Modeling of the thermal state of an ingot in the crystallizer of a slab CCM with straight and beveled corners

The procedure of cooling ingots in continuous-casting machines affects both the reliability and productivity of the equipment and the quality of ingots obtained as a result. Insufficient heat exchange between the liquid metal and the wall of the mold leads to a decrease in the thickness of the solid shell of the ingot promoting the formation of surface defects and, in the process of pulling of the ingot out of the mold, leads to the appearance of emergency ruptures. At the same time, excessive heat transfer leads to an increase in the thickness of the solid shell, which results in the redundant shrinkage of the ingot surface accompanied by the formation of a gap between the solid shell of the ingot and the walls of the mold. The appearance of a gap filled with air leads to a sharp decrease in the intensity of heat transfer and accelerates the process wear of the copper walls of the mold. There exists a design of the copper walls with end bevels (protrusions, shoulders, and “whiskers”), which makes it possible to decrease the normal component of forces formed in the process of wear, lower the temperature gradient and the level of stress concentration in the corners of the ingot by increasing the angle from 90 to 135°, and also make the thickness of the “stocking” of solid crust in the corner of the mold closer to the perimeter of the crystallizer. However, the thermal state of the formed ingot for the indicated design of the crystallizer remains poorly studied. We develop a mathematical model and an algorithm for the evaluation of the thermal state of an ingot (with rectangular cross section and angles beveled at 45°) placed in the mold. This enables us to analyze the process of solidification of the ingot in a slab continuous-casting machine. Based on the created mathematical model and the proposed algorithm for solving the boundary-value problem, we created a computer program “Simulation of slab hardening.” By using the results of computer simulations, we obtained the diagrams of temperature distributions in the cross section of the ingot at the exit of the mold of the continuous-casting machine with straight or beveled corners. We also present the dependences of variations of the thickness of solid crust along the height of the crystallizer. The results obtained in the present work can be used to choose the rational shape and the rate of taper of the mold walls in a slab continuous casting machine guaranteeing the decrease in the size of the gap between the solid crust of the ingot and the working surface of the mold.