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SCIENTIA SINICA Physica, Mechanica & Astronomica, Volume 48 , Issue 9 : 094704(2018) https://doi.org/10.1360/SSPMA2018-00157

Direct numerical simulation on transition of viscoelasticTaylor-Couette flow

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  • ReceivedMay 1, 2018
  • AcceptedJun 21, 2018
  • PublishedAug 10, 2018
PACS numbers

Abstract


Funding

国家自然科学基金(11472268,91752110)

科学挑战专题(TZ2016001)


References

[1] Rubin H, Elata C. Stability of Couette flow of dilute polymer solutions. Phys Fluids, 1966, 91929-1933 CrossRef ADS Google Scholar

[2] Denn M M, Roisman J J. Rotational stability and measurement of normal stress functions in dilute polymer solutions. AIChE J, 1969, 15454-459 CrossRef Google Scholar

[3] Sun Z S, Denn M M. Stability of rotational Couette flow of polymer solutions. AIChE J, 1972, 181010-1015 CrossRef Google Scholar

[4] Hayes J W, Hutton J F. The effect of very dilute polymer solutions on the formation of Taylor vortices. Comparison of theory with experiment. Prog Heat Mass Transfer, 1972, 5: 195–209. Google Scholar

[5] Taylor G I. Stability of a viscous liquid contained between two rotating cylinders. Philos Trans R Soc A-Math Phys Eng Sci, 1923, 223289-343 CrossRef ADS Google Scholar

[6] Coles D. Transition in circular Couette flow. J Fluid Mech, 1965, 21385-425 CrossRef ADS Google Scholar

[7] Gollub J P, Swinney H L. Onset of turbulence in a rotating fluid. Phys Rev Lett, 1975, 35927-930 CrossRef ADS Google Scholar

[8] Andereck C D, Liu S S, Swinney H L. Flow regimes in a circular Couette system with independently rotating cylinders. J Fluid Mech, 1986, 164155-183 CrossRef ADS Google Scholar

[9] Larson R G, Shaqfeh E S G, Muller S J. A purely elastic instability in Taylor-Couette flow. J Fluid Mech, 1990, 218573-600 CrossRef ADS Google Scholar

[10] Groisman A, Steinberg V. Couette-Taylor flow in a dilute polymer solution. Phys Rev Lett, 1996, 771480-1483 CrossRef PubMed ADS Google Scholar

[11] Groisman A, Steinberg V. Mechanism of elastic instability in Couette flow of polymer solutions: Experiment. Phys Fluids, 1998, 102451-2463 CrossRef ADS Google Scholar

[12] Steinberg V, Groisman A. Elastic versus inertial instability in Couette-Taylor flow of a polymer solution: Review. Philos Mag B, 1998, 78253-263 CrossRef Google Scholar

[13] Thomas D G, Sureshkumar R, Khomami B. Pattern formation in Taylor-Couette flow of dilute polymer solutions: Dynamical simulations and mechanism. Phys Rev Lett, 2006, 97054501 CrossRef PubMed ADS Google Scholar

[14] Thomas D G, Khomami B, Sureshkumar R. Nonlinear dynamics of viscoelastic Taylor-Couette flow: Effect of elasticity on pattern selection, molecular conformation and drag. J Fluid Mech, 2009, 620353-382 CrossRef ADS Google Scholar

[15] Dutcher C S, Muller S J. The effects of drag reducing polymers on flow stability insights from the Taylor-Couette problem. Korea-Australia Rheol J, 2009, 21: 213–223. Google Scholar

[16] Dutcher C S, Muller S J. Effects of weak elasticity on the stability of high Reynolds number co- and counter-rotating Taylor-Couette flows. J Rheology, 2011, 551271-1295 CrossRef ADS Google Scholar

[17] Dutcher C S, Muller S J. Effects of moderate elasticity on the stability of co- and counter-rotating Taylor-Couette flows. J Rheology, 2013, 57791-812 CrossRef ADS Google Scholar

[18] Huisman S G, van der Veen R C A, Sun C, et al. Multiple states in highly turbulent Taylor-Couette flow. Nat Commun, 2014, 53820 CrossRef PubMed ADS arXiv Google Scholar

[19] Groisman A, Steinberg V. Elastic turbulence in curvilinear flows of polymer solutions. New J Phys, 2004, 629 CrossRef ADS Google Scholar

  • Figure 1

    (Color online) Paths in parameter space. (a) Three kinds of transition paths; (b) three kinds of paths, which have same departures and destinations.

  • Figure 2

    (Color online) Space-time plots of radial velocity ur. (a) Re=56, We=10, transition from AZI to regular RSW state; (b) Re=56, We=10, transition from regular RSW to strong-weak RSW state. Data sampled along an axial line at r=(Ri+Ro)/2,θ=π.

  • Figure 3

    (Color online) Space-time plots of radial velocity ur. (a) Re=86, We=10, transition from strong-weak RSW to regular RSW state; (b) Re=254, We=10, regular RSW state. Data sampled along an axial line at r=(Ri+Ro)/2,θ=π.

  • Figure 4

    (Color online) Space-time plots of radial velocity ur. (a) Re=86, We=10, transition from AZI to regular RSW state; (b) Re=50, We=25, transition from regular RSW to axisymmetric OS state; (c) Re=74, We=37, transition from axisymmetric OS to non-axisymmetric OS state; (d) Re=98, We=49, transition from non-axisymmetric OS to traveling-wave-like state. Data sampled along an axial line at r=(Ri+Ro)/2,θ=π.

  • Figure 5

    (Color online) PSDs of radial velocity ur. (a) Re=50, We=25, axisymmetric OS state; (b) Re=74, We=37, non-axisymmetric OS state; (c) Re=98, We=49, traveling-wave-like state.

  • Figure 6

    (Color online) Space-time plots of radial velocity ur. (a) Re=20, We=16, transition from AZI to regular RSW state; (b) Re=20, We=28, transition from regular RSW to axisymmetric OS state;(c) Re=20, We=76, transition from axisymmetric OS to a state of intermittent solitary wave (ISW), (d) enlarged view of ISW state. Data sampled along an axial line at r=(Ri+Ro)/2,θ=π.

  • Figure 7

    (Color online) PSDs of radial velocity ur. (a) Re=20, We=28, axisymmetric OS state; (b) Re=20, We=73, axisymmetric OS state;(c) Re=20, We=76, ISW state.

  • Figure 8

    (Color online) Space-time plots of radial velocity ur at parameters (Re,We)=(50,25) after approached through different paths. (a) Path1, regular RSW state; (b) path2, axisymmetric OS state; (c) path3, axisymmetric OS state. Data sampled along an axial line at r=(Ri+Ro)/2,θ=π.

  • Figure 9

    (Color online) PSDs of radial velocity ur of different states at parameters (Re,We)=(50,25) approached through different paths. (a) Near the inner wall; (b) core region; (c) near the outer wall.

  • Figure 10

    (Color online) Space-time plots of radial velocity ur at parameters (Re,We)=(62,31) after approached through different paths. (a) Path1, non-axisymmetric OS state; (b) path2, axisymmetric OS state; (c) path3, axisymmetric OS state. Data sampled along an axial line at r=(Ri+Ro)/2,θ=π.

  • Figure 11

    (Color online) PSDs of radial velocity ur of different states at parameters (Re,We)=(62,31) approached through different paths.(a) Near the inner wall; (b) core region; (c) near the outer wall.

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