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Research Papers: Porous Media

Numerical Modeling of Multidirectional Flow and Heat Transfer in Graphitic Foams

[+] Author and Article Information
S. A. Mohsen Karimian

Flow Simulation and Analysis Group, George Washington University, Washington, DC 20052karimian@gwu.edu

Anthony G. Straatman1

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 131(5), 052602 (Mar 18, 2009) (11 pages) doi:10.1115/1.3084122 History: Received December 07, 2007; Revised December 04, 2008; Published March 18, 2009

To investigate the feasibility of the use of foams with an interconnected spherical pore structure in heat transfer applications, models for heat transfer and pressure drop for this type of porous materials are developed. Numerical simulations are carried out for laminar multidirectional thermofluid flow in an idealized pore geometry of foams with a wide range of geometry parameters. Semiheuristic models for pressure drop and heat transfer are developed from the results of simulations. A simplified solid-body drag equation with an extended high inertia term is used to develop the hydraulic model. A heat transfer model with a nonzero asymptotic term for very low Reynolds numbers is also developed. To provide hydraulic and heat transfer models suitable for a wide range of porosity, only a general form of the length-scale as a function of pore structure is defined a priori, where the parameters of the function were determined as part of the modeling process. The proposed ideal models are compared to the available experimental results, and the source of differences between experimental results and the ideal models is recognized and then calibrated for real graphitic foam. The thermal model is used together with volume-averaged energy equations to calculate the thermal dispersion in graphitic foam. The results of the calculations show that the linear models for thermal dispersion available in literature are oversimplified for predicting thermal dispersion in this type of porous material.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 3

Normalized pressure drop ΠH versus cell-based Reynolds number ReH for the range of 0.75≤ε≤0.90

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Figure 4

A unit solid body of an idealized SVP foam with ε=0.80

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Figure 5

Variation in the cell passability versus porosity

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Figure 6

(a) Inertia coefficient and (b) the Darcy term for the range of 0.75≤ε≤0.90

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Figure 7

Normalized pressure drop ΠH versus cell-based Reynolds number ReH for real foams: experimental measurements compared to the calibrated model

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Figure 8

Variation in the cell-based Nusselt number NuH versus cell-based Reynolds number ReH for the range of 0.75≤ε≤0.90

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Figure 9

Plot of heat transfer model parameters, (a) X(ε) and (b) Y(ε), versus the normalized equivalent particle diameter DE

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Figure 10

Convective heat transfer model compared to the results of simulations for the case of Freon-12 and the range of porosity 0.75≤ε≤0.90

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Figure 11

Cell-based Nusselt number NuH versus cell-based Reynolds number ReH for real foams: experimental measurements compared to the calibrated model

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Figure 12

Normalized thermal dispersion D∥/αf versus pore-level Reynolds number ReH: (a) ε=0.75 and (b) ε=0.90

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Figure 1

(a) CAD images showing the unit-cube model (3); detailed dimensions of the unit-cube cell geometry. (b) Computational domain for an idealized SVP foam with ε=0.80.

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Figure 2

The results of the simulations for the case of ε=0.80, with Re=40: (a) two-dimensional streamlines in an X-Y plane. Colors of the markers indicate the local flow temperature. (b) Temperature field in a plane parallel to the flow direction.

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