Modeling of Liquid Magnesium Turbulent Convection in a Titanium Reduction Apparatus Using the RANS and LES Approaches

—This study focuses on turbulent convection of molten magnesium in a titanium reduction reactor. The reactor retort is a cylindrical vessel with a radius of 0.75 m and a height of 4 m, which contains liquid magnesium at a temperature of 850°C. During a process that lasts for more than 2 days, significant temperature gradients occur in the reduction apparatus due to an exothermic chemical reaction on the metal surface and simultaneous cooling of the side wall of the retort and heating of its bottom. Temperature gradients cause convective flows inside the reactor, which in turn significantly affect the formation of the titanium block. The mathematical model of convective flows in the reactor is based on the equations of thermogravitational convection for a single-phase medium in the Boussinesq approximation. We consider the possibility of modeling turbulent convective flows in a titanium reduction reactor using RANS (Reynolds-averaged Navier–Stokes equations) k –ε and k –ω SST (Shear Stress Transport) models. The results of simulations performed with the k –ω SST model on relatively coarse grids (0.825 million finite volumes) are shown to qualitatively and quantitatively agree with the results of LES simulations on fine grids (3.7 million finite volumes). However, the k –ε model does not always produce acceptable results. RANS simulations produce average velocity and temperature fields with averaging times much longer than those possible in LES simulations. Several different configurations of heating and cooling of the apparatus were examined, including those that were previously unstudied. It has been found that using the k –ω SST model allows simulation of flow dynamics taking into account changes in the heating and cooling conditions of the apparatus during the entire process and identification of single- and double-vortex large-scale flows in the retort, as well as the transition between them, so the degree of convection influence on the reaction can be assessed.