Choked flow 1

[deancdn]

I was wondering if there's anyone out there who can help me to understand choked flow. I'm modelling a full-bore rupture of a pipeline and the gas (methane) is released to the atmosphere. I'm using a software called PHAST to perform the modelling and it's not giving me results because of an error - the software log shows - "Long Pipeline calculation ignoring Atmospheric expansion method" & "as this calculation always assumes Conversation of Energy". I'm not sure if this is related to choked flow or not. Anyone got any idea as to why it's not giving me results?

Any help would be greatly appreciated.

Thanks,

dean

 

[israelkk]

If the pressure in the pipe is more than approximately twice of the atmospheric pressure, the flow is choked.

 

[Montemayor]

Dean:

If you need help in understanding Choked Flow and the parameters controlling it, go to Milton Beychok's webpage at:

http://www.air-dispersion.com/feature2.html

israelkk is absolutely right. You've got Choked Flow on your hands since 99% of all compressible flow has a P2/P1 ratio greater than 2 - with the only exception possibly being the A/C industry.

I wouldn't apply or refer to any software regarding compressible flow unless I knew exactly what I'm dealing with and the algorithm involved.

 

[katmar]

Dean,

Just a note of clarification - A pressure ratio of over 2 across a long pipeline does not necessarily make for choked flow, so your analysis must take into account where along the pipeline the rupture occurs.

As an extreme case take the example of a pipe 10000 meters long, 25mm ID, with an air supply connected at one end at 10 bar gauge, and the other end open to atmosphere. Although the P1/P2 ratio here is 11:1 the air would flow out of the open end at a leisurely 33 m/s, which is certainly not choked or sonic. If you ruptured this pipe 9000 meters from the source the flowrate would increase to 35 m/s - still not a problem.

But if you rupture the pipe anywhere within approximately 130 meters from the source the air will hit sonic velocities and will be choked.

The well known P1/P2 ratio of 2 really applies to a pressure difference cross a plane, rather than down a pipe. If you punch a hole into the side of a pressure vessel, or you open a valve from the vessel directly to the atmosphere, then you have a ratio of 2 across a very short distance and you will get choked flow.

Seeing that you are talking of "Long Pipeline Calculations" I think you need to take this into account.

regards
Katmar

 

[katmar]

Dean,

Another note to clarify my previous clarification!

If the pressure in the pipeline at the point of rupture is over 1 bar gauge you will of course have a period of choked flow, even if the flow eventually decreases to the point of not being choked any more.

So you could have a transient period of choked flow before you reach steady state, and this may be what is "choking" your software.

Katmar

 

[zdas04]

If I can quibble. The magic ratio is not "2", it is:

P(down) < P(up)*[(2/(k+1))^(k/(k-1))]

so for air (k=1.4) the value works out to 0.528 - close enough to half for quick calculations. For natural gas (k=1.28) it is 0.549, still pretty close. Disregard the fact that the ratio of specific heats is gas specific and can vary and you'll make some bad choices.

Like I said, it is a quibble, but I don't want people to leave this thread thinking that the relationship is the integer "2".

Katmar's point about the pressures being across a plane is too important to be skipped over. His example of a very long 1-inch pipe barely spurting out the end is very real and I've had engineers do PSV calculations disregarding this important point.

David Simpson, PE
MuleShoe Engineering

http://www.muleshoe-eng.com

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

The harder I work, the luckier I seem

 

[davefitz]

as Katmar explained, for a long pipe in steady state, the flow wold be frictionally choked, and teh flow rate can be predicted using the "Fanno curves" for isenthalpic flow of a perfect gas. Please note the qualifier "steady state".

At the instant of the initial burst, the flow would be acoustically choked, , but would quickly degrade to frictionally choked . The overall pipeline dynamics would need to be roughly modeled to determine how fast the flow degraded from acoustically choked (zdas04) to frictionally choked(katmar).

 

[sailoday28]

For unsteady flow of a perfect gas with constant specific heat.AND aassuming zero initial flow and negligible friction
choking will occur at the exit in accordance with the following:

Pexit/Pinitial= [2/(gamma+1)] ^[(2gamma)/(gamma-1)]

With gamma =1.4
Pexit/Pinitial=(1/1.2)^7 = 3.58
This results from integration of Reimanns equation which is similar to that for water hammer-ONLY compressible flow is used. change in velocity =+ or - integral of dp/(rho*c)
Where p is pressure, rho the density and c, the sound velocity.


If the pipe pressure is fed by a source (a larger reservoir) at the same initial pressure, supersonic flow will temperarilly exist in portions of the pipe and exit.
Eventually steady state will be established and choking at pressure ratios of about 2:1 will be established (if friction is neglected and gamma=1.4)

 

[zdas04]

Saioday28,
I've just checked 5 references and none of them has that extra "2" in the exponent (which is the only difference between the equation you put up and the one I put up). I found one reference that had a square-root early in the derivation that vanished later for reasons that were more than a bit vague -- maybe that is where the "2" goes away?

Also a number less than 1.0 raised to a power greater than 1.0 will always be smaller than the number you started with. So 1/1.2= 0.83333 and if you raise that to the power of 7.0, you get 0.279, not 3.58 (if you raise it to 3.5 you get 0.528).

Please check your math, something is disconnected here.

DaveFitz,
That was a really productive clarification, I've never considered frictionally-choked flow as a viable category. I've dealt with the concept forever without having a label for it. Thanks.

David

 

[sailoday28]

zdas04 (Mechanical) You are correct. I was sloppy
Pexit/Pinitial =(1/1.2)^7 =0.279 for gamma=1.4
Please remember, this formulation is for a transient.

Integration of the frictionless compressible hammer equation will yield the following
U velocity A sound speed

Uinitial +2*Ainitial/(gamma-1)=Uexit+2*Aexit/(gamma-1)
for gamma=1 Uinitial+5Ainitial=Uexit +5Aexit.
At the exit, upon rupture Uexit=Aexit

Uinitial +5 Ainitial=6 Aexit
For Uinital =0 Aexit/Ainitail=5/6 or 1/1.2

For isentropic process
Pexit/Pinitail= (exit/Ainitail)^(2gamma/(gamma-1))
= (1/1.2)^7 = 0.279

 

[sailoday28]

Correction again --My last post is for gamma=1.4
I have a typo of gamma=1