Three-dimensional iterative solution for the multiconductor eddy current and free surface calculations

Abstract

In the three-dimensional (3-D) eddy current calculations, the obtaining of an accurate numerical solution with reasonable size and less computation efforts is still undertaken in many recent articles. Nowadays, such a solution becomes urgently required for designing and developing the electromagnetic confinement application, where the problem is not only 3-D but also involves more than one conducting region having a free boundary that is unknown a priori. For this class of applications, the present paper is devoted to discuss the developing of a 3-D iterative solution proposed for the analysis of an electromagnetic continuous casting (EMC) of an aluminum rectangular ingot installed in the Egyptalum Company. This solution is based on a derived 3-D Boundary Element (BE)—Impedance Boundary Condition (IBC) formulation, which leads to a significant reduction in the CPU time and the calculation efforts, as compared to the use of the regular BE formulation. In the present iterative solution, the IBC is applied to the resistively molten aluminum region, while the full BE formulation is used to present the field shaping screen. The validity of this iterative solution is tested by predicting the equilibrium meniscus shape of the free surface for an EMC mold having the size of 1050×280 mm for which experimental measurements for both the meniscus and the total active power supplied are available. Numerical results showing the magnetic flux density distributions over the boundaries of this mold are presented. The corresponding total surface power induced are estimated and compared with the corresponding actual (experimental) values. Also, the meniscus of the molten aluminum free surface is predicted and compared as well.