﻿ MATHEMATICAL MODEL AND METHOD OF CALCULATION OF CRYSTALLIZATION OF TWO-COMPONENT MELTS 2010 2(4)

Short abstract

MATHEMATICAL MODEL AND METHOD OF CALCULATION OF CRYSTALLIZATION OF TWO-COMPONENT MELTS

Ginkin V.P.1, Ganina S.M.1, Kartavykh A.V.2, Chernov K.G.1

1 State Scientific Center of the Russian Federation - Institute For Physics And Power Engineering Named After A.I.Leypunsky, Obninsk, Russia
2Institute of Chemical Problems of Microelectronics, Moscow, Russia

 Citation: Ginkin, V.P., Ganina, S.M., Kartavykh, A.V. and Chernov, K.G., (2010) Mathematical model and method of calculation of crystallization of two-component melts, Modern Science: Researches, Ideas, Results, Technologies, Iss. #2(4), PP. 48 - 55.

 Keywords:two-component melts crystallization; mathematical model; flow in porous media; Stefan problem; numerical calculation method; experiment calculation

 Abstracts: A mathematical model of the crystallization process is proposed in which a Stefan problem with two boundaries is solved numerically, the boundaries being between the solid phase and the two-phase transition zone and between the two-phase transition zone and the liquid phase. The two-phase zone is represented as a porous medium with variable porosity. The authors pioneer the use of square-law dependance of porosity on temperature in a two-phase zone. An additional force introduced by analogy with Darcy’s law is taken into account in the two-phase zone, namely, a force resisting to the melt flow due to conditions of porosity. The resulting equation system is solved by an implicit relaxation method making use of an exponential approximation method, the Patankar-Spalding method, and the incomplete factorization method. The testing of the model in the calculation of the Sn+20%Pb (mass percentage) alloy crystallization experiment shows good agreement between the calculation and experimental data.

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