NUMERICAL-SIMULATION OF FLOW STRUCTURES AND INSTABILITIES OCCURRING IN A LIQUID-ENCAPSULATED CZOCHRALSKI PROCESS

This paper concerns the prediction and the analysis of the steady and time-dependent flow regimes that develop in liquid-encapsulated Czochralski (LEC) systems for material processing. The combined effects of temperature gradient and rotation on the flow and the temperature field, and especially the influence of the encapsulant layer (of Prandtl number 10 less-than-or-equal-to Pr(e) less-than-or-equal-to 3270) on the melt (Pr(m) = 0.015), are investigated using axisymmetric modeling. The accuracy of the solutions based on a finite element method is discussed. The effects of the Grashof number (up to Gr = 1.9 x 10(7)) and of the rotation Reynolds numbers of the crystal (up to \Re(s)\ = 10(4)) and of the crucible (up to Re(c) = 1.5 x 10(4)) are analyzed.