Modeling the Floating Zone: Instabilities in the Half Zone and Full Zone

摘要

Linear stability analyses are performed on steady, axisymmetric base flows in a laterally heated floating zone (full zone) in microgravity. We treat fully three-dimensional disturbances for a range of Prandtl numbers less than 0.2 and aspect ratios (total zone height to diameter) varying from 1/2 to 2. In all cases, the critical mode is a transition to a steady three-dimensional flow. Axial symmetry of the disturbance, and the critical wave number, vary with both Prandtl number and aspect ratio. Results are compared and contrasted to the linear stability of the half-zone model, which is commonly used to approximate one-half of the full zone. Findings indicate that the stability analysis of the half zone is a reasonable approximation to that of the full zone for Prandtl numbers less than approximately 0.05, in zones with aspect ratios near unity. The dominant mechanism for feeding energy into the perturbation, as well as the critical wave number, is the same in both models. However, the driving force required for the onset of instability in the half zone is 25-50% larger than that in the full zone. As the Prandtl number is increased, the two models become more divergent, first with respect to the predicted critical values, and then in the instability mechanisms themselves.