The effect of AC magnetic fields on liquid-metal free surfaces in industrialMHD.
Spragg, K. J. (2009). The effect of AC magnetic fields on liquid-metal free surfaces in industrialMHD. (Thesis, Doctor of Philosophy (PhD)). The University of Waikato, Hamilton, New Zealand. Retrieved from https://hdl.handle.net/10289/3517
Permanent Research Commons link: https://hdl.handle.net/10289/3517
In this thesis we investigate free-surface instabilities which occur in variousindustrial processes involving liquid metal. Specifically, we examine a numberof simple problems with a view to developing a plausible theoretical descriptionbased on MHD. Of particular interest is the behaviour of the free surface of apool of liquid metal when it is submitted to an alternating magnetic field. The first problem we examine considers the effect of a low-frequency mag-netic field on a pool of liquid metal. An initially circular pool is deformed intoradially oscillating starfish modes at certain critical magnetic field strengths.We study these azimuthal modes theoretically by investigating the behaviourof an isolated mode. We also consider the influence of geometry in our studiesof a related problem invloving a rectangular strip of liquid metal. At certaincritical magnetic field strengths, an elongated pool is deformed into transversemodes. Aside from complicated mode coupling, the behaviour of these trans-verse modes is similar to the starfish . Both the starfish and transversemodes are caused by a Mathieu-type subharmonic instability. We next consider the effect of a medium-frequency magnetic field on aninitially circular pool of liquid metal. Experimentally we study the effect ofa vertical alternating medium-frequency magnetic field on an initially circularpool. We observe two types of behaviour: slow radial oscillation of the poolperimeter and rotation of the pool about its centre. The physics of this problemare significantly more complicated than the starfish and strip problems.Accordingly a description in terms of the previous theory is not possible. The final problem we consider is the effect of a high-frequency magneticfield the surface of a conductor. Using a phase-field approach we consider twosimple problems: the first is to calculate the rest shape of an infinite stripof liquid resting on a substrate in a vertical gravitational field; the second isto calculate the equilibrium shape of the cross-section of a column of a liquidconductor submitted to a high-frequency magnetic field whose field lines areparallel far from the conductor. Our numeric solutions compare well withpreviously known analytic solutions.
The University of Waikato
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