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

Abstract

This paper considers the stability of a horizontal liquid-metal free surface in the presence of a horizontal alternating magnetic field. A weak formulation is used to derive a generalized Mathieu-Hill equation for the evolution of surface perturbations. Previous studies which rely on time-averaging the electromagnetic force over one field cycle have predicted a generally weak instability, but we find much larger growth rates near the resonances, where the surface wave frequency is an integral multiple of the field frequency. The method can be extended to include viscous and ohmic damping; the former has little effect, while the latter damps all waves except those whose frequency is close to the field frequency. Growth rates can be closely approximated by simple algebraic formulae, as can the critical magnetic field strength for the onset of instability.

Inhibiting bulging deformation of liquid metal free surface by magnetic pressure

“…As depicted, the magnetic pressure of B = 0.0287 T can induce slight fluctuations in the free surface with amplitude of 0.8 mm. This phenomenon was also found in the study of Fautrelle and Sneyd [28], Mchale and Melcher [11] and Suda et al [12], where the reason is considered as synthetic action of the electromagnetic force uneven distribution and thermal disturbance. When the jet hits the free surface, the fluctuation with maximum amplitude of 4 mm is violent and much larger than the fluctuation caused by magnetic pressure.…”

The H-trough: a model for liquid metal electric current limiters

“…However, modelling of this behaviour is beyond the scope of the present work. Finally, we note that the three-dimensional instabilities, which prevented a continuation of the experimental curves in figure 8(a) to higher α, represent an interesting hydrodynamic phenomenon, closely related to the interface instabilities studied by Fautrelle & Sneyd (1998) as well as to pinch-off effects known from ordinary hydrodynamics (Eggers 1993(Eggers , 1997. A natural first step towards the understanding of such instabilities would be to consider a single infinitely long vertical liquid-metal sheet carrying a prescribed electric current.…”

Generation of liquid metal structures of high aspect ratio by application of an ac magnetic field

“…Another interesting point for further investigation is the question of the drop stability, as instabilities might be responsible for the unwanted wavy pattern observed in the real process. Such instabilities are also known to develop when a ac magnetic field is applied to a free surface, [8][9][10] and the condition of their appearance in the configuration studied here could be analyzed by modifying the numerical model developed in this paper.…”