Validation and Simulation of Cellular Automaton Model for Dendritic Growth during the Solidification of Fe–C Binary Alloy with Fluid Flow

Abstract

Based on our previous developed 2D CA-FVM model, where the transport phenomna and kinetics conditions of solute-driven dendritic growth occurred in the solidification process with fluid flow were totally taken into consideration, an extensive model validation and furhter model application are demonstrated here. Firstly, the flow pattern of the lid-driven cavity is well predicted and quantitatively coincides with the classic benchmark solutions, as Re is in the range of 100 to 3200. Secondly, the numerical simulations of the free dendritic growth of Fe-0.82 wt%C alloy in the static undercooled melt and the convectional undercooled melt agree well with the LGK predictions in a relatively low undercooling range and the Oseen-Ivantsov solutions, respectively. After the detailed model validation, numerical simulations of the equiaxed/columnar dendritic growth of Fe-0.82 wt%C alloy with fluid flow have been carried out and the results show that the dendrite morphologies and solute profiles are significantly affected by the fluid flow and the asymmetries of the dendrite morphologies and solute profiles become more and more serious with the increase of the flow Péclet number. For the equiaxed dendritic growth in the undercooled melt with fluid flow, the solute is washed away from the upstream to the downstream region, resulting in accelerating the dendritic growth of the upstream tip and perpendicular tip and inhibiting the dendritic growth of the downstream tip. For the columnar dendritic growth in the lid-driven cavity, the circulation flow facilitates the side branch of the dendrite trunk edge, which faces to the incoming flow, and promotes the asymmetrical dendrite morphology and solute profile.