Steady and oscillatory thermocapillary convection in liquid columns with free cylindrical surface

Preißer, Felix; Schwabe, D.; Scharmann, A.

doi:10.1017/s0022112083000324

Cited by 373 publications

(158 citation statements)

References 16 publications

(20 reference statements)

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“…Experiments [2] performed with transparent liquids (with Prandtl numbers higher than those typical of liquid metals) have shown that for sufficiently small values of the Marangoni number, the convection in the liquid column is laminar, steady and axisymmetrical, but when the Marangoni number exceeds certain critical values depending on the Prandtl number of the liquid, on the geometry and on the boundary conditions, the liquid motion can undergo a transition to an oscillatory three-dimensional complex flow pattern. The appearance of these instabilities provides a possible explanation to justify the presence of undesirable macroscopic and microscopic imperfections in the final crystals obtained in microgravity conditions.…”

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

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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.

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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

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“…NaNO 3 , KCl, silicon oils) where the first instability is oscillatory (e.g. Preisser et al 1983;Velten, Schwabe & Scharmann 1991) and due to hydrothermal waves as discussed by Wanschura et al (1995).…”

Section: Methodsmentioning

confidence: 99%

“…Variation of the aspect ratio Both experimental (Preisser et al 1983) and numerical studies (Wanschura et al 1995) pointed out that the critical wavenumber m is roughly proportional to the inverse aspect ratio 1/Γ of the half-zone since the azimuthal wavelength scales with the characteristic length d. As described in § 4.1 axial magnetic fields introduce a new, smaller length scale by reducing the radial extent of the thermocapillary flow. Thus, we would expect a tendency toward larger critical wavenumbers with increasing Hartmann number.…”

Section: 3mentioning

confidence: 98%

Linear stability of thermocapillary convection in cylindrical liquid bridges under axial magnetic fields

Prange¹,

Wanschura²,

Kuhlmann³

et al. 1999

J. Fluid Mech.

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The stability of axisymmetric steady thermocapillary convection of electrically conducting fluids in half-zones under the influence of a static axial magnetic field is investigated numerically by linear stability theory. In addition, the energy transfer between the basic state and a disturbance is considered in order to elucidate the mechanics of the most unstable mode. Axial magnetic fields cause a concentration of the thermocapillary flow near the free surface of the liquid bridge. For the low Prandtl number fluids considered, the most dangerous disturbance is a non-axisymmetric steady mode. It is found that axial magnetic fields act to stabilize the basic state. The stabilizing effect increases with the Prandtl number and decreases with the zone height, the heat transfer rate at the free surface and buoyancy when the heating is from below. The magnetic field also influences the azimuthal symmetry of the most unstable mode.

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“…The three-dimensional supercritical flow is characterized by formation of a spatially organized pattern with integer number of pairs of hot and cold cells (see e.g., [3]). The properties of the wave are governed by the physical parameters of the system, such as strength of buoyancy [4,5], height of the column [6,7] and liquid volume [8,9]. In industrial applications related to crystal growth, the oscillatory thermocapillary convection was often accused of being responsible for periodic concentration variations in single crystals (see e.g., [10]).…”

Section: Introductionmentioning

confidence: 99%

“…In industrial applications related to crystal growth, the oscillatory thermocapillary convection was often accused of being responsible for periodic concentration variations in single crystals (see e.g., [10]). Aiming to understand the onset of oscillatory instability and suppress it, much efforts were put into studying convection in liquid bridge both theoretically [11][12][13] and experimentally [6,14]. The critical temperature difference, or suitably defined as the critical thermocapillary Reynolds number Re cr / DT cr , as well http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.02.058 0017-9310/Ó 2014 Elsevier Ltd. All rights reserved.…”

Section: Introductionmentioning

confidence: 99%

The Stability of a Thermocapillary-Buoyant Flow in a Liquid Bridge with Heat Transfer Through the Interface

Watanabe

Melnikov

Matsugase

et al. 2014

Microgravity Sci. Technol.

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a b s t r a c tThe hydrodynamic stability of a thermocapillary flow in a finite-size liquid bridge, with a non-deformable interface, heated from above and surrounded by a passive gas is examined by means of three-dimensional direct numerical simulations. Convective flow in 1 cSt silicone oil with Pr ¼ 18 is driven by combined effects of buoyancy and thermocapillary forces. Effects of the interfacial heat exchange on hydrothermal stability of the bulk flow are evaluated for various external thermal conditions in the gas phase. Cooling the interface can significantly shift the bifurcation point where the thermocapillary flow becomes oscillatory. If the Biot number Bi, which is a measure of the rate of the heat exchange, is not large, the effect of the interfacial heat flux can be either stabilizing or destabilizing, depending on both the temperature profile in the gas and the height of the liquid bridge. For a high value of heat loss rate, stabilization occurs regardless of the temperature distribution in the ambient gas. Various flow regimes are identified, and detailed stability maps are made for the flow under the considered ambient thermal conditions. It was found that the critical azimuthal mode of the flow changes according to the surrounding conditions in the gas phase. Observations have revealed three distinct azimuthal modes: m ¼ 0 (critical for a long liquid bridge at small Biot numbers), m ¼ 1 and m ¼ 2. Any mode change of the flow is accompanied by an abrupt change of the frequency of temperature oscillations.

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Steady and oscillatory thermocapillary convection in liquid columns with free cylindrical surface

Cited by 373 publications

References 16 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

Linear stability of thermocapillary convection in cylindrical liquid bridges under axial magnetic fields

The Stability of a Thermocapillary-Buoyant Flow in a Liquid Bridge with Heat Transfer Through the Interface

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