Analysis of flow instabilities in convex and concave floating zones heated by an equatorial ring under microgravity conditions

Abstract

This analysis deals with advances in models concerning the floating zone technique as well as with novel results on the relative importance of various parameters in the crystal-growth process. The attention is focused in particular on microgravity fluid-dynamic aspects and on the effect of the volume of the liquid melt since the cylindrical configuration is expected to be only a very special case under microgravity conditions. The instability of Marangoni flow is investigated by direct three-dimensional and time-dependent simulation of the problem and parallel computations. Body-fitted curvilinear co-ordinates are adopted to handle the non-cylindrical shape. A novel realistic distribution is considered to model the surface heat flux generated by a ring heater positioned around the equatorial plane at a fixed distance from the axis of the liquid (full) zone. The fluid-dynamic environment that occurs inside the melt is very sensitive to the geometrical aspect ratio A F (length/diameter) of the floating zone and to the volume factor S (ratio of the volume of the liquid zone and the volume of the corresponding cylindrical configuration: convex S>1, concave S<1). The role played by the geometrical constraints and degrees of freedom of the Marangoni toroidal rolls in determining the azimuthal structure and the stability of the flow field is discussed.