Hostname: page-component-5d59c44645-l48q4 Total loading time: 0 Render date: 2024-03-04T07:59:20.793Z Has data issue: false hasContentIssue false

Direct numerical simulation of elastic turbulence in the Taylor–Couette flow: transition pathway and mechanistic insight

Published online by Cambridge University Press:  06 October 2022

Jiaxing Song
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China Max Planck Institute for Solar System Research, Göttingen 37077, Germany
Nansheng Liu*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Xi-Yun Lu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR 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

Three-dimensional elastic turbulence in Taylor–Couette flows of dilute polymer solutions has been realized and thoroughly investigated via direct numerical simulations. A novel flow transition pathway from elastically dominated turbulence to solitary vortex pairs (or diwhirls) and eventually to elastic turbulence is observed by decreasing the fluid inertia ($Re$) over seven orders of magnitude, i.e. from $Re=1000$ to $0.0001$. The dominant spatio-temporal flow features in the elastic turbulence regime are those of large-scale unsteady diwhirls and small-scale axial and azimuthal travelling waves in the outer and inner halves of the gap, respectively. Moreover, it is conclusively shown that production of turbulent kinetic energy in purely elastic turbulence solely arises due to the stochastic nature of polymer stretch/relaxation. Overall, based on this comprehensive numerical investigation, the differences in the underlying fluid physics that give rise to turbulent fluctuations in elastically dominated and purely elastic turbulence have been delineated.

Type
JFM Papers
Copyright
© The Author(s), 2022. 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

Alves, M.A., Oliveira, P.J. & Pinho, F.T. 2021 Numerical methods for viscoelastic fluid flows. Annu. Rev. Fluid Mech. 53, 509541.CrossRefGoogle Scholar
Avgousti, M. & Beris, A.N. 1993 Non-axisymmetric modes in the viscoelastic Taylor–Couette flow. J. Non-Newtonian Fluid Mech. 50, 225251.CrossRefGoogle Scholar
Benzi, R. & Ching, E.S.C. 2018 Polymers in fluid flows. Annu. Rev. Condens. Matter Phys. 9, 163181.CrossRefGoogle Scholar
Berti, S., Bistagnino, A., Boffetta, G., Celani, A. & Musacchio, S. 2008 Two-dimensional elastic turbulence. Phys. Rev. E 77, 055306(R).CrossRefGoogle ScholarPubMed
Berti, S. & Boffetta, G. 2010 Elastic waves and transition to elastic turbulence in a two-dimensional viscoelastic Kolmogorov flow. Phys. Rev. E 82, 036314.CrossRefGoogle Scholar
Bird, R.B., Curtiss, C.F., Armstrong, R.C. & Hassager, O. 1987 Kinetic theory. In Dynamics of Polymeric Fluids, pp. 1397–1398. Wiley.Google Scholar
Buel, R.V., Schaaf, C. & Stark, H. 2018 Elastic turbulence in two-dimensional Taylor–Couette flows. Europhys. Lett. 142, 14001.CrossRefGoogle Scholar
Dallas, V. & Vassilicos, J.C. 2010 Strong polymer-turbulence interactions in viscoelastic turbulent channel flow. Phys. Rev. E 82, 066303.CrossRefGoogle ScholarPubMed
De, S., van der Schaaf, J., Deen, N.G., Kuipers, J.A.M., Peters, E.A.J.F. & Padding, J.T. 2017 Lane change in flows through pillared microchannels. Phys. Fluids 29, 113102.CrossRefGoogle Scholar
Dubief, Y., Terrapon, V.E. & Soria, J. 2013 On the mechanism of elasto-inertial turbulence. Phys. Fluids 25, 110817.CrossRefGoogle ScholarPubMed
Dutcher, C.S. & Muller, S.J. 2009 The effects of drag reducing polymers on flow stability : insights from the Taylor–Couette problem. Korea-Austral. Rheol. J. 21, 223233.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.CrossRefGoogle Scholar
Fouxon, A. & Lebedev, V. 2003 Spectra of turbulence in dilute polymer solutions. Phys. Fluids 15, 20602072.CrossRefGoogle Scholar
Garg, H., Calzavarini, E. & Berti, S. 2021 Statistical properties of two-dimensional elastic turbulence. Phys. Rev. E 104, 035103.CrossRefGoogle ScholarPubMed
Groisman, A. & Steinberg, V. 1996 Couette–Taylor flow in a dilute polymer solution. Phys. Rev. Lett. 77, 14801483.CrossRefGoogle Scholar
Groisman, A. & Steinberg, V. 1997 Solitary vortex pairs in viscoelastic Couette flow. Phys. Rev. Lett. 78, 14601463.CrossRefGoogle Scholar
Groisman, A. & Steinberg, V. 2000 Elastic turbulence in a polymer solution flow. Nature 405, 5355.CrossRefGoogle Scholar
Groisman, A. & Steinberg, V. 2004 Elastic turbulence in curvilinear flows of polymer solutions. New J. Phys. 6, 29.CrossRefGoogle Scholar
Khomami, B. & Moreno, L.D. 1997 Stability of viscoelastic flow around periodic arrays of cylinders. Rheol. Acta 36, 367383.CrossRefGoogle Scholar
Larson, R.G., Shaqfeh, E.S.G. & Muller, S.J. 1990 A purely elastic transition in Taylor–Couette flow. J. Fluid Mech. 218, 573600.CrossRefGoogle Scholar
Liu, N.S. & 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., 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
Renardy, M., Renardy, Y., Sureshkumar, R. & Beris, A.N. 1996 Hopf-Hopf and steady-Hopf interactions in Taylor–Couette flow of an upper-convected fluid. J. Non-Newtonian Fluid Mech. 63, 131.CrossRefGoogle Scholar
Shaqfeh, E.S.G. 1996 Purely elastic instabilities in viscometric flows. Annu. Rev. Fluid Mech. 28, 129185.CrossRefGoogle Scholar
Shaqfeh, E.S.G. & Khomami, B. 2021 The Oldroyd-B fluid in elastic instabilities, turbulence and particle suspensions. J. Non-Newtonian Fluid Mech. 298, 104672.CrossRefGoogle 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.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, 602616.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
Steinberg, V. 2019 Scaling relations in elastic turbulence. Phys. Rev. Lett. 123, 234501234505.CrossRefGoogle ScholarPubMed
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
Talwar, K.K., Ganpule, H.K. & Khomami, B. 1994 A note on selection of spaces in computation of viscoelastic flows using the hp-finite element method. J. Non-Newtonian Fluid Mech. 52, 293307.CrossRefGoogle Scholar
Taylor, G.I. 1923 Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. R. Soc. Lond. A 223, 289343.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.CrossRefGoogle ScholarPubMed
Varshney, A. & Steinberg, V. 2019 Elastic Alfven waves in elastic turbulence. Nat. Commun. 10, 652.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
Yang, B. & Khomami, B. 1999 Simulations of sedimentation of a sphere in a viscoelastic fluid using molecular based constitutive models. J. Non-Newtonian Fluid Mech. 82, 429452.CrossRefGoogle Scholar
Zhu, L. & Xi, L. 2020 Inertia-driven and elastoinertial viscoelastic turbulent channel flow simulated with a hybrid pseudo-spectral/finite-difference numerical scheme. J. Non-Newtonian Fluid Mech. 286, 104410.CrossRefGoogle Scholar