The effect of solutal undercooling on double-diffusive convection and macrosegregation during binary alloy solidification: a numerical investigation

In this paper, we present a macroscopic numerical model that is capable of capturing the interaction between the double-diffusive convective field and a localized fluid flow on account of solutal undercooling during non-equilibrium solidification of binary alloys. The model is essentially based on a fixed-grid enthalpy based control volume approach. In the present model, microscopic features pertaining to non-equilibrium effects on account of solutal undercooling are incorporated through the formulation of a modified partition-coefficient. The effective partition-coefficient is numerically modelled by means of a number of macroscopically observable parameters related to the solidifying domain. This feature has made the present treatment different from micro-macro modelling of alloy solidification, which involves certain parameters that may not be macroscopically resolvable. Numerical simulations are performed for the case of two-dimensional transient solidification of Pb-Sn alloys (both hypoeutectic and hypereutectic) in a rectangular cavity, employing the present model. The simulation results are also compared with the corresponding experimental results quoted in the literature, and the agreement is excellent. From the results, it can be concluded that non-equilibrium effects on account of solutal undercooling result in a more enhanced macrosegregation