Digital simulation of flow patterns in the czochralski crystal-pulling process

Abstract

A procedure is described for the numerical solution of the time-dependent equations governing the flow in a crystal-growth crucible. The molten crystal material is taken to be a Newtonian fluid with constant viscosity. The Boussinesq approximation is employed, i.e. compressibility is neglected except insofar as thermal expansion modifies the gravitational body force. Crucible rotation is the main driving force, but a series of numerical experiments suggests that buoyancy effects can modify appreciably the impurity-blending estimates obtained from an isothermal study. © 1977.