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The correspondence between drag enhancement and vortical structures in turbulent Taylor–Couette flows with polymer additives: a study of curvature dependence

Published online by Cambridge University Press:  25 October 2019

Jiaxing Song
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
Hao Teng
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
Nansheng Liu*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
Hang Ding
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
Xi-Yun Lu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
Bamin Khomami*
Affiliation:
Department of Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, TN 37996, USA
*
Email addresses for correspondence: lns@ustc.edu.cn, bkhomami@utk.edu
Email addresses for correspondence: lns@ustc.edu.cn, bkhomami@utk.edu

Abstract

We report direct numerical simulation results that clearly elucidate the mechanism that leads to curvature dependence of drag enhancement (DE) in viscoelastic turbulent Taylor–Couette flow. Change in the angular momentum transport and its inherent link to transitions in vortical flow structures have been explored to depict the influence of the curvature of the flow geometry on DE. Specifically, it has been demonstrated that a transition in vortical structures with increasing radius ratio leads to weakening and elimination of the small-scale Görtler vortices and development and better organization (occupying the entire gap) of large-scale Taylor vortices as also evinced by the patterns of angular momentum current. The commensurate change in DE and its underlying mechanism are examined by contributions of convective flux and polymeric stress to the angular momentum current. The present finding paves the way for capturing highly localized elastic turbulence structures in direct numerical simulation by increasing geometry curvature in traditional turbulent curvilinear flows.

Type
JFM Papers
Copyright
© 2019 Cambridge University Press 

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References

Avgousti, M. & Beris, A. N. 1993 Non-axisymmetric modes in the viscoelastic Taylor–Couette flow. J. Non-Newtonian Fluid Mech. 50, 225251.Google Scholar
Bird, R. B., Curtiss, C. F., Armstrong, R. C. & Hassager, O. 1987 Kinetic theory. In Dynamics of Polymeric Fluids, pp. 13971398. Wiley.Google Scholar
Choueiri, G. H., Lopez, J. M. & Hof, B. 2018 Exceeding the asymptotic limit of polymer drag reduction. Phys. Rev. Lett. 120, 124501.Google Scholar
Dutcher, C. S. & Muller, S. J. 2009 Spatio-temporal mode dynamics and higher order transitions in high aspect ratio Newtonian Taylor–Couette flows. J. Fluid Mech. 641, 85113.Google Scholar
Dutcher, C. S. & Muller, S. J. 2013 Effects of moderate elasticity on the stability of co- and counter-rotating Taylor–Couette flows. J. Rheol. 57, 791812.Google Scholar
Eckhardt, B., Grossmann, S. & Lohse, D. 2007 Torque scaling in turbulent Taylor–Couette flow between independently rotating cylinders. J. Fluid Mech. 581, 221250.Google Scholar
Graham, M. D. 2014 Drag reduction and the dynamics of turbulence in simple and complex fluids. Phys. Fluids 26, 101301.Google Scholar
Groisman, A. & Steinberg, V. 2000 Elastic turbulence in a polymer solution flow. Nature 405, 5355.Google Scholar
Groisman, A. & Steinberg, V. 2004 Elastic turbulence in curvilinear flows of polymer solutions. N. J. Phys. 6, 29.Google Scholar
Grossmann, S., Lohse, D. & Sun, C. 2016 High-Reynolds number Taylor–Couette turbulence. Annu. Rev. Fluid Mech. 48, 5380.Google Scholar
Gupta, A. & Vincenzi, D. 2019 Effect of polymer-stress diffusion in the numerical simulation of elastic turbulence. J. Fluid Mech. 870, 405418.Google Scholar
Joo, Y. L. & Shaqfeh, E. S. G. 1992 The effects of inertia on the viscoelastic Dean and Taylor–Couette flow instabilities with application to coating flows. Phys. Fluids A 4, 24152431.Google Scholar
Kim, K., Li, C.-F., Balachandar, S., Sureshkumar, R. & Adrian, R. J. 2007 Effects of polymer stresses on eddy structures in drag-reduced turbulent channel flow. J. Fluid Mech. 584, 281299.Google Scholar
Larson, R. G., Shaqfeh, E. S. G. & Muller, S. J. 1990 A purely elastic instability in Taylor–Couette flow. J. Fluid Mech. 218, 573600.Google Scholar
Latrache, N., Crumeyrolle, O. & Mutabazi, I. 2012 Transition to turbulence in a flow of a shear-thinning viscoelastic solution in a Taylor–Couette cell. Phys. Rev. E 86, 056305.Google Scholar
Li, C.-F., Sureshkumar, R. & Khomami, B. 2006 Influence of rheological parameters on polymer induced turbulent drag reduction. J. Non-Newtonian Fluid Mech. 140, 2340.Google Scholar
Li, C.-F., Sureshkumar, R. & Khomami, B. 2015 Simple framework for understanding the universality of the maximum drag reduction asymptote in turbulent flow of polymer solutions. Phys. Rev. E 92, 043014.Google Scholar
Liu, N. & Khomami, B. 2013a Elastically induced turbulence in Taylor–Couette flow: direct numerical simulation and mechanistic insight. J. Fluid Mech. 737, R4.Google Scholar
Liu, N. & Khomami, B. 2013b Polymer-induced drag enhancement in turbulent Taylor–Couette flows: direct numerical simulations and mechanistic insight. Phys. Rev. Lett. 111, 114501.Google Scholar
Lopez, J. M., Choueiri, G. H. & Hof, B. 2019 Dynamics of viscoelastic pipe flow at low Reynolds numbers in the maximum drag reduction limit. J. Fluid Mech. 874, 699719.Google Scholar
Lumley, J. L. 1977 Drag reduction in two phase and polymer flows. Phys. Fluids 20, S64.Google Scholar
Martińez-Arias, B., Peixinho, J., Crumeyrolle, O. & Mutabazi, I. 2014 Effect of the number of vortices on the torque scaling in Taylor–Couette flow. J. Fluid Mech. 748, 756767.Google Scholar
McKinley, G. H., Byars, J. A., Brown, R. A. & Armstrong, R. C. 1991 Observations on the elastic instability in cone-and-plate and parallel-plate flows of a polyisobutylene Boger fluid. J. Non-Newtonian Fluid Mech. 40, 201229.Google Scholar
McKinley, G. H., Pakdel, P. & Oeztekin, A. 1996 Rheological and geometric scaling of purely elastic flow instabilities. J. Non-Newtonian Fluid Mech. 67, 1947.Google Scholar
Metzner, A. B. 1977 Polymer solution and fiber suspension rheology and their relationship to turbulent drag reduction. Phys. Fluids 20, S145.Google Scholar
Ostilla-Mońico, R., Huisman, S. G., Jannink, T. J. G., Van Gils, D. P. M., Verzicco, R., Grossmann, S., Sun, C. & Lohse, D. 2014 Optimal Taylor–Couette flow: radius ratio dependence. J. Fluid Mech. 747, 129.Google Scholar
Pakdel, P. & McKinley, G. H. 1996 Elastic instability and curved streamlines. Phys. Rev. Lett. 77, 12.Google Scholar
Samanta, D., Dubief, Y., Holznera, M., Schäfer, C., Morozov, A. N., Wagner, C. & Hof, B. 2013 Elasto-inertial turbulence. Proc. Natl Acad. Sci. USA 110, 1055710562.Google Scholar
Saric, W. S. 1994 Görtler vortices. Annu. Rev. Fluid Mech. 26, 379409.Google Scholar
Schäfer, C., Morozov, A. & Wagner, C. 2018 Geometric scaling of elastic instabilities in the Taylor–Couette geometry: a theoretical, experimental and numerical study. J. Non-Newtonian Fluid Mech. 259, 7890.Google Scholar
Shaqfeh, E. S. G., Muller, S. J. & Larson, R. G. 1992 The effects of gap width and dilute solution properties on the viscoelastic Taylor–Couette instability. J. Fluid Mech. 235, 285317.Google Scholar
Shekar, A., McMullen, R. M., Wang, S., McKeon, B. J. & Graham, M. D. 2019 Critical-layer structures and mechanisms in elastoinertial turbulence. Phys. Rev. Lett. 122, 124503.Google Scholar
Sid, S., Terrapon, V. E. & Dubief, Y. 2018 Two-dimensional dynamics of elasto-inertial turbulence and its role in polymer drag reduction. Phys. Rev. Fluids 3 (1), 011301.Google Scholar
Sureshkumar, R., Beris, A. N. & Avgousti, M. 1994 Non-axisymmetric subcritical bifurcations in viscoelastic Taylor–Couette flow. Proc. R. Soc. Lond. A 447, 135153.Google Scholar
Sureshkumar, R., Beris, A. N. & Avgousti, M. 1995 Effect of artificial stress diffusivity on the stability of numerical calculations and the dynamics of time-dependent viscoelastic flows. J. Non-Newtonian Fluid Mech. 60, 5380.Google Scholar
Sureshkumar, R., Beris, A. N. & Handler, R. A. 1997 Direct numerical integration of turbulent channel flow of a polymer solution. Phys. Fluids 9, 743.Google Scholar
Teng, H., Liu, N., Lu, X. & Khomami, B. 2015 Direct numerical simulation of Taylor–Couette flow subjected to a radial temperature gradient. Phys. Fluids 27 (12), 125101.Google Scholar
Teng, H., Liu, N., Lu, X. & Khomami, B. 2018 Turbulent drag reduction in plane Couette flow with polymer additives: a direct numerical simulation study. J. Fluid Mech. 846, 482507.Google Scholar
Thomas, D. G., Khomami, B. & Sureshkumar, R. 2006 Pattern formation in Taylor–Couette flow of dilute polymer solutions: dynamical simulations and mechanism. Phys. Rev. Lett. 97, 054501.Google Scholar
Thomas, D. G., Khomami, B. & Sureshkumar, R. 2009 Nonlinear dynamics of viscoelastic Taylor–Couette flow: effect of elasticity on pattern selection, molecular conformation and drag. J. Fluid Mech. 620, 353382.Google Scholar
Toms, B. A. 1948 Some observations on the flow of linear polymer solutions through straight tubes at large Reynolds numbers. In Proceedings of the First International Congress on Rheology (ed. Burgers, J. M.), pp. 135141. North Holland.Google Scholar
Virk, P. S. 1975 Drag reduction fundamentals. AIChE J. 21, 625656.Google Scholar
Wei, T., Kline, E. M., Lee, S. H.-K. & Woodruff, S. 1992 Görtler vortex formation at the inner cylinder in Taylor–Couette flow. J. Fluid Mech. 245, 4768.Google Scholar
White, C. M. & Mungal, M. G. 2008 Mechanics and prediction of turbulent drag reduction with polymer additives. Annu. Rev. Fluid Mech. 40, 235256.Google Scholar
Xie, Y.-C., Huang, S.-D., Funfschilling, D., Li, X.-M., Ni, R. & Xia, K.-Q. 2015 Effects of polymer additives in the bulk of turbulent thermal convection. J. Fluid Mech. 784, R3.Google Scholar
Zhu, L., Schrobsdorf, H., Schneider, T. M. & Xi, L. 2018 Distinct transition in flow statistics and vortex dynamics between low- and high-extent turbulent drag reduction in polymer fluids. J. Non-Newtonian Fluid Mech. 262, 115130.Google Scholar
Zilz, J., Poole, R. J., Alves, M. A., Bartolo, D., Levaché, B. & Lindner, A. 2012 Geometric scaling of a purely elastic flow instability in serpentine channels. J. Fluid Mech. 712, 203218.Google Scholar