GEEK Alert - Sonic Choking!

[Jim_Hbar]

You have to be careful thinking about this.  Those diagrams show venting to ambient, not pushing an obstruction/mass

There may be transient chokes as the flow establishes, but considering that Mach 1 ~= 1 inch/( .000 07 seconds), I would suggest that those effects can safely be ignored for a reasonable airgun design.

The choke defines the upper limit of the mass flow rate that is possible, for a particular design. 
But that all changes when there is something restricting the flow down stream, such as a pellet. 

Bob has shown us info on how the sonic velocity varies with pressure in post #4 - it's linear enough that one could pick a value, and go with it...
I would use this info as a point to check, if you are trying for a design that exceeds Mach1 at STP, or you have a port restriction..

A very interesting point:
- Bob has told me that evidence suggests that ports should be larger than 75% of bore size..  calculating areas 1/.75^2 = 1.78,
- This is just less than the pressure ratio of 1.893 where choking occurs.  Is this a coincidence??  1/.73^2 ~= 1.893

My head hurts enough - I need to go fire up the snowblower.

[PakProtector]

There is a lot of good stuff to consider. It is thoroughly mixed up in the, 'just how big can I make the ports?' How big a port can be squeezed into a .375 OD transfer sleeve, or into a .375 barrel spot face...and then given the divide-by-cosine growth lengthwise as the valve port is angled, how big can that be done...LOL
sheers,
Douglas

[Cal]

A few comments on this discussion
1)
What is the significance in restriction on the propelling gas Mass?  (Sonic choked flow)
Pressure is what internal ballistics calculations are based upon.    Hot and/or light gasses work just fine.  Can a rarified body of charge gas be "sped up" and provide equivalent energy to propel the projectile?  I think so.
Perhaps it the general vision of "choked" that implies the vital force does not get through,  but of course,  that is not the case.
 
2)  In any conducting pipework associated with an airgun,  there will very likely be several obstructions that will contribute to choked flow.
Friction and eddy, or changes in area are enough.  Even the muzzle end chokes the flow. (dump into 1 atm.)  There will not likely be an entire description obtained from the single analysis of the sinusoidal motion of the valve port.  (even if the difference in real world performance might be modeled by assigning "factors" for various deviations from the ideal.  Call them "losses?

3) the actual time that the pressure ratio conditions on either side of any restriction are met (1.8 :1 or so) may be so small as to be inconsequential.

Lastly, the flow dynamics through the plumbing is sure interesting!  (internal ballistics in airguns really)  Hats off to the "geeks"!

further reading
http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=8&ved=0CEwQFjAH&url=http%3A%2F%2Fdigitalcommons.unl.edu%2Fcgi%2Fviewcontent.cgi%3Farticle%3D1132%26context%3Dusdoepub&ei=eXF2VMmNA_TfsASKj4HIBw&usg=AFQjCNF3zIc2DwHRQq8EBm7PirtAvdWupg&bvm=bv.80642063,d.cWc

[rsterne]

I really think that any attempt to get a C-D nozzle design working in a airgun is very unlikely to succeed.... Rocket nozzles are very carefully designed, and they don't make two 90* turns and then have a bolt probe in the way.... Maybe (and it's a big maybe) if you used an axial-flow design like a Condor.... and some very careful shaping of the flow path....

Surely the purpose of using a C-D nozzle in the first place, however, is to achieve velocities of over Mach 1.... That puts you squarely up against the huge increase in drag on the projectile after it leaves the barrel if it's going faster than about Mach 0.85 - 0.9 because of Drag Divergence.... which is that point where the Drag Coefficient skyrockets.... So, what is the point in driving the bullet supersonic, wasting great quantities of air to do that, just to lose that extra velocity right after the muzzle, accompanied by increased wind drift?....

Oh, and Jim.... Welcome to the GTA and the Geek Gate....

Bob

[Jim_Hbar]

3) the actual time that the pressure ratio conditions on either side of any restriction are met (1.8 :1 or so) may be so small as to be inconsequential.

I agree that is likely the case, in a normal design. 

Supersonic dump shots?  Choking has to be a factor, but as Bob points out, what's the point.
If I want to go fast I'll go get one of my powder burners.. The 25/06 can hit Mach 3 with 75 grain bullets........

Thanks for the invite and the welcome, Bob.

[Bill G]

I'm going to try and simplify this, for myself at least.  As the air velocity goes past mach 1, the mass goes down.  As i see it, the whole action is a work calculation complicated by thermal dynamics and flow dynamics.  Turns don't help but have less to do with performance than porting and restrictions there of.  As the poppet opens, flow begins.  The pressure differential is abrupt but stabilizes as the pellet begins to move (avg psi of shot cycle).  Flow increases, while velocity of air decreases, as the poppet reaches 1/4 inlet diameter.  when the poppet returns to the certain distance, the air velocity increases until mach 1 is reached.  Flow decreases because velocity increased. All the while, air column in the bore is expanding.  The expansion of this mass does work not much unlike a spring.  The key is, to get a certain amount of air mass, to be metered in an amount specific for the amount of work that needs to be done.  More and we waist and less we fall short of desired performance.    I imagine that if an air gun were used in the vacuum of space, the pellet would be sucked out of the bore rather than pushed out.  This is how I see lighter gases being used.  Helium or hydrogen would act, in this atmosphere and to a lesser degree, similar to space.  This is how we get higher fps with light gases.  Gases of the same make up are simply going to achieve equilibrium while light gases are absorbed.  In our case we are using gases of same make up and that is how I see it as a spring.  When calculating the velocity of a mass propelled by a spring, there are basically 2 formulas.  One considers the mass of the spring, since it has to be accelerated too.  I don't recall the factor that allows the spring mass to be excused but that is the second formula.  I imagine that air would need to be calculated with the first formula.  with my model, I can get calculations to predict the velocity from one shot to the next within 1%.  The problem that I have is when I change to big bore calibers.  My model doesn't calculate  a bell curve unless I increase the psi of lower the power output.  I don't have a big bore to shoot, collect data or examine the porting, so it is a bit hard to compare model to performance.  I'm fairly certain it has to do with flow performance along with a couple other factors that will require measuring. 

I can see where sonic choking could be a cause for the famous bell curve. I see it reasonable to suggest that choking occurs until the knee of the fill is hit.  At whatever that psi is, the flow becomes matched to the porting and pressure thus ending choking. This also makes me believe that it is reasonable to suggest that guns with larger porting, tend to be harder to tune to a curve.  When the curve is made, it tends to be very steep.  Then again there is a lot of stuff that I don't understand yet.                     

[TimmyMac1]

Simplest example I can think of is the V350 Crosman. Inline spring air arrangement. BB system using a piston driven air charge to be transferred to the barrel with a small part called a pop valve. The air charge moves the pop valve forward to block the BB hole and push the BB into the bore as well as seal to the back of the barrel. The hole in it is going to determine the barrel pressure profile. The early ones had a fairly large hole and when they made the 3500 they discovered a smaller hole would generate more air speed and help get the entire charge through the system while the BB was still in the barrel. This means it shot faster because of the convergence and divergence making energy transfer more efficient. We can go supersonic in porting to generate a choke point that will be an aid to our tuning tool box. I've done it by accident and done it on purpose.
Supersonic flow is a good thing as it creates chaos and it won't last. Stalled flow is what helps us get valves shut quick. That is why a port restrictor can increase efficiency so drastically. It helps the valve timeout.

TimmyMac1

[rsterne]

When Timmy speaks, it pays to listen.... Even if I don't necessarily agree on his reasoning, just the fact that he has observed a FACT during his many years of working on airguns of huge diversity means that he has seen things many of us haven't.... If our models don't explain those FACTS, then we reject them at our own peril.... Instead, it is best to re-examine our view of what we think is happening and come up with an explanation that includes both OUR observations and HIS.... The words "that can't happen" are the most devoured, and most sour tasting, we can utter.... when they are served up to you on a platter of harsh reality....

"Guilty as charged".... but hopefully learning.... *grin*....

Bob

[hutnicks]

Agreed .

Sometimes I need some visual stimulus to get my head around Tim's stuff though. Not having ever seen a V350 in the flesh I found this of some help. Page 4 has the exploded view.

http://www.crosman.com/pdf/manuals/CV350-OM.pdf

I would also be very curious to see the temperatures generated at the port for some of the graphed results. I think there is a potential another method of additional tuning there.

[rsterne]

Generally speaking, in a PCP, the temperature should be dropping during the shot, due to adiabatic expansion.... particularly after the valve has closed and the air in the barrel is simply expanding....

Bob

[Cal]

A graphical isothermal  portrayal of the regions around choked flow would be fun if anyone comes across such tid-bits"

I've been looking, 

[Cal]

I really think that any attempt to get a C-D nozzle design working in a airgun is very unlikely to succeed.... Rocket nozzles are very carefully designed, and they don't make two 90* turns and then have a bolt probe in the way.... Maybe (and it's a big maybe) if you used an axial-flow design like a Condor.... and some very careful shaping of the flow path....



Bob

We may end up with a CD nozzle in spite of ourselves

http://www.thermopedia.com/content/659/


The stagnant regions defining the effective shape
A lot would depend on the poppet valve flow shaping.

[hutnicks]

A graphical isothermal  portrayal of the regions around choked flow would be fun if anyone comes across such tid-bits"

I've been looking,

Me too. Thus far coming up empty handed.

[rsterne]

That maybe so.... but I repeat, to what benefit?....

Bob

[Cal]

understanding

[rsterne]

The article you linked to talks about a pressure LOSS due to the constriction which accompanies the increase in velocity.... good ol' Bernoulli.... How can we use a decease in pressure to our advantage?.... The force on the base of the pellet is area (caliber) times pressure....

Bob

[Cal]

Without trying to divert the question,  Perhaps in efficiency.  In the same way that early valve closing makes use of declining pressure while pellet velocity continues to increase.

There also could be something in the energy of inertia that is worth paying attention to.   MV^2  holds promise.

[Cal]

If I may just "think out loud on this topic:

For myself,  "choked flow" describes a condition where additional Mass per unit time may not be induced to cross a boundary regardless of any reduction in the downstream pressure.  Key to the effect is that the downstream pressure,  It  no longer influences the mass flow rate as long as it stays low enough.

Increasing the upstream pressure will result in increased mass flow. (if that were possible, and may be in complicated plumbing systems)

In PCP airguns,  we are attempting to keep the pressure on all sides of any restriction as close to unity as possible.  If that can be at reservoir pressure,  so much the better.  In the idealized case,  no restrictions would be imposed,  and only pressure and valve opening duration would be considered.  That would surely simplify calculations. ;-)

Please correct me where I've gone astray.

[rsterne]

I agree, for maximum performance, we want to keep the restrictions in the system to a minimum.... The only useful purpose I can see for intentionally inducing choked flow is to limit the velocity to something less than what the gun is capable of.... This can be used to great advantage detuning a bullet shooter for (much lighter) pellets, for example.... I use this in my Disco Double to detune for pellets and achieve stellar efficiency by doing that, while still being able to utilize a full pressure fill.... something you can't do by reducing hammer strike....

Bob

[hutnicks]

I suspect that with an elegant enough implementation one could employ choking to influence barrel harmonics.