GEEK Alert - Sonic Choking!

[Jim_Hbar]

When I was snooping about the web last night, looking for those last couple of links, I found some videos of on-line lectures about compressible flow...... It's about 3rd or 4th year of engineering school stuff....
I watched over an hours worth, and they start from thermodynamics and jump right into the deep end of the pool. 
My eyes glazed over for a lot of it, and I'm sure I got "the deer in the headlights look" more than a few times, but it brought back some more memories, and re-inforced why "we" normally stay away from choked flow in pneumatic systems!!!! 

This is the start -   - Right off the bat, he states compressibility effects start at about mach .3.  He get's into "Stagnation Temperature" calculations at around the 12 minute mark.  That's interesting stuff, and applies to our choked situation, and also shows why we can largely ignore temperature effects until Mach1 is approached...  That's what we do in the industrial world, but for our application here, temperature may have significant effects as speeds increase. 

The 3rd video in the series, starts with a nozzle flow calculation, and has some interesting numbers just after the 7 minute mark.  It points out why we can no longer ignore temperature when things go sonic and beyond.
It really rang a bell, when I noted that the lecturer defined the position through the nozzle in terms of the pressure! 

I also stumbled across some other salient information, and this one was about the flow efficiency of various orifice shapes.. 
They state that a well shaped smooth nozzle can approach 98% of the theoretical flow of the ideal nozzle with the same throat area.  Conversely, a "sharp edged" orifice may only flow 60% of the theoretical number.  http://www.superflow.com/support/supportDocuments/airflow_basics.pdf

Lloyd -
If you attempt to chase the "pressure drop" approach right to the muzzle of the barrel, I strongly suspect that the pressure drop that you calculate (due to the force required to accelerate the mass of air) is effectively the same as the pressure drop arrived at by other methods, other than a small frictional loss.
The BIG caution I would offer is that all the pressure drop formulae I've found are predicated on steady-state results, and your mass based approach deals with the acceleration, which is what we are interested in.  The pressure drop along the barrel is just a different approach to dealing with the same effects that I understand that you have all ready quantified.  If you are doing the acceleration effects the way I would attack it, it's likely easier and more valid than trying to chase a pressure drop in the barrel, using data and relationships that were developed without a moving cork in the pipe!

Bob -
You've asked a couple of times if it the pressure drop across the restriction, or the pressure drop across the system is what matters for the choked flow condition.
The answer is - it's always the orifice, but sometimes the orifice is the system (or vica versa)..... 
(I'm just going to fly at it here, and state how I think about it - I know it's full of holes, but it's how I get my head around it)....
Cv's are flow coefficients - their reciprocal's are flow resistances and those flow resistances add together to define the flow resistance of the system and thus it's Cv.  Using Lloyd's words, the system is a "continuum of pressure gradients".   
So 1/Cvsys = Sum(1/Cvn) where n=1,2,3....

Example - Pulling numbers out of the air... 
Example one. Valve Cv=.5, Transfer port Cv=.1,  therefore Cv sys = .083 = 1/(2 + 10) - the transfer port clearly governs, and if we ignore the valve, close enough.
Example two. Valve Cv=.5, Transfer port Cv=.4,  therefore Cv sys = .22 = 1/(2 + 2.5) - It's getting complicated - but the Cv of the system is used to set the maximum mass flow rate, implying a choke...  I agree, it doesn't really make sense, with the simplifications of the physics we are using here.  But that's the way it is done, and it works..   

[rsterne]

I've run a few simulations using Lloyd's spreadsheet, dropping the pressure by 47% when the calculated port velocity hits Mach 1 for the upstream pressure.... All I can tell you is that the calculated results are WAYYYYYYYYYYY worse than my measurements.... The theory predicts a HUGE drop in FPE as soon as the port chokes, compared to the nice smooth (and logical) curve I get when I gradually reduce the port size.... Here is what I got for a stock .22 cal Disco, both measured and calculated....



The theory predicts no choking with the 0.156" and 0.166" transfer ports as the valve closes before the pellet reaches the velocity that would require supersonic flow through the port.... A stock transfer port of 0.140" should choke just before the valve closes, and you can see the huge predicted drop in the FPE compared to the negligible drop I measured with a stock port compared to oversize ones.... Even if Lloyd's spreadsheet was way out of whack, and the valve was closing earlier, all that would happen is that sudden drop would move to a slightly smaller port size....

I know that the theory is saying there is a ~1.9:1 drop in pressure across a choked port, but that is so drastic as to predict a much greater drop in FPE than we observe.... This leads me to the conclusion that the either the port isn't choked, or something is drastically wrong with the way we are approaching the problem.... I think possibly approaching the decrease in performance as a mass flow limit issue instead of a pressure drop may be necessary.... It might be interesting to plot mass flow limit vs port diameter for a pressure of 1600 psi and see if the curve is more similar to what I measured....

Bob

[rsterne]

Well I used the formula I proposed in Post #116 to calculate the Mass Flow Limit for a .22 cal Disco at 1600 psi, using the dwell time of 0.002 sec.... The formula I used was....

MFL (grams) = 15 x 1600 x 0.002 x D^2 .... where D is the port diameter in inches.... Here is the results for the same port sizes I used above in Post #121....



Now remember that for the two larger ports, there should be no choking, so that part of the graph really does not apply.... This appears to be a better fit with my measured data, but of course there is no way to correlate the Mass Flow Limit with the downstream pressure or the FPE developed.... so this remains an interesting calculation but nothing more at the moment....

Bob

[Jim_Hbar]

Bob:

The pressure drop calculations and sonic choke mass flow limits are real phenomena, and probably go a long way to explain the dropping efficiencies of transonic and super-sonic shots in Lloyd's model.  Beyond that, if the model is working for you guys, then there is no reason to invest the effort in changing the fundamental method of calculation used.  Like I've said many times, sonic choking only potentially comes into play when the ports are way too small, or supersonic shots are done - neither of which are of much interest to me.

Me, I'm back to the drawing board now.

Jim

[rsterne]

Jim, I don't blame you.... Thanks very much for putting up with all this nonsense and your detailed explanations.... VERY much appreciated....

I agree, if we stay away from intentionally choking the gun and stay away from shooting wide open guns at Mach 1, this is really only a curiosity.... In reality, we don't NEED to know WHY choking up the transfer port reduces the power, only that it does and that we can use that for tuning when necessary.... There is one thing we CAN state after having looked closely at this, however.... and that is we can say definitively that once the pellet passes Mach 1 inside the barrel (at the pressure being used) the flow WILL choke (somewhere) and the pressure available to further accelerate the pellet will be half (or less) of what it was shooting subsonic.... For me, that is one more arrow in my quiver to argue against those guys who want to push past Mach 1 muzzle velocities with a PCP running on air.... At the very least, they should run Helium if they want to play that game....

Bob

[Cal]

from the 'E' panel...Mach Cones are the visible effects of the shockwaves... One of my favourite visuals.
http://www.aerospaceweb.org/question/propulsion/q0224.shtml
cheers,
Douglas

Though not quite the same mechanism,  this visual and narrative is interesting.
 

It highlights the element of flows captive within the directed stream.

[Cal]

I read now that most of the energy in this topic has been spent, or at least whirled around until it's direction is in question. ;-)
While I was off on travel,  I had some thoughts go through. (again,  passing mostly empty spaces ;-)

I feel there are some significant aspects of the choking phenomena that have to do with even low velocity/power applications. And so will post a bit of a parting shot.
I'll explore some random thoughts with words here.  If I ramble and misspeak,  please forgive, but Correct!

Relative to air guns,  there is a sequence of events that follow a logical progression during the expulsion of a projectile.  If we break  these events into components, we may better understand each cause and effect.

For  sake of example,  lets consider a firing sequence into a stopped barrel with the stoppage at the normal pell breech location. This approximates the conditions prior to significant pell movement and during the time period of relatively low velocities. (I.E. not rapidly changing volume)
The trigger is squeezed, the hammer falls, the valve opens and releases some mass of gas from the reservoir into the "chamber"(read Tport volume) . The valve then closes on a new set of conditions.
What happens?

The reservoir losses some of it's population, and so the pressure decreases slightly and the remaining gas cools as it expands to fill the volume.

The high pressure gas is allowed to communicate with the low pressure gas on the other side of the valve restriction.  Since this pressure differential is greater than 2:1,  the flow is sonic and likely choked, and so limited to constant mass flow entirely based on port area and reservoir pressure.  This implies that the flow past the valve and into the Tport is in a constant mass flow/ unit area condition UNTIL, the pressure behind the stopped pell is 1/2 of the reservoir pressure.   This is important.
 After the downstream pressure rises above .5 Pres, the mass flow per unit time decreases proportional with pressure and area.

A plot of changing  port pressure* vs time, the plot would be fixed slope during the initial filling to .5Pres.  Then an asymptotic curve to equilibrium.  (*Including port area in the function, noting that the opening period is very short indeed .  Is it significant in light of the "nothing much happens until the valve lift is X "?  we mentioned this earlier)

During this port filling sequence we may, for simplicity, model 100% pressure change due to the arrival of the gas molecules from the reservoir.  Pressure would  increase in that volume 100-200 fold in < .002 seconds.  Quite a storm!  There will be compression heating and stirring due to turbulent conditions. In the first fractions of that time, what would be observed as "flow" will quickly stagnate to pressure. Calculation based on density, velocity,area and time certainly could be made to arrive at a likely pressure curve.

The valve closes on a small pressure differential if the flow is "efficient". Certainly the pressure differential will not be sufficient to maintain supersonic flow past the valve face.  This observation justified by internal ballistics calculations).
Note too,  In our real world,  the pell inertia will influence  the pressure rise time.
 
A similar extreme example can be made for the case of no pell at all,  just "shooting" out a column of air. (or not ;-)  A sufficient length of barrel could replace the pell inertia without too much mental gymnastics.

Of course we must ultimately account for the increasing volume requirements behind the pell as it moves down the barrel,  Again I mention that time may be the best measure of that significance.  If we give relative merit  to concepts such as "sonic horizon", we might conclude that the exact nature of the valve closing has a progressively diminishing effect as the pell moves down the bore and away from the valve restriction.

The study of the Tport volume expansion as it presses the projectile will take another sleepless night, or at least undistracted contemplation.  I believe the inclusion and combination of both flow and expansion aspects into one discussion  has made any conclusion of this topic difficult.

Jim,  Thank you for those on-line references.  I have not had time to take them in,  but the quality looks fine.

regards

Cal

[rsterne]

Cal, your description of what happens in the transfer port volume, including the heating of that volume and slight cooling of the (much larger) reservoir are quite accurate, if the pellet has infinite mass (ie a plug as you say).... Since it only takes a few lbs. force (at most) to get the pellet moving, however, I submit that any brief heating of that air will be quickly overwhelmed by the cooling of the air expanding as the pellet moves down the barrel after the initial brief pressure rise.... The pellet should be moving long before the choke breaks down at the valve seat from the pressure at the pellet reaching 0.5 reservoir pressure.... likely within a few microseconds.... Lloyd's spreadsheet is, in fact, integrated over time, in increments of 0.00001 sec.... so there are 100-300 calculations made before the valve closes, and 300-600 typically made before the pellet exits the barrel....

Your reference to the concept of "sonic horizon" aside, the idea that the further down the barrel the pellet has moved, the less effect what is happening at the valve has, is exactly correct.... If the valve closes at 12" in a 24" barrel, the pellet has already reached about 97% of it's muzzle velocity for a typical PCP.... Keeping the valve open after that can add little to the power, but it sure does use up air in a hurry....

Bob

[Cal]

Bob  and all

The relationships to sonic choking is the heart of this thread.

Do you feel that the additional volume, that is is part of the pells movement up the barrel, contributes some other event sequence than that of a stopped barrel?
Imagine designs with large transfer port volumes.
That is,  if the volume behind the pell is made tenfold as the pell moves out,  will the situation at the open valve change materially?  I think not.  The compressed gas still rushes into the low pressure volume until equilibrium, with the pressure increasing rapidly at the base of the pell even as it moves away.
Choking will still  manifest until the pressure behind the pell is .5 Pres.   The latter of which,  Is about the entire time. This consistent with your comment that the firing event might be best considered as a constant pressure condition.  Has that changed?  When does the pressure rise cease, and pressure fall dominate the event?  I suppose that is the crux.  'Using the power source expansively    Are we re-investigating the steam engine?

The comments regarding heating and "sonic horizon" are made to be inclusive of details and views.  If there were no pell at all,  how would "expansive cooling" play out?  With  frictional drag acting to limit flow and support expansion....   All the while inertia of the barrel gas volume in  opposition, requiring  pressure via compression to achieve the end result.   Quite a dynamic isn't it?

Question?  how can Expanding/Cooling air provide sufficient pressure to accelerate the pell down the barrel?  Does that match internal ballistic calculations?  (I contend it does not )     Perhaps that will be a difficult data set to determine.
 I contend that the volume behind the pell is filled and remains filled from the reservoir until the valve effectively closes!   (to some high level anyway)  ;-)     It's all a matter of time.
 Will a considered pressure vs displacement plot ever go below .5 Pres after filling and prior to a "typical valve"  closing?   A dump valve with a large volume behind it being one extreme,  (big bore tech!) ,   with a light strike at the opposite extreme.

Regarding your comment of "a few pounds force".  There have been observations posted here and elsewhere of trials based on pell sizing of near ten pounds force to break away condition.  The maths will tell the tale. ( 200+  psi?  Not 3000,  but still many times over 1 bar.)

Your observation regarding "keeping the valve open" confirms that "sonic choking" at the valve on closing has little to do with shot cycle.  But there remains an issue of such occurrence at the restriction of probe and port etc. .  Can there be significant differences between "straight through" designs and the more common?
There are no probes in the Evanix AR6 series revolver design,  and I have not noted any wild divergence of performance from those and "regular" designs.
Perhaps there is an avenue of exploration in flow smoothing, without specific consideration for "choking" .  It still would be nice to add the mass velocity to the static pressure to obtain the sum of the effect. 

Cheers

Cal

[rsterne]

I see a huge difference between craming air into 1/2 cc or the entire barrel, perhaps you do not.... I would suggest that pressure rise ceases before the pellet has moved very far at all, and pressure fall dominates the event for 99% of the shot cycle.... I am of the opinion that the valve open part of the cycle is mostly Isothermal (overall, disregarding local, momentary heating in the transfer port for ~0.00001 seconds) because the reservoir volume is (usually) so large (compared to the volume behind the pellet), and I feel we are dealing mostly with flow at nearly constant pressure behind the pellet during that phase.... Once the valve closes, however, it makes sense that the expansion phase is mostly Adiabatic, or something between that and Isothermal.... I have measured pellet breakaway forces of 2 lbs. and less for many pellets, and sliding friction in the order of 1 lb.... It can be much higher for a bullet that is too tight, of course.... For sure 100 psi (from a shop compressor) is PLENTY to fire a pellet from a barrel at quite considerable velocity, likely even 10-20 psi.... I think that the choking that occurs while the poppet is nearing the seat (and it will) does little except square off the end of the air pulse, just like choking at the beginning does (see diagram post #44)....

Beyond that, I find it exceedingly difficult to navigate your posts, perhaps I am just not smart enough.... You certainly manage to cram a lot into them....

Bob

[rkr]

This might be of interest. Two double sound tracks from the same gun. Upper two tracks with HDD and lower ones without. The upper of those two tracks measures noise at the muzzle while the lower measures noise at the action. You can see the hammer released and accelerating, hammer hitting the valve, air bursting in to barrel and blasting out, valve hitting the hammer etc. Up to your to say what's what but it's rather interesting as it shows time milliseconds and should give you an idea of how long valve stays open.

[Cal]

From an earlier post by Jim regarding time:
[clip from up page]
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.[end]


The pell will only begin to move while the pressurized gas fill  could traverse > 250 mm   displacements. (10 X ~=1 inch, Even more with the Mach above 400m/s in 200 bar air.)
Lloyd's internal ballistics plots suggest a pell translation of < 60mm during the entire valve open event (.002 sec) under some conditions.

Effective expansion should only take place after the valve is shut again,

[Jim_Hbar]

One point that perhaps isn't fully appreciated here, regarding flow through a nozzle/orifice, is the fact that pressure is lost for any amount of flow...  So I dug through some reference material and pulled the equations and plotted a few graphs.

I normalized the calculations, so they are all representative for any pressure or orifice.
100% Pressure = Inlet Pressure.
100% Mass Flow = Mass flow when Choked.
The Green line I call "Q'xPout" has a close relationship to "available power". (Energy/time). - The green line is simply the product of "%-Outlet Pressure" and "%-Mass Flow". 

The first graph shows Mass Flow as a function of Pressure Drop.  The Outlet Pressure (1-dP) is plotted for reference (Blue line)



The second is the same equation flipped around, with Mass flow as the independent variable, and Outlet Pressure as the dependent.



Hope that helps.

(Post edited to make the colors consistent between graphs, correct the first graph title, and change what I had been calling power )

[rsterne]

Jim, I'm confused.... If I understand correctly, if the outlet pressure equals the inlet pressure you have no mass flow, and hence no power.... As the outlet pressure drops, you get more mass flow and more power, but once the outlet pressure drops to 53% of the inlet pressure, the flow chokes and no further increases in mass flow can occur.... I would think that the power would peak before that occurs.... Then as you further reduce the outlet pressure, with no further increase in mass flow the power is dropping, and reaches zero when the outlet pressure reaches zero.... I think I've got all that.... Wouldn't that mean that the peak power would occur when the outlet pressure is greater than 53% of the inlet pressure?.... I'm looking for that on the graphs and I don't see it on the first graph.... The way I'm looking at the first graph, it seems that the x-axis if labelled backwards if it represents the outlet pressure as a percentage of inlet pressure.... ie 0% and 100% should be reversed.... That would put peak power at the point where outlet pressure is about 70% of inlet pressure, and pretty flat from 60-80%, which makes sense to me.... The second graph makes sense, and I note that the power peaks at 80% of the mass flow, which agrees with the first graph.... On that graph, the outlet pressure at that power peak is about 70%, which also makes sense to me.... Is the x-axis of the first graph backwards?....

Bob

[Jim_Hbar]

Yeah, I was being sloppy - but what can I say, it was late!!   Fixed the graphs and edited my post

I would think that the power would peak before that occurs....

The green line does!    I've decided to stop calling the green line "power"..  The line is an interesting observation, but I'm not sure how it actually relates to airguns.

The second graph deals with the first 47% (1-53%) of the same data represented in the first graph.. 
Since once the downstream pressure reaches 53% of the upstream pressure, and Mass flow reaches maximum, Pout can no longer be a function of MassFlow.

Again, this is just nozzle flow, and free flowing air.  Not a pipe with a cork in it!

In Hydraulics -
Given Hp = Horsepower, Q= Flow in USgpm, and P = Pressure in psi. results in Hp=(P x Q)/1714 at 100% effy.
So there, Power is proportional to Pressure times Flow - and since the fluid is incompressible, the Flow is both mass flow and volume...  They are the same thing. 
In compressible flows, not so much.........

[rsterne]

The second graph deals with the first 47% (1-53%) of the same data represented in the first graph..

I kind of knew that intuitively, but thanks for pointing it out.... Whether you call it "power" or not, it peaks when the pressure drop is about 30% (ie outlet pressure is 70% of inlet pressure).... and the choke occurs at 47% drop (outlet 53% of inlet), at which point the "power" is only down about 10% from ITS peak value.... From your spreadsheet, the "power" is 53/59ths of the peak when it chokes.... THAT may be a workable figure for the reduction in the acceleration being applies to the pellet when the flow JUST chokes, instead of the 47% drop looking at the pressure alone....

Bob

[Jim_Hbar]

Maximum MassFlow at max. available pressure is similar to what is defined as "Corner Horsepower" in Hydraulics (max. torque at max. speed)..  A condition that is never obtained, but it defines the boundary's of the maximum performance envelope.

Messing with the spreadsheet to get more decimal digits, the maximum Q'xPout occurs at 83.5% of Massflow, when Pout is at 71% of inlet pressure (29% pressure drop).

The pressure and Massflow lines cross at 76.27% - another interesting point.

If the units of that green line were corrected, and it was truly "Power", (and the x-axis expressed in units of time), then I believe that the area under the curve would be the energy that made it through the port.....

Since I regard "efficiency" to be the most important factor, I'm happy just staying away from the choked condition!!

BTW, the design progresses slowly.. I'm not a very good CAD pilot...

[Cal]

.. I think that the choking that occurs while the poppet is nearing the seat (and it will) does little except square off the end of the air pulse, just like choking at the beginning does (see diagram post #44)....

Bob

Bob,  What mechanism do you feel provides the 2:1 pressure ratio across the valve seat required to achieve choked flow  during the valve closing event?   Inertia is the only thing that comes to my mind.  And I can't see that occurrence. 

Jim
With your comment:

"Since I regard "efficiency" to be the most important factor, I'm happy just staying away from the choked condition!!

Have you designed out choked flow conditions on poppet valve opening?   by what mechanism of efficiency?

[Bill G]

Due to another project, I haven't given my internal ballistics model the attention that I had been pouring into it.  The sonic choking aspect of this does have influence on the performance, I have no doubt.  I think the better part of the picture is the avoidance of sonic choking for a combination of power and efficiency.  Then again, It may be usefully applied at lower power yet consistent unregulated shot strings, used to flatten the string perhaps.  Either way, Being able to know when and where it will influence a tune is the reward.
I do know that Bob has demonstrated very accurate predictions using Lloyd's model.  With my model, I am able to predict shot count, ending reservoir psi, and shot to shot deviation.  The valve duration is the part that I have problems with. In that, what I mean is, it has proven very difficult to get the calculated valve duration from hammer strike to match calculated flow duration.  Still wrestling with some theory here but I suspect that it has to do with the choking of flow in the beginning and end of the valve cycle.  What I do know, based on lots of trial, is that my predicted shot to shot velocities are within 1-2.5% of actual shot string, depending on pellet weight and and FPE being developed.  This is likely due to varying degrees of choking perhaps.  Any way you go about it, that small % of difference is darned small.  The model never has a peak velocity as high as what occurs in the string and the peak is where the largest %  deviation is.  There are a lot of measurements that have to be known and as with anything, garbage in, garbage out.  If I could remember how to screen shot, I'd post a pic of it.  IT is very busy and may cause some eyes to cross.  Perhaps one of these days it will be worth publishing but for now, I'm not satisfied with it enough to let it out.  I have over 5yrs worth of R&D and it has facilitated me in lots of discovery and understanding, as little as that may be.

In short (too late), recognizing choking to minimize or use it, is the goal as I see it.  I accept that it is there and fully understanding it may very well be an exercise in futility.  At least for me. 

Bill

Bill         

[rsterne]

Bob,  What mechanism do you feel provides the 2:1 pressure ratio across the valve seat required to achieve choked flow  during the valve closing event?

You are correct, the only way the flow can choke on closing is for there to be a choke further along in the system that disappears (no longer a sufficient DeltpP) from the valve closing and the section between expands into the much lower pressure in the barrel, moving the choke to the valve seat.... OR if you are talking a dump shot where the valve is still open with no cork in it and the barrel is evacuating.... I struck out that statement in the post above because it is not the "norm"....

As an aside, in working on my BAM B-51 I just made a change from a 0.166" (76% boresize) transfer port to a 0.125" one (58% boresize), and at the peak of the shot string at 2400 psi, the velocity only dropped from 995 fps to 960 fps with 18 gr. JSBs.... despite having only 57% of the area of the larger port.... with no other changes to the gun.... The small port should choke at less than 450 fps airflow (pellet) velocity in the barrel as the area is 1/3 the bore area.... so obviously we (or at least I) have a lot to learn....

Bob