Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-13T12:27:40.424Z Has data issue: false hasContentIssue false
  • English
  • Français

A reverse transition route from inertial to elasticity-dominated turbulence in viscoelastic Taylor–Couette flow

Published online by Cambridge University Press:  23 September 2021

Jiaxing Song Open the ORCID record for Jiaxing Song [Opens in a new window] ,
Zhen-Hua Wan Open the ORCID record for Zhen-Hua Wan [Opens in a new window] ,
Nansheng Liu Open the ORCID record for Nansheng Liu [Opens in a new window] ,
Xi-Yun Lu Open the ORCID record for Xi-Yun Lu [Opens in a new window]  and
Bamin Khomami Open the ORCID record for Bamin Khomami [Opens in a new window]
Jiaxing Song
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Zhen-Hua Wan
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
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: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A high-order transition route from inertial to elasticity-dominated turbulence (EDT) in Taylor–Couette flows of polymeric solutions has been discovered via direct numerical simulations. This novel two-step transition route is realized by enhancing the extensional viscosity and hoop stresses of the polymeric solution via increasing the maximum chain extension at a fixed polymer concentration. Specifically, in the first step inertial turbulence is stabilized to a laminar flow much like the modulated wavy vortex flow. The second step destabilizes this laminar flow state to EDT, i.e. a spatially smooth and temporally random flow with a $-3.5$ scaling law of the energy spectrum reminiscent of elastic turbulence. The flow states involved are distinctly different to those observed in the reverse transition route from inertial turbulence via a relaminarization of the flow to elasto-inertial turbulence in parallel shear flows, underscoring the importance of polymer-induced hoop stresses in realizing EDT that are absent in parallel shear flows.

JFM classification

Non-Newtonian Flows: Viscoelasticity Instability: Transition to turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 927 , 25 November 2021 , A10
Check for updates
Copyright
© The Author(s), 2021. 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

Al-Mubaiyedh, U.A., Sureshkumar, R. & Khomami, B. 1999 Influence of energetics on the stability of viscoelastic Taylor–Couette flow. Phys. Fluids 11, 3217–3226.Google Scholar
Al-Mubaiyedh, U.A., Sureshkumar, R. & Khomami, B. 2000 Linear stability of Taylor–Couette flow: influence of fluid rheology and energetics. J. Rheol. 44, 1121–1138.CrossRefGoogle Scholar
Al-Mubaiyedh, U.A., Sureshkumar, R. & Khomami, B. 2002 The effect of viscous heating on the stability of Taylor–Couette flow. J. Fluid Mech. 462, 111–132.CrossRefGoogle Scholar
Benzi, R. & Ching, E.S.C. 2018 Polymers in fluid flows. Annu. Rev. Condens. Matter Phys. 9, 163–181.Google 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
Cagney, N., Lacassagne, T. & Balabani, S. 2020 Taylor–Couette flow of polymer solutions with shear-thinning and viscoelastic rheology. J. Fluid Mech. 905, A28.Google Scholar
Choueiri, G.H., Lopez, J.M. & Hof, B. 2018 Exceeding the asymptotic limit of polymer drag reduction. Phys. Rev. Lett. 120, 124501.CrossRefGoogle ScholarPubMed
Crumeyrolle, O. & Mutabazi, I. 2002 Experimental study of inertio-elastic Couette–Taylor instability modes in dilute and semidilute polymer solutions. Phys. Fluids 14, 1681–1688.CrossRefGoogle Scholar
Denn, M.M. 2004 Fifty years of non-Newtonian fluid dynamics. AIChE J. 50, 2335–2345.CrossRefGoogle Scholar
Dong, S. 2007 Direct numerical simulation of turbulent Taylor–Couette flow. J. Fluid Mech. 587, 373–393.CrossRefGoogle Scholar
Dubief, Y., Terrapon, V.E. & Soria, J. 2013 On the mechanism of elasto-inertial turbulence. Phys. Fluids 25, 110817.Google ScholarPubMed
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, 85–113.Google Scholar
Dutcher, C.S. & Muller, S.J. 2011 Effects of weak elasticity on the stability of high Reynolds number co- and counter-rotating Taylor–Couette flows. J. Rheol. 55, 1271–1295.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, 791–812.CrossRefGoogle Scholar
Fouxon, A. & Lebedev, V. 2003 Spectra of turbulence in dilute polymer solutions. Phys. Fluids 15, 2060–2072.Google Scholar
Ghanbari, R. & Khomami, B. 2014 The onset of purely elastic and thermo-elastic instabilities in Taylor–Couette flow: influence of gap ratio and fluid thermal sensitivity. J. Non-Newtonian Fluid Mech. 208–209, 108–117.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.Google Scholar
Groisman, A. & Steinberg, V. 1998 a Elastic vs inertial instability in a polymer solution flow. Europhys. Lett. 43, 165–170.CrossRefGoogle Scholar
Groisman, A. & Steinberg, V. 1998 b Mechanism of elastic instability in Couette flow of polymer solutions: experiment. Phys. Fluids 10, 2451–2463.CrossRefGoogle Scholar
Groisman, A. & Steinberg, V. 2000 Elastic turbulence in a polymer solution flow. Nature 405, 53–55.Google Scholar
Groisman, A. & Steinberg, V. 2004 Elastic turbulence in curvilinear flows of polymer solutions. New J. Phys. 6, 29.CrossRefGoogle Scholar
Lacassagne, T., Cagney, N. & Balabani, S. 2021 Shear-thinning mediation of elasto-inertial Taylor–Couette flow. J. Fluid Mech. 915, A91.Google 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 (1), 113303.CrossRefGoogle Scholar
Larson, R.G. 1992 Instabilities in viscoelastic flows. Rheol. Acta 31, 213–263.Google Scholar
Larson, R.G. & Desai, P.S. 2015 Modeling the rheology of polymer melts and solutions. Annu. Rev. Fluid Mech. 47, 47–65.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, 573–600.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
Lee, S.H.K., Sengupta, S. & Wei, T. 1995 Effect of polymer additives on Görtler vortices in Taylor–Couette flow. J. Fluid Mech. 282, 115–129.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 ScholarPubMed
Liu, N.S. & 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.S. & Khomami, B. 2013 b Polymer-induced drag enhancement in turbulent Taylor–Couette flows: direct numerical simulations and mechanistic insight. Phys. Rev. Lett. 111, 114501.Google 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, 699–719.CrossRefGoogle Scholar
Lumley, J.L. 1969 Drag reduction by additives. Annu. Rev. Fluid Mech. 1, 367–384.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, 19–47.CrossRefGoogle Scholar
Morozov, A.N. & van Saarloos, W. 2007 An introductory essay on subcritical instabilities and the transition to turbulence in visco-elastic parallel shear flows. Phys. Rep. 447, 112–143.Google Scholar
Muller, S.J. 2008 Elastically-influenced instabilities in Taylor–Couette and other flows with curved streamlines: a review. Korea-Aust. Rheol. J 20, 117–125.Google Scholar
Pakdel, P. & McKinley, G.H. 1996 Elastic instability and curved streamlines. Phys. Rev. Lett. 2459, 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, 10557–10562.Google ScholarPubMed
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, 78–90.Google Scholar
Shaqfeh, E.S.G. 1996 Purely elastic instabilities in viscometric flows. Annu. Rev. Fluid Mech. 28, 129–185.Google Scholar
Shekar, A., McMullen, R.M., McKeon, B.J. & Graham, M.D. 2020 Self-sustained elastoinertial Tollmien–Schlichting waves. J. Fluid Mech. 897, A3, 1–16.CrossRefGoogle 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.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.-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
Steinberg, V. 2019 Scaling relations in elastic turbulence. Phys. Rev. Lett. 123, 234501–234505.Google ScholarPubMed
Steinberg, V. 2021 Elastic turbulence: an experimental view on inertialess random flow. Annu. Rev. Fluid Mech. 53, 27–58.CrossRefGoogle Scholar
Sureshkumar, R., Beris, A.N. & Avgousti, M. 1994 Non-axisymmetric subcritical bifurcations in viscoelastic Taylor–Couette flow. Proc. R. Soc. Lond. A 447, 135–153.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, 53–80.Google Scholar
Sureshkumar, R., Beris, A.N. & Avgousti, M. 1997 Direct numerical simulation of the turbulent channel flow of a polymer solution. Phys. Fluids 9, 743–755.CrossRefGoogle Scholar
Taylor, G.I. 1923 Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. R. Soc. Lond. A 223, 289.Google Scholar
Thomas, D.G., Al-Mubaiyedh, U.A., Sureshkumar, R. & Khomami, B. 2006 a Time dependent simulations of non-axisymmetric patterns in Taylor–Couette flow of dilute polymer solutions. J. Non-Newtonian Fluid Mech. 138, 111–133.Google Scholar
Thomas, D.G., Khomami, B. & Sureshkumar, R. 2006 b Pattern formation in Taylor–Couette flow of dilute polymer solutions: dynamical simulations and mechanism. Phys. Rev. Lett. 97, 054501.Google ScholarPubMed
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.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. J.M. Burgers), pp. 135–141. North Holland.Google Scholar
Virk, P.S. 1975 Drag reduction fundamentals. AIChE J. 21, 625–656.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, 47–68.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.Google Scholar