Abstract
A front-tracking technique on a fixed Cartesian grid, based on the kinetics of dendritic growth, is used to model the progress of an undercooled columnar dendritic front in non-equilibrium 2D solidification controlled by conduction and thermal natural convection. The effect of the alloy latent heat of fusion is included in this single-domain model through a careful definition of source terms in the energy conservation equation to account for both the advance of solidification front and subsequent thickening of the mushy zone within a control volume. The model is compared with the enthalpy approach showing its superiority in the detection of the undercooled liquid zone and, thus, in potentially modelling of columnar/equiaxed grain structures. It is used to predict the influence of both alloy composition and convective heat transfer coefficient on the size of the undercooled liquid zone in front of columnar dendrite tips during solidification of Al–Cu in a square mould. The predictions obtained confirm that natural convection in the melt reduces local temperature gradients and thus widens the undercooled liquid zone ahead of a curve joining columnar dendrite tips, increasing the potential for growth of equiaxed grains.
