Modeling air temperature and pressure in an open system (decompressing tank)

[fflachowski]

I am trying to determine how to accurately model an open system which includes:

A tank: Volume = 1320 gallons
An exit pipe from tank: Diameter = 3 inches

The tank is compressed from atmospheric conditions to a final pressure of 100 psig. Then the tank is allowed to decompress by opening a valve at the exit (blow down test).

The air in the tank is initially at 400 F and 100 psig.

The temperature in the tank decreases as pressure decreases. How do I model the temperature change in the tank as well as pressure.

Keep in mind choke conditions at the pipe exit. Assume isentropic behavior and perfect insulation. Ignore frictional losses of the exit pipe and bends.

Hope you guys can help me with this. Thanks!


FYI: The problem I am having is that, we known, PV=mRT but the pressure changes with the temperature, but the mass also changes due to decompression (open system).

 

[emerhawk]

Joule–Thomson effect on Wikipedia along with the equations

 

[Mech_Engineer]

There are a couple of different ways to approach the problem, the more accurate of which utilize differential equations. You basically need to look at the mass flow rate out of the tank as a function of pressure, which in turn is a function of time. It isn't straightforward, but it can be done.

The basic form of the relationship would be something like this:
$\frac{d}{dt}m(t)=-m_{dot}$

Where m.dot is the flow rate out of the orifice, and dependent on p(t) and rho(t).

$m_{dot}(t)=C*A*\sqrt{2*\rho(t)*(P_{ambient}-P_{tank}(t))}$

 

[Mech_Engineer]

Oops also noticed this thread is almost a year old and was never followed-up on by the OP. Thanks emerhawk.

 

[fflachowski]

Yes it has been almost a year since I received a response. If other ideas/ methods keep rolling in, I appreciate them. Thank you.