Three-dimensional numerical simulation of unsteady Marangoni convection inthe CZ method using GSMAC-FEM

Citation
H. Kohno et T. Tanahashi, Three-dimensional numerical simulation of unsteady Marangoni convection inthe CZ method using GSMAC-FEM, CMES-COMP M, 2(2), 2001, pp. 155-170
Citations number
10
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Computer Science & Engineering
Journal title
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
ISSN journal
1526-1492 → ACNP
Volume
2
Issue
2
Year of publication
2001
Pages
155 - 170
Database
ISI
SICI code
1526-1492(2001)2:2<155:TNSOUM>2.0.ZU;2-Q
Abstract
Three-dimensional (3D) unsteady numerical simulations are carried out by me ans of the finite element method (FEM) with the generalized simplified mark er and cell (GSMAC) method in silicon melt with a non-deformable free surfa ce 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 earlie r by increasing the absolute value of the thermal coefficient of surface te nsion in the range of sigma (T) = 0.0 - 1.5 x 10(-5)N/mK. Although the velo city distribution in the circumferential direction is isotropy in any direc tion 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 di stribution is observed just under the single crystal, and the amplitude is found to depend on the value of sigma (T). After imposing the vertical magn etic field more than 0.05T to the melt from 50s, the flow pattern becomes r estored to symmetry. But the instability remains under the single crystal a nd it indicates that the influence of Marangoni convection can not be negle cted in the crystal growing process.