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Transonic Flow without Wings

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zdas04

zdas04

Mechanical
Jun 25, 2002
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I've tried to calculate blowdown times for pipelines for 15 years with pretty miserable success. I can predict the end of choked flow with pretty good success, but the flow after the line reaches the critical pressure has always been way off.

I recently found an equation for the sub-critical flow, but found that the mass flow rate at Mach = 0.99999 was 66% of the mass flow rate at Mach=1.0. I've spent the day today digging through all the compressible flow material that I can find and every discussion I can find suggests the sub-critical flow equation (incompressible) probably eases into applicability between Mach = 0.6 and Mach = 0.8. In the missing region, the flow is "transonic" and is sort of sonic-ish and sort of incompressible-ish.

Everything I can find about transonic flow is focused on transonic behavior on an air foil. I don't have an air foil, just a line blowing into the atmosphere. Anyone have any suggestions? [Host hands over a stack of bar napkins and a grease pencil]

David
 
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I've been looking at straight nozzles and convergent/divergent nozzles all day, but the math is all sonic or super sonic. I read a really interesting piece about de Laval's supersonic nozzles on the 10 hp steam turbine that he showed in the 1893 Chicago Exposition, interesting but not helpful.

I know that in an ejector steam chamber there is a period of transonic flow, but I can't find anything that describes it. I have a program to test the design of an ejector and the last one I designed had a predicted power-nozzle exit velocity of 1.36 Mach and a throat entry velocity of 0.53 Mach, but the program documentation doesn't describe how they calculate the transition.

David
 
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David...it is the same as the jump from transitional to turbulent flow in hydraulics...can't necessarily predict the exact occurrence, but it does happen and quickly.

There are numerous academics who have modeled these things, but they don't seem to hold under varying conditions...too many variables, not enough equations!
 
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all,

a completely different method of looking at blowdown times; however, it requires some empirical data - at least initially when the blowdown starts. the method i have used in the past, with some success, is the exponential decay function (P=Po exp(-kt)). [as aside, i've not tried the logarythmic decay function, but something to consider ???].

i started using it some years ago after determining the leakage rate from regenerators/recupuerators on gas turbine units. this function/method was provided by the regenerator/recuperator mfg to determine the leakage rate; so, since the blowdown of pipelines is usually through a constant flow area (same for leakage in a regenerator), why not apply it to blowdown times. i've also used it on determining gas leakage on a section of pipeline and for using recip compressors to lower an isolated section of pipeline (i.e. reduce amount of gas blown to atmosphere before construction work is conducted).

the critical factor is determining the k constant. If Pressure vs time data is known coupled with pipeline volume & other parameters, i believe one can reasonable determine blowdown times.

unfortunately, i do not have any pressure vs time data available for others to analyze . . .

i may(?) still have the workbook i created some years ago (mid-90s); however, after two hard drive failures, not sure if i still have the workbook. i will look for the file and upload is there is interest . . .

something to ponder and think about. regardless, wish you good luck and i will be glad to assist.

Lastly, Thanks David for the invite. i am pleased!
-pmover (Doug - not Eng-Tips partner for Dave).
 
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VE1BILL,
You and Fermat?

KNAT,
I started to go over there, but I didn't want to start another cross-discipline food fight.

Ron,
It seems really similar, and I can't find many relationships that work in that transition either.

Pmover,
I need to think about your post when I haven't been working for 20 hours.

David
 
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What I'm normally looking at is a 8-inch or bigger line and a 2-inch blowdown valve. At high pressure, the Reynolds Numbers out in the system are usually really low (laminar, transition, slow turbulent at the fastest). At the critical pressure, the bulk flow is usually under Mach 0.2. Neither friction nor choking of the bulk stream has ever been a factor that had a measurable impact on the calculation. On one evolution I was blowing down 7 miles of 20-inch pipe through a 2-inch. The system was configured such that I could see line pressure at several points on the line in the automation system. The pressure traverse was never greater than 2 psi over the whole length.

David
 
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Ok, that bounds the problem and is what I originally started to write about, but figgered I'd make sure first (i.e. we're not talking about a ruptured pipe, open end, some hundreds of miles long).

I don't have my notes here, but have seen some stuff that modelled the transition flow, and was used to predict/model the decay of small rocket engine thrusters that are used for spacecraft attitude control (bang-bang thrusters). Will dig thru my boxes at home this weekend and see if anything elightening turns up. (Note, that is unlikely to happen, as the boxes are right next to the SO's Xmas supplies, and my shotshell reloading equipment...)
 
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Latexman,
BigInch pointed me to a technical paper on those equations in another thread I started to try to figure out a problem with a sub-critical flow equation. The equations referenced are all for choked flow.

David
 
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It doesn't matter as long as it is greater than:

P(atm)*(2/(k+1))^-(k/(k-1))

(call it 27 psia at sea level). Until I reach that pressure, I have choked flow and my arithemetic seems to work fine. My concern is between the critical pressure and some lower pressure where the compressible flow calculations become valid (call it Mach 0.6).

David
 
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It matters when you want to know what % is choked flow and what % is subcritical flow and if the % subcritical is negligible in the grand scheme of things.

Good luck,
Latexman
 
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Is it probable there are some heavies condensing out at high pressure, and re-gasifying during blowdown screwing up the calcs.? A little condensate generates a lot of vapor.

Good luck,
Latexman
 
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That certainly can happen, but the stuff I've dealt with is in the range of 85% CH4 and 15% CO2 and heavies aren't an issue in that stream. The systems I've been working with usually start around 100-150 psig and blow to zero. I've always been able to predict the end of choked flow pretty accurately. My predictions of the end of flow have never been close. On the 20-inch job I mentioned above, the time to the end of choked flow was something like 26 minutes (and I predicted 25 minutes). The time to zero was an additional 3 hours (and I predicted 20 minutes).

I've been working with an equation for subcritical flow when beta ratio < 25%. This is an incompressible flow equation that is only valid below Mach 0.6-0.8 (depending on the author). The area from Mach 0.6 to 1.0 is Transonic and all the arithmetic I can find for that region involves an airfoil of some sort. I don't have an airfoil. What I'm really trying to find is how to determine when the flow is a close enough approximation to incompressible to start using the incompressible equation.

David
 
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