Flow instabilities are analyzed within a destabilized vertical Bridgman crystal growth system, first studied experimentally by Kim et al. (J. Electrochem. Soc. 119(1972) 1218), using a distributed-parameter model consisting of balance equations for energy and momentum transport. Numerical solution of the governing equations via a Galerkin finite element method reveals multiple operating states and dynamic phenomena. Bifurcation analysis shows that the onset of time-periodic flows occurs in the model system via a supercritical Hopf bifurcation, consistent with prior experimental observations on the dynamics of flow in similar systems.
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This material is based upon work supported by the National Science Foundation under Grant No. 0201486. This work was also supported in part by the United States National Aeronautics and Space Administration and the Minnesota Supercomputing Institute. PS also expresses thanks to the University of Minnesota Graduate School for a Doctoral Dissertation Fellowship.