Macroscopic model for predicting columnar to equiaxed transitions using columnar front tracking and average equiaxed growth

A macroscopic model of Columnar-to-Equiaxed Transition (CET) formation is presented. The growth of a columnar zone and an equiaxed zone are treated separately and modeled on a fixed grid. The model uses a columnar Front Tracking (FT) formulation to compute the motion of the columnar front and the solidification of the dendritic columnar mushy zone. The model for the equiaxed zone calculates the average growth of equiaxed grains within the control volumes of undercooled liquid. The proposed model, which calculates the average equiaxed growth, is different from previous FT models which consider each equiaxed grain envelope separately. A lognormal size distribution model of seed particles is used for the equiaxed nucleation in the undercooled liquid zone. After nucleation, average equiaxed growth is computed by considering the equiaxed envelopes as spherical. The extended volume concept is used to deal with grain impingement. The Scheil equation is used to calculate the solid fraction and latent heat release. When the equiaxed fraction is great enough, advancement of the columnar front is halted and the CET position is determined. CET formation was simulated for directional solidification of an aluminium-silicon alloy. The results were compared with a previous FT-CET prediction model as well as with experimental data. Agreement was found in both cases.