Aspect ratio effects on three-dimensional incompressible flow in a two-sided non-facing lid-driven parallelepiped cavity

Fakher Oueslati; Brahim Ben Beya; Taieb Lili

doi:10.1016/j.crme.2011.06.002

Aspect ratio effects on three-dimensional incompressible flow in a two-sided non-facing lid-driven parallelepiped cavity

Fakher Oueslati ¹ ; Brahim Ben Beya ¹; Taieb Lili ¹

¹ Laboratoire de mécanique des fluides, Faculté des sciences de Tunis, Département de physique, 2092 El Manar 2, Tunis, Tunisia

Comptes Rendus. Mécanique, Volume 339 (2011) no. 10, pp. 655-665.

Abstract

A numerical study of the three-dimensional fluid flow has been carried out to determine the effects of the transverse aspect ratio, $A_{y}$ , on the flow structure in two-sided non-facing lid-driven cavities. The flow is complex, unstable and can undergo bifurcation. The numerical method is based on the finite volume method and multigrid acceleration. Computations have been investigated for several Reynolds numbers and various aspect ratio values. At a fixed Reynolds number, $Re = 500$ , the three-dimensional flow characteristics are analyzed considering four transverse aspect ratios, $A_{y} = 1, 0.75, 0.5$ and 0.25. It is observed that the transition to the unsteady regime follows the classical scheme of a Hopf bifurcation. An analysis of the flow evolution shows that, at $A_{y} = 0.75$ , the flow bifurcates to a periodic regime at ( $Re = 600$ ) with a frequency $f = 0.093$ less than the predicted value in the cubical cavity. A correlation is established when $A_{y} = 0.5$ and gives the critical Reynolds number value. At $A_{y} = 0.25$ , the periodic regime occurs at high Re value beyond 3500, after which the flow becomes chaotic. It is shown that, when increasing $A_{y}$ over the unit, the flow in the cavity exhibits a complex behavior. The kinetic energy transmission from the driven walls to the cavity center is reduced at low $A_{y}$ values.

Received: 2011-05-10
Accepted: 2011-06-16
Published online: 2011-07-23

DOI: 10.1016/j.crme.2011.06.002

Keywords: Fluid mechanics, Aspect ratio, 3D lid-driven cavity, Unsteady flow, Bifurcation

Author's affiliations:

Fakher Oueslati ¹; Brahim Ben Beya ¹; Taieb Lili ¹

¹ Laboratoire de mécanique des fluides, Faculté des sciences de Tunis, Département de physique, 2092 El Manar 2, Tunis, Tunisia

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     author = {Fakher Oueslati and Brahim Ben Beya and Taieb Lili},
     title = {Aspect ratio effects on three-dimensional incompressible flow in a two-sided non-facing lid-driven parallelepiped cavity},
     journal = {Comptes Rendus. M\'ecanique},
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     year = {2011},
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Fakher Oueslati; Brahim Ben Beya; Taieb Lili. Aspect ratio effects on three-dimensional incompressible flow in a two-sided non-facing lid-driven parallelepiped cavity. Comptes Rendus. Mécanique, Volume 339 (2011) no. 10, pp. 655-665. doi : 10.1016/j.crme.2011.06.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2011.06.002/

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