Choked flow in an air gun

[lloyd-ss]

This topic rose its ugly head again in a thread of Bob's, and was hijacking that thread a wee bit too much so I started this new topic for it. Totally geek stuff, totally esoteric, probably not good for much more than a mind exercise for the sicker ones among us.
This was the original location:
https://www.gatewaytoairguns.org/GTA/index.php?topic=128036.0


I think I have most of it right, but discussion is needed!

We've been discussing this topic on and off for years, and I finally realized yesterday that we had the application of the concept wrong. At least, I am 90% sure of that. We (at least myself and Bob) had been thinking  that if the airflow reached Mach 1 in the T-port, flow would drop by approx 50%. What is actually the case is that if the pressure drop across the port is more than 48% of the input pressure, then the flow Velocity will be limited to Mach 1. There is no big drop, or burp, or anything like that. The velocity stagnates, but the mass flow (weight of air moving thru the port can still increase, and then expand and increase velocity on the other side.

So, here is my entry for today. A few excerpts from the 6mm thread are quoted below.
Lloyd
----------------------------------------------
April 11, 2018
I have been fumbling thru the math on this choked/not choked flow situation and thought I’d try a real-world example to see if it makes sense. I’ll be using my internal ballistics spreadsheet, but will also be cross checking it with some mass flow calculations to look for correlation or lack thereof.

The example I’ll be working with is a .25 cal, 33 gn, 3000 psi, 300cc tank, 24” barrel airgun, with full bore size porting (.25” dia minimum).
The gun in this example shoots the pellet at (all numbers are rounded slightly) 1200fps, 105fpe, air efficiency of .68 (meaning, it uses a lot of air), total psi drop in the system after the shot is 121 psi, air used 153 standard cubic inches of air. This configuration was chosen to simulate a gun that would need to flow a lot of air and possibly run into a choked flow situation.  The spreadsheet simulation shows that the valve stays open approximately 1.9 milliseconds, and closes when the bullet is half way down the barrel (12”).

The principle of choked flow says that if the pressure drop through a flow restriction (like a valve or T-port) is greater than about 48%,  the flow will choke, which means that the flow thru the orifice will become stuck at Mach 1 and cannot flow any faster until the pressure drop decreases to about 30%, and normal flow an then resume. In other words, if you have 3000 psi entering the T-port, and the T-port is tiny enough that the pressure coming out is only 1560psi, then the flow will choke and the velocity thru the T-port will be stuck at Mach 1, which is about 1120fps. Even though we are talking about psi on the one hand, and fps on the other, the problem can be solved.

Is there choked flow in this example?
It’s actually not too difficult to figure out, given the info that we already have. The pellet travel in the barrel is divided into 2 phases. Remember that the entire time in the barrel, the pellet is acting like a cork and is causing back pressure that is actually the force that accelerates the pellet out of the barrel. The first phase is when the valve is open and the air is flowing thru the valve and T-port, which are both restrictions, and therefore, possible choke points.
Let's look at the simpler phase, first.

After the valve closes-
The second phase is when the valve closes and all the air is trapped between the pellet and the valve, but it keeps expanding to accelerate the pellet out of the barrel. During this phase, because all we have is air expanding inside a straight-walled tube, with no restriction anywhere, by definition, choked flow cannot occur.  There will be  pressure and velocity gradients within the barrel because the pellet is still being pushed forward. The pressure will be greatest back near the valve (because it is stationary) and the pressure will be lowest  right behind the pellet (approximately). Remember, air can only flow from a high pressure region to a lower pressure region, but the pressure differential does not have to be much to cause significant flow. Think of how fast air rushes out of a tire after you take out the valve stem with only a 30psi differential. So, the pressure is lowest right behind the pellet, but because the air is expanding , the VELOCITY of the air right behind the pellet is the highest, and will increase to the actual MV of the pellet. Even if this velocity is well above Mach 1, the flow after the valve closes, and in the main part of the barrel, can not choke.

Before the valve closes-
We’ve already stated that the flow could possibly choke if the pressure differential (pressure drop) through the T-port is 48%. So, is this going to happen? Calculations are required, but because almost all formulas and calculators are based on air flowing out of an OPEN tube, rather than one with a cork in it, we have to approach this in a round about way.

Here is my approach. Based on the output from my internal ballistics spreadsheet this shot used 153 standard cubic inches of air, and the valve was open approximately 1.9 milliseconds. Based on pressure readings , the amount of air used can be validated, but the open (dwell) time is a calculation and may, or may not, be correct. Let’s say the flow thru the valve can be averaged, so we have 153 cuin in 1.9 millisecond. So the big question is, what will the pressure differential across the T-port be to flow this volume of air? The calculator that I am using requires standard cubic feet per minute (scfm) so we convert the 153 cuin/1.9 millisec to scfm, we get 2,800 scfm.  That is a tremendous amount of airflow, but it is at very high pressure and only for an instant.

Can the valve flow that much air, or will it choke? Remember, this is an inefficient airgun (.68cuin/fpe) shooting at very high power, so we are looking at a questionable situation.

Here is the calculator I am using. You can see the 2 decision blocks in the formulas with the top section being non-choked flow, and the bottom section being for choked flow. This is for flow thru an orifice, but you can go to advanced options and change the discharge coefficient if you wish.
https://www.tlv.com/global/TI/calculator/air-flow-rate-through-orifice.html?advanced=on#

Well, it looks like with this high powered inefficient gun, even with full bore size porting, we DO have choked flow. With 3000 psi input, your output pressure (on the output side of the T-port) would have to stay above 1560 psi to avoid choked flow. But at that pressure drop, the flow is only 2,086 scfm, but we needed 2,800 scfm. So the valve and T-port, even with full bore porting, can not support the required flow rate without choking…. some where, at some time. So what is happening? Well, let’s take a few guesses. When the flow chokes, the velocity doesn’t drop in the port, it just doesn’t increase anymore (as I understand it). Usually, the first major restriction point (and a restriction point is needed to choke the flow) encountered by the air, is at the valve poppet, and then the T-port, and those are turbulent areas anyway, with all sorts of messy airflow. We know for a fact that 153 cuin of air had to flow thru the valve, so my best guess is that the valve actually stayed open longer than the estimated 1.9 msec. Is that a problem? Somewhat, because it limits the fill RATE into the barrel. The bullet doesn’t accelerate as fast and it needs more time and a longer barrel to reach top speed.

So, in this particular case, choked flow probably occurred.
This is just the tip of the iceberg, and there is much more to come.
Lloyd


Here are a few quotes from where this topic used to be.
----------------------------------------------

Bob,
Given the fact that you were using a 29" barrel and I was using a 46" barrel, if we extrapolate the velocity in your gun to 48", the velocity is about 2305fps, quite a bit faster than my 2162fps. But it also seems that the difference in projectile weight, 1.8gn vs 7.7gn could account for that difference in velocity. In other words, well done Bob.

It appears that your 1.8gn BB might actually be leading the front edge of the expanding air in the barrel, almost like surfing.
All of these velocities are well above Mach 1, so what about choked flow? How is it limiting the velocity... or is it limiting the velocity?

After some serious reading, I believe that, just as the 1650fps  velocity limit was the result of the misapplication of a physics principle, we have been misapplying the idea of choked flow inside an airgun. Please correct me if I am wrong, BUT: We have been saying that if the velocity through the most restricted passage within the flow path exceeded Mach 1, the flow would become choked.  Actually, that is false.  What really causes choked flow is the pressure drop across the restricted section, and a pressure drop of almost 50% is required to cause choked flow. I believe that the only time there will be a pressure drop that great is the instant (a few micro seconds) the valve poppet lifts off the seat, and the final instant as the poppet closes.

Here is my reasoning. Before the shot, the bullet is wedged into the breech end of the barrel just like a cork. The bullet has mass that must be accelerated out of the barrel. As soon as the valve opens, the air blasts past the valve  poppet and starts to stack up behind the bullet. As soon as the air starts to stack up, the pressure differential within the system becomes very low (less than 10%, maybe?), and certainly nowhere near the 50% needed to cause choked flow. As the bullet starts to move, it is still acting like a cork for the expanding air, and the pressure differential is still very low because the air is building up faster than the bullet is accelerating.  That magical 50% pressure drop never occurs within the system, and therefore choked flow does not occur, even though the velocity of the bullet and a major portion of the air column greatly exceed Mach 1.

Consider this as additional proof.  Given a gun operating at 3000psi with .25 cal and .25" passages, a 20% pressure drop across the valve could produce a flow rate of 2000scfm, which is 57,600 standard cuin/sec, or 57cuin/millisec. Considering the fact that most of our guns will produce about 1 fpe/cuin, and the valve open time might vary in the 1.5 to 5 millisecond range, that 20% pressure drop across the valve is probably quite adequate for a .25 cal system. Now, if the pressure drop goes to 40% (as with a very light projectile) the flow rate increases to about 74 cuin/millisec. So even though the pressure drop doubled, the mass flow did not. But the real point is that we are almost always, IMO, operating safely below the that 50% pressure drop that would initiate choked flow. Therefore, no choked flow!

Is this what is really happening? It certainly makes a lot of sense and explains what our empirical data demonstrates.
Lloyd

WOW, JUST WOW !!!

just as the 1650fps  velocity limit was the result of the misapplication of a physics principle, we have been misapplying the idea of choked flow inside an airgun.

Lloyd, I think you may have a SOLID REASON for the lack of choked flow.... insufficient pressure differential.... This may be a chicken-and-egg problem and we have been looking at it from the wrong end of the chicken !!!

We have been saying that if the velocity through the most restricted passage within the flow path exceeded Mach 1, the flow would become choked.  Actually, that is false.  What really causes choked flow is the pressure drop across the restricted section, and a pressure drop of almost 50% is required to cause choked flow.

We have been saying "well the flow is supersonic, so it must be choked, which causes a 50% pressure loss".... when in fact we SHOULD have been saying "nowhere in the system (with one exception below) is the pressure differential approaching 50%, so even though the flow is supersonic, it is NOT choked".... BRILLIANT, MY FRIEND.... SIMPLY BRILLIANT....

The exception I mentioned above is when the poppet is CLOSING only, just before the poppet touches the seat.... At that point the flow rate is high (as is the velocity of the pellet and air column), but the area under the poppet is decreasing, and the pressure differential increasing.... When it reaches 50%, the flow chokes for a few microseconds before the valve shuts.... At the other end of the shot cycle, when the valve is opening, there is no comparable choking because all the air is doing is filling the dead space between valve seat and pellet (which is stationary), so there is no real flow volume or air velocity, beyond the random vibration of the air molecules, so no choking....

I was playing with your two spreadsheets last night (the unchoked and choked versions), and they both underpredict the velocity of my shot, with the choked version predicting a lower value.... I think you are correct that in the case of this ultralight BB, it is "surfing" the front of the moving wave of air, which is expanding away from the valve instead of being contained inside the barrel by the mass, inertia, and friction of the projectile.... There is no question in my mind that the difference between my 1.8 gr. BB and your 7.7 gr. "pellet" is the big reason for the ease with which I broke 2000 fps.... Let's face it, it doesn't get any easier than what I did.... 

Bob

[Sfttailrdr46]

I am watching this thread because I find your experiments fascinating.

[lloyd-ss]

I am watching this thread because I find your experiments fascinating.

Thank you Don.  This one is really tough to wrap my head around.

[Motorhead]

As I read the above paragraphs, it brings back my past on being a 2 stroke engine tuner and all the porting / timing dynamics such as how in the heck can an engine that functions on the principal of pressure differential run at 30,000 rpm doing intake & exhaust cycles ACTUALLY moving air threw the engine at 500 cycles per second !!
All the tuned pipe dynamics of pulse waves, pressure fronts and how pressure pulse amplitude changes with cross sectional area of ports & passages.

DEEP STUFF and my minds sorta hurts thinking about just how deep the rabbit hole go's on such subjects !!

Sorry for the wandering off subject ...

Scott 

[rsterne]

Good thread, Lloyd, I'm sure it will bog us down and keep us out of the shop for quite a while.... *LOL*.... First, we need to look at the definition of Choked Flow (this from Wiki)....

Choked flow is a compressible flow effect. The parameter that becomes "choked" or "limited" is the fluid velocity.

Choked flow is a fluid dynamic condition associated with the Venturi effect. When a flowing fluid at a given pressure and temperature passes through a restriction (such as the throat of a convergent-divergent nozzle or a valve in a pipe) into a lower pressure environment the fluid velocity increases. At initially subsonic upstream conditions, the conservation of mass principle requires the fluid velocity to increase as it flows through the smaller cross-sectional area of the restriction. At the same time, the Venturi effect causes the static pressure, and therefore the density, to decrease downstream beyond the restriction. Choked flow is a limiting condition where the mass flow will not increase with a further decrease in the downstream pressure environment while upstream pressure is fixed. Note that the limited parameter is velocity, and thus mass flow can be increased with increased upstream pressure (increased fluid density).

You argued yesterday that thinking about this LITERALLY from the above definition may be incorrect, and I think that is the case because we are not dealing with a system where the downstream pressure and density is dropping, because of the "cork in the bottle" effect of the bullet in the barrel, which does not allow the downstream pressure to drop to the point where the flow chokes....

I had a look at the calculator you linked, and it seems like the Discharge Coefficient is the big unknown.... the default is 0.7, but what happens if we allow that to be 1.0 (the maximum) because of the unusual conditions inside our barrel.... Then the flow rate at 1585 psi (3000 x 0.5283) from the calculator becomes 2974 SCFM, and the flow is not choked.... In fact you can get your 2800 SCFM required and still have a downstream pressure of 1870 psi.... In addition, I tried doubling the orifice size and dividing the pressures by a factor of 4 (at the point where choked flow occurs, P_out = 0.5283 x P_in), and the flow rate stays the same.... Therefore that calculator does not take into account the increase in the speed of sound at high pressure.... At 3000 psi Mach 1 in air is 1360 fps, not 1126....

Even if you reduce the downstream pressure to only 1870 psi, it still causes us problems with our spreadsheet.... there is not enough pressure to provide the acceleration we are seeing in some cases.... That is the problem every time we try and work choked flow into the spreadsheet.... I haven't looked at this recently, but I did come across an old graph I did showing the Maximum Mass Flow Rate through a 1" bore, which I arrived at by multiplying the air density times the bore area times the speed of sound at whatever pressure.... I then reworked the units to those in this graph....

Here is the calculation for the above at 3000 psi for a 1" bore....

Air density = 238.6 kg/m^3
Speed of sound = 414.5 m/sec
Bore area = (0.5^2) x PI = 0.7854 sq.in. = 5.067 sq.cm. (there are 100 x 100 = 10,000 sq.cm. per m^2)

Mass of air moving through a 1" bore at Mach 1 at 3000 psi = 238.6 x (414.5 x 5.067 / 10000) = 238.6 x 0.2100 = 50.11 kg/sec.
Checking the units we get.... (kg/m^3) x (m/sec) x (m^2) = (kg/sec).... just as it should be....

I did this for various pressures, and then converted for the graph by taking (50.11 x 1000) / 3000 = 16.7 g/sec/psi to show how the mass flow rate varies vs. pressure.... It is not a constant because of the VanDerWaals effect and change in Mach 1 with pressure....

Using that data, at 3000 psi we have 16.7 grams per second, so for a dwell of 1.9 mSec and a bore of 0.25" (1/16th the area of a 1" bore), that works out to (16.7 x 3000 x 0.0019 /16) = 5.95 grams of air.... (double-checking the math, 50.11 kg/sec x 1000 g/kg x 0.0019 sec / 16 = 5.95 grams).... At 3000 psi (density 238.6 kg/m^3) that works out to 25 cc of HPA.... or in SCF (density 1.205 kg/m^3) it is 4.94 litres (300 std. CI) or 0.174 CF.... which averaged over 1.9 mSec is (60 x 0.174 / 0.0019) = 5,495 SCFM....  Thus, based on how much air mass could be moved through a .25 cal barrel at 3000 psi at Mach 1, we are only at about 51% of that value.... Of course the peak mass flow is not the same as the average, so maybe the flow might choke just before the valve closes?....

I realize the above is not the "normal" way of calculating mass flow through an orifice, but maybe it is a valid way of looking at the problem for our situation.... You can visualize it by thinking of a mass of air at 3000 psi travelling through a 1" pipe at Mach 1 at that pressure.... In that case, there would be 50 kg. of air moving past a given point in one second.... If the airflow is limited to Mach 1 (and we can even ask why it should be), then is that not the maximum possible mass flow rate?....

Bob

[rsterne]

Here is another calculator, from the same site.... airflow through a pipe.... https://www.tlv.com/global/TI/calculator/air-flow-rate-through-piping.html?advanced=on

If you go to "advanced" and specify a 1.00" ID pipe, 3000 psig @ 68*F, and 414.5 m/sec (Mach 1 at 3000 psi).... you get 12.6018 m^3/min.... The density at 3000 psi is 238.6 kg/m^3, so that is (238.6 x 12.6018 / 60) = 50.11 kg/sec.... That is exactly what my calculations above show.... so if nothing else, my math is correct...

Change the ID to 0.250" and you get 0.7876 m^3/min.... and if you set the "Normal" box to SCFM you get 5316 SCM.... 
Drop the velocity to your 1200 fps, and you get 4690 SCFM.... way above your 2800 average required.... so according to this calculator, you can definitely "flow" enough air through the bore to do the job.... Considering that the pellet is travelling much less than 1200 at the instant the valve closes (actually about 1000 fps), I don't see any problem.... Flow rate at 1000 fps is still 3909 SCFM....

Note that no "warning messages" show up in the calculator to indicate that the pressure or velocity are "off scale" for the calculator.... This would lead credence to the idea that we are not working with an "orifice" in the case of a PCP with bore-area porting throughout.... but simply flow through a pipe.... 

Bob

[shorty]

Posted to follow thread.

If it helps, and please ignore if I throw off the mojo:

I have always tried to figure this out as well but could only come up with fudge factors. Interestingly enough, a colleague of mine "Purdue guy" mentioned about incalculable pressures >1000psi through orifices.  Something about how pressure changes through an orifice and is not predictable "pressures/flow".

I have always used my spreadsheet to calculate fpe with a given porting size (the choke point). Unfortunately, I can't do the physics calculations so I used actual values from the gun over historical data.
What I notice is that the larger the porting, the closer to actual reservoir pressure across the port when calculating PSI behind the projectile.

The pressure Delta "well that's what I called it".

Here's my porting with corrections "fudge factors" to calculate the MAX force "behind the projectile" before the poppet closes".
port      correction (fudge factor)
0.14      0.08254
0.16           0.10960
0.19          0.12859
0.21          0.15296
0.23          0.17599
0.26          0.19901
0.28          0.22204
0.30          0.24506

What I find interesting is that the "choking point/fudge factor" If you put it in a percentage, you get the actual pressure "MAX-pressure blast" that the projectile will see.

Like I said early, please disregard if I am out in left field. Mainly posting to follow.

[rsterne]

Welcome Tim.... I'm a bit confused by your chart, since the port diameter goes up to 0.30 (inches?) are you talking .30 cal or what? .... You are basically correct that as you make the port smaller the projectile sees less force pushing on it, which means less pressure because of reduced airflow caused by partial choking (ie a pressure differential) showing up across the restriction....

We first have to understand what happens when we have no restrictions (full bore-area porting throughout).... before we can start trying to quantify what happens when we start restricting the flow with a smaller transfer port.... I have done a LOT of testing and in practical terms I have found that the final result (FPE in the pellet) is pretty close to proportional to the transfer port diameter (as a percentage of caliber).... It's not quite linear, but pretty close, for dump shots where the valve is open until the pellet leaves the muzzle....

Trying to calculate what is actually happening to produce that drop in FPE is much harder than it seems.... The shorter the dwell, and the earlier the valve closes as a percentage of barrel length, the less effect we see from a smaller transfer port, because the projectile spends more time being accelerated by the expanding air in the barrel when the valve closes, and less time being pushed by the restricted flow through the port....

Bob

[shorty]

I am not sure dwell is influencing as much as pressure difference unless barrel length plays a large role which we see already with volume calculations.

Like I said, I am just following and do not have the physics calcs to back anything up.

[rsterne]

The dwell affects where the pellet is when the valve closes.... Short dwell means less acceleration during the "flow" stage (valve open) when the transfer port makes a difference.... and a greater percentage of the final velocity and energy coming from the expansion stage after the valve is closed.... As such, TP diameter must have a greater influence on a "dump shot" than on a very efficient one with ultra-short dwell....

Bob

[shorty]

I hear ya Bob. I really can't contribute too much as I don't fully get it either but, I have a feeling dwell doesn't do it like that as much as the MAX air pulse (regardless of air volume) "to a point".

The way I think about it is that you can have a really low efficiency (long dwell) same lift or high efficiency (short dwell) with the same lift.

Just following, and really interested to see what you guys come up with. It's been a long time that a post comes up like this and they are usually my favorites.

[lloyd-ss]

Been outside all day so just getting a chance to reply.  Will add more in a while.
Bob, I agree that the barrel bore will flow plenty of air to get the job done, IF you can get all of the air into the barrel fast enough.  The flow through a pipe is really for the perfect situation in the airgun, but the awkward path that the air has to take to get to the barrel bore is where the problem is. Even with full bore porting, the air has to get thru the valve, as it opens and closes.  Add a small T-port and there can be an opportunity for choked flow. Also, as the air leaves the reservoir and enters the valve, with a poorly designed transition, problems can occur. Maybe in a full bore porting situation the chance of choked flow is reduced or eliminated, but most guns don't have full bore porting.
More investigation to do.

[shorty]

I am sorry I didn't answer your question.

The table doesn't have anything to do with caliber and it is in inches for port and correction factor as a percentage.

It is the smallest air passage with a "correction factor" to calculate the (true) max force behind a projectile.

It's a heck of alot better reading what you guys come up with so keep up the great work guys.

[rsterne]

Lloyd, I think the thing to remember is that there WILL be choked flow just before the valve closes in every PCP, because the curtain area under the poppet approaches zero at the instant the flow is moving the fastest (during the valve open portion).... and at the same time there is a pressure differential across the head of the poppet developing.... When that reaches 47% drop, the flow chokes.... For most modestly tuned PCPs, that is only the last few microseconds as the valve closes....

Whether or not the flow chokes downstream of that point earlier in the shot cycle is the question.... I think if the ports are all full bore area the answer is no, unless the pellet velocity before the flow at the valve seat chokes exceeds Mach 1 at the barrel pressure involved.... So, for full bore area porting and subsonic muzzle velocities, no choking.... If you insert a restricted transfer port, then there is a venturi effect at that point, and you get a pressure drop which is greater the smaller you make the transfer port.... Eventually, if the relationship between the transfer port area and the bore area is small enough, compared to the pellet velocity, then you can get choked flow.... For a constant valve dwell, as you make the transfer port smaller and smaller, towards the end of the valve cycle the pellet sees less and less pressure, so achieves a lower velocity.... This reduces the flow velocity through the transfer port, and delays the choking, but eventually you get to the point the pressure in the barrel is half the valve/reservoir pressure, and the flow chokes.... If you go even smaller on the TP, that occurs sooner in the cycle, and the velocity and energy fall more....

It is trying to come up with a mathematical model for the pressure at the pellet that relates to the transfer port diameter/area that is the challenge.... We have pretty good empirical data.... we just have to come up with a model for it....

Bob

[lloyd-ss]

As I read the above paragraphs, it brings back my past on being a 2 stroke engine tuner and all the porting / timing dynamics such as how in the heck can an engine that functions on the principal of pressure differential run at 30,000 rpm doing intake & exhaust cycles ACTUALLY moving air threw the engine at 500 cycles per second !!
All the tuned pipe dynamics of pulse waves, pressure fronts and how pressure pulse amplitude changes with cross sectional area of ports & passages.

DEEP STUFF and my minds sorta hurts thinking about just how deep the rabbit hole go's on such subjects !!

Sorry for the wandering off subject ...

Scott 

Scott, I agree with you about the difficulty of comprehending the speed at which those events can take place in a small high speed engine. And a combustion event 500 times a second? It seems impossible.    Its like trying to understand the vastness of the universe, or looking at the leg of an almost invisible insect under a microscope and wondering how something that tiny can function at all. Way out of my comfort zone.

I think that's part of the problem of trying to figure the fluid dynamics of the PCP out. For 99.9% of folks its probably a "who cares?" type of question. All this concern and effort is certainly self inflicted. But we are better people because of it, right?? 

[lloyd-ss]

Bob, This is all very difficult to comprehend, and the lack of understanding and the semantics of the new or unfamiliar concepts don't help the situation. We are on the same wave length and are probably in 95% agreement, but describing the actual events taking place is difficult, although I like your descriptions better than my own, LOL.

I am going to step back from the theoretical details (the trees) and try to look at the big picture (the forest).

Quantifying the choked flow, if it occurs, is difficult. During the process of tuning a new gun and using all of its adjustability to go from minimum power to maximum power, I have yet to see the test data velocities change in a manner where I could honestly say, "Yup, look at that velocity change, choked flow is happening." We can tell when we fall off the regulator, or add more spring, or use a lighter pellet, etc, etc., and we can often almost predict the outcome of a particular change. But a choked flow event.....I've yet to identify one.

Let's take 2 hypothetical pcps. Let's say, one like an Airforce, and one like a Marauder. Both .25 cal with same barrel length and pellet and tuned to the same velocity. Two things we can be sure of: 1) after the valve closes, both pellets will behave identically inside the barrel. The air will expand and the pellets will exit the barrel at the same MV. 2)Even though both pellets have the same MV, the point in the pellet travel when the valve closed is probably not the same for the two guns.

Given the commonality of the events AFTER the valve closes, it seems that all of the variability takes place while the valve is open. The Airforce in-line valve design seems to have a slight advantage in max power. All of the turbulence and flow restrictions and convoluted passages, whether they be choked flow or something else affect the airflow Before the valve closes. Maybe there is so much turbulence in the air passages leading into the valve, and thru the valve, and thru the T-port and barrel port, that choked flow, in the most literal (definition-wise) sense, either does not occur, or is impossible to separate out from everything else that is interfering with the flow of air that is trying to get to the back end of the pellet.

Are we back at the point of having a single "empirical adjustment factor" for each gun, along with a "new" T-port associated adjustment, and of course, the VanDerWaals density adjustment?  There is certainly nothing wrong with having an "empirical adjustment factor", and they are not at all uncommon in certain types of engineering calculations.   Flow of compressible fluids, especially when it goes thru a valve and around two 90 degree corners, is extremely difficult to calculate.  Bob, your T-port to bore relationship ought to pin a lot ot this down.
Lloyd

Edit- An afterthought- Given that the entire valve open-to-closed cycle is only a few milliseconds, I wonder if a few microseconds of choked flow is at all significant. Maybe if the flow hadn't choked, the flow through the restriction might have been 10 or 20% higher for those few micro seconds. Is that difference really relevant? (Probably sounds like I am trying to talk myself out of the choked flow enhancement to the spreadsheet.   )

[rsterne]

While I agree that the Air-Force style of valve may have a slight power advantage at the limit, I bristle every time it is called an "in-line" design.... We can call it axial flow (like a jet engine), maybe.... but the air certainly does NOT flow in a straight line, or anything like a straight line, through the valve.... The poppet is very conventional, it just happens to be inside the bottle.... The air must make two, virtually 90 deg. turns to get through between the poppet and valve seat, just like in all our other valves.... In addition, after flowing past the poppet and into the "throat", it then has to travel another serpentine path to get from there to the barrel.... Doug Nobles modded valves use much larger passages, and on a shallower angle, than the original Air-Force valves, so the path becomes more like that in your .50 cal, an "S" bend, or slalom, instead of turning 180 deg. like a conventional PCP.... but the idea that the air path from bottle to pellet is straight through is simply not true.... *rant off*....

I agree that there is so much turbulence and/or convoluted flow that it can't likely be separated from the effect of choked flow, if indeed it occurs.... I haven't seen any evidence of choked flow that shows up as a sudden reduction in the power available.... and indeed, since choked flow requires a 47% or greater pressure drop across the choke point, it gets difficult to explain the amount of power we get from the best PCPs and factor in such a pressure drop.... If we meet the conditions for choked flow, there really isn't enough pressure left to create the energy in the pellet we get, once you take into account the mass of air as well.... That is why I was so excited the other day when you talked about the "cork in the bottle" effect of the pellet keeping the barrel (downstream) pressure well above 53% of the reservoir pressure, which means that choked flow is not possible.... I still think that for 99% of our operating conditions, that is indeed what is happening....

However, what we do see is a plateau, past which we can't get any more power without increasing either the (upstream, reservoir) pressure, or the size of the restriction (generally the transfer port).... I'm not talking about the plateau you see when you plot velocity vs. hammer strike (ie lift and dwell), that is because, at the limit, the valve is open until the pellet leaves the muzzle.... with the transition (the knee) between that and the downslope occurring between that dwell and a much shorter dwell (maybe 20-25% of barrel length) where velocity and FPE are governed mostly by dwell.... I'm talking about the two obvious relationships we see between pressure and FPE, and port size and FPE.... Both are, when dwell is maxed out (and therefore no longer a variable because the valve is always open), pretty linear, direct relationships....

For a given port size, and maxed out dwell, FPE is both in theory and practice proportional to average reservoir pressure during the shot.... If instead we have constant pressure and maximum dwell, and starting from full bore-area porting, we start restricting the flow by using a smaller transfer port, we see a reduction in FPE that is NEARLY linear in proportion to the diameter of the port as a percentage of caliber.... One explanation I can think of is that we are getting a partial venturi effect, where the airflow accelerates through the restriction (lowering the pressure) and then slows again as it enters the (larger) barrel, recovering some but not all of the pressure loss (in a lossless venturi, the velocity and pressure should recover completely, unless the flow chokes).... An alternative explanation is that we are simply causing more turbulence and/or friction losses at the restriction, robbing energy that should accelerate the pellet, but if that is happening, where is it going?.... Heat?.... I don't think so....

I don't believe choking to be a sudden event, where the outlet pressure equals the inlet pressure until the flow chokes, at which point it magically drops to 53% of that.... I think it is a gradual thing that takes place as the flow accelerates, causing some pressure drop, and when that pressure drop gets to 47%, the flow chokes, the mass flow limit is reached, and further reduction of outlet pressure cannot add more flow rate.... The only way to do that is increase the inlet pressure or diameter of the restriction.... I don't think we have ever observed a pressure drop even approaching 47%.... so let's put the egg before the chicken and assume the flow (with maybe rare exceptions) doesn't choke....

Bob

[lloyd-ss]

.... I don't think we have ever observed a pressure drop even approaching 47%.... so let's put the egg before the chicken and assume the flow (with maybe rare exceptions) doesn't choke....

Bob

I agree with that!   

Very efficient discussion about choked flow. Scratch it off the to-do list.  It was almost like we had to pay THE FORUM by the hour until we reached an agreement, LOL. Hmmmmmm, I can think of places other than the forum where that would be a darn good idea, too. 
Lloyd

[rsterne]

I'm still awaiting the "Founding Member" to stake his claim....   

Bob

[shorty]

Thought this was some interesting reading:

Choked Flow:
https://en.wikipedia.org/wiki/Choked_flow

and
De Laval nozzle
https://en.wikipedia.org/wiki/De_Laval_nozzle

An interesting thing about orifice plates and "air pulse / shock wave" when comparing a piston gun to the PCP I would consider the orifice plate on a springer to be extremely small while the projectile sits on it. Although if you push the pellet forward slightly, velocity is decreased. Using the PCP, the projectile is extremely far away from the HPA side compared to the springer.

I guess the reason for me comparing or thinking of the 2 different platforms is that the springer is extremely efficient with it's HPA/volume when comparing to PCP.

Interesting about thin orifice plates:
"Thin-plate orifices
The flow of real gases through thin-plate orifices never becomes fully choked. The mass flow rate through the orifice continues to increase as the downstream pressure is lowered to a perfect vacuum, though the mass flow rate increases slowly as the downstream pressure is reduced below the critical pressure.[9] Cunningham (1951) first drew attention to the fact that choked flow will not occur across a standard, thin, square-edged orifice.[10][11"