Трехмерное численное моделирование процесса переноса паров кремния в условиях среднего вакуума в задаче с цилиндрической симметрией

This paper presents the results of three-dimensional numerical simulation of silicon vapor transport through a rarefied inert gas atmosphere from a melt surface to a cylindrical product during vapor-phase silicification. The process is carried out under medium vacuum conditions and is designed for saturating porous thin-walled carbon products with silicon. The computation is carried out using a modified nonlinear diffusion equation that takes into account convective mass transfer in the system as an additional factor. The problem is solved by making use of the finite difference software package developed by the authors. The calculations are performed for parameters, whose values are determined by the formulas of molecular kinetic theory and filtration theory, that is, the proposed physical-mathematical model does not include adjustable phenomenological parameters. The developed approach predicts the silicification time, which is an order of magnitude shorter than the values obtained from the classical diffusion equation, and is consistent with experimental data. This demonstrates the superior predictive value of the proposed model compared to earlier approaches. The dynamics and steady-state distributions of silicon vapor concentration fields are studied for several system configurations that differ in the location of crucibles in the retort. The results of calculation are compared with the limiting case of classical diffusion. Since the nonlinear term in the modified equation is not small, there is a fundamental quantitative difference between the results of simulation done and the data of classical theory. The analysis of the obtained results explains why the modified nonlinear diffusion equation used in the calculations yields a silicon flux at the inlet of the sample that qualitatively agrees with experimental observations. In particular, the effect of weaker sample saturation at a height greater than the level of the crucible location is confirmed. It is shown that the total mass flow of silicon vapor into the sample is sufficient to silicify the sample in a reasonable time.