Modelling columnar and equiaxed growth
A novel computer model of the evolution of columnar and equiaxed microstructure during alloy solidification has been developed. A control volume finite difference model of conduction heat transfer is applied to a two-dimensional domain bounded by a relatively cold mould. The initial condition is that of superheated liquid, and nucleation occurs either at the mould wall, leading to columnar dendritic growth, or within the bulk liquid, leading to the growth of equiaxed dendrites. The columnar front or the equiaxed grain boundaries are represented by computationally sharp interfaces, which separate liquid from partially solid alloy. Interpolation between discrete computational markers is employed to describe these interfaces, and a front-tracking technique is used to predict the evolution of the grain structure, via movement of the markers, across the fixed grid. The front velocity is determined via considerations of the kinetics of dendrite growth. The heat equation is fully coupled to the front-tracking algorithm by means of source terms which represent the evolution of latent heat due to the dendritic growth (advancing tips and thickening mushy zone). The model, applied to binary Al-Cu alloys, is computationally efficient. It predicts the variation of the extent of liquid undercooling ahead of the growing columnar front, and new metrics have been established to determine the likelihood of the formation of an equiaxed zone here. The employment of these metrics to establish the influence of heat extraction rate and alloy composition agrees with reports from the literature. The model does not distinguish between individual grains of the columnar zone, but it is shown that this is not an important limitation for most metal casting applications. Direct simulation of the nucleation and growth of multiple equiaxed crystals has been carried out, in which the nucleation and growth of individual grams can be observed via animation, and the influence of melt superheat and heat extraction rate on equiaxed solidification has been determined.