Comptes Rendus
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.

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.

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.

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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

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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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] 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

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