THE EFECT OF POLYMERS ON THE DYNAMICS OF TURBULENCE IN A DRAG REDUCED FLOW

Abstract

An experimental investigation of a polymer drag reduced flow using state-of-the-art laser-Doppler anemometry in a refractive index-matched pipe flow facility is reported. The measured turbulent stresses deep in the viscous sublayer are analyzed using the tools of invariant theory. It is shown that with higher polymer concentration the anisotropy of the Reynolds stresses increases. This trend is consistent with the trends extracted from DNS data of non-Newtonian fluids yielding different amounts of drag reduction. The interaction between polymer and turbulence is studied by considering local stretching of the molecular structure of a polymer by small-scale turbulent motions in the region very close to the wall. The stretching process is assumed to re-structure turbulence at small scales by forcing these to satisfy local axisymmetry with invariance under rotation about the axis aligned with the main flow. It is shown analytically that kinematic constraints imposed by local axisymmetry force turbulence near the wall to tend towards the one-component state and when turbulence reaches this limiting state it must be entirely suppressed across the viscous sublayer. Based on this consideration it is suggested that turbulent drag reduction by high polymers resembles the reverse transition process from turbulent to laminar. Theoretical considerations based on the elastic behavior of a polymer and spatial intermittency of turbulence at small scales enabled quantitative estimates to be made for the relaxation time of a polymer and its concentration that ensure maximum drag reduction in turbulent pipe flows, and it is shown that predictions based on these are in very good agreement with available experimental data.

Keywords

Dates

  • Submission Date2004-12-01
  • Revision Date2005-01-04
  • Acceptance Date2005-04-06

References

  1. Metzner, A.B. and Park, M.G. 1964 Turbulent flow characteristics of viscoelastic fluids. J. Fluid Mech. 20, 291-303.
  2. Lumley, J.L. 1969 Drag reduction by additives. Annu. Rev. Fluid Mech. 1, 367-384.
  3. Lumley, J.L. 1973 Drag reduction in turbulent flow by polymer additives. J. Polymer Sci. Macrom. Rev. 7, 363-290.
  4. Virk, P.S. 1975 Drag reduction fundamentals. AIChE J. 21, 625-656.
  5. Berman, N.S. 1978 Drag reduction by polymers. Annu. Rev. Fluid Mech. 10, 47-64.
  6. Tabor, M. and Gennes, P.G. de 1986 A cascade theory of drag reduction. Europhys. Lett. 2, 519-522.
  7. Ryskin, G. 1987 Turbulent drag reduction by polymers: a quantitative theory. Phys. Rev. Lett. 59, 2059-2062.
  8. Thirumalai, D. and Bhattacharjee, J.K. 1996 Polymer-induced drag reduction in turbulent flows. Phys. Rev. E 53, 546-551.
  9. Sreenivasan, K.R. and 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.
  10. Rudd, M.J. 1972 Velocity measurements with a laser-Doppler meter on the turbulent flow of a dilute polymer solution. J. Fluid Mech. 51, 673-685.
  11. Logan, S.E. 1972 Laser velocimeter measurements of Reynolds stress in dilute polymer solutions. AIAA J. 10, 962-964.
  12. Reischman, M.A. and Tiederman, W.G. 1975 Laser-Doppler anemometer measurements in drag reduction g channel flow. J. Fluid Mech. 70, 369-392.
  13. Luchik, T.S. and Tiederman, W.G. 1988 Turbulent structure in low-concentration drag-reducing channel flow. J. Fluid Mech. 198, 241-263.
  14. Walker, D.T. and Tiederman, W.G. 1990 Turbulent structure in a channel flow with polymer injection at the wall. J. Fluid Mech. 204, 377-403.
  15. Willmarth, W.W., Wei, T. and Lee, O. 1987 Laser anemometer measurements of Reynolds stress in a turbulent channel flow with drag reducing polymer additives. Phys. Fluids 30, 933-935.
  16. Wei, T. and Willmarth, W.W. Modifying turbulent structure with drag-reducing polymer additives in turbulent channel flows. J. Fluid Mech. 245, 619-641.
  17. Warholic, M.D., Massah, H. and Hanratty, T.J. 1999 Influence of drag-reducing polymers on turbulence: effects of Reynolds number, concentration and mixing. Exp. Fluids 27, 461-472.
  18. Toonder, J.M.J. den, Hulsen, M.A., Kuiken, G.D.C. and Nieuwstadt, F. 1997 Drag reduction by polymer additives in turbulent pipe flow: numerical and laboratory experiments. J. Fluid Mech. 337, 193-231.
  19. Sureshkumar, R., Beris, A.N. and Handler, R.A. 1997 Direct numerical simulations of turbulent channel flow of a polymer solution. Phys. Fluids 9, 743-755.
  20. Dimitropulos, C.R., Suresikumar, R. and Berais, A.N. 1998 Direct numerical simulation of viscoelastic turbulent channel exhibiting drag reduction: effect of the variation of rheological parameters. J. Non-Newtonian Fluid Mech. 79, 443-468.
  21. Sibilla, S. and Baron, A. 2002 Polymer stress statistics in the near-wall turbulent flow of a drag-reducing solution. Phys. Fluid 14, 1123-1136.
  22. Angelis, E.D., Casciola, C.M. and Piva, R. 2002 DNS of wall turbulence: dilute polymers and self-sustaining mechanisms. Computers & Fluids 31, 495-507.
  23. Dubief, Y. 2002 Numerical simulation of turbulent polymer solutions. Ann. Res. Briefs, Center for Turbulence Research, Stanford University, 377-388.
  24. Dubief, Y., White, C., Terrapon, V., Shaqfeh, E., Moin, P., Lele, S. 2004 On the coherent drag-reducing and turbulence enhancing behaviour of polymers in wall flows. J. Fluid Mech.,514 , 271- 280.
  25. Jovanovic, J. 2004 The Statistical Dynamics of Turbulence, Springer-Verlag, Berlin-Heidelberg.
  26. Jovanovic, J. and Hillerbrand, R. 2003 On peculiar properties of the velocity fluctuations in wall-bounded flows. J. Fluid Mech., submitted.
  27. Durst, F., Jovanovic, J. and Sender, J. 1995 LDA measurements in the near-wall region of a turbulent pipe flow. J. Fluid Mech. 295, 305-335.
  28. Mansour, N.N., Moser, R.D. and Kim, J. 1998 Fully developed turbulent channel flow simulations. In AGARD Advisory Report 345, 119-121.
  29. Koskinen, K.K. 2004 On investigating turbulent reactive flows: case studies of combustion and drag reduction by polymer additives. Ongoing Ph.D. thesis, Tampere University of Technology, Tampere, Finland.
  30. Lumley, J.L. and Newman, G. 1977 The return to isotropy of homogeneous turbulence. J. Fluid Mech. 82, 161-178.
  31. Lumley, J.L. 1978 Computational modeling of turbulent flows. Adv. Appl. Mech. 18, 123-176.
  32. Jovanovic, J., Hillerbrand, R. and Pashtrapanska, M. 2001 Mit statistischer DNS-Datenanalyse der Enstehung von Turbulenz auf der Spur. KONWIHR Quartl 31, 6-8.
  33. Kim, J., Moin, P. and Moser, R. 1987 Turbulence statistics in a fully developed channel flow at low Reynolds numbers. J. Fluid Mech. 177, 133-166.
  34. Jovanovic, J., Ye, Q.-Y. and Durst, F. 1995 Statistical interpretation of the turbulent dissipation rate in wall-bounded flows. J. Fluid Mech. 293, 321-347.
  35. Monin, A.S. and Yaglom, A.M. 1987 The Statistical Fluid Mechanics. Vol. 1, MIT Press, Cambridge, Massachusetts.
  36. Durst, F., Fischer, M., Jovanovic, J. and Kikura, H. 1998 Methods to set up and investigate low Reynolds number, fully developed turbulent plane channel flows. J. Fluids Eng. 120, 496-503.
  37. Fischer, M., Jovanovic, J. and Durst, F. 2001 Reynolds number effects in the near-wall region of turbulent channel flows. Phys. Fluids 13, 1755-1767.
  38. Jovanovic, J. and Pashtrapanska, M. 2003 On the criterion for the determination transition onset and breakdown to turbulence in wall-bounded flows. J. Fluids Eng. submitted.
  39. Durst, F., Hass, R., Interhal, W. and Keck, T. 1982 Polymerwirkung in Stroömungen-Mechanismen und praktische Anwendungen. Chem.-Ing.-Tech. 54, 213-221.
  40. Kolmogorov, A.N. 1941 Local structure of turbulence in an incompressible fluid at very high Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 299-303.
  41. Sreenivasan, K.R. 1984 On the scaling of the turbulence energy dissipation rate. Phys. Fluids 27, 1048-1051.
  42. Hinze, J.O. 1975 Turbulence, 2nd edn., McGraw Hill, New York.
  43. Rotta, J. 1951 Statistische Theorie nichthomogener Turbulenz. Z. Physik 129, 547-572.
  44. Batchelor, G. K. and Townsend, A.A. 1947 Decay of vorticity in isotropic turbulence. Proc. Roy. Soc. A 190, 534.
  45. Kuo, A.Y. and Corrsin, S. 1971 Experiments on internal intermittency and fine-structure distribution functions in fully turbulent fluid. J. Fluid Mech. 50, 285-319.
  46. Tilli, M., Maaranen, J., Timonen, J., Kataja, M. and Korppi-Tommola, J. 2003 Effect mechanisms of DR molecules. Technical Report, University of Jyvä, Finland.
  47. George, W.K. and Hussein, H.J. 1991 Locally axisymmetric turbulence. J. Fluid Mech. 233, 1-23.
  48. Schenck, T. and Jovanovic, J. 2002 Measurements of the instantaneous velocity gradients in plane and axisymmetric wake flows. J. Fluids Eng. 124, 143-153.
  49. Antonia, R.A., Teitel, M., Kim, J. and Browne, L.W.B. 1992 Low-Reynolds-number effects in a fully developed turbulent channel flow. J. Fluid Mech. 236, 579-605.
  50. Chou, P.Y. 1945 On the velocity correlation and the solution of the equation of turbulent fluctuation. Quart. Appl. Math. 3, 38-54.
  51. Kolovandin, B.A. and Vatutin, I.A. 1969 On statistical theory of non-uniform turbulence. Int. Seminar on Heat and Mass Transfer, Herceg-Novi, Yugoslavia.
  52. Spalart, P.R. 1986 Numerical study of sink-flow boundary layers. J. Fluid Mech. 172, 307-328.
  53. Spalart, P.R. 1988 Direct simulation of a turbulent boundary layer up to Re = 1410. J. Fluid Mech. 187, 61-98.
  54. Moser, R.D., Kim, J. and Mansour, N.N. 1999 Direct numerical simulation of turbulent channel flow up to Re =590. Phys. Fluids 11, 943-945.
  55. Gilbert, N. and Kleiser, L. 1991 Turbulence model testing with the aid of direct numerical simulation results. Proc. Eighth Symp. on Turbulent Shear Flows, Munich, 26.1.1-26.1.6.
  56. Eggels, J.G.M., Unger, F., Weiss, M.H., Westerweel, J., Adrian, R.J., Friedrich, R. and Nieuwstadt, F.T.M. 1994 Fully developed turbulent pipe flow: a comparison between direct numerical simulation and experiment. J. Fluid Mech. 268, 175-209.
  57. Horiuti, K. 1992 Establishment of the direct numerical simulation data base of turbulent transport phenomena. Ministry of Education, Science and Culture Japan, Co-operative Research No. 012302043, http://www.thtlab.t.u-tokyo.ac.jp/.
  58. Kuroda, A., Kasagi, N. and Hirata, M. 1993 Direct numerical simulation of the turbulent plane Couette-Poiseulle flows: effect of mean shear on the near wall turbulence structures. Proc. Ninth Symp. on Turbulent Shear Flows, Kyoto, 8.4.1-8.4.6, http://www.thtlab.t.u-tokyo.ac.jp/.
  59. Laufer, J. 1953 The structure of turbulence in fully developed pipe flow. NACA Tech. Note 2954.
  60. Koskinen, K.K. 2004 On investigating turbulent reactive flows: case studies of combustion and drag reduction by polymer additives. Ongoing Ph.D. thesis, Tampere University of Technology, Tampere, Finland.
Volume 9, Issue 1, Pages13 -41