Front Tracking Based Macroscopic Calculations of Columnar and Equiaxed Solidification of a Binary Alloy

The paper explores the potential of a recently developed special front tracking method in the identification of the interface between columnar and equiaxed structures formed during a binary alloy solidification, driven by thermosolutal convection. The method, based on theoretical and experimental dendrite tip kinetics, is capable of directly distinguishing between the columnar mush and the undercooled liquid/equiaxed region developing ahead of the dendrite tip curve. A new numerical model and its computational algorithm are proposed, where the classical Eulerian volume averaged description of the transport processes is coupled with the Lagrangian front tracking method on a fixed control-volume grid. Having thus distinguished zones of different dendrite structures, distinct simulation models are used within each of the zones, e.g., the Darcy’s porous medium model in the stationary dendrite region, and a model of slurry with floating dendrites in the equiaxed part of the mush. The calculated temperature and solute concentration fields are compared with the relevant results of the classical enthalpy-porosity model, for an example problem of Pb-48 $wt%$ Sn alloy solidification driven by diffusion and thermosolutal convection. And a good match with both solutions is exhibited. A preliminary validation study is also presented by comparing the available experimental data with the model predictions. Possible reasons for some observed discrepancies between the calculations and the experimental findings are discussed. Finally, the proposed front tracking approach is used to address the question of the impact of dendrites floating in the liquid on the flow pattern and macrosegregation in the solidifying alloy.