Calculating flow conductance through an orifice.

[chrismb]

This is a pretty straight question; what is the equation of molecular flow conductance through a circular orifice?

Due to convenience and availability, I am aiming to use an NW40 right angle valve as a gate valve. It has a rated flow conductance of 45l/s, which is prob good enough for my 60l/s turbo system but will, obviously, be the limiting pumping factor. However, there are other restrictions in the system so if these are all sub 45l/s then I need not worry about this valve at all.

One other smally point - my pump (Varian V60) is rated 60l/s for N2 and 45 l/s for H2. Where such valves as I am looking to use here have a manufacturer's rating of 45l/s, is that in some way for all gases, as it is just a plain orifice, or does even a plain orifice also vary according to gas type?... I'm guessing I'll see the answer to that in the answer to my question!

I've had a look but not seen anything specific to this question. I could spend a lot more time looking, but if you chaps already know the answer then I would be grateful for you jotting down the answer or directing me accordingly. In fact, a secondary question might be even more interesting for 'archival' value; what is the flow conductance through various length and diameters of bellow pipe?

thanks,

Chris MB.

[chrismb]

The answer has presented itself here; http://cas.web.cern.ch/cas/Spain-2006/PDFs/Dylla-1.pdf , on slide 43.

The answer is [apparently] pi.v.d^3/12.L

Unfortunately, it turns out flow conductance works out like capacitors; 1/total_conductance = 1/conductance(1) + 1/conductance(2) + &c. So bottom line is that any bellow pipes pretty much scupper a system's max flow.

[Doug Coulter]

Ah, you beat me to it, I was having a lazy weekend. The fact is, fluid dynamics (or whatever you want to call it) doesn't roll out to a few simple equations, not hardly, though there are useful rules of thumb. There appear to be no equations that for example, handle the region between pure viscous flow and pure molecular flow, and the curves are kind of spliced in that region by hand. Of course, I always send people to Kurt Lesker tech notes which are now online (but the catalog is still better), or that paper JohnF put up here for things like this, or even John Strong. These mostly cover flow through a system and pump, not say, controlled flow through an orifice, but the ideas are all the same. And it can get real complex when the flow at one end of a piece of capillary tubing it viscous, but makes the transition to molecular somewhere inside the tubing, as in my gas inlet control system. At that point, it became at least for me, an empirical cut and try exercise.

I know Richard is using a piece of small bellows tubing to throttle his diff pump, and it's working for him, but for example, a short full diameter piece between my big turbo and the system seems to have little or no effect on the pumping speed I get -- tried it both ways. The true evil of bellows tubing is the increased surface area to have to outgas, and the likelihood that gas will get trapped in the "innies" on every bounce in there. But in my case, a 4" long piece of 6" id bellows (to get rid of vibration) had no effect other than the additional outgassing, which I solved by using some heater tape on it.

Orifices, capillary tubing, small valves all kind of stink for gas flow controls for various reasons. Fixed things like orifices and cap tubing tend to get junk in them. It's just plain really hard to make a valve tiny enough to get to the flow levels we generally want repeatably. So most pros use some kind of feedback system with a bang-bang valve, so the valve when open flows quick (and stays clean by allowing junk to pass through at that point) then slams shut, with duty cycle controlling the average flow. As I've reached "purity" in my system, that's what I'm doing now in essence. I let in some gas (too fast to easily control, and there's lag in the system as there's some volume between the valve and the rest), then pulse the pumping via a solenoid valve between the turbo and forepump in short pulses till I get to the place I want, then run completely sealed off, with the turbo still spinning, which seems to help with gas purity, as it pumps heavier gases better -- they all wind up in the foreline for removal on the next pulse. To make even this manageable, the inlet valve is a tiny needle, and the turbo is spun down to about 25% of full speed for the run. In my case (and as lesker warns) the stem of my needle valve broke, so the screw can only either push it in hard, or not -- it no longer "opens", but this turned out to be a good thing in my system, as there's just enough spring in the O ring seal to open it very slightly, making flow rates near what I want a lot easier to obtain! It's broke in a way that makes me not want to fix it! We got the nifty solenoid valve we are using around a manual valve in the foreline (we open the manual valve for pumpdowns and standby vacuum so we don't have to heat up the solenoid) from an old leak detector system, and it really is the final step that made things work well and allow hand's off fusor runs (I believe we're the first to achieve that).
For a flow through system, I think either a factory mass flow controller with feedback is going to be needed, or something homebrew (like an automotive fuel injector) also with feedback.

We tried for a long time to shut down pump flow (that big butterfly valve I made plus spinning the turbo slower) and control inlet flow, via a very small needle followed by capillary tubing, and basically to stay on the good pressure point was quite a balancing act needing constant hands-on operation. It was probably the single largest problem in getting good runs, and I feel lucky we have such a nice clean tight system I don't have to do that anymore and can just run "sealed off" now. Part of this almost has to be the fact that there's a lot of "inactive" volume in my tank to kind of buffer pressures a little.

And yes, conductances are like resistors in parallel or capacitors in series. Meaning that if you have a 60l/s pump with a 60l/s path to the system, you have ~30l/s on the far side, more or less.
Bent pipes are worse than straight ones as well, though different sources don't agree on how much (and may not be using the same basic level of vacuum, which would explain why).

Lesker of course will happily sell you an expensive software tool to model all this, and they claim it's pretty good, but I doubt it handles all the cases, like transition region flows, and things like situations where the Reynolds numbers come into play.