Modeling of liquid magnesium turbulent convection in the titanium reduction apparatus using RANS and LES approaches

Abstract

Turbulent convection of molten magnesium in a titanium reduction reactor is investigated. The reactor retort is a cylindrical vessel of radius 0.75 m and height 4 m, which contains liquid magnesium maintained at a temperature of 850°C. During the process lasting for more than two days, significant temperature gradients occur in the reduction apparatus due to an exothermic chemical reaction on the metal surface, cooling of the side wall of the retort and simultaneous 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 a reactor is based on the equations of thermogravitational convection for a single-phase medium in the Boussinesq approximation. 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 is considered. It is shown that the simulations performed with the k - ω SST model on relatively coarse grids (0.825 million finite volumes) give the results which 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 demonstrate acceptable results in some cases. The RANS simulations produce average velocity and temperature fields with averaging times much longer than those available in LES simulations. Several different configurations of the system of apparatus heating and cooling rate control, including previously unstudied ones, were examined. It has been found that the use of the k - ω SST model permits 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-vortex and two-vortex large-scale flows in the retort and a transition between them, and hence the degree of influence of convection on the reaction can be assessed.