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Stability of an Axisymmetric Liquid Metal Flow Driven by a Multi-Pole Rotating Magnetic Field

1
Department of Aeronautics and Astronautics, Tokyo Metropolitan University, Hino 191-0065, Japan
2
School of Mechanical Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China
*
Author to whom correspondence should be addressed.
Fluids 2019, 4(2), 77; https://doi.org/10.3390/fluids4020077
Received: 13 March 2019 / Revised: 11 April 2019 / Accepted: 18 April 2019 / Published: 21 April 2019
(This article belongs to the Special Issue Numerical Analysis of Magnetohydrodynamics Flows)
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Abstract

The stability of an electrically conducting fluid flow in a cylinder driven by a multi-pole rotating magnetic field is numerically studied. A time-averaged Lorentz force term including the electric potential is derived on the condition that the skin effect can be neglected and then it is incorporated into the Navier-Stokes equation as a body force term. The axisymmetric velocity profile of the basic flow for the case of an infinitely long cylinder depends on the number of pole-pairs and the Hartmann number. A set of linearized disturbance equations to obtain a neutral state was successfully solved using the highly simplified marker and cell (HSMAC) method together with a Newton–Raphson method. For various cases of the basic flow, depending on both the number of pole-pairs and the Hartmann number, the corresponding critical rotational Reynolds numbers for the onset of secondary flow were obtained instead of using the conventional magnetic Taylor number. The linear stability analyses reveal that the critical Reynolds number takes its minimum at a certain value of the Hartmann number. On the other hand, the velocity profile for cases of a finite length cylinder having a no-slip condition at the flat walls generates the Bödewadt boundary layers and such flows need to be computed including the non-linear terms of the Navier-Stokes equation. View Full-Text
Keywords: rotating magnetic field; magnetohydrodynamics; secondary flow; skin effect; Taylor-Görtler instability rotating magnetic field; magnetohydrodynamics; secondary flow; skin effect; Taylor-Görtler instability
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Tagawa, T.; Song, K. Stability of an Axisymmetric Liquid Metal Flow Driven by a Multi-Pole Rotating Magnetic Field. Fluids 2019, 4, 77.

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