A NASA colleague recently showed me that the differential equation for pressure and temperature versus time for gas venting from a vessel can sometimes be separated and integrated to closed form solutions for pressure or temperature versus time. I haven't worked through all the details yet, but...
Vidaman -
You'll find this relationship derived in most any text which treats flow in constant area ducts, or you can see it in Isentropic Flow Tables, the most famous of which is "Gas Tables", by J.H. Keenan and J. Kaye, published in 1948. The text I use is "Introduction to Gas...
Correct, no heat is transferred. You squirt out a bit of gas over a small time step. Then the remaining gas in the vessel expands to replace the lost gas, and the temperature and pressure drop according to the adiabatic expansion laws. Repeat 50 or 100 (or whatever makes you happy) times, and...
In my last post of Oct 7, I seem to have baffled myself with big words (or maybe b.s.). In response to a question from TD2K, I said that my assumption was an "isenthalpic" expansion. Later it occurred to me that I meant "adiabatic" expansion, not "isenthalpic."...
Thanks for the input. Hands-on experience can't be beat sometimes. Just a few comments:
1. I posted my equations in an earlier post, same day. Have a look and see if you can find anything wrong. Send me an address and I'll email you my derivation.
2. Yes, I did the pressure and temperature...
As promised, I put your parameters (600 psia, .228 in dia opening, 206 cu in vessel) in my equations, and here's what I got:
1. My formulation doesn't account for unchoked flow, so I'm only good to down around 28 psia in the vessel.
2. My calculations go below 28 psia in the vessel in about 1.7...
Don't forget about the temperature of the gas remaining in the vessel. As gas escapes through the orifice the remaining gas is expanding, and its temperature will be dropping, which also affects the exit flow conditions. Equations which work for me in the typical spreadsheet, small time-step...
Agree with all you said, butejla. The pipe flow is the easier part of the problem, assuming it stays subsonic until it exits (which it may not). I'm struggling more with the thermodynamics of the gas in the vessel. As the gas escapes the pressure and temperature in the vessel drop, which...
I need to calculate flow rate and gas thermodynamics of vessels onboard the International Space Station venting overboard into the space vacuum. The vessels contain a few liters or less of air (sometimes other gases) at a starting pressure of 40 psi or less, and vent through a system of ducts...
