Effects of dendritic arm coarsening on macroscopic modelling of solidification of binary alloys

A pure macroscopic two-dimensional numerical model has been developed, capable of capturing the effects of dendritic arm coarsening on the transport phenomena occurring during a binary alloy solidification process. The general continuum conservation equations are aptly modified to take into account shrinkage induced fluid flow. Simultaneously, the effective permeability of the mushy zone is numerically modelled according to the microscopic coarsening kinetics. Moreover, a new nodal latent heat updating algorithm is proposed that takes into account dendritic arm coarsening considerations. The numerical results are first tested against experimental results reported in the literature, corresponding to the solidification of an Al-Cu alloy in a bottom cooled cavity. It is concluded that dendritic arm coarsening leads to an increased effective permeability of the mushy region as well as an enhanced eutectic fraction of the solidified ingot. Consequently, an enhanced macrosegregation is predicted, compared with that dictated by shrinkage induced fluid flow alone. Physical insights are also developed regarding the effects of various parameters on the overall macrosegregation