Numerical simulation of directional solidification of binary alloys with high thermal gradients

Abstract

Directional Solidification (DS) processing of metals and alloys results in castings with uniformly aligned microstructure with enhanced material properties and orderly grain boundaries running in one direction. Unfortunately, during DS density gradients caused by temperature and/or composition changes can initiate convection in the liquid, which leads to macrosegregation and deteriorates the material-properties. One example of severe macrosegregation is channel segregates (freckles) that can be produced during unidirectional solidification. A main goal of this research is to understand the formation of freckles through numerical studies and comparison with experimental results at high thermal gradients. A numerical model to analyze directional solidification (DS) processes is utilized. The simulator solves the momentum, energy, and species conservation equations, and maintains the thermodynamic constraints dictated by the equilibrium phase diagram of the alloy. The Boussinesq approximation is applied in the momentum equation to account for density gradients that induce convection in the solidifying stem. The region in which solid and liquid coexist is commonly called the "mushy zone" to separate it from the all liquid and completely solid regions in solidifying castings and ingots. The Darcy term is included in the momentum equation; the fraction of liquid is treated as an independent variable that allows us to use one set of equations to model the heat and mass transport in all the regions. In the mushy region, we assume local equilibrium. A finite element numerical model based on bilinear isoparametric Lagrangian elements with four nodes, the penalty formulation, and a Petro-Galerkin method is used. This model is capable of simulating formation of channel segregates (freckles), as illustrated by examples representing the conditions of experiments in which freckles are observed. Simulations in a microgravity environment are also presented. It is shown that convection is suppressed and no channels appear under this condition. Compared to the effect of the gravitational acceleration on convection, simple periodic acceleration perturbations in the frequency range of 0.01 to 10 (Hz), and gravitational acceleration range of 9.8x10⁻³ to 9.8 (m s⁻²), show that the perturbations play no significant role in influencing convection.