Influence of high frequency vibrations on fluid flow and heat transfer in a floating zone

This paper deals with the numerical simulation of fluid flow and heat transfer in a silicon floating zone (FZ) subjected to axial vibrations. Corresponding experiments were performed under microgravity conditions within the framework of the European sounding rocket Maxus-4 flight. The study concerns a liquid zone maintained between two rigid rods of equal radii. The growing crystal is subjected to vibrations in the direction of the zone axis. Numerical modelling of the convective heat transfer in the liquid zone is carried out accounting for melting and crystallization. The flows and the heat transfer in the melt are calculated on the basis of the equations of thermal vibrational convection under non-uniform vibrations. The calculations are made for zero gravity and 1-g conditions accounting for both pulsational and average deformations of the free surface. The temperature at the free surface is fixed and corresponds to the experimental one. The shape and the position of the solid-liquid interfaces are given by the isotherm of the melting point of the material. The problem is solved by a finite difference method. The boundary-fitted curvilinear coordinate system is employed. The calculations are made for the parameters corresponding to the radiation heated floating zone growth of silicon, i.e. a crystal diameter of 10 mm and an aspect ratio of the melt zone between 1 and 1.5. The vibration amplitude is varied in the range of 3 to 4.5 μm and the vibration frequency lays in the interval of 2 to 4.5 kHz. It is shown that for zero gravity and for 1-g conditions, the vibrations lead to a decrease of the thermocapillary flow intensity near the crystal-melt interface. For zero gravity conditions vibrations lead to a flattening of the crystallization front.