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Vortex merging and splitting events in viscoelastic Taylor–Couette flow

Published online by Cambridge University Press:  08 August 2022

Jose M. Lopez Open the ORCID record for Jose M. Lopez [Opens in a new window]
Jose M. Lopez*
Affiliation:
Physics Department, Universitat Politècnica de Catalunya, Campus Nord UPC, 08034 Barcelona, Spain
*
†Email address for correspondence: [email protected]
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Abstract

Recent experiments have reported a novel transition to elasto-inertial turbulence in the Taylor–Couette flow of a dilute polymer solution. Unlike previously reported transitions, this newly discovered scenario, dubbed vortex merging and splitting (VMS) transition, occurs in the centrifugally unstable regime and the mechanisms underlying it are two-dimensional: the flow becomes chaotic due to the proliferation of events where axisymmetric vortex pairs may be either created (vortex splitting) or annihilated (vortex merging). In this paper, we present direct numerical simulations, using the finitely extensible nonlinear elastic-Peterlin (FENE-P) constitutive equation to model the polymer dynamics, which reproduce the experimental observations with great accuracy and elucidate the reasons for the onset of this surprising dynamics. Starting from the Newtonian limit and increasing progressively the fluid's elasticity, we demonstrate that the VMS dynamics is not associated with the well-known Taylor vortices, but with a steady pattern of elastically induced axisymmetric vortex pairs known as diwhirls. The amount of angular momentum carried by these elastic vortices becomes increasingly small as the fluid's elasticity increases and it eventually reaches a marginal level. When this occurs, the diwhirls become dynamically disconnected from the rest of the system and move independently from each other in the axial direction. It is shown that vortex merging and splitting events, along with local transient chaotic dynamics, result from the interactions among diwhirls, and that this complex spatio-temporal dynamics persists even at elasticity levels twice as large as those investigated experimentally.

JFM classification

Instability: Transition to turbulence Non-Newtonian Flows: Viscoelasticity
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 946 , 10 September 2022 , A27
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Al-Mubaiyedh, U.A., Sureshkumar, R. & Khomami, B. 1999 Influence of energetics on the stability of viscoelastic Taylor–Couette flow. Phys. Fluids 11 (11), 3217–3226.CrossRefGoogle Scholar
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, 155–183.CrossRefGoogle Scholar
Aref, H. 1983 Integrable, chaotic, and turbulent vortex motion in two-dimensional flows. Annu. Rev. Fluid Mech. 15 (1), 345–389.CrossRefGoogle Scholar
Avila, M., Grimes, M., Lopez, J.M. & Marques, F. 2008 Global endwall effects on centrifugally stable flows. Phys. Fluids 20 (10), 104104.CrossRefGoogle Scholar
Batchelor, G.K. 2000 An Introduction to Fluid Dynamics. Cambridge University Press.CrossRefGoogle Scholar
Baumert, B.M. & Muller, S.J. 1995 Flow visualization of the elastic Taylor–Couette instability in Boger fluids. Rheol. Acta 34 (2), 147–159.CrossRefGoogle Scholar
Baumert, B.M. & Muller, S.J. 1997 Flow regimes in model viscoelastic fluids in a circular Couette system with independently rotating cylinders. Phys. Fluids 9 (3), 566–586.CrossRefGoogle Scholar
Baumert, B.M. & Muller, S.J. 1999 Axisymmetric and non-axisymmetric elastic and inertio-elastic instabilities in Taylor–Couette flow. J. Non-Newtonian Fluid Mech. 83 (1), 33–69.CrossRefGoogle Scholar
Beris, A.N. & Dimitropoulos, C.D. 1999 Pseudospectral simulation of turbulent viscoelastic channel flow. Comput. Meth. Appl. Mech. Engng 180 (3), 365–392.CrossRefGoogle Scholar
Bird, R., Dotson, P. & Johnson, N. 1980 Polymer solution rheology based on a finitely extensible bead–spring chain model. J. Non-Newtonian Fluid Mech. 7 (2), 213–235.CrossRefGoogle Scholar
Cagney, N., Lacassagne, T. & Balabani, S. 2020 Taylor–Couette flow of polymer solutions with shear-thinning and viscoelastic rheology. J. Fluid Mech. 905, A28.CrossRefGoogle Scholar
Coles, D. 1965 Transition in circular Couette flow. J. Fluid Mech. 21 (3), 385–425.CrossRefGoogle Scholar
Crumeyrolle, O., Mutabazi, I. & Grisel, M. 2002 Experimental study of inertioelastic Couette–Taylor instability modes in dilute and semidilute polymer solutions. Phys. Fluids 14 (5), 1681–1688.CrossRefGoogle Scholar
Czarny, O., Serre, E., Bontoux, P. & Lueptow, R.M. 2003 Interaction between Ekman pumping and the centrifugal instability in Taylor–Couette flow. Phys. Fluids 15 (2), 467–477.CrossRefGoogle Scholar
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
Dessup, T., Tuckerman, L.S., Wesfreid, J.E., Barkley, D. & Willis, A.P. 2018 Self-sustaining process in Taylor–Couette flow. Phys. Rev. Fluids 3, 123902.CrossRefGoogle Scholar
Dubief, Y., Terrapon, V.E. & Soria, J. 2013 On the mechanism of elasto-inertial turbulence. Phys. Fluids 25 (11), 110817.CrossRefGoogle ScholarPubMed
Eckhardt, B., Grossmann, S. & Lohse, D. 2007 Torque scaling in turbulent Taylor–Couette flow between independently rotating cylinders. J. Fluid Mech. 581, 221–250.CrossRefGoogle Scholar
Fenstermacher, P.R., Swinney, H.L. & Gollub, J.P. 1979 Dynamical instabilities and the transition to chaotic Taylor vortex flow. J. Fluid Mech. 94 (1), 103–128.CrossRefGoogle Scholar
Fouxon, A. & Lebedev, V. 2003 Spectra of turbulence in dilute polymer solutions. Phys. Fluids 15 (7), 2060–2072.CrossRefGoogle Scholar
Gorman, M. & Swinney, H.L. 1982 Spatial and temporal characteristics of modulated waves in the circular Couette system. J. Fluid Mech. 117, 123–142.CrossRefGoogle Scholar
Groisman, A. & Steinberg, V. 1996 Couette–Taylor flow in a dilute polymer solution. Phys. Rev. Lett. 77, 1480–1483.CrossRefGoogle Scholar
Groisman, A. & Steinberg, V. 1997 Solitary vortex pairs in viscoelastic Couette flow. Phys. Rev. Lett. 78, 1460–1463.CrossRefGoogle Scholar
Groisman, A. & Steinberg, V. 1998 Mechanism of elastic instability in Couette flow of polymer solutions: experiment. Phys. Fluids 10 (10), 2451–2463.CrossRefGoogle Scholar
Groisman, A. & Steinberg, V. 2000 Elastic turbulence in a polymer solution flow. Nature 405, 53–55.CrossRefGoogle Scholar
Groisman, A. & Steinberg, V. 2004 Elastic turbulence in curvilinear flows of polymer solutions. New J. Phys. 6, 29.CrossRefGoogle Scholar
Hegseth, J.J., Baxter, G.W. & Andereck, C.D. 1996 Bifurcations from Taylor vortices between corotating concentric cylinders. Phys. Rev. E 53, 507–521.CrossRefGoogle ScholarPubMed
Jones, C.A. 1981 Nonlinear Taylor vortices and their stability. J. Fluid Mech. 102, 249–261.CrossRefGoogle Scholar
Jones, C.A. 1985 The transition to wavy Taylor vortices. J. Fluid Mech. 157, 135–162.CrossRefGoogle Scholar
King, G.P., Lee, Y., Li, W., Swinney, H.L. & Marcus, P.S. 1984 Wave speeds in wavy Taylor-vortex flow. J. Fluid Mech. 141, 365–390.CrossRefGoogle Scholar
Lacassagne, T., Cagney, N. & Balabani, S. 2021 Shear-thinning mediation of elasto-inertial Taylor–Couette flow. J. Fluid Mech. 915, A91.CrossRefGoogle Scholar
Lacassagne, T., Cagney, N., Gillissen, J.J.J. & Balabani, S. 2020 Vortex merging and splitting: a route to elastoinertial turbulence in Taylor–Couette flow. Phys. Rev. Fluids 5, 113303.CrossRefGoogle Scholar
Lange, M. & Eckhardt, B. 2001 Vortex pairs in viscoelastic Couette-Taylor flow. Phys. Rev. E 64, 027301.CrossRefGoogle ScholarPubMed
Larson, R.G., Shaqfeh, E.S.G. & Muller, S.J. 1990 A purely elastic instability in Taylor–Couette flow. J. Fluid Mech. 218, 573–600.CrossRefGoogle Scholar
Latrache, N., Abcha, N., Crumeyrolle, O. & Mutabazi, I. 2016 Defect-mediated turbulence in ribbons of viscoelastic Taylor–Couette flow. Phys. Rev. E 93, 043126.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
Latrache, N. & Mutabazi, I. 2021 Transition to turbulence via flame patterns in viscoelastic Taylor–Couette flow. Eur. Phys. J. E 44 (5), 63.CrossRefGoogle ScholarPubMed
Liu, N. & Khomami, B. 2013 Elastically induced turbulence in Taylor–Couette flow: direct numerical simulation and mechanistic insight. J. Fluid Mech. 737, R4.CrossRefGoogle Scholar
Lopez, J.M. & Avila, M. 2017 Boundary-layer turbulence in experiments on quasi-Keplerian flows. J. Fluid Mech. 817, 21–34.CrossRefGoogle 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, 699–719.CrossRefGoogle Scholar
López, J.M., Feldmann, D., Rampp, M., Vela-Martín, A., Shi, L. & Avila, M. 2020 nsCouette–a high-performance code for direct numerical simulations of turbulent Taylor–Couette flow. SoftwareX 11, 100395.CrossRefGoogle Scholar
Marcus, P.S. 1984 a Simulation of Taylor–Couette flow. Part 1. Numerical methods and comparison with experiment. J. Fluid Mech. 146, 45–64.CrossRefGoogle Scholar
Marcus, P.S. 1984 b Simulation of Taylor–Couette flow. Part 2. Numerical results for wavy-vortex flow with one travelling wave. J. Fluid Mech. 146, 65–113.CrossRefGoogle Scholar
Martinand, D., Serre, E. & Lueptow, R.M. 2014 Mechanisms for the transition to waviness for Taylor vortices. Phys. Fluids 26 (9), 094102.CrossRefGoogle Scholar
Muller, S.J., Larson, R.G. & Shaqfeh, E.S. 1989 A purely elastic transition in Taylor–Couette flow. Rheol. Acta 28 (6), 499–503.CrossRefGoogle Scholar
Ruelle, D. & Takens, F. 1971 On the nature of turbulence. Commun. Math. Phys. 20, 167–192.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. 110 (26), 10557–10562.CrossRefGoogle ScholarPubMed
Shaqfeh, E.S.G. 1996 Purely elastic instabilities in viscometric flows. Annu. Rev. Fluid Mech. 28 (1), 129–185.CrossRefGoogle Scholar
Shi, L., Rampp, M., Hof, B. & Avila, M. 2015 A hybrid MPI-openmp parallel implementation for pseudospectral simulations with application to Taylor–Couette flow. Comput. Fluids 106, 1–11.CrossRefGoogle Scholar
Song, J., Lin, F., Liu, N., Lu, X.-Y. & Khomami, B. 2021 a Direct numerical simulation of inertio-elastic turbulent Taylor–Couette flow. J. Fluid Mech. 926, A37.CrossRefGoogle Scholar
Song, J., Teng, H., Liu, N., Ding, H., Lu, X.-Y. & 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, 602–616.CrossRefGoogle Scholar
Song, J., Wan, Z.-H., Liu, N., Lu, X.-Y. & Khomami, B. 2021 b A reverse transition route from inertial to elasticity-dominated turbulence in viscoelastic Taylor–Couette flow. J. Fluid Mech. 927, A10.CrossRefGoogle Scholar
Taylor, G.I.S. 1923 Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. R. Soc. A 223, 289–343.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, 353–382.CrossRefGoogle Scholar
Thomas, D.G., Sureshkumar, R. & Khomami, B. 2006 Pattern formation in Taylor–Couette flow of dilute polymer solutions: dynamical simulations and mechanism. Phys. Rev. Lett. 97, 054501.CrossRefGoogle ScholarPubMed
Wereley, S.T. & Lueptow, R.M. 1998 Spatio-temporal character of non-wavy and wavy Taylor–Couette flow. J. Fluid Mech. 364, 59–80.CrossRefGoogle Scholar
Willis, A.P. 2017 The openpipeflow Navier–Stokes solver. SoftwareX 6, 124–127.CrossRefGoogle Scholar
Xi, L. & Graham, M.D. 2010 Turbulent drag reduction and multistage transitions in viscoelastic minimal flow units. J. Fluid Mech. 647, 421–452.CrossRefGoogle Scholar
Yamani, S., Keshavarz, B., Raj, Y., Zaki, T.A., McKinley, G.H. & Bischofberger, I. 2021 Spectral universality of elastoinertial turbulence. Phys. Rev. Lett. 127, 074501.CrossRefGoogle ScholarPubMed
Zhu, Y., Song, J., Lin, F., Liu, N., Lu, X. & Khomami, B. 2022 Relaminarization of spanwise-rotating viscoelastic plane Couette flow via a transition sequence from a drag-reduced inertial to a drag-enhanced elasto-inertial turbulent flow. J. Fluid Mech. 931, R7.CrossRefGoogle Scholar
Zhu, Y., Song, J., Liu, N., Lu, X. & Khomami, B. 2020 Polymer-induced flow relaminarization and drag enhancement in spanwise-rotating plane Couette flow. J. Fluid Mech. 905, A19.CrossRefGoogle Scholar