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Research Papers: Fundamental Issues and Canonical Flows

Numerical Modeling of Laminar Pulsating Flow in Porous Media

[+] Author and Article Information
S.-M. Kim1 n2

G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405kim698@purdue.edu

S. M. Ghiaasiaan1

G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405mghiaasiaan@gatech.edu

1

Corresponding author.

2

Present address at Boiling and Two-Phase Flow Laboratory, School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907-1288

J. Fluids Eng 131(4), 041203 (Mar 09, 2009) (9 pages) doi:10.1115/1.3089541 History: Received August 08, 2008; Revised January 05, 2009; Published March 09, 2009

The laminar pulsating flow through porous media was numerically studied. Two-dimensional flows in systems composed of a number of unit cells of generic porous structures were simulated using a computational fluid mechanics tool, with sinusoidal variations in flow with time as the boundary condition. The porous media were periodic arrays of square cylinders. Detailed numerical data for the porosity ranging from 0.64 to 0.84, with flow pulsation frequencies of 20–64 Hz were obtained. Based on these numerical data, the instantaneous as well as the cycle-average permeability and Forchheimer coefficients, to be used in the standard unsteady volume-averaged momentum conservation equation for flow in porous media, were derived. It was found that the cycle-average permeability coefficients were nearly the same as those for steady flow, but the cycle-average Forchheimer coefficients were significantly larger than those for steady flow and were sensitive to the flow oscillation frequency. Significant phase lags were observed between the volume-averaged velocity and the pressure waves. The phase difference between pressure and velocity waves, which is important for pulse tube cryocooling, depended strongly on porosity and the mean-flow Reynolds number.

Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Different porous structure geometries showing a unit cell of continuous porous structures

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Figure 2

Computational domain with boundary conditions

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Figure 3

Sample grid system for ε=0.84

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Figure 4

Steady-state streamline patterns for (a) ReL=0.11 and (b) ReL=560 in the case of ε=0.75

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Figure 5

Nondimensional pressure gradient along the flow direction with Reynolds number for the steady flow

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Figure 6

Nondimensional pressure gradient as a function of Reynolds number for steady flow

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Figure 7

The Forchheimer term as a function of Reynolds number for steady flow

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Figure 8

Time independence test for the base case of ε=0.75 with the grid size of 20×40 per unit cell

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Figure 9

Convergence check for ε=0.75 with 20×40 nodes per unit cell for (a) velocity and (b) pressure

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Figure 17

Comparison of the Forchheimer coefficients between the steady and pulsating flow for different porosities

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Figure 16

Comparison of the permeability coefficients between the steady and pulsating flow for different porosities

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Figure 15

Variation in the instantaneous Forchheimer coefficients for different porosities (f=40 Hz calculated from Rem,L=0.11 and 560)

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Figure 14

Variation in the instantaneous permeability coefficients for different porosities (f=40 Hz calculated from Rem,L=0.11)

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Figure 13

Phase shifts ΔθV, ΔθP, and ΔθVP in terms of porosities for pulsating high Reynolds number flow (Rem,L=560)

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Figure 12

Phase shifts ΔθV, ΔθP, and ΔθVP in terms of porosities for pulsating low Reynolds number flow (Rem,L=0.11)

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Figure 11

Variation in the instantaneous (a) velocity and (b) pressure waves along the flow direction for Rem,L=560 and ε=0.84

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Figure 10

Variation in the instantaneous (a) velocity and (b) pressure waves along the flow direction for Rem,L=0.11 and ε=0.7975

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