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Physics of Fluids / Volume 24 / Issue 1 / ARTICLES / Instability and Transition

Phys. Fluids 24, 014101 (2012); http://dx.doi.org/10.1063/1.3673608 (9 pages)

Three-dimensional swirling flows in a tall cylinder driven by a rotating endwall

J. M. Lopez

School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287, USA and Department of Mathematics, Kyungpook National University, Daegu 702-701, South Korea

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(Received 2 September 2011; accepted 23 November 2011; published online 4 January 2012)

The onset and nonlinear dynamics of swirling flows in relatively tall cylinders driven by the rotation of an endwall are studied numerically. These flows are distinguished from the more widely studied swirling flows in shorter cylinders; the instability in the taller cylinders is direct to three-dimensional flows rather than to unsteady axisymmetric flows. The simulations are in very good agreement with recent experiments in terms of the critical Reynolds number, frequency, and azimuthal wavenumber of the flows, but there is disagreement in the interpretation of these flows. We show that these flows are indeed rotating waves and that they have the same vorticity distributions as the flows measured using particle image velocimetry in the experiments. Identifying these as rotating waves gives a direct connection with prior linear stability analysis and the three-dimensional flows found in shorter cylinders as secondary instabilities leading to modulated rotating waves.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. GOVERNING EQUATIONS AND NUMERICAL METHODS
  3. RESULTS
  4. CONCLUSIONS

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KEYWORDS and PACS

Keywords

boundary layers, confined flow, flow instability, flow simulation, numerical analysis, vortices, waves

PACS

  • 47.32.Ef

    Rotating and swirling flows

  • 47.32.cd

    Vortex stability and breakdown

  • 47.35.-i

    Hydrodynamic waves

  • 47.20.Lz

    Secondary instabilities

  • 47.20.Ky

    Nonlinearity, bifurcation, and symmetry breaking

  • 02.60.Cb

    Numerical simulation; solution of equations

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3673608

PUBLICATION DATA

ISSN

1070-6631 (print)  
1089-7666 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    F. Marques and J. M. Lopez, “Precessing vortex breakdown mode in an enclosed cylinder flow,” Phys. Fluids 13, 1679 (2001)PHFLE6000013000006001679000001.

    T. T. Lim and Y. D. Cui, “On the generation of a spiral-type vortex breakdown in an enclosed cylindrical container,” Phys. Fluids 17, 044105 (2005)PHFLE6000017000004044105000001.

    J. N. Sorensen, A. Y. Gelfgat, I. V. Naumov, and R. F. Mikkelsen, “Experimental and numerical results on three-dimensional instabilities in a rotating disk-tall cylinder flow,” Phys. Fluids 21, 054102 (2009)PHFLE6000021000005054102000001.


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