MODELO MATEMÁTICO DETERMINÍSTICO-ESTOCÁSTICO PARA PREVISÃO DA MACROESTRUTURA BRUTA DE SOLIDIFICAÇÃO SOB EFEITO DA DECANTAÇÃO DE GRÃOS

Abstract

A mathematical model is proposed to predict the as-cast macrostructure formation under the effect of grain settling. This model combines the macroscopic conservation equations for mass, energy, and chemical species with the cellular automaton technique to simulate the nucleation, growth, and settling of grains within the liquid metal. The model is applied to the solidification of a single grain settling in an undercooled liquid and showed an increase in temperature and solute concentration in the lower regions of the domain owing to the latent heat release and solute transfer from the grain envelopes to the liquid. The model is also applied to the upwards or downwards unidirectional solidification. In the upwards solidification, the settling of grains results in a completely columnar grain structure which otherwise, in the absence of settling, gives a mixed columnar and equiaxed grain structure. In the downwards solidification, the columnar grains growing downwards are blocked by a layer of equiaxed grains that settle and grow upwards at the ingot base.