Modeling the Floating Zone: Instabilities in the Half Zone and Full Zone

Houchens, Brent C.; Walker, John S.

doi:10.2514/1.2178

Cited by 10 publications

(8 citation statements)

References 19 publications

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“…10,15,16 A comparison between the half-zone and full-zone has been carried out in Ref. 17 and shows that the dominant mechanism for the leading instability is qualitatively captured by the half-zone for Prandtl numbers less than 0.05. This justifies most of the studies on the half-zone configuration, at least to the first instability.…”

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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“…The first instability for Pr < 0.4 is characterized by stationary disturbances [Bouizi et al 2007]. Within this range, [Houchens and Walker 2005] further suggested three subregimes with different axial symmetries of the perturbations, which were confirmed in [Bouizi et al 2007], both in full-zone geometries. In [Levenstam and Amberg 1995;Leypoldt et al 2000] the secondary instability was found to be three-dimensional and oscillatory in the half-zone.…”

Section: Introductionmentioning

confidence: 64%

“…Note that Pr = 0.001 is chosen because its critical curve very likely marks the lower limit of critical curves for Pr → 0. According to [Houchens and Walker 2005], at Ha = 0 the Re FZ,cr for Pr = 10 −10 is less than 1% smaller than Re FZ,cr for Pr = 0.001. Details of the perturbation flow field and the energy analysis between the base state and perturbed field are presented and validated with other liquid bridge studies in [Huang and Houchens 2011].…”

Section: Introductionmentioning

confidence: 99%

“…However, the onset of flow instabilities tend to be delayed in the half-zone by the presence of the no-slip boundary that replaces the midplane and removes momentum from the flow through viscous effects. An extensive comparison of the half-zone and full-zone models can be found in [Houchens and Walker 2005].…”

Section: Introductionmentioning

confidence: 99%

“…Second-order vorticity transport formulation. In [Houchens and Walker 2005], a fourth-order stream function formulation was introduced for the base flow problem, with the stream function ψ defined as…”

Section: Introductionmentioning

confidence: 99%

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Numerical linear stability analysis of a thermocapillary-driven liquid bridge with magnetic stabilization

Huang¹,

Houchens²

2011

J. Mech. Mater. Struct.

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A full-zone model of a thermocapillary-driven liquid bridge exposed to a steady, axial magnetic field is investigated using a global spectral collocation method for low-Prandtl number (Pr) fluids. Flow instabilities are identified using normal-mode linear stability analyses. This work presents several numerical issues that commonly arise when using spectral collocation methods and linear stability analyses in the solution of a wide range of partial differential equations. In particular, effects such as discontinuous boundary condition regularization, identification of spurious eigenvalues, and the use of pseudospectra to investigate the robustness of the stability analysis are addressed. Physically, this work provides simulations in the practical range of experimentally utilized magnetic field stabilization in optically heated float-zone crystal growth. A second-order vorticity transport formulation enables modeling of the liquid bridge up to these intermediate magnetic field strength ranges, measured by the Hartmann number (Ha). The thermocapillary driving and magnetic stabilization effects are observed up to Ha = 500 for Pr = 0.001 and up to Ha = 300 for Pr = 0.02. Prandtl number effects on temperature and flow fields are investigated within Pr ∈ (10 −12 , 0.0667) and indicate that Pr = 0.001 is a good representation of the base state in the Pr → 0 limit, at least up to Ha = 300.

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Numerical investigation of the effect of rotation on the oscillatory thermocapillary convection and dopant transport in a silicon liquid bridge

Liu

2019

Journal of Crystal Growth

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Modeling the Floating Zone: Instabilities in the Half Zone and Full Zone

Cited by 10 publications

References 19 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

Numerical linear stability analysis of a thermocapillary-driven liquid bridge with magnetic stabilization

Numerical investigation of the effect of rotation on the oscillatory thermocapillary convection and dopant transport in a silicon liquid bridge

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