What is the Real-Life Example of a De Laval Nozzle with Low Exit Pressure?

[T C]

TL;DR Summary

When a pressurized flow is released through a De Laval nozzle, the pressure at the exit can be upto 1/3rd of the ambient/release pressure. I want to know in details of any such example of flow through a De Laval nozzle.

In case of De Laval nozzle, the static pressure at the exit can be as low as 1/3rd of the ambient/release pressure. Kindly look at the conditions of operation part of the page. At present, I want to know any real life example (in as much detail as possible) of a De Laval nozzle where the exit static pressure would be sufficiently less than the ambient/release pressure. I want a real life example.

 

[russ_watters]

At present, I want to know any real life example (in as much detail as possible) of a De Laval nozzle where the exit static pressure would be sufficiently less than the ambient/release pressure.

What do you mean by "sufficiently..."? Sufficient for what?

I want a real life example.

Basically any atmospheric rocket engine is an example of this. The search term you need (discussed in the wiki you linked) is "overexpanded". You can find photos of the phenomena and papers with technical analysis of real rockets.

Supersonic wind tunnels too, but they have diffusers on the end.

 

[cjl]

A good real life example is the Space Shuttle Main Engine, which has an exit pressure around 4.5 PSI if I remember right.

Is there something specific you're trying to figure out here? A great many liquid fueled rocket engines used for the first stage of rockets are overexpanded, as Russ stated, so it's not a particularly uncommon situation.

 

[boneh3ad]

Pick literally any application of a de Laval nozzle and there is a use case where the exhaust pressure is less than ambient. It's called an overexpanded nozzle. The result is shock diamonds.

 

[T C]

What do you mean by "sufficiently..."? Sufficient for what?

Sufficiently means less than half of the release/ambient pressure.

A good real life example is the Space Shuttle Main Engine, which has an exit pressure around 4.5 PSI if I remember right.

Can you give me a source/reference?
To be precise, I am looking for an example simple compressed air/gas being released through an overexpanded nozzle.

 

[russ_watters]

Sufficiently means less than half of the release/ambient pressure.

Can you give me a source/reference?
To be precise, I am looking for an example simple compressed air/gas being released through an overexpanded nozzle.

I think you're unlikely to find real examples of that because people need a reason for doing things and there isn't a good reason I can think of to do that. Like I said, people could do it with a supersonic wind tunnel, but they don't; they put diffusers on the end.
[edit]
Maybe this: https://www.airspade.com/pages/airspade-supersonic-nozzle#/

 

[boneh3ad]

I think you're unlikely to find real examples of that because people need a reason for doing things and there isn't a good reason I can think of to do that. Like I said, people could do it with a supersonic wind tunnel, but they don't; they put diffusers on the end.
[edit]
Maybe this: https://www.airspade.com/pages/airspade-supersonic-nozzle#/

I mean... I'd make an educated guess that most supersonic wind tunnels operating in pressure-vacuum mode are running underexpanded like this, particularly at high Mach number. And not all have diffusers directly attached to the nozzle via a test section. Many operate in a free jet configuration where you can see the shocks coming off of the nozzle walls due to overexpansion. There simply isn't enough controllability on the vacuum side to maintain a pressure that doesn't result in overexpansion.

 

[T C]

Maybe this: https://www.airspade.com/pages/airspade-supersonic-nozzle#/

It's supersonic, but not clear whether overexpanded or not.

 

[boneh3ad]

It's supersonic, but not clear whether overexpanded or not.

This is why it's important to do background research before making statements like this that are easily verifiable. The site says the nozzles are Mach 2 and operate ideally at 90 psi total pressure. That means the exit pressure is just a bit over 11 psi, which is below ambient unless you use it up in the mountains.

 

[cjl]

Can you give me a source/reference?

No, because that's a number I remember calculating a while back. The chamber pressure and expansion ratio are both readily available though, so you can verify it easily enough yourself.

 

[cjl]

This is why it's important to do background research before making statements like this that are easily verifiable. The site says the nozzles are Mach 2 and operate ideally at 90 psi total pressure. That means the exit pressure is just a bit over 11 psi, which is below ambient unless you use it up in the mountains.

Huh, that's a cool little nozzle. Maybe I'll have to get one since I already have an air compressor. I live at an altitude where ambient is 12.4 PSI too, and my compressor will go well over 100, so I should be able to get it perfectly expanded. A bit irritatingly expensive though... maybe I just need to buy a lathe instead.

 

[russ_watters]

maybe I just need to buy a lathe instead.

Everyone needs a lathe.

 

[T C]

From yesterday onwards, I have started to study overexpanded nozzles and I found a curious point. In case of overexpanded nozzles, the flow coming out of the nozzle is compressed by the surrounding atmosphere (or the release fluid) in the plane perpendicular to the direction of motion, not towards the direction of motion. IMO the possible reason is the gross pressure (sum of static and dynamic pressure) towards the direction of motion is high enough and that prevents any compression towards the direction of motion. But in the plane perpendicular to the direction of motion, the dynamic pressure is useless as it can perform only towards the direction of motion. Am I right?

 

[boneh3ad]

From yesterday onwards, I have started to study overexpanded nozzles and I found a curious point. In case of overexpanded nozzles, the flow coming out of the nozzle is compressed by the surrounding atmosphere (or the release fluid) in the plane perpendicular to the direction of motion, not towards the direction of motion.

I don't understand what this means. Pressure is a scalar and does not have a direction. The pressure gradient does, but it, in general, is not parallel nor orthogonal to the flow direction in the case of an overexpanded nozzle.

the gross pressure (sum of static and dynamic pressure)

Gross pressure is not a technical term used in the field of aerodynamics as far as I am aware, and it is not a definition of the sum of the static and dynamic pressures. In an incompressible flow, those two pressures sum to the total pressure or stagnation pressure, but this is not true in a compressible flow such as this.

IMO the possible reason is the gross pressure (sum of static and dynamic pressure) towards the direction of motion is high enough and that prevents any compression towards the direction of motion. But in the plane perpendicular to the direction of motion, the dynamic pressure is useless as it can perform only towards the direction of motion. Am I right?

Again, pressure does not have a direction so the rest of this is meaningless. Further, in a typical de Laval nozzle, the flow expands isentropically, so the total pressure is constant along its length unless and until it encounters a shock or a boundary layer.

 

[T C]

I don't understand what this means. Pressure is a scalar and does not have a direction. The pressure gradient does, but it, in general, is not parallel nor orthogonal to the flow direction in the case of an overexpanded nozzle.

I mean dynamic pressure here. It arises due to velocity that's why should have a direction.

Gross pressure is not a technical term used in the field of aerodynamics as far as I am aware, and it is not a definition of the sum of the static and dynamic pressures. In an incompressible flow, those two pressures sum to the total pressure or stagnation pressure, but this is not true in a compressible flow such as this.

Ok. My mistake. In future, I will mention this as total pressure.

Again, pressure does not have a direction so the rest of this is meaningless. Further, in a typical de Laval nozzle, the flow expands isentropically, so the total pressure is constant along its length unless and until it encounters a shock or a boundary layer.

I am talking about the part where the flow encounters a boundary layer i.e. where it started to be compressed instead of being expanded.

 

[boneh3ad]

I mean dynamic pressure here. It arises due to velocity that's why should have a direction.

I am talking about the part where the flow encounters a boundary layer i.e. where it started to be compressed instead of being expanded.

Dynamic pressure has no direction. It is kinetic energy per unit volume, and energy has no direction.

 

[T C]

Dynamic pressure has no direction. It is kinetic energy per unit volume, and energy has no direction

Dynamic pressure is associated with momentum. Pressure may be a scalar quantity, but not dynamic pressure because that's associated with momentum. In case of overexpanded nozzles, the force towards the direction of the flow is higher but lower in the plane perpendicular to the direction of motion..

 

[cjl]

Fluid pressure is a scalar quantity because a unit area also has a direction (usually defined by its normal vector), and the pressure is effectively always projected along this vector.

(It's also a scalar because of equivalent other definitions, such as the energy per unit volume boneh3ad mentioned above, but it's good for the different methods of arriving at pressure to be consistent with each other).

 

[T C]

Ok. No debate now on this point. The pressure is present everywhere. But in the direction of the flow, the dynamic pressure has reduced its effectiveness while in the plane perpendicular to the direction of motion, dynamic pressure has no effect as it's vector (associated with momentum).

 

[boneh3ad]

Ok. No debate now on this point. The pressure is present everywhere. But in the direction of the flow, the dynamic pressure has reduced its effectiveness while in the plane perpendicular to the direction of motion, dynamic pressure has no effect as it's vector (associated with momentum).

This statement has no meaning. What do you mean by "dynamic pressure has reduced its effectiveness?"

 

[T C]

Reduced effectiveness means it opposes the pressure and that's why the pressure was unable to compress the flow in the direction of flow. Not very complicated.

 

[boneh3ad]

Reduced effectiveness means it opposes the pressure and that's why the pressure was unable to compress the flow in the direction of flow. Not very complicated.

Clearly it's complicated because you are repeatedly just spewing word soup and demonstrating you don't actually understand the terms you are using.

Dynamic pressure doesn't oppose or promote anything. It doesn't push or accelerate anything. It's just a scalar measure of kinetic energy. Your postulates here are not only wrong, but based on a poor understanding of what pressure is.

 

[T C]

Dynamic pressure doesn't oppose or promote anything.

In case of a flow coming out of a De Laval nozzle, it certainly opposes the backpressure. "The pressure measured in the direction of the motion is called the total pressure and is equal to the sum of the static and dynamic pressureas described by Bernoulli's equation."
From this source. It may be a scalar quantity, but it certainly have a direction.

 

[boneh3ad]

In case of a flow coming out of a De Laval nozzle, it certainly opposes the backpressure. "The pressure measured in the direction of the motion is called the total pressure and is equal to the sum of the static and dynamic pressureas described by Bernoulli's equation." From this source.

This is a remarkably poorly-worded article on NASA's site. What it means is that if you orient a pressure probe such that the flow stagnates against it, then it measures the total pressure. This is a Pitot probe.

Again, dynamic pressure does not oppose anything. The only "type of pressure" that does any pushing of any kind is static pressure. Dynamic pressure is just kinetic energy.

The articles you cite are about Bernoulli's equation, which is only valid under certain circumstances, one of which being that the flow is incompressible. This is violated in a de Laval nozzle. Total pressure is not equal to static pressure plus dynamic pressure in a compressible flow.

It may be a scalar quantity, but it certainly have a direction.

If you truly believe this and refuse to listen to us telling you otherwise, then there is no point in further discussion. Pressure is a scalar quantity, which by definition means it does not have a direction. Full stop.