Effect of pool rotation on thermocapillary convection in shallow annular pool of silicone oil

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

doi:10.1016/j.jcrysgro.2006.06.051

Cited by 40 publications

(14 citation statements)

References 39 publications

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“…It was concluded that the crystal rotation rate was a sensitive parameter for the characteristics of the flow field. Moreover, Shi et al [41] and Li et al [42] reported the results of three-dimensional numerical simulations of thermocapillary flow for silicone oil and silicon melt in a rotating shallow annular pool, respectively. It was certified that rotation rate of the annular pool had an important influence on the critical temperature difference and the propagating direction of the traveling waves.…”

Section: Introductionmentioning

confidence: 99%

Instability of forced flow in a rotating cylindrical pool with a differentially rotating disk on the free surface

2010

Sci. China Technol. Sci.

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The instability of forced flow in a rotating cylindrical pool with a differentially rotating disk on the free surface is investigated through a series of unsteady three-dimensional numerical simulations. The results show that the basic flow state of this system is axisymmetric and steady, but has rich structures at the meridian plane. However, when the rotation Reynolds number exceeds a critical value, the flow will undergo a transition to three-dimensional oscillatory flow, characterized by the velocity fluctuation waves traveling in the azimuthal direction. The main characteristics of the flow patterns are presented, including the propagating direction, velocity, amplitude and wave number, which depend on the rotation rates and directions of the disk and the cylindrical pool, and the critical conditions for the onset of oscillatory flow are also determined. For the case of disk-only rotation, the centrifugal instability is responsible for the flow transition, and when the disk iso-and counter-rotates with the cylindrical pool, the mechanisms for the transition are elliptic and of circular shear instabilities, respectively. rotation, flow transition, flow instabilityCitation:Wu C M, Li Y R. Instability of forced flow in a rotating cylindrical pool with a differentially rotating disk on the free surface.

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Section: Introductionmentioning

confidence: 99%

Instability of forced flow in a rotating cylindrical pool with a differentially rotating disk on the free surface

2010

Sci. China Technol. Sci.

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“…It has an open top free surface, a solid bottom, an inner solid wall (radius R i = 20 mm), an outer solid wall (radius R o = 40 mm), and depth d = 1 mm. This geometry is the same as that of Shi et al (2006). The fluid is silicon melt, and its physical properties are listed in Table 1.…”

Section: Physical and Mathematical Modelsmentioning

confidence: 99%

“…They have found that the critical Reynolds number decreases with increasing the rotation rate of the annulus, i.e., the rotation destabilizes the thermocapillary convection. Shi et al (2006) have performed the LSA and nonlinear numerical simulations about the effects of pool rotation on the basic thermocapillary flow and the critical conditions for the incipience of HTWs in a rotating shallow annular pool of silicone oil (Pr = 6.7) heated from the outer wall. Their results also indicated that the pool rotation destabilizes the basic steady axisymmetric thermocapillary flow in the range of Ta = 0 to 322.2.…”

Section: Introductionmentioning

confidence: 99%

“…However, the critical conditions for the incipience of HTW haven't been determined in that work. In this work, a series of LSA are conducted to determine the critical conditions for the incipience of oscillatory flow of silicon melt in differentially heated shallow annular pools with the same geometry as those used for the silicone oil problems (Shi et al 2006;Shi and Imaishi 2007) to reveal the effect of pool rotation on the stability of steady 2-D basic flow of silicon melt under the microgravity condition.…”

Section: Introductionmentioning

confidence: 99%

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

Shi

Ermakov

et al. 2010

Microgravity Sci. Technol.

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In order to understand the effect of pool rotation on stability of thermocapillary convection, the critical conditions for the incipience of oscillatory flow in rotating shallow annular pools of silicon melt (Pr = 0.011) are investigated by means of linear stability analysis (LSA) under different pool rotation rates ranging from Ta = 0 to 1,513.9 and under microgravity condition. The results indicate that with increase of Ta numbers, the critical Marangoni for the incipience of hydrothermal wave (HTW) increases, i.e., pool rotation stabilizes the steady axisymmetric thermocapillary convection of silicon melt. The critical azimuthal wave number m c decreases linearly with increase of Ta number when Ta ≤ 378.5. However, when Ta > 378.5, m c almost keeps constant with m c = 34. When Ta < 550 the HTW propagates in the same direction as the pool rotation direction, while it is reversed when Ta > 550.

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“…Various factors, which influenced the process of flow transition and the possible unstable flow patterns, are confirmed. However, there are a few studies on the thermocapillary convection in an annular pool (Shi et al 2006). …”

Section: Introductionmentioning

confidence: 99%

Stability of Thermocapillary Convection in Annular Pools with Low Prandtl Number Fluid

Liu

Shi

et al. 2009

Microgravity Sci. Technol.

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In order to understand the stability characteristics of thermocapillary convection in an annular pool with low Prandtl number (Pr = 0.011) fluid, a linear stability analysis had been performed. The annular pool was heated from the outer cylindrical wall and cooled at the inner wall. Bottom and top surface were adiabatic. The results show that the critical Marangoni number and the critical wave number decrease with the increase of the aspect ratio, which is defined as the ratio of the depth to the gap width of the annular pool. When the aspect ratio exceeds 0.12, the critical wave number keeps almost constant. As the radius ratio increases, the critical Marangoni number decreases slightly, while the critical wave number increases. In the gravity condition, the effect of the buoyancy on the critical Marangoni number and wave number increases gradually with the increase of the aspect ratio.

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Effect of pool rotation on thermocapillary convection in shallow annular pool of silicone oil

Cited by 40 publications

References 39 publications

Instability of forced flow in a rotating cylindrical pool with a differentially rotating disk on the free surface

Instability of forced flow in a rotating cylindrical pool with a differentially rotating disk on the free surface

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

Stability of Thermocapillary Convection in Annular Pools with Low Prandtl Number Fluid

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