Self-Consistent Open-Celled Metal Foam Model for Thermal Applications

[+] Author and Article Information
Eric N. Schmierer

Applied Engineering Technology, MS J580, Los Alamos National Laboratory, Los Alamos, NM 87545schmierer@lanl.gov

Arsalan Razani

Mechanical Engineering Department, The University of New Mexico, Albuquerque, NM 87131razani@unm.edu

J. Heat Transfer 128(11), 1194-1203 (Apr 11, 2006) (10 pages) doi:10.1115/1.2352787 History: Received May 20, 2005; Revised April 11, 2006

Many engineering applications require thermal cycling of granular materials. Since these materials generally have poor effective thermal conductivity various techniques have been proposed to improve bed thermal transport. These include insertion of metal foam with the granular material residing in the interstitial space. The use of metal foam introduces a parasitic thermal capacitance, disrupts packing, and reduces the amount of active material. In order to optimize the combined high porosity metal foam-granular material matrix and study local thermal nonequilibrium, multiple energy equations are required. The interfacial conductance coefficients, specific interface area, and the effective thermal conductivities of the individual components, which are required for a multiple energy equation analysis, are functions of the foam geometry. An ideal three-dimensional geometric model of open-celled Duocell® foam is proposed. Computed tomography is used to acquire foam cell and ligament diameter distribution, ligament shape, and specific surface area for a range of foam parameters to address various shortcomings in the literature. These data are used to evaluate the geometric self-consistency of the proposed geometric model with respect to the intensive and extensive geometry parameters. Experimental thermal conductivity data for the same foam samples are acquired and are used to validate finite element analysis results of the proposed geometric model. A simple relation between density and thermal conductivity ratio is derived using the results. The foam samples tested exhibit a higher dependence on relative density and less dependence on interstitial fluid than data in the literature. The proposed metal foam geometric model is shown to be self-consistent with respect to both its geometric and thermal properties.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Photo of real metal foam (see Ref. 27)

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Figure 2

One cell of the proposed TetraK Model with pertinent geometric parameters indicated

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Figure 3

Image progression to extract ligament cross-sectional information; (a) cropped gray-scale image, (b) binary image with Asolid∕Atotal matched to relative density, and (c) large perimeter objects filtered out

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Figure 4

FEA model of tetrakaidecahedronal (1∕16 model) lattice (ρ=0.07, β=2). Mesh was refined at heat flux boundaries and at the dissimilar material interfaces.

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Figure 5

Cross section of the cylindrical test cell used to measure thermal conductivity showing thermocouple location and numbering

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Figure 6

Ligament hydraulic diameter histograms at 1×

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Figure 7

Mean ligament diameter at 1.6× magnification compared to data in literature (symbol shape indicates PPI and symbol shading indicates source)

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Figure 8

Average Heywood circularity factor (Eq. 16) for each sample at 1.6× (above) and for various ideal geometric shapes (below)

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Figure 9

Comparison of mean cell diameter results to data in the literature

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Figure 10

Sv comparison versus mode of measured cell diameter (8–8.7% density)

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Figure 11

All keff data for Duocell® foam in literature (present data for vacuum)

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Figure 12

Comparison of TetraK model numerical keff and present experimental data for vacuum. Present experimental data has linear least squares curve fit and experimental error from Eq. 19.




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