BIFURCATION AND STABILITY ANALYSES OF HORIZONTAL BRIDGMAN CRYSTAL-GROWTH OF A LOW PRANDTL NUMBER MATERIAL

Stability and bifurcation analyses are conducted for horizontal Bridgm an crystal growth of a low Prandtl number material. The model consider s two-dimensional heat transfer and fluid flow in the melt, the growth interface, and the heat conduction in the crystal. In addition to the construction of bifurcation diagrams, the stability of various soluti on families is further examined by their leading eigenvalues based on linear stability analysis. Transient calculation is also performed to illustrate the global behavior of the basic states after a disturbance . For the cases with a fixed interface, the results for periodically o scillatory flows are in good agreement with previous reports. With a f ree interface, the bifurcation diagram is slightly changed due to inte rface deformation, but its qualitative characteristics remain the same . Nevertheless, the dynamic evolution of the interface due to convecti on provides useful information for crystal growth. The oscillation amp litude of the interface velocity, which decreases with the increasing heat of fusion, is in the same order of a common growth rate used in p ractice. (C) 1998 Elsevier Science B.V. All rights reserved.