Experimental and theoretical studies of the motion generated by a two-frequency magnetic field at the free surface of a
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8/28/03
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Experimental and Theoretical Studies of the Motion Generated by a Two-Frequency Magnetic Field at the Free Surface of a Gallium Pool D. PERRIER, Y. FAUTRELLE, and J. ETAY The behavior of a free surface of liquid metal in the presence of a periodic magnetic field pulsating at two frequencies (a midrange frequency f1 and a low frequency f2, referred to as the modulation frequency) has been investigated. An expression for the forces induced in an electroconductive material by such a field is established for f2 f1, and a heuristic model is developed to describe the free surface axisymmetric deformations of an inviscid liquid metal submitted to modulated electromagnetic forces. The electromagnetic forces generate standing waves with an oscillation frequency of f2 or 2f2. Experiments performed on a cylindrical gallium pool show that the observed surface waves are concentric. The maximum amplitude of the surface oscillations and their frequency are measured by means of a contact probe and analyzed with respect to the modulation frequency f2. The oscillation amplitude exhibits resonance peaks for values of f2 corresponding to the eigenfrequencies of the free surface modes. The various free surface oscillation modes are identified. Depending on the value of f2, the free surface oscillates at the frequency f2 or at the frequency 2f2. The experimental features of the free surface oscillations agree qualitatively with those predicted by the proposed heuristic model.
I. INTRODUCTION
WHEN a liquid metal is submitted to an alternating magnetic field, electromagnetic forces are created in the metal due to the interaction of induced electric currents and the magnetic field. According to the value of the frequency f of the magnetic field, the electromagnetic forces have various effects on motion in the bulk and at the free surface of the liquid metal.[1] For single-phase applications, the frequency is expressed in the form of a dimensionless number referred to as the shield number R, related to the electromagnetic skin depth by L Rv msvL2 2 ( )2 d
[1]
where is the magnetic permeability, the electrical conductivity, L the radius of the pool, and the angular frequency defined by 2f. In the frequency range extending from 50 Hz to a few hundred kHz (R 1), the direct component of the electromagnetic forces is responsible for a significant bulk fluid flow.[1–7] This is the electromagnetic stirring often used in induction furnaces. Given the inertia of the fluid, the alternating component of the electromagnetic forces has no significant effect. This phenomenon has been studied by many authors.[1–7] In typical applications, the liquid metal flow is turbulent, with two mean vertices in a half meridian plane in an induction furnace–type geometry. For a fixed coil current, the velocity strongly depends on the frequency or, more precisely, the shield number R.[6] As R increases, the skin
D. PERRIER, Postdoctor, CNRS-EPM, Y. FAUTRELLE, Professor, INPG, and J. ETAY, Senior Scientist, CNRS
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