THREE-DIMENSIONAL NUMERICAL COMPUTATION OF CZOCHRALSKI CONVECTION OF LIQUID METAL IN A ROTATING CRUCIBLE UNDER A HORIZONTAL MAGNETIC FIELD
Solar Energy Thermal Applications Laboratory Oita University, Oita 870-11, Japan; Institute of Advanced Material Study, Kyushu University, Kasuga Koen 6-1, Kasuga, Fukuoka 816, JAPAN
Institute of Advanced Material Study Kyushu University, Kasuga, Fukuoka, Japan
Institute of Advanced Material Study, Kyushu University, Kasuga, Japan; and Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong University, Xi'an 710049, P. R. China
Numerical computations were carried out for a Czochralski bulk flow of liquid metal in a rotating crucible with a rotating crystal rod. A uniform horizontal magnetic field was assumed for which a fully three-dimensional model in a cylindrical coordinate system was required. Numerical computations are for Ha=0 and 1000, and for Pr = 0.01, Gr = 107,Rerod = 1620 and Recru = −3240.
Transient responses of the average velocity and temperature are found to be smooth after a step rotation of a crucible. Detailed flow modes are visualized with velocity vectors for both without and with a magnetic field. Even without a magnetic field, the rotational velocity field is complicated but axially symmetric in terms of an axial center to indicate somewhat the reliability of the present numerical scheme. In a strong magnetic field Ha=1000, velocity and temperature profiles converged smoothly and quickly from a steady state in a rotating crucible. The resulting flow is just rotating under a crystal rod on the liquid surface and the rest of the liquid is almost stagnant except very near a crucible wall. Detailed view of the velocity field proves very complicated and is dependent on the circumferential location to reflect a strong three-dimensional effect. Based on these flow fields, dopant concentration C is numerically solved for Sc=10.