numerical modelling of transport phenomena and macrosegregation during ternary alloy solidification: solutal undercooling effects

In this paper, a macroscopic mathematical model is developed for simulation of transport phenomena during ternary alloy solidification processes, taking into account non-equilibrium effects due to solutal undercooling. the model is based on a fixedgrid, enthalpy-based, control volume approach. microscopic features pertaining to non-equilibrium effects on account of solutal undercooling are incorporated through a novel formulation of a modified partition coefficient. the effective partition coefficient is numerically modeled by means of macroscopic parameters related to the solidifying domain. numerical simulations are performed for ternary steel alloy by employing the present model and the resulting convection and macrosegregation patterns are analyzed. it is observed that the consideration of non-equilibrium solidification in the present mathematical approach is able to capture the thermosolutal convection and leads to prediction of accurate value of macrosegregation. the results from the present model matches well with the experimental observations published in the literature.