The permeability of porous materials
Summary (3 min read)
INTRODUCTION
- Accurate and comprehensive information on the permeability characteristics of porous materials is essential to the proper design of areasuction installations on wings, flaps, inlets, and wind tunnels.
- It was found in the course of designing a wing using suction through a porous material that available calibration information was not sufficient for predicting permeability characteristics for the range of operating conditions (absolute pressure levels) anticipated.
- If a calibration test is made with the.
- In addition, previous investigations were found to include no information regarding choking of the flow following the occurrence of sonic velocity within the pores, bending the material, and, in the case of wire cloth, rolling the material.
NACA TN 3596
- The need for information on the aforementioned factors is emphasized by the following considerations.
- Consideration of the limitation on inflow velocity imposed by flow choking is important in some installations.
- The investigation reported herein was undertaken to determine the influence on the permeability of porous material of the aforementioned factors.
- The analysis includes comparison of the wire-cloth calibrations with a calibration for the same material bent to form the,leading edge of a wing model which was tested in the Langley 19-foot pressure tunnel.
- An occurrence of this sort shows that correlation based on anything but the fundamental variables, Mach number, and Reynolds number, should be used only with great caution.
APPARATUS
- The apparatus used in the tests with constant upstream pressure is shown schematically in figure 1 .
- This apparatus was the same as that used for constant upstream pressure except that an additional length of 2-inch pipe was attached upstream of the sample, and the downstream pipe and valve were moved upstream of the entire setup.
- Fine wire screens were placed 2 diameters upstream of the sample to help maintain flow uniformity.
- High and low pressure sources used were the Langley 19-foot pressure tunnel and the suction side of a centrifugal compressor.
- Downstream flow velocities were determined by applying onedimensional-flow relations between stations d and t (figs. 1 and 2) as follows: Continuity and isdthermal conditions were used to relate stations u and d.
MATERIAL
- Two flat samples of 30-by 250-mesh Dutch weave Monel metal wire cloth were calibrated.
- The wire diameters for these samples were O.OOSO inch for the wires that were 30 per inch and 0.00^0 inch for the wires that were 250 per inch.
- Results presented herein for the wire cloth are, therefore, considered to be typical.
- A 6-percent difference occurred between the flow velocities for the two samples at a given value of Ap.
- A 16 theoretical and experimental investigation of the permeability of various sintered metals is reported in reference k.
PROCEDURE
- In the calibrations made for this investigation, three methods of pressure variation were used.
- The first method employed a pressure p upstream of the sample of approximately 1 atmosphere and a variable suction pressure p-, downstream; the second method employed p u of approximately 2.-atmospheres with a variable p^; and the third method employed a variable p with p^ of 1 atmosphere.
- Before each calibration the sample was thoroughly cleaned with acetone.
- The pressures indicated by the manometers shown in figures 1 and 2 were recorded for various values of £p.
- For each value of £p, the flow velocities were obtained from the calibration equation (eq. l).
ACCURACY
- The repeatability of the'wire-cloth calibrations was determined by making several duplicate calibrations.
- The results indicated that the calibrations were repeatable within about 1 percent.
- No repeatability check was made for the sintered materials.
- The venturi calibration was based on the assumption of incompressible flow in the venturi.
- This assumption resulted in a maximum error of about 1 percent at the highest velocities obtained.
RESULTS AND DISCUSSION
- The basic permeability data are presented as plots of V against tip, inasmuch as the quantity desired for boundary-layer-suction applications is inflow velocity for a given pressure drop.
- Also, since the porous-material flow phenomena depend only on Mach number and Reynolds number, any dimensionless flow characteristic (for example, ^P/Pu or £gp/q u ) plotted as a function of M and R will completely describe the flow.
- For purposes of analysis, plots of this type are used herein.
- The quotient Ru/DMu was chosen because this quantity is constant for calibrations with constant p u and T u .
- Since the length which appears in the expression for R is significant only in comparisons between different materials, and since only a single wire cloth is considered, this length has been eliminated from the Reynolds number by using the quantity RU/D instead of R u .
Effect of Rolling the Material
- The effect of rolling on the permeability of metal filter cloth is shown in figure 9 as obtained from data taken in the Langley cascade aerodynamics laboratory.
- Rolling or hammering the material apparently has little effect on the form of the calibration curve but changes only the magnitude of the velocities.
- Figure 10 is a cross plot of the data of figure 9 -This plot and the other data examined indicate approximately linear variation of downstream velocity V^ with thickness, at least over the range of thickness presented.
- The scatter of some of the points of figure 10 is attributed to the fact that the thicknesses were determined with a precision no better than ±0.0001 inch.
- Differences between the permeabilities of two samples of the same thickness were mentioned previously in the section entitled "Material".
Effect of Bending the Material
- Figure 8 presents a comparison of V u and V^ curves for flat and curved specimens of the JO-by 250-mesh filter cloth.
- The V u curve for the 0.017-inch thickness is that of the present investigation.
- Inch, measured perpendicular to the leading edge.
- A comparison of these curves for V u indicates that the amount of tending present in the model leading edge caused no noticeable change in the form of the .curve, although more extreme bending might possibly produce a change.
SINTERED METAL
- Calibration curves are shown in figure 11 for two samples (designated A and B) of sintered bronze similar to that used in references 6, 11, and 12.
- The curves for samples A and B (fig. 11 ) show a variation with absolute pressure level similar to that for the wire-cloth, calibrations.
- In view of this difference of results each set of data, that is, for sample A, sample B, and the sample of reference 13, was examined for consistency within itself.
- At higher velocities, n becomes greater, and the effect of absolute pressure level should be more noticeable.
- Equation (3) indicates that for the Darcy flow, £p will vary linearly with V u .
CONCLUSIONS
- The permeability characteristics of representative samples of wire cloth and sintered metal have been investigated by means of flow calibration tests made over an independent range of Mach number and Reynolds number.
- The results and comparison with other data revealed the following information: 1. Since the permeability characteristics of a given porous material depend only on Mach number and Reynolds number, values of absolute pressure and temperature affect the usual calibration curve of upstream velocity as a function of pressure drop by changing the Mach number and Reynolds number of the flow.
- The results may be expected to be reasonably accurate up to conditions where appreciable choking occurs in the pores.
- For a given wire cloth, the spread between calibrations obtained by using, different absolute pressure levels can be greatly reduced by plotting upstream velocity against the ratio of pressure drop to upstream pressure.
- When the thickness of wire cloth is reduced by rolling or hammering, the velocity downstream of the material varies almost linearly with thickness for a given pressure drop, at least within the range of this study.
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References
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"The permeability of porous material..." refers background in this paper
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...For a non-shrinking material such as sand, the distribution function/(r) may be derived satisfactorily from the moisture characteristic, i.e. from the curve relating moisture content to the hydrostatic pressure a t th a t content (Childs 1940, 1942)....
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"The permeability of porous material..." refers background in this paper
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