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Shear-dependant toroidal vortex flow

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Abstract

Pseudoplastic circular Couette flow in annulus is investigated. The flow viscosity is dependent on the shear rate, which directly affects the conservation equations that are solved in the present study by the spectral method in the present study. The pseudoplastic model adopted here is shown to be a suitable representative of nonlinear fluids. Unlike the previous studies, where only the square of shear rate term in the viscosity expression was considered to ease the numerical manipulations, in the present study takes the term containing the quadratic power into account. The curved streamlines of the circular Couette flow can cause a centrifugal instability leading to toroidal vortices, known as Taylor vortices. It is further found that the critical Taylor number becomes lower as the pseudoplastic effect increases. Comparison with existing measurements on pseudoplastic circular Couette flow results in good agreement.

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References

  1. S. Chandrasekhar, Hydrodynamics and Hydromagnetic Stability, Dover, New York (1961).

    Google Scholar 

  2. P. G. Drazin, W.H. Reid, Hydrodynamic Stability, second ed., Cambridge University Press, Cambridge, England (2004).

    Book  MATH  Google Scholar 

  3. P. Chossat and G. Iooss, The Couette-Taylor Problem, Springer-Verlag, (1994).

  4. H. Schlichting, Boundary Layer Theory, seventh ed., Springer, Berlin (1979).

    MATH  Google Scholar 

  5. G. I. Taylor, Stability of a viscous liquid contained between two rotating cylinders, Philosophical Transactions of the Royal Society of London. Series A, 223 (1923) 289–343.

    Article  MATH  Google Scholar 

  6. R. J. Donnelly, Taylor-Couette flow: the early days, Phys. Today, 44(11) (1991) 32–39.

    Article  Google Scholar 

  7. R. Tagg, The Couette-Taylor problem, Nonlinear Science Today, 4 (1994) 2–25.

    Google Scholar 

  8. M. Brenner and H. Stone, Modern classical physics through the work of G. I. Taylor, Phys. Today, 5 (2000) 30–35.

    Article  Google Scholar 

  9. C. Hoffmann, S Altmeyer, A Pinter and M Lucke, Transitions between Taylor vortices and spirals via wavy Taylor vortices and wavy spirals. New J. Physics, 11 (2009) 1–24.

    Google Scholar 

  10. GR. Sell, C. Foias and R. Temam, Turbulence in Fluid Flows: A Dynamical Systems Approach, Springer: New York (1993).

    Book  MATH  Google Scholar 

  11. P. Berge, Y. Pomeau and C. Vidal, Order within Chaos, Hermann and John Wiley & Sons: Paris (1984).

    MATH  Google Scholar 

  12. H. Kuhlmann, Model for Taylor Couette flow, Phys. Rev. A 32(3) (1985) 1703–1707.

    Article  Google Scholar 

  13. H. Kuhlmann, D. Roth and M. Lucke, Taylor flow and harmonic modulation of the driving force, Physical Review A, 39(2) (1988) 745–762.

    Article  Google Scholar 

  14. H. R. Berger, Mode Analysis of Taylor-Couette Flow in Finite Gaps, Z. Angew. Math. Mech., 79(2) (1999) 91–96.

    Article  MathSciNet  MATH  Google Scholar 

  15. N. Ashrafi, Stability analysis of shear-thinning flow between rotating cylinders, Applied Mathematical Modelling, 35 (2011) 4407–4423.

    Article  MathSciNet  MATH  Google Scholar 

  16. Z. Li and R. Khayat, A non-linear dynamical system approach to finite amplitude Taylor-Vortex flow of shearthinning fluids, Int. J. Numer. Meth. Fluids, 45 (2004) 321–40.

    Article  MathSciNet  MATH  Google Scholar 

  17. R. Khayat, Low-dimensional approach to nonlinear overstability of purely elastic Taylor-vortex flow, Physical Review Letters, 78(26) (1997) 4918–4921.

    Article  Google Scholar 

  18. R. Khayat, Finite-amplitude Taylor-vortex flow of viscoelastic fluids, Journal of Fluid Mechanics, 400 (1999) 33–58.

    Article  MathSciNet  MATH  Google Scholar 

  19. S. J. Muller, E. Shaqfeh and R. G. Larson, Experimental study of the onset of oscillatory instability in viscoelastic Taylor-Couette flow, Journal of Non-Newtonian Fluid Mechanics, 46 (1993) 315–330.

    Article  Google Scholar 

  20. R. G. Larson, Instabilities in viscoelastic flows, Rheol. Acta 31 (1992) 213–263.

    Article  Google Scholar 

  21. R. G. Larson, E. Shaqfeh and S. J. Muller, A purely elastic instability in Taylor-Couette flow, Journal of Fluid Mechanics, 218 (1990) 573–600.

    Article  MathSciNet  MATH  Google Scholar 

  22. J. Dusting and S. Balbani, Mixing in a Taylor-Couette reactor in the non-wavy regime, Chem. Eng. Sci. 64 (2009) 3103–3111.

    Article  Google Scholar 

  23. J. A. Yorke and E. D. Yorke Hydrodynamic Instabilities and the Transition to turbulence, edited by H. L. Swinney and J.P. Gollub, Springer-Verlag, Berlin (1981).

    Google Scholar 

  24. H. Yahata, Temporal development of the Taylor vortices in a rotating field. 1, Prog. Theor. Phys., 59 (1978) 1755.

    Article  Google Scholar 

  25. R. B. Bird, R. C. Armstrong and O. Hassager, Dynamics of Polymeric Liquids (2nd edn), vol. 1. Wiley: New York (1987).

    Google Scholar 

  26. W. T. Ashurst and W. G. Hoover, Dense-fluid shear viscosity via nonequilibrium molecular dynamics, Physical Review A, 11(2) (1975) 658–678.

    Article  Google Scholar 

  27. J. J. Erpenbeck, Non-equilibrium molecular dynamics calculations of the shear viscosity of hard spheres, Physica A, 118(1) (1983) 144–156.

    Article  MathSciNet  Google Scholar 

  28. D. M. Heyes, Shear-thinning of the Lennard-Jones fluid by molecular dynamics, Physica A, 133(3) (1985) 473–496.

    Article  Google Scholar 

  29. K. Khellaf and G. Lauriat, Numerical study of heat transfer in a non-Newtonian Carreau-fluid between rotating concentric vertical cylinders, J. Non-Newtonian Fluid Mech., 89 (2000) 45–61.

    Article  MATH  Google Scholar 

  30. J. P. Pascal and H. Rasmussen, Stability of power law fluid flow between rotating cylinders, Dyn. Syst. 10 (1995) 65–93.

    Article  MathSciNet  MATH  Google Scholar 

  31. N. Ashrafi and H. Karimi Haghighi, Effect of gap width on stability of non-Newtonian Taylor-Couette flow, Z. Angew. Math. Mech., 92(5) (2012) 393–408.

    Article  MathSciNet  MATH  Google Scholar 

  32. O. Crumeryrolle, I. Mutabazi and M. Grisel, Experimental study of inertioelastic Couette-Taylor instability modes in dilute and semidilute polymer solutions. Physics of Fluids, 14(5) (2002) 1681–1688.

    Article  Google Scholar 

  33. O. Coronado-Matutti, P. R. Souza Mendes and M. S. Carvalho, Instability of Inelastic Shear-thinning Liquids in a Couette Flow between Concentric Cylinders, J. Fluid Eng., 126 (2004) 385–390.

    Article  Google Scholar 

  34. S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering. Rerseus Publishing (1994).

    Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Payame Noor University, 19395-3697, Tehran, Iran

    Nariman Ashrafi Khorasani & Habib Karimi Haghighi

Authors
  1. Nariman Ashrafi Khorasani
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  2. Habib Karimi Haghighi
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Corresponding author

Correspondence to Nariman Ashrafi Khorasani.

Additional information

Recommended by Associate Editor Dongshin Shin

Nariman Ashrafi holds a Ph.D in Mechanical Engineering from University of Western Ontario in Canada. His research interests include non-Newtonian fluid dynamics, stability, rheology. He has so far published more than 20 papers in reputable international journals as well as several conference proceedings. He has held several positions in research and industry e.g. postdoctoral fellowship at the University of Wales (UK), researcher at Shell Research Center (UK), faculty member at Georgia Southern University (USA), University of Natal (South Africa) and Islamic Azad university (Iran).

Habib Karimi Haghighi holds an M.Sc in Mechanical Engineering from Science and Research Branch, IAU, Tehran, Iran. His research interests include nonlinear dynamics, hydrodynamic instability and non-Newtonian flow.

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Khorasani, N.A., Haghighi, H.K. Shear-dependant toroidal vortex flow. J Mech Sci Technol 27, 85–94 (2013). https://doi.org/10.1007/s12206-012-1222-9

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  • DOI: https://doi.org/10.1007/s12206-012-1222-9

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