Lattice Boltzmann method for melting/solidification problems

El Alami Semma; Mohammed El Ganaoui; Rachid Bennacer

doi:10.1016/j.crme.2007.05.015

Lattice Boltzmann method for melting/solidification problems
[Une méthode de type gaz sur réseau pour la transition solide/liquide]

El Alami Semma ¹ ; Mohammed El Ganaoui ² ; Rachid Bennacer ³

¹ Université Hassan I, laboratoire de mécanique, FST de Settat, B.P. 577, Settat, Morocco
² Université de Limoges/CNRS, SPCTS, UMR CNRS 6638, 123, Albert-Thomas, 87000 Limoges, France
³ Université de Cergy-Pontoise, laboratoire LEEVAM, 5, mail Gay-Lussac, Neuville-sur-Oise, 95031 Cergy-Pontoise cedex, France

Comptes Rendus. Mécanique, Melting and solidification: processes and models, Volume 335 (2007) no. 5-6, pp. 295-303.

Résumé
Abstract

Il s'agit de montrer dans le présent travail la possibilité de traiter des problèmes de transition de phase solide/liquide par une approche de type gaz sur réseau. Les résultats illustrent un bon accord avec les résultats existants dans le cas d'écoulement de convection naturelle en cavité ainsi que dans le cadre d'un problème test de solidification dirigée.

The present work uses the Lattice Boltzmann method for solving solid/liquid phase change problems. The computed results demonstrate a good agreement with the existing benchmark solution for natural convection and with the experimental solution for solid/liquid interface interacting with the flow field.

Publié le : 2007-05-01

DOI : 10.1016/j.crme.2007.05.015

Keywords: Computational fluid mechanics, Solid/liquid phase change, Lattice Boltzmann, Enthalpy method
Mots-clés : Mécanique des fluides numérique, Changement de phase solide/liquide, Gaz sur réseau, Méthode enthalpique

Affiliations des auteurs :

El Alami Semma ¹ ; Mohammed El Ganaoui ² ; Rachid Bennacer ³

¹ Université Hassan I, laboratoire de mécanique, FST de Settat, B.P. 577, Settat, Morocco
² Université de Limoges/CNRS, SPCTS, UMR CNRS 6638, 123, Albert-Thomas, 87000 Limoges, France
³ Université de Cergy-Pontoise, laboratoire LEEVAM, 5, mail Gay-Lussac, Neuville-sur-Oise, 95031 Cergy-Pontoise cedex, France

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     author = {El Alami Semma and Mohammed El Ganaoui and Rachid Bennacer},
     title = {Lattice {Boltzmann} method for melting/solidification problems},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {295--303},
     publisher = {Elsevier},
     volume = {335},
     number = {5-6},
     year = {2007},
     doi = {10.1016/j.crme.2007.05.015},
     language = {en},
}

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El Alami Semma; Mohammed El Ganaoui; Rachid Bennacer. Lattice Boltzmann method for melting/solidification problems. Comptes Rendus. Mécanique, Melting and solidification: processes and models, Volume 335 (2007) no. 5-6, pp. 295-303. doi : 10.1016/j.crme.2007.05.015. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.05.015/

Bibliographie
Cité par

[1] 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: Statist. Mech. Appl., Volume 368 (2006) no. 2, pp. 481-494

[2] A. Mezrhab; M. Jami; C. Abid; M. Bouzidi; P. Lallemand Lattice-Boltzmann modelling of natural convection in an inclined square enclosure with partitions attached to its cold wall, Int. J. Heat Fluid Flow, Volume 27 (2006) no. 3, pp. 456-465

[3] F.J. Alexander; S. Chen; J.D. Sterling Lattice Boltzmann thermohydrodynamics, Phys. Rev. E, Volume 47 (1993), p. R2249

[4] X. He; S. Chen; G.D. Doolen A novel thermal model for the lattice Boltzmann method incompressible limit, J. Comput. Phys., Volume 146 (1998), pp. 282-300

[5] W. Miller The lattice Boltzmann method: a new tool for numerical simulation of the interaction of growth kinetics and melt flow, J. Crystal Growth, Volume 230 (2001), pp. 263-269

[6] W. Miller; S. Succi; D. Mansutti Lattice Boltzmann model for anisotropic liquid–solid phase transition, Phys. Rev. Lett., Volume 86 (2001) no. 16, pp. 3578-3581

[7] W. Miller; I. Rasin; F. Pimentel Growth kinetics and melt convection, J. Crystal Growth, Volume 266 (2004), pp. 283-288

[8] S. Succi The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Clarendon Press, Oxford, 2001

[9] C.K. Chen; T.S. Yen; Y.T. Yang Lattice Boltzmann method simulation of backward-facing step on convective heat transfer with field synergy principle, Int. J. Heat Mass Transfer, Volume 49 (2006), pp. 1195-1204

[10] F.J. Higuera; J. Jimenez Boltzmann approach to lattice-gas simulations, Europhys. Lett., Volume 9 (1989) no. 7, pp. 663-668

[11] F.J. Higuera; S. Succi; R. Benzi Lattice gas dynamics with enhanced collisions, Europhys. Lett., Volume 9 (1989), pp. 345-349

[12] F.J. Benzi; S. Succi; M. Vergassola The lattice Boltzmann equation: theory and applications, Phys. Rep., Volume 222 (1992), pp. 145-197

[13] S. Hou; Q. Zou; S. Chen; G. Doolen; A.C. Cogley Simulation of cavity flow by the lattice Boltzmann method, J. Comput. Phys., Volume 118 (1995), pp. 329-347

[14] B.I. Pavel; A.A. Mohamad A numerical study on vortex shedding from two side by side cylinders using the lattice Boltzmann method (R. Bennacer; M. El Ganaoui; A.A. Mohamad; J. Sicard, eds.), Progress in Computational Heat and Mass Transfer, vol. I, Lavoisier-Tec & Doc., 2006, pp. 411-416

[15] G. de Vahl Davis Natural convection of air in a square cavity: a benchmark numerical solution, Int. J. Numer. Fluid Meth. Fluids, Volume 3 (1983), pp. 249-264

[16] C. Gau; R. Viskanta Melting and solidification of a metal system in a rectangular cavity, Int. J. Heat Mass Transfer, Volume 27 (1984), pp. 113-123

[17] F. Wolff; R. Viskanta Solidification of pure metal at a vertical wall in the presence of liquid superheat, Int. J. Heat Mass Transfer, Volume 31 (1988), pp. 1735-1744

[18] J.E. Simpson; R.S. Garimella An investigation of solutal thermal and flow fields in unidirectional alloy solidification, Int. J. Heat Mass Transfer, Volume 41 (1998), pp. 2485-2502

[19] M. El Ganaoui; A. Lamazouade; P. Bontoux; D. Morvan Computational solution for fluid flow under solid/liquid phase change conditions, Int. J. Comput. Fluids, Volume 31 (2002) no. 4–7, pp. 539-556

[20] E. Semma, Etude numérique des transferts de chaleur et de masse durant la croissance dirigée : effet de paramètres de contrôle, Thèse de doctorat Franco-Marocaine, Université de la Méditerranée/Université Mohamed V, 2004

[21] J. Kaenton; E. Semma; V. Timchenko; M. El Ganaoui; E. Leonardi; G. de Vahl Davis Effects of anisotropy and solid/liquid thermal conductivity ratio on flow instabilities during inverted Bridgman growth, Int. J. Heat Mass Transfer, Volume 47 (2004), pp. 3403-3413

[22] E. Semma, M. El Ganaoui, R. Bennacer, A.A. Mohamad, Melting and solidification problem, the lattice Boltzmann method, Int. J. Thermal Sci. (2007), in press

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