Flow through porous metal matrix

[tsurikov]

Hello all,

This is my first time posting to this forum... I'm wondering if any of you can help me with a nagging question...

I have a flow of gases through a porous metal matrix with 12 micron pore size. As I understand it, this thing consists of small metal spheres that were bonded together by heat. So now I switch to a matrix with 8 micron pore size. The flow RATE is kept the same (flow controller). Will the SPEED coming out of the matrix be different? I can't convince myself either way. On one hand, I imagine the smaller pore size results in a smaller open area, and by Q=UA, U should be higher. On the other hand, I imagine the tiny jets emerging from the matrix surface and being equilibrated by viscosity to the same speed (I calculate a Reynolds number of about 0.1). Neither argument seems very compelling.

If anyone has any insight, would you share it with me? Thanks,
--MT

 

[kenvlach]

Hi,
Are you working on a filtration project or what? Is the material bronze?
What flow rates are you using?

I think that perhaps because of fabrication variables (molding pressure, temperature, time, sintering aids) that you should first determine some basic properties of your material. If you determine the % open porosity in each material, then you can get some idea of flow rates within each material.
Example: Gas volumetric flow is A cc/min. Consider the flow through a 1 cc cube that is 20% free volume. Then the nominal linear flow through this cube will be
(A cc/min)/(0.20 cc/cm) = 5A cm/min

To make weight and buoyancy measurements to determine total porosity and free (open) porosity:
1) Measure the weight and gross volume of each matrix sample in air, then calculate the apparent (gross) densities.
2) With the density of the alloy used, calculate the total porosity and % density of each matrix. But some pores are sealed, only some are open.
3) To measure the open porosity, you need a a buoyancy balance (or modify an existing one that uses hanger style) so that you can weigh the sample while it is suspended in a beaker of liquid such as water. To make sure that the water enters the pores, add a wetting agent to the water or use water pressure while the sample is submerged in a deep container (then remove it inside a beaker) or to heat the water to lower its viscosity (but then need to re-equilibrate temperature).

The buoyancy force is the weight of displaced water (of total sample volume – open pore volume). So, the gross weight – weight in water = buoyancy. Then, the wt. of water in pores = wt. of water of gross sample volume – buoyancy.
So from wt. of water in the open pores, you get the open pore volume.

 

[rkinga2]

Hi. I'm also dabbling in flow thru porous media for the first time. I did some digging in the library & the best book that I found was The Flow of Homogeneous Fluids Through Porous Media by M. Muskat. It's a classic petroleum engineering text - written in 1937, the version I have was updated in 1982.

Porosity (% of the volume that is voids) is not what you are interested in.

What you need to know is the permeability (resistance to flow thru the material). It's defined in a unit called the Darcy & laminar flow is modeled by the Darcy equation.

Your case sounds very similar to flow thru packed sand. Course sand with large grains is much more permeable than fine sand with small grains.For example, from his table 10, going from coarse to fine:

Mesh Porosity Permeability
Size % (Darcys)
--------------------------------
30-40 40 345
40-45 40 66
50-60 40 44
60-70 40 31
70-78 40 26
80-100 40 10.5
100-120 40 9.9
120-140 40 9.2

The finest mesh size, 120-140 will pass thru a 120 mesh screen (.124 mm opening), but not thru a 140 mesh screen (.104 mm opening).

 

[tsurikov]

Thanks for the insight, kenvlach! The matrix is bronze, and I am using it in a laboratory combustion setup (the flame gases pass through the matrix). A typical flow rate through the matrix is 15 sl/min. I don't have the equipment to perform the porosity measurements you suggest, but think I could get all the relevant specifications from the manufacturer. But I wonder... is the material that relevant? My question is whether the flow SPEED through the matrix would change if the matrix pore size changed (again, Q is fixed by a flow controller). It seems to me this question would apply whether the material was bronze, glass, steel, or anything - I could have 1 mm and 3 mm glass beads, for example, and I'd have the same predicament...

--MT

 

[saxon]

tsurikov, It looks as if your looking at rate process within a transport problem. You may want to take a look at Poiseuille's Equation that deals with "flux" (such that flux rate is volume flow per unit cross sectional area).
The basic equation is as follows:

J=V/At=(A/8*pi*mu)*(P1-P2)/x=(A/8*pi*mu)*dP/x
LIMIT(laminar flow conditions only)

j=flux rate
V=volume
A=area
t=time
mu=viscosity
P1=pressure in
P2=pressure out
x=distance

Hope this helps.
saxon

 

[saxon]

tsurikov, It looks as if your looking at rate process within a transport problem. You may want to take a look at Poiseuille's Equation that deals with "flux" (such that flux rate is volume flow per unit cross sectional area).
The basic equation is as follows:

J=V/At=(A/8*pi*mu)*(P1-P2)/x=(A/8*pi*mu)*dP/x
LIMIT(laminar flow conditions only)

j=flux rate
V=volume
A=area
t=time
mu=viscosity
P1=pressure in
P2=pressure out
x=distance

Hope this helps.
saxon

 

[kenvlach]

Hi,
rkinga2 is correct that you want permeability, and to answer some of your questions, for the same total flow rate, the filter with the lower permeability requires a higher dP. And, the internal velocity of the gas within the less permeable material must be higher (due to either less passageway area or more convoluted path or both) to give the same total flow.
But, if you are studying effect of the matrix on the gas reaction, it is beneficial to measure all the material properties, because of surface effects such as stagnant layers and catalysis. There can be a big difference in internal geometry between sand and sintered metal (during sintering, the surface area decreases, pores become smaller and gross volume decreases), the sand is more like unsintered metal.
But as a practical matter, do you have a situation like the following?

CH4 + 2 O2 + 10 N2 = CO2 + 2 H2O + 10 N2

If so, no change in volume, flow rate in = flow rate out. I suggest measuring the permeability at room temperature using compressed air. This is a pretty simple task if you have both a pressure regulator and a flowmeter. You just measure the flow as a function of the inlet pressure P1. Let the outlet be ambient air.

From these data, you get the permeability directly, and from equation provided by saxon, you can determine the viscosity. You can also get Reynolds numbers.

But, now you want data for combustion gases at high temperature.
I think there are equations to calculate or estimate the decrease in viscosity and surface layer for air as function of temperature, but don’t know about converting to the reacting mixture (then again, I’m no combustion expert, so maybe wrong). So, figure out how to make the dP & V measurements for the combustion gases.

I don’t fully understand your set-up; is the combustion occurring both before and during passage through the filter (catalytic converter?)? Is the set-up like for a gas welder, with 2 supply hoses going to a mixing valve (with ‘flash-back’ preventer)? Maybe you can put a flowmeter on each supply hose, and put a stainless steel ‘tee’ and pressure gauge between the mixing valve and the filter. You also need the hot temperature to make volumetric gas correction.

 

[gunnarhole]

tsurikov,

I may be a little out of my depth here but it seems to me that the following must be true:

The relative proportion of the the filter volume that is metal and that is "void" is the same regardless of the size of the bronze powder used in fabricating the matrix. That is if we assume that the powder is sperical and is not substantially deformed during the sintering process. I guess you could confim this by measuring and comparing the densities of the two filters.

This implies that the open area of both filters is identical. The path cross sections of the smaller mesh filter will be smaller but there will be more of them.

This would seem to imply that the overall average velocity through the two filters would be the same even though the pressure drop through the finer mesh filter is greater.

Regards,

Gunnar