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

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...