Aptitude of a lattice Boltzmann method for evaluating transitional thresholds for low Prandtl number flows in enclosures

Mohammed El Ganaoui; R. Djebali

doi:10.1016/j.crme.2009.12.008

Aptitude of a lattice Boltzmann method for evaluating transitional thresholds for low Prandtl number flows in enclosures

Presented by: Michel Combarnous

Mohammed El Ganaoui ¹ ; R. Djebali ¹

¹ Université de Limoges/CNRS, faculté des sciences et techniques, 123, avenue Albert-Thomas, 87060 Limoges, France

Comptes Rendus. Mécanique, Volume 338 (2010) no. 2, pp. 85-96.

Abstract
Résumé

Lattice Boltzmann (LB) method is considered versus classical discretisation approaches to solve the problem of heat and fluid flow. The work considers situations with symmetry breaking for low Prandtl number fluids flowing in enclosures interesting directional solidification industry. The computed results demonstrate a good LB method's ability to captivate flow bifurcation thresholds. Particularly cavities exhibiting bifurcation sequences are considered and results are consistent with prior observations.

L'approche gaz sur réseaux est comparée aux méthodes de discrétisation classiques pour résoudre le problème de transferts de chaleur et d'écoulement. Le travail considère des situations de faible nombre de Prandtl avec brisure de symétrie dans des cavités intéressant des configurations de solidification dirigée. Les résultats illustrent un bon accord avec les scénarios existants dans le cas d'écoulements avec bifurcation.

Received: 2009-03-25
Accepted: 2009-12-16
Published online: 2010-02-01

DOI: 10.1016/j.crme.2009.12.008

Keywords: Continuum mechanics, Symmetry breaking, Lattice Boltzmann
Mot clés : Milieux continus, Brisure de symétrie, Gaz sur réseau

Author's affiliations:

Mohammed El Ganaoui ¹; R. Djebali ¹

¹ Université de Limoges/CNRS, faculté des sciences et techniques, 123, avenue Albert-Thomas, 87060 Limoges, France

@article{CRMECA_2010__338_2_85_0,
     author = {Mohammed El Ganaoui and R. Djebali},
     title = {Aptitude of a lattice {Boltzmann} method for evaluating transitional thresholds for low {Prandtl} number flows in enclosures},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {85--96},
     publisher = {Elsevier},
     volume = {338},
     number = {2},
     year = {2010},
     doi = {10.1016/j.crme.2009.12.008},
     language = {en},
}

TY  - JOUR
AU  - Mohammed El Ganaoui
AU  - R. Djebali
TI  - Aptitude of a lattice Boltzmann method for evaluating transitional thresholds for low Prandtl number flows in enclosures
JO  - Comptes Rendus. Mécanique
PY  - 2010
SP  - 85
EP  - 96
VL  - 338
IS  - 2
PB  - Elsevier
DO  - 10.1016/j.crme.2009.12.008
LA  - en
ID  - CRMECA_2010__338_2_85_0
ER  -

%0 Journal Article
%A Mohammed El Ganaoui
%A R. Djebali
%T Aptitude of a lattice Boltzmann method for evaluating transitional thresholds for low Prandtl number flows in enclosures
%J Comptes Rendus. Mécanique
%D 2010
%P 85-96
%V 338
%N 2
%I Elsevier
%R 10.1016/j.crme.2009.12.008
%G en
%F CRMECA_2010__338_2_85_0

Mohammed El Ganaoui; R. Djebali. Aptitude of a lattice Boltzmann method for evaluating transitional thresholds for low Prandtl number flows in enclosures. Comptes Rendus. Mécanique, Volume 338 (2010) no. 2, pp. 85-96. doi : 10.1016/j.crme.2009.12.008. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2009.12.008/

References
Cited by

[1] A.A. Mohamad Applied Lattice Boltzmann Method for Transport Phenomena, Momentum, Heat and Mass Transfer, 2007

[2] M. Bouzidi; D. d'Humières; P. Lallemand; L.-S. Luo Lattice Boltzmann equation on a two-dimensional rectangular grid, Journal of Computational Physics, Volume 172 (2001), pp. 704-717

[3] Y. Peng; C. Shu; Y.T. Chew Simplified thermal lattice Boltzmann model for incompressible thermal flows, Physical Review E, Volume 68 (2003), p. 026701

[4] J.I.D. Alexander; S. Chen; J.D. Sterling Lattice Boltzmann thermohydrodynamics, Physical Review E, Volume 47 (1993), p. R2249

[5] M. Jami; A. Mezrhab; M. Bouzidi; P. Lallemand Lattice-Boltzmann computation of natural convection in a partitioned enclosure with inclined partitions attached to its hot wall, Physica A: Statistical Mechanics and Its Applications, Volume 368 (2006) no. 2, pp. 481-494

[6] R. Djebali; M. El Ganaoui; H. Sammouda Investigation of a side wall heated cavity by using lattice Boltzmann method, Revue Europeenne de Mecanique Numérique (REMN), Volume 18 (2009) no. 2, pp. 217-238

[7] R. Djebali; M. El Ganaoui; H. Sammouda; R. Bennacer Some benchmark solutions of a side wall heated cavity using lattice Boltzmann approach, Fluid Dynamics & Material Processing (FDMP), Volume 164 (2009) no. 1, pp. 1-21

[8] A.A. Mohamad; M. El Ganaoui; R. Bennacer Lattice Boltzmann simulation of natural convection in an open ended cavity, International Journal of Thermal Sciences (IJTS), Volume 48 ( October 2009 ) no. 10, pp. 1870-1875

[9] E. Semma; M. El Ganaoui; R. Bennacer; A.A. Mohamad Investigation of flows in solidification by using the lattice Boltzmann method, International Journal of Thermal Sciences, Volume 47 (2008), pp. 201-208

[10] E.A. Semma; M. El Ganaoui; R. Bennacer Lattice Boltzmann method for melting/solidification problems, Comptes Rendus Mécanique, Volume 335 ( May–June 2007 ) no. 5–6, pp. 295-303

[11] P.-H. Kao; R.-J. Yang Simulating oscillatory flows in Rayleigh–Bénard convection using the lattice Boltzmann method, International Journal of Heat and Mass Transfer, Volume 50 (2007), pp. 3315-3328

[12] G. Muller; G. Neumann; W. Weber Natural convection in vertical Bridgman configuration, Journal of Crystal Growth, Volume 70 (1984), pp. 78-93

[13] A. Semma; M. El Ganaoui; A. Cheddadi; A. Farchi High order finite volume scheme for phase change problems (F. Benkhaldoun; D. Ouazar; S. Raghay, eds.), Finite Volumes for Complex Applications, vol. IV, Hermès Science Publishing, 2005, pp. 493-503

[14] X. He; S. Chen; G.D. Doolen A novel thermal model for the lattice Boltzmann method in incompressible limit, Journal of Computational Physics, Volume 146 (1998), pp. 282-300

[15] G. de Vahl Davis Natural convection of air in a square cavity: A benchmark numerical solutions, International Journal of Numerical Methods in Fluids, Volume 3 (1983), pp. 249-264

[16] Xiao Dong Wang; Yves Fautrelle An investigation of the influence of natural convection on tin solidification using a quasi two-dimensional experimental benchmark, International Journal of Heat and Mass Transfer, Volume 52 ( November 2009 ) no. 23–24, pp. 5624-5633

[17] E. Semma; V. Timchenko; M. El Ganaoui; E. Leonardi The effect of wall temperature fluctuations on the heat transfer and fluid flow occurring in a liquid enclosure, International Journal of Heat and Fluid Flow, Volume 26 (2005), pp. 547-557

[18] E.A. Semma; M. El Ganaoui; V. Timchenko; E. Leonardi Some thermal modulation effects on directional solidification, Fluid Dynamics & Materials Processing (FDMP), Volume 2 (2006) no. 3, pp. 191-202

[19] M. El Ganaoui, P. Bontoux, A homogenization method for solid–liquid phase change during directional solidification, HTD-vol. 361-5, in: Proceeding of the ASME Heat Transfer Division, vol. 5, ASME, 1998

[20] R. Bennacer; M. El Ganaoui; E. Leonardi Symmetry breaking of melt flow typically encountered in a Bridgman configuration heated from below, Applied Mathematical Modelling, Volume 30 (2006), pp. 1249-1261

[21] F. Mechighel; M. El Ganaoui; M. Kadja; B. Pateyron; S. Dost Numerical simulation of three dimensional low Prandtl liquid flow in a parallelepiped cavity under an external magnetic field, Fluid Dynamics & Materials Processing (FDMP), Volume 5 (2009) no. 4, pp. 313-330

[22] J.P. Pullicani; E.C. Del Arco; A. Randriamampianina; P. Bontoux; R. Peyret Spectral simulations of oscillatory convection at low Prandtl number, International Journal of Numerical Methods in Fluids, Volume 10 (1990), p. 481

[23] H. Zhou; A. Zebib Oscillatory convection in solidifying pure metal, Numerical Heat Transfer, Part A, Volume 22 (1992), pp. 435-468

[24] A. Semma, Etude numérique des transferts de chaleur et de masse durant la croissance dirigée : effet de paramètres de contrôle, Thèse de doctorat de l'école Mohammadia d'Ingénieurs, Université Mohamed V, Maroc, 2004

[25] P. Larroudé; J. Ouazzani; L.I.D. Alexander; P. Bontoux Symmetry breaking flow transitions and oscillatory flows in a 2D directional solidification model, European Journal of Mechanics B, Volume 13 (1994) no. 3, pp. 353-381

[26] M. El Ganaoui; D. Morvan; P. Larroude; P. Bontoux Numerical simulation of gravitational effects during directional solidification, Advances in Space Research, Volume 22 (1998) no. 8, pp. 1175-1178

[27] A.Yu. Gelfgat; P.Z. Bar-Yoseph The effect of an external magnetic field on oscillatory instability of convective flows in a rectangular cavity, Physics of Fluids, Volume 13 (2001) no. 8, pp. 2269-2278

[28] M.C. Ece; E. Büyük Natural-convection flow under a magnetic field in an inclined rectangular enclosure heated and cooled on adjacent walls, Fluid Dynamics Research, Volume 38 (2006), pp. 564-590

[29] Z. Guo; C. Zheng; B. Shi Discrete lattice effects on the forcing term in the lattice Boltzmann method, Physical Review E, Volume 65 (2002), p. 046308

Cited by Sources:

Comments - Policy