NUMERICAL MODELING OF THE PROCESS OF FILLING THE CCM MOLD WITH METAL

Abstract

Mathematical modeling of the liquid melt flow in the mold of the continuous casting plant is still poorly investigated. Analytic solutions of melt flow in the general case are a complex mathematical problem. Nevertheless, for some cases, exact solutions have been found. Such analytical solutions serve as a means of verifying the results of numerical methods of solution. The purpose of this work is the use of the numerical method proposed by Professor V.I. Odinokov, based on the finite-difference representation of the original system of equations. The method has been successfully used in the mechanics of continuous media, in the lithium manufacturing for the mathematical modeling of the strained deformed state of shell molds of cast models, as well as in other technological works, which indicates its universality. In the present work, hydrodynamic and thermal flows of liquid metal during the steel casting into the rectangular section mold of a continuous cast steel have become objects of research, and the result is a spatial mathematical model describing the flows of liquid metal in the mold. To simulate the processes that take place during filling, the software complex “Odyssey” is used. The basis of theoretical calculations includes the fundamental equations of hydrodynamics, the equations of mathematical physics (the equation of heat conductivity with regard to mass-transfer) and the approved numerical method. The solution of the system of differential equations formulated in this work was carried out numerically. The investigated area was divided into elements of finite dimensions, for each element the resulting system of equations was recorded in the difference form. The solution result is the metal flow velocity fields and the temperature fields in the mold volume. To solve the obtained system of algebraic equations, the numerical schemes and calculation algorithms were developed. Based on the developed numerical schemes and algorithms a computational program was compiled in Fortran-4. The mathematical model allows to vary the geometric dimensions of the crystal-mash and sectional metal exit holes from the submerged nozzle, and may also help to understand the scheme of the cast metal movement that affects the heat sink walls of the mold, and to find the optimal parameters of the output of liquid metal from the submerged nozzle at different modes of casting. An example of calculating the casting of steel into a rectangular mold with a height of 100 cm and cross-sectional dimensions of 2000.40 cm is given. The casting was carried out from a submerged nozzle symmetrically on both sides in a horizontal plane. The result of the solution is presented in the graphical form. The motion of liquid metal flows in different sections of the mold is shown. The areas of the circular flow of metal are revealed, as well as the areas in the mold volume, where the vortex motion of the liquid metal is observed, their magnitudes and intensity are determined. The presented temperature field indicates the presence of a local area with a high temperature at the wall of the mold, which is explained by the directed flow of hot metal emerging from the hole in the submerged nozzle.