Magnetohydrodynamic stability in the electromagnetic levitation of horizontal molten-metal sheets

Abstract

High-frequency electromagnetic (EM) fields are investigated for the levitation of thin horizontal sheets of liquid metal. A magnetic configuration is analyzed in which inductance stabilization provides global stability and magnetic flux compression provides local stability. Stability analysis indicates that frequencies greater than about 24 kHz are desirable to stably levitate 6 mm thick steel. For stability in systems without active feedback, a conducting screen is required below the metal, with a gap between the screen and the molten metal of no more than twice the metal thickness. Experiments in which 10 kHz EM fields were used to statically levitate sheets of molten tin indicate that dominant magnetohydrodynamic instabilities are of the Rayleigh–Taylor type and correspond to theory.

Instability of a plane conducting free surface submitted to an alternating magnetic field

“…Hull, Wiencek & Roe (1989) have studied experimentally electromagnetic levitation of a liquid metal layer, and the Rayleigh-Taylor instability. Our results are at least consistent with their finding that the metal layer is most unstable when the wavenumber vector is perpendicular to the applied field.…”

Stability of an electromagnetically levitated spherical sample in a set of coaxial circular loops

“…Consequently, the perturbation of the inner field and the corresponding induced field outside the sphere can be obtained straightforwardly by replacing the coefficients I m by J m l in the corresponding solutions (8,9) for the base field. Although the solution of the perturbed field obtained in such a way satisfies (6,7) and the boundary conditions, it turns out that the induced field outside does not satisfy the Coulomb gauge unless the problem is axisymmetric, i.e., the offset is along the symmetry axis. Thus, although the Laplace equation is satisfied we formally have…”

“…The perturbation of the inner field A 1 is governed by the same Eqs. (6,7) as the base field with the difference that now the external field is given by A e 1 (r). Consequently, the perturbation of the inner field and the corresponding induced field outside the sphere can be obtained straightforwardly by replacing the coefficients I m by J m l in the corresponding solutions (8,9) for the base field.…”

“…Otherwise, the equilibrium will be statically unstable and the solid sample will fall out of the coil or touch it when it is slightly perturbed. Similarly, a molten sample may leak out of the coil in the result of surface folding and deformation [6]. The static stability alone may also be insufficient for a successful levitation because sometimes the sample exhibits overstability.…”

The stability of an interface between viscous fluids subjected to a high-frequency magnetic field and consequences for electromagnetic casting

“…The issue of stability in the levitation of a thin metal sheet by a high-frequency (kHz) magnetic field was studied both experimentally and analytically by Hull, Wiencek & Rote (1989). There the instability is primarily of Rayleigh-Taylor type in the presence of EM fields.…”