Skip to main content
SpringerLink
Log in

An asymmetrical periodic vortical structures and appearance of the self induced pressure gradient in the modified Taylor flow

  • Published:
Theoretical and Computational Fluid Dynamics Aims and scope Submit manuscript

Abstract

An incompressible liquid flow in the gap between two coaxial cylinders, such that the inner rotating (wavy) cylinder has a periodically varying radius along the axial direction while the outer stationary cylinder has a constant radius, is studied experimentally and theoretically. Basic attention is focused on the symmetry-breaking phenomenon of the vortex flow arising from the rotation of the inner wavy cylinder. It is found that the symmetry-breaking phenomenon of the vortical flow structures in this geometry is accompanied by the occurrence of a self-induced axial pressure gradient. A theoretical formulation of the problem of periodic vortical flow prevailing in such a geometry having large axial length is presented. The comparison between the computed and the experimental results is presented and the underlying phenomena are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Chandrasekhar, S.: Hydrodynamic and Hydromagnetic Stability. NY, Dover Publ. (1981)

  2. Di Prima, R.C., Swinney, H.L. (Eds.): Instabilities and Transitions in flow between concentric rotating cylinders. Hydrodynamic instabilities and the transition to turbulence, 45, Springer Verlag (1985)

  3. Drozdov, S.M.: A Numerical Investigation of a Modified Couette–Taylor Apparatus with Application to Industrial Mixing. Theoret. Comput. Fluid Dynamics 16(1), 17–28 (2002)

  4. Drozdov, S.M.: Rotor mixer for liquid media. Patent of Russia, 2001-120445 (IPC-B01F 7/00) (2002)

  5. Iooss, G., Chossat, P.: The Couette–Taylor Problem. Applied Maths Sciences, v. 102, Springer Verlag (1994)

  6. Kudrolli, A., Gollub, J.P.: Patterns and spatiotemporal chaos in parametrically forced surface waves: a systematic survey at large aspect ratios. Physica D 97, 133–154 (1996)

  7. Nakabayashi, K.: Transitions of Taylor Görtler vortex flow in spherical Couette flow. J. Fluid Mech. 132, 209–230 (1983)

  8. Nakabayashi, K., Tsuchida, Y.: Modulated and unmodulated traveling azimuthal waves on the toroidal vortices in a spherical Couette system. J. Fluid Mech. 195, 495–522 (1988)

  9. Nakabayashi, K., Tsuchida, Y.: Spectral study of the laminar-turbulent transition in spherical Couette flow. J. Fluid Mech. 194, 101–132 (1988)

  10. Noui-Mehidi, M.N., Wimmer, M.: Free surface effects on the flow between conical cylinders. Acta Mech. 135, 13–25 (1999)

  11. Rafique, M.: Etude de l’ecoulement entre deux cylinders coaxiaux a entrefer constant at a entrefer ondule par la surface du cylinder interieur tournant. D. Sc. Thesis, Institut National Polytechnique de Lorraine, Nancy, France (1999)

  12. Rafique, M., Skali-Lami, S.: A study of steady state flow in modified Taylor–Couette system: Inner rotating wavy cylinder coaxial with a smooth stationary outer cylinder. 11th Int. Taylor–Couette Workshop, Bremen, Germany, pp. 105–106 (1999)

  13. Stepless, A.E., Alexande, J.S.: The dynamics of spatially modulated Taylor–Couette flow. 12th Int. Couette–Taylor Workshop, Northwestern Uni., Evanston, IL, USA (2001)

  14. Stockert, M., Lueptow, R.M.: Velocity field in Couette–Taylor flow with axial flow. 10th Int. Couette–Taylor Workshop, Normand, C., Wesfreid, J.E. (eds.), 147–148, Paris, France (1997)

  15. Signoret, Iooss: J. Méca. Theor. Appl. 7, 545–572 (1988)

  16. Taylor, G.I.: Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. R. Soc. London, Series A 223, 289–343 (1923)

  17. Wimmer, M.: Experiments on a viscous fluid flow between concentric rotating spheres. J. Fluid Mech. 78(1), 317–335 (1976)

  18. Wimmer, M.: An experimental investigation of Taylor vortex flow between conical cylinders. J. Fluid Mech. 292, 205–227 (1995)

  19. Wereley, S.T., Lueptow, R.M.: Spatio-temporal character of non-wavy and wavy Taylor–Couette flow. J. Fluid Mech. 364, 59–80 (1998)

Download references

Author information

Authors and Affiliations

  1. TsAGI, Department-8, Zhukovsky str. 1, Zhukovsky, 140180, Russia

    S. Drozdov

  2. INPL, France

    M. Rafique & S. Skali-Lami

Authors
  1. S. Drozdov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Rafique
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Skali-Lami
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Drozdov.

Additional information

Communicated by

H.J.S. Fernando

Rights and permissions

Reprints and permissions

About this article

Cite this article

Drozdov, S., Rafique, M. & Skali-Lami, S. An asymmetrical periodic vortical structures and appearance of the self induced pressure gradient in the modified Taylor flow. Theor. Comput. Fluid Dyn. 18, 137–150 (2004). https://doi.org/10.1007/s00162-004-0137-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00162-004-0137-1

Keywords

Search

Navigation