Solutal convection during directional solidification
Abstract
During directional solidification of a binary alloy at constant velocity, buoyancydriven fluid flow may occur due to the solute gradients generated by the solidification process. Numerical calculations of the solute and fluid flow fields in the melt have been carried out using finite differences in a twodimensional, timedependent model that assumes a planar crystalmelt interface and allows timedependent gravitational accelerations. The container walls are rigid and perfectly insulating for solute. For constant vertical gravitational accelerations, as the solutal Rayleigh number is varied, multiple steady states and timedependent states may occur. The bifurcation from the quiescent state may be subcritical or transcritical, depending on the aspect ratio of the container. Calculations have also been performed for a gravitational acceleration that is assumed to be uniform in magnitude with its direction rotating uniformly. Numerical results have been obtained for a Schmidt number of 10 and a gravitational acceleration of 0.0001 G. The maximum variation in the solute concentration at the crystalmelt interface is calculated for various values of the rotation rate of the gravitational acceleration.
 Publication:

AIAA, ASME, SIAM, and APS, National Fluid Dynamics Congress
 Pub Date:
 1988
 Bibcode:
 1988aiaa.conf.1572M
 Keywords:

 Binary Alloys;
 Convective Heat Transfer;
 Directional Solidification (Crystals);
 Finite Difference Theory;
 Melts (Crystal Growth);
 Buoyancy;
 Flow Distribution;
 Gravitational Effects;
 Microgravity Applications;
 Space Commercialization;
 Temperature Gradients;
 Temporal Distribution;
 Two Dimensional Models;
 Fluid Mechanics and Heat Transfer