Thermodynamics and subsonic/supersonic exhaust

[cursorkeys]

This is possibly a question of semantics but I'm running through a complete engine on paper and just had a thought about the gas leaving the nozzle.
The velocity is 520m/s which is supersonic compared to the air around the exhaust but subsonic for the exhaust gas itself at that temperature (726K). So, would we consider the exhaust to be subsonic or supersonic?

I did a couple of hours of Googling last night and both answers are presented as the correct one in various places

[rythmnbls]

My understanding ( which could be completely wrong ) is if the nozzle pressure ratio is above the critical pressure ratio, then the flow is above mach 1

Regards

Steve.

[cursorkeys]

Hi Steve,

Thanks for the reply. The nozzle is definitely choked here, with the gas flow at Mach 1.55 (from the point of view of the surrounding air at STP).

Thinking about it a bit more I guess you need to consider it as two separate things. The flow up to the nozzle exit is subsonic by dint of the temperature and the flow out of the nozzle is supersonic as that gas is impinging on the ambient air so should be considered as referenced to it's lower speed of sound.

Jon

[finiteparts]

Hi Jon,

Hopefully I can help you understand this more clearly...

If the exhaust gas conditions at the throat are not sonic, then the nozzle will not choke and the flow will not be able to go sonic...remember that the flow must go through a local minimum in area to go sonic, then as it expands, it can do so supersonically. The flow has to go sonic before it can expand to supersonic velocities.

The ambient conditions are not how you define the sonic condition of the exhaust flow. They are included though, because the pressure ratio between the exhaust and ambient pressure determines the flow rate and thus the exhaust gas velocity. If the exhaust gas pressure is not sufficiently high enough to drive the flow to sonic at the throat, then there is no way you can have a supersonic flow.

Since the exhaust gases take time to cool, you can not just instantly change the relative gas conditions and use the ambient sonic speed to define it's Mach number. That would require the gas internal temperature to discontinuously drop to the ambient, which would mean a discontinuous jump in density. Your exhaust flow is subsonic. As it cools towards ambient conditions where you can use the ambient sonic velocity, it diffuses and slows down.

I hope that helps to clarify the idea...if not, let's discuss it some more.

~ Chris

[cursorkeys]

Hi Chris,

Thanks very much for the detailed reply. I'm still not certain I understand completely here, though although I think I understand why you don't compare it to the ambient gas now.

Would you mind checking I'm not still misunderstanding this?

1. This exhaust gas stream is subsonic. We can calculate that by using the equation for the speed of sound in an ideal gas (using the adiabatic constant and molecular weight for plain air as it's close enough) and seeing that it's still just higher than our nozzle exit gas velocity of 520m/s.

2. The nozzle is choked here ((Pstation5/ambient pressure) greater than the critical nozzle pressure ratio) but our exhaust is not yet supersonic as nozzle choking is a requirement for supersonic flow but not a definition. If we had a higher upstream pressure we could have a supersonic exhaust as increased pressure would drive more mass flow through the nozzle.

Is that correct?

[racket]

Hi Jon

The gases won't go supersonic in 2 unless theres a convergent/divergent CD nozzle , with just a plain convergent nozzle there'll be a static pressure higher than ambient at the nozzle exit , the engine will be producing reaction as well as pressure thrust .

Unless the jetpipe pressure is well above the critical pressure ratio its generally not worth fitting a CD nozzle as the losses associated with the CD nozzle will probably outweigh the slight benefit obtained from the increased velocity and its"reaction thrust", compared to the combined "reaction plus pressure thrust" from the plain nozzle .

Cheers
John

[finiteparts]

Hi Jon,

I have a question, because I am not sure if you are talking about two different cases.

How can the nozzle be choked and yet the exhaust flow is subsonic based on the local gas conditions? Are you not calculating the exhaust flow at the nozzle exit plane?

~Chris

[cursorkeys]

Thanks for the reply John, I've found my Zucrow so I'll go read the nozzle parts again very carefully.


Hi Chris, I've made a serious calculation error then? That is all supposed to be at the nozzle exit and for this one case.

I'll go back though everything and try to figure out what's incorrect. I was using Kenneth Weston's design flow from his book 'Energy Conversion'.

Many thanks again for your help,

Jon

[finiteparts]

Hi Jon,

I don't think you made a serious error...there is probably a few small things that add up.

If the nozzle chokes, the throat velocity has to be M=1 for the local gas conditions.

Have you watched these old movies that go over all kinds of fluid dynamics put out by the National Committee for Fluid Mechanics? This one is on compressible channel flow...

www.youtube.com/watch?v=JhlEkEk7igs&list=PL0EC6527BE871ABA3&index=8

I think they are pretty helpful...we had to watch them back when I was in a fluid dynamics class (and no, that was only back in the 1990's, not when they were made! Ha!).

Good luck!

Chris