Direct numerical simulation and global stability analysis of three-dimensional instabilities in a lid-driven cavity

Jérèmie Chicheportiche; Xavier Merle; Xavier Gloerfelt; Jean-Christophe Robinet

doi:10.1016/j.crme.2008.04.007

Direct numerical simulation and global stability analysis of three-dimensional instabilities in a lid-driven cavity

Presented by: Geneviève Comte-Bellot

Jérèmie Chicheportiche ¹ ; Xavier Merle ¹; Xavier Gloerfelt ¹; Jean-Christophe Robinet ¹

¹ Laboratoire SINUMEF, Arts et Métiers ParisTech, 75013 Paris, France

Comptes Rendus. Mécanique, Volume 336 (2008) no. 7, pp. 586-591.

Abstract (Original language)
Résumé

The first bifurcation in a lid-driven cavity characterized by three-dimensional Taylor–Görtler-Like instabilities is investigated for a cubical cavity with spanwise periodic boundary conditions at $Re = 1000$ . The modes predicted by a global linear stability analysis are compared to the results of a direct numerical simulation. The amplification rate, and the shape of the three-dimensional perturbation fields from the direct numerical simulation are in very good agreement with the characteristics of the steady S1 mode from the stability analysis, showing that this mode dominates the other unstable unsteady modes.

Le but de cette étude est d'étudier les instabilités de type Taylor–Görtler qui mènent à la première bifurcation d'un écoulement de cavité entraînée. Les modes prédits par une analyse de stabilité linéaire globale sont comparés aux résultats d'une simulation numérique directe d'une cavité cubique à $Re = 1000$ avec des conditions aux limites périodiques dans la troisième direction. Le taux d'amplification et la forme des perturbations issues de la simulation numérique directe permettent clairement d'identifier le mode stationnaire S1 de l'analyse de stabilité, qui domine les autres instabilités instationnaires.

Received: 2008-01-08
Accepted: 2008-04-14
Published online: 2008-05-15

DOI: 10.1016/j.crme.2008.04.007

Keywords: Fluid mechanics, Lid-driven cavity, Global instabilities, Direct numerical simulation
Mots-clés : Mécanique des fluides, Cavité entraînée, Instabilités globales, Simulation numérique directe

Author's affiliations:

Jérèmie Chicheportiche ¹; Xavier Merle ¹; Xavier Gloerfelt ¹; Jean-Christophe Robinet ¹

¹ Laboratoire SINUMEF, Arts et Métiers ParisTech, 75013 Paris, France

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     title = {Direct numerical simulation and global stability analysis of three-dimensional instabilities in a lid-driven cavity},
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Jérèmie Chicheportiche; Xavier Merle; Xavier Gloerfelt; Jean-Christophe Robinet. Direct numerical simulation and global stability analysis of three-dimensional instabilities in a lid-driven cavity. Comptes Rendus. Mécanique, Volume 336 (2008) no. 7, pp. 586-591. doi : 10.1016/j.crme.2008.04.007. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2008.04.007/

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