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 . 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 . 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.
Accepté le :
Publié le :
Mot clés : Mécanique des fluids, Fluide incompressible, Cavité entrainée 3D, Bifurcation
Brahim Ben Beya 1 ; Taieb Lili 1
@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 -
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/
[1] Annu. Rev. Fluid Mech., 32 (2000), pp. 93-136
[2] Accurate three-dimensional lid-driven cavity flow, J. Comput. Phys., Volume 206 (2005), pp. 536-558
[3] Benchmark spectral results on the lid-driven cavity flow, Comput. & Fluids, Volume 27 (1998), pp. 421-433
[4] The 2D lid-driven cavity problem, Comput. & Fluids, Volume 35 (2006), pp. 326-348
[5] Numerical solution of three-dimensional velocity–vorticity Navier–Stokes equations by finite difference method, Int. J. Numer. Meth. Fluids (2004)
[6] 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] Flow in two-sided lid-driven cavities: non-uniqueness, instability, and cellular structures, J. Fluid Mech., Volume 336 (1997), pp. 267-299
[8] 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] Numerical investigation on the stability of singular driven cavity flow, J. Comput. Phys., Volume 183 (2002), pp. 1-25
[11] 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] Visualization studies of a shear driven three-dimensional recirculating flow, ASME J. Fluid Eng., Volume 33 (1984), pp. 594-602
[13] Direct numerical simulation and global stability analysis of three-dimensional instabilities in a lid-driven cavity, C. R. Mecanique, Volume 336 (2008)
[14] Accurate projection methods for the incompressible Navier–Stokes equations, J. Comput. Phys., Volume 168 (2001), pp. 464-499
[15] A calculation procedure for two-dimensional elliptic situations, Numer. Heat Transfer, Volume 34 (1981), pp. 409-425
[16] 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] 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] 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] Hopf bifurcation of the unsteady regularized driven cavity flow, J. Comput. Phys., Volume 95 (1991), pp. 228-245
Cité par Sources :
Commentaires - Politique