Metal flow in the mold of a continuous-casting machine

Analysis of the flow of liquid metal in the mold during continuous casting is a challenging mathematical problem. Nevertheless, precise solutions have bene found for some cases. Such analytical solutions may be used to verify numerical solutions. In the present work, the melt flow in the mold is studied numerically on the basis of the finite-difference approximation of the initial system of equations. This method is relatively universal: it has been successfully used in continuum mechanics, in mathematical modeling of the stress–strain state of shells in casting, and in other industrial contexts. In the present work, it is applied to the hydrodynamic and thermal fluxes of liquid metal in steel casting in a rectangular mold in a continuous-casting machine. The three-dimensional mathematical model that is obtained describes the liquid-metal fluxes in the mold. The processes that accompany the filling of the mold with melt are simulated by means of Odissei software. The calculations are based on the fundamental hydrodynamic equations, a formula from mathematical physics (the heat-conduction equation with allowance for mass transfer), and a familiar numerical method. The resulting system of differential equations is solved numerically. The region investigated is divided into finite elements. For each element, the system of equations is written in finite-difference form. Solution yields the field of flow velocities of the metal and the temperature field within the mold. The algebraic equations obtained by this means are solved by means of numerical algorithms. On that basis, a program is written in Fortran-4. The mathematical model permits variation of the mold dimensions and the cross section of the metal outlet from the submersible nozzle. It may also assist in understanding the motion of the cast metal, which affects the heat transfer by the mold walls, and in finding the optimal parameters of the liquid metal as it leaves the submersible nozzle. As an example, steel casting in a rectangular mold (height 100 cm) is considered. In casting, the metal leaves the submersible nozzle symmetrically on both sides, in the horizontal plane. The results are graphically displayed. The motion of the metal flux is shown in different cross sections of the mold. Regions of circular flow are identified, as well as regions of vertical motion in the mold. The magnitude and intensity of these regions are determined. The temperature field indicates a local hot zone at the mold wall. That may be attributed to the direct flux of hot metal from the aperture in the submersible nozzle.