On the surface stability of liquid conductors in electromagnetic shaping

Abstract

In a process involving electromagnetic shaping, a high-frequency electromagnetic field is used to deform a liquid conductor into a required shape. This is particularly relevant to processes such as levitation melting. In this paper the stability of such configurations are investigated. The second variation of an appropriate energy functional is derived whose minimum states correspond to stable configurations, thus providing a stability criterion. As an example, this is applied to the shaping of a levitated cylinder of circular cross-section and to an almost spherical axisymmetric shape. In both cases we find that these shapes are unstable. We then consider enclosing the entire shaping device in a metal shield, thus preventing the escape of the magnetic field. It is then shown that in general the shield has a stabilizing effect, whose exact nature depends on the topology of the liquid shape and on the field structure on its surface. This differing behaviour is discussed for two-dimensional spherical and toroidal shapes.

Shape and topology optimal design problems in electromagnetic casting

“…Brancher and Séro-Guillaume (1985) considered a uniform non-vanishing magnetic field at infinity. Felici (1995) considered liquid metal shapes that are not simply connected (toroidal shapes).…”

“…The reader can also find more information about physical analysis and simplifying assumptions in the case of the forward EMC problem in the following papers (Mestel, 1982; Brancher et al , 1983; Brancher and Séro-Guillaume, 1985; Etay et al , 1988; Séro-Guillaume et al , 1992; Coulaud, 1998). In the case of the forward EML problem we mention the papers (Sneyd and Moffatt, 1982; Mestel, 1982; Gagnoud et al , 1986; Zouaoui et al , 1990; Felici, 1991, 1995). The existence, stability and regularity of the optimal solution of the forward EML and EMC problems have been studied in the papers (Henrot et al , 1989; Henrot and Pierre, 1991; Henrot, 1993; Crouzeix and Descloux, 1990; Crouzeix, 1991; Descloux, 1991, 1994; Briancon, 2004; Briançon et al , 2005; Dambrine and Pierre, 2000; Hayouni and Novruzi, 2002; Barkatou et al , 2006; Barkatou and Henrot, 1997).…”

Точные Решения Для Равновесных Конфигураций Поверхности Проводящей Жидкости В Неоднородном Магнитном Поле

“…Свободная поверхность проводящей жидкости (жидкого металла) деформируется под влиянием приложенного высокочастотного магнитного поля (см. статью [1] и ссылки в ней). Поле проникает только в тонкий поверхностный слой проводника (так называемый скин-эффект).…”

Dual-frequency electromagnetic confinement of liquid aluminum

“…Although these technologies could form ingots with less contamination, better roughness surface, the confined shapes achieved by alternating electromagnetic fields are restricted to simple configurations, only for spherical, circular and rectangular cross-section shapes. According to the principle of electromagnetic confinement of liquid metal, more shapes may be confined or shaped, but so far only a few investigations have contributed to this important area [4][5][6]. Most works are simulations and theoretical analyses of the stability of the axisymmetric complicated shapes.…”