Mathematical modeling of the process of formation shrinkage cavity in end slabs during casting on continuous casting machine

The modeling of the dynamics of the profile formation and the depth of the shrinkage cavity is performed based on mathematical models of the process of volumetric and linear shrinkage, constructed using the finite difference method with an explicit scheme of approximation of partial derivatives. These models, unlike the known previous ones, take into account the different nature of the metal solidification process depending on the chemical composition and use a two-dimensional computational domain divided into a given number of nodes along the x and z coordinates. The modeling uses a system of algorithms for calculating the solidification dynamics of a continuously cast billet, linear and volumetric shrinkage of metal, as well as the process of formation of a shrinkage cavity. In addition, the influence of the carbon concentration in steel, its thermophysical properties and technological parameters of continuous casting on the process of metal solidification is taken into account. The implementation is presented in the form of a computer program, the input parameters of the modeling are the chemical composition of steel and the technological parameters of casting, the output parameters are the values of the thermophysical coefficients and the profile of the shrinkage cavity in the final slab. Verification was performed by comparing the calculated data with the experimental data and showed that the calculated data differ from the experimental data by less than 1%. The possibility of increasing the accuracy of the results by increasing the number of nodes in the thickness and height of the workpiece is shown, while the dependence of the accuracy on the number of nodes in the thickness of the workpiece is most pronounced. The proposed model allows reducing metal losses during casting associated with the formation of a shrinkage cavity and increasing the energy and resource efficiency of modern metallurgical enterprises.

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