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Physics of Fluids / Volume 24 / Issue 1 / LETTERS

Phys. Fluids 24, 011704 (2012); http://dx.doi.org/10.1063/1.3675893 (7 pages)

An analogy of Taylor’s instability criterion in Couette and rotating-magnetic-field-driven flows

Marius Ungarish

Department of Computer Science, Technion, Haifa 32000, Israel

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(Received 29 August 2011; accepted 6 December 2011; published online 11 January 2012)

The classical stability solution of Taylor for the Couette flow between a rotating inner cylinder and a stationary outer cylinder is used to model the “critical magnetic Taylor number,” Tacr, in a flow of a liquid metal driven by a rotating magnetic field (RMF) in a cylindrical cavity characterized by the parameter H = height/radius. (The magnetic Taylor number is defined as Ta = σωBo2Ro4/(2ρν2), where σ,ν, and ρ are the electrical conductivity, kinematic viscosity, and density of the liquid; ω and Bo are the magnetic field frequency and induction; Ro is the radius of the cavity; the cr superscript means “critical”) In typical conditions, the RMF flow develops a solid-body-rotating core analogous to the inner rotating cylinder, embedded in a layer in which the swirl decays to zero at the outer wall. Using small-Ekman-number approximations for the core and gap flow, the analogy yields an insightful expression for Tacr. In particular, the model indicates that Tacr depends strongly on the parameter H. Comparisons of the present theoretical results with available realistic data show a good qualitative agreement and plausible quantitative agreement. The model was improved by an empirical adjustment of a coefficient and can be used as simple approximate prediction tool for Tacr in a quite wide range of cylindrical cavity configurations.

© 2012 American Institute of Physics

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KEYWORDS and PACS

Keywords

confined flow, Couette flow, electrohydrodynamics, flow instability, liquid metals, magnetohydrodynamics, swirling flow, viscosity

PACS

  • 47.15.Fe

    Stability of laminar flows

  • 47.15.Rq

    Laminar flows in cavities, channels, ducts, and conduits

  • 47.32.Ef

    Rotating and swirling flows

  • 47.65.-d

    Magnetohydrodynamics and electrohydrodynamics

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3675893

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.
    P. A. Nikrityuk, M. Ungarish, K. Eckert, and R. Grundmann, “Spin-up of a liquid metal flow driven by a rotating magnetic field in a finite cylinder: A numerical and an analytical study,” Phys. Fluids 17, 067101 (2005)PHFLE6000017000006067101000001.

    L. M. Witkowski, J. S. Walker, and P. Marty, “Nonaxisymmetric flow in a finite-length cylinder with a rotating magnetic field,” Phys. Fluids 11(7), 1821 (1999)PHFLE6000011000007001821000001.


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