Dr. Anna Ivanova

Summary

The mathematical model of convective-conductive heat transfer in a continuous billet was developed to simulate the temperature distribution and the boundary position of phase changes in the ingot during the casting process. The model takes into account the temperature dependence of metal's thermal properties and the heat transfer with moving metal. The heat transfer in an ingot and the heat exchange inside the walls of the mold are described by nonlinear unsteady partial differential equations. The boundary conditions assigned for the part of the ingot inside the mold correspond to the nature of heat transfer under the slag during casting. Also they reflect the fact that a gap filled partially with encrusted slag and partially with gas located between the ingot surface and the wall of the mold. The unknown boundary between liquid and solid phases is considered as a mushy zone given by the condition of temperature equality and the Stefan condition. A finite-difference method was used to numerical solve the problem. The analysis of the qualitative behaviour of the mushy zone was held. The results of calculations of the influence of variations of the casting speed, secondary cooling water rate and thermal parameters on the depth and shape of the mushy zone are received. These results can be used in the future to assess the adequacy of the mathematical model of temperature field of continuous casting ingot and to develop an automatic control system of casting machine.

Key Words: Continuous casting, mathematical modelling, temperature field, phase-change boundary, mushy zone, metallurgical length, liquid pool, shell dynamics