Sonic velocity inside a convergent nozzle

[T C]

TL;DR Summary

How compressible flows behave when they reach sonic velocity inside a convergent nozzle.

This time, i have a question that came to my mind a few days ago. There is an ideal nozzle having inlet to throat ratio of 8:1. Air will enter the nozzle at around 84 m/s velocity. it can be easily understood that the velocity will become sonic much ahead of the throat. And I am wondering what will happen to the flow when the velocity will become sonic.
Just remember how the compressor part of the all kinds of jet engines work.

 

[russ_watters]

This time, i have a question that came to my mind a few days ago. There is an ideal nozzle having inlet to throat ratio of 8:1. Air will enter the nozzle at around 84 m/s velocity. it can be easily understood that the velocity will become sonic much ahead of the throat. And I am wondering what will happen to the flow when the velocity will become sonic.

The flow is compressible, so the area/velocity ratio doesn't hold; the flow reaches sonic velocity at the throat.

 

[cjl]

You can't have a compressible flow entering an 8:1 nozzle at 84m/s, at least not steady state (you could probably achieve it briefly in a transient situation). As Russ said, the flow will choke at the throat, and then the backpressure will increase and slow the upstream flow until you have equilibrium. If you're using room temperature air as your inlet, with an 8:1 area ratio, you'll end up with the inlet flowing at 7.3% of the speed of sound, or around 24.7 m/s.

EDIT: Minor correction. This flow condition would be possible if you had a gas such that 84m/s was no higher than 7.3% of the speed of sound. This would require a sonic velocity of ~1140m/s, which would be reasonable in a flow of room temperature hydrogen (or a heated flow of helium at a bit over 260C)

 

[T C]

Good answer. But, I am just wondering what happens to the air that enters the inlet of the engine of a RAM Jet.

 

[russ_watters]

Good answer. But, I am just wondering what happens to the air that enters the inlet of the engine of a RAM Jet.

A ramjet inlet is the opposite of what you described in the OP. It uses a diffuser at the inlet, not a nozzle:

Diffuser[edit]
Ramjets try to exploit the very high dynamic pressure within the air approaching the intake lip. An efficient intake will recover much of the freestream stagnation pressure:

https://en.wikipedia.org/wiki/Ramjet#Diffuser
Which is it that you are really interested in? Can you be more descriptive about what you really want to know?

Incidentally, googling "ramjet diffuser" yields this 14 year old thread as the very first hit:
https://www.physicsforums.com/threads/ramjet-diffuser-question.68337/

 

[boneh3ad]

A ramjet still is going to generate a shock of some variety at the inlet, so there is definitely going to be a nice, hefty pressure loss up front (literally). Ideally, you'd like to minimize that with a carefully-designed compression ramp and using one or more oblique shocks rather than a single, strong normal shock.

Of course, that's not terribly relevant to what OP was asking, but since we don't really know what OP is asking, I typed it anyway.

The bottom line is that a ramjet is intended to utilize the incoming dynamic pressure as a replacement for a traditional compressor, and the goal is to slow that flow to subsonic speeds before it reaches the combustor.

 

[T C]

@cji By the word backpressure, do you want to mean the pressure/resistance created by the flow when it reaches close to sonic velocity? And as it's exerting a pressure, that simply means it's also experiencing some kind of pressure. In short, it's pressure will increase. Am I right?

 

[boneh3ad]

I think you need to draw a picture to illustrate what you want to know.

 

[russ_watters]

There are a lot of images/graphs available showing pressure inside ramjets, if that's what you are after.

 

[T C]

At present I just want to know one thing. Whether pressure will increase inside the nozzle in such a scenario or not. If the flow inside insert backpressure, that means it itself is under pressure.

 

[boneh3ad]

In what scenario? You've done a poor job of explaining your question and we are asking if you can explain it again from the beginning, perhaps with a picture to show what you mean.

 

[T C]

My question is plain and simple. Now, I am just elaborating it a little bit. The air will enter the nozzle 84 m/s velocity and the velocity will increase until it reaches the sonic level. What I want to know is what happened after that. As the velocity can't increase anymore, will the pressure increase to keep the mass flow rate intact? In short, in the subsonic level the velocity will increase but as the velocity can't increase after sonic level, the pressure/density need to be increased to keep mass flow rate intact.

 

[T C]

OK. I make it further simple. When the flow remains within the subsonic level, the pressure doesn't increase but rather decrease. But when the velocity reached (or can reach sonic level) inside the convergent nozzle, do the pressure increase inside?

 

[boneh3ad]

What I want to know is what happened after that. As the velocity can't increase anymore, will the pressure increase to keep the mass flow rate intact?

That has already been answered, though. You've got a converging duct with subsonic air going into it. The only portion of that duct that can sustain sonic flow is exactly at the throat, i.e. the narrowest portion. You cannot have sustained sonic flow anywhere else in the nozzle. If your 84 m/s number works out that the flow will be sonic before the throat, then the bottom line is that the inlet you describe cannot support that kind of velocity/mass flow going in because it is choked at the throat, and your inlet velocity will have to decrease.

In short, in the subsonic level the velocity will increase but as the velocity can't increase after sonic level, the pressure/density need to be increased to keep mass flow rate intact.

Who says the mass flow rate has to remain intact? I think that's the point you are missing. The flow system you describe simply cannot handle the mass flow rate from the incoming flow if that would lead to a sonic condition anywhere other than at the throat. If the incoming flow was 84 m/s, then some of that mass flow would have to be deflected around the engine and the actual inlet velocity would have to be reduced in order to physically support flow through the inlet.

 

[russ_watters]

OK. I make it further simple. When the flow remains within the subsonic level, the pressure doesn't increase but rather decrease. But when the velocity reached (or can reach sonic level) inside the convergent nozzle, do the pressure increase inside?

You're using the word "nozzle" incorrectly: the device is named for what it does. So that informs to the answer. This is probably what you are looking for:

https://www.public.navy.mil/netc/ce...uides/Eng_studentguide_18Jun2014 Change 1.pdf

 

[russ_watters]

OK. I make it further simple. When the flow remains within the subsonic level, the pressure doesn't increase but rather decrease. But when the velocity reached (or can reach sonic level) inside the convergent nozzle, do the pressure increase inside?

In a CD nozzle supporting a supersonic exit, the pressure decreases throughout the entire length. See scenario f:

 

[cjl]

My question is plain and simple. Now, I am just elaborating it a little bit. The air will enter the nozzle 84 m/s velocity and the velocity will increase until it reaches the sonic level. What I want to know is what happened after that.

That can only happen if it hits the sonic level exactly at the throat. It cannot hit sonic before the throat. If your geometry is such that you'd expect it to hit sonic before the throat, what will actually happen is that the pressure will increase through the entire flowfield, slowing down the incoming flow.

If it's constrained so all the flow has to go through the nozzle, this pressure increase allows for increasing massflow through the nozzle due to the increase in density. If the flow is unconstrained, some of it will spill around the nozzle instead.

Regardless, something will change and cause the incoming flow to not be at 84m/s at the entry to the nozzle, since a steady flow that goes sonic before the throat is not physically possible.

 

[boneh3ad]

You're using the word "nozzle" incorrectly: the device is named for what it does. So that informs to the answer. This is probably what you are looking for:

View attachment 243577

https://www.public.navy.mil/netc/ce...uides/Eng_studentguide_18Jun2014 Change 1.pdf

I don't know who made that figure, but they should know that flow goes left to right in images like this. It's just so awkward the other way around.