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Analysis of coherent structures in drag-reducing polymer solution flow based on proper orthogonal decomposition

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Abstract

Direct numerical simulation (DNS) of forcing homogeneous isotropic turbulence with polymers was performed. In order to understand the polymers effect on turbulent coherent structures, proper orthogonal decomposition was performed to identify coherent structures based on DNS data, so as to analyze the remarkable difference due to the addition of polymers. The results showed that the numbers for eigenmodes required for capturing coherent structures were 32 and 24 for the Newtonian fluid and polymer solution flows, respectively, which means the decrease of the complexity in polymer solution flow. Through the POD energy spectrum, it was found that the turbulent kinetic energy is distributed onto a large number of eigenmodes whether in the Newtonian fluid flow or polymer solution flow, suggesting that polymer solution flow is still turbulent in one aspect. Besides, the POD eigenmodes were investigated, which found that the small-scale structures are inhibited in polymer solution flow.

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References

  1. Toms B A. Some observation on the flow of linear polymer solutions through straight tubes at large Reynolds number. In: Proceedings of the first International Congress of Rheology, North Holland, 1949. 135–148

  2. Lumley J L. Drag reduction in turbulent flow by polymer additives. J Polymer Sci Macrom Rew, 1973, 7: 263–290

    Article  Google Scholar 

  3. Ptasinski P K, Boersma B J, Nieuwstadt F T M, et al. Turbulent channel flow near maximum drag reduction: simulations, experiments and mechanisms. J Fluid Mech, 2003, 490: 251–291

    Article  ADS  MATH  Google Scholar 

  4. Walker D T, Tiederman W G. Turbulent structure in a channel flow with polymer injection at the wall. J Fluid Mech, 1990, 218: 377–403

    Article  ADS  Google Scholar 

  5. Den Toonder J M J, Hulsen M A, Kuiken G D C, et al. Drag reduction by polymer additives in a turbulent pipe flow: Numerical and laboratory experiments. J Fluid Mech, 1997, 337: 193–231

    Article  ADS  Google Scholar 

  6. Li F C, Kawaguchi Y, Segawa T, et al. Reynolds-number dependence of turbulence structures in a drag-reducing surfactant solution channel flow investigated by PIV. Phys Fluids, 2005, 17: 075104

    Article  ADS  Google Scholar 

  7. Sureshkumar R, Beris A N, Handler A H. Direct numerical simulation of turbulent channel flow of a polymer solution. Phys Fluids, 1997, 9: 743–755

    Article  ADS  Google Scholar 

  8. Yu B, Kawaguchi Y. Direct numerical simulation of viscoelastic drag-reducing flow: A faithful finite difference method. J Non-Newtonian Fluid Mech, 2004, 116: 431–466

    Article  MATH  Google Scholar 

  9. van Doorn E, White C M, Sreenivasan K R. The decay of grid turbulence in polymer and surfactant solutions. Phys Fluids, 1999, 8: 2387–2393

    Article  Google Scholar 

  10. De Angelis E, Casciola C M, Benzi R, et al. Homogeneous isotropic turbulence in dilute polymers. J Fluid Mech, 2005, 531: 1–10

    Article  ADS  MATH  Google Scholar 

  11. Berti S, Bistagnino A, Boffetta G, et al. Small-scale statistics of viscoelastic turbulence. Europhys Letts, 2006, 76: 63–69

    Article  ADS  Google Scholar 

  12. Perlekar P, Mitra D, Pandit R. Manifestations of drag reduction by polymer additives in decaying, homogenous, isotropic turbulence. Phys Rev Lett, 2006, 97: 264501

    Article  ADS  Google Scholar 

  13. Cai W H, Li F C, Zhang H N. DNS study of decaying homogeneous isotropic turbulence with polymer additives. J Fluid Mech, 2010, 665: 334–356

    Article  ADS  MATH  Google Scholar 

  14. Liberzon A, Guala M, Luthi B, et al. Turbulence in dilute polymer solutions. Phys Fluids, 2005, 17: 031707

    Article  ADS  Google Scholar 

  15. Ouellette N T, Xu H T, Bodenschatz E. Bulk turbulence in dilute polymer solutions. J Fluid Mech, 2009, 629: 375–385

    Article  ADS  MATH  Google Scholar 

  16. Kim K, Li C F, Sureshkumar R, et al. Effects of polymer stresses on eddy structures in drag-reduced turbulent channel flow. J Fluid Mech, 2007, 584: 281–299

    Article  ADS  MATH  Google Scholar 

  17. Kim K, Adrian R J, Balachandar S, et al. Dynamics of hairpin vortices and polymer-induced turbulent drag reduction. Phys Rev Letts, 2008, 100: 134504

    Article  ADS  Google Scholar 

  18. Sibilla S, Beretta C P. Near-wall coherent structures in the turbulent channel flow of a dilute polymer solution. Fluid Dyn Res, 2005, 37: 183–202

    Article  ADS  MATH  Google Scholar 

  19. Yu Z S, Lin J Z, Fan X J. Numerical simulation of interactions between rigid rod-like polymers and coherent structures in a mixing layer. J Non-Newtonian Fluid Mech, 1999, 83: 1–18

    Article  MATH  Google Scholar 

  20. Shao X M, Lin J Z, Yu Z S. Research on coherent structures in a mixing layer of the FENE-P polymer solution. Appl Math Mech, 2001, 22(3): 304–311

    Article  MATH  Google Scholar 

  21. Vaithianathan T, Robert A, Brasseur J G, et al. An improved algorithm for simulating three-dimensional, viscoelastic turbulence. J Non-Newtonian Fluid Mech, 2006, 140: 3–22

    Article  MATH  Google Scholar 

  22. Canuto C, Hussaini M Y, Quarteroni A, et al. Spectral Methods in Fluid Dynamics. New York: Spring-Verlag, 1988

    MATH  Google Scholar 

  23. Chen S, Doolen G D, Kraichnan R H. On statistical correlations between velocity increments and locally averaged dissipation in homogeneous turbulence. Phys Fluids, 1993, 5: 458–463

    Article  ADS  Google Scholar 

  24. Li F C, Cai W H, Zhang H N. Influence of polymer additives on turbulent energy cascading in forced homogeneous isotropic turbulence studied by DNS. J Non-Newtonian Fluid Mech, 2011, in Submitted

  25. Samanta G, Oxberry G M, Beris A N, et al. Time-evolution K-L analysis of coherent structures based on DNS of turbulent Newtonian and viscoelastic flows. J Turbul, 2008, 41: 1–25

    MathSciNet  Google Scholar 

  26. Samanta G, Beris A N, Handler R A, et al. Velocity and conformation statistics based on reduced Karhunen-Loeve projection data from DNS of viscoelastic turbulent channel flow. J Non-Newtonian Fluid Mech, 2009, 160: 55–63

    Article  Google Scholar 

  27. Cai W H, Li F C, Zhang H N, et al. Study on the characteristics of turbulent drag-reducing channel flow by particle image velocimetry combining with proper orthogonal decomposition analysis. Phys Fluids, 2009, 21: 115103

    Article  ADS  Google Scholar 

  28. Lumley J L. The structure of inhomogeneous turbulent flows. Atmospheric Turbulence and Radio Wave Propagation. Yaglom A M, Tararsky V I, eds. Moscow: Nauka, 1967

    Google Scholar 

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Correspondence to WeiHua Cai or FengChen Li.

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Cai, W., Li, F., Zhang, H. et al. Analysis of coherent structures in drag-reducing polymer solution flow based on proper orthogonal decomposition. Sci. China Phys. Mech. Astron. 55, 854–860 (2012). https://doi.org/10.1007/s11433-012-4672-2

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