On the aptitude of the lattice Boltzmann approach for the treatment of the transient heat transfer with crack resistance

M. El Ganaoui; S. Addakiri; E. Semma

doi:10.1016/j.crme.2012.03.010

On the aptitude of the lattice Boltzmann approach for the treatment of the transient heat transfer with crack resistance

M. El Ganaoui ¹ ; S. Addakiri ^1,²; E. Semma ²

¹ Université de Lorraine, Lermab-Longwy, IUT Henri Poincaré, 186, rue de Lorraine, 54400 Cosnes et Romain, France
² Université Hassan I, Laboratoire de Mécanique, FST de Settat, B.P. 577, Settat, Morocco

Comptes Rendus. Mécanique, Analytical and innovative solutions for heat transfer problems involving phase change and interfaces, Volume 340 (2012) no. 7, pp. 518-525.

Abstract
Résumé

A numerical approach is introduced within the outline of the thermal lattice Boltzmann method developments to solve problems with cracks. It consists on an extension of the termed Partial Bounce Back scheme (PBB) to transient situations. A special case of the scheme leads to account the thermal contact resistance between surfaces. Numerical examples are provided to validate and demonstrate the accuracy of the proposed methodology and its applicative potential.

Une nouvelle approche numérique est introduite dans le sillage des développements des méthodes de gaz sur réseaux pour résoudre des problèmes en présence de contact imparfait. Lʼapproche consiste en une extension du schéma PBB (Partial Bounce Back) aux situations transitoires. Le développement permet la prise en compte de la nature du contact entre deux milieux solides. Des exemples numériques permettent de valider et de montrer la précision de cette approche ainsi que son potentiel applicatif.

Published online: 2012-05-17

DOI: 10.1016/j.crme.2012.03.010

Keywords: Lattice Boltzmann model, Heat transfer, Thermal contact resistance, Numerical simulation, Modelling, Boundary conditions
Mots-clés : Méthode de gaz sur réseaux, Transferts thermiques, Resistance thermique du contact, Simulation numérique, Modélisation, Conditions aux limites

Author's affiliations:

M. El Ganaoui ¹; S. Addakiri ^{1, 2}; E. Semma ²

¹ Université de Lorraine, Lermab-Longwy, IUT Henri Poincaré, 186, rue de Lorraine, 54400 Cosnes et Romain, France
² Université Hassan I, Laboratoire de Mécanique, FST de Settat, B.P. 577, Settat, Morocco

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     author = {M. El Ganaoui and S. Addakiri and E. Semma},
     title = {On the aptitude of the lattice {Boltzmann} approach for the treatment of the transient heat transfer with crack resistance},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {518--525},
     publisher = {Elsevier},
     volume = {340},
     number = {7},
     year = {2012},
     doi = {10.1016/j.crme.2012.03.010},
     language = {en},
}

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M. El Ganaoui; S. Addakiri; E. Semma. On the aptitude of the lattice Boltzmann approach for the treatment of the transient heat transfer with crack resistance. Comptes Rendus. Mécanique, Analytical and innovative solutions for heat transfer problems involving phase change and interfaces, Volume 340 (2012) no. 7, pp. 518-525. doi : 10.1016/j.crme.2012.03.010. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2012.03.010/

References
Cited by

[1] Z.L. Guo; B.C. Shi; C.G. Zheng A lattice BGK model for the Bouessinesq equation, Internat. J. Numer. Methods Fluids, Volume 39 (2002), pp. 325-342

[2] S. Feng; P. Dong; M. Tsutahara; N. Takada Simulation of shockwave for propagation with a thermal lattice Boltzmann model, Int. J. Numer. Methods Fluids, Volume 41 (2003), pp. 1137-1146

[3] J. Wang; M. Wang; Z. Li A lattice Boltzmann algorithm for fluid solid conjugate heat transfer, Int. J. Thermal Sci., Volume 46 (2007), pp. 228-234

[4] C. Shu; X.D. Niu; Y.T. Chew A lattice Boltzmann kinetic model for microflow and heat transfer, J. Stat. Phys., Volume 121 (2005) no. 1/2, pp. 239-255

[5] Z. Guo; B. Shi; C. Zheng A coupled lattice BGK model for the Boussinesq equations, Internat. J. Numer. Methods Fluids, Volume 39 (2002), pp. 325-342

[6] X. He; L.-S. Luo Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation, Phys. Rev. E, Volume 56 (1997), pp. 6811-6817

[7] A. Dupuis, From a lattice Boltzmann model to a parallel and reusable implementation of a virtual river, Thèse soutenue à Genève en Suisse, 2002.

[8] U. Frisch; B. Hasslacher; Y. Pomeau Lattice-gas automata for the Navier–Stokes equations, Phys. Rev. Lett., Volume 56 (1986), pp. 1505-1508

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

[10] A.Z. DʼOrazio; M. Corcione; G.P. Celata Application to natural convection enclosed flows of a lattice Boltzmann BGK model coupled with a general purpose thermal boundary condition, Int. J. Thermal Sci., Volume 43 (2004), pp. 575-586

[11] G.H. Tang; W.Q. Tao; Y.L. He Thermal boundary condition for the thermal lattice Boltzmann equation, Phys. Rev. E, Volume 72 (2005), p. 016703

[12] H. Huang; T.S. Lee; C. Shu Thermal curved boundary treatment for the thermal lattice Boltzmann equation, Int. J. Modern Phys. C, Volume 17 (2006) no. 5, pp. 631-643

[13] N. Laraqi; A. Baïri; L. Segui Temperature and thermal resistance in frictional devices, Appl. Thermal Eng., Volume 24 (2004) no. 17, pp. 2567-2581

[14] H. Belghazi; M. El Ganaoui; J.C. Labbe Analytical solution of unsteady heat conduction in a two-layered material in imperfect contact subjected to a moving heat source, Int. J. Thermal Sci., Volume 49 (2010) no. 2, pp. 311-318

[15] H. Belghazi; M. El Ganaoui; J.-C. Labbe Analytical solution of unsteady heat diffusion within a porous copper layer deposited on alumina substrate and subjected to a moving laser beam, Defect Diffusion Forum, Volume 273–276 (2008), pp. 52-57

[16] A. Grimaud; M. Bouneder; S. Menecier; M. El Ganaoui Faisabilité dʼune méthode dʼévaluation de la résistance thermique de contact entre une lamelle céramique écrasée sur un substrat métallique, Mécanique & Industries, Volume 8 (2007), pp. 71-75

[17] G. Shen; S.L. Semiatin; E. Kropp; T. Altan A technique to compensate for temperature history effect in the simulation of non-isothermal forging processes, J. Mater. Process. Technol., Volume 33 (1992) no. 1–2, pp. 125-140

[18] A. Degiovanni; A.S. Lamine; C.H. Moyne Thermal contact in transient state – A new model and two experiments, J. Thermophys. Heat Transfer, Volume 6 (1992) no. 2, pp. 356-363

[19] T. Jurkowski, Y. Jarny, D. Delaunay, Simultaneous identification of thermal conductivity and thermal contact resistance without internal temperature measurements, in: Proceedings of the 3rd UK Conference on Heat Transfer, Birmingham, 1992.

[20] M. Amara; V. Timchenko; M. El Ganaoui; E. Leonardi; G. de Vahl Davis A 3D computational model of heat transfer coupled to phase change in multilayer materials with random thermal contact resistance, Int. J. Thermal Sci., Volume 48 (2009), pp. 421-427

[21] X. Zhang; P. Cong; S. Fijiwara; M. Fujii A new method for numerical simulation of thermal contact resistance in cylindrical coordinates, Int. J. Heat Mass Transfer, Volume 47 (2004), pp. 1091-1098

[22] S. Ben Naoua; M. El Ganaoui; H. Sammouda; P. Fauchais A model for rapid solidification for plasma spraying, Mater. Sci. Forum, Volume 553 (2007), pp. 223-230

[23] T. Loulou; J.P. Bardon Premiers instants du refroidissement dʼune goutte métallique après son impact sur une paroi, Revue Générale de Thermique, Volume 36 (1997) no. 9, pp. 682-689

[24] T. Loulou; E.A. Artyukhin; J.P. Bardon Estimation of thermal contract resistance during the first stages of metal solidification process. II. Experimental setup and results, Int. J. Heat Mass Transfer, Volume 42 (1999) no. 12, pp. 2129-2142

[25] K. Han; Y.T. Feng; D.R.J. Owen Modelling of thermal contact resistance within the framework of the thermal lattice Boltzmann method, Int. J. Thermal Sci., Volume 47 (2008), pp. 1276-1283

[26] Jie Bao; Peng Yuan; Laura Schaefer A mass conserving boundary condition for the lattice Boltzmann equation method, J. Comput. Phys., Volume 227 (2008), pp. 8472-8487

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