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Purpose. To develop a mathematical model that describes the dependence of the size and amount of sulfide inclusions for various zones of the cross-section of a casting on the parameters of the gas-dynamic effect. Research methods. A computer program, ASImprints, has been developed for processing digital images of sulfur imprints. Digital images of sulfur imprints of 35Л steel casting templates obtained by traditional die-casting technology and under various gas-dynamic modes were processed. A mathematical description of the nature of sulfide inclusions distribution along the casting template as a power function is proposed. Results. A model of the sulfide inclusions distribution in a cross section of a cylindrical cast of carbon steel with 240 mm diameter, that solidifies in an uncooled chill mold under various gas-dynamic modes, was obtained. Scientific novelty. Analytical dependences are obtained that allow interpolating parameters values of the power distribution and, thus, make a prediction of the sulfide inclusions distribution in selected areas of the cross section of this cast that solidifies in an uncooled mold under a given gas-dynamic effect mode. Practical value. The suggested model makes it possible to interpolate the parameters values of a power distribution for predicting sulfide inclusions distribution in a cross section of a given cylindrical cast that solidifies in an uncooled chill mold, for a given mode of gas dynamic effect. The correlation analysis of the probability density function of the power distribution obtained for each of the considered fragments of selected casting section areas showed the statistical homogeneity of the fragments belonging to one zone and the possibility of conducting a quantitative analysis of the digital image of a sulfur imprint.

Представлений аналіз стеку розрахункових схем та математичних моделей, які можуть бути використані під час визначення режимів реалізації комплексних технологій внутрішньоформенного газодинамічного впливу на розплав.

To describe filtration processes in complex dendritic-porous media, a number of fractional-differential mathematical models of diffusion type have been proposed.A nonlinear equation containing fractional Riemann-Liouville derivatives with respect to time is described, which can be used to correctly describe the single-phase filtration of a non-Newtonian fluid in a porous medium.