Model Experiment and Numerical Simulation on Czochralski Method

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Experiment and numerical simulation of critical transition flow modes in Czochralski convection model were performed. Rotational Reynolds number Re, Prandtl number Pr and Rayleigh number Ra emerge in the non-dimensional governing equations. Effects of the rotations of a cylindrical red (a model for a single crystal ingot of Czochralski method) and a cylindrical container (a model for a crucible) on flow regime in a cylindrical container were investigated separately. Studies were carried out in a broad range of mixed convection parameter Ra/PrRe^2 and for the three different Prandtl numbers.Effect of the accelerated crystal rotation technique (ACRT) was also investigated. The attention is directed to the suppression of temperature oscillation by changing the rotation rates, OMEGA = OMEGA_0 (1+A sin (2pift/tp)), where OMEGA_0 represents the constant rotation rate of cylindrical rod without the application of ACRT.An assessment is made of the optimal values to suppress the temperature oscillations.From the results the following conclusions are obtained :Buoyancy-and forced-convection dominant flow modes and transition from one mode to another were found to be characterized by the parameter Ra/PrRe^2. The critical value (Ra/PrRe^2) _c for the transition was 120 for the case of Pr = 4.45x10^3 and Ra = 4.83 x 10^6. In the region of Ra/PrRe^2>120, i.e.the buoyancy effect is dominant, as Ra/PrRe^2 decreases the time period of temperature oscillation gradually increases. Effect of the Prandtl number on the critical value (Ra/PrRe^2) _c was not substantial.Temperature oscillation was suppressed considerably by adjusting A nearly equal to 0.3 and f nearly equal to 0.9 of ACRT in the rotation-dominant region. However, the temperature oscillation was not suppressed in the buoyancy dominant region. Present experimental results agree qualitatively with the numerical results.