Simple pressure/temp eq

[NZBen]

I'm trying to figure out the temperature of air when it expands out of an orifice I have air at -30deg C and 2.5MPa, what temperature will it be when it expands to atmosphere? I presume if I can run it past a turbine it will become even cooler. The only equations I have - also take volume into account - u know p1.v1/t1=p2.v2/t2, would appreciate if anyone could give me a suitable formula for figuring this out, cheers

 

[NZBen]

I've just done some more research and found that the temp drop is negligable if the airflow is not moving fast - so would I get more cold air out of a vortex tube or a turbine? How cold could i get it? With 2.5MPa and initial temp of -30C

 

[Latexman]

An orifice is non-ideal, messy math-wise, and requires empirical data to "fudge" it to reality, i.e. too much work for me to do for you.

If the air is initially at rest (large pipe or vessel) and it flows to an ideal isentropic nozzle (adiabatic and frictionless), I estimate the air at the nozzle exit is about -72 C and 1.26 MPa and at sonic velocity.

Good luck,
Latexman

 

[NZBen]

Thanks latex man, so does the air warm back up when it slows down? is it only at that temp at the nozzle tip? How far off would a thin section hole be? -60 degrees?

I just have this stream of high pressure low temp air in large volumes and want to get as much cooling capacity that I can from it - turbine or vortex tube be best? I am thinking a turbine as you would have a larger throughput of air as the vortex you lose half your air.

 

[Latexman]

In depends how it slows down. Think in terms of an energy balance. Will the air slow down AND the pressure rise or will the air slow down AND the pressure fall? Frictional effects? Shock waves? Expanding jets? Is work extracted? Adiabatic? Heat gain? These all come into play in determinimg what the temperature does.

Good luck,
Latexman