Haruhiko Kohno, Takahiko Tanahashi1
CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 155-170, 2001, DOI:10.3970/cmes.2001.002.155
Abstract Three-dimensional (3D) unsteady numerical simulations are carried out by means of the finite element method (FEM) with the generalized simplified marker and cell (GSMAC) method in silicon melt with a non-deformable free surface with Prandtl number Pr = 1.8534 × 10-2, Marangoni number Ma = 0.0 - 6.2067 × 102, Grashof number Gr = 7.1104 × 106, and the aspect ratio As = 1.0 in the Czochralski (CZ) method. The flow state becomes unstable earlier by increasing the absolute value of the thermal coefficient of surface tension in the range of σT =0.0 - 1.5 × 10-5N/mK. Although… More >
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