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Events of high polymer activity in drag reducing flows. (English) Zbl 1200.76108

Summary: The mechanism of drag reduction in turbulent flows due to polymers has been investigated with help of a direct numerical simulation. In particular, we consider the interaction between turbulent velocity fluctuations and polymers in terms of elastic energy that can be stored in the polymer. To this end all the terms of the elastic energy budget have been computed. The most interesting term is the production of elastic energy due to turbulent fluctuations, because it describes the interaction between polymers and turbulence. Although this term appears to be small in the average, it turns out that it can reach very large values instantaneously and intermittently, and the energy transfer from polymer to turbulence is located in very well defined areas inside the channel. This implies that locally there is a strong interaction between the polymer and the turbulent flow structure, and this strong interaction is mostly seen in areas of high velocity fluctuations.

MSC:

76F70 Control of turbulent flows
76A05 Non-Newtonian fluids
76M20 Finite difference methods applied to problems in fluid mechanics

References:

[1] Toms, B.A.: Some observations of the flow of linear polymer solutions though straight tubes at large Reynolds numbers. In: Proceedings of the 1st International Congress on Rheology, pp. 135–141. North Holland, Amsterdam (1949)
[2] Lumley, J.L.: Drag reduction by polymer additives. Annu. Rev. Fluid Mech. 1, 367–384 (1969) · doi:10.1146/annurev.fl.01.010169.002055
[3] De Gennes, P.G.: Introduction to Polymer Dynamics. Cambridge University Press, Camridge (1990)
[4] Den Toonder, J.M.F., Hulsen, M.A., Kuiken, G.D.C., Nieuwstadt, F.T.M.: Drag reduction by polymer additives in a turbulent pipe flow: numerical and laboratory experiments. J. Fluid Mech. 337, 193–231 (1997) · doi:10.1017/S0022112097004850
[5] Orlandi, P.: A tentative approach to direct numerical simulation of drag reduction by polymers. J. Non-Newton. Fluid Mech. 60, 277–301 (1995) · doi:10.1016/0377-0257(95)01388-7
[6] Massah H., Kontomaris, K., Schowalter, W.R., Hanratty, T.J.: The configurations of a FENE bead-spring chain in transient rheological flows and turbulent flow. Phys. Fluids 5, 881–889 (1993) · doi:10.1063/1.858634
[7] Dimitropoulos, D.D., Sureshkumar, R., Beris, A.N.: Direct numerical simulation of viscoelastic turbulent flow exhibiting drag reduction: effect of the variation of rheological properties. J. Non-Newton. Fluid Mech. 79, 433–468 (1998) · Zbl 0960.76057 · doi:10.1016/S0377-0257(98)00115-3
[8] Ptasinski, P.K., Boersma, B.J., Nieuwstadt, F.T.M., Hulsen, M.A., van den Brule, B.H.A.A., Hunt, J.C.R.: Turbulent channel flow near maximum drag reduction: simulations, experiments and mechanisms. J. Fluid Mech. 490, 251–291 (2003) · Zbl 1063.76580 · doi:10.1017/S0022112003005305
[9] Bird, R.B., Curtiss, C.F., Armstrong, R.C., Hassager, O.: Dynamics of Polymer Liquids, vol. 2, 2nd edn. Wiley, New York (1987)
[10] Bird, R.B., Dotson, P.J., Johnson, N.L.: Polymer solution rheology based on a finitely extensible bead-spring chain model. J. Polym. Sci., B, Polym. Lett. 7, 213–235 (1980) · Zbl 0432.76012
[11] Jimenez, J., Moin, P.: The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213–240 (1991) · Zbl 0721.76040 · doi:10.1017/S0022112091002033
[12] Sureshkumar, R., Beris, A.N., Handler, R.A.: Direct numerical simulation of turbulent channel flow of polymer solution. Phys. Fluids 9, 743–755 (1997) · doi:10.1063/1.869229
[13] Kim, J., Moin, P., Moser, R.: Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166 (1987) · Zbl 0616.76071 · doi:10.1017/S0022112087000892
[14] Gyr, A., Bewersdorff, H.-W.: Drag Reduction of Turbulent Flows by Additives. Kluwer, Dordrecht (1995) · Zbl 0973.76616
[15] Dubief, Y., White, C.M., Terrapon, V., Shaqfeh, E.S.G., Moin, P., Lele, S.K.: On the coherent drag-reducing and turbulence enhancing behaviour of polymer in wall flows. J. Fluid Mech. 514, 271–280 (2004) · Zbl 1067.76052 · doi:10.1017/S0022112004000291
[16] Massah, H., Hanratty, T.: Added stresses because of the precence of FENE-P bead-spring chains in a random velocity field. J. Fluid Mech. 337, 67–101 (1997) · Zbl 0900.76026 · doi:10.1017/S0022112097004916
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