Depressurisation time calculation 4

[IngGasP]

Hi!
I have an air cylinder that is compressed to 150 PSI with a volume of 7.3 cu in. I am trying to find out how long it will take for the 150PSI to vent down to atmospheric pressure through an opening that is 1.77mm in diameter.

Greetings

 

[zdas04]

There is not a closed form answer to this (classic) problem. Exhaust velocity (down to the end of critical flow) is sonic, but mass flow rate is a function of upstream pressure. From the critical pressure down do a number around 90% of critical pressure you have transsonic flow that is usually modeled as a straight line because it nearly is and there is not a reasonable model for it. After the end of transsonic flow the stream can be modeled as incompressible flow, but the flow rate is still a function of upstream pressure.

I calculate the mass flow rate (using critical flow at the critical pressure. Then I calculate the mass flow rate at 90% of critical using incompressible flow equations. Then I generate a straight line function between these two points for a transsonic function.

I always model this in time steps. I look at the conditions, calculate a mass flow rate using either sonic, transsonic, or incompressible models; deduct 1 second's flow; and recalculate the mass flow rate. Repeat until depressurized. I sucks, but I can usually get within 15% of actual field measurements.

David Simpson, PE
MuleShoe Engineering

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.

 

[Latexman]

IngGasP,

This web page is a good reference for you:

air-dispersion

Also, I would recommend looking over the entire website.

Good luck,
Latexman

 

[Latexman]

I should add, the reference above is not a perfect fit for your application. The reference is meant for high pressure applications where the majority of the release time is in choked flow. 150 psi is pretty much low pressure. However, the method will be applicable from 150 psi down to about 15 psi, then you will need methods covered very well by zdas04.

Good luck,
Latexman

 

[IngGasP]

Dear zdas04!

The steps described in your message seems to be very interesting, however,I've never work out this type of problem flow . Please could you work it out and send it to me in atteched form in order to show me how.

Thanks for your help.

 

[zdas04]

I must say you don't ask for much. I think I'll pass on your kind offer to allow me to do your job for you.

David Simpson, PE
MuleShoe Engineering

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.

 

[SNORGY]

150 psig air, 7.3 cubic inch volume, 1.77 mm hole.

My "guess" would be a very short time, like a matter of seconds.

I base that on nothing more than the time it takes to bleed the pressure down from the regulator to the face mask when you take off an SCBA.

How accurate does the answer need to be?

 

[IngGasP]

I tried to calculate it using the global energy balance equation as follows:

d H+ d Ek+ d Ep= q + (Vm * dP)
Assuming air as Ideal Gas and Isentropic transformation and No machine:
q = 0
(Vm * dP)=0
d Ep =0 because its effect which is neglected due to very small density of the air
We'll have:

d H+ d Ek= 0
By integrating
Delta H+ Delta Ek= Constant; Delta H= H out - H in cylinder; Delta Ek=1/2 (C^2 out - C^2 in cylinder)
Calulating the theoritical maximum velocity:
Now we have: H in + 1/2 C^2 in= H out + 1/2 C^2 out
C^2 in = 0 (Very small velocity compared to out one)
assuming all the H in is converted to velocity
We obtain:
H in = 1/2 C^2 out and H in = Cp T ; Cp= k*r/(k-1)
so; k*Vm*P/(k-1) = 1/2 C^2 and sound velocity Cs= k*Vm*P
For ideal gas in isentropic transformation we have:

C max = SQR(2*k*r* T inside cylinder/(k-1)); k=1.4 , T=20°C
We noticed for this case only the inside temperture affects the velocity
So we find: Cmax @ 20°C = 763.89 m/s

and for limit theoritical massic Flow, we have sonic flow @ the opening (small diameter)
Flow = Densiy * cross area of the opening *Cs @ opening

 

[LeoChem]

IgnGasP

I found a good reference for the problem you are trying to solve:

http://www.ijee.ie/articles/Vol13-2/ijee924.pdf

This is a article about a model for charging and discharging of vessels. They solve for the small vessel problem (your adiabatic case) and for the large vessel (isothermal expansion).

The matter with the article is that they give the solution but not de development of it. They begin defining a control volume for the case and solve the integral continuity equation substituting Fliegner's formula for choked flow and integrating.

Fliegner's:

http://www.potto.org/gasDynamics/node84.php

The article shows good results for the aplications of the models developed

Hope it could help