Vortex forces in a liquid metal in the field of a single-phase inductor

L. L. Tir

Abstract
Vortex forces in a single-phase axisymmetric electromagnetic system with a molten metal are discussed. Expressions are given for the curl of the forces in the general case of an axisymmetric system and in the partial cases of the azimuthal orientation of the current density or the magnetic induction. The role of the frequency and the boundary conditions in the vortex of the forces is analyzed. The article gives formulas and the data of a numerical calculation of the field of forces in a system with azimuthal currents, with a different character of the distribution of the induction at the boundary of the melt. It is shown that inhomogeneity of the boundary conditions lowers the effective depth of the penetration of the field and the maximal value of the forces in the metal. The effect of the ratio of the thickness of the skin layer and the characteristic dimension of the Inductor on the values of the curl of the forces and the integral characteristics of the vortex zone are illustrated by curves. It is shown that, with a height of the metal exceeding the length of the inductor, the integral action of the vortical electromagnetic forces in the melt is approximately characterized by the maximal values of the pressure of these forces in the surface layer of the metal.