Numerical study of molten magnesium convection in the apparatus for titanium reduction

Numerical study of the structure of convective flows of molten magnesium in the apparatus for metallothermic reduction of titanium is performed for different configurations of vessel cooling and heating zones. A mathematical model is based on the Boussinesq equations for thermogravitational convection of a single-phase fluid. The LES (Large Eddies Simulations) technique is used for turbulence modeling. Simulations were carried with a non-uniform numerical grid consisting of 5 million points. Three-dimensional nonstationary simulations allow one to get instant and average characteristics of the process and to study the fields of velocity and temperature pulsations. It is shown that axisymmetric stationary flows exist under moderate Grashof numbers (Gr ~ 10 7-10 8), but nonstationary turbulent flows are established under Grashof numbers, which correspond to the actual titanium reduction process (Gr ~ 10 12). Analysis was performed for uniform and non-uniform heat emission provided on the magnesium surface by the reaction of titanium reduction, as well as for two configurations of the system of apparatus heating rate control: with furnace heaters operating at full capacity and with furnace heaters switched off. The principal differences in the convective flow structure in these two cases are revealed. An estimate is made for the maximal velocity of magnesium flows in the reactor. It is shown that more intensive velocity and temperature pulsations occur near the interface between the cooled and heated parts of the lateral surface of the vessel.