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Turbulent drag reduction with polymer additive in rough pipes

Published online by Cambridge University Press:  11 December 2009

SHU-QING YANG  and
G. DOU
SHU-QING YANG*
Affiliation:
School of Civil, Mining & Environmental Engineering, University of Wollongong NSW 2522, Australia
G. DOU
Affiliation:
Nanjing Hydraulic Research Institute, 223 Guangzhou Road, Nanjing, China, 210024
*
†Email address for correspondence: [email protected]
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Abstract

Friction factor of drag-reducing flow with presence of polymers in a rough pipe has been investigated based on the eddy diffusivity model, which shows that the ratio of effective viscosity caused by polymers to kinematic viscosity of fluid should be proportional to the Reynolds number, i.e. u∗R/ν and the proportionality factor depends on polymer's type and concentration. A formula of flow resistance covering all regions from laminar, transitional and fully turbulent flows has been derived, and it is valid in hydraulically smooth, transitional and fully rough regimes. This new formula has been tested against Nikuradse and Virk's experimental data in both Newtonian and non-Newtonian fluid flows. The agreement between the measured and predicted friction factors is satisfactory, indicating that the addition of polymer into Newtonian fluid flow leads to the non-zero effective viscosity and it also thickens the viscous sublayer, subsequently the drag is reduced. The investigation shows that the effect of polymer also changes the velocity at the top of roughness elements. Both experimental data and theoretical predictions indicate that, if same polymer solution is used, the drag reduction (DR) in roughened pipes becomes smaller relative to smooth pipe flows at the same Reynolds number.

JFM classification

Mathematical Foundations: General fluid mechanics Non-Newtonian Flows: Polymers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 642 , 10 January 2010 , pp. 279 - 294
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Benzi, R., Ching, E. S. C., Horesh, N. & Procaccia, I. 2004 a Theory of concentration dependence in drag reduction by polymers and the maximum drag reduction asymptote. Phys. Rev. Lett. 92 (7), 078302.CrossRefGoogle ScholarPubMed
Benzi, R., L'vov, V. S., Procaccia, I. & Tiberkevich, V. 2004 b Saturation of turbulent drag reduction in dilute polymer solutions. Europhys. Lett. 68, 825–831.CrossRefGoogle Scholar
Bewersdorff, H. W. & Thiel, H. 1993 Turbulence structure of dilute polymer and surfactant solutions in artificially roughened pipes. Appl. Sci. Res. 50, 347–368.CrossRefGoogle Scholar
Bradshaw, P. 2000 A note on “Critical roughness height” and “Transitional roughness”. Phys. Fluids 12 (6), 1611–1614.CrossRefGoogle Scholar
Cadot, O., Bonn, D. & Douady, S. 1998 Turbulent drag reduction in a closed flow system: boundary layer versus bulk effects. Phys. Fluids 10, 426–436.CrossRefGoogle Scholar
Daugherty, R. L., Franzini, J. B. & Finnemore, E. J. 1985 Fluid Mechanics with Engineering Applications. McGraw-Hill.Google Scholar
Dou, G. R. 1981 Turbulent structure in open channels and pipes. Sci. Sin. 24, 727–737.Google Scholar
Dou, G. R. 1996 Basic law in mechanics of turbulent flows. China Ocean Engng 10 (1), 1–44.Google Scholar
Dou, G. & Yang, S. Q. 1989 The drag-reducing mechanism of polymer dilute solution and its energy spectrum. J. Nanjing Hydraul. Res. Inst. (4), 1–12 (in Chinese).Google Scholar
Draad, A. A., Kuiken, G. D. C. & Niu-euwstadt, F. T. M. 1998 Laminar-turbulent transition in pipe flow for Newtonian and non-Newtonian fluids. J. Fluid Mech. 377, 267–312.CrossRefGoogle Scholar
Escudier, M. P. & Smith, S. 1999 Turbulent flow of Newtonian and shear-thinning liquids through a sudden axisymmetric expansion. Exp. Fluids 27 (5), 427–434.CrossRefGoogle Scholar
Goldshtik, M. A., Zametalin, V. V. & Shtern, V. N. 1982 Simplified theory of the near wall turbulent layer of Newtonian and drag-reducing fluids. J. Fluid Mech. 119, 423–441.CrossRefGoogle Scholar
Keefe, L. Moin, P. & Kim, J. 1992 The dimension of attractors underlying periodic turbulent Poiseuille flow. J. Fluid Mech. 242, 1–29.CrossRefGoogle Scholar
L'vov, V. S., Pomyalov, A., Procaccia, I. & Tiberkevich, V. 2004 Drag reduction by polymers in wall-bounded turbulence. Phys. Rev. Lett. 92, 244503.CrossRefGoogle ScholarPubMed
Lindgren, E. R. & Hoot, T. G. 1968 Effects of dilute high molecular weight polymers on turbulent flows of water in very rough pipes. ASME. J. Appl. Mech. 35, 417–418.CrossRefGoogle Scholar
Lumley, J. L. 1969 Drag reduction by additives. Annu. Rev. Fluid Mech. 1, 367–374.CrossRefGoogle Scholar
Massah, H. & Hanratty, T. J. 1997 Added stresses because of the presence of FENE-P bead-spring chains in a random velocity field. J. Fluid Mech. 337, 67–101.CrossRefGoogle Scholar
Matas, J. P., Morris, J. F. & Guazzelli, E. 2003 Transition to turbulence in particular pipe flow. Phys. Rev. Lett. 90 (1), 014501.CrossRefGoogle Scholar
McComb, W. 1990 The Fluid of Physics Turbulence. Oxford University Press.CrossRefGoogle Scholar
Min, T., Yoo, J. Y., Choi, H. & Joseph, D. D. 2003 Drag reduction by polymer additives in a turbulent channel flow. J. Fluid Mech. 486, 213–238.CrossRefGoogle Scholar
Mun, R. P., Byars, J. A. & Boger, D. V. 1998 The effects of polymer concentration and molecular weight on the breakup of laminar capillary jets. J. Non-Newton. Fluid Mech. 74 (8), 285–297.CrossRefGoogle Scholar
Nikuradse, J. 1933 Law of flow in rough pipes NACA TM, 1292 (English translated in 1950).Google Scholar
Petrie, H. L., Deutsch, S., Brungart, T. A. & Fontaine, A. A. 2003 Polymer drag reduction with surface roughness in flat-pate turbulent boundary layer flow. Exp. Fluids 35 (1), 8–23.Google Scholar
Ptasinski, P. K., Nieuwstadt, F. T. M., Van Den Brule, B. H. A. A. & Hulsen, M. A. 2001 Experiments in turbulent pipe flow with polymer additives at maximum drag reduction. Flow Turbul. Combust. 66, 159–182.CrossRefGoogle Scholar
Procaccia, I., L'vov, V. S. & Benzi, R. 2008 Colloquium: theory of drag reduction by polymers in wall bounded turbulence. Rev. Mod. Phys. 80, 225–247CrossRefGoogle Scholar
Schlichting, H. 1979 Boundary Layer Theory. McGraw-Hill.Google Scholar
Sibilla, S. & Baron, A. 2002 Polymer stress statistics in the near-wall turbulent flow of a drag-reducing solution. Phys. Fluids 14 (3). 1123–1136.CrossRefGoogle Scholar
Sreenivasan, K. R. & White, C. M. (2000), Onset of drag reduction and the maximum drag reduction asymptote. J. Fluid Mech. 409, 149–164.CrossRefGoogle Scholar
Street, R. L., Watters, G. Z. & Vennard, J. K. 1996 Elementary Fluid Mechanics. John Wiley & Sons.Google Scholar
Virk, P. S. 1971 a Drag reduction in rough pipes. J. Fluid Mech. 45 (2), 225–246.CrossRefGoogle Scholar
Virk, P. S. 1971 b An elastic sublayer model for drag reduction by dilute solutions of linear macromolecules. J. Fluid. Mech. 45, 417–440.CrossRefGoogle Scholar
Virk, P. S. 1975 Drag reduction fundamentals. AIChE J. 21 (4), 625–657.CrossRefGoogle Scholar
Vlachogiannis, M. & Hanratty, T. J. 2004 Influence of wavy structured surfaces and large scale polymer structures on drag reduction. Exp. Fluids 36, 685–700.CrossRefGoogle Scholar
Warholic, M. D., Heist, D. K., Katcher, M. & Hanratty, T. J. 2001 A study with particle-image velocimetry of the influence of drag-reducing polymers on the structures of turbulence. Exp. Fluids 31, 474–483.CrossRefGoogle Scholar
White, C. M. & Mungal, M. G. 2008 Mechanics and prediction of turbulent drag reduction with polymer additives. Annu. Rev. Fluid Mech. 40, 235–256.CrossRefGoogle Scholar
Wojs, K. 1993 Laminar and turbulent flow of dilute polymer solutions in smooth and rough pipes. J. Non-Newton. Fluid Mech. 48, 337–355.CrossRefGoogle Scholar
Yang, S. Q. & Dou, G. 2005 Drag reduction in flat-plate turbulent boundary layer flow by polymer additive. Phys. Fluids 17 (6), 065104CrossRefGoogle Scholar
Yang, S. Q. & Dou, G. 2008 Modelling of viscoelatic turbulent flow in open channel and pipe Phys. Fluids 20 (6), 065105.CrossRefGoogle Scholar
Yang, S. Q. & Tan, S. K. 2008 Flow resistance over mobile bed in an open-channel flow. J. Hydraul. Engng ASCE 134 (7), 937–947.CrossRefGoogle Scholar
Yang, S. Q., Tan, S. K. & Lim, S. Y. 2005 Relation between flow resistance and bed-form geometry in wide alluvial channels. Water Resour. Res. 41 (9), W09419.CrossRefGoogle Scholar