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Research Papers: Porous Media

Numerical Results for the Effective Flow and Thermal Properties of Idealized Graphite Foam

[+] Author and Article Information
Christopher T. DeGroot1

Anthony G. Straatman

Department of Mechanical and Materials Engineering,  The University of Western Ontario, London, ON, N6A 5B9, Canadaastraatman@eng.uwo.ca

1

Corresponding author.

J. Heat Transfer 134(4), 042603 (Feb 13, 2012) (12 pages) doi:10.1115/1.4005207 History: Received June 17, 2011; Revised September 26, 2011; Accepted September 27, 2011; Published February 13, 2012; Online February 13, 2012

To simulate the heat transfer performance of devices incorporating high-conductivity porous materials, it is necessary to determine the relevant effective properties to close the volume-averaged momentum and energy equations. In this work, we determine these effective properties by conducting direct simulations in an idealized spherical void phase geometry and use the results to establish closure relations to be employed in a volume-averaged framework. To close the volume-averaged momentum equation, we determine the permeability as defined by Darcy’s law as well as a non-Darcy term, which characterizes the departure from Darcy’s law at higher Reynolds numbers. Results indicate that the non-Darcy term is nonlinearly related to Reynolds number, not only confirming previous evidence regarding such behavior in the weak inertia flow regime, but demonstrating that this is generally true at higher Reynolds numbers as well. The volume-averaged energy equation in the fluid phase is closed by the thermal dispersion conductivity tensor, the convecting velocity, and the interfacial Nusselt number. Overall, it has been found that many existing correlations for the effective thermal properties of graphite foams are oversimplified. In particular, it has been found that the dispersion conductivity is not well characterized using the Péclet number alone, rather the Reynolds and Prandtl numbers must be considered as separate influences. Additionally, the convecting velocity modification, which is not typically considered, was found to be significant, while the interfacial Nusselt number was found to exhibit a nonzero asymptote at low Péclet numbers. Finally, simulations using the closed volume-averaged equations reveal significant differences in heat transfer when employing the present dispersion model in comparison to a simpler dispersion model commonly used for metallic foams, particularly at high Péclet numbers and for thicker foam blocks.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 2

An illustration of a periodic unit-cell for an array of cylinders with the relevant geometric parameters indicated

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Figure 3

Schematic diagram of the computational domain for direct simulation of the pore-level fields, in this case for a graphite foam with ɛ = 0.85

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Figure 4

A plot of the tetrahedral grids used for the (a) ɛ = 0.8 and (b) ɛ = 0.9 cases generated with a grid size at the wall of δw  = 0.0118H (where H is the unit-cube size), a growth rate of 8% per row, and a maximum grid size of δmax  = 3δw

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Figure 13

Contour plots of the dimensionless fluid temperature, θf , along the center plane defined by y*=12Ld for Red  = 100 using (a) the dispersion model of Calmidi and Mahajan [15] and (b) the present dispersion model

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Figure 1

Electron micrograph images of a graphite foam specimen (a) and (b) in comparison to a CAD model of the idealized pore geometry proposed by Ref. [14] (c) and (d)

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Figure 10

Plot of the interfacial Nusselt number as a function of the Péclet number

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Figure 11

Schematic diagram of the domain under consideration for the volume-averaged simulations

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Figure 12

Contour plots of the dimensionless fluid temperature, θf , along the center plane defined by y*=12Ld for Red  = 50 using (a) the dispersion model of Calmidi and Mahajan [15] and (b) the present dispersion model

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Figure 5

Plot of the non-Darcy drag term, Fxx , as a function of the Reynolds number obtained from the solution of the momentum closure problem in comparison to results obtained directly from the computed pressure field

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Figure 6

A plot of the dimensionless axial thermal dispersion conductivity as a function of Reda1Pra2(1-ɛ)a3, where the coefficients (a1 ,a2 ,a3 ) are obtained using a least-squares fit of the data

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Figure 7

A plot of the dimensionless transverse thermal dispersion conductivity as a function of Ped

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Figure 8

Plots of the dimensionless transverse thermal dispersion conductivity as a function of the dimensionless groups Ped1.78(1-ɛ)1.37 and Red1.21Pr0.776(1-ɛ)0.786, obtained by least-squares fits for the regimes (a) Ped  < 10 and (b) Red1.21Pr0.776(1-ɛ)0.786>30, respectively

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Figure 9

A plot of the dimensionless convecting velocity modification in the flow direction as a function of the Péclet number

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