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Bulk turbulence in dilute polymer solutions

Published online by Cambridge University Press:  15 June 2009

NICHOLAS T. OUELLETTE ,
HAITAO XU  and
EBERHARD BODENSCHATZ
NICHOLAS T. OUELLETTE*
Affiliation:
Max Planck Institute for Dynamics and Self-Organization, D-37077 Göttingen, Germany Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY 14853, USA International Collaboration for Turbulence Research
HAITAO XU
Affiliation:
Max Planck Institute for Dynamics and Self-Organization, D-37077 Göttingen, Germany Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY 14853, USA International Collaboration for Turbulence Research
EBERHARD BODENSCHATZ
Affiliation:
Max Planck Institute for Dynamics and Self-Organization, D-37077 Göttingen, Germany Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY 14853, USA Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA Institute for Nonlinear Dynamics, Universität Göttingen, D-37073 Göttingen, Germany International Collaboration for Turbulence Research
*
†Present address: Department of Mechanical Engineering, Yale University, New Haven, CT 06520, USA. Email address for correspondence: nicholas.ouellette@yale.edu
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Abstract

By tracking small particles in the bulk of an intensely turbulent laboratory flow, we study the effect of long-chain polymers on the Eulerian structure functions. We find that the structure functions are modified over a wide range of length scales even for very small polymer concentrations. Their behaviour can be captured by defining a length scale that depends on the solvent viscosity, the polymer relaxation time and the Weissenberg number. This result is not captured by current models. Additionally, the effects we observe depend strongly on the concentration. While the dissipation-range statistics change smoothly as a function of polymer concentration, we find that the inertial-range values of the structure functions are modified only when the concentration exceeds a threshold of approximately 5 parts per million (p.p.m.) by weight for the 18 × 106 atomic mass unit (a.m.u.) molecular weight polyacrylamide used in the experiment.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 629 , 25 June 2009 , pp. 375 - 385
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Arratia, P. E., Voth, G. A. & Gollub, J. P. 2005 Stretching and mixing of non-Newtonian fluids in time-periodic flows. Phys. Fluids 17, 053102.CrossRefGoogle Scholar
Balkovsky, E., Fouxon, A. & Lebedev, V. 2001 Turublence of polymer solutions. Phys. Rev. E 64, 056301.CrossRefGoogle ScholarPubMed
Bonn, D., Amarouchène, Y., Wagner, C., Douady, S. & Cadot, O. 2005 Turbulent drag reduction by polymers. J. Phys. 17, S1195–S1202.Google Scholar
Bonn, D., Couder, Y., van Dam, P. H. J. & Douady, S. 1993 From small scales to large scales in three-dimensional turbulence: the effect of diluted polymers. Phys. Rev. E 47, R28–R31.CrossRefGoogle ScholarPubMed
Bourgoin, M., Ouellette, N. T., Xu, H., Berg, J. & Bodenschatz, E. 2006 The role of pair dispersion in turbulent flow. Science 311, 835–838.CrossRefGoogle ScholarPubMed
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
Casciola, C. M. & De Angelis, E. 2007 Energy transfer in turbulent polymer solutions. J. Fluid Mech. 581, 419–436.CrossRefGoogle Scholar
Crawford, A. M. 2004 Particle tracking measurements in fully developed turbulence: water and dilute polymer solutions. PhD thesis, Cornell University.Google Scholar
Crawford, A. M., La Porta, A., Mordant, N. & Bodenschatz, E. 2002 Effect of dilute polymer solutions on dissipation range quantities in bulk turbulence. In Advances in Turbulence IX (ed. Castro, I. P., Hancock, P. E. & Thomas, T. G.), Kluwer Academic Publisher, p. 306.Google Scholar
Crawford, A. M., Mordant, N., Xu, H. & Bodenschatz, E. 2008 Fluid acceleration in the bulk of turbulent dilute polymer solutions. New J. Phys. 10, 123015.CrossRefGoogle Scholar
Davoudi, J. & Schumacher, J. 2006 Stretching of polymers around the Kolmogorov scale in a turbulent shear flow. Phys. Fluids 18, 025103.CrossRefGoogle Scholar
De Angelis, E., Casciola, C. M., Benzi, R. & Piva, R. 2005 Homogeneous isotropic turbulence in dilute polymers. J. Fluid Mech. 531, 1–10.CrossRefGoogle Scholar
van Doorn, E., White, C. M. & Sreenivasan, K. R. 1999 The decay of grid turbulence in polymer and surfactant solutions. Phys. Fluids 11, 2387–2393.CrossRefGoogle Scholar
Eyink, G. L. 2003 Local 4/5-law and energy dissipation anomaly in turbulence. Nonlinearity 16, 137–145.CrossRefGoogle Scholar
Fouxon, A. & Lebedev, V. 2003 Spectra of turbulence in dilute polymer solutions. Phys. Fluids 15, 2060–2072.CrossRefGoogle Scholar
Frisch, U. 1995 Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press.CrossRefGoogle Scholar
Groisman, A. & Steinberg, V. 2000 Elastic turbulence in polymer solution flow. Nature 405, 53–55.CrossRefGoogle ScholarPubMed
Groisman, A. & Steinberg, V. 2001 Efficient mixing at low Reynolds number using polymer additives. Nature 410, 905–908.CrossRefGoogle ScholarPubMed
Groisman, A. & Steinberg, V. 2004 Elastic turbulence in curvilinear flows of polymer solutions. New J. Phys. 6, 29.CrossRefGoogle Scholar
Kolmogorov, A. N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 301–305.Google Scholar
La Porta, A., Voth, G. A., Crawford, A. M., Alexander, J. & Bodenschatz, E. 2001 Fluid particle accelerations in fully developed turbulence. Nature 409, 1017–1019.CrossRefGoogle ScholarPubMed
Liberzon, A., Guala, M., Kinzelbach, W. & Tsinober, A. 2006 On turbulent kinetic energy production and dissipation in dilute polymer solutions. Phys. Fluids 18, 125101.CrossRefGoogle Scholar
Liberzon, A., Guala, M., Lüthi, B., Kinzelbach, W. & Tsinober, A. 2005 Turbulence in dilute polymer solutions. Phys. Fluids 17, 031707.CrossRefGoogle Scholar
Lumley, J. L. 1973 Drag reduction in turbulent flow by polymer additives. J. Polymer Sci. 7, 263–290.Google 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
McComb, W. D., Allan, J. & Greated, C. A. 1977 Effect of polymer additives on the small-scale structure of grid-generated turbulence. Phys. Fluids 20, 873–879.CrossRefGoogle Scholar
Ouellette, N. T., Xu, H. & Bodenschatz, E. 2006 a A quantitative study of three-dimensional Lagrangian particle tracking algorithms. Exp. Fluids 40, 301–313.CrossRefGoogle Scholar
Ouellette, N. T., Xu, H., Bourgoin, M. & Bodenschatz, E. 2006 b An experimental study of turbulent relative dispersion models. New J. Phys. 8, 109.CrossRefGoogle Scholar
Perlekar, P., Mitra, D. & Pandit, R. 2006 Manifestations of drag reduction by polymer additives in decaying, homogeneous, isotropic turbulence. Phys. Rev. Lett. 97, 264501.CrossRefGoogle ScholarPubMed
Ryskin, G. 1987 Turublent drag reduction by polymers: a quantitative theory. Phys. Rev. Lett. 59, 2059–2062.CrossRefGoogle ScholarPubMed
Sreenivasan, K. R. 1995 On the universality of the Kolmogorov constant. Phys. Fluids 7, 2778–2784.CrossRefGoogle Scholar
Sreenivasan, K. R. & White, C. M. 2000 The onset of drag reduction by dilute polymer additives, and the maximum drag reduction asymptote. J. Fluid Mech. 409, 149–164.CrossRefGoogle Scholar
Tabor, M. & de Gennes, P. G. 1986 A cascade theory of drag reduction. Europhys. Lett. 2, 519–522.CrossRefGoogle Scholar
Toms, B. A. 1948 Some observations on the flow of linear polymer solutions through straight tubes at large Reynolds numbers. Proceedings of the First International Congress on Rheology, North-Holland Publishing Co. 2, 135–141.Google Scholar
Tong, P., Goldburg, W. I. & Huang, J. S. 1992 Measured effects of polymer additives on turbulent-velocity fluctuations at various length scales. Phys. Rev. A 45, 7231–7241.CrossRefGoogle ScholarPubMed
Vaithianathan, T., Robert, A., Brasseur, J. G. & Collins, L. R. 2006 An improved algorithm for simulating three-dimensional viscoelastic turbulence. J. Non-Newton. Fluid Mech. 140, 3–22.CrossRefGoogle Scholar
Virk, P. S., Merill, E. W., Mickley, H. S., Smith, K. A. & Mollo-Christensen, E. L. 1967 The Toms phenomenon: turbulent pipe flow of dilute polymer solutions. J. Fluid Mech. 30, 305–328.CrossRefGoogle Scholar
Voth, G. A., La Porta, A., Crawford, A. M., Alexander, J. & Bodenschatz, E. 2002 Measurement of particle accelerations in fully developed turbulence. J. Fluid Mech. 469, 121–160.CrossRefGoogle Scholar