Mathematical Modelling for Electromagnetic Field and Shaping of Melts in Cold Crucible

Abstract

For the better understanding of the phenomena in the cold crucible, advanced electromagnetic field models have been developed for both vertical and horizontal cross sections of the crucible. In the former model, the axi-symmetric sheet model was assumed and the influence of the number of slits was taken into account by the use of parameter representing the magnitude of the electromagnetic interaction. In the latter one, the conservation problem of the current density in a finite cell was successfully solved through the introduction of Newton method for the simultaneous convergence of both scalar and vector potentials. The validity of the models was confirmed through experimental measurements of the magnetic flux density, the coil voltage and the elevation height of the Al-Cu alloy melts.
Regardless of the number of slits and the shape of the crucible, the induced current on the internal and external sheets of the crucible flows on the horizontal path. An increase in the number of slits resulted in the increase of the magnetic flux density. This is mainly explained by the reason that the partition ratio of the induced current into the segmented part of the crucible increases with the number of slits. Since the melt is expected to contact with the internal wall near the slit bottom in case of the straight type crucible, the solidification is preferable to be complete just above the bottom for the improvement of the ingot surface during continuous casting.