Séminaire de Mécanique d'Orsay

Le Jeudi 22 octobre à 14h00 - Salle de conférences du LIMSI

Influence of the spanwise aspect ratio on the stability of three-dimensional lid-driven cavity flows

Jean-Christophe Loiseau[1] , Jean-Christophe Robinet[2], and Emmanuel Leriche[3]
[1] Department of Mechanics, Royal Institute of Technology (KTH), SE-100 44 Stockholm, SWEDEN [2] Laboratoire Dynfluid, Arts et Métiers ParisTech, 75013 Paris, FRANCE [3] Laboratoire de Mécanique des Fluides, Université Lille 1, 59655 Villeneuve d’Ascq, FRANCE

The flow within three-dimensional lid-driven cavities characterized by L/D = 1 with spanwise end-walls has been investigated by means of steady state computations and fully three-dimensional linear stability analyses. The present work focuses on the influence of the spanwise aspect ratio of the cavity on the centrifugal instability at play and the corresponding critical Reynolds number. Depending on the aspect ratio of the cavity considered, two different bifurcations are encountered. In both cases however, the leading instability is characterized by Taylor-Görtler-like vortices. Results of the linear stability analyses emphasize on the connections between the present fully three-dimensional modes and their 2D-periodic counterparts. Indeed, these three-dimensional modes are related either to the S1 family of steady modes or to the T1 family of oscillating ones observed in 2D-periodic LDC flows. Finally, a joint use of Reynolds-Orr and Endogeneity analyses of the instability confirms its centrifugal nature and allows us to re-interpretate it as a closed-loop instability where the perturbation essentially extracts its energy from the base flow through the lift-up andanti lift-up mechanisms.