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.

Prediction of the Formation of an Equiaxed Zone Ahead of a Columnar Front in Binary Alloy Castings: Indirect and Direct Methods

The as-cast properties of components with a columnar grain structure are very different from those with an equiaxed one. Under certain solidification conditions, zones of both structures can occur in an alloy casting; the boundary between the zones is the columnar-to-equiaxed transition (CET). A front-tracking model of dendritic solidification has been developed, which can predict the nucleation and growth of solid in undercooled liquid during a casting process. The growth process is described by dendrite tip kinetics, and is fully coupled to a fixed-grid control volume model of heat transfer during solidification. Using the front-tracking model, two methods for predicting the likelihood of an equiaxed zone forming ahead of a columnar front have been formulated, namely, an indirect method and a direct method. The indirect method is based on modelling the growth of the columnar front in the absence of equiaxed nucleation. The bulk liquid undercooling is monitored and an equiaxed indicator is calculated at each time step based on the extent of such undercooling at that time. The equiaxed indicator is a measure of the relative likelihood of an equiaxed zone forming. In the direct method nucleation and growth of individual equiaxed grains is treated ahead of the advancing columnar front. In this case, if impingement of neighbouring fronts is treated, the simulation to complete solidification will yield the macrostructure and the CET. In this paper, details of both methods of equiaxed prediction are presented. Results from the indirect method are compared to experimental results found in literature and agreement is found.