Flow Instabilities of Coupled Rotation and Thermal-Solutal Capillary Convection of Binary Mixture in Czochralski Configuration

Abstract

In order to understand the flow instabilities of coupled rotation and thermal-solutal capillary convection of binary mixture in a Czochralski configuration subjected to simultaneous radial thermal and solutal gradients, a series of three-dimensional direct numerical simulation have been conducted. The capillary ratio of the silicon-germanium mixture is −0.2. The rotation Reynolds numbers of crystal and crucible, Res and Rec range from 0 to 3506 and 0 to 1403, respectively. Results show that the basic flow is axisymmetric and steady. It has rich flow structures in the meridian plane, depending on the competitions among the driving forces. With the increase of thermocapillary and rotation Reynolds numbers, the basic flow will transit to three dimensional oscillatory flow. For different combination of rotation rate and thermocapillary Reynolds number, the oscillatory flow can be displayed as spoke patterns which is steady in time but oscillate in space, spoke patterns propagate in azimuthal direction, rotational waves or coexistence of spokes and rotational waves. The crucible rotation has an inhibitory effect on the flow instability, inducing the monotonically increase of critical value for flow transitions, however, for crystal rotation, the critical thermocapillary Reynolds number increases at first and then decreases. When the rotation rate is large, two flow transitions are captured.