RADIAL MACROSEGREGATION INDUCED BY 3D PATTERNS OF SOLUTAL CONVECTION IN UPWARD BRIDGMAN SOLIDIFICATION

We have developed a numerical approach of the natural convection prese nt in the melt during the growth of a binary alloy rod in the upward V ertical Bridgman configuration. This flow is induced by the density dr op appearing in the liquid phase above the solidification front. We sh ow that, even if the front deformation is neglected, the flow patterns are rather complex. This is maintained in the close vicinity of the c onvection threshold. The pattern selection is furthermore made intrica te by the subcritical nature of the convective bifurcation. We present in detail three different 3D flow patterns, the appearance of which i s expected as the most plausible in a cylindrical crucible and for a m oderate range of parameters. This result remains in agreement with lin ear stability analysis. We study their signature on the radial macrose gregation pattern that occurs during the directional solidification of a Pb-30%Tl alloy. We then investigate quantitatively the influence of higher Rayleigh numbers for a rather confined situation. We show that the relative amplitude of radial segregation admits a maximum in the weakly non-linear domain. Moreover, even if 3D numerical constraints r educe the investigated range of physical parameters (in terms of solut al Rayleigh number and crucible radius), it is possible by extrapolati ng the present results to predict the order of magnitude of crystal co mposition variations. The resulting amplitude of macrosegregation howe ver underestimates the one reported from experiments. The discrepancy is attributed to front deformation that tends to amplify the depletion in thallium at the bottom of ascending flow columns.