Simulation of channel segregation using a two-phase columnar solidification model – Part I: Model description and verification

Abstract

A numerical investigation on the formation of channel segregation using a two-phase columnar solidification model is presented in this two-part paper. Part I includes a model summary and model verification and Part II presents an in-depth discussion and parameter study on the formation mechanisms of channel segregation. The two phases considered in the model are the liquid melt and solid columnar phase. The morphology of the columnar dendrite trunks is approximated by step-wise growing cylinders with constant primary dendrite arm spacing. The columnar dendrites grow from the mold wall following the liquidus isotherm. The growth kinetics of the columnar trunks is governed by diffusion of the rejected solute surrounding the columnar trunks near the solid–liquid interface. The conservation equations for mass, momentum, species and enthalpy are solved for each phase. The permeability of the two-phase mushy zone is treated with the Blake–Kozeny approach. The model is applied in 2D and 3D simulations of segregation in a Sn–10wt.% Pb benchmark ingot, as defined by Bellet et al. (2009) [1]. The 3D calculations show channel segregation patterns of predominantly discontinuous lamellar structure with a few rod-like channels. A series of 3D simulations with increasing thickness clarify that, with thickness greater than 0.05m, the influence of the front and back mold walls on the center plane segregation becomes negligible. Thus, the segregation pattern on the center plane in the 3D case can be sufficiently reproduced by computationally inexpensive 2D calculations. Verification was made by comparison with published models and experimental results.