Mathematical Modeling of Cooling of a Continuously Cast Ingot for Reducing Heat Losses

We consider thermal processes running in the course of cooling of a continuously cast ingot in a continuous billet casting machine with regard for the heat of phase transformations. For the solution of the problem of rational utilization of the heat of melts, we propose to improve the technology of continuous casting of steel, which would make it possible to use the heat of the liquid core of an ingot for leveling the temperature field over its cross section and guarantee the minimum losses of the heat at the exit of the continuous billet-casting machine. We develop a mathematical model of cooling of continuously cast ingots in a two-dimensional space representation with regard for the release of the heat of crystallization in the two-phase zone. The numerical realization of the model is performed with the help of the implicit difference scheme of coordinate-wise splitting. The adequacy of the model is checked by analyzing the convergence of the experimental and numerical data according to the Fisher, Student, and Mann–Whitney criteria. In modeling, we simulated the control action in the zone of secondary cooling. It is established that, in the case of application of the control action in this zone, the surface temperature increases by 160°C, while the average mass temperature increases by 100–160°C. We choose criteria for the rational modes of cooling of continuously cast ingots. To preserve the heat content of an ingot, it is proposed to use heat insulation after the zone of water–air cooling. We determine relationships between the parameters affecting the surface temperature of the ingot and represent them in the form of nomograms. It is shown that, before the machine of gas cutting, as a result of heat insulation in the zone of air cooling, the ingot is thermostatted as a result of which the temperature of its most vulnerable zones (corners and surfaces) increases. It is established that, for the rational modes of casting of steels, the ratio of the length of the zone of heat insulation to the total length of the continuous billet casting machine varies within the range 0.3–0.6. To determine the heat losses in the process of subsequent cooling of the ingot in air after leaving the zone of machine gas cutting, according to the existing technology of transportation of slabs to compression, the time of modeling was set equal to 90–105 min. To preserve the heat content of the ingot and level temperatures over its cross section, it is also necessary either to use a thermally insulated transmission roller conveyer or to hold ingots in a thermostat.