Stability of Thermocapillary Convection in Rotating Shallow Annular Pool of Silicon Melt

Shi, Wan-Yuan; Li, You Rong; Ermakov, M. K.; Imaishi, Nobuyuki

doi:10.1007/s12217-010-9194-9

Cited by 16 publications

(2 citation statements)

References 10 publications

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“…The destabilization of a Marangoni (or buoyant) flow by weak rotation has also been observed in different crystal growth configurations, namely the Czochralski technique, for both small and large Prandtl number fluids. [28][29][30] To complete this short survey, Minakuchi et al 31 seems the only study to have performed a three-dimensional simulation corresponding to the full-zone with rotation. In the exact counter-rotating configuration, it was shown qualitatively that the oscillatory thermocapillary flow is stabilized by rotation for three rotation rates, a small Prandtl number fluid and a short aspect ratio such that the distance between the feed rod and the crystal is equal to the radius.…”

Section: Introductionmentioning

confidence: 99%

Thermocapillary instabilities in a laterally heated liquid bridge with end wall rotation

2011

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The effect of rotation on the stability of thermocapillary driven flow in a laterally heated liquid bridge is studied numerically using the full-zone model of the floating-zone crystal growth technique. A small Prandtl number (0.02) fluid, relevant for semiconductor melts, is studied with an aspect ratio (height to diameter of the melt) equal to one. Buoyancy is neglected. A linear stability analysis of three-dimensional perturbations is performed and shows that for any ratio of angular velocities, a weak rotation rate has the surprising effect of destabilizing the base flow. By systematically varying the rotation rate and ratio of angular velocities, the critical threshold and azimuthal wave number of the most unstable mode is found over a wide range of this two parameter space. Depending on these parameters, the leading eigenmode is a wave propagating either in the positive or negative azimuthal direction, with kinetic energy typically localized close to one of the end walls. These results are of practical interest for industrial crystal growth applications, where rotation is often used to obtain higher quality crystals.

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Section: Introductionmentioning

confidence: 99%

Thermocapillary instabilities in a laterally heated liquid bridge with end wall rotation

2011

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“…11 Results showed that the system rotation has an important influence on the flow transition and the effect of Coriolis force must be taken into account in the design of space experiments. Shi et al 12,13 performed a linear stability analysis on the effect of pool rotation on the basic thermocapillary flow and the critical conditions for the onset of hydrothermal waves in a rotating annular pool heated from the outer wall. The fluids of both silicone oil (Pr = 6.7) and silicon melt (Pr = 0.011) were investigated.…”

Section: Introductionmentioning

confidence: 99%

Rotating and thermocapillary-buoyancy-driven flow in a cylindrical enclosure with a partly free surface

Liao

2014

Physics of Fluids

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In order to understand the characteristics of the complex flow driven by the combined thermocapillary-buoyancy effect and differential rotation of a cylindrical pool and a disk on the free surface, a series of unsteady three-dimensional numerical simulations were performed. Results indicate that the flow is axisymmetric and steady at a small temperature difference and low rotation rates. The basic meridional flow structures are composed of toroidal circulations. With an increase of the rotation rate and/or temperature difference, the basic flow transits to a three-dimensional oscillatory flow. Without rotation, the unstable thermocapillary-buoyancy flow is characterized by pulsating spoke patterns with the periodic growth and decay of temperature and velocity oscillations. When the disk and/or cylinder rotate, the oscillatory flow behaves as temperature and velocity fluctuation waves traveling in the azimuthal direction. The wave propagation velocity and direction, fluctuation amplitude, and wave number depend on the interaction of the thermocapillary, buoyancy, centrifugal and Coriolis forces. The critical conditions for the flow transition are determined. It is found that the critical thermocapillary Reynolds number initially increases before decreasing with the increase of the disk rotation rate, but the rotation of cylinder always retards the flow instability. In addition, the mechanisms of the flow instabilities are discussed and briefly summarized.

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Linear Stability Analysis of Thermocapillary Flow in Rotating Shallow Pools Heated from Inner Wall

et al. 2019

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Stability of Thermocapillary Convection in Rotating Shallow Annular Pool of Silicon Melt

Cited by 16 publications

References 10 publications

Thermocapillary instabilities in a laterally heated liquid bridge with end wall rotation

Thermocapillary instabilities in a laterally heated liquid bridge with end wall rotation

Rotating and thermocapillary-buoyancy-driven flow in a cylindrical enclosure with a partly free surface

Linear Stability Analysis of Thermocapillary Flow in Rotating Shallow Pools Heated from Inner Wall

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