Hydrodynamic Instabilities in Czochralski Process of Crystal Growth
نویسندگان
چکیده
Abstract. This paper deals with axisymmmetry breaking instabilities in Czochralski process of crystal growth. Numerical linear stability analysis was carried out using the axisymmetric bulk flow model. Stability diagrams of critical Grashof numbers Grc and frequencies ωc dependent on aspect ratio α(=height/radius), 0.4 ≤ α ≤ 1.0 and Prandtl number Pr = 0.01 are shown. Computations were carried out using the spectral element method in the meridional plane with Fourier decomposition in the azimuthal direction. It was found that convective instability sets in through an Hopf bifuraction. For Pr = 0.01 computations were carried out for the first 10 modes, only the first 5 (0,1,2,3,4) were important. Sensitivity of mode transitions was observed at parameter range of α > 0.65 and in some regions modes were observed approaching each other closely. For 0.4 ≤ α ≤ 0.85 and Pr = 0.01 dispersion relation analysis reveals convective instability effects while for larger α rotational effects appear.
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