Abstract

This study reexamines past studies of how drag-reducing polymer solutions modify the log-region of a developing turbulent boundary layer (TBL). The classical view was that the polymers modify the intercept constant without impacting the von Kármán coefficient, which results in the log-region being unaltered though shifted outward from the wall. However, recent work has shown this to be not accurate, especially at high drag reduction (HDR) (>40%). While the deviations to the von Kármán coefficient were conjectured to be related to polymeric properties, this had not been explored. This work examines the scatter in both log-region parameters and estimates the local polymeric properties. This shows that the scatter of the von Kármán coefficient between studies is related to the inner variable based Weissenberg number. In addition, recent polymer ocean results are included that support the implicit assumption in past studies that the maximum wall concentration should be used to define the local polymeric properties.

References

1.
Virk
,
P. S.
,
1975
, “
Drag Reduction Fundamentals
,”
AIChE J.
,
21
(
4
), pp.
625
656
.10.1002/aic.690210402
2.
White
,
C. M.
,
Dubief
,
Y.
, and
Klewicki
,
J.
,
2012
, “
Re-Examining the Logarithmic Dependence of the Mean Velocity Distribution in Polymer Drag Reduced Wall-Bounded Flow
,”
Phys. Fluids
,
24
(
2
), p.
021701
.10.1063/1.3681862
3.
Elbing
,
B. R.
,
Perlin
,
M.
,
Dowling
,
D. R.
, and
Ceccio
,
S. L.
,
2013
, “
Modification of the Mean Near-Wall Velocity Profile of a High-Reynolds Number Turbulent Boundary Layer With the Injection of Drag-Reducing Polymer Solutions
,”
Phys. Fluids
,
25
(
8
), p.
085103
.10.1063/1.4817073
4.
Elsnab
,
J. R.
,
Monty
,
J. P.
,
White
,
C. M.
,
Koochesfahani
,
M. M.
, and
Klewicki
,
J. C.
,
2019
, “
High-Fidelity Measurements in Channel Flow With Polymer Wall Injection
,”
J. Fluid Mech.
,
859
, pp.
851
886
.10.1017/jfm.2018.873
5.
Elbing
,
B. R.
,
Solomon
,
M. J.
,
Perlin
,
M.
,
Dowling
,
D. R.
, and
Ceccio
,
S. L.
,
2011
, “
Flow-Induced Degradation of Drag-Reducing Polymer Solutions Within a High-Reynolds-Number Turbulent Boundary Layer
,”
J. Fluid Mech.
,
670
, pp.
337
364
.10.1017/S0022112010005331
6.
Fontaine
,
A.
,
Petrie
,
H.
, and
Brungart
,
T.
,
1992
, “
Velocity Profile Statistics in a Turbulent Boundary Layer With Slot-Injected Polymer
,”
J. Fluid Mech.
,
238
, pp.
435
466
.10.1017/S0022112092001770
7.
White
,
C. M.
,
Somandepalli
,
V. S. R.
, and
Mungal
,
M. G.
,
2004
, “
The Turbulence Structure of Drag-Reduced Boundary Layer Flow
,”
Exp. Fluids
,
36
(
1
), pp.
62
69
.10.1007/s00348-003-0630-0
8.
Petrie
,
H.
,
Fontaine
,
A.
,
Money
,
M.
, and
Deutsch
,
S.
,
2005
, “
Experimental Study of Slot-Injected Polymer Drag Reduction
,”
Proceedings of the Second International Symposium on Seawater Drag Reduction
, Busan, South Korea, May 23–26, pp.
605
620
.
9.
Hou
,
Y. X.
,
Somandepalli
,
V. S. R.
, and
Mungal
,
M. G.
,
2008
, “
Streamwise Development of Turbulent Boundary-Layer Drag Reduction With Polymer Injection
,”
J. Fluid Mech.
,
597
, pp.
31
66
.10.1017/S0022112007009718
10.
Somandepalli
,
V. S. R.
,
Hou
,
Y. X.
, and
Mungal
,
M. G.
,
2010
, “
Concentration Flux Measurements in a Polymer Drag-Reduced Turbulent Boundary Layer
,”
J. Fluid Mech.
,
644
, pp.
281
319
.10.1017/S0022112009992382
11.
Farsiani
,
Y.
,
Saeed
,
Z.
,
Jayaraman
,
B.
, and
Elbing
,
B. R.
,
2020
, “
Modification of Turbulent Boundary Layer Coherent Structures With Drag Reducing Polymer Solution
,”
Phys. Fluids
,
32
(
1
), p.
015107
.10.1063/1.5127293
12.
Winkel
,
E. S.
,
Oweis
,
G. F.
,
Vanapalli
,
S. A.
,
Dowling
,
D. R.
,
Perlin
,
M.
,
Solomon
,
M. J.
, and
Ceccio
,
S. L.
,
2009
, “
High-Reynolds-Number Turbulent Boundary Layer Friction Drag Reduction From Wall-Injected Polymer Solutions
,”
J. Fluid Mech.
,
621
, pp.
259
288
.10.1017/S0022112008004874
13.
Elbing
,
B. R.
,
Winkel
,
E. S.
,
Ceccio
,
S. L.
,
Perlin
,
M.
, and
Dowling
,
D. R.
,
2010
, “
High-Reynolds-Number Turbulent-Boundary-Layer Wall-Pressure Fluctuations With Dilute Polymer Solutions
,”
Phys. Fluids
,
22
(
8
), p.
085104
.10.1063/1.3478982
14.
Elbing
,
B. R.
,
Dowling
,
D. R.
,
Perlin
,
M.
, and
Ceccio
,
S. L.
,
2010
, “
Diffusion of Drag-Reducing Polymer Solutions Within a Rough-Walled Turbulent Boundary Layer
,”
Phys. Fluids
,
22
(
4
), p.
045102
.10.1063/1.3371957
15.
Grandbois
,
M.
,
Beyer
,
M.
,
Rief
,
M.
,
Clausen-Schaumann
,
H.
, and
Gaub
,
H. E.
,
1999
, “
How Strong is a Covalent Bond?
,”
Science
,
283
(
5408
), pp.
1727
1730
.10.1126/science.283.5408.1727
16.
Vanapalli
,
S. A.
,
Islam
,
M. T.
, and
Solomon
,
M. J.
,
2005
, “
Scission-Induced Bounds on Maximum Polymer Drag Reduction in Turbulent Flow
,”
Phys. Fluids
,
17
(
9
), p.
095108
.10.1063/1.2042489
17.
Farsiani
,
Y.
,
Saeed
,
Z.
, and
Elbing
,
B. R.
,
2020
, “
Drag Reduction Performance of Mechanically Degraded Dilute Polyethylene Oxide Solutions
,”
ASME J. Fluids Eng.
,
142
(
9
), p.
091201
.10.1115/1.4047118
18.
Zimm
,
B. H.
,
1956
, “
Dynamics of Polymer Molecules in Dilute Solution: Viscoelasticity, Flow Birefringence and Dielectric Loss
,”
J. Chem. Phys.
,
24
(
2
), pp.
269
278
.10.1063/1.1742462
19.
Bailey
,
F. E.
, Jr.
, and
Callard
,
R. W.
,
1959
, “
Some Properties of Poly(Ethylene Oxide) in Aqueous Solution
,”
J. Appl. Polym. Sci.
,
1
(
1
), pp.
56
62
.10.1002/app.1959.070010110
20.
Kalashnikov
,
V. N.
,
1998
, “
Dynamical Similarity and Dimensionless Relations for Turbulent Drag Reduction by Polymer Additives
,”
J. Non-Newtonian Fluid Mech.
,
75
(
2–3
), pp.
209
230
.10.1016/S0377-0257(97)00093-1
21.
Larson
,
R. G.
,
1999
,
The Structure and Rheology of Complex Fluids
,
Oxford University Press
,
New York
.
22.
Vanapalli
,
S. A.
,
Ceccio
,
S. L.
, and
Solomon
,
M. J.
,
2006
, “
Universal Scaling for Polymer Chain Scission in Turbulence
,”
Proc. Natl. Acad. Sci.
,
103
(
45
), pp.
16660
16665
.10.1073/pnas.0607933103
23.
Poreh
,
M.
, and
Cermak
,
J. E.
,
1964
, “
Study of Diffusion From a Line Source in a Turbulent Boundary Layer
,”
Int. J. Heat Mass Transfer
,
7
(
10
), pp.
1083
1095
.10.1016/0017-9310(64)90032-8
24.
Collins
,
D. J.
, and
Gorton
,
C. W.
,
1976
, “
An Experimental Study of Diffusion From a Line Source in a Turbulent Boundary Layer
,”
AIChE J.
,
22
(
3
), pp.
610
612
.10.1002/aic.690220333
25.
Giles
,
W. B.
,
1968
, “
Similarity Laws of Friction-Reduced-Flows
,”
J. Hydronautics
,
2
(
1
), pp.
34
40
.10.2514/3.62771
26.
Gebel
,
C.
,
Reitzer
,
H.
, and
Bues
,
M.
,
1978
, “
Diffusion of Macromolecular Solutions in the Boundary Layer
,”
Rheol. Acta
,
17
(
2
), pp.
172
175
.10.1007/BF01517708
27.
Vdovin
,
A. V.
, and
Smol'yakov
,
A. V.
,
1982
, “
Turbulent Diffusion of Polymers in a Boundary Layer
,”
J. Appl. Mech. Tech. Phys.
,
22
(
4
), pp.
526
531
.10.1007/BF00906264
28.
Vdovin
,
A. V.
, and
Smol'yakov
,
A. V.
,
1978
, “
Diffusion of Polymer Solutions in a Turbulent Boundary Layer
,”
J. Appl. Mech. Tech. Phys.
,
19
(
2
), pp.
196
201
.10.1007/BF00850033
29.
White
,
C. M.
, and
Mungal
,
M. G.
,
2008
, “
Mechanics and Prediction of Turbulent Drag Reduction With Polymer Additives
,”
Annu. Rev. Fluid Mech.
,
40
(
1
), pp.
235
256
.10.1146/annurev.fluid.40.111406.102156
30.
Virk
,
P. S.
,
Mickley
,
H. S.
, and
Smith
,
K. A.
,
1970
, “
The Ultimate Asymptote and Mean Flow Structure in Toms' Phenomenon
,”
ASME J. Appl. Mech.
,
37
(
2
), pp.
488
493
.10.1115/1.3408532
31.
Marusic
,
I.
,
Monty
,
J. P.
,
Hultmark
,
M.
, and
Smits
,
A. J.
,
2013
, “
On the Logarithmic Region in Wall Turbulence
,”
J. Fluid Mech.
,
716
, p.
R3
.10.1017/jfm.2012.511
32.
Hultmark
,
M.
,
Vallikivi
,
M.
,
Bailey
,
S. C. C.
, and
Smits
,
A. J.
,
2012
, “
Turbulent Pipe Flow at Extreme Reynolds Numbers
,”
Phys. Rev. Lett.
,
108
(
9
), p.
094501
.10.1103/PhysRevLett.108.094501
33.
Hutchins
,
N.
,
Chauhan
,
K.
,
Marusic
,
I.
,
Monty
,
J. P.
, and
Klewicki
,
J.
,
2012
, “
Towards Reconciling the Large-Scale Structure of Turbulent Boundary Layers in the Atmosphere and Laboratory
,”
Boundary-Layer Meteorol.
,
145
(
2
), pp.
273
306
.10.1007/s10546-012-9735-4
34.
Kulandaivelu
,
V.
,
2012
, “
Evolution of Zero Pressure Gradient Turbulent Boundary Layers From Different Initial Conditions
,” Ph.D. thesis,
University of Melbourne
, Melbourne, Australia.
35.
Winkel
,
E. S.
,
Cutbirth
,
J. M.
,
Ceccio
,
S. L.
,
Perlin
,
M.
, and
Dowling
,
D. R.
,
2012
, “
Turbulence Profiles From a Smooth Flat-Plate Turbulent Boundary Layer at High Reynolds Number
,”
Exp. Therm. Fluid Sci.
,
40
, pp.
140
149
.10.1016/j.expthermflusci.2012.02.009
36.
Koskie
,
J. E.
, and
Tiederman
,
W. G.
,
1991
, “
Polymer Drag Reduction of a Zero-Pressure-Gradient Boundary Layer
,”
Phys. Fluids
,
3
(
10
), pp.
2471
2473
.10.1063/1.858187
You do not currently have access to this content.