Three-dimensional time dependent modelling of the marangoni convection in zone melting configurations for GaAs

Rupp, Robin; Müller, G.; Neumann, G.

doi:10.1016/0022-0248(89)90244-3

Cited by 132 publications

(50 citation statements)

References 7 publications

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“…As in previous studies without magnetic field (Rupp et al 1989;Kuhlmann & Rath 1993;Levenstam & Amberg 1995) no critical axisymmetric (i.e. m = 0) mode was found despite extensive parameter variations.…”

Section: Discussionsupporting

confidence: 82%

“…Levenstam & Amberg (1995) found the transition to the unsteady state to take place at Re = 6250 for P r = 0.01 and unit aspect ratio. Values given by Rupp et al (1989) for aspect ratio Γ = 1.2 are higher. They range from 14 286 for P r = 0.007 to 26 471 for P r = 0.068.…”

Section: Discussionmentioning

confidence: 82%

“…Hence, it follows that the low Prandtl number (P r 1) instability is due to the large strain rate present in the basic axial shear flow. Up to now, the stationary instability in small Prandtl number fluids was only observed in numerical studies (Rupp et al 1989;Kuhlmann & Rath 1993;Levenstam & Amberg 1995;Wanschura et al 1995). Experimental evidence is still missing since model experiments are usually carried out with large Prandtl number liquids (e.g.…”

Section: Methodsmentioning

confidence: 99%

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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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Section: Discussionsupporting

confidence: 82%

Section: Discussionmentioning

confidence: 82%

Section: Methodsmentioning

confidence: 99%

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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 development of supercomputers and efficient numerical methods led the investigators to study the problem through direct numerical solution of the non linear and timedependent Navier Stokes equations. Rupp et al [5] and Levenstan and Amberg [6], Imaishi et al [7], Yasushiro et al [8], Leypoldt et al [9] found that for liquid metals the first bifurcation is stationary (i.e. the supercritical three-dimensional state is steady) and that the regime becomes oscillatory only when the Marangoni number is further increased (second oscillatory bifurcation).…”

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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“…[2,3], have been reported due to the difficulties in conducting well-controlled experiments induced by the opacity, reactivity, and high melting temperature of low-Pr fluids (mostly liquid metals). On the other hand, since the first prediction through the numerical study conducted by Rupp et al [4], theoretical studies including both linear instability analyses, e.g. Ref.…”

Section: Introductionmentioning

confidence: 99%

Proper orthogonal decomposition of oscillatory Marangoni flow in half-zone liquid bridges of low-Pr fluids

Imaishi

Jing

et al. 2007

Journal of Crystal Growth

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Proper orthogonal decomposition (POD) using method of snapshots was performed on three different types of oscillatory Marangoni flows in half-zone liquid bridges of low-Pr fluid (Pr ¼ 0.01). For each oscillation type, a series of characteristic modes (eigenfunctions) have been extracted from the velocity and temperature disturbances, and the POD provided spatial structures of the eigenfunctions, their oscillation frequencies, amplitudes, and phase shifts between them. The present analyses revealed the common features of the characteristic modes for different oscillation modes: four major velocity eigenfunctions captured more than 99% of the velocity fluctuation energy form two pairs, one of which is the most energetic. Different from the velocity disturbance, one of the major temperature eigenfunctions makes the dominant contribution to the temperature fluctuation energy. On the other hand, within the most energetic velocity eigenfuction pair, the two eigenfunctions have similar spatial structures and were tightly coupled to oscillate with the same frequency, and it was determined that the spatial structures and phase shifts of the eigenfunctions produced the different oscillatory disturbances. The interaction of other major modes only enriches the secondary spatio-temporal structures of the oscillatory disturbances. Moreover, the present analyses imply that the oscillatory disturbance, which is hydrodynamic in nature, primarily originates from the interior of the liquid bridge. r

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Three-dimensional time dependent modelling of the marangoni convection in zone melting configurations for GaAs

Cited by 132 publications

References 7 publications

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

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

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

Proper orthogonal decomposition of oscillatory Marangoni flow in half-zone liquid bridges of low-Pr fluids

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