Research Papers: Porous Media

Lord Kelvin and Weaire–Phelan Foam Models: Heat Transfer and Pressure Drop

[+] Author and Article Information
Salvatore Cunsolo

Dipartimento di Ingegneria Industriale,
Università degli Studi di Napoli Federico II,
P.le Tecchio, 80,
Napoli 80125, Italy
e-mail: sal.cuns@gmail.com

Marcello Iasiello

Dipartimento di Ingegneria Industriale,
Università degli Studi di Napoli Federico II,
P.le Tecchio, 80,
Napoli 80125, Italy
e-mail: marcello.iasiello@unina.it

Maria Oliviero

Istituto per i materiali compositi e biomedici,
Consiglio Nazionale delle Ricerche,
P.le Fermi, 1,
Portici, Napoli 80055, Italy
e-mail: maria.oliviero@unina.it

Nicola Bianco

Dipartimento di Ingegneria Industriale,
Università degli Studi di Napoli Federico II,
P.le Tecchio, 80,
Napoli 80125, Italy
e-mail: nicola.bianco@unina.it

Wilson K. S. Chiu

Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269
e-mail: wchiu@engr.uconn.edu

Vincenzo Naso

Dipartimento di Ingegneria Industriale,
Università degli Studi di Napoli Federico II,
P.le Tecchio, 80,
Napoli 80125, Italy
e-mail: vincenzo.naso@unina.it

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received January 7, 2015; final manuscript received July 16, 2015; published online October 21, 2015. Assoc. Editor: Antonio Barletta.

J. Heat Transfer 138(2), 022601 (Oct 21, 2015) (7 pages) Paper No: HT-15-1016; doi: 10.1115/1.4031700 History: Received January 07, 2015; Revised July 16, 2015

The knowledge of thermal transport characteristics is of primary importance in the application of foams. The thermal characteristics of a foam heavily depend on its microstructure and, therefore, have to be investigated at a pore level. However, this analysis is a challenging task, because of the complex geometry of a foam. The use of foam models is a promising tool in their study. The Kelvin and the Weaire–Phelan foam models, among the most representative practical foam models, are used in this paper to numerically investigate heat transfer and pressure drop in metallic foams. They are developed in the “surface evolver” open source software. Mass, momentum, and energy equations, for air forced convection in open cell foams, are solved with a finite-element method, for different values of cell size and porosity. Heat transfer and pressure drop results are reported in terms of volumetric Nusselt number and Darcy–Weisbach friction factor, respectively. Finally, a comparison between the numerical predictions obtained with the two foam models is carried out, in order to evaluate the feasibility to substitute the more complex and computationally heavier Weaire–Phelan foam structure with the simpler Kelvin foam representation. Negligible differences between the two models are exhibited at high porosities.

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Grahic Jump Location
Fig. 1

Lord Kelvin model of the foam

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Fig. 2

Weaire–Phelan model of the foam

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Fig. 3

Kelvin model generated domain

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Fig. 4

Weaire–Phelan model generated domain

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Fig. 5

Grid independence check for Kelvin model

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Fig. 6

Grid independence check for the Weaire–Phelan model

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Fig. 7

Volumetric Nusselt number versus Reynolds number, for ε = 0.85

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Fig. 8

Volumetric Nusselt number versus Reynolds number, for ε = 0.90

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Fig. 9

Volumetric Nusselt number versus Reynolds number, for ε = 0.95

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Fig. 10

(a) K foam grayscale streamlines and (b) W–P foam flow fields, for ε = 0.85 and Re ≈ 231

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Fig. 11

Darcy–Weisbach friction factor versus Reynolds number, for ε = 0.85, 0.90, and 0.95



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