論文 - 河野 晴彦

Three-dimensional numerical simulation of unsteady Marangoni convection in the CZ method using GSMAC-FEM 査読有り 国際誌

Haruhiko Kohno, Takahiko Tanahashi

Computer Modeling in Engineering & Sciences ( Tech Science Press )   2 ( 2 )   155 - 170   2001年06月

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（学術雑誌）

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 x 10(-2), Marangoni number Ma = 0.0 - 6.2067 x 10(2), Grashof number Gr = 7.1104 x 10(6), 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 sigma (T) = 0.0 - 1.5 x 10(-5)N/mK. Although the velocity distribution in the circumferential direction is isotropy in any direction first, its magnitude becomes periodic and has the wavelength equal to 1/8 of the circumference. Then the wavelength doubles, and the flow pattern becomes finally asymmetrical. Moreover, the oscillation of the velocity distribution is observed just under the single crystal, and the amplitude is found to depend on the value of sigma (T). After imposing the vertical magnetic field more than 0.05T to the melt from 50s, the flow pattern becomes restored to symmetry. But the instability remains under the single crystal and it indicates that the influence of Marangoni convection can not be neglected in the crystal growing process.

DOI： 10.3970/cmes.2001.002.155