Convective Instability in Annular Pools

Abstract: The convective instabilities in semiconductor or oxide melts, significantly affect the quality of large crystals grown from the melts by the Czochralski method. This paper reviews our recent numerical studies of thermal convection in annular pools of low-Pr silicon melt and moderate-Pr silicone oil. The mechanisms of the convective instability are discussed and the critical conditions for the onset of three-dimensional flow are determined. The results show that the hydrothermal wave, characterized by curved spokes, is dominant in a shallow thin pool. In a thick pool of the low-Pr silicon melt, there appears a standing wave type of oscillatory longitudinal rolls, which moves in the azimuthal direction and looks very similar to the hydrothermal waves. In deep pools of moderate-Pr silicone oil, a three-dimensional steady flow pattern, consisting of pairs of counter-rotating longitudinal rolls, arises, which corresponds to the RayleighBenard instability

State-to-State Rotational Relaxation Rate Constants for CO+Ne from IR-IR Double-Resonance Experiments: Comparing Theory to Experiment

IR-IR double-resonance experiments were used to study the state-to-state rotational relaxation of CO with Ne as a collision partner. Rotational levels in the range Ji=2-9 were excited and collisional energy transfer of population to the levels Jf=2-8 was monitored. The resulting data set was analyzed by fitting to numerical solutions of the master equation. State-to-state rate constant matrices were generated using fitting law functions. Fitting laws based on the modifed exponential gap (MEG) and statistical power exponential gap (SPEG) models were used; the MEG model performed better than the SPEG model. A rate constant matrix was also generated from scattering calculations that employed the ab initio potential energy surface of McBane and Cybulski [J. Chem. Phys. 110, 11 734 (1999)]. This theoretical rate constant matrix yielded kinetic simulations that agreed with the data nearly as well as the fitted MEG model and was unique in its ability to reproduce both the rotational energy transfer and pressure broadening data for Ne-CO. The theoretical rate coefficients varied more slowly with the energy gap than coefficients from either of the fitting laws

Two bifurcation transitions of the floating half zone convection in a fat liquid bridge of larger Pr

The transient process of the thermocapillary convection was obtained for the large Pr floating half zone by using the method of three-dimensional and unsteady numerical simulation. The convection transits directly from steady and axisymmetric state to oscillatory flow for slender liquid bridge, and transits ®rst from steady and axisymmetric convection to the steady and non-axisymmetric convection, then, secondly to the oscillatory convection for the fatter liquid bridge. This result implies that the volume of liquid bridge is not only a sensitive critical parameter for the onset of oscillation, but also relates to the new mechanism for the onset of instability in the floating half zone convection even in case of large Prandtl number fluid.The transient process of the thermocapillary convection was obtained for the large Pr floating half zone by using the method of three-dimensional and unsteady numerical simulation. The convection transits directly from steady and axisymmetric state to oscillatory flow for slender liquid bridge, and transits ®rst from steady and axisymmetric convection to the steady and non-axisymmetric convection, then, secondly to the oscillatory convection for the fatter liquid bridge. This result implies that the volume of liquid bridge is not only a sensitive critical parameter for the onset of oscillation, but also relates to the new mechanism for the onset of instability in the floating half zone convection even in case of large Prandtl number fluid

Proper orthogonal decomposition of oscillatory Marangoni flow in half-zone liquid bridges of low-Pr fluids

Proper orthogonal decomposition (POD) using method of snapshots was performed on three different types of oscillatory Marangoni flows in half-zone liquid bridges of low-Pr fluid (Pr = 0.01). For each oscillation type, a series of characteristic modes (eigenfunctions) have been extracted from the velocity and temperature disturbances, and the POD provided spatial structures of the eigenfunctions, their oscillation frequencies, amplitudes, and phase shifts between them. The present analyses revealed the common features of the characteristic modes for different oscillation modes: four major velocity eigenfunctions captured more than 99% of the velocity fluctuation energy form two pairs, one of which is the most energetic. Different from the velocity disturbance, one of the major temperature eigenfunctions makes the dominant contribution to the temperature fluctuation energy. On the other hand, within the most energetic velocity eigenfuction pair, the two eigenfunctions have similar spatial structures and were tightly coupled to oscillate with the same frequency, and it was determined that the spatial structures and phase shifts of the eigenfunctions produced the different oscillatory disturbances. The interaction of other major modes only enriches the secondary spatio-temporal structures of the oscillatory disturbances. Moreover, the present analyses imply that the oscillatory disturbance, which is hydrodynamic in nature, primarily originates from the interior of the liquid bridge. (C) 2007 Elsevier B.V. All rights reserved

Thermocapillary Flows In Liquid Bridges Of Molten Tin With Small Aspect Ratios

Numerical simulations were conducted to study thermocapillary flows in short half-zone liquid bridges of molten tin with Prandtl number Pr = 0.009, under ramped temperature difference. The spatio-temporal structures in the thermocapillary flows in short half-zone liquid bridges with aspect ratios As = 0.6, 0.8, and 1.0 were investigated. The first critical Marangoni numbers were compared with those predicted by linear stability analyses (LSA). The second critical Marangoni numbers for As = 0.6 and 0.8 were found to be larger than that for As = 1.0. The time evolutions of the thermocapillary flows exhibited unusual features such as a change in the azimuthal wave number during the three-dimensional stationary (non-oscillating) flow regime, a change in the oscillation mode during the three-dimensional oscillatory flow regime, and the decreasing and then increasing of amplitudes in a single oscillation mode. The effects of the ramping rate of the temperature difference on the flow modes and critical conditions were studied as well. In this paper, the experimental observability of the critical conditions was also discussed. (C) 2008 Elsevier Inc. All rights reserved