How does stacking and creating an air gap affect fabric air permeability?

[Martin D]

I have a fabric from a windshirt testing at 40 CFM under ASTM D 737 (125 Pa). I am interested in understanding what would happen to air velocity if two layers were stacked and tested. Next, how would the results be affected by an air gap between the two layers?

 

[256bits]

40 CFM under ASTM D 737 (125 Pa).

Is that per square foot of fabric.

two layers were stacked

Easiest would be if the fabric threads line up. Then you just have thicker ( longer ) orifices.

 

[Martin D]

That's for a 5.93 in2 circular piece as per the standard test.

I see this basically as a filter in a pipe. We have pressure and and velocity measures. Can we determine from that some kind of coefficient for that material that can be used to evaluate what the flow would be past the second layer. So say you have a section of pire, one layer, an other section of pipe half an inch long and then a second layer of material, then free air.

What formulas would be involved to evaluate the pressure in the section of pipe between the two layers of fabric and the final velocity of of the air through the second layer?

 

[256bits]

Δ

That's for a 5.93 in2 circular piece as per the standard test.

I see this basically as a filter in a pipe. We have pressure and and velocity measures. Can we determine from that some kind of coefficient for that material that can be used to evaluate what the flow would be past the second layer. So say you have a section of pire, one layer, an other section of pipe half an inch long and then a second layer of material, then free air.

What formulas would be involved to evaluate the pressure in the section of pipe between the two layers of fabric and the final velocity of of the air through the second layer?

Here is how I am thinking about it.

A tube with 2 barriers, 1 and 2, sufficiently far enough apart forming a chamber and with an orifice in each barrier.
P, ρ, T, v(velocity) are the bulk conditions of the fluid on the pressurized side.
Similarly, we have conditions within the chamber, and on the atmospheric side.
Need Q.

Incompressible:
Case 1: Simplest case: well mixed chamber
v = v_c = v_atm for continuity.
Same for ρ and T.
P_c = ({P+P_atm)/2
Half of what it is with one barrier.
Difference in pressure determines the flow across the orifices.
Assume linear relationship of P and Q through an orifice. ( Is that true ? )
Thus, Q with 2 barriers is half that with one barrier.

Case 2: NOT well mixed.
Here the barriers are brought closer together, so that the velocity of the fluid leaving barrier 1 impacts upon the orifice in barrier 2.
Does it matter if the orifices are in line, or not.
As a result, is this Q less than, the same, or greater than that of case 1.
Perhaps try something Bernoulli, or more advanced if need be.

Compressible:
The density of the fluid should decrease as it moves from higher pressures to lower through the barriers.
We should use mass flow rate, mdot, since volumetric flow rates are unequal on either side of the orifice.
Let's see, high pressure, high density mdot expands through an orifice into the chamber. Same mdot at lower density and larger volume has to exit the chamber to the low pressure side, needing either a larger second orifice or a larger pressure within the chamber through a same size orifice. So the chamber should with same size orifices be above the average pressure between high and low sides.

Moving the barriers closer together, we meet the same situations of unmixed flow and orifice1 velocity impacting upon orifice 2.

For multiple orifices on each barrier, things should be similar to single orifices.

Considerations:
1. Does Q or mdot through an orifice follow a linear relationship with ΔP across the orifice.
2. How much change in density would there be for air at moderate pressures.
3. Using the incompressible flow analysis, how much error does that give to an actual measured real flow.
3. Is an orifice model sufficient or the correct model to use.

Sorry if I can't give a definitive answer for stacked filters, but at least you have something to think about and research.
Any errors in the modelling, please feel and obligated to correct as you wish.
DU

 

[JBA]

Using a 40 cfm flow rate value in a multiple orifice flow program for compressible flow I have, it would appear, for air, that a 49% effective flow area through each fabric disc is required to achieve that flow rate with the 125 Pascal inlet pressure; and, the interim pressure (as proposed above) will be 62.50 pascal between the two separated filters. (Note: In my program the result is actually in scfm at 65°F, but your inlet pressure is so low that there should be a negligible difference between the calculated scfm and cfm values).

Basically the program uses standard orifice flow equation and iterates the flow through the two orifices until the mass flow is equal for both orifices and then displays the resulting interim pressure(s) and the resulting flow rate in lb/hr and scfm (In your case the fabric area was used and the percent of effective flow area adjusted until the approximately 40.223 scfm flow rate resulted.)

I am curious to know how this compares to your actual test(s).