Direct Simulation of Transport in Open-Cell Metal Foam

[+] Author and Article Information
Shankar Krishnan, Jayathi Y. Murthy, Suresh V. Garimella

NSF Cooling Technologies Research Center, School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907

J. Heat Transfer 128(8), 793-799 (Jan 09, 2006) (7 pages) doi:10.1115/1.2227038 History: Received July 06, 2005; Revised January 09, 2006

Flows in porous media may be modeled using two major classes of approaches: (a) a macroscopic approach, where volume-averaged semiempirical equations are used to describe flow characteristics, and (b) a microscopic approach, where small-scale flow details are simulated by considering the specific geometry of the porous medium. In the first approach, small-scale details are ignored and the information so lost is represented in the governing equations using an engineering model. In the second, the intricate geometry of the porous structures is accounted for and the transport through these structures computed. The latter approach is computationally expensive if the entire physical domain were to be simulated. Computational time can be reduced by exploiting periodicity when it exists. In the present work we carry out a direct simulation of the transport in an open-cell metal foam using a periodic unit cell. The foam geometry is created by assuming the pore to be spherical. The spheres are located at the vertices and at the center of the unit cell. The periodic foam geometry is obtained by subtracting the unit cell cube from the spheres. Fluid and heat flow are computed in the periodic unit cell. Our objective in the present study is to obtain the effective thermal conductivity, pressure drop, and local heat transfer coefficient from a consistent direct simulation of the open-cell foam structure. The computed values compare well with the existing experimental measurements and semiempirical models for porosities greater than 94%. The results and the merits of the present approach are discussed.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Schematic of the body-centered-cubic model

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Figure 2

Schematic diagram of (a) the geometry creation and (b) a periodic unit cell

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Figure 3

Sample images of (a) the Representative Elementary Volume (REV) and (b) the computational mesh of the solid-foam (fluid zone grid points are omitted for clarity)

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Figure 4

Schematic illustration of a periodic domain

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Figure 5

Effective thermal conductivity as a function of porosity for aluminum foam saturated with (a) air and (b) water. The thermal conductivity values used for aluminum, air, and water are 218, 0.0265, and 0.613W∕mK, respectively (5)

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Figure 6

Predicted results for (a) dimensionless velocity field, and (b) dimensionless velocity field at different locations (x∕L=−0.4, 0.0, 0.4, and y∕L=0)

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Figure 7

Predicted results for (a) dimensionless temperature field and (b) dimensionless temperature maps at different locations (x∕L=−0.4, 0 and 0.4, and y∕L=0)

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Figure 8

Predicted normalized permeability of the foam as a function of the porosity of the foam. Also plotted are experimental data points from Bhattacharya (14).

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Figure 9

Predicted friction factor as a function of Reynolds number based on the flow penetration length (√K). Also plotted are experimental correlations from Paek (26) and Vafai and Tien (29). Symbols are defined in Fig. 1.

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Figure 10

Predicted Nusselt number based on effective diameter of the pore as a function of the square root of the Peclet number [RedPr∕(1−ε)]. Also plotted is the correlation from Calmidi and Mahajan (30).



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