Trasversaly Isotropic Fluids
,”
Kolloidn. Zh.
0023-2912,
173
, pp.
117
122
.
34.
Aris
,
R.
, 1962,
Vectors, Tensors, and the Basic Equations of Fluid Mechanics
,
Dover
,
New York
.
35.
Stover
,
C. A.
,
Koch
,
D. L.
, and
Cohen
,
C.
, 1992, “
Observations of Fibre Orientation in Simple Shear Flow of Semi-Dilute Suspensions
,”
J. Fluid Mech.
0022-1120,
238
, pp.
277
296
.
36.
Keiller
,
R. A.
, and
Hinch
,
E. J.
, 1991, “
Corner Flow of a Suspension of Rigid Rods
,”
J. Non-Newtonian Fluid Mech.
0377-0257,
40
, pp.
323
335
.
37.
Batchelor
,
G. K.
, 1971, “
The Stress Generated in a Non-Dilute Suspension of Elongated Particles by Pure Straining Motion
,”
J. Fluid Mech.
0022-1120,
46
(
4
), pp.
813
829
.
38.
Shaqfeh
,
E. S. G.
, and
Frederickson
,
G. H.
, 1990, “
The Hydrodynamic Stress in a Suspension of Rods
,”
Phys. Fluids A
0899-8213,
2
, pp.
7
24
.
39.
Pao
,
R. H. F.
, 1967,
Fluid Dynamics
,
Charles E. Merrill Books
,
Columbus
.
40.
Barnes
,
H. A.
,
Huton
,
J. F.
, and
Walters
,
K.
, 1991,
An Introduction to Rheology
,
Elsevier
,
Amsterdan
.
41.
Batchelor
,
G. K.
, and
Green
,
J. T.
, 1972, “
The Hydrodynamic Interaction of Two Small Freely-Moving Spheres in a Linear Flow Field
,”
J. Fluid Mech.
0022-1120,
56
, pp.
375
400
.
42.
Lim
,
S. T.
,
Choi
,
H. J.
,
Lee
,
S. Y.
,
So
,
S. J.
, and
Chan
,
C. K.
, 2003, “
λ-DNA Induced Turbuelnt Drag Reduction and Its Characteristics
,”
Macromolecules
0024-9297,
36
, pp.
5348
5354
.
43.
Virk
,
P. S.
, 1975, “
Drag Reduction Fundamentals
,”
AIChE J.
0001-1541,
21
, pp.
625
656
.
44.
Kline
,
S. J.
, and
McClintock
,
F. A.
, 1991, “
Describing Uncertainties in Single-Sample Experiments
,”
Mech. Eng. (Am. Soc. Mech. Eng.)
0025-6501,
75
, pp.
3
8
.
45.
Hinch
,
E. J.
, 2004, Private communication.
46.
Press
,
W. H.
,
Teukolsky
,
S. A.
,
Vetterling
,
W. T.
, and
Flannery
,
B. P.
, 1992,
Numerical Recipes in Fortran
,
Cambridge University Press
,
Cambridge, England
.
47.
Landau
,
L. D.
, and
Lifshitz
,
E. M.
, 1987,
Course in Theoretical Physics: Fluid Mechanics
,
Pergamon
,
Oxford
.
You do not currently have access to this content.