Micro-macroscopic coupling in the cellular automaton model of solidification

Abstract

A cellular automaton (CA) model to predict the formation of grain macrostructure during solidification has been implemented and the coupling between the microscopic and the macroscopic submodels has been investigated. The microscopic submodel simulates the nucleation and growth of grains, whereas the macroscopic solves the heat conduction equation. The directional solidification of an Al-7 wt. (%) Si alloy was simulated, enabling the calculation of the temperature and solid fraction profiles. The calculated temperature was used to obtain the solid fraction profile by an application of Scheil equation. This solid fraction disagrees with that calculated in the micro-macro coupling of the model, although this coupling is completely based on Scheil equation. Careful examination of the discrepancies shows that it is a result of the undercoolings for nucleation and growth of grains and also of the interpolations of enthalpy change and temperature from the finite volume mesh to the CA cell mesh.