Prediction and control of the transient oscillating flow in Czochralski convection

Abstract

A numerical study was made of prediction and control of the transient oscillatory flows in Czochralski convection. The temperature oscillation was computed over a broad range of the mixed convection paraemters, $Ra/PrRe^2$. Inherent temporal characteristics of the transient oscillating flow modes in Czochralski convection were investigated numerically. The effect of the Prandtl number on flow modes was discussed. It is found that the analogy of the mixed convection parameter to predict the onset state was coming into existence. Additional scalar transport equation, concentration equation, was computed for the various Re numbers. A close correlation between the temperature and the concentration was found out. The suppression of temperature oscillation was achieved by changing the rotation rate of crystal rod $Ω_S=Ω_{so}(1+A_s sin(2π/t_p f_S t))$, where $A_s$ denotes the rotation amplitude and $f_s$ is the dimensionless frequency. Based on the inherent oscillatory time period of the melt $(t_p)$, the suppression rate of temperature oscillation was characterized by the mixed convection parameter $Ra/PrRe^2$. The mixed convection was ranged 0.225≤$Ra/PrRe^2$≤0.929, which encompasses the buoyancy and forced convection dominant regimes. Computational results revealed that the temperature oscillation can be suppressed significantly by adjusting the control parameters. The uniformity of temperature distribution in space and in time near the crystal interface was scruntinized. The suppression of temperature oscillation was also examined for a realistic low Prandtl number flow.