Thermal conductive and radiative properties of solid foams: Traditional and recent advanced modelling approaches

Jaona Randrianalisoa; Dominique Baillis

doi:10.1016/j.crhy.2014.09.002

Thermal conductive and radiative properties of solid foams: Traditional and recent advanced modelling approaches

Jaona Randrianalisoa ¹ ; Dominique Baillis ²

¹ GRESPI, Université de Reims, EA 4694, Campus Moulin de la Housse, BP 1039, 51687 Reims cedex 2, France
² LaMCoS, INSA-Lyon, UMR CNRS 5259, 18-20, rue des Sciences, 69621 Villeurbanne cedex, France

Comptes Rendus. Physique, Liquid and solid foams / Mousses liquides et solides, Volume 15 (2014) no. 8-9, pp. 683-695.

Abstract
Résumé

The current paper presents an overview of traditional and recent models for predicting the thermal properties of solid foams with open- and closed-cells. Their effective thermal conductivity has been determined analytically by empirical or thermal-resistance-network-based models. Radiative properties crucial to obtain the radiative conductivity have been determined analytically by models based on the independent scattering theory. Powerful models combine three-dimensional (3D) foam modelling (by X-ray tomography, Voronoi tessellation method, etc.) and numerical solution of transport equations. The finite-element method (FEM) has been used to compute thermal conductivity due to solid network for which the computation cost remains reasonable. The effective conductivity can be determined from FEM results combined with the conductivity due to the fluid, which can be accurately evaluated by a simple formula for air or weakly conducting gas. The finite volume method seems well appropriate for solving the thermal problem in both the solid and fluid phases. The ray-tracing Monte Carlo method constitutes the powerful model for radiative properties. Finally, 3D image analysis of foams is useful to determine topological information needed to feed analytical thermal and radiative properties models.

Cet article présente une vue globale des modèles traditionnels et récents de prédiction des propriétés thermiques et radiatives des mousses solides ayant des cellules ouvertes ou fermées. Leur conductivité thermique effective est déterminée par des modèles empiriques ou analytiques basés sur le réseau de résistances. Les propriétés radiatives nécessaires pour remonter à la conductivité radiative sont déterminées par des modèles analytiques basés sur la théorie de diffusion indépendante. Les approches robustes couplent la modélisation tridimensionnelle (3D) de mousses (par exemple, par la tomographie à rayons X, la mosaïque de Voronoï, etc.) et la résolution numérique des équations de transport. La conductivité thermique due à la phase solide est directement calculée par la méthode des éléments finis (EF), avec un coût de calcul raisonnable. La conductivité thermique effective, quant à elle, peut être déterminée à partir des calculs EF combinés avec la conductivité thermique due à la phase fluide. Cette dernière peut être évaluée de façon précise par des formules simples dans le cas de l'air ou d'un gaz faiblement conducteur thermique. Cependant, la méthode des volumes finis apparaît la mieux appropriée pour résoudre le problème thermique, à la fois dans la phase solide et la phase fluide. La méthode de Monte Carlo et de tracé de rayons constitue une approche solide pour calculer les propriétés radiatives. Enfin, la reconstruction d'image 3D des mousses est essentielle pour déterminer les informations topologiques nécessaires pour alimenter les modèles analytiques de conductivité thermique et de propriétés radiatives.

Published online: 2014-10-01

DOI: 10.1016/j.crhy.2014.09.002

Keywords: Metallic foams, Ceramic foams, Polymer foams, Cellular materials, Voronoi tessellation, Laguerre–Voronoi tessellation
Mots-clés : Mousses métalliques, Mousses céramiques, Mousses polymères, Matériaux cellulaires, Mosaïque de Voronoï, Mosaïque de Voronoï–Laguerre

Author's affiliations:

Jaona Randrianalisoa ¹; Dominique Baillis ²

¹ GRESPI, Université de Reims, EA 4694, Campus Moulin de la Housse, BP 1039, 51687 Reims cedex 2, France
² LaMCoS, INSA-Lyon, UMR CNRS 5259, 18-20, rue des Sciences, 69621 Villeurbanne cedex, France

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     title = {Thermal conductive and radiative properties of solid foams: {Traditional} and recent advanced modelling approaches},
     journal = {Comptes Rendus. Physique},
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Jaona Randrianalisoa; Dominique Baillis. Thermal conductive and radiative properties of solid foams: Traditional and recent advanced modelling approaches. Comptes Rendus. Physique, Liquid and solid foams / Mousses liquides et solides, Volume 15 (2014) no. 8-9, pp. 683-695. doi : 10.1016/j.crhy.2014.09.002. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2014.09.002/

References
Cited by

[1] L.J. Gibson; M.F. Ashby Cellular Solids: Structure and Properties, Cambridge University Press, Cambridge, UK, 1997

[2] P.G. Collishaw; J.R.G. Evans An assessment of expressions for the apparent thermal conductivity of cellular materials, J. Mater. Sci., Volume 29 (1994), pp. 486-498

[3] E. Placido; M.C. Arduini-Schuster; J. Kuhn Thermal properties predictive model for insulating foams, Infrared Phys. Technol., Volume 46 (2005), pp. 219-231

[4] R. Coquard; D. Baillis Modeling of heat transfer in low-density EPS foams, J. Heat Transf., Volume 128 (2006), pp. 538-549

[5] A. Kaemmerlen; C. Vo; F. Asllanaj; G. Jeandel; D. Baillis Radiative properties of extruded polystyrene foams: predictive model and experimental results, J. Quant. Spectrosc. Radiat. Transf., Volume 111 (2010), pp. 865-877

[6] Q. Wang; X.H. Han; A. Sommers; Y. Park; C. T' Joen; A. Jacobi A review on application of carbonaceous materials and carbon matrix composites for heat exchangers and heat sinks, Int. J. Refrig., Volume 35 (2012), pp. 7-26

[7] K. Boomsma; D. Poulikakos; F. Zwick Metal foams as compact high performance heat exchangers, Mech. Mater., Volume 35 (2003), pp. 1161-1176

[8] B. Ozmat; B. Leyda; B. Benson Thermal applications of open-cell metal foams, Mater. Manuf. Process., Volume 19 (2004), pp. 839-862

[9] S.A. Khateeb; S. Amiruddin; M. Farid; J.R. Selman; S. Al-Hallaj Thermal management of Li-ion battery with phase change material for electric scooters: experimental validation, J. Power Sources, Volume 142 (2005), pp. 345-353

[10] S.-T. Hong; D.R. Herling Open-cell aluminum foams filled with phase change materials as compact heat sinks, Scr. Mater., Volume 55 (2006), pp. 887-890

[11] M. Kaplan; M.J. Hall The combustion of liquid fuels within a porous media radiant burner, Exp. Therm. Fluid Sci., Volume 11 (1995), pp. 13-20

[12] J.R. Howell; M.J. Hall; J.L. Ellzey Combustion of hydrocarbon fuels within porous inert media, Prog. Energy Combust. Sci., Volume 22 (1996), pp. 121-145

[13] R. Mital; J.P. Gore; R. Viskanta A study of the structure of submerged reaction zone in porous ceramic radiant burners, Combust. Flame, Volume 111 (1997), pp. 175-184

[14] S. Gauthier; A. Nicolle; D. Baillis Investigation of the flame structure and nitrogen oxides formation in lean porous premixed combustion of natural gas/hydrogen blends, Int. J. Hydrog. Energy, Volume 33 (2008), pp. 4893-4905

[15] J. Randrianalisoa; Y. Bréchet; D. Baillis Materials selection for optimal design of a porous radiant burner for environmentally driven requirements, Adv. Eng. Mater., Volume 11 (2009), pp. 1049-1056

[16] W.M. Carty; P.W. Lednor Monolithic ceramics and heterogeneous catalysts: honeycombs and foams, Curr. Opin. Solid State Mater. Sci., Volume 1 (1996), pp. 88-95

[17] M.V. Twigg; J.T. Richardson Theory and applications of ceramic foam catalysts, Chem. Eng. Res. Des., Volume 80 (2002), pp. 183-189

[18] M.I. Roldán; O. Smirnova; T. Fend; J.L. Casas; E. Zarza Thermal analysis and design of a volumetric solar absorber depending on the porosity, Renew. Energy, Volume 62 (2014), pp. 116-128

[19] T. Fend; B. Hoffschmidt; R. Pitz-Paal; O. Reutter; P. Rietbrock Porous materials as open volumetric solar receivers: experimental determination of thermophysical and heat transfer properties, Energy, Volume 29 (2004), pp. 823-833

[20] P. Furler; J. Scheffe; M. Gorbar; M. Moes; U. Vogt; A. Steinfeld Solar thermochemical CO2 splitting utilizing a reticulated porous ceria redox system, Energy Fuels, Volume 26 (2012), pp. 7051-7059

[21] L. Giani; G. Groppi; E. Tronconi Mass-transfer characterization of metallic foams as supports for structured catalysts, Ind. Eng. Chem. Res., Volume 44 (2005), pp. 4993-5002

[22] C.Y. Zhao Review on thermal transport in high porosity cellular metal foams with open cells, Int. J. Heat Mass Transf., Volume 55 (2012), pp. 3618-3632

[23] L.R. Glicksman Heat transfer in foams (N.C. Hilyard; A. Cunningham, eds.), Low Density Cellular Plastics: Physical Basis of Behaviour, Chapman and Hall, 1994, pp. 105-152

[24] F.P. Incropera; D.P. DeWitt Fundamentals of Heat and Mass Transfer, John Wiley & Sons, Inc., New York, 1996

[25] J. Randrianalisoa; R. Coquard; D. Baillis Microscale direct calculation of solid phase conductivity of Voronoi's foams, J. Porous Media, Volume 16 (2013) no. 5, pp. 411-426

[26] A. Ahern; G. Verbist; D. Weaire; R. Phelan; H. Fleurent The conductivity of foams: a generalisation of the electrical to the thermal case, Colloids Surf. A, Physicochem. Eng. Asp., Volume 263 (2005), pp. 275-279

[27] R. Coquard; D. Baillis Numerical investigation of conductive heat transfer in high-porosity foams, Acta Mater., Volume 57 (2009), pp. 5466-5479

[28] H.W. Russell Principles of heat flow in porous insulators, J. Am. Ceram. Soc., Volume 18 (1935), pp. 1-5

[29] E. Solórzano; J.A. Reglero; M.A. Rodríguez-Pérez; D. Lehmhus; M. Wichmann; J.A. De Saja An experimental study on the thermal conductivity of aluminium foams by using the transient plane source method, Int. J. Heat Mass Transf., Volume 51 (2008), pp. 6259-6267

[30] T.H. Bauer A general analytical approach toward the thermal conductivity of porous media, Int. J. Heat Mass Transf., Volume 36 (1993), pp. 4181-4191

[31] K. Boomsma; D. Poulikakos On the effective thermal conductivity of a three-dimensionally structured fluid-saturated metal foam, Int. J. Heat Mass Transf., Volume 44 (2001), pp. 827-836

[32] A. Bhattacharya; V.V. Calmidi; R.L. Mahajan Thermophysical properties of high porosity metal foams, Int. J. Heat Mass Transf., Volume 45 (2002), pp. 1017-1031

[33] R. Singh; H.S. Kasana Computational aspects of effective thermal conductivity of highly porous metal foams, Appl. Therm. Eng., Volume 24 (2004), pp. 1841-1849

[34] R. Coquard; D. Baillis Radiative and conductive thermal properties of foams (A. Öchsner; G.E. Murch; M. de Lemos, eds.), Thermal Properties of Cellular and Porous Materials, Wiley-VCH, Weinheim, 2008, pp. 343-384

[35] X.H. Yang; J.X. Bai; H.B. Yan; J.J. Kuang; T.J. Lu; T. Kim An analytical unit cell model for the effective thermal conductivity of high porosity open-cell metal foams, Transp. Porous Media, Volume 102 (2014), pp. 403-426

[36] P. Kumar; F. Topin; J. Vicente Determination of effective thermal conductivity from geometrical properties: application to open cell foams, Int. J. Therm. Sci., Volume 81 (2014), pp. 13-28

[37] J.E. Li; B. Wang Equivalent thermal conductivity of open-cell ceramic foams at high temperatures, Int. J. Thermophys., Volume 35 (2014), pp. 105-122

[38] M. Wang; N. Pan Modeling and prediction of the effective thermal conductivity of random open-cell porous foams, Int. J. Heat Mass Transf., Volume 51 (2008), pp. 1325-1331

[39] A.M. Kraynik; D.A. Reinelt; F. van Swol Structure of random monodisperse foam, Phys. Rev. E, Volume 67 (2003), p. 031403

[40] A.M. Kraynik; D.A. Reinelt; F. van Swol Structure of random foam, Phys. Rev. Lett., Volume 93 (2004), p. 208301

[41] C. Lautensack; T. Sych 3D image analysis of open foams using random tessellation, Image Anal. Stereol., Volume 25 (2006), pp. 87-93

[42] C. Lautensack Fitting three-dimensional Laguerre tessellations to foam structures, J. Appl. Stat., Volume 35 (2008), pp. 985-995

[43] T. Wejrzanowski; J. Skibinski; J. Szumbarski; K.J. Kurzydlowski Structure of foams modeled by Laguerre–Voronoi tessellations, Comput. Mater. Sci., Volume 67 (2013), pp. 216-221

[44] I. Vecchio; C. Redenbach; K. Schladitz Angles in Laguerre tessellation models for solid foams, Comput. Mater. Sci., Volume 83 (2014), pp. 171-184

[45] A.M. Kraynik; Douglas A. Reinelt; F. van Swol Structure of random bidisperse foam, Colloids Surf. A, Physicochem. Eng. Asp., Volume 263 (2005), pp. 11-17

[46] J. Randrianalisoa; D. Baillis; C. Martin; R. Dendievel Microstructural effects on thermal conductivity of open-cell Laguerre–Voronoï foams, Int. J. Therm. Sci. (2014) (submitted for publication)

[47] S. Kanaun; S.B. Kochekseraii Conductive properties of foam materials with open or closed cells, Int. J. Eng. Sci., Volume 50 (2012), pp. 124-131

[48] W.-Y. Jang; A.M. Kraynik; S. Kyriakides On the microstructure of open-cell foams and its effect on elastic properties, Int. J. Solids Struct., Volume 45 (2008), pp. 1845-1875

[49] A. Liebscher; C. Redenbach Statistical analysis of the local strut thickness of open cell foams, Image Anal. Stereol., Volume 32 (2013), pp. 1-12

[50] T. Dillard; F. N'guyen; E. Maire; L. Salvo; S. Forest; Y. Bienvenu; J.-D. Bartout; M. Croset; R. Dendievel; P. Cloetens 3D quantitative image analysis of open-cell nickel foams under tension and compression loading using X-ray microtomography, Philos. Mag., Volume 85 (2005), pp. 2147-2175

[51] M. Loretz; E. Maire; D. Baillis Analytical modelling of the radiative properties of metallic foams: contribution of X-ray tomography, Adv. Eng. Mater., Volume 10 (2008), pp. 352-360

[52] R. Coquard; D. Baillis; E. Maire Numerical investigation of the radiative properties of polymeric foams from tomographic images, J. Thermophys. Heat Transf., Volume 24 (2010), pp. 647-658

[53] Z. Li; J. Zhang; Z. Wang; Y. Song; L. Zhao Study on the thermal properties of closed-cell metal foams based on Voronoi random models, Numer. Heat Transf., Part A, Appl., Volume 64 (2013), pp. 1038-1049

[54] M.W.D. Van Der Burg; V. Shulmeister; E. Van Der Geissen; R. Marissen On the linear elastic properties of regular and random open-cell foam models, J. Cell. Plast., Volume 33 (1997), pp. 31-54

[55] J. Randrianalisoa; R. Coquard; D. Baillis Microscale direct calculation of solid phase conductivity of Voronoi's foams, J. Porous Media, Volume 16 (2013), pp. 411-426

[56] S. Kanaun; O. Tkachenko Effective conductive properties of open-cell foams, Int. J. Eng. Sci., Volume 46 (2008), pp. 551-571

[57] R. Coquard; D. Rochais; D. Baillis Conductive and radiative heat transfer in ceramic and metal foams at fire temperatures, Fire Technol., Volume 48 (2012), pp. 699-732

[58] T. Fiedler; E. Solórzano; F. Garcia-Moreno; O. Öchsner; I.V. Belova; G.E. Murch Lattice Monte Carlo and experimental analyses of the thermal conductivity of random-shaped cellular aluminum, Adv. Eng. Mater., Volume 11 (2009), pp. 843-847

[59] T. Fiedler; M.A. Sulong; M. Vesenjak; Y. Higa; I.V. Belova; A. Öchsner; G.E. Murch Determination of the thermal conductivity of periodic APM foam models, Int. J. Heat Mass Transf., Volume 73 (2014), pp. 826-833

[60] K.K. Bodla; J.Y. Murthy; S.V. Garimella Resistance network-based thermal conductivity model for metal foams, Comput. Mater. Sci., Volume 50 (2010), pp. 622-632

[61] M.A.A. Mendes; S. Ray; D. Trimis A simple and efficient method for the evaluation of effective thermal conductivity of open-cell foam-like structures, Int. J. Heat Mass Transf., Volume 66 (2013), pp. 412-422

[62] M.A.A. Mendes; S. Ray; D. Trimis Evaluation of effective thermal conductivity of porous foams in presence of arbitrary working fluid, Int. J. Therm. Sci., Volume 79 (2014), pp. 260-265

[63] L.A. Dombrovsky; D. Baillis Thermal Radiation in Disperse Systems: An Engineering Approach, Begell House, New York and Redding, CT, 2010

[64] J.F. Sacadura; D. Baillis Experimental characterization of thermal radiation properties of dispersed media, Int. J. Therm. Sci., Volume 41 (2002), pp. 699-707

[65] D. Baillis; R. Coquard; J. Randrianalisoa; L. Dombrovsky; R. Viskanta Thermal radiation properties of highly porous cellular foams, Spec. Top. Rev. Porous Media, Volume 4 (2013), pp. 111-136

[66] J. Kuhn; H.P. Ebert; M.C. Arduini-Schuster; D. Büttner; J. Fricke Thermal transport in polystyrene and polyurethane foam insulations, Int. J. Heat Mass Transf., Volume 35 (1992), pp. 1795-1801

[67] L.R. Glicksman; M.A. Schuetz Radiation heat transfer in foam insulation, Int. J. Heat Mass Transf., Volume 30 (1987), pp. 187-197

[68] R. Coquard; D. Baillis; D. Quenard Radiative properties of expanded polystyrene foams, J. Heat Transf., Volume 131 (2009), p. 012702

[69] D. Doermann; J.F. Sacadura Heat transfer in open-cell foams, J. Heat Transf., Volume 118 (1996), pp. 88-93

[70] D. Baillis; M. Raynaud; J.F. Sacadura Spectral radiative properties of open-cell foam insulation, J. Thermophys. Heat Transf., Volume 13 (1999), pp. 292-298

[71] D. Baillis; M. Raynaud; J.F. Sacadura Determination of spectral radiative properties of open cell foam: model validation, J. Thermophys. Heat Transf., Volume 14 (2000), pp. 137-143

[72] M. Loretz; R. Coquard; D. Baillis; E. Maire Metallic foams: radiative properties/comparison between different models, J. Quant. Spectrosc. Radiat. Transf., Volume 109 (2008), pp. 16-27

[73] R. Coquard; D. Rochais; D. Baillis Modelling of the coupled conductive and radiative heat transfer in NiCrAl foams from photothermal measurements and X-Ray tomography, Spec. Top. Rev. Porous Media, Volume 2 (2011), pp. 249-265

[74] C.Y. Zhao; S.A. Tassou; T.J. Lu Analytical considerations of thermal radiation in cellular metal foams with open cells, Int. J. Heat Mass Transf., Volume 51 (2008), pp. 929-940

[75] B. Zeghondy; E. Iacona; J. Taine Determination of the anisotropic radiative properties of a porous material by radiative distribution function identification (RDFI), Int. J. Heat Mass Transf., Volume 49 (2006), pp. 2810-2819

[76] B. Zeghondy; E. Iacona; J. Taine Experimental and RDFI calculated radiative properties of a mullite foam, Int. J. Heat Mass Transf., Volume 49 (2006), pp. 3702-3707

[77] M. Tancrez; J. Taine Direct identification of absorption and scattering coefficients and phase function of a porous medium by a Monte Carlo technique, Int. J. Heat Mass Transf., Volume 47 (2004), pp. 373-383

[78] J. Petrasch; P. Wyss; A. Steinfeld Tomography-based Monte Carlo determination of radiative properties of reticulate porous ceramics, J. Quant. Spectrosc. Radiat. Transf., Volume 105 (2007), pp. 180-197

[79] R. Coquard; B. Rousseau; P. Echegut; D. Baillis; H. Gomart; E. Iacona Investigations of the radiative properties of Al–NiP foams using tomographic images and stereoscopic micrographs, Int. J. Heat Mass Transf., Volume 55 (2011), pp. 1606-1619

[80] R. Coquard; D. Baillis Radiative characteristics of opaque spherical particles beds: a new method of prediction, J. Thermophys. Heat Transf., Volume 18 (2004), pp. 178-186

[81] J. Randrianalisoa; D. Baillis Radiative properties of densely packed spheres in semitransparent media: a new geometric optics approach, J. Quant. Spectrosc. Radiat. Transf., Volume 111 (2010), pp. 1372-1388

[82] R. Coquard; J. Randrianalisoa; D. Baillis Computational prediction of radiative properties of polymer closed-cell foam with random structure, J. Porous Media, Volume 16 (2013), pp. 137-154

[83] P. Furler; J. Scheffe; D. Marxer; M. Gorbar; A. Bonk; U. Vogt; A. Steinfeld Thermochemical CO2 splitting via redox cycling of ceria reticulated foam structures with dual-scale porosities, Phys. Chem. Chem. Phys., Volume 16 (2014), pp. 10503-10511

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