Comptes Rendus
no. 11-12
Instabilities and bifurcations due to buoyancy in a cylindrical container heated from below with and without a free surface

Présenté par : Jean-Baptiste Leblond

Anas El Gallaf1  ; Ridha Touihri2  ; Daniel Henry1  ; Hamda Ben Hadid1
1 Laboratoire de mécanique des fluides et d'acoustique, CNRS/Université de Lyon, École centrale de Lyon/Université Lyon 1/INSA de Lyon, ECL, 36, avenue Guy-de-Collongue, 69134 Ecully cedex, France
2 LAMSIN, ENIT, campus universitaire, le belvédère, BP 37, 1002 Tunis, Tunisie
Comptes Rendus. Mécanique, Volume 337 (2009) no. 11-12, pp. 716-721.

Three-dimensional simulations of the buoyant convection in a cylindrical container heated from below are presented. Both the thresholds for the onset of the convection and the nonlinear evolution of this convection are calculated. The simulations concern two configurations: a cavity with a rigid upper surface (Rigid-Rigid case) and a cavity with a non-constrained free surface (Rigid-Free case). The results show a similar variation of the primary thresholds with the aspect ratio for the two configurations. In contrast, the nonlinear evolution of the convection is much changed between the two configurations. In particular, subcritical secondary branches with a very large subcriticity are obtained in the R-F case.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2009.10.001
Mots clés : Instability, Computational fluid mechanics, Stability, Buoyant flow, Free surface, Cylindrical cavity, Bifurcation analysis
Anas El Gallaf 1 ; Ridha Touihri 2 ; Daniel Henry 1 ; Hamda Ben Hadid 1

1 Laboratoire de mécanique des fluides et d'acoustique, CNRS/Université de Lyon, École centrale de Lyon/Université Lyon 1/INSA de Lyon, ECL, 36, avenue Guy-de-Collongue, 69134 Ecully cedex, France
2 LAMSIN, ENIT, campus universitaire, le belvédère, BP 37, 1002 Tunis, Tunisie 
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     title = {Instabilities and bifurcations due to buoyancy in a cylindrical container heated from below with and without a free surface},
     journal = {Comptes Rendus. M\'ecanique},
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Anas El Gallaf; Ridha Touihri; Daniel Henry; Hamda Ben Hadid. Instabilities and bifurcations due to buoyancy in a cylindrical container heated from below with and without a free surface. Comptes Rendus. Mécanique, Volume 337 (2009) no. 11-12, pp. 716-721. doi : 10.1016/j.crme.2009.10.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2009.10.001/

[1] R. Touihri; H. Ben Hadid; D. Henry On the onset of convective instabilities in cylindrical cavities heated from below. I. Pure thermal case, Phys. Fluids, Volume 11 (1999), pp. 2078-2088

[2] E.L. Koschmieder; S.A. Prahl Surface-tension-driven Bénard convection in small containers, J. Fluid Mech., Volume 215 (1990), pp. 571-583

[3] P. Cerisier; S. Rahal; H. Azuma Pattern dynamics of the Bénard–Marangoni instability in a medium aspect ratio container, Second International Symposium on Instability and Bifurcations in Fluid Dynamics, J. Physics: Conference Series, vol. 64, 2007, p. 012004

[4] S. Rahal; P. Cerisier; H. Azuma Bénard–Marangoni convection in a small circular container: Influence of the Biot and Prandtl numbers on pattern dynamics and free surface deformation, Exp. Fluids, Volume 43 (2007), pp. 547-554

[5] A.A. Zaman; R. Narayanan Interfacial and buoyancy-driven convection – The effect of geometry and comparison with experiments, J. Colloid Interface Sci., Volume 179 (1996), pp. 151-162

[6] P.C. Dauby; G. Lebon; E. Bouhy Linear Bénard–Marangoni instability in rigid circular containers, Phys. Rev. E, Volume 56 (1997), pp. 520-530

[7] P. Assemat; A. Bergeon; E. Knobloch Nonlinear Marangoni convection in circular and elliptical cylinders, Phys. Fluids, Volume 19 (2007), p. 104101

[8] D. Henry; H. Ben Hadid Multiple flow transitions in a box heated from the side in low-Prandtl-number fluids, Phys. Rev. E, Volume 76 (2007), p. 016314

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