On the Extension of Polymer Molecules in Turbulent Viscoelastic Flows: Statistical and Tensor Investigation

  • Anselmo Soeiro PereiraEmail author
  • Ramon Silva Martins
  • Gilmar Mompean
  • Laurent Thais
  • Roney Leon Thompson
Conference paper
Part of the ERCOFTAC Series book series (ERCO, volume 23)


In the present work, direct numerical simulations of turbulent channel flow of a viscoelastic FENE-P fluid, at zero-shear friction Reynolds number equal to 180, are used to analyze the polymer extension mechanism. As a primary focus, the relative polymer stretch and the probability distribution function of the alignment between the conformation tensor and other relevant entities are investigated. In near-wall regions, polymers present a strong tendency to orient along the streamwise direction of the flow. Furthermore, the polymer extension seems to be strongly correlated to the alignment between both conformation tensor and the velocity fluctuations product tensor, \(\mathbf { {\tau }^{\prime } }\) (defined as \({{u^{\prime }}_i}{{u^{\prime }}_j}\)). Joint probability density functions show that large positive polymer work fluctuations, \({{E^{\prime }}_x}\), are closely related to the positive growth rate of the product of streamwise velocity fluctuations, \({\partial _{t} {u^{\prime }}^2_x}\). In contrast, small negative fluctuations of polymer work are observed in the regions of negative rate of \({u^{\prime }}^2_x\). However, in both cases, polymers are predominantly oriented along the principal direction of \(\mathbf { {\tau }^{\prime } }\), which indicates the relevance of this tensor for the polymer-turbulence interaction mechanism.


Direct Numerical Simulation Streamwise Direction Joint Probability Density Function Turbulent Channel Flow Wall Distance 
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The authors are grateful to Dr. Enrico Calzavarini and Dr. Stefano Berti from the Laboratoire de Mécanique de Lille of Université Lille Nord de France for their useful comments and suggestions. This work was granted access to the HPC resources of IDRIS under the allocation 2014-i20142b2277 made by GENCI. The authors would also like to express their acknowledgment and gratitude to the Brazilian Scholarship Program Science Without Borders, managed by CNPq (National Council for Scientific and Technological Development), for the partial financial support for this research.


  1. 1.
    F. Forrest, G.A. Grierson, Pap. Trade J. 92, 39 (1931)Google Scholar
  2. 2.
    B.A. Toms, Proceedings of the International Congress of Rheology, Section II (Holland, North-Holland, Amsterdam, 1948), pp. 135–141Google Scholar
  3. 3.
    K.J. Mysels, US Patent 2 492, 173, 27 December 1949Google Scholar
  4. 4.
    R.H.J. Sellin, J.W. Hoyt, J. Poliert, O. Scrivener, J. Hydraul. Res. 20, 235 (1982)CrossRefGoogle Scholar
  5. 5.
    P.S. Virk, H.S. Mickley, K.A. Smith, J. Fluid Mech. 22, 22 (1967)Google Scholar
  6. 6.
    C.M. White, M.G. Mungal, Annu. Rev. Fluid Mech. 40, 235 (2008)MathSciNetCrossRefGoogle Scholar
  7. 7.
    J.L. Lumley, Annu. Rev. Fluid Mech. 11, 367 (1969)CrossRefGoogle Scholar
  8. 8.
    F.A. Seyer, A.B. Metzner, AIChE J. 492, 426 (1949)Google Scholar
  9. 9.
    G. Ryskin, Phys. Rev. Lett. 59, 2059 (1987)CrossRefGoogle Scholar
  10. 10.
    M. Tabor, P.G. de Gennes, Europhys. Lett. 7, 519 (1986)CrossRefGoogle Scholar
  11. 11.
    V.S. L’vov, A. Pomyalov, I. Procaccia, V. Tiberkevich, Phys. Rev. Lett. 92, 244503 (2004)Google Scholar
  12. 12.
    E. De Angelis, C. Casciola, V.S. L’vov, A. Pomyalov, I. Procaccia, V. Tiberkevich, Phys. Rev. E 70, 055301 (2004)Google Scholar
  13. 13.
    R. Benzi, E.D. Angelis, V.S. L’vov, I. Procaccia, Phys. Rev. Lett. 95, 194502 (2005)Google Scholar
  14. 14.
    T. Min, J.Y. Yoo, H. Choi, D.D. Joseph, J. Fluid Mech. 486, 213 (2003)CrossRefzbMATHGoogle Scholar
  15. 15.
    V. Dallas, J.C. Vassilicos, G.F. Hewitt, Phys. Rev. E 82, 066303 (2010)CrossRefGoogle Scholar
  16. 16.
    Y. Dubief, C.M. White, V.E. Terrapon, E.S.G. Shaqfeh, P. Moin, S.K. Lele, J. Fluid Mech. 514, 271 (2004)CrossRefzbMATHGoogle Scholar
  17. 17.
    R. Sureshkumar, A.N. Beris, J. Non-Newton. Fluid Mech. 60, 53 (1995)CrossRefGoogle Scholar
  18. 18.
    K.D. Housiadas, A.N. Beris, Phys. Fluids 15(8), 2369 (2003)CrossRefGoogle Scholar
  19. 19.
    L. Thais, A. Tejada-Martinez, T.B. Gatski, G. Mompean, Comput. Fluids 43, 134 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    J.C.R. Hunt, A.A. Wray, P. Moin, in Proceedings of Summer Program. Center for Turbulence Research, Report CTR-S88 (1988) p. 193Google Scholar
  21. 21.
    K. Kim, C.F. Li, R. Sureshkumar, L. Balachandar, R.J. Adrian, J. Fluid Mech. 584, 281 (2007)CrossRefzbMATHGoogle Scholar
  22. 22.
    K. Kim, R.J. Adrian, L. Balachandar, R. Sureshkumar, Phys. Fluids 100, 134504 (2008)Google Scholar
  23. 23.
    M.D. Warholic, H. Massah, T.J. Hanratty, Exp. Fluids 27, 461 (1999)CrossRefGoogle Scholar
  24. 24.
    L. Thais, T.B. Gatski, G. Mompean, J. Turbul. 13, 1 (2012)MathSciNetCrossRefGoogle Scholar
  25. 25.
    C.D. Dimitropoulos, Y. Dubief, E.S.G. Shaqfeh, P. Moin, S.K. Lele, Phys. Fluids 17, 1 (2005)CrossRefGoogle Scholar
  26. 26.
    A.S. Pereira, E.J. Soares, J. Non-Newton. Fluid Mech. 179, 9 (2012)CrossRefGoogle Scholar
  27. 27.
    A.S. Pereira, R.M. Andrade, E.J. Soares, J. Non-Newton. Fluid Mech. 202, 72 (2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Anselmo Soeiro Pereira
    • 1
    Email author
  • Ramon Silva Martins
    • 1
  • Gilmar Mompean
    • 1
  • Laurent Thais
    • 1
  • Roney Leon Thompson
    • 2
  1. 1.Laboratoire de Mécanique de Lille (LML), CNRS, UMR 8107École Polytechnique Universitaire de Lille, Université Lille Nord de FranceVilleneuve D’ascqFrance
  2. 2.Laboratório de Mecânica Teórica Aplicada (LMTA), Department of Mechanical EngineeringUniversidade Federal FluminenseNiteróiBrazil

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