Compressible flow

[seanf]

Something I was looking into while back but still not really found an answer, so though I would try you lot.

I had been reading a beginners fluid mechanics book, which briefly introduced compressible flow with examples of nozzles, shock waves, Rayleigh and Fanno flow. It runs through the use of equations for basic calculations, but it doesn’t go very far with descriptions of what is physically happening with the fluid. Something I can’t seem to find with online searches either.

I think I’ve got my head round the movements and property changes to the fluid in sub/supersonic nozzles with isentropic flow. But when it looks at the effects of heat addition/removal and the effects of friction on sub/supersonic flows in a duct, I don’t seem to be able to picture/visualise what is happening that gives the strange changes in the fluid properties.

Below is a stab at what is happening in Rayleigh flow, maybe someone will be able to see where I’m going wrong.

Ideal gas with constant mass flow rate, no frictional effects, through constant cross-section duct with heat addition or removal.

Subsonic - heat added

I can see a dense gas expanding with the heat addition, the expansion pushing out giving this increase in velocity downstream, and with the relatively slow flow, acting somewhat against the upstream flow. So gives a drop in density and pressure across the heating point.

Subsonic – cooling

The flow energy is reduced with cooling and it slows (would there be a contraction?), this slower wall of gas has the upstream flow pushing on it increasing the pressure and density.

Supersonic – heat added

Having a guess here. The increase in energy is causing the molecules to become more excited and that increases the pressure, this wall of pressure is acting against the flow and slows it, but as the flow is moving very fast it doesn’t affect the upstream. It just puts a break on it as it passes the heating point. The flow backs-up downstream increasing the density and pressure further.

Supersonic - cooling

A guess. The reduction in the energy the molecules have after cooling, gives the reduction in pressure. This low pressure void that’s created allows the upstream to push through into the lower pressure downstream increasing the velocity. The molecules are moving off at a higher velocity giving the reduction in density.

Thanks.

[WAYNE3298]

The mass flow rate is determined by the upstream flow because that is the initial flow. If the mass flow rate doesn't change your analysis is flawed if I'm understanding what you are saying.

[seanf]

Hi WAYNE3298,

From what Ive read the mass flow rate does not change in Rayleigh flow, which seems to makes sense when looking at the property changes.

Thanks

[WAYNE3298]

What I'm driving at is under subsonic heat added for example you state "acting somewhat against the upstream flow". If you make that statement you need to define how the flow is impacted and state that the characteristics can change but not the mass flow rate. The statement in quotes is actually not necessary since you established that the mass flow rate was steady state. Not trying to be picky but when attempting to define your analyses you have to be very careful about the statements made.
The point is when dealing with "ideal gases" you have to start with an assumption such as constant flow, pressure or temperature and stick with it. Your final answer depends on it. In this case the problem is to define theoretically actions and reactions of an external force and since it is all theoretical and there are no calculations a calculation error cannot result.

[WAYNE3298]

I'm interested in seeing the input from others on this subject before going any farther. It could get interesting.

[seanf]

What I'm driving at is under subsonic heat added for example you state "acting somewhat against the upstream flow". If you make that statement you need to define how the flow is impacted and state that the characteristics can change but not the mass flow rate. The statement in quotes is actually not necessary since you established that the mass flow rate was steady state. Not trying to be picky but when attempting to define your analyses you have to be very careful about the statements made.
The point is when dealing with "ideal gases" you have to start with an assumption such as constant flow, pressure or temperature and stick with it. Your final answer depends on it. In this case the problem is to define theoretically actions and reactions of an external force and since it is all theoretical and there are no calculations a calculation error cannot result.

Thats a fair enough point. I guess I was trying to show my thought process a bit, and probably relying on what Ive seen Rayleigh flow defined as. Cheers WAYNE3298.

[WAYNE3298]

I'm hoping you will get a lot more input on this.

[WAYNE3298]

The lack of comments on this is probably because Rayleigh flow is determined by differential equations. The purpose of his work was I as I understand it for use in designing equipment. Your descriptions are not based on the higher math calculations so I expected you to get a lot of responses on that level. Supersonic flow takes you into another world when resolving flow expectations because it in essence throws the "ideal gas" out the window. That may sound contradictory to the gas laws but really isn't. Supersonic flow in heating for example creates a reaction that emulates friction loss and results in a reduction in mass flow even though the initial assumption is to ignore friction loss. Excitation of the molecules is the result of energy input and is an accurate superficial explanation of the process.
I hope that answers your question and encourages others to respond.

[seanf]

Should I be thinking more towards the idea of the heating or cooling at the duct wall as creating a sort of artaficial diffuser or nozzle?

[WAYNE3298]

I haven't dealt with this in years so remember that as I try to help. If I remember correctly the effect is more like a nozzle. An engineering forum would be best suited for your questions because odds are there are people on there that know this subject well. I barely remember the subject and can no longer remember enough calculus to solve any of the problems.
I'm the only one responding which tells me no one else hear can help you. You are searching for knowledge and deserve valid answers.

[Answer-Man]

Get yourself a copy of Crane's, Flow of Fluids Through Pipes and Valves, Technical Paper No 410 it should cover all you desire and more. You can get one from ebay or number of other online site's. The copy I have was printed in 1980. I have looked at older and newer the information is still the same

[seanf]

I haven't dealt with this in years so remember that as I try to help. If I remember correctly the effect is more like a nozzle. An engineering forum would be best suited for your questions because odds are there are people on there that know this subject well. I barely remember the subject and can no longer remember enough calculus to solve any of the problems.
I'm the only one responding which tells me no one else hear can help you. You are searching for knowledge and deserve valid answers.

The property changes (Velocity, Density, Pressure, Temp) for supersonic heating match that of a supersonic diffuser (reduction in cross section in flow direction). And with you mentioning it emulating friction losses its got me thinking maybe its just a reduction in the cross section of the main flow that gives the property changes.

Supersonic cooling matches a supersonic nozzle.
Subsonic heating matches a subsonic nozzle, but not the temp other than when Ma > 1/k^1/2.
Subsonic cooling matches a subsonic diffuser, but not the temp other than when Ma > 1/k^1/2.

It was worth posting, worth a try. I suspect it would be much easier to get an answer on the mathematical side than what Im asking about.

Thanks WAYNE3298.

[seanf]

Get yourself a copy of Crane's, Flow of Fluids Through Pipes and Valves, Technical Paper No 410 it should cover all you desire and more. You can get one from ebay or number of other online site's. The copy I have was printed in 1980. I have looked at older and newer the information is still the same

Ill have a look for it. Thanks Answer-Man.