In this paper, steady-oscillatory transition of the convective flow in a Czochralski (Cz) growth system was numerically studied. In this configuration, rapid variations in density across narrow region of the flow in the vicinity of the crystallization front leads to an unstable stratification of the flow in this region. Time-dependent, finite volume method calculation of the momentum and heat transport equations shows that an instability mechanism, giving rise to the formation of cold plumes beneath the phase boundary, might be associated with an irreversible change in the convexity of the front. Dynamics of the crystallization front was found to be correlated with the periodic oscillation of the flow. It was shown that the interface inversion process occurs at a critical Reynolds number significantly (∼25%) lower than that predicted by the steady-state Cz-oxide model analysis. Consistently, the time-averaged maximum value of stream function was found to be larger than its corresponding steady-state value. This indicates that the mechanism behind the oscillatory transition of the flow has a positive feedback on the intensity of forced convection flow. These numerical results were attributed to the baroclinic instability mechanism characterized by oscillations of a cold plume appearing at the crystal periphery and descending along the symmetry axis. The time period of oscillations was found to be considerably (30–40%) decreases and, simultaneously, the inclination angle of isopycnals increases (∼48%) at a critical rotation rate of the crystal for which the interface inversion occurs.
A numerical study was carried out to describe the effect of the melt hydrodynamics on the crystallization front shape in the Czochralski growth of a semitransparent oxide crystal. In the present model calculation, the enthalpy-porosity method was used to solve the phase change problem with the convection due to buoyant, thermocapillary and centrifugal forces. It was shown that the rotationally-driven flow protrudes into the mushy zone when the crystal rotation rate was increased to a certain critical value corresponding to Gr/Re 2 =0.89 as the ratio between the intensity of buoyancy and forced convection flow in the melt. The ratio between the vertical and horizontal temperature gradients beneath the mushy zone was found to be decreased by increasing the crystal rotation rate. It was shown that the shape of the zone deforms abruptly when the ratio between the axial and radial temperature gradients decreased to the values smaller than the unity. The Burger's number condition was found to be violated in the case Gr/Re 2 <0.89, at which the onset of geostrophic instability is expected.
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