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Research Papers: Fundamental Issues and Canonical Flows

An Alternating Magnetic Field Driven Flow in a Spinning Cylindrical Container

[+] Author and Article Information
Victor Shatrov

 Forschungszentrum Dresden-Rossendorf, P.O. Box 510119, D-01314 Dresden, Germany

Gunter Gerbeth1

 Forschungszentrum Dresden-Rossendorf, P.O. Box 510119, D-01314 Dresden, Germanyg.gerbeth@fzd.de

Regina Hermann

 Leibniz Institute for Solid State and Materials Research (IFW) Dresden, Helmholtzstrasse 20, D-01069 Dresden, Germany

1

Corresponding author.

J. Fluids Eng 130(7), 071201 (Jul 16, 2008) (10 pages) doi:10.1115/1.2948374 History: Received October 24, 2007; Revised April 27, 2008; Published July 16, 2008

This paper presents a numerical analysis of the free surface liquid metal flow driven by an alternating current magnetic field in a spinning cylindrical container. The axisymmetric flow structure is analyzed for various values of the magnetohydrodynamic interaction parameter and Ekman numbers. The governing hydrodynamic equations are solved by a spectral collocation method, and the alternating magnetic field distribution is found by a boundary-integral method. The electromagnetic and hydrodynamic fields are fully coupled via the shape of the liquid free surface. It is found that the container rotation may reduce the meridional flow significantly.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Sketch of the spinning cylindrical container filled with a free-surface liquid metal

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Figure 2

The relative errors in total power for a sphere for various nondimensional frequencies ω and number of elements Nelem

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Figure 3

The relative errors in total power for a cylinder for various nondimensional frequencies ω and number of elements Nelem

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Figure 4

The distribution R(Ψ)=R(rAϕ) along a contour L(s) for nondimensional frequency ω=2×104(δ=0.01), and boundary element numbers Nelem=80 and Nelem=160, which are, however, not distinguishable with the precision of the line drawing

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Figure 5

Stream function ψ (on the left) and angular velocity Ω (on the right) isolines for interaction parameter N=2×107 and Ekman numbers E=1 (a), 0.1 (b), 1×10−2 (c), 1×10−3 (d), 1.5×10−4 (e)

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Figure 6

The meridional Reynolds number Re versus Ekman number E for various interaction parameter values

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Figure 7

The maximum of the azimuthal velocity versus Ekman number E for various interaction parameter values

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Figure 8

Stream function ψ isolines for N=2×107, E=2×10−3 and contact angles α0=3π∕4 (a) and α0=π∕4 (b)

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Figure 9

The meridional Reynolds number Re versus Ekman number E for N=2×107 and three values of the contact angle α0

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Figure 10

The maximum of the azimuthal velocity versus Ekman number E for N=2×107 and three values of the contact angle α0

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Figure 11

Stream function ψ (on the left) and angular velocity Ω (on the right) isolines for N=2×107, E=1.5×10−4. The surface of the liquid metal is covered by a thin oxide layer

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Figure 12

The meridional Reynolds number Re versus Ekman number E for various interaction parameter values. The surface of the liquid metal is covered by a thin oxide layer. The dashed lines correspond to the free-slip case of Fig. 6.

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Figure 13

The maximum of the azimuthal velocity versus Ekman number E for various interaction parameter values. The surface of the liquid metal is covered by a thin oxide layer. The dashed lines correspond to the free-slip case of Fig. 7.

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