Blower fitted with De Laval Nozzle

[T C]

I want to know whether we can create supersonic flow with a blower fitted with De Laval Nozzle. We all know that convergent-divergent i.e. De Laval Nozzles can create supersonic flow.
Let's make it more clear. Suppose we have blower in our hand that can create an airlfow (air will be at STP) of 100 m/s speed. Now a De Laval nozzle has been set before the blower and the throat to inlet ratio for this nozzle is 1:4 (cross sectional area), Now with a convergent nozzle, the speed at the throat can't be 400 m/s as speed of sound in this case is the barrier here. But, what I want to know, can we get 400 m/s airflow if we use a convergent-divergent i.e. De Laval nozzle instead of a simple convergent nozzle?

 

[boneh3ad]

As long as your blower can support the pressure ratio required to maintain such a flow, then yes. Whether or not a CV nozzle can sustain supersonic flow with no shocks is entirely dependent on the ratio between its back pressure and supply pressure (and whether any blower can supply air at a mass flow rate fast enough to maintain that supply pressure).

 

[T C]

As long as your blower can support the pressure ratio required to maintain such a flow

What do you mean by "pressure ratio" for a blower.

Whether or not a CV nozzle

What's a CV nozzle?

 

[boneh3ad]

I meant to type "CD", not "CV".
CD = Convergent-divergent nozzle

By the pressure ratio, I mean that the function of a blower is not just to move air. It also increases the pressure from atmospheric to something that corresponds to the rate of air flow it is producing. That pressure has to be sufficient to "start" a CD nozzle.

 

[T C]

That pressure has to be sufficient to "start" a CD nozzle.

How much pressure is necessary to start a CD nozzle and how that can be calculated?

 

[boneh3ad]

That depends on the shape and is a pretty basic component of and compressible flow course. The easiest way to tell is look at the isentropic pressure rator at the design Mach number.

 

[T C]

Can you give some examples?

 

[boneh3ad]

Examples of what?

 

[T C]

I mean a specific example of a CD nozzle with its starting pressure and how that pressure can vary with the specific parameters of the CD nozzle.

 

[boneh3ad]

Are you at all familiar with compressible flows? What is your background? I could rattle off the expansion and pressure ratio parameters for, say, a Mach 5 nozzle, but unless you are familiar at some level with compressible flow, it's probably not going to help much. That's why it's helpful to know about your background.

 

[T C]

I have a background of college level physics and have no specialisation in compressible fluid flow. Whatsoever, kindly give an example and I will try to understand that.

 

[russ_watters]

Here's the equations and a calculator:
https://www.grc.nasa.gov/www/k-12/airplane/isentrop.html

Here's some more explanation:
https://en.wikipedia.org/wiki/Choked_flow

What kind of "blower" is this? A pressure ratio of 0.5 or lower is needed to get supersonic flow, which means your upstream pressure needs to be at least 15 psi. Can your blower do that?

 

[T C]

Thanks for the information. As far as I can understood from the links is that the maximum limit of velocity at the throat is sonic velocity (though I already know that before) and in case of a CD nozzle the velocity increases even after leaving the throat. What I want to know is that whether with the conditions that I have mentioned in my starting post of this thread, the maximum velocity achieved can be 400 m/s or not. To me, it's not that important what's the velocity of the compressible fluid at the throat but rather what's the maximum velocity attainable by a CD nozzle with ratio 4:1.

What kind of "blower" is this? A pressure ratio of 0.5 or lower is needed to get supersonic flow, which means your upstream pressure needs to be at least 15 psi. Can your blower do that?

Kindly read my first post where I have mentioned the conditions. The air/compressible fluid is at STP and the blower can give rise to a flow of 100 m/s. I just want to know whether we can achieve 400 m/s flow with a CD nozzle fitted to it.

 

[JBA]

To clarify a basic statement regarding the C/D nozzle location relative to the blower, in your first post you state "Now a De Laval nozzle has been set before the blower". Does this mean "ahead of the blower inlet"?

 

[T C]

No, not at the inlet but rather at the exit. The air/compressible fluid will come out at 100 m/s speed and will enter the CD nozzle. I want to know with what speed it will come out of the nozzle.

 

[russ_watters]

What I want to know is that whether with the conditions that I have mentioned in my starting post of this thread, the maximum velocity achieved can be 400 m/s or not...

Kindly read my first post where I have mentioned the conditions. The air/compressible fluid is at STP and the blower can give rise to a flow of 100 m/s. I just want to know whether we can achieve 400 m/s flow with a CD nozzle fitted to it.

You didn't give the most important condition: the pressure the blower can generate. That's the input information for the pressure ratio we were discussing. "A flow of 100 m/s" is essentially meaningless information. Nor did you say what kind of blower it is (which would enable me to find more information on it myself).

But I'll take a guess and say you're probably using something like a leaf blower, which actually advertises that velocity, so I'll say no, it it not capable of generating anywhere near enough pressure.

 

[T C]

Well fine! Then how much speed can be achieved by the CD nozzle. As far as I know, if the pressure is higher, then the speed of the released gas is supersonic without a nozzle i.e. when the input pressure is around 9 barA and it's released at 1 barA. But, as far as I know, nozzles (both convergent and CD) increases speed of compressible fluid while passing through it.
If it's not, then what would be the possible speed at the exit?

 

[jack action]

The equation you need to find the exhaust velocity of a CD nozzle can be found here:

As you can see, for any inlet temperature $T$, there is an exit/inlet pressure ratio $\frac{p_e}{p}$ that is required to maintain the desired exhaust velocity (in your case, 400 m/s). With air and a standard inlet temperature, the inlet pressure (of the nozzle) must be maintained at around 3 times higher than the exit pressure to get a 400 m/s exit velocity.

So what is important is the outlet pressure and temperature of your blower, not the flow.

 

[boneh3ad]

That equation is a tad misleading as well. It's easier to start at the beginning: every expansion ratio, i.e. the ratio of exit area to throat area, corresponds to a fixed design Mach number. For an expansion ratio of 4, this corresponds to $M_e\approx 2.94$. This also carries with it a few other assumptions, most notably that the flow through the nozzle is isentropic. This has several important ramifications:

1. The Mach number has a specific pressure ratio between the exit pressure and the total (reservoir) pressure. In this case, for this expansion ratio, that is $p_e/p_0 = 0.030$. In other words, to achieve isentropic flow throughout the flow path with no shocks or expansion waves, you need roughly 33 times more pressure upstream than you have at the nozzle exit.
   
2. The same exit Mach number has associated with it a similar temperature ratio, in this case $T_e/T_0 = 0.366$. This means whatever your upstream total temperature is, the exit temperature will be just over a third of that (on an absolute scale).
   
3. The temperature comment above is important because, ultimately, the speed of sound is a function of temperature alone and that exit temperature combined with the exit Mach number will determine the exit velocity. Even if your Mach number is some constant design value, the velocity will depend on the temperature you supply.

This is why I asked if you are at all familiar with compressible flows. There are a different set of considerations involved than for incompressible flows. Just for grins, if we use your suggested expansion ratio of 4 and its associated Mach number, and assume it exhausts to atmospheric pressure and that the supply temperature is room temperature, then we can come up with the following characteristics:

Reservoir total pressure:
$$p_0 = p_e\left(\dfrac{p_0}{p_e}\right) = 33.3\text{ atm}$$

Exit temperature:
$$T_e = T_0\left(\dfrac{T_e}{T_0}\right) = 108\text{ K}$$

Exit speed of sound:
$$a_e = \sqrt{\gamma R T} = 209\text{ m/s}$$

Exit velocity:
$$v_e = M_e a_e = 614.8\text{ m/s}$$

 

[russ_watters]

Incidentally @T C , you can get most of those answers from the calculator I posted in post #12 (working backwards, but still...). I recommend you play with it a little and try to understand what it and the equations are telling you.

 

[etudiant]

That equation is a tad misleading as well. It's easier to start at the beginning: every expansion ratio, i.e. the ratio of exit area to throat area, corresponds to a fixed design Mach number. For an expansion ratio of 4, this corresponds to $M_e\approx 2.94$. This also carries with it a few other assumptions, most notably that the flow through the nozzle is isentropic. This has several important ramifications:

1. The Mach number has a specific pressure ratio between the exit pressure and the total (reservoir) pressure. In this case, for this expansion ratio, that is $p_e/p_0 = 0.030$. In other words, to achieve isentropic flow throughout the flow path with no shocks or expansion waves, you need roughly 33 times more pressure upstream than you have at the nozzle exit.
   
2. The same exit Mach number has associated with it a similar temperature ratio, in this case $T_e/T_0 = 0.366$. This means whatever your upstream total temperature is, the exit temperature will be just over a third of that (on an absolute scale).
   
3. The temperature comment above is important because, ultimately, the speed of sound is a function of temperature alone and that exit temperature combined with the exit Mach number will determine the exit velocity. Even if your Mach number is some constant design value, the velocity will depend on the temperature you supply.

This is why I asked if you are at all familiar with compressible flows. There are a different set of considerations involved than for incompressible flows. Just for grins, if we use your suggested expansion ratio of 4 and its associated Mach number, and assume it exhausts to atmospheric pressure and that the supply temperature is room temperature, then we can come up with the following characteristics:

Reservoir total pressure:
$$p_0 = p_e\left(\dfrac{p_0}{p_e}\right) = 33.3\text{ atm}$$

Exit temperature:
$$T_e = T_0\left(\dfrac{T_e}{T_0}\right) = 108\text{ K}$$

Exit speed of sound:
$$a_e = \sqrt{\gamma R T} = 209\text{ m/s}$$

Exit velocity:
$$v_e = M_e a_e = 614.8\text{ m/s}$$

Oh wow!
An exit temperature of 108*K, that is almost cold enough to liquefy the nitrogen in the air (77*K). A fancy setup indeed.

 

[boneh3ad]

Oh wow!
An exit temperature of 108*K, that is almost cold enough to liquefy the nitrogen in the air (77*K). A fancy setup indeed.

It's even closer to causing the oxygen to liquefy. This is why wind tunnels operating at high Mach numbers (generally Mach 5 and above) must be heated. Most of the time, we researchers don't really like it when we have liquid oxygen droplets flying down our wind tunnels at several times the speed of sound.

 

[T C]

So far, most of the answers here are associated with flow of pressurised compressible fluid being released through a c/d nozzle. I have also searched for my answers about using blower with convergent and/or c/d nozzle but haven't found any proper answer anywhere. Then suddenly this thought comes to my mind that I want to share here.
In all kind of nozzles, all phenomenons occur just to keep the mass flow rate to be constant throughout the process. As for example, when air/pressurised gas is released from 3 barA pressure to atmospheric level through a convergent nozzle having inlet to throat ratio to be 4:1, then the speed of gas at the throat will be around 331 m/s assuming the atmospheric temperature to be around 0°C. But the density of the air/pressurised gas at the throat will be higher just to keep the mass flow rate to be equal to the case where the gas/pressurised gas will be released through a simple orifice.
Now, why shouldn't we expect the same phenomenon when a blower is used?

 

[jack action]

Now, why shouldn't we expect the same phenomenon when a blower is used?

Nobody on this thread said the contrary. Conservation of mass has always been one of the assumption for anyone posting on this thread.

According to posts #14 & #15, your blower is ahead of your nozzle. So in your example, the blower must be able to maintain a 3 barA pressure AND the mass flow rate that produces a velocity of 331 m/s for whatever size your throat nozzle is.

The nozzle analysis is really independent of how the pressure is created. All you need to know are the inlet and outlet conditions of the nozzle. By definition, the blower outlet conditions have to be the same as the nozzle inlet conditions.

 

[russ_watters]

In all kind of nozzles, all phenomenons occur just to keep the mass flow rate to be constant throughout the process. As for example, when air/pressurised gas is released from 3 barA pressure to atmospheric level through a convergent nozzle having inlet to throat ratio to be 4:1, then the speed of gas at the throat will be around 331 m/s assuming the atmospheric temperature to be around 0°C. But the density of the air/pressurised gas at the throat will be higher just to keep the mass flow rate to be equal to the case where the gas/pressurised gas will be released through a simple orifice.

For low pressure and speed, the velocity changes to ensure mass flow. The density doesn't. That's the Venturi effect. For your high speed application it will be both...though the compression does not really happen at the throat.

Now, why shouldn't we expect the same phenomenon when a blower is used?

Because a blower can't generate the pressure required to compress air.
[caveat: you still haven't told us anything useful about this "blower"]

 

[russ_watters]

Oh wow!
An exit temperature of 108*K, that is almost cold enough to liquefy the nitrogen in the air (77*K). A fancy setup indeed.

...which is why a similar setup is used in both supersonic wind tunnels and air liqurfication plants.

 

[JBA]

But the density of the air/pressurised gas at the throat will be higher just to keep the mass flow rate to be equal to the case where the gas/pressurised gas will be released through a simple orifice.
Now, why shouldn't we expect the same phenomenon when a blower is used?

The key question is whether or not your blower is capable of raising the inlet pressure at the C/D nozzle to a pressure above the the nozzle discharge back pressure sufficient to create a sonic flow at the nozzle throat, which is a mandatory condition for supersonic flow to be created in the diverging section of the nozzle.

 

[T C]

Nobody on this thread said the contrary. Conservation of mass has always been one of the assumption for anyone posting on this thread.

What I am talking about is mass flow rate and I don't think it has anything to do with conservation of mass.

For low pressure and speed, the velocity changes to ensure mass flow. The density doesn't. That's the Venturi effect. For your high speed application it will be both...though the compression does not really happen at the throat.

As per this page on choked flow, in a convergent nozzle when the speed at the throat reached its limit i.e. sonic speed, no further increase in speed occurs despite increase in input pressure but the number of particles at the throat increase. In short, as the speed can't increase, to keep the mass flow rate constant, the number of particles at the throat increase. Increase in number of particles at the throat means increase in density and that means increase in pressure.
In case of a convergent nozzle, there is no way to measure the speed of the fluid after the throat. But in case of c/d nozzle or De Laval nozzle, the speed can be measured and it has been found that the speed increases after the flow exits the throat. How that can happen? In my opinion, the increase in pressure at the throat is released and that is converted into more speed at the divergent section.
What I want to say is that the same phenomenon can occur when we use a blower.

The key question is whether or not your blower is capable of raising the inlet pressure at the C/D nozzle to a pressure above the the nozzle discharge back pressure sufficient to create a sonic flow at the nozzle throat, which is a mandatory condition for supersonic flow to be created in the diverging section of the nozzle.

If not, then what will happen?

 

[russ_watters]

What I am talking about is mass flow rate and I don't think it has anything to do with conservation of mass.

It does. In fluid mechanics, it's called "continuity":
https://en.wikipedia.org/wiki/Continuity_equation

Simply put, the fact that mass flow in has to equal mass flow out unless you are filling a tank is a consequence of conservation of mass.

As per this page on choked flow, in a convergent nozzle when the speed at the throat reached its limit i.e. sonic speed, no further increase in speed occurs despite increase in input pressure but the number of particles at the throat increase.

That's correct.

In short, as the speed can't increase, to keep the mass flow rate constant, the number of particles at the throat increase. Increase in number of particles at the throat means increase in density and that means increase in pressure...

But in case of c/d nozzle or De Laval nozzle, the speed can be measured and it has been found that the speed increases after the flow exits the throat. How that can happen? In my opinion, the increase in pressure at the throat is released and that is converted into more speed at the divergent section.

That isn't correct.

I may not have been clear enough about this before: prior to the throat, pressure is at its maximum and it decreases toward the throat as velocity increases (and of course, density decreases with it). This is a basic consequence of Bernoulli's Principle applied to Venturi tubes. As you get faster, this decrease in pressure and density gets more significant. The wiki on isotropic nozzles has a graph of pressure along the nozzle at different pressure ratios:

https://en.wikipedia.org/wiki/Isentropic_nozzle_flow

How is all this possible? How do you get more pressure to get faster flow then? You have to start with high pressure. That - again - is why a typical blower won't work for this application.

What I want to say is that the same phenomenon can occur when we use a blower.

If not, then what will happen?

As you make the nozzle smaller, the airflow profile will ride the blower curve until it reaches a maximum pressure at which point you've reached your maximum velocity...and it may stall and drop the pressure/velocity.

 

[JBA]

Then you will end up with subsonic flow through the nozzle in which the the gas density and velocity will increase in the convergent section to a maximum at the nozzle throat and then the diverging section of the nozzle it will simply acts as an piping expansion that reduces the flow density and velocity of the gas.

At the same time, you might get additional input on the issue if you would post more (some) information on your blower.

Failing that, I think your best first step is to, if possible, obtain the blower's flow rate vs backpressure curve from the manufacturer. The blower stall point on that curve will show the maximum operating backpressure for that unit.

PS I posted this before seeing the above russ_waters post

 

[boneh3ad]

As per this page on choked flow, in a convergent nozzle when the speed at the throat reached its limit i.e. sonic speed, no further increase in speed occurs despite increase in input pressure but the number of particles at the throat increase. In short, as the speed can't increase, to keep the mass flow rate constant, the number of particles at the throat increase. Increase in number of particles at the throat means increase in density and that means increase in pressure.

That's correct.

No, it's not correct. When the nozzle becomes choked, the speed can absolutely still change, e.g. if the temperature changes. What becomes fixed is the Mach number. It also means that, no matter what you do to the back pressure, the mass flow rate remains constant because the conditions at the throat have not changed, and mass has to be conserved. That said, if you change the reservoir conditions, you can still change the mass flow rate through the throat or the velocity, but the Mach number is still fixed at 1.

That - again - is why a typical blower won't work for this application.

As long as the blower can create sufficient pressure on its downstream edges, there is no reason a blower couldn't work in principle. That said, the requirements of CD nozzles will rapidly outpace a blower's ability to keep up.

In case of a convergent nozzle, there is no way to measure the speed of the fluid after the throat.

Wait, what? Why do you say this? You can measure speed in any flow if you have the right instrument (subject to the usual constraints of experimental uncertainty).

But in case of c/d nozzle or De Laval nozzle, the speed can be measured and it has been found that the speed increases after the flow exits the throat. How that can happen? In my opinion, the increase in pressure at the throat is released and that is converted into more speed at the divergent section.
What I want to say is that the same phenomenon can occur when we use a blower.

This isn't really a matter of opinion. In a subsonic flow, a decrease in area results in a flow acceleration and its complementary pressure decrease (after all, you need a pressure gradient to provide the force for the acceleration). For a supersonic flow, the situation is reversed, and an increase in area results in the same effect (faster flow, lower pressure). In other words, throughout the entire length of a de Laval nozzle, the pressure monotonically decreases and the speed and Mach number each monotonically increase provided that the pressure ratio is large enough to fully start the nozzle.

It makes no difference whether the pressure was provided by a blower or an air storage system. As long as the pressure can be maintained at the desired mass flow rate, then the nozzle runs as designed.

 

[russ_watters]

No, it's not correct. When the nozzle becomes choked, the speed can absolutely still change, e.g. if the temperature changes.

When someone states their dependent variable is is unreasonable/argumentative to add your own.

As long as the blower can create sufficient pressure on its downstream edges, there is no reason a blower couldn't work in principle. That said, the requirements of CD nozzles will rapidlyoutpace a blower's ability to keep up.

I'd be interested to see if such a blower exists anywhere, but again you are reaching beyond the bounds of what was said in search of an error that isn't contained in what was said.

[edit] I can think of a way that might go: since there is no fundamental difference between a "fan", a "blower" and a "compressor", you could take a centrifugal compressor, label it a "blower" and say it fits. It wouldn't be reasonable, but here we are.

 

[jack action]

I'd be interested to see if such a blower exists anywhere, but again you are reaching beyond the bounds of what was said in search of an error that isn't contained in what was said.

Maybe a single stage blower cannot increase the pressure enough from atmospheric pressure - assuming the nozzle outlet pressure is atmospheric as well - but:

1. No one specified that the blower inlet pressure and nozzle outlet pressure are the same;
2. One could put blowers in series to increase the potential total pressure ratio.

Like I said earlier, it really doesn't matter how the inlet & outlet conditions are created at the nozzle. And the inlet conditions depends on the blower inlet conditions as well - if such machine is used (but it really doesn't matter if there is one or not).

 

[boneh3ad]

When someone states their dependent variable is is unreasonable/argumentative to add your own.

I don't know what this means, but I don't think what I said was in any way unreasonable. There were some misstated facts about how de Laval nozzles operate, and I thought it important to straighten those out in the context of this thread. That doesn't make me unreasonable. In fact, it is important to understand that, in order for any of the previous assumptions about speed here to be true, one must hold the temperature constant. That is remarkably difficult to achieve at times with compressible flows, especially when we are talking about using some kind of blower that is not doing anything to control for temperature changes.

I'd be interested to see if such a blower exists anywhere, but again you are reaching beyond the bounds of what was said in search of an error that isn't contained in what was said.

[edit] I can think of a way that might go: since there is no fundamental difference between a "fan", a "blower" and a "compressor", you could take a centrifugal compressor, label it a "blower" and say it fits. It wouldn't be reasonable, but here we are.

Blower, fan, compressor... they all operate in fundamentally similar ways. They take air from an inlet at (presumably) atmospheric pressure, and use the powered motion of the blades to increase the pressure just downstream, which provides the pressure required for the application in question. A box fan has a relatively small pressure ratio, and on the other end, a jet engine has a very high one. Since @T C did not really specify at all what he is using, it is not really possible to determine what sort of system he or she actually has.

 

[russ_watters]

I don't know what this means, but I don't think what I said was in any way unreasonable.

The statement you responded to (which I agreed with) was: "...no further increase in speed occurs despite increase in input pressure..." It doesn't mention temperature, so it is reasonable to assume the intent is for temperature to remain constant. It is unhelpful and argumentative to go beyond the bounds of what was stated (without at least dealing with the statement as given). For example, a more reasonable response would have been: "That's correct as stated, but be careful; there are other things not mentioned, such as temperature, that could be changed that you didn't mention, that could allow the speed to change."

Blower, fan, compressor... they all operate in fundamentally similar ways. They take air from an inlet at (presumably) atmospheric pressure, and use the powered motion of the blades to increase the pressure just downstream, which provides the pressure required for the application in question. A box fan has a relatively small pressure ratio, and on the other end, a jet engine has a very high one. Since @T C did not really specify at all what he is using, it is not really possible to determine what sort of system he or she actually has.

Agreed. So do you think it is reasonable to assume the OP has a device that has a label that says "compressor" on it, but he called it a "blower" instead?

It would be more helpful if you tried to answer the OP's questions in a way that makes a reasonable effort to interpret the question in the way the OP intended...and for that matter, apply that to other posts/posters as well. Otherwise, you are going off on tangents that distract from the question being asked.