Three-dimensional numerical simulation of thermocapillary flow of moderate Prandtl number fluid in an annular pool

Li, You Rong; Peng, Lan; Akiyama, Yoshikatsu; Imaishi, Nobuyuki

doi:10.1016/j.jcrysgro.2003.07.034

Cited by 67 publications

(50 citation statements)

References 27 publications

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“…The validity of the code for the thermocapillary flow simulation has also been well confirmed in Refs. [24,25,27] performed for case A at ∆T=21 K. These three grids produced similar surface spoke patterns and space-time characteristics. However, the period and the amplitude of temperature oscillation at the monitoring point P on the liquid surface at r=20 mm and θ=0 showed small grid dependence as shown in Table 1.…”

Section: Model Formulation and Numerical Methodsmentioning

confidence: 80%

“…At the same time, many authors performed two-dimensional (2D) simulations of thermocapillary-buoyancy convection in pools of low-Pr fluids and showed the existence of a multicellular steady flow and a transition to oscillatory convection [5,[20][21][22]. Xu and Zebib [22], Sim et al [23] and Li et al [24] also performed three-dimensional (3D) calculations in rectangular geometries and annular pools for fluids with moderate Pr number, respectively. In our previous paper [25], unsteady 3D numerical simulation of thermocapillary flow in annular pool of silicon melt (Pr=0.011) was performed and the existence of the hydrothermal waves was confirmed.…”

Section: Introductionmentioning

confidence: 99%

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Thermocapillary‐buoyancy flow of silicon melt in a shallow annular pool

Li¹,

Peng

et al. 2004

Cryst. Res. Technol.

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In order to understand the nature of surface spoke patterns on silicon melt in industrial Czochralski furnaces, a series of unsteady three-dimensional numerical simulations were conducted for thermocapillary-buoyancy flow of silicon melt in annular pool (inner radius r i =15 mm, outer radius r o =50 mm, depth d=3mm). The pool is heated from the outer cylindrical wall and cooled at the inner wall. Bottom and top surfaces either are adiabatic or allow heat transfer in the vertical direction. Results show that a small temperature difference in the radial direction generates steady roll-cell thermocapillary-buoyancy flow. With large temperature difference, the simulation can predict three-dimensional oscillatory flow, which is characterized by spoke patterns traveling in the azimuthal direction. The small vertical heat flux (3W/cm 2 ) does not have significant effects on the characteristics of this oscillatory flow. Details of the flow and temperature disturbances are discussed and the critical conditions for the onset of the oscillatory flow are determined.

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Section: Model Formulation and Numerical Methodsmentioning

confidence: 80%

Section: Introductionmentioning

confidence: 99%

Thermocapillary‐buoyancy flow of silicon melt in a shallow annular pool

Li¹,

Peng

et al. 2004

Cryst. Res. Technol.

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“…Concerning the annular pool, we consider 0.65 cs silicone oil (Pr=6.7) and internal and external radii (a=20 mm and b=40 mm) 24,25 Indeed, these figures provide evidence that PAS tend to "stay attached" for most of their azimuthal extension to the isosurfaces of fluid axial angular velocity  fluid (= z /2) such that…”

Section: Resultsmentioning

confidence: 99%

Assessment of the role of axial vorticity in the formation of particle accumulation structures in supercritical Marangoni and hybrid thermocapillary-rotation-driven flows

Lappa¹

2013

Physics of Fluids

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“…Another widely studied model of axisymmetric thermocapillary convection is the flow in an annular pool (see [16][17][18] and references therein). The flow region is bounded by two coaxial cylinders maintained at different temperatures.…”

Section: Annular Poolmentioning

confidence: 99%

“…To reach a convergence of the critical values, a further mesh refinement should be used. To illustrate how different are results obtained on different coarse grids, we refer to Table I of [16], Table II of [17], and Table I of [18]. For this study, we used parameters of [16][17][18] and recalculated the marginal and critical parameters on fine grids used here.…”

Section: Annular Poolmentioning

confidence: 99%

Three‐dimensional instability of axisymmetric flows: solution of benchmark problems by a low‐order finite volume method

Gelfgat

2006

Numerical Methods in Fluids

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SUMMARYSeveral problems on three-dimensional instability of axisymmetric steady flows driven by convection or rotation or both are studied by a second-order finite volume method combined with the Fourier decomposition in the periodic azimuthal direction. The study is focused on the convergence of the critical parameters with mesh refinement. The calculations are done on the uniform and stretched grids with variation of the stretching. Converged results are reported for all the problems considered and are compared with the previously published data. Some of the calculated critical parameters are reported for the first time. The convergence studies show that the three-dimensional instability of axisymmetric flows can be computed with a good accuracy only on fine enough grids having about 100 nodes in the shortest spatial direction. It is argued that a combination of fine uniform grids with the Richardson extrapolation can be a good replacement for a grid stretching. It is shown once more that the sparseness of the Jacobian matrices produced by the finite volume method allows one to enhance performance of the Newton and Arnoldi iteration procedures by combining them with a direct sparse linear solver instead of using the Krylov-subspace-based iteration methods.

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Three-dimensional numerical simulation of thermocapillary flow of moderate Prandtl number fluid in an annular pool

Cited by 67 publications

References 27 publications

Thermocapillary‐buoyancy flow of silicon melt in a shallow annular pool

Thermocapillary‐buoyancy flow of silicon melt in a shallow annular pool

Assessment of the role of axial vorticity in the formation of particle accumulation structures in supercritical Marangoni and hybrid thermocapillary-rotation-driven flows

Three‐dimensional instability of axisymmetric flows: solution of benchmark problems by a low‐order finite volume method

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