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Fundamental Issues and Canonical Flows

Inlet and Outlet Pressure-Drop Effects on the Determination of Permeability and Form Coefficient of a Porous Medium

[+] Author and Article Information
C. Naaktgeboren

Hydraulic Engineering, CFD Andritz Hydro Ltd., 6100 Trans Canada Hwy., Pointe-Claire, Québec,H9R 1B9, Canada

P. S. Krueger, J. L. Lage

Department of Mechanical Engineering, Bobby B. Lyle School of Engineering,  Southern Methodist University, Dallas, TX 75275-0337

J. Fluids Eng 134(5), 051209 (May 22, 2012) (8 pages) doi:10.1115/1.4006614 History: Revised April 13, 2011; Received November 09, 2011; Published May 18, 2012; Online May 22, 2012

The determination of permeability K and form coefficient C, defined by the Hazen-Dupuit-Darcy (HDD) equation of flow through a porous medium, requires the measurement of the total pressure drop caused by the porous medium (i.e., inlet, core, and outlet) per unit of porous medium length. The inlet and outlet pressure-drop contributions, however, are not related to the porous medium length. Hence, for situations in which these pressure drops are not negligible, e.g., for short or very permeable porous media core, the definition of K and C via the HDD equation becomes ambiguous. This aspect is investigated analytically and numerically using the flow through a restriction in circular pipe and parallel plates channels. Results show that inlet and outlet pressure-drop effects become increasingly important when the inlet and outlet fluid surface-fraction φ decreases and the Reynolds number Re increases for both laminar and turbulent flow regimes. A conservative estimate of the minimum porous medium length beyond which the core pressure drop predominates over the inlet and outlet pressure drop is obtained by considering a least restrictive porous medium core. Finally, modified K and C are proposed and predictive equations, accurate to within 2.5%, are obtained for both channel configurations with Re ranging from 10−2 to 102 and φ from 6% to 95%.

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Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Copy of the original sketch of Darcy’s experimental apparatus, found in Fig. 3, chart 24 of the Atlas (the figures of Darcy’s book were published in a separate Atlas, as an addendum to the book [6])

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Figure 2

(a) Schematic of parallel-plates or circular pipe channel obstructed by a thin planar restriction and (b) schematic of parallel-plates or circular pipe channel with the planar restriction replaced by a core section

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Figure 3

Streamlines for the parallel-plates case (only the top half of the channel is shown): (a) φ = 0.5, Reh  = 0.01; (b) φ = 0.5, Reh  = 100; (c) φ = 0.25, Reh  = 0.01; and (d) φ = 0.25, Reh  = 100

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Figure 4

Streamlines for the circular pipe case (only half of the channel is shown): (a) φ = 0.5, Reh  = 0.01; (b) φ = 0.5, Reh  = 100; (c) φ = 0.25, Reh  = 0.01; and (d) φ = 0.25, Reh  = 100

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Figure 5

Dimensionless static pressure variation along the parallel-plates channel centerline for φ = 0.5 and Reh  = 0.01. The planar restriction is located at X = 0.

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Figure 6

Dimensionless static pressure variation along the parallel-plates channel centerline for φ = 0.5 and Reh  = 100. The planar restriction is located at X = 0.

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Figure 7

Restriction pressure-drop ΔPr versus Reh for various φ values in the parallel-plates configuration. Symbols indicate numerical results and solid lines are the corresponding curve fits following Eq. 17. Dashed lines represent extension of the low Reh linear trend to higher Reh for φ = 0.5 and 0.69.

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Figure 8

Restriction pressure-drop ΔPr versus Reh for various φ values in the circular pipe configuration. Symbols indicate numerical results and experimental data from [15] while lines are curve fits of the corresponding numerical data following Eq. 17.

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Figure 9

Dimensionless viscous drag coefficient κ versus φ for the parallel-plates and circular pipe (axisymmetric) cases, and experimental data from [15]

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Figure 10

Dimensionless form drag coefficient χ versus φ for the parallel-plates and circular pipe (axisymmetric) cases, and experimental data from [15] for laminar and turbulent flow regimes

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Figure 11

Minimum dimensionless obstructive channel length Ec-min versus Reh for parallel plates and various φ values. Continuous lines represent Eq. 24, with ΔPr determined from Eq. 17.

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Figure 12

Minimum dimensionless obstructive channel length Ec-min versus Reh for the circular pipe and various φ values. Ec-min values, obtained using experimental results for ΔPr from [15], are also shown. Continuous lines represent Eq. 24 with ΔPr determined from Eq. 17.

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