Numerical simulation of two-dimensional Rayleigh–Bénard convection in an enclosure

Nasreddine Ouertatani; Nader Ben Cheikh; Brahim Ben Beya; Taieb Lili

doi:10.1016/j.crme.2008.02.004

Numerical simulation of two-dimensional Rayleigh–Bénard convection in an enclosure

Presented by: Sébastien Candel

Nasreddine Ouertatani ¹; Nader Ben Cheikh ¹ ; Brahim Ben Beya ¹; Taieb Lili ¹

¹ Faculté des sciences de Tunis, département de physique, campus universitaire, 2092 El-Manar II, Tunisia

Comptes Rendus. Mécanique, Volume 336 (2008) no. 5, pp. 464-470.

Abstract
Résumé

In this Note, a numerical approach based on the finite volume method and a full multigrid acceleration is used, applied to the classical Rayleigh Bénard convection problem. Fine grids corresponding to 256² nodes are used and Benchmark solutions are proposed for Rayleigh numbers ranging from 10³ to 10⁶. Some streamlines and isotherms are presented to analyze the natural convection flow patterns set up by the buoyancy force.

La présente investigation porte sur une étude numérique bidimensionnelle relative à un problème de convection naturelle. Il s'agit en l'occurrence d'une convection de type Rayleigh Bénard dans une cavité carrée. Il est à noter qu'une convection de type Rayleigh Bènard peut être rencontrée dans de nombreuses applications physiques. On peut citer à titre d'exemple, le chauffage d'une pièce dans un immeuble ou encore le refroidissement de composants électroniques. Afin de correctement simuler l'écoulement, nous avons utilisé dans cette étude un maillage assez fin correspondant à 256² nœuds de calcul. La résolution numérique est basée sur une formulation de type volumes finis et une accélération multigrille. Des solutions Benchmark sont alors proposées relativement aux nombres de Rayleigh 10³, 10⁴, 10⁵ et 10⁶. Une comparaison des résultats obtenus par la méthode classique RBSOR et la méthode multigrille est également faite et montre qu'un facteur gain de 17 peut être atteint.

Received: 2007-12-06
Accepted: 2008-02-01
Published online: 2008-03-07

DOI: 10.1016/j.crme.2008.02.004

Keywords: Heat transfer, Rayleigh–Bénard convection
Mot clés : Transferts thermiques, Convection Rayleigh–Bénard

Author's affiliations:

Nasreddine Ouertatani ¹; Nader Ben Cheikh ¹; Brahim Ben Beya ¹; Taieb Lili ¹

¹ Faculté des sciences de Tunis, département de physique, campus universitaire, 2092 El-Manar II, Tunisia

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     author = {Nasreddine Ouertatani and Nader Ben Cheikh and Brahim Ben Beya and Taieb Lili},
     title = {Numerical simulation of two-dimensional {Rayleigh{\textendash}B\'enard} convection in an enclosure},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {464--470},
     publisher = {Elsevier},
     volume = {336},
     number = {5},
     year = {2008},
     doi = {10.1016/j.crme.2008.02.004},
     language = {en},
}

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Nasreddine Ouertatani; Nader Ben Cheikh; Brahim Ben Beya; Taieb Lili. Numerical simulation of two-dimensional Rayleigh–Bénard convection in an enclosure. Comptes Rendus. Mécanique, Volume 336 (2008) no. 5, pp. 464-470. doi : 10.1016/j.crme.2008.02.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2008.02.004/

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