Flow structures during solidification of metallic alloys affected by a rotating magnetic field

In order to improve the microstructure of casting ingots a rotating magnetic field (RMF) is widely used to stir the liquid phase during solidification. Usually, the interaction between the solidification process and the RMF driven flow has been discussed only in terms of the flow pattern well-known from the laminar, isothermal case being a superposition of a primary swirling flow in azimuthal direction and a secondary flow occurring as a double vortex in the r-z plane. Effects arising from the propagation of the solidification front, the extension of the mush zone or the spin-up of the flow at higher cooling rates are almost not taken into account. We present experimental and numerical investigations concerning the influence of a RMF driven flow on the momentum, heat and mass transfer within a binary Sn-Pb alloys solidified directionally.
Solidification experiments were carried out using a Sn-15wt%Pb alloy in a cylindrical mold positioned on a water-cooled copper chill. The ultrasound Doppler velocimetry (UDV) was applied to measure the bulk flow during solidification. The temperature field was monitored using thermocouples. The set-up was enclosed by an inductor providing the RMF. The Taylor numbers Ta were varied between 10e5 and 10e8.
The continuum formulation based model has been adopted for numerical simulations using the following assumptions: all transport properties, such as thermal and electrical conductivity or viscosity, are assumed to be constant; the density of solid phase equals the density of liquid phase; the phases are in local thermodynamic equilibrium; the velocity of solid phase in the upper part of the mushy zone is equal to the velocity of the liquid phase. The mushy region is modeled using a mixture viscosity formulation. The Lorentz force in the Navier-Stokes equation has been calculated by means of an analytical solution for the time-averaged Lorentz force for a finite cylinder. The resulting set of eqiuations is discretized by an implicit finite-volume, finite-difference based method, and solved by using the SIMPLE algorithm.
Our results show that the velocity field undergoes distinct modifications during solidification indicating the occurrence of more sophisticated flow patterns as known from the isothermal case.