Influence of rheological parameters in all drag reduction regimes of turbulent channel flow with polymer additives

Abstract

The influence of rheological parameters on vortex dynamics and the extent of drag reduction (DR) were deciphered via extensively analyzing the hi-fidelity direct numerical simulation results of the turbulent channel flow with polymer solutions. It has been observed that in all drag reduction regimes from the onset of DR to maximum drag reduction (MDR) limit, the Deborah number is defined as the product of an effective Weissenberg number, and the root mean square streamwise vorticity fluctuation remains O(1) in the near wall region. The ratio of the average lifetime of axial vortices to the vortex rotating duration decreases with increasing DR, and MDR is achieved when these time scales become nearly equal. Based on these observations a simple framework is proposed adequately to describe the influence of polymer additives on the extent of DR from onset to MDR as well as the universality of the MDR in flow systems with polymer additives.

Keywords

drag reduction / dilute polymeric solutions / turbulent channel flows / FENE-P model

References

[1] LumleyJ. L.. Drag reduction by additives [J]. Annu Rev Fluid Mech, 1969, 1: 367-384

[2] LumleyJ. L.. Drag reduction in turbulent flow by polymer additives [J]. Journal of Polymer Science, 1973, 7: 263-290

[3] VirkP. S.. Drag reduction fundamentals [J]. AIChE Journal, 1975, 21: 625-656

[4] GRAHAM M D. Drag reduction in turbulent flow of polymer solutions[C]// Binding D M, Walters K eds. Rheology Reviews, British Society of Rheology, 2004: 143–170.

[5] KlineS. J., ReynoldsW. C., SchraubF. A., RunstadlerP. W.. The structure of turbulent boundary layers [J]. J Fluid Mech, 1967, 30: 741-773

[6] KimH. T., KlineS. J., ReynoldsW. C.. The production of turbulence near a smooth wall in a turbulent boundary layer [J]. J Fluid Mech, 1971, 50: 133-160

[7] KimJ., MoinP., MoserP.. Turbulence statistics in fully developed channel flow at low Reynolds numbers [J]. J Fluid Mech, 1987, 177: 133-166

[8] SeyerF. A., MetznerA. B.. Turbulence phenomena in drag reducing systems [J]. AIChE J, 1969, 15: 426-434

[9] DonohueG. L., TiedermanW. G., ReischmaM. M.. Flow visualization in the near-wall region in a drag reducing flow [J]. J Fluid Mech, 1972, 56: 559-575

[10] AchiaB. U., ThompsonD. W.. Structure of the turbulent boundary layer in drag reducing pipe flow [J]. J Fluid Mech, 1977, 81: 439-464

[11] TiedermanW. G., LuchikT. S., BogardD. G.. Wall-layer structure and drag reduction [J]. J Fluid Mech, 1985, 156: 419-437

[12] Den ToonderJ. M. J., HulsenM. A., KuikenG. D. C., NiuwstadtF. T. M.. Drag reduction by polymers in a turbulent pipe flow: Numerical and laboratory experiments [J]. J Fluid Mech, 1997, 337: 193-231

[13] WarholicM. D., MassahH., HanrattyT. J.. Influence of drag reducing polymers on turbulence: Effects of Reynolds number, concentration and mixing [J]. Exps Fluids, 1999, 27: 461-472

[14] PtasinskiP. K., BoersmaB. J., NiuwstadtF., HulsenM. A., Van Den BruleB., HuntJ.C.R.. Turbulent channel flow near maximum drag reduction: simulations, experiments and mechanisms [J]. J Fluid Mech, 2003, 490: 251-291

[15] SureshkumarR., BerisA. N., HandlerR. A.. Direct numerical simulation of turbulent channel flow of a polymer solution [J]. Phys Fluids, 1997, 9: 743-755

[16] De AngelisE., CasciolaC. M., PivaR.. DNS of wall turbulence: Dilute polymers and self-sustaining mechanisms [J]. Comp Fluids, 2002, 31: 495-507

[17] HousiadasK. D., BerisA. N.. Polymer-induced drag reduction: Effects of the variations in elasticity and inertia in turbulent viscoelastic channel flow [J]. Phys Fluids, 2003, 15: 2369-2384

[18] MinT., YooJ., ChoiH., JosephD. D.. Drag reduction by polymer additives in a turbulent channel flow [J]. J Fluid Mech, 2003, 486: 213-238

[19] De GennesP. G.. Towards a scaling theory of drag reduction [J]. Physica A, 1986, 140: 9-25

[20] DubiefY., WhiteC. M., TerraponV. E., ShaqfehE., MoinP., LeleS. K.. On the coherent drag reducing and turbulence enhancing behavior of polymers in wall flows [J]. J Fluid Mech, 2004, 514: 271-280

[21] LiC. F., SureshkumarR., KhomamiB.. Influence of rheological parameters on polymer induced turbulent drag reduction [J]. J Non-Newton Fluid Mech, 2006, 140: 23-40

[22] KimJ., HussainF.. Propagation velocity of perturbations in turbulent channel flow [J]. Phys Fluids, 2003, 5: 695-706

[23] KimK., LiC. F., SureshkumarR., BalachandarS., AdrianR. J.. Effects of the polymer stresses on eddy structures in drag-reduced turbulent channel flow [J]. J Fluid Mech, 2007, 584: 281-299

[24] LI C F, SURESHKUMAR R, KHOMAMI B. Polymer induced drag reduction: The interplay between vortex dynamics and drag reduction[J]. Phys Rev Lett, 2008 (submitted)