Convective instabilities in the Czochralski model with different radii ratios

Abstract

In this work, we explore the instability of the complex convection in the Czochralski model concerning the effects of the radii ratio, melt materials, and crystal rotation. Particularly, linear stability analysis is conducted based on the spectral element method for three groups of cases with the same interval for the variation of the radii ratio ( Λ) but different material Prandtl number ( Pr) and dimensionless crystal rotation velocity ωs. We observe that, for both ωs = 0 and ωs = 300, the mixed convection of silicon melt ( Pr =  0.011) becomes less stable with the increase in radii ratio and the instability is of purely inertial mechanism. In contrast, as for the LiCaAlF6 melt ( Pr =  1.4), a larger radii ratio would improve the stability and the instability is dominated by buoyancy mechanism for ωs = 300. Moreover, two times of critical wavenumber transitions occur in the critical stability curve for silicon melt ( Pr =  0.011). Each transition associates with a convex turning point of the critical stability curve for ωs = 0, while only one turning point remains when ωs shifts to 300.