Modeling the columnar-to-equiaxed transition with a three-phase Eulerian approach

A three-phase Eulerian approach is developed to model the columnar-to-equiaxed transition (CET) during solidification. The three phases are the parent melt, the solidifying columnar dendrites and the solidifying equiaxed grains. They are considered as spatially interpenetrating and interacting continua. We solve the conservation equations of mass, momentum, species and enthalpy for all three phases. Additionally we define and solve an additional transport equation for the number density of equiaxed grains which also accounts for grain nucleation. Diffusion controlled growth for both columnar and equiaxed phases, drag forces, species partitioning at the solid/liquid interface, heat of fusion, etc. are taken into account with the corresponding closure laws. A binary 'steel' (Fe-0.34 wt.% C) ingot casting as benchmark was simulated to demonstrate the model potentials. Preliminary results of the mixed columnar and equiaxed solidification including the motion of the columnar tip front, the occurrence of the CET, the formation of macrosegregations, and the resulting melt convection and grain sedimentation and their influence on the final macroscopic phase distribution are presented