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# Vessel exhaust into vacuum

## Vessel exhaust into vacuum

(OP)
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 and valves.
Replies continue below

### RE: Vessel exhaust into vacuum

Assuming all tubing is uniform diameter, you will have choked flow that is sonic (Mach = 1.0) at the discharge.  The mass flow rate will vary in direct proportion to the absolute pressure in the vessel.  If you can convert all of your fittings into equivalent lengths of pipe, then you can model the flow as either isothermal or adiabatic.  In reality, it will probably be somewhere in between the 2 cases.  For general treatment of compressible flow in pipes, get a copy of the Crane 410 technical manual for Flow of Fluids Through Valves, Fittings, and Pipe.

If you have reduced diameter sections (orifices, valves, etc.) in the tubing, then the flow can become choked (sonic, Mach = 1.0) at places other than the discharge.  This is much more complex, and computer modeling is the way to go.  EASY5 software from Boeing should handle this easily.

### RE: Vessel exhaust into vacuum

(OP)
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 changes the pipe flow characteristics.  How do I relate the pressure and temperature of the gas in the vessel to the exhaust mass flow?

### RE: Vessel exhaust into vacuum

To bracket the problem, the 2 cases would be an adiabatic vessel or an isothermal vessel.  As before, reality will be somewhere in between.

T2 = T1(P2/P1)^((k-1)/k)

For the isothermal case:

T2 = T1, by definition

Use ideal gas law P*V=m*R*T to calculate mass of gas in vessel for both cases at any 1 time increment.

All of the above, as well as the pipe flow solution must be re-calculated at "small" time steps to solve the transient problem.

If you wish to get more detailed, then transient heat transfer must be considered, making the calculations an order of magnitude more difficult.

### RE: Vessel exhaust into vacuum

jparks,

I worked on a similar problem in a future life.  Never got the program to work right.  The problem is not trivial by any means.  The only way to capture how the pressure/temperature in the tank is changing is to perform a transient analysis as suggested by butelja.

You might want to look at a few references to see how others have done it:  (1) "Sizing an Emergency Venting System for a Cryogenic Dewar", Liu,C.K. et.al., Advances in Cryogenic Engineering, Volume 31, 1986, pp. 973 - 981, (2) "Blow-down analysis of Helium from a Cryogenic Dewar", Khan, H.J., et.al., Cryogenics, Vol. 32, 1992, pp. 388 - 398, (3) Introduction to Unsteady Thermofluid Mechanics, Moody, F.J., John Wiley & Sons, 1990, especially Chapters 2 and 6.

I hope this helps.  Good luck.

### RE: Vessel exhaust into vacuum

Sorry.

My previous post should have said "former" life.

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