Orifice Sizing

I have been mulling over the flow control problem for a small test reactor and I think I have at least a partial solution. First lets lay out the dimensions of the problem. Let us say that the reactor is a sphere with a diameter of .9 meter and a core diameter of .3 meter. The volume of a sphere is 4/3 π r³. A fair approximation for our work is 4 r³. So the volume of the outer sphere is 4 * (.45)³ = .36 m³. Minus the inner volume of 4 * (.15)³ = .014 m³ hardly worth worying about. So we won't. So we are at about .35E6 cm³ for volume.

Now how about pressure. We want to keep the pressure in that volume below 1E-7 torr. What is that in atmospheres? To help us along we have a handy pressure calculator. The answer is 1.3E-10 atmosphere. Times .35E6 cc. So it takes about 5E-5 cc at STP to fill the chamber.

Now it turns out that there is a dandy orifice company called Lenox Laser who appear to have just what we need. An orifice calculator. Let us set it up to fill our tank in one second. That should give us pressure control of better than 1% if we can get our valve to go from on to off in a millisecond. So we start with an inlet pressure of 1 torr to our control valve. The other side of the orifice will be at chamber pressure. 1E-7 torr. Since we are figuring this for Deuterium we will use He4 as a substitute for 2H2 (a Deuterium molecule). Use 273.15 Kelvin for the gas temperature. A flow rate of 5E-5 cc/sec. And we have an answer. 9.7 microns. Say 10 to make it even. A small orifice. Not the smallest (they go down to 1 micron).

From their catalog [pdf] you can scroll down to page 28 and find a nice 10 micron orifice that is drilled into a 1/4-28 set screw for under $100 bucks. Or if you get a disc from page 3 under $35.

Now of course we haven't taken into account any gas the turbo pumps are taking out or that is being burned up as the Deuteriums fuse (a minuscule amount) but at least we know what ball park we are in and at the lowest flow we are likely to want we can do the job. Now for that 1 torr regulator.

Update 1924z 19 Nov 007

We can look at some turbo pump estimates. Let us suppose we have 6 turbo pumps each capable of 3,000 l/s pumping speed. How much flow would be required? Let us look at the low end. That would be 18,000 l/sec or 1.8E6 cc/sec. If we start at 1E-7 torr that would be about .24E-3 cc/sec at STP. I have decided to have an intermediate regulator to get the gas pressure down to 1E-3 torr to the final regulator.

So what hole sizes do we need? Let us start with our original

Inlet to Outlet
1E-3 to 1E-7 torr 5.0E-5 cc/sec 40 microns

1E-3 to 1E-8 torr 2.4E-5 cc/sec   28 microns
1E-3 to 1E-7 torr 2.4E-4 cc/sec   87 microns
1E-3 to 1E-6 torr 2.4E-3 cc/sec 275 microns
1E-3 to 1E-5 torr 2.4E-2 cc/sec 870 microns