Computational Modeling of Columnar to Equiaxed Transition in Alloy Solidification



The columnar to equiaxed transition (CET) provides a challenging simulation goal for computational models of alloy solidification, in addition to being an important technological feature of many casting processes. CET thus provides an industrially relevant test-case for those developing numerical models across a range of scales. Whether or not CET occurs depends on numerous experimental parameters such as cooling rate, speed of columnar growth, thermal gradient in the liquid, and level of grain refiner in the alloy. Information on columnar and equiaxed grain structure, and the transition between the two, is very useful for foundry engineers, at the macroscopic scale of the casting. The detailed microstructure within each grain is determined by typically dendritic growth and local transport of solute and heat. This paper presents a review of recent progress on modeling CET at multiple length scales. It is evident that, whilst micro-models can provide simulations of physical phenomena, such as the evolution of dendrite morphology, at scales 10−3 to 10−5 m, finite computational resources preclude this resolution over the length scale of castings which is in the 10−2–100 m range. Instead, reasonably accurate models of CET formation in castings can be achieved by meso-scale modeling featuring 10−3–10−2 m phenomena. Such meso-scale models make use of analytical expressions to simulate dendrite growth in undercooled melts. Recent progress in modeling of CET, at both macro/meso- and micro-scales is reviewed, and computational challenges yet to be met are summarized.