Comptes Rendus
no. 3
Buoyant–thermocapillary flows in a multilayer system
[Écoulements provoqués simultanément par des gradients de densité et par thermocapillarité dans un système multicouche]

Présenté par : Évariste Sanchez-Palencia

Ilya B. Simanovskii1  ; Antonio Viviani2  ; Jean-Claude Legros3
1 Department of Mathematics, Technion – Israel, Institute of Technology, 32000 Haifa, Israel
2 Seconda Universita di Napoli (SUN), Dipartimento di Ingegneria Aerospaziale e Meccanica (DIAM), via Roma 29, 81031 Aversa, Italy
3 Université Libre de Bruxelles, service de chimie physique EP, CP165-62, 50, avenue F.D. Roosevelt, B-1050 Brussels, Belgium
Comptes Rendus. Mécanique, Volume 336 (2008) no. 3, pp. 262-268.

Une étude est menée sur les écoulements induits dans un système composé de trois couches de liquides superposés, en tenant compte des effets non-linéaires. Ces liquides sont contenus dans une cavité fermée et soumise à un gradient de température parallèle aux interfaces. Les simulations numériques des régimes convectifs non-linéaires sont effectuées par la méthode des différences finies. Il est montré que pour des valeurs suffisamment grandes des nombres de Grashof, les rouleaux de convection longitudinaux se transforment en structures multicellulaires.

The nonlinear buoyant–thermocapillary flows in a three-layer system, filling a closed cavity and subjected to a temperature gradient directed along the interfaces, are investigated. The nonlinear simulations of convective regimes are performed by the finite-difference method. It is found that for sufficiently large values of the Grashof number, the long vortices turn into multicell structures.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2007.11.023
Keywords: Computational fluid mechanics, Multilayer, Thermocapillarity convection, Gravity-induced convection, Flow stability, Grashof number, Marangoni number
Mot clés : Mécanique des fluides numérique, Multicouche, Convection thermocapillaire, Convection induite par densité, Stabilité des écoulements, Nombre de Grashof, Nombre de Marangoni
Ilya B. Simanovskii 1 ; Antonio Viviani 2 ; Jean-Claude Legros 3

1 Department of Mathematics, Technion – Israel, Institute of Technology, 32000 Haifa, Israel
2 Seconda Universita di Napoli (SUN), Dipartimento di Ingegneria Aerospaziale e Meccanica (DIAM), via Roma 29, 81031 Aversa, Italy
3 Université Libre de Bruxelles, service de chimie physique EP, CP165-62, 50, avenue F.D. Roosevelt, B-1050 Brussels, Belgium 
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Ilya B. Simanovskii; Antonio Viviani; Jean-Claude Legros. Buoyant–thermocapillary flows in a multilayer system. Comptes Rendus. Mécanique, Volume 336 (2008) no. 3, pp. 262-268. doi : 10.1016/j.crme.2007.11.023. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.11.023/

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[3] Q. Liu, B. Roux, Instability of thermocapillary convection in multiple superposed in immiscible liquid layers, in: Proc. VIII European Symposium on Materials and Fluid Sciences in Microgravity, Brussels, Belgium, ESA SP-333, 1992, p. 735

[4] P. Georis; M. Hennenberg; I. Simanovskii; A. Nepomnyashchy; I. Wertgeim; J.-C. Legros Thermocapillary convection in multilayer system, Phys. Fluids A, Volume 5 (1993), p. 1575

[5] A. Prakash; J.N. Koster Convection in multilayers of immiscible liquids in shallow cavities, Part 1: Steady natural convection, Int. J. Multiphase Flow, Volume 20 (1994), p. 383

[6] A. Prakash; J.N. Koster Convection in multilayers of immiscible liquids in shallow cavities, Part 2: Steady thermocapillary convection, Int. J. Multiphase Flow, Volume 20 (1994), p. 397

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[8] V.M. Shevtsova; I.B. Simanovskii; A.A. Nepomnyashchy; J.-C. Legros Thermocapillary convection in a symmetric three-layer system with the temperature gradient directed along the interfaces, C. R. Mecanique, Volume 333 (2005), p. 311

[9] I.B. Simanovskii Thermocapillary flows in a three-layer system with a temperature gradient along the interfaces, Europ. J. Mech. B/Fluids, Volume 26 (2007), p. 422

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[11] I.B. Simanovskii Nonlinear buoyant–thermocapillary flows in a three-layer system with a temperature gradient along the interfaces, Phys. Fluids, Volume 19 (2007), p. 082106

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[13] I.B. Simanovskii; A.A. Nepomnyashchy Convective Instabilities in Systems with Interface, Gordon and Breach, London, 1993

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