Numerical study of molten magnesium convection in a titanium reduction apparatus

Abstract

The structure of a convective flow of molten magnesium in a metallothermic titanium reduction apparatus has been studied numerically for various retort heating and cooling configurations. The mathematical model is based on the thermogravitational convection equations for a singlephase fluid in the Boussinesq approximation. A nonuniform computational grid with a total of 5 million grid points was used. The LES (Large Eddy Simulation) technique was applied to take into account the turbulence. The problem was considered in a three-dimensional nonstationary formulation, which allowed one to construct the instantaneous and average characteristics of the process and to analyze the velocity and temperature pulsation fields. It has been found that steady axisymmetric flows occur at moderate Grashof numbers (Gr ~ 10⁷–10⁸), while unsteady turbulent flows take place at Grashof numbers corresponding to the actual titanium reduction process (Gr ~ 10¹²). The influence of the degree of nonhomogeneity of the heat release due to the titanium reduction reaction that runs mainly on the magnesium surface has been studied. The computations have been performed for two configurations of the system for maintaining the apparatus heating regime: with furnace heaters operating at full power and with switched-off furnace heaters. Fundamental differences in convective flow structure for these two heating methods have been revealed. It has been established that the most intense velocity and temperature pulsations arise in the region adjacent to the interface between the cooled and heated parts of the retort side surface.