Hostname: page-component-5c6d5d7d68-7tdvq Total loading time: 0 Render date: 2024-08-19T20:09:38.210Z Has data issue: false hasContentIssue false
  • English
  • Français

Statistics and tensor analysis of polymer coil–stretch mechanism in turbulent drag reducing channel flow

Published online by Cambridge University Press:  05 July 2017

Anselmo S. Pereira ,
Gilmar Mompean Open the ORCID record for Gilmar Mompean [Opens in a new window] ,
Laurent Thais  and
Roney L. Thompson
Anselmo S. Pereira
Affiliation:
Polytech’Lille and Laboratoire de Mécanique de Lille (LML), Université de Lille 1 – Sciences et Technologies, Cité Scientifique, 59655 Villeneuve d’Ascq, France
Gilmar Mompean*
Affiliation:
Polytech’Lille and Laboratoire de Mécanique de Lille (LML), Université de Lille 1 – Sciences et Technologies, Cité Scientifique, 59655 Villeneuve d’Ascq, France
Laurent Thais
Affiliation:
Polytech’Lille and Laboratoire de Mécanique de Lille (LML), Université de Lille 1 – Sciences et Technologies, Cité Scientifique, 59655 Villeneuve d’Ascq, France
Roney L. Thompson
Affiliation:
COPPE, Department of Mechanical Engineering, Universidade Federal do Rio de Janeiro, Centro de Tecnologia, Ilha do Fundão, 21945-970, Rio de Janeiro, RJ, Brazil
*
†Email address for correspondence: gilmar.mompean@polytech-lille.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

The polymer coil–stretch mechanism in turbulent drag reducing flows is analysed using direct numerical simulations of viscoelastic finitely extensible nonlinear elastic fluids with the Peterlin approximation. The study is carried out taking into account low and high drag reduction regimes. The polymer stretching and the alignment between the conformation tensor and other relevant entities are investigated using statistical and tensor analysis. The significant alignment between the former and the velocity fluctuations product tensor indicates that the initial polymer stretching due to the mean shear is increased by the flow stress fluctuations, providing a supplementary polymer extension. In addition, interactions between the turbulence and the polymer are evaluated from an instantaneous turbulent energy exchange perspective by considering streamwise work fluctuating terms in elliptical and hyperbolic flow regions separately. Near the wall, polymers not only release energy to the streaks, but also to the elliptical (or vortical) and hyperbolic (or extensional) structures. However, polymers can also be dragged around near-wall vortices, passing through hyperbolic regions and experiencing a significant straining within both these turbulent structures and storing their energy. Hence, polymers weaken elliptical and hyperbolic structures leading to a tendency toward relaminarization of the flow. Polymer release of energy occurs primarily in the streamwise direction, which is in agreement with the enhanced streamwise velocity fluctuation observed in drag reducing flows. A detailed polymer coil–stretch mechanism is provided.

JFM classification

Flow Control: Drag reduction Non-Newtonian Flows: Non-Newtonian Flows Turbulent Flows: Turbulence simulation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 824 , 10 August 2017 , pp. 135 - 173
Check for updates
Copyright
© 2017 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adrian, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19, 041301.CrossRefGoogle Scholar
Andrade, R. M., Pereira, A. S. & Soares, E. J. 2014 Drag increase at the very start of drag reducing flows in a rotating cylindrical double gap device. J. Non-Newtonian Fluid Mech. 212, 73–79.CrossRefGoogle Scholar
Armfield, S. W. & Street, R. L. 2000 Fractional step methods for the Navier–Stokes equations on non-staggered grids. ANZIAM J. 42(E), C134–C156.CrossRefGoogle Scholar
Bagheri, F., Mitra, D., Perlekar, P. & Brandt, L. 2012 Statistics of polymer extensions in turbulent channel flow. Phys. Rev. E 86, 056314.Google ScholarPubMed
Benzi, R., Angelis, E. D., L’vov, V. S. & Procaccia, I. 2005 Identification and calculation of the universal asymptote for drag reduction by polymers in wall-bounded turbulence. Phys. Rev. Lett. 95, 194502.CrossRefGoogle ScholarPubMed
Bewersdorff, H. W. 1982 Effect of a centrally injected polymer thread on drag in pipe flow. Rheol. Acta 21, 587–589.CrossRefGoogle Scholar
Bewersdorff, H. W. & Singh, R. P. 1988 Rheological and drag reduction characteristics of xanthan gum solutions. Rheol. Acta 27, 617–627.CrossRefGoogle Scholar
Bird, R., Armstrong, R. & Hassager, O. 1987 Dynamics of Polymeric Liquids. Kinetic Theory. Wiley.Google Scholar
Burger, E. D. & Chorn, L. G. 1980 Studies of drag reduction conducted over a broad range of pipeline conditions when flowing Prudhoe Bay crude oil. J. Rheol. 24, 603–626.CrossRefGoogle Scholar
Dallas, V., Vassilicos, J. C. & Hewitt, G. F. 2010 Strong polymer–turbulence interactions in viscoelastic turbulent channel flow. Phys. Rev. E 82, 066303.Google ScholarPubMed
De Angelis, E., Casciola, C., L’vov, V. S., Pomyalov, A., Procaccia, I. & Tiberkevich, V. 2004 Drag reduction by a linear viscosity profile. Phys. Rev. E 70, 055301.Google ScholarPubMed
Dean, R. B. 1978 Reynolds number dependence of skin friction and other bulk flow variables in two-dimensional rectangular duct flow. Trans. ASME J. Fluids Engng 100, 215–223.CrossRefGoogle Scholar
Dimitropoulos, C. D., Dubief, Y., Shaqfeh, E. S. G., Moin, P. & Lele, S. K. 2005 Direct numerical simulation of polymer-induced drag reduction in turbulent boundary layer flow. Phys. Fluids 17, 1–4.CrossRefGoogle Scholar
Dubief, Y., White, C. M., Terrapon, V. E., Shaqfeh, E. S. G., Moin, P. & Lele, S. K. 2004 On the coherent drag-reducing and turbulence-enhancing behaviour of polymers in wall flows. J. Fluid Mech. 514, 271–280.CrossRefGoogle Scholar
Escudier, M. P., Nickson, A. & Poole, R. 2009 Turbulent flow of viscoelastic shear-thinning liquids through a rectangular duct: quantification of turbulence anisotropy. J. Non-Newtonian Fluid Mech. 160, 2–10.CrossRefGoogle Scholar
Escudier, M. P., Presti, F. & Smith, S. 1999 Drag reduction in the turbulent pipe flow of polymers. J. Non-Newtonian Fluid Mech. 81, 197–213.CrossRefGoogle Scholar
Fabula, A. G. 1971 Fire-fighting benefits of polymeric friction reduction. Trans ASME J. Basic Engng 93, 453–455.CrossRefGoogle Scholar
Forrest, F. & Grierson, G. A. 1931 Friction losses in cast iron pipe carrying paper stock. Paper Trade J. 92, 39–41.Google Scholar
Golda, J. 1986 Hydraulic transport of coal in pipes with drag reducing additives. Chem. Engng Commun. 45, 53–67.CrossRefGoogle Scholar
Greene, H. L., Mostardi, R. F. & Nokes, R. F. 1980 Effects of drag reducing polymers on initiation of atherosclerosis. Polym. Engng Sci. 20–449.Google Scholar
Gyr, A. & Tsinober, T. 1995 On the rheological nature of drag reduction phenomena. J. Non-Newtonian Fluid Mech. 73, 153–162.CrossRefGoogle Scholar
Hershey, H. C. & Zakin, J. L. 1967 A molecular approach to predicting the onset of drag reduction in the turbulent flow of dilute polymer solutions. Chem. Engng Sci. 22, 184–187.CrossRefGoogle Scholar
Housiadas, K. D. & Beris, A. N. 2003 Polymer-induced drag reduction: effects of the variations in elasticity and inertia in turbulent viscoelastic channel flow. Phys. Fluids 15 (8), 2369–2384.CrossRefGoogle Scholar
Housiadas, K. D. & Beris, A. N. 2004 Characteristic scales and drag reduction evaluation in turbulent channel flow of nonconstant viscosity viscoelastic fluids. Phys. Fluids 16, 1581–1586.CrossRefGoogle Scholar
Hunt, J. C. R., Wray, A. A. & Moin, P. 1988 Eddies, stream, and convergence zones in turbulent flows. In Center for Turbulence Research – Proceedings of Summer Program Report CTR-S88, pp. 193–208. Stanford University.Google Scholar
Jiménez, J. & Pinelli, A. 1999 The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389, 335–359.CrossRefGoogle Scholar
Joseph, D. D. 1990 Fluid Dynamics of Viscoelastic Liquids. Springer.CrossRefGoogle Scholar
Kalashnikov, V. N. 1998 Dynamical similarity and dimensionless relations for turbulent drag reduction by polymer additives. J. Non-Newtonian Fluid Mech. 75, 209–230.CrossRefGoogle Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.CrossRefGoogle Scholar
Kim, K., Adrian, R. J., Balachandar, L. & Sureshkumar, R. 2008 Effects of polymer stresses on eddy structures in drag-reduced turbulent channel flow. Phys. Fluids 100, 134504.Google Scholar
Kim, K., Li, C.-F., Sureshkumar, R., Balachandar, L. & Adrian, R. J. 2007 Effects of polymer stresses on eddy structures in drag-reduced turbulent channel flow. J. Fluid Mech. 584, 281–299.CrossRefGoogle Scholar
Kravchenko, A. G., Choi, H. & Moin, P. 1993 On the relation of near-wall streamwise vortices to wall skin friction in turbulent boundary layers. Phys. Fluids A 5, 3307–3309.CrossRefGoogle Scholar
Lumley, J. L. 1969 Drag reduction by additives. Annu. Rev. Fluid Mech. 11, 367–384.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
Martins, R. S., Pereira, A. S., Mompean, G., Thais, L. & Thompson, R. L. 2016 An objective perspective for classic flow classification criteria. C. R. Méc. 344, 52–59.CrossRefGoogle Scholar
Merrill, E. W. & Horn, A. F. 1984 Scission of macromolecules in dilute solution: extensional and turbulent flows. Polym. Commun. 25, 144–146.Google 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
Moussa, T. & Tiu, C. 1994 Factors affecting polymer degradation in turbulent pipe flow. Chem. Engng Sci. 49, 1681–1692.CrossRefGoogle Scholar
Mysels, K. J.1949 Flow of thickened fluids. U.S. Patent 2 Dec. 27 492, 173.Google Scholar
Orlandi, P. 1996 A tentative approach to the direct simulation of drag reduction by polymers. J. Non-Newtonian Fluid Mech. 60, 277–301.CrossRefGoogle Scholar
Paterson, R. W. & Abernathy, F. H. 1970 Turbulent flow drag reduction and degradation with dilute polymer solutions. J. Fluid Mech. 43, 689–710.CrossRefGoogle Scholar
Pereira, A. S., Andrade, R. M. & Soares, E. J. 2013 Drag reduction induced by flexible and rigid molecules in a turbulent flow into a rotating cylindrical double gap device: comparison between poly (ethylene oxide), polyacrylamide, and xanthan gum. J. Non-Newtonian Fluid Mech. 202, 72–87.CrossRefGoogle Scholar
Pereira, A. S., Mompean, G., Thais, L. & Soares, E. J. 2017 Transient aspects of drag reducing plane couette flows. J. Non-Newtonian Fluid Mech. 241, 60–69.CrossRefGoogle Scholar
Pereira, A. S. & Soares, E. J. 2012 Polymer degradation of dilute solutions in turbulent drag reducing flows in a cylindrical double gap rheometer device. J. Non-Newtonian Fluid Mech. 179, 9–22.CrossRefGoogle Scholar
Peterlin, A. 1961 Streaming birefringence of soft linear macromolecules with finite chain length. Polymer 2, 257–291.CrossRefGoogle Scholar
Pinho, F. T. & Whitelaw, J. H. 1990 Flow of non-Newtonian fluids in a pipe. J. Non-Newtonian Fluid Mech. 34, 129–144.CrossRefGoogle Scholar
Ptasinski, P. K., Nieuwstadt, F. T., Van den Brule, B. H. A. A. & Hulsen, M. A. 2001 Experiments in turbulent pipe flow with polymer additives at maximum drag reduction. Turbul. Combust. 66, 159–182.CrossRefGoogle Scholar
Ryskin, G. 1987 Turbulent drag reduction by polymers: a quantitative theory. Phys. Rev. Lett. 59, 2059–2062.CrossRefGoogle ScholarPubMed
Sellin, R. H. J., Hoyt, J. W., Poliert, J. & Scrivener, O. 1982 The effect of drag reducing additives on fluid flows and their industrial applications part II: present applications and future proposals. J. Hydraul Res. 20, 235–292.CrossRefGoogle Scholar
Seyer, F. A. & Metzner, A. B. 1969 Turbulence phenomena in drag reducing systems. AIChE J. 15, 426–434.CrossRefGoogle Scholar
Soares, E. J., Sandoval, G. A. B., Silveira, L., Pereira, A. S., Trevelin, R. & Thomaz, F. 2015 Loss of efficiency of polymeric drag reducers induced by high Reynolds number flows in tubes with imposed pressure. Phys. Fluids 27, 125105.CrossRefGoogle Scholar
Sureshkumar, R. & Beris, A. N. 1995 Effect of artificial stress diffusivity on the stability of numerical calculations and the dynamics of time-dependent viscoelastic flows. J. Non-Newtonian Fluid Mech. 60, 53–80.CrossRefGoogle Scholar
Sureshkumar, R., Beris, A. N. & Handler, R. A. 1997 Direct numerical simulation of the turbulent channel flow of a polymer solution. Phys. Fluids 9, 743–755.CrossRefGoogle Scholar
Tabor, M. & de Gennes, P. G. 1986 A cascade theory of drag reduction. Europhys. Lett. 2, 519–522.CrossRefGoogle Scholar
Terrapon, V. E., Dubief, Y., Moin, P., Shaqfeh, E. S. G. & Lele, S. K. 2004 Simulated polymer stretch in a turbulent flow using brownian dynamics. J. Fluid Mech. 504, 61–71.CrossRefGoogle Scholar
Thais, L., Gatski, T. B. & Mompean, G. 2012 Some dynamical features of the turbulent flow of a viscoelastic fluid for reduced drag. J. Turbul. 13, 1–26.CrossRefGoogle Scholar
Thais, L., Gatski, T. B. & Mompean, G. 2013 Analysis of polymer drag reduction mechanisms from energy budgets. Intl J. Heat Fluid Flow 43, 52–61.CrossRefGoogle Scholar
Thais, L., Tejada-Martinez, A., Gatski, T. B. & Mompean, G. 2011 A massively parallel hybrid scheme for direct numerical simulation of turbulent viscoelastic channel flow. Comput. Fluids 43, 134–142.CrossRefGoogle Scholar
Toms, B. A. 1948 Some observations on the flow of linear polymer solutions through straight tubes at large Reynolds numbers. In Proceedings of the International Congress of Rheology, Holland, North-Holland, Amsterdam, Section II, pp. 135–141. North-Holland.Google Scholar
den Toonder, J. M. J., Nieuwstadt, F. T. M. & Kuiken, G. D. C. 1995 The role of elongational viscosity in the mechanism of drag reduction by polymer additives. Appl. Sci. Res. 54, 95–123.CrossRefGoogle Scholar
Virk, P. S. 1975 Drag reduction fundamentals. AIChE J. 21, 625–656.CrossRefGoogle Scholar
Virk, P. S., Mickley, H. S. & Smith, K. A. 1967 The Toms phenomenon: turbulent pipe flow of dilute polymer solutions. J. Fluid Mech. 22, 22–30.Google Scholar
Virk, P. S., Mickley, H. S. & Smith, K. A. 1970 The ultimate asymptote and mean flow structure in Toms’ phenomenon. Trans. ASME J. Appl. Mech. 37, 488–493.CrossRefGoogle Scholar
Warholic, M. D., Massah, H. & Hanratty, T. J. 1999 Influence of drag-reducing polymers on turbulence: effects of Reynolds number, concentration and mixing. Exp. Fluids 27, 461–472.CrossRefGoogle Scholar
Wei, T. & Willmarth, W. W. 1992 Modifying turbulent structure with drag-reducing polymer additives in turbulent channel flows. J. Fluid Mech. 245, 619–641.CrossRefGoogle Scholar
White, C. M., Dubief, Y. & Klewicki, J. 2012 Re-examining the logarithmic dependence of the mean velocity distribution in polymer drag reduced wall-bounded flow. Phys. Fluids 24, 021701.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
White, C. M., Somandepalli, V. S. R. & Mungal, M. G. 2004 The turbulence structure of drag-reduced boundary layer flow. Exp. Fluids 36, 62–69.CrossRefGoogle Scholar