This work undertakes a numerical study of turbulent incompressible flows in lid-driven cubical cavities using Large Eddy Simulation and two sub-grid scale models, i.e., the WALE (Wall-Adapting Local Eddy-viscosity) model and the corresponding dynamic sub-grid model (DSGS). In the process of using DSGS, an optimal value of constant of the WALE model was determined for a pre-set Reynolds number . The computed numerical results showed very good agreement with those Direct Numerical Simulation (DNS) results and with the experimental measurements found in the literature. Optimal values of were determined afterwards with the DSGS model and they were proposed for the analysis of higher Reynolds number turbulent flows. At the end, a power law correlation between and Re was proposed for the range .
Accepted:
Published online:
Nader Ben-Cheikh 1; Faycel Hammami 1; Antonio Campo 2; Brahim Ben-Beya 1
@article{CRMECA_2012__340_10_721_0, author = {Nader Ben-Cheikh and Faycel Hammami and Antonio Campo and Brahim Ben-Beya}, title = {A dynamic sub-grid scale model for large eddy simulation of turbulent flows in a lid-driven cubical cavity}, journal = {Comptes Rendus. M\'ecanique}, pages = {721--730}, publisher = {Elsevier}, volume = {340}, number = {10}, year = {2012}, doi = {10.1016/j.crme.2012.10.001}, language = {en}, }
TY - JOUR AU - Nader Ben-Cheikh AU - Faycel Hammami AU - Antonio Campo AU - Brahim Ben-Beya TI - A dynamic sub-grid scale model for large eddy simulation of turbulent flows in a lid-driven cubical cavity JO - Comptes Rendus. Mécanique PY - 2012 SP - 721 EP - 730 VL - 340 IS - 10 PB - Elsevier DO - 10.1016/j.crme.2012.10.001 LA - en ID - CRMECA_2012__340_10_721_0 ER -
%0 Journal Article %A Nader Ben-Cheikh %A Faycel Hammami %A Antonio Campo %A Brahim Ben-Beya %T A dynamic sub-grid scale model for large eddy simulation of turbulent flows in a lid-driven cubical cavity %J Comptes Rendus. Mécanique %D 2012 %P 721-730 %V 340 %N 10 %I Elsevier %R 10.1016/j.crme.2012.10.001 %G en %F CRMECA_2012__340_10_721_0
Nader Ben-Cheikh; Faycel Hammami; Antonio Campo; Brahim Ben-Beya. A dynamic sub-grid scale model for large eddy simulation of turbulent flows in a lid-driven cubical cavity. Comptes Rendus. Mécanique, Volume 340 (2012) no. 10, pp. 721-730. doi : 10.1016/j.crme.2012.10.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2012.10.001/
[1] Natural convection flow in a square cavity calculated with low-Reynolds-number turbulence models, Int. J. Heat Mass Transfer, Volume 34 (1991), pp. 377-388
[2] A numerical method for simulation of attached cavitation flows, Int. J. Numer. Methods Fluids, Volume 52 (2006), pp. 639-658
[3] The complementary RANS equations for the simulation of viscous flows, Int. J. Numer. Methods Fluids, Volume 48 (2005), pp. 199-229
[4] Evaluation of turbulence models using direct numerical and large-eddy simulation data, J. Fluids Eng., Volume 133 (2011)
[5] Large-Eddy Simulations for Incompressible Flows: An Introduction, Springer, Berlin, Germany, 2001
[6] General circulation experiments with the primitive equations: I. The basic experiment, Mon. Weather Rev., Volume 91 (1963), pp. 99-136
[7] A dynamic subgrid-scale eddy viscosity model, Phys. Fluids A, Volume 3 (1991), pp. 1760-1765
[8] A proposed modification of the Germano subgrid-scale closure method, Phys. Fluids A, Volume 4 (1992), pp. 633-635
[9] Subgrid-scale modelling based on the square of the velocity gradient tensor, Flow Turbul. Combust., Volume 62 (1999) no. 3, pp. 183-200
[10] Large Eddy Simulation of Turbulence, Cambridge University Press, London, England, 2005
[11] B. Ben-Beya, Simulation numérique dʼun écoulement bidimensionnel en aval dʼune marche descendante, PhD Thesis, Faculty of Sciences of Tunis, El-Manar II, Tunisia, 1995.
[12] N. Ben-Cheikh, Etude de la convection naturelle laminaire et de lʼécoulement turbulent dans une cavité entraînée par simulation des grandes échelles, PhD Thesis, Faculty of Sciences of Tunis, El-Manar II, Tunisia, 2008.
[13] Convergence analysis of a finite element projection Lagrange–Galerkin method for the incompressible Navier–Stokes equations, SIAM J. Numer. Anal., Volume 37 (2000), pp. 799-826
[14] A dynamic subgrid-scale eddy viscosity model, Phys. Fluids A, Volume 7 (1991), pp. 1760-1765
[15] The lid-driven cavity flow: a synthesis of qualitative and quantitative observations, J. Fluid Mech., Volume 106 (1984), pp. 390-398
[16] Reynolds number and end-wall effects on a lid-driven cavity flow, Phys. Fluids A, Volume 1 (1989), pp. 208-218
[17] Parallel finite element calculation of flow in a three-dimensional lid-driven cavity using the CM-5 and T3D, Int. J. Numer. Methods Fluids, Volume 24 (1997), pp. 1449-1461
[18] Direct numerical simulation of the flow in a lid-driven cubical cavity, Phys. Fluids, Volume 12 (2000), pp. 1363-1376
[19] Direct numerical simulation in a lid-driven cubical cavity at high Reynolds number by a Chebyshev spectral method, J. Sci. Comput., Volume 27 (2006), pp. 335-345
[20] Large-eddy simulation of the lid-driven cubic cavity flow by the spectral element method, J. Sci. Comput., Volume 27 (2006), pp. 151-162
[21] Large-eddy simulation of the flow in a lid-driven cubical cavity, Phys. Fluids, Volume 19 (2007), pp. 1-20
[22] Start-up flow in a three-dimensional lid-driven cavity by means of a massively parallel direction splitting algorithm, Int. J. Numer. Methods Fluids, Volume 68 (2012), pp. 856-871
[23] A.A. Wray, J.C.R. Hunt, Algorithms for classification of turbulent structures, in: Proceedings of the IUTAM Symposium on Topological Fluid Mechanics, 1989, pp. 95–104.
[24] The use of sub-grid transport equations in a three-dimensional model of atmospheric turbulence, J. Fluids Eng., Volume 95 (1973), pp. 429-438
[25] Generalized Smagorinsky model for anisotropic grids, Phys. Fluids A, Volume 5 (1993), pp. 2306-2308
[26] Large-eddy simulation of rotating channel flows using a localized dynamic model, Phys. Fluids, Volume 7 (1995) no. 4, pp. 839-848
[27] Numerical Heat Transfer and Fluid Flow, McGraw–Hill, New York, 1980 (pp. 113–137)
[28] A stable and accurate convective modelling procedure based on quadratic upstream interpolation, Comput. Methods Appl. Mech. Eng., Volume 19 (1979), pp. 59-98
[29] Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, SIAM, Philadelphia, PA, USA, 1994
[30] Benchmark solution for time-dependent natural convection flows with an accelerated full-multigrid method, Numer. Heat Transf. B, Volume 52 (2007), pp. 131-151
[31] Robust implicit multigrid Reynolds–Stress model computation of 3D turbomachinery flows, J. Fluids Eng., Volume 129 (2007)
[32] Usability of explicit filtering in large eddy simulation with a low-order numerical scheme and different subgrid-scale models, Int. J. Numer. Methods Fluids, Volume 57 (2008), pp. 905-928
[33] Large eddy simulation using a dynamic mixing length subgrid-scale model, Int. J. Numer. Methods Fluids, Volume 69 (2012), pp. 1457-1472
[34] A multiscale subgrid model for both free vortex flows and wall-bounded flow, Phys. Fluids, Volume 21 (2009), p. 105102/1-105102/12
[35] H. Baya Toda, K. Truffin, F. Nicoud, Is the dynamic procedure appropriate for all SGS models?, in: J.C.F. Pereira, A. Sequeira (Eds.), V European Conference on Computational Fluid Dynamics, ECCOMAS, Lisbon, Portugal, June 2010, pp. 14–17.
[36] Dynamic global model for large eddy simulation of transient flow, Phys. Fluids, Volume 22 (2010), p. 075106
[37] Using singular values to build a sub-grid scale model for large eddy simulations, Phys. Fluids, Volume 23 (2011), p. 085106
[38] On the model coefficients for the standard and the variational multi-scale Smagorinsky model, J. Fluid Mech., Volume 569 (2006), p. 287319
Cited by Sources:
Comments - Policy