As you can tell if you have been reading these recent posts I'm working on gas valve design. We are going to need good control of very low flow rates. Very low. On the order of 1E-3 to 1E-6 cc/second at STP.
A gas valve with a major orifice .200" in diameter will not give us much control. It goes from fully on to fully off (at the very low flow rates required) with a travel of .1 thousandth of an inch. What can be done to increase the travel and also increase the flow control?
Angle the sealing plate (assuming a soft seal such as an O-ring). This will give more control as the valve comes closer to full off. It will also make the control algorithms trickier as the gain goes up with increased opening. An orifice plate in the vale would be a help in limiting maximum flow (gain) and it would help increase control in the proportional range by adding a flow resistance to the valve resistance.
It also looks like we will need a multi stage regulator. 20 psia (5 psig) to 5 torr. 5 torr to 1E-3 torr. And the final control stage of 1E-3 torr to 1E-7 torr. Individual stages for the experimental reactor should be able to vary pressures over at least a 10 to 1 range (100 to 1 is better) to account for required gas flow variations depending on operating pressure. Once we understand operation better we can optimize for actual flow requirements.
It looks like piezo electric benders are not going to work since the travel is much too small. Something on the order of 1 to 2 micro meters. What we need is something better. A voice coil motor. That can easily give +/- 30 thousandths of an inch travel. It has a drawback in that it is magnetic in nature and thus can't be placed inside the the magnetically shielded grids. For small reactors a 2 ft length tube will add about 2 mS delay to the control system. Not good. Not insurmountable.
As the reactors increase in size delay will go up linearly with size. This is bad. Volume will go up as the cube of size. This is good. More volume reduces the need for fast control.
In fact the whole gas system may need a number of reservoirs to make the control problems tractable. It is pretty much a truism in business these days that the faster the manufacturing system can respond to demand the smaller the required inventory. So it is with any control system. We will adjust our inventories accordingly.
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I thought I'd throw a few things out for flow through small orifices, namely Knudsen Diffusion. Hopefully this will be helpful if it is an effect that hasn't been considered yet, but poses some sort of problem. Namely, when a pore is small enough the probability that the species of interest will exit through the pore is of importance. Think of the analogy of the marble in a child's whiffle ball that Dr. Bussard gave.
A few websites:
Micro-Scale Flow:
http://www.cfm.brown.edu/
people/beskok/muflow.html
Note the limits of Pressure, but also the Monte Carlo Analysis for low Knudsen numbers:
http://www.timedomaincvd.com/
CVD_Fundamentals/xprt/
Knudsen.html
Mass Transport in Small Pores:
http://www.mse.ufl.edu/~ssinn/
Backgrounds/theo02_diff.html
This is an interesting patent that provides an application of Knudsen Diffusion. It is possibly useful for understanding the effects of this phenomenon.
http://www.patentstorm.us/
patents/5057160-description.html
A note on continuity:
Most transport equations neglect the fact that a gas is composed of discrete atoms or molecules, but instead average effects over a volume. I believe that Wikipedia gives a good explanation of this. See the Continuum Hypothesis.
http://en.wikipedia.org/wiki/
Fluid_mechanics
November 17, 2007 7:50 AM
Brent,
I hadn't considered that at all. Thanks for the heads up!
For the final valve stage I'm considering a 100 um hole size so that may not be a problem.
Upstream the holes are smaller but the pressures are higher so the problems may still be limited.
In any case something to watch out for when we begin experimenting in the lab. The orifices I'm considering are replaceable so if one doesn't work out a different size can be installed.
BTW if you want to make permalinks here is how:
Here is how you make permalinks:
<a href="url">text to display</a>
replace url with:
http://powerandcontrol.blogspot.com/
leave the quote marks
replace text to display
with:
Power and Control
Power and Control
Micro-Scale Flow
Knudsen
Mass Transport in Small Pores
Patent
Wiki - Fluid Mechanics
This is my understanding of Knudsen Diffusion given no hands-on experience. Maybe it will be helpful at some time, but hopefully any supplier will have already considered this for the given conditions (if even necessary!!). This is quite complex.
It looks like with a pore of 100 microns Knudsen Diffusion may not need to be considered since the Knudsen number is less than 1 for hydrogen (around 0.27 at STP). Of course the boundary between the continuum domain the statistical mechanics domain is rapidly being approached since 0.27 is much closer to 1 than many other situations. In a pipe 1 millimeter in diameter, the Knudsen number is 2.761x10-4. Basically what I’m getting at is the Knudsen number is a rule of thumb, so even if it is less than 1 but very close to 1 there may be unacceptable error. At Knudsen numbers close or greater than 1 efflux through the pore becomes diffusion limited, and not so dependant on a pressure gradient. In the patent that I mentioned, gas actually moves from a region of lower pressure to higher pressure. It appears also from the mean free path calculator that I used, that the mean free path and the Knudsen number (see: Wiki- Knudsen Number) have a stronger dependence on temperature than pressure. So the Knudsen Diffusion effect does appear to change with heating or cooling of the gas more than pressurization. I suppose the effect of heating the gas could change depending on the configuration of your valve. When gases pass through valves and then depressurize most of the time they cool, other times they heat up. This effect may be realized by the Joule-Thompson coefficient, which may be derived from James Clerk Maxwell’s thermodynamic derivative relations, or found in a textbook in addition to many other places (You might want to check the assumptions, if any, if this is of interest). At this point, I am not aware of how hydrogen behaves, as each gas to my knowledge has a different J-T coefficient. But when I find out, I could post it.
Other sources:
J.B. Calvert’s site about Hydrogen that describes many of its properties. I found it to be useful to estimate the diameter of a diatomic hydrogen molecule, which I took to be the sum of the distance in-between the two hydrogen atoms and the radius of a hydrogen atom (see the hydrogen atom section). This may be visualized by drawing two circles along a line, then putting a dot at the center of each circle. The distance from the edge of one circle to the edge of the other is the distance I used. I assumed that the hydrogen atoms remained perfectly spherical in their covalent –bonded state.
Another useful source is the Hydrogen Properties Module on the DOE’s EERE site.
Another note:
Heating up the gas increases the probability that the gas molecules will hit the pores in a given period of time. Just think of the game of JezzBall and imagine the balls moving ever faster with increasing temperature. It would become increasingly difficult to wall-in the balls as they move more quickly. In this I’m considering the kinetic theory of gases.
Another note:
The ideal-gas assumption as you have made is valid at very low pressures since there is little molecule-to -molecule interaction. I’m not sure how it would work in the pores, but I would assume that at such low gas densities it would be an unlikely that two molecules would be in the pore at the same time. Don’t quote me on this since I have no idea what the residence time in the pores would be. The higher the residence time the more likely that another molecule will enter the pore. Will they interact? I’d imagine it would depend on the relative velocities of the two molecules. If they have the same velocity it is probable that the distance between them would remain constant and they would never see each other. The catalyst guys probably have a lot to say about gas diffusion through small pores.
Brent,
I think what will make this work is the fact that I am not predicting any definite flow at a given pressure and orifice size.
I'm using feedback (with judicious adjustments of intermediate volumes) to make it work.
My attitude at this point is that adjustments will be made. I am really glad for the info, because if something funny shows up in testing understanding of how to fix it should come faster.
I'm going to read the additional links. (thanks for htmlizing them!)
BTW have you looked at my bit on turbo pumps and pumping hydrogen?
Any suggestions?
It sounds like your model which changes the volume does assume the continuum hypothesis such that at any given scale there is some gas velocity and or flow at all points. If indeed that it what you are doing. I will need to read over your blog more carefully. What happened is that I saw small orifices mentioned, and I almost immediately recalled Knudsen Diffusion. It was a knee jerk approach almost since I recently heard it mentioned.
I'll have to get back to you about the turbo pumps. I know a little, namely about rating the performance and certain applications for different types of pumps.
Edit for reference:
Admittingly,I did something silly. I calculated the mean free path using STP rather than a very low pressure
at 273K. This makes the Knudsen numbers larger. I also thought a little bit more about Knudsen Diffusion and its effects on modeling the flow rate through an orifice.
This is a little brief so I will add to it.
Brent,
You are correct about the model I used.
At this time it will have to serve to get us into the ball park since the geometry of the final configuration is TBD.
The gas "pressure" in the final stage of the regulator will be in the range of 1E-3 to 1E-4 torr.
Here is what I am proposing for the electrical servo valves:
EValve-1: 5 torr to 1E-3 torr
EValve-2: 1E-3 torr to 1E-7 torr
EValve-1 is going to be a little twitchy since the orifice will be on the order of 10 micro meter.
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