Three-dimensional incompressible flow in a two-sided non-facing lid-driven cubical cavity

Brahim Ben Beya; Taieb Lili

doi:10.1016/j.crme.2008.10.004

Three-dimensional incompressible flow in a two-sided non-facing lid-driven cubical cavity
[Écoulement tridimensionnel de fluide incompressible dans une cavité cubique doublement entrainée par des faces adjacentes]

Présenté par : Sébastien Candel

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 336 (2008) no. 11-12, pp. 863-872.

Résumé
Abstract

Nous présentons dans cette Note une étude numérique de l'écoulement tridimensionnel de fluide dans une cavité cubique doublement entrainée par des faces adjacentes. Les calculs ont été menés à plusieurs valeurs du nombre de Reynolds depuis des valeurs faibles jusqu'à 700. A faible nombre de Reynolds l'écoulement est stationnaire. Les caractéristiques de l'écoulement tridimensionnel ont été analysées à un nombre de Reynolds $Re = 500$ . L'analyse de l'évolution de l'écoulement montre qu'avec l'augmentation du Re au-delà d'une certaine valeur critique l'écoulement devient instable et subit une bifurcation. Il a été observé que la transition vers l'instationnarité s'effectue par une bifurcation de Hopf. Le nombre de Reynolds critique au-delà duquel l'écoulement devient instationnaire est déterminé.

Numerical simulations of the three-dimensional fluid flow in a two-sided non-facing lid-driven cubical cavity are presented. Computations have been carried out for several Reynolds numbers from a low value to 700. At low Reynolds numbers the flow is steady. The three dimensional flow characteristics are analyzed at $Re = 500$ . An analysis of the flow evolution shows that, when increasing Re beyond a certain critical value the flow becomes unstable and bifurcates. It is observed that the transition to unsteadiness follows the classical scheme of a Hopf bifurcation. The time dependent solution is studied and the critical Reynolds number is localized.

Reçu le : 2008-05-11
Accepté le : 2008-10-08
Publié le : 2008-11-01

DOI : 10.1016/j.crme.2008.10.004

Keywords: Fluid mechanics, Incompressible flow, 3D lid-driven cavity, Bifurcation
Mot clés : Mécanique des fluids, Fluide incompressible, Cavité entrainée 3D, Bifurcation

Affiliations des auteurs :

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

@article{CRMECA_2008__336_11-12_863_0,
     author = {Brahim Ben Beya and Taieb Lili},
     title = {Three-dimensional incompressible flow in a two-sided non-facing lid-driven cubical cavity},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {863--872},
     publisher = {Elsevier},
     volume = {336},
     number = {11-12},
     year = {2008},
     doi = {10.1016/j.crme.2008.10.004},
     language = {en},
}

TY  - JOUR
AU  - Brahim Ben Beya
AU  - Taieb Lili
TI  - Three-dimensional incompressible flow in a two-sided non-facing lid-driven cubical cavity
JO  - Comptes Rendus. Mécanique
PY  - 2008
SP  - 863
EP  - 872
VL  - 336
IS  - 11-12
PB  - Elsevier
DO  - 10.1016/j.crme.2008.10.004
LA  - en
ID  - CRMECA_2008__336_11-12_863_0
ER  -

%0 Journal Article
%A Brahim Ben Beya
%A Taieb Lili
%T Three-dimensional incompressible flow in a two-sided non-facing lid-driven cubical cavity
%J Comptes Rendus. Mécanique
%D 2008
%P 863-872
%V 336
%N 11-12
%I Elsevier
%R 10.1016/j.crme.2008.10.004
%G en
%F CRMECA_2008__336_11-12_863_0

Brahim Ben Beya; Taieb Lili. Three-dimensional incompressible flow in a two-sided non-facing lid-driven cubical cavity. Comptes Rendus. Mécanique, Volume 336 (2008) no. 11-12, pp. 863-872. doi : 10.1016/j.crme.2008.10.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2008.10.004/

Bibliographie
Cité par

[1] P.N. Shankar; M.D. Despande Annu. Rev. Fluid Mech., 32 (2000), pp. 93-136

[2] S. Albensoeder; H.C. Kuhlmann Accurate three-dimensional lid-driven cavity flow, J. Comput. Phys., Volume 206 (2005), pp. 536-558

[3] O. Botella; R. Peyret Benchmark spectral results on the lid-driven cavity flow, Comput. & Fluids, Volume 27 (1998), pp. 421-433

[4] C.-H. Bruneau; M. Saad The 2D lid-driven cavity problem, Comput. & Fluids, Volume 35 (2006), pp. 326-348

[5] D.C. Lo; K. Murugesan; D.L. Young Numerical solution of three-dimensional velocity–vorticity Navier–Stokes equations by finite difference method, Int. J. Numer. Meth. Fluids (2004)

[6] H. Ding; C. Shu; K.S. Yeo; D. Xu Numerical computation of three-dimensional incompressible viscous flows in the primitive variable form by local multiquadric differential quadrature method, Comput. Methods Appl. Mech. Engrg., Volume 195 (2006), pp. 516-533

[7] H.C. Kuhlmann; M. Wanschura; H.J. Rath Flow in two-sided lid-driven cavities: non-uniqueness, instability, and cellular structures, J. Fluid Mech., Volume 336 (1997), pp. 267-299

[8] W.-J. Luo; R.-J. Yang Multiple fluid flow and heat transfer solutions in a two-sided lid-driven cavity, Int. J. Heat Mass Transfer, Volume 50 (2007), pp. 2394-2405

[9] E.M. Wahba, Multiplicity of states for two-sided and four-sided lid driven cavity flows, Computers & Fluids (2008), | DOI

[10] F. Auteri; N. Parolini; L. Quartapelle Numerical investigation on the stability of singular driven cavity flow, J. Comput. Phys., Volume 183 (2002), pp. 1-25

[11] Min Chan Kim; Sin Kim; Chang Kyun Choi The convective stability of circular Couette flow induced by a linearly accelerated inner cylinder, Eur. J. Mech. B/Fluids, Volume 25 (2006), pp. 74-82

[12] J.R. Koseff; R.L. Street Visualization studies of a shear driven three-dimensional recirculating flow, ASME J. Fluid Eng., Volume 33 (1984), pp. 594-602

[13] J. Chicheportiche; X. Merle; X. Gloerfelt; J.-C. Robinet Direct numerical simulation and global stability analysis of three-dimensional instabilities in a lid-driven cavity, C. R. Mecanique, Volume 336 (2008)

[14] D.L. Brown; R. Cortez; M.L. Minion Accurate projection methods for the incompressible Navier–Stokes equations, J. Comput. Phys., Volume 168 (2001), pp. 464-499

[15] S.V. Patankar A calculation procedure for two-dimensional elliptic situations, Numer. Heat Transfer, Volume 34 (1981), pp. 409-425

[16] T. Hayase; J.A.C. Humphrey; R. Greif A consistently formulated QUICK scheme for fast and stable convergence using finite-volume iterative calculation procedures, J. Comput. Phys., Volume 98 (1992), pp. 108-118

[17] N.B. Cheikh; B.B. Beya; T. Lili Benchmark solution for time-dependent natural convection flows with an accelerated full-multigrid method, Numer. Heat Transfer B, Volume 52 (2007), pp. 131-151

[18] H. Wang; S. Xin; P. Le Quéré Etude numérique du couplage de la convection naturelle ave le rayonnement de surfaces en cavités remplie d'air, C. R. Mecanique, Volume 334 (2006), pp. 48-57

[19] J. Shen Hopf bifurcation of the unsteady regularized driven cavity flow, J. Comput. Phys., Volume 95 (1991), pp. 228-245

Cité par Sources :

Commentaires - Politique