How to design an overexpanded nozzle

[T C]

TL;DR Summary

If there is a steady source of compressed air/gas at 5 barA pressure, that will be released through an overexpanding convergent-divergent nozzle, I want to know how to design the nozzle and what can be necessary parameters. And what would be the minimum pressure at the exit?

Suppose there is a steady source of compressed air/gas at 5 barA pressure, and that will be released through an overexpanded convergent-divergent nozzle. I want to know how to design such a nozzle and what would be the parameters for that. And also what would be the minimum pressure at the exit?

 

[berkeman]

TL;DR Summary: If there is a steady source of compressed air/gas at 5 barA pressure, that will be released through an overexpanding convergent-divergent nozzle, I want to know how to design the nozzle and what can be necessary parameters. And what would be the minimum pressure at the exit?

Suppose there is a steady source of compressed air/gas at 5 barA pressure, and that will be released through an overexpanded convergent-divergent nozzle. I want to know how to design such a nozzle and what would be the parameters for that. And also what would be the minimum pressure at the exit?

What research have you done so far?

https://www.grc.nasa.gov/www/k-12/airplane/nozzled.html

 

[T C]

So far, what I have found is convergent-divergent nozzles can generate supersonic velocity. But, no idea about design parameters of an overexpanded nozzle.

 

[berkeman]

So far, what I have found is convergent-divergent nozzles can generate supersonic velocity. But, no idea about design parameters of an overexpanded nozzle.

Supersonic velocity of what? Links please?

 

[jack action]

And also what would be the minimum pressure at the exit?

The pressure at the exit is always a constraint: It usually is the atmospheric pressure.

If the exit pressure is very low compared to the input pressure, then a shock wave will occur either in the divergent part of the nozzle or at the exit.

 

[T C]

The pressure at the exit is always a constraint: It usually is the atmospheric pressure.

It's the release pressure, but the pressure of the flow coming out of the nozzle can be less than that. Kindly go through this thread.

Supersonic velocity of what?

Supersonic velocity of the fluid coming out of the nozzle.

 

[T C]

Now, I want to simplify the matter more. As I have already mentioned, that the pressure of the air/gaseous fluid is 5 barA. Now, let's consider that the flow rate 3 cubic meter per minute. Kindly tell the just the radius at the inlet, at the throat and also at the exit of a perfectly designed De Laval nozzle made for such flow rate and pressure level.

 

[boneh3ad]

Now, I want to simplify the matter more. As I have already mentioned, that the pressure of the air/gaseous fluid is 5 barA. Now, let's consider that the flow rate 3 cubic meter per minute. Kindly tell the just the radius at the inlet, at the throat and also at the exit of a perfectly designed De Laval nozzle made for such flow rate and pressure level.

This phrase has no meaning. There is no such thing as a perfectly designed anything. There are only designs that meets all the appropriate design specifications.

For years you've come on this site asking questions about compressible flow and supersonic nozzles and asked over and over for people to do the work for you rather than making any meaningful effort to learn or do it yourself. And the nature of your questions here suggest you still don't care to actually learn it for yourself.

Please go obtain a basic text in gas dynamics (by whatever appropriate means for you). Find an online course and take it. Do something.

 

[T C]

By "perfectly designed nozzle", I want to mean that the static pressure of the flow at the exit would be the same as the backpressure. In case of overexpanded nozzles, the static pressure of the exit flow can be much lower than the backpressure. And, before posting this thread, I have searched net regarding how to design a De Laval nozzle, but haven't got much information.
And, as far as I can understand, this forum is for discussing matters those can't be understood easily.

 

[boneh3ad]

The forum does expect a certain degree of effort on the part of the people asking the questions, though. Your posts, almost invariably, end up with you asking posters to do things for you rather than showing a good-faith attempt to understand the topic.

 

[Benjies]

A couple of important notes:

1. The throat radius depends on the radius of your combustion chamber. The flow is subsonic and therefore, for the converging portion of the nozzle, we also need to know the temperature, pressure, and density of the exhaust products to avoid shocks at the throat, but successfully reach sonic condition at, or very near, the throat (not precisely at the throat because in real engines, combustion is persisting at the throat). But this is also contingent on what you're assuming about your system. Are you assuming equilibrium combustion conditions leaving the CC?

2. Ramjets have a minimum operating Mach number where below this Mach number, the engine unstarts. Similar to what @jack action has stated, there is an expansion ratio at which you over expand your flow to a point where shocks occur in the nozzle, the nozzle bows, and the engine fails. So, the altitude at which you want to operate this engine is now in question.

3. You haven't mentioned whether you ask your question for actual applications in a system you are working on, or if this is just homework. If this is homework, what are your assumptions?Ultimately, our answers are completely contingent on what you're trying to do. I site the ramjet because you can theoretically provide operating Mach ranges for the J-58 engine on the SR-71, but in reality, there are an absurd amount of controls and odd flow bleeds to make the engine actually work (see page 5-22). I'd agree with my cohorts here in that when you provide no context for your question and then expect answers, you are in the wrong place. I hope my questions above and the link I've provided display to you that, even though your question is simple in theory, there are a slew of complications that may surround your question and it can be very hard to answer.

 

[Benjies]

If this is for homework:

1. Run NASA's CEA code with the propellants you plan to use, operating conditions, etc.

2. Take the P/T/gamma at the throat.

3. Using isentropic flow equations (again, a gross assumption), derive Tt and Pt.

4. Take NASA's MFP equation and derive your throat area.

Again, in reality, the stuff going on around the throat is tough to model, but that's what I'd do.

 

[T C]

The throat radius depends on the radius of your combustion chamber.

There is no combustion chamber. Just simple pressurised air/gas is released through a nozzle.

 

[Klystron]

There is no combustion chamber. Just simple pressurised air/gas is released through a nozzle.

Perhaps practical design papers may offer insights. Basic fire extinguishers direct compressed fluids, often gases such as CO2, from a tank connected to a nozzle. Research-gate offers many such practical nozzle designs with experiment results.

https://www.researchgate.net/public...ozzle_Spray_Using_Design_of_Experiment_Method

 

[sophiecentaur]

I have searched net

Which part and with what terms? The really clever stuff is accessed so rarely the search engines only place it deep down in their hit lists.