Numerical simulation of Bridgman solidification of binary alloys

Abstract

A transient 2D axisymmetric numerical model for the Bridgman solidification process for a stationary furnace and moving sample is presented. The model is able to predict the evolution of temperature and solid fraction of binary alloys in cases where buoyancy induced convection is negligible, such as in microgravity conditions. A dimensionless form of the governing equations was derived in order to identify the dimensionless parameters that characterize the process, those being the Stefan, Péclet, and Biot numbers. The problem was solved using a finite volume method and an explicit time stepping scheme. To test the efficacy of the model, simulated results were compared with experimental data from the literature and acceptable agreement was obtained. Finally, a parametric analysis was performed for understanding the influence of the process parameters on solidification. One key feature of this study was the inclusion of a term describing the advection of latent heat due to the translation of the mushy zone with varying solid fraction. This thermal transport mechanism was shown to be significant, since its magnitude was comparable to the advection of sensible heat. It was also found that when small Biot numbers were due to low values of the heat transfer coefficients at the surface of the sample, rather than to small sample radii, advective mechanisms were enhanced resulting in more convex shapes of the liquidus isotherm. This highlighted the importance of considering both axial and radial heat fluxes when describing the process.

Concurrent model for sharp and progressive columnar to equiaxed transitions validated by directional solidification experiments processed in microgravity conditions

“…The discretisation scheme used was an Eulerian method similar to that used in Battaglioli et al [38] but without the need for latent heat or advection terms. The thermal conditions were mainly imposed by the relative motion between the moving furnace elements and the stationary sample; hence, it was appropriate to use a fixed-grid mesh but with time-dependent boundary conditions.…”