Convective instability mechanisms in thermocapillary liquid bridges

Wanschura, M.; Shevtsova, Valentina; Kuhlmann, Hendrik C.; Rath, H. J.

doi:10.1063/1.868567

Cited by 289 publications

(243 citation statements)

References 26 publications

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“…As highlighted in reference [4], for low Prandtl number liquids, the bifurcation of the flow field to a steady three-dimensional configuration is directly related to the inertial instability of the shear layer below the free surface; the instability takes energy from the radial gradient of the …”

Section: Discussionmentioning

confidence: 99%

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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: Discussionmentioning

confidence: 99%

“…A number of theoretical and numerical studies have been carried out based on the linear stability theory [3,4]. 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.…”

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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“…The axisymmetric oscillatory mode m ¼ 0 is somehow elusive, and there is no agreement on that subject up to now. The appearance of m ¼ 0 mode in a finite-size liquid bridge is not supported by the results of the linear stability analysis [11] but was predicted by Xu and Davis [22] in an infinitely long LB with Pr > 50. Shevtsova and Legros [8] found the instability with wave number m ¼ 0 in a liquid with Pr ¼ 105 (in the framework of an axisymmetric problem with the interface deformed by gravity).…”

Section: Two-dimensional Oscillatory Instability Of the Flowmentioning

confidence: 87%

“…The local and the net heat fluxes are essentially different for each of the three distributions of the air temperature given by Eqs. (9)- (11). For all these cases the local heat flux qðzÞ is shown in Fig.…”

Section: Heat Fluxes and Kinetic Features Of The Flowmentioning

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%

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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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Parallel solution of three-dimensional Marangoni flow in liquid bridges

Lappa

Savino

1999

Int. J. Numer. Meth. Fluids

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This paper describes the implementation and performances of a parallel solver for the direct numerical simulation of the three-dimensional and time-dependent Navier Stokes equations on distributed-memory, massively parallel computers. The feasibility of this approach to study Marangoni flow instability in half zone liquid bridges is examined. The results indicate that the incompressible, non linear Navier-Stokes problem, governing the Marangoni flows behaviour, can effectively be parallelized on a distributedmemory parallel machine by remapping the distributed data structure. The numerical code is based on a three-dimensional Simplified Marker and Cell primitive variable method applied to a staggered finitedifference grid. Using this method, the problem is split in two problems, one parabolic and the other elliptic. A parallel algorithm, explicit in time, is utilized to solve the parabolic equations. A parallel multisplitting kernel is introduced for the solution of the pseudo-pressure elliptic equation, representing the most time-consuming part of the algorithm. A grid-partition strategy is used in the parallel implementations of both the parabolic equations and the multisplitting elliptic kernel. A Message Passing Interface (MPI) is coded for the boundary conditions; this protocol is portable to different systems supporting this interface for interprocessor communications. Numerical experiments illustrate good numerical properties and parallel efficiency. In particular, good scalability on a large number of processors can be achieved as long as the granularity of the parallel application is not too small. However, increasing the number of processors, the Speed-Up is ever smaller than the ideal linear Speed Up. The communication timings indicate that complex practical calculations, such as the solutions of the Navier-Stokes equations for the numerical simulation of the instability of Marangoni flows, can be expected to run on a massively parallel machine with good efficiency.

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Convective instability mechanisms in thermocapillary liquid bridges

Cited by 289 publications

References 26 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

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

Parallel solution of three-dimensional Marangoni flow in liquid bridges

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