Electromagnetically-driven convection during solidification: Heat and mass transfer in solidifying Pb-Sn melts

Swirling flows generated by the application of a rotating magnetic field (RMF) during the solidification significantly modify the heat and mass transport in the melt. Their enormous potential to modify the microstructure is known since long but was systematically studied only recently [1,2]. However, the understanding of flow field driven by the RMF in the solidifying melt and the corresponding temperature and concentration distributions is far from being complete. By means of a combination of experiments and numerical simulations important relations shall be established.
To calculate the flow field we use a code based on the SIMPLE algorithm which has been carefully validated on the isothermal problem of the RMF-driven acceleration of a melt from rest [3,4]. The solidification is treated by using a mixture-theory-model following Voller et al. [Int. J. Heat Mass Transfer 32 (1989), 1719]. The geometry studied is a Pb-Sn melt in a cylindrical cavity directionally solidified from below. The simulations cover Taylor numbers, Ta, up to 2*106 where Ta determines the magnitude of the bulk flow.
The solidification in the RMF depends on the degree of development of the forced convection (spin-up problem). The flow fields belonging to characteristic stages are discussed. Generally, the RMF significantly modifies the solidification as soon as the average flow velocity of the meridional flow becomes comparable or larger as the velocity of the solidification front. We discuss the impact of the flow on heat transfer in the melt thereby providing a detailed comparison of experimental and numerical date with respect to cooling rates and temperature gradients. Emphasis is given to the temperature gradients in vicinity of the solidication front which are hardly accessible in experiments. Their tendency with growing Ta is examined and linked with the accelerated onset of the transition from columnar to equiaxed growth (CET) found in the experiments [2]. Furthermore the macrosegregation to be expected in the RMF case are discussed.