Experimental study on time evolution of Marangoni flow instability in molten silicon bridge

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Temperature oscillations due to Marangoni flow instability in molten silicon half zone bridges with various aspect ratios of As = 0.5–2.0 were measured using six thermocouples set azimuthally 60° apart in the liquid bridge close to the cold rod. The Marangoni number was estimated to range from 3000 to 14000, based on the measured axial temperature difference. Fourier spectra of the temperature oscillations were broad and continuous; each peak was not clearly distinguished but rather appeared as a frequency band. Thus, the convection was estimated to be turbulent-like. The time evolution of the azimuthal wave number was observed by analyzing the time-dependence of the phase relationship of the temperature oscillation detected by the six thermocouples. Analyzing the mode appearance coefficient MAC as a function of the aspect ratio, the relationship between the azimuthal mode number m and the aspect ratio As was observed to be m · As ≈ 2.4; the basic structure of flow instability is sustained even under high Marangoni number. The temperature oscillation data was decomposed into that for each frequency band by using wavelet analysis. The frequencies for the m = 1 and m = 3 modes were estimated to be 0.08 to 0.2 Hz and 0.01 to 0.2 Hz, respectively.

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