Temperature fluctuations of the Marangoni flow in a liquid bridge of molten silicon under microgravity on board the TR-IA-4 rocket

Nakamura, Shin; Hibiya, Taketoshi; Kakimoto, Koichi; Imaishi, Nobuyuki; Nishizawa, Shin Ichi; Hirata, Akira; Mukai, Kusuhiro; Yoda, S.; Morita, Tomoji

doi:10.1016/s0022-0248(97)00440-5

Cited by 73 publications

(35 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since it is very difficult to do well controlled experiments with liquid metals of small Prandtl numbers (due to opacity, reactivity and high temperatures of the melts), there are only few experiments on the flow instability in half zone liquid bridges of semiconductor materials [15][16][17][18][19][20]. Nakamura et al [17] and Hibiya et al [19] studied the Marangoni flow azimuthal organization in a half zone of Silicon (Pr=0.02, diameter D = 1 [cm]) under highly supercritical conditions using a Xray radiography with zirconium-core tracers.…”

Section: Introductionmentioning

confidence: 99%

3D Analysis of Crystal/Melt Interface Shape and Marangoni Flow Instability in Solidifying Liquid Bridges

Lappa

Savino

2002

Journal of Computational Physics

View full text Add to dashboard Cite

This version is available at https://strathprints.strath.ac.uk/62646/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. AUTHOR'S POST PRINT AbstractSolidification of Gallium (Pr=0.02) in liquid bridges in zero gravity conditions is investigated by numerical solutions of the three-dimensional and time-dependent flow-field equations. A single region (continuum) formulation based on the enthalpy method is adopted to model the phase change problem. The paper analyzes the influence of the azimuthally asymmetric and steady first bifurcation of the Marangoni flow on the shape of the solid/melt interface during the crystal growth process. The numerical results show that this interface is distorted in the azimuthal direction. The distortion is related to the sinusoidal three-dimensional temperature disturbances due to the instability of the Marangoni flow. The three-dimensional flow field organization, related to the wave number, changes during the solidification process; this behaviour is explained according to the variation of the aspect ratio of the solidifying liquid bridge. A correlation law is found for the azimuthal wave number of the instability as function of the melt zone aspect ratio.

show abstract

Section: Introductionmentioning

confidence: 99%

3D Analysis of Crystal/Melt Interface Shape and Marangoni Flow Instability in Solidifying Liquid Bridges

Lappa

Savino

2002

Journal of Computational Physics

View full text Add to dashboard Cite

show abstract

“…Only a few experiments, such as those conducted by CroK ll et al [5] and Han et al [9], have been reported on the onset of oscillatory convection in the #oating half-zone of small Pr #uid; a critical Marangoni number for the onset of time-dependence is observed to be about 900 in the case of a mercury liquid bridge [9]. Observation of #ow and temperature "elds in the liquid bridge is generally very di$cult in the case of low Pr #uids because of its opaqueness, and only very sophisticated and expensive techniques such as X-ray diagnostics, can provide some information on the velocity "eld in semiconductor melts [8]. Stability analysis and numerical simulation can therefore be very useful in the study of thermocapillary convection in a #oating half-zone melt of small Prandtl number #uids.…”

Section: Introductionmentioning

confidence: 99%

Effect of liquid bridge volume on the instability in small-Prandtl-number half zones

Chen

Prasad

1999

Journal of Crystal Growth

View full text Add to dashboard Cite

A perturbation method is used to examine the linear instability of thermocapillary convection in a liquid bridge of #oating half-zone "lled with a small Prandtl number #uid. The in#uence of liquid bridge volume on critical Marangoni number and #ow features is analyzed. The neutral modes show that the instability is mainly caused by the bulk #ow that is driven by the nonuniform thermocapillary forces acting on the free surface. The hydrodynamic instability is dominant in the case of small Prandtl number #uid and the "rst instability mode is a stationary bifurcation. The azimuthal wave number for the most dangerous mode depends on the liquid bridge volume, and is not always two as in the case of a cylindrical liquid bridge with aspect ratio near 0.6. Its value may be equal to unity when the liquid bridge is relatively slender.

show abstract

“…These free-surface shapes have been simulated in both half-zone [Morthland and Walker 1996] and full-zone [Lappa 2004] models, respectively. In [Nakamura et al 1998], m = 1 and 2 oscillating instability modes were observed in molten silicon in an optically heated half-zone configuration on the TR-IA rocket. The hydrodynamic and hydrothermal instability mechanisms of low and high-Pr liquid bridges, respectively, have been confirmed in [Chen et al 1997;Lappa 2005a;Bouizi et al 2007] and elsewhere.…”

Section: Introductionmentioning

confidence: 99%

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

Huang¹,

Houchens²

2011

J. Mech. Mater. Struct.

View full text Add to dashboard Cite

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.

show abstract

Temperature fluctuations of the Marangoni flow in a liquid bridge of molten silicon under microgravity on board the TR-IA-4 rocket

Cited by 73 publications

References 0 publications

3D Analysis of Crystal/Melt Interface Shape and Marangoni Flow Instability in Solidifying Liquid Bridges

3D Analysis of Crystal/Melt Interface Shape and Marangoni Flow Instability in Solidifying Liquid Bridges

Effect of liquid bridge volume on the instability in small-Prandtl-number half zones

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

Contact Info

Product

Resources

About