Proper selection of the stability parameter determines the accuracy of dendrite tip kinetics at a single crystal scale. Recently developed sophisticated phase field modelling of a single grain evolution provides evidence that this parameter is not constant during the process. Nevertheless, in the commonly used micro-macroscopic simulations of alloy solidification, it is a common practice to use a constant value of the stability parameter, resulting from the marginal stability theory. This paper aims to address the issue of how this inaccuracy in modelling crystal growth kinetics can influence numerically predicted zones of columnar and equiaxed dendrites and the macro-segregation formation.
Using the original authors’ micro-macroscopic computer simulation model of binary alloy solidification, the calculations have been performed for the Kurz-Giovanola-Trivedi (KGT) crystal growth kinetics with two different values of the stability parameter, and for two different compositions of Al-Cu alloys. The computational model is based on single domain-based formulation of transport equations, which are discretized on control-volume mesh. To identify zones of different grain structures, developing within the two-phase liquid-solid region, an envelope of columnar dendrite tips is tracked on a fixed non-orthogonal, triangular control volume grid. The models of porous and slurry media are used, along with the concept of the switching function, to account for diverse flow resistances in the columnar and equiaxed crystal zones. The numerical predictions are carefully studied to address the question of how the chosen stability parameter influences macroscopic structures of a cast, the most important issue from the engineering point of view.
The carried-out comprehensive numerical analysis shows that the value of the stability parameter of the KGT-constrained dendrite growth model does not have a direct significant impact on the macrosegregation formation. It, however, visibly influences the undercooling along the front, separating different dendritic structures and the size of the undercooled melt region where the equiaxed grains can develop. It also affects the amount of eutectic phase created.
To the best of the authors’ knowledge, this is the first attempt at estimating the influence of some inaccuracies, caused by possible ambiguities in choosing the stability constant of the KGT law, on numerically predicted macroscopic fields of solute concentration, the developing zones of columnar and equiaxed crystals and the macrosegregation patterns.
Seredyński, M. and Banaszek, J. (2019), "Numerical study of crystal growth kinetics influence on prediction of different dendritic zones and macro-segregation in binary alloy solidification", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 30 No. 5, pp. 2363-2377. https://doi.org/10.1108/HFF-11-2018-0712
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