Aspect ratio effects on three-dimensional incompressible flow in a two-sided non-facing lid-driven parallelepiped cavity

Fakher Oueslati; Brahim Ben Beya; Taieb Lili

doi:10.1016/j.crme.2011.06.002

Aspect ratio effects on three-dimensional incompressible flow in a two-sided non-facing lid-driven parallelepiped cavity

Fakher Oueslati ¹ ; 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 339 (2011) no. 10, pp. 655-665.

Abstract

A numerical study of the three-dimensional fluid flow has been carried out to determine the effects of the transverse aspect ratio, $A_{y}$ , on the flow structure in two-sided non-facing lid-driven cavities. The flow is complex, unstable and can undergo bifurcation. The numerical method is based on the finite volume method and multigrid acceleration. Computations have been investigated for several Reynolds numbers and various aspect ratio values. At a fixed Reynolds number, $Re = 500$ , the three-dimensional flow characteristics are analyzed considering four transverse aspect ratios, $A_{y} = 1, 0.75, 0.5$ and 0.25. It is observed that the transition to the unsteady regime follows the classical scheme of a Hopf bifurcation. An analysis of the flow evolution shows that, at $A_{y} = 0.75$ , the flow bifurcates to a periodic regime at ( $Re = 600$ ) with a frequency $f = 0.093$ less than the predicted value in the cubical cavity. A correlation is established when $A_{y} = 0.5$ and gives the critical Reynolds number value. At $A_{y} = 0.25$ , the periodic regime occurs at high Re value beyond 3500, after which the flow becomes chaotic. It is shown that, when increasing $A_{y}$ over the unit, the flow in the cavity exhibits a complex behavior. The kinetic energy transmission from the driven walls to the cavity center is reduced at low $A_{y}$ values.

Received: 2011-05-10
Accepted: 2011-06-16
Published online: 2011-07-23

DOI: 10.1016/j.crme.2011.06.002

Mots-clés : Fluid mechanics, Aspect ratio, 3D lid-driven cavity, Unsteady flow, Bifurcation

Author's affiliations:

Fakher Oueslati ¹; 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_2011__339_10_655_0,
     author = {Fakher Oueslati and Brahim Ben Beya and Taieb Lili},
     title = {Aspect ratio effects on three-dimensional incompressible flow in a two-sided non-facing lid-driven parallelepiped cavity},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {655--665},
     publisher = {Elsevier},
     volume = {339},
     number = {10},
     year = {2011},
     doi = {10.1016/j.crme.2011.06.002},
     language = {en},
}

TY  - JOUR
AU  - Fakher Oueslati
AU  - Brahim Ben Beya
AU  - Taieb Lili
TI  - Aspect ratio effects on three-dimensional incompressible flow in a two-sided non-facing lid-driven parallelepiped cavity
JO  - Comptes Rendus. Mécanique
PY  - 2011
SP  - 655
EP  - 665
VL  - 339
IS  - 10
PB  - Elsevier
DO  - 10.1016/j.crme.2011.06.002
LA  - en
ID  - CRMECA_2011__339_10_655_0
ER  -

%0 Journal Article
%A Fakher Oueslati
%A Brahim Ben Beya
%A Taieb Lili
%T Aspect ratio effects on three-dimensional incompressible flow in a two-sided non-facing lid-driven parallelepiped cavity
%J Comptes Rendus. Mécanique
%D 2011
%P 655-665
%V 339
%N 10
%I Elsevier
%R 10.1016/j.crme.2011.06.002
%G en
%F CRMECA_2011__339_10_655_0

Fakher Oueslati; Brahim Ben Beya; Taieb Lili. Aspect ratio effects on three-dimensional incompressible flow in a two-sided non-facing lid-driven parallelepiped cavity. Comptes Rendus. Mécanique, Volume 339 (2011) no. 10, pp. 655-665. doi : 10.1016/j.crme.2011.06.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2011.06.002/

References
Cited by

[1] E. Erturk Discussions on driven cavity flow, Internat. J. Numer. Methods Fluids (2009), pp. 275-294

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

[3] L. Lin; Yi-Cheng Chen; Chao-An Lin Multi relaxation time lattice Boltzmann simulations of deep lid driven cavity flows at different aspect ratios, Comput. & Fluids (2011)

[4] K.L. Wong; A.J. Baker A 3D incompressible Navier–Stokes velocity-vorticity weak form finite element algorithm, Internat. J. Numer. Methods Fluids, Volume 38 (2002), pp. 99-123

[5] Q.T. Li; T. Cheng; T.T.H. Tsang Transient solutions for three-dimensional lid-driven cavity flows by a least-squares finite element method, Internat. J. Numer. Methods Fluids, Volume 21 (1995), pp. 413-432

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

[8] C. Migeon; G. Pineau; A. Texier Three-dimensionality development inside standard parallelepipedic lid-driven cavities at $Re = 1000$ , J. Fluids Struct., Volume 17 (2003), pp. 717-738

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

[10] 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)

[11] Y. Peng; Yuo-Hsien Shiau; Robert R. Hwang Transition in a 2-D lid-driven cavity flow, Comput. & Fluids, Volume 32 (2003), pp. 337-352

[12] S. Albensoeder; H.C. Kuhlmann Three-dimensional instability of two counter-rotating vortices in a rectangular cavity driven by parallel wall motion, Europ. J. Mech. B/Fluids, Volume 21 (2002), pp. 307-316

[13] E.M. Wahba Multiplicity of states for two-sided and four-sided lid driven cavity flows, Comput. & Fluids, Volume 38 (2008), pp. 247-253

[14] B. Ben Beya; Taieb Lili Three-dimensional incompressible flow in a two-sided non-facing lid-driven cubical cavity, C. R. Mecanique, Volume 336 (2008), pp. 863-872

[15] 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

[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. Ben 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] R. Barrett; M. Berry; T.F. Chan et al. Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, SIAM, 1994

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

Cited by Sources:

Comments - Policy