Numerical Modeling of Melting and Columnar Solidification with Convection in a Gradient Zone Furnace in a Centrifuge

Abstract

A numerical model is built for the solidification of a binary alloy with thermosolutal convection under centrifugal condition. The model is based on the macroscopic transport equations derived using the volume-averaging method. New formulations are derived for a non-linear phase diagram and temperature-dependent thermophysical properties. Simulations are performed to substantiate experiments with TiAl alloys carried out on ESA’s Large Diameter Centrifuge (LDC) using different angular velocities, ω. These experiments comprise a region of transient columnar growth of β-Ti dendrites under decreasing temperature gradient and increasing growth velocity followed by the columnar-to-equiaxed transition (CET). The simulation results show that CET is triggered by a sudden drop of the temperature gradient ahead of the advancing solidification front being a consequence of a sudden change of the flow pattern. We show that the flow pattern driven by density inversion changes abruptly once the permeability of the columnar structure increases above some critical value. This promotes the Rayleigh–Benard instability and the development of local convection cells along with an extended region of very low temperature gradient. The intensity and asymmetry of the flow in the local convection cells increase with increasing ω. The results show that a mushy zone developing in transient conditions and with gradually increasing permeability can significantly alter the flow pattern even in centrifugal conditions with a dominant contribution from Coriolis forces.