Thermocapillary convection in cylindrical liquid bridges and annuli

Bok-Cheol Sim; Abdelfattah Zebib

doi:10.1016/j.crme.2004.02.017

Microgravity and transfers/Process control

Thermocapillary convection in cylindrical liquid bridges and annuli
[Convection thermocapillaire dans les ponts liquides en géométries cylindrique et annulaire]

Bok-Cheol Sim ¹ ; Abdelfattah Zebib ²

¹ Department of Mechanical Engineering, Hanyang University, Ansan, Kyunggi-Do 425-791, South Korea
² Department of Mechanical and Aerospace Engineering, Rutgers University, Piscataway, NJ 08855-8058, USA

Comptes Rendus. Mécanique, Volume 332 (2004) no. 5-6, pp. 473-486.

Résumé
Abstract

La convection thermocapillaire dans des ponts liquides et les domaines cylindriques annulaires ouverts est étudiée dans des configurations bi et tri-dimensionnelles. En modèle 3D, les surfaces libres indéformables sont soit planes, soit courbées, suivant l'effet du volume de fluide, V et l'équation de Young–Laplace. Les déformations dynamiques de surface libre sont discutées pour le modèle axisymétrique. La convection est stationnaire et symétrique à de faibles valeurs de Re avec une surface déformable ou non. Pour la gamme des paramètres considérée, les résultats n'ont pas révélé d'état oscillatoire axisymétrique dans le pont liquide tant avec des surfaces libres déformables ou indéformables. La transition au régime tridimensionnel oscillant se produit en augmentant Re, au delà d'une valeur critique élevée dépendante du rapport de forme, du nombre de Prandtl, Pr et de V. Un bon accord avec les valeurs expérimentales disponibles est bien démontré dans chacun des cas étudiés.

Thermocapillary convection in liquid bridges and open cylindrical annuli is investigated in two- and three-dimensional numerical studies. The nondeformable free surfaces are either flat or curved as determined by the fluid volume, V, and the Young–Laplace equation. Dynamic free-surface deformations are discussed only in the axisymmetric models. Convection is steady and axisymmetric at sufficiently low values of the Reynolds number, Re, with either nondeformable or deformable surfaces. For the parameter ranges considered, it is found that only steady convection is possible at any Re in strictly axisymmetric computations. Transition to oscillatory three-dimensional motions occurs as Re increases beyond a critical value dependent on the aspect ratio, the Prandtl number, Pr, and V. Good agreement with available experiments is achieved in all cases.

Publié le : 2004-04-09

DOI : 10.1016/j.crme.2004.02.017

Keywords: Fluid mechanics, Oscillatory thermocapillary convection, Surface deformation, Liquid bridge, Open cylindrical annulus
Mot clés : Mécanique des fluides, Convection thermocapillaire oscillatoire, Déformation de surface, Pont liquide, Cylindrique annulaire ouvert

Affiliations des auteurs :

Bok-Cheol Sim ¹ ; Abdelfattah Zebib ²

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Bok-Cheol Sim; Abdelfattah Zebib. Thermocapillary convection in cylindrical liquid bridges and annuli. Comptes Rendus. Mécanique, Volume 332 (2004) no. 5-6, pp. 473-486. doi : 10.1016/j.crme.2004.02.017. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.02.017/

Bibliographie
Cité par

[1] D. Schwabe Marangoni effects in crystal growth melts, Phys. Chem. Hydrodynam., Volume 2 (1981), pp. 263-280

[2] D. Schwabe; A. Zebib; B.-C. Sim Oscillatory thermocapillary convection in open cylindrical annuli. Part 1. Experiments under microgravity, J. Fluid Mech., Volume 491 (2003), pp. 239-258

[3] P. Rudolph Fundamental studies on bridgman growth of CdTe, Prog. Crystal Growth and Charact., Volume 29 (1994), pp. 275-381

[4] F. Preisser; D. Schwabe; A. Scharmann Steady and oscillatory thermocapillary convection in liquid columns with free cylindrical surface, J. Fluid Mech., Volume 126 (1983), pp. 545-567

[5] R. Velten; D. Schwabe; A. Scharmann The periodic instability of thermocapillary convection in cylindrical liquid bridges, Phys. Fluids, Volume 3 (1991), pp. 267-279

[6] L. Carotenuto; D. Castagnolo; C. Albanese; R. Monti Instability of thermocapillary convection in liquid bridges, Phys. Fluids, Volume 10 (1998), pp. 555-565

[7] R. Monti; R. Savino; M. Lappa Flight results on Marangoni flow instability in liquid bridges, Acta Astonautica, Volume 47 (2000), pp. 325-334

[8] K. Muehlner; M. Schatz; V. Petrov; W. McCormick; J. Swift; H. Swinney Observation of helical traveling-wave convection in a liquid bridge, Phys. Fluids, Volume 9 (1997), pp. 1850-1852

[9] D. Schwabe; S. Frank Experiments on the transition to chaotic thermocapillary flow in floating zones under microgravity, Adv. Space Res., Volume 24 (1999), pp. 1391-1396

[10] D. Schwabe; R. Velten The multi-roll-structure of thermocapillary flow and its transition to oscillatory flow in long floating zones with length L near the Rayleigh-limit and restationarization above the critical Marangoni number, J. Jpn Soc. Microgravity Appl., Volume 15 (1998), pp. 425-430

[11] W. Hu; J. Shu; R. Zhou; Z. Tang Influence of liquid bridge volume on the onset of oscillation in floating zone convection. I. Experiments, J. Cryst. Growth, Volume 142 (1994), pp. 379-384

[12] J. Masud; Y. Kamotani; S. Ostrach Oscillatory thermocapillary flow in cylindrical columns of high Prandtl number fluids, J. Thermophys. Heat Transfer, Volume 11 (1997), pp. 105-111

[13] V. Shevtsova; M. Mojahed; J. Legros The loss of stability in ground based experiments in liquid bridges, Acta Astronautica, Volume 44 (1999), pp. 625-634

[14] L. Sumner; G. Neitzel; J.-P. Fontaine; P. Dell'Aversana Oscillatory thermocapillary convection in liquid bridges with highly deformed free surfaces: Experiments and energy-stability analysis, Phys. Fluids, Volume 13 (2001), pp. 107-120

[15] M. Smith; S. Davis Instabilities of dynamic thermocapillary liquid layers: Part 1. Convective instabilities, J. Fluid Mech., Volume 132 (1983), pp. 119-144

[16] J.-J. Xu; S. Davis Convective thermocapillary instabilities in liquid bridges, Phys. Fluids, Volume 27 (1984), pp. 1102-1107

[17] H. Kuhlmann; H. Rath Hydrodynamic instabilities in cylindrical thermocapillary liquid bridges, J. Fluid Mech., Volume 247 (1993), pp. 247-274

[18] M. Levenstam; G. Amberg Hydrodynamic instabilities of thermocapillary flow in a half-zone, J. Fluid Mech., Volume 297 (1995), pp. 357-372

[19] M. Wanschura; V. Shevtsova; H. Kuhlmann; H. Rath Convective instability mechanisms in thermocapillary liquid bridges, Phys. Fluids, Volume 7 (1995), pp. 912-925

[20] G. Neitzel; K.-T. Chang; D. Jankowski; H. Mittelmann Linear-stability theory of thermocapillary convection in a model of the float-zone crystal-growth process, Phys. Fluids, Volume 5 (1993), pp. 108-114

[21] M. Levenstam; G. Amberg; C. Winkler Instabilities of thermocapillary convection in a half-zone at intermediate Prandtl numbers, Phys. Fluids, Volume 13 (2001), pp. 807-816

[22] Q. Chen; W. Hu Influence of liquid bridge volume on instability of floating half zone convection, Int. J. Heat Mass Transfer, Volume 41 (1998), pp. 825-837

[23] Y. Tao; R. Sakidja; S. Kou Computer simulation and flow visualization of thermocapillary flow in a silicone oil floating zone, Int. J. Heat Mass Transfer, Volume 38 (1995), pp. 503-510

[24] R. Savino; R. Monti Oscillatory Marangoni convection in cylindrical liquid bridges, Phys. Fluids, Volume 8 (1996), pp. 2906-2922

[25] V. Shevtsova; J. Legros Oscillatory convective motion in deformed liquid bridges, Phys. Fluids, Volume 10 (1998), pp. 1621-1634

[26] J. Leypoldt; H. Kuhlmann; H. Rath Three-dimensional numerical simulation of thermocapillary flows in cylindrical liquid bridges, J. Fluid Mech., Volume 414 (2000), pp. 285-314

[27] V. Shevtsova; D. Melnikov; J. Legros Three-dimensional simulations of hydrodynamic instability in liquid bridges: influence of temperature-dependent viscosity, Phys. Fluids, Volume 13 (2001), pp. 2851-2865

[28] M. Lappa; R. Savino; R. Monti Three-dimensional numerical simulation of Marangoni instabilities in non-cylindrical liquid bridges in microgravity, Int. J. Heat Mass Transfer, Volume 44 (2001), pp. 1983-2003

[29] B.-C. Sim; A. Zebib Thermocapillary convection in open cylinders with undeformable curved surfaces, Int. J. Heat Mass Transfer, Volume 45 (2002), pp. 4983-4994

[30] B.-C. Sim; A. Zebib Thermocapillary convection in liquid bridges with undeformable curved surfaces, J. Thermophys. Heat Transfer, Volume 16 (2002), pp. 553-561

[31] B.-C. Sim, Thermocapillary convection in cylindrical geometries, Ph.D. dissertation, Rutgers University, 2002

[32] M. Mundrane; A. Zebib Low Prandtl number Marangoni convetion with a deformable interface, J. Thermophys. Heat Transfer, Volume 9 (1995), pp. 795-797

[33] B.-C. Sim, W.-S. Kim, A. Zebib, Dynamic free-surface deformations in axisymmetric liquid bridges, Adv. Space Res. (2003), submitted for publication

[34] H. Kuhlman; C. Nienhuser Dynamic free-surface deformations in thermocapillary liquid bridges, Fluid Dynamics Res., Volume 31 (2002), pp. 103-127

[35] B.-C. Sim; A. Zebib; D. Schwabe Oscillatory thermocapillary convection in open cylindrical annuli. Part 2. Simulations, J. Fluid Mech., Volume 491 (2003), pp. 259-274

[36] J. Xu; A. Zebib Oscillatory two- and three-dimensional thermocapillary convection, J. Fluid Mech., Volume 364 (1998), pp. 187-209

[37] B.-C. Sim; A. Zebib Effect of surface heat loss and rotation on transition to oscillatory thermocapillary convection, Phys. Fluids, Volume 14 (2002), pp. 225-231

[38] D. Schwabe; U. Moller; J. Schneider; A. Scharmann Instabilities of shallow dynamic thermocapillary liquid layers, Phys. Fluids, Volume 4 (1992), pp. 2368-2381

[39] Y. Kamotani; S. Ostrach; J. Masud Microgravity experiments and analysis of oscillatory thermocapillary flows in cylindrical containers, J. Fluid Mech., Volume 410 (2000), pp. 211-233

[40] N. Garnier; A. Chiffaudel Two dimensional hydrothermal waves in an extended cylindrical vessel, Eur. Phys. J. B, Volume 19 (2001), pp. 87-95

[41] B.-C. Sim, W.-S. Kim, A. Zebib, Axisymmetric thermocapillary convection in open cylindrical annuli with deforming interfaces, Int. J. Heat Mass Transfer (2003), submitted for publication

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