Understanding Gas Flow through Tubes: Choking at the Speed of Sound

[RKT]

Hiya ! Got a problem about gas flow ...

I understand that gas flow speed through an orifice is choked to the local speed of sound once the upstream to downstream pressure ratio crosses a certain number. Any increase of pressure beyond that point does not speed up the flow anymore (though the mass flow rate will increase as density increases with pressure)

Now if instead of an orifice, if I talk about a tube/pipe, does this still apply ? That is to say, I discharge a gas from a high pressure scuba tank through a tube/pipe into the atmosphere. Would the flow speed still choke at speed of sound ? I guess what I am really asking is whether a tube can be considered as a bunch of orifices lined up together.

Regards
RT

 

[stewartcs]

Now if instead of an orifice, if I talk about a tube/pipe, does this still apply ? That is to say, I discharge a gas from a high pressure scuba tank through a tube/pipe into the atmosphere. Would the flow speed still choke at speed of sound ?

For a straight constant diameter pipe, yes.

http://en.wikipedia.org/wiki/Choked_flow


Caveat: A CD nozzel will accelerate the flow of a gas passing through it to a supersonic speed.

http://en.wikipedia.org/wiki/De_Laval_nozzle

 

[Q_Goest]

... I discharge a gas from a high pressure scuba tank through a tube/pipe into the atmosphere. Would the flow speed still choke at speed of sound ?

Generally, there can be a choked condition at a tube or pipe outlet. This is not uncommon in fact, it is fairly commonly found for example where a pressure relief valve is discharging to atmosphere through a tube or pipe.

Note that as pressure drops as air goes through a tube, the density also decreases and velocity increases. Generally, this phenomena is stable such that a shock wave is set up at the tube outlet.

 

[RKT]

Thanks guys ! Guess your answer is that a tube will also limit the velocity to SoS.

Yes, I am aware that a CD nozzle can get the flow supersonic. Problem is there is no CD nozzle involved here. I am seeing a case where simple HPA (high pressure air) is going supersonic out of a uniform section tube and I am at a loss to explain how its happening.

 

[stewartcs]

I am seeing a case where simple HPA (high pressure air) is going supersonic out of a uniform section tube and I am at a loss to explain how its happening.

What is your setup? How are you determining the velocity is supersonic?

 

[RKT]

Stewartcs,

I have'nt setup any apparatus. I am doing a restoration of a pneumatic gun. It operates by discharging HPA through a barrel. The pellet sits between the reservoir valve and the barrel. I was trying to clean the barrel using a soft pellet made of 'felt'. When I fired the cleaning pellet, it made a loud sonic crack (very distinctive, not the normal boom sound it makes). I inquired with many people as to whether there was a CD nozzle in it, and they said no chance - that's an airgun not a rocket. Yea, I know that but then why is it going supersonic ? Decided that maybe the SoS in the HPA was higher than air at atmospheric pressure. So I posted a thread here asking that - see thread below on SoS. Well, that theory got ruled out as well, so here I am. Totally lost ...

Regards
RT

 

[RKT]

BTW, I am not too sure about my initial assumption of a CD nozzle being present inside. As I understand it, such a nozzle produces a low pressure air flow (albeit at very high velocity) Is such a low pressure air column capable of pushing a pellet with such force as to make it exit at these speeds ? I don't know.

Regards
RT

 

[stewartcs]

When I fired the cleaning pellet, it made a loud sonic crack (very distinctive, not the normal boom sound it makes).

I believe two "sonic cracks" are required when the speed of sound is surpassed. Per the article below, the sound level may exceed 200 dB (really loud, probably will cause hearing damage).

http://en.wikipedia.org/wiki/Sonic_boom

I really doubt you're pellet is experiencing supersonic flight. It's probably the same effect (noise you hear) when popping a balloon.

I suppose you could test this by putting a silencer on the end of the barrel and see if the noise goes away. If it does go away, then it's not a sonic boom.

 

[stewartcs]

BTW, what is the pressure level?

 

[RKT]

The site was experiencing problems yesterday ? I could not view it ...

Anyway, the fill pressure is 3000 psi. About the speed, I am going to get myself a chronograph, but meanwhile, I'm pretty sure that's its supersonic. I did a little research, you see. It seems supersonic is not a big deal at all. Almost all the PCP airguns go supersonic when using very light pellets, and some do it even with standard weight pellets (they avoid it for accuracy concerns) !

Check this out for instance : www.pyramydair.com/blog/2005/03/why-cant-i-go-supersonic.html

This is just one of many articles that will leave you with no doubt that it does go supersonic. This article does not tell you HOW it goes supersonic. It tells you why you should not go supersonic. Think that says it all.

 

[stewartcs]

I found some interesting information that should answer your question...apparently this is not your typical choked gas flow problem...read the source document for the full benefit.

A gas gun differs from a conventional powder gun in that the energy required to accelerate the projectile is derived from a compressed gas reservoir rather than the combustion of a propellant charge. Quantitative studies of the gas gun (e.g. Seigel, 1965) have shown that reducing the molecular weight of the propelling gas can increase projectile muzzle velocity. This is because the gas must accelerate itself along with the projectile. In fact, a simple analysis (Seigel, 1965) will show that the maximum theoretical muzzle velocity is directly related to the speed of sound in the driving chamber,

u = [2 / (gamma - 1)]*a

Where,

u = muzzle velocity
gamma = specific heat ratio of the gas (1.4 for air in this case)
a = speed of sound in gas

Hence by reducing the molecular weight, the speed of sound increases and a higher muzzle velocity is achieved. Further increases in muzzle velocity can be realized by heating the driving gas.

Source: http://dspace.dsto.defence.gov.au/dspace/bitstream/1947/4048/1/DSTO-TR-1092 PR.pdf


This of course assumes that the tube you're using doesn't have some type of CD nozzle in it. If it does then that would explain it also.

Hope this helps...

 

[RKT]

Thanks a lot Stewartcs !

I had read abt light gas guns long ago and did'nt bother investigating it again as I remembered that they use hydrogen ... not 'air' that I use ...

This is a good find ! So for air, the theoretical max. vel becomes :
u = [2 / (gamma - 1)]*a
= [2 / (1.4 - 1)]*a
= 5*a

Thats five times the speed of sound at NTP ! Very interesting ... I wonder how they arrived at this formula though ... need to find out about this 'Seigel, 1965'. But yes, as you said, its not the typical choked flow case ... Conclusion : a tube cannot be treated as a bunch of orifices bundled together.

Regards
RT

 

[stewartcs]

...I wonder how they arrived at this formula though...

Start reading from page 9 of the paper below (page 21 of the pdf).

http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19890006594_1989006594.pdf

 

[RKT]

Man ! You have an answer for everything ! So give me your opinion on this :

That formula is basically max. wavefront speed for free expansion of an ideal gas, if I am not mistaken. Does it take into account the heat generated by compression ? The term 'a' depends on temperature ... so if I compress the gas quickly and immediately expand it, i'll get higher speed, but if I allow the heat generated by compression to dissipate into the surroundings before expanding the gas, then the max. speed will be lower due to lower SoS ... yes ? The formula will work for the second case too, won't it ?

Of course, its theoretical max. speed and there's no way you can approach that value, I understand that.

Regards
RT

 

[stewartcs]

If I understand your question correctly, the temperature increase is accounted for when finding the speed of sound in whatever gas you are using to propel your projectile.

So, looking at the first link I sent you, equation 1 gives you the max theoretical velocity. That velocity is based in part on the speed of sound (a0). The compression ratio is then used to account for the temperature increase due to compression of the gas (see equation 5 of the same link).

Based on that it seems the answer to your question is yes, it takes into account the heat generated by compression.

so if I compress the gas quickly and immediately expand it, i'll get higher speed, but if I allow the heat generated by compression to dissipate into the surroundings before expanding the gas, then the max. speed will be lower due to lower SoS ... yes ?

Yes.


BTW, this is not free expansion because, 1, the gas is not expanding into a vacuum, and 2, the gas is doing work on an object (those are related I know).

Hope that helps.

 

[RKT]

Thanks Stewartcs.

In my case, the heat generated by compression is lost before the gas is expanded. The formula takes the heat generated into account. That only means a higher value of sound speed (a0). So if I use the normal value of a0 (a0 at normal temp.) then the formula should give me the theoretical maximum speed of gas when the heat due to compression is allowed to dissipate away ... or so I think. Anyway that's what I was looking for.

Funny thing though ... is that the formula doesn't contain any pressure term. I had imagined that if this is different from the normal choking phenomenon, there should be a pressure dependency.

Regards
RT