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Physics of Fluids / Volume 24 / Issue 2 / LETTERS
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Phys. Fluids 24, 021701 (2012); http://dx.doi.org/10.1063/1.3681862 (6 pages)

Re-examining the logarithmic dependence of the mean velocity distribution in polymer drag reduced wall-bounded flow

C. M. White1, Y. Dubief2, and J. Klewicki1

1Mechanical Engineering Department, University of New Hampshire, Durham, New Hampshire 03824, USA
2Mechanical Engineering Department, University of Vermont, Burlington, Vermont 05405, USA

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(Received 12 August 2011; accepted 22 December 2011; published online 3 February 2012)

A re-examination of the logarithmic dependence of the mean velocity distribution in polymer drag reduced flows shows that drag reducing polymers modify the von Kármán coefficient and, in channel flow, eradicate the log-layer at high drag reductions. It is also found that the “ultimate profile,” corresponding to the state of maximum drag reduction is not logarithmic.

© 2012 American Institute of Physics

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KEYWORDS and PACS

Keywords

boundary layer turbulence, channel flow, computational fluid dynamics, drag reduction, polymers

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3681862

PUBLICATION DATA

ISSN

1070-6631 (print)  
1089-7666 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

  1. B. A. Toms , “Some observations on the flow of linear polymer solutions through straight tubes at large Reynolds numbers,” in Proceedings of the First International Congress on Rheology, Scheveningen, 21–24 September 1948, Vol. 2, edited by J. M. Burgers (North-Holland, Amsterdam, Netherlands, 1949), pp. 135–141.
  2. J. L. Lumley, “Drag reduction by additives,” Ann. Rev. Fluid Mech. 1, 367 (1969).
  3. P. S. Virk, “Drag reduction fundamentals,” AICHE J. 21, 625 (1975).
  4. C. M. White and M. G. Mungal, “Mechanics and prediction of turbulent drag reduction with polymer additives,” Ann. Rev. Fluid Mech. 40, 235 (2008).
  5. V. L'vov, A. Pomyalov, I. Procaccia, and V. Tiberkevich, “Drag reduction by polymers in wall bounded turbulence,” Phys. Rev. Lett. 92, 244503 (2004). [MEDLINE]
  6. R. Benzi, E. D. Angelis, V. L'vov, I. Procaccia, and V. Tiberkevich, “Maximum drag reduction asymptotes and the cross-over to the newtonian plug,” J. Fluid Mech. 551, 185 (2006).
  7. I. Procaccia, V. L'vov, and R. Benzi, “Colloquium: Theory of drag reduction by polymers in wall-bounded turbulence,” Rev. Mod. Phys. 80, 225 (2008).
  8. R. Benzi, “A short review on drag reduction by polymers in wall bounded turbulence,” Physica D 239, 1338 (2010).
  9. H. M. Nagib and K. A. Chauhan, “Variations of the von Kármán coefficient in canonical flows,” Phys. Fluids 20, 101518 (2008)PHFLE6000020000010101518000001.
  10. P. Virk, H. Mickley, and K. Smith, “The ultimate asymptote and mean flow structure in Toms phenomenon,” Trans. ASME, J. Appl. Mech. 37, 488 (1970)JAMCAV000037000002000488000001.
  11. M. Escudier, A. Nickson, and R. Poole, “Turbulent flow of viscoelastic shear-thinning liquids through a rectangular duct: Quantification of turbulence anisotropy,” J. Non-Newtonian Fluid Mech. 160, 2 (2009). [Inspec]
  12. P. K. Ptasinski, F. T. M. Nieuwstadt, B. H. A. A. V. D. Brule, and M. A. Hulsen, “Experiments in turbulent pipe flow with polymer additives at maximum drag reduction,” Flow, Turbul. Combust. 66, 159 (2001). [ISI]
  13. J. M. J. den Toonder, M. A. Hulsen, G. D. C. Kuiken, and F. T. M. Niewstadt, “Drag reduction by polymer additives in a turbulent pipe flow: numerical and laboratory experiments,” J. Fluid Mech. 337, 193 (1997). [Inspec] [ISI]
  14. M. Escudier, F. Presti, and S. Smith, “Drag reduction in the turbulent pipe flow of polymers,” J. Non-Newtonian Fluid Mech. 81, 197 (1999). [Inspec] [ISI]
  15. M. D. Warholic, H. Massah, and T. J. Hanratty, “Influence of drag-reducing polymers on turbulence: effects of Reynolds number, concentration and mixing,” Exp. Fluids 27, 461 (1999).
  16. Y. Dubief, C. M. White, V. E. Terrapon, E. S. G. Shaqfeh, P. Moin, and S. K. Lele, “On the coherent drag-reducing turbulence-enhanching behaviour of polymers in wall flows,” J. Fluid Mech. 514, 271 (2004). [ISI]
  17. R. S. C.-F. Li and B. Khomani, “Influence of rheological parameters on polymer induced drag reduction,” J. Non-Newtonian Fluid Mech. 140, 23 (2006).
  18. S. Tamano, M. Itoh, K. Hoshizaki, and K. Yokota, “Direct numerical simulation of the drag-reducing turbulent boundary layer of viscoelastic fluid,” Phys. Fluids 19, 075106 (2007)PHFLE6000019000007075106000001. [ISI]
  19. Y. Hou, V. S. R. Somandepalli, and M. G. Mungal, “Streamwise development of turbulent boundary layer drag reduction with polymer injection,” J. Fluid Mech. 597 (2008).

Figures (3) Tables (3)

Figures (click on thumbnails to view enlargements)

FIG.1
A schematic of the behaviors of the mean velocity distribution for wall-bounded flow of polymer solutions as summarized by Virk3: (i) math+ = y+, (ii) is the Newtonian “law of the wall” given by math+ = 2.5log(y+)+5.0, and (iii) is the “ultimate profile” given by Eq. ( 2 ). With DR, the mean velocity distribution initially follows (iii) and then crosses over to a “Newtonian plug flow” with the same value of κ as (ii) and C1 increasing with increasing DR.

FIG.1 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.2
Mean velocity profiles in polymer drag reduced wall-bounded flows. Closed symbols denote experimental data, key given in Table 1; open symbols denote present DNS data, key given in Table 2.

FIG.2 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.3
Indicator function typically used to investigate logarithmic dependence of the mean velocity profile. (a) Channel flow where symbol key is the same as in Fig. 2. (b) Zero-pressure-gradient boundary layer flow where symbol key is given in Table 3. The “—”corresponds to 2.5 and “−· −” corresponds to 11.7.

FIG.3 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

Tables

Table I. Description of experimental mean velocity data plotted in Fig. 2.

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Table II. Polymer parameters used for the viscoelastic simulations and symbol used for plotting data.

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Table III. Description of boundary layer data plotted in Fig. 3a, where Reθ is the momentum thickness Reynolds number.

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