Hostname: page-component-848d4c4894-sjtt6 Total loading time: 0 Render date: 2024-06-19T18:10:22.027Z Has data issue: false hasContentIssue false

Polymer-induced flow relaminarization and drag enhancement in spanwise-rotating plane Couette flow

Published online by Cambridge University Press:  27 October 2020

Yabiao Zhu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, HefeiAnhui230026, PR China
Jiaxing Song
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, HefeiAnhui230026, PR China
Nansheng Liu*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, HefeiAnhui230026, PR China
Xiyun Lu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, HefeiAnhui230026, PR China
Bamin Khomami*
Affiliation:
Department of Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, TN37996, USA
*
Email addresses for correspondence: lns@ustc.edu.cn, bkhomami@utk.edu
Email addresses for correspondence: lns@ustc.edu.cn, bkhomami@utk.edu

Abstract

Direct numerical simulation of polymer-induced flow relaminarization of turbulent spanwise-rotating plane Couette flow (RPCF) is reported for the first time. Specifically, the reverse transition pathway from a Newtonian turbulent RPCF to a fully relaminarized drag enhanced viscoelastic flow has been elucidated. Evidently, this transition occurs gradually by weakening and eventual elimination of small-scale vortices as the Weissenberg number ($Wi$) is enhanced, paving the way for a two-dimensional laminar flow consisting of large-scale and highly organized roll cells. The influence of polymer additives on convective momentum exchange by large-scale roll cells and small-scale turbulent vortices, namely, the drag reduction (DR) realized by elimination of turbulent vortices and the significant drag enhancement (DE) that results from polymer roll cell interactions has been identified as the mechanism of DE. The observed vortical changes point to a universal mechanism for the coupling of polymer chains and turbulent vortices in wall-bounded viscoelastic DE and DR flows.

Type
JFM Papers
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Andereck, C. D., Liu, S. S. & Swinney, H. L. 1986 Flow regimes in a circular Couette system with independently rotating cylinders. J. Fluid Mech. 164, 155183.CrossRefGoogle Scholar
Bech, K. H. & Andersson, H. I. 1996 Secondary flow in weakly rotating turbulent plane Couette flow. J. Fluid Mech. 317, 195214.CrossRefGoogle Scholar
Bech, K. H. & Andersson, H. I. 1997 Turbulent plane Couette flow subject to strong system rotation. J. Fluid Mech. 347, 289314.CrossRefGoogle Scholar
Brauckmann, H. J., Salewski, M. & Eckhardt, B. 2016 Momentum transport in Taylor–Couette flow with vanishing curvature. J. Fluid Mech. 790, 419452.CrossRefGoogle Scholar
Chandra, B., Shankar, V. & Das, D. 2020 Early transition, relaminarization and drag reduction in the flow of polymer solutions through microtubes. J. Fluid Mech. 885, A47.CrossRefGoogle Scholar
Choueiri, G. H., Lopez, J. M. & Hof, B. 2018 Exceeding the asymptotic limit of polymer drag reduction. Phys. Rev. Lett. 120 (12), 124501.CrossRefGoogle ScholarPubMed
Dallas, V., Vassilicos, J. C. & Hewitt, G. F. 2010 Strong polymer-turbulence interactions in viscoelastic turbulent channel flow. Phys. Rev. E 82 (6), 066303.CrossRefGoogle ScholarPubMed
Dubief, Y., Terrapon, V. E. & Soria, J. 2013 On the mechanism of elasto-inertial turbulence. Phys. Fluids 25 (11), 110817.CrossRefGoogle ScholarPubMed
Dubief, Y., White, C. M., Terrapon, V. E., Shaqfeh, E. S., Moin, P. & Lele, S. K. 2004 On the coherent drag-reducing and turbulence-enhancing behaviour of polymers in wall flows. J. Fluid Mech. 514, 271280.CrossRefGoogle Scholar
Dubrulle, B., Dauchot, O., Daviaud, F., Longaretti, P. Y., Richard, D. & Zahn, J. P. 2005 Stability and turbulent transport in Taylor–Couette flow from analysis of experimental data. Phys. Fluids 17 (9), 095103.CrossRefGoogle Scholar
Gai, J., Xia, Z., Cai, Q. & Chen, S. 2016 Turbulent statistics and flow structures in spanwise-rotating turbulent plane Couette flows. Phys. Rev. Fluids 1 (5), 054401.CrossRefGoogle Scholar
Groisman, A. & Steinberg, V. 1998 Mechanism of elastic instability in Couette flow of polymer solutions: experiment. Phys. Fluids 10 (10), 24512463.CrossRefGoogle Scholar
Grossmann, S., Lohse, D. & Sun, C. 2016 High-Reynolds number Taylor–Couette turbulence. Annu. Rev. Fluid Mech. 48, 5380.CrossRefGoogle Scholar
Gupta, A. & Vincenzi, D. 2019 Effect of polymer-stress diffusion in the numerical simulation of elastic turbulence. J. Fluid Mech. 870, 405418.CrossRefGoogle Scholar
Kim, K., Li, C.-F., Sureshkumar, R., Balachandar, S. & Adrian, R. J. 2007 Effects of polymer stresses on eddy structures in drag-reduced turbulent channel flow. J. Fluid Mech. 584, 281299.CrossRefGoogle Scholar
Kumar, K. A. & Graham, M. D. 2001 Finite-amplitude solitary states in viscoelastic shear flow: computation and mechanism. J. Fluid Mech. 443, 301328.CrossRefGoogle 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 (1–3), 2340.CrossRefGoogle 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.CrossRefGoogle ScholarPubMed
Liu, N. & Khomami, B. 2013 a Elastically induced turbulence in Taylor–Couette flow: direct numerical simulation and mechanistic insight. J. Fluid Mech. 737, R4.CrossRefGoogle Scholar
Liu, N. & Khomami, B. 2013 b Polymer-induced drag enhancement in turbulent Taylor–Couette flows: direct numerical simulations and mechanistic insight. Phys. Rev. Lett. 111, 114501.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
Martínez-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.CrossRefGoogle Scholar
Pereira, A. S., Mompean, G., Thais, L. & Soares, E. J. 2017 a Transient aspects of drag reducing plane Couette flows. J. Non-Newtonian Fluid Mech. 241, 6069.CrossRefGoogle Scholar
Pereira, A. S., Mompean, G., Thais, L., Soares, E. J. & Thompson, R. L. 2017 b Active and hibernating turbulence in drag-reducing plane Couette flows. Phys. Rev. Fluids 2 (8), 084605.CrossRefGoogle Scholar
Pereira, A., Thompson, R. L. & Mompean, G. 2019 Beyond the maximum drag reduction asymptote: the pseudo-laminar state. arXiv:1911.00439.Google Scholar
Salewski, M. & Eckhardt, B. 2015 Turbulent states in plane Couette flow with rotation. Phys. Fluids 27 (4), 045109.CrossRefGoogle Scholar
Samanta, D., Dubief, Y., Holzner, M., Schäfer, C., Morozov, A. N., Wagner, C. & Hof, B. 2013 Elasto-inertial turbulence. Proc. Natl Acad. Sci. USA 110 (26), 1055710562.CrossRefGoogle ScholarPubMed
Shekar, A., McMullen, R. M., Wang, S.-N., McKeon, B. J. & Graham, M. D. 2019 Critical-layer structures and mechanisms in elastoinertial turbulence. Phys. Rev. Lett. 122 (12), 124503.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
Song, J., Teng, H., Liu, N., Ding, H., Lu, X. & Khomami, B. 2019 The correspondence between drag enhancement and vortical structures in turbulent Taylor–Couette flows with polymer additives: a study of curvature dependence. J. Fluid Mech. 881, 602616.CrossRefGoogle Scholar
Sureshkumar, R. & Beris, A. N. 1995 Effect of artificial stress diffusivity on the stability of numerical calculations and the flow dynamics of time-dependent viscoelastic flows. J. Non-Newtonian Fluid Mech. 60 (1), 5380.CrossRefGoogle Scholar
Sureshkumar, R., Beris, A. N. & Handler, R. A. 1997 Direct numerical simulation of the turbulent channel flow of a polymer solution. Phys. Fluids 9 (3), 743755.CrossRefGoogle 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.CrossRefGoogle Scholar
Thais, L., Gatski, T. B. & Mompean, G. 2013 Analysis of polymer drag reduction mechanisms from energy budgets. J. Fluid Mech. 43, 5261.Google Scholar
Tsukahara, T., Ishigami, T., Yu, B. & Kawaguchi, Y. 2011 DNS study on viscoelastic effect in drag-reduced turbulent channel flow. J. Turbul. 12, 14685248.CrossRefGoogle Scholar
Tsukahara, T., Tillmark, N. & Alfredsson, P. H. 2010 Flow regimes in a plane Couette flow with system rotation. J. Fluid Mech. 648, 533.CrossRefGoogle Scholar
White, C. M. & Mungal, M. G. 2008 Mechanics and prediction of turbulent drag reduction with polymer additives. Annu. Rev. Fluid Mech. 40, 235256.CrossRefGoogle Scholar
Xi, L. & Graham, M. D. 2010 Turbulent drag reduction and multistage transitions in viscoelastic minimal flow units. J. Fluid Mech. 647, 421452.CrossRefGoogle Scholar
Xia, Z., Shi, Y., Wan, M., Sun, C., Cai, Q. & Chen, S. 2019 Role of the large-scale structures in spanwise rotating plane Couette flow with multiple states. Phys. Rev. Fluids 4 (10), 104606.CrossRefGoogle Scholar