Numerical simulation of Bridgman solidification of binary alloys

• 2D axisymmetric Bridgman solidification of binary alloys is investigated.
• Advection of latent heat in the mushy zone strongly influences the results.
• 2D effects in the mushy zone are present at low Biot numbers due to advection.
• The ratios Pe/Ste, Bi/Pe and Bi/(Pe/Ste) give relevant information on the process.

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 characterise 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.