GTA
All Springer/NP/PCP Air Gun Discussion General => "Bob and Lloyds Workshop" => Topic started by: rsterne on April 26, 2014, 03:20:46 PM
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OK, fellow GEEKs, here is something new (at least to me) to think about.... You are probably aware of the concept of "sonic choking" of ports in a PCP (or other) airguns due to the velocity of the airflow increasing through the restriction of the port.... For a given amount of air to flow through a restriction in a given time, the smaller the area the faster the flow, right?.... A while back, Steve in NC came up with a chart (which I won't use here because it's his) showing the muzzle velocity at which a given size port would become choked, based on the area compared to the caliber.... Basically, if the port diameter was half the caliber, the area would be 1/4, so the flow would have to be 4 times as fast.... Since the speed of sound in air is 1130 fps (and 917 fps in CO2), you can calculate the muzzle velocity at which the air flowing through the port must break the speed of sound, and of course it is pretty low.... For the example above (50% port diameter), the velocity would only be 1130/4 = 283 fps.... We often use ports that are 75% of the bore, so they are (0.75 x 0.75) only 56.3% of the bore area, so the muzzle velocity at which the airflow would exceed the speed of sound in the port would be 1130 x 0.563 = 636 fps.... According to Steve's chart, ports that are 75% of boresize should exhibit sonic choking above that velocity....
While I agree with Steve's math, the velocities in his chart seemed way to low to me.... First of all, we know that much higher muzzle velocities are possible, even past Mach 1, so any sonic choking must only act to reduce the efficiency (how much air gets through the ports while the valve is open), not as a "hard" limit.... The other part eluded me until last night during another discussion here on the GTA.... It suddenly occurred to me that is wasn't the MUZZLE velocity that was important to this calculation at all, but the pellet velocity inside the barrel at the moment the valve closed.... After that, there is no more significant "flow" through the ports (they are, after all at the breech end), all that is happening is that the air in the barrel and ports is EXPANDING to provide a fairly good percentage of the muzzle velocity.... Therefore, instead of using the muzzle velocity in the calculation, we need to use the pellet velocity (and hence the air column velocity) at the moment of valve closure to do our port size calculation.... Don't you love light-bulb moments?....
The best tool I have available to estimate valve dwell, and hence pellet position at valve closure, is Lloyd's Spreadsheet on internal PCP ballistics.... Here is a generic example of the output from that spreadsheet in graphic form....
(http://i378.photobucket.com/albums/oo221/rsterne/Important/InternalBallistics.jpg) (http://s378.photobucket.com/user/rsterne/media/Important/InternalBallistics.jpg.html)
Note that although the muzzle velocity (green line) is about 870 fps, at the point the valve closes (the step in the blue line), the pellet is only moving about 530 fps.... My proposal is that we should be using 530 fps (in this example) to calculate whether or not the ports are sonically choked.... Using the 75% diameter port which we commonly use, the answer is no.... as the port velocity would only be (530 / 0.563 = ) 941 fps.... However, using the muzzle velocity (870 fps) they would be.... in fact the airflow velocity would be (870 / 0.563 = ) 1545 fps.... I would further propose that we can predict the point (and dwell) at which such sonic choking would occur.... For the above example, it would be when the pellet is about 5" from the breech, where the velocity is 636 fps.... Now of course if we leave the valve open longer (increased dwell) then that 636 fps pellet velocity would occur sooner, closer to the breech.... but you get the idea....
What does this mean?.... Well probably a whole lot of things.... Firstly it means that for any given port size and pellet weight combination there will be a maximum dwell, beyond which the valve is still open when the port experiences the onset of sonic choking.... My idea is that at that point, the efficiency starts to take a dive.... Secondly, it means that once you reach that point, opening up the ports to increase the velocity at which choking occurs will increase the efficiency at those increased velocities.... Thirdly, it likely means that as the ports increase compared to the boresize, you can use more of the barrel to provide useful acceleration while the valve is open.... The limiting case would be boresize porting, in which case the velocity through the port should remain subsonic providing the muzzle velocity remains subsonic.... effectively eliminating sonic choking as a loss to efficiency....
One thing that I have learned from Lloyd's spreadsheet is how well it tracks the real world results I have observed, once you find the right values for dwell and efficiency.... It predicts things like the loss of efficiency from excessive dwell once the valve is open for more than half the barrel length.... It is that which shows up as the "plateau" when you plot velocity vs. hammer strike at a constant pressure.... IMO, we still shouldn't be using such long dwell times, they just waste air.... However, this new line of thinking about eliminating sonic choking as a loss in efficiency certainly would seem to point towards using larger ports, up to boresize.... There may very well be a (nearly) predictable minimum portsize below which we can expect a loss in efficiency for any given point of valve closure....
One other small point.... as the valve closes, and the area between the poppet and the seat decreases below the throat area, sonic choking WILL occur there.... If won't at the beginning of the shot, as the flow velocity is very low.... However, this sonic choking of the flow, in addition to the pure reduction in area as the valve closes.... will have the effect of shortening the effective dwell of the valve at the end of the shot cycle.... This may be why we continue to see small gains in power when using a throat that is a bit larger in area than the rest of the ports.... I have found useful gains in FPE at 10% more area that the rest of the ports, for example....
Bob
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OK :D Now you have me trying to visualize the shock waves in the porting, and trying to figure out how to utilize them. I do love those light bulbs, especially the 1KW ones. ;D ;D
One thing that just came to mind is boundary layer effects. How would that play into the equation? I know they play hob when turning corners, which is why blending the throat pays big time.
Anybody have a good Fluid Dynamics program? ::) ;D
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I think the point is that we should use ports larger enough to avoid the problem, IMO....
Bob
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I think the point is that we should use ports larger enough to avoid the problem, IMO....
Bopb
That sums it up nicely, until I examine your writings on applying a porting restriction to good effect. Such as the adjustable stop to leave the bolt tip occluding the port...:)
cheers,
Douglas
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ahhhhh.... but then I'm intentionally creating a restriction, taking advantage of the effect.... but I get your point.... As George Bernard Shaw once said....
"all generalizations are false.... probably including this one"....
Food for thought.... If you restrict the transfer port (or occlude the barrel port as I did).... the effect will be different at different pressures....
(http://i378.photobucket.com/albums/oo221/rsterne/Discovery/DiscoInternalBallistics.jpg) (http://s378.photobucket.com/user/rsterne/media/Discovery/DiscoInternalBallistics.jpg.html)
Note that the pellet velocity when the valve closes is lowest at high pressure and highest at low pressure.... and therefore the degree of sonic choking at valve closure would increase as the pressure drops.... However, it would start later in the shot cycle, so it would be effective for a shorter time.... Perhaps this is part of the flattening effect on the bell-curve we see with restricted ports?.... There are many conflicting things happening once the ports become choked, but the net effect of smaller ports is to flatten the bell-curve by reducing the power in the middle of the pressure range more than at the ends, that much we know....
Bob
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With reference to the Speed of Sound in HPA, as noted in this thread: http://www.gatewaytoairguns.org/GTA/index.php?topic=66866.0 (http://www.gatewaytoairguns.org/GTA/index.php?topic=66866.0) .... let's look at the above chart for the stock .22 cal Disco at 3 pressures again....
2000 psi, velocity at valve closure ~ 430 fps, pressure ~ 1980 psi, speed of sound ~ 1250 fps
1700 psi, velocity at valve closure ~ 500 fps, pressure ~ 1670 psi, speed of sound ~ 1220 fps
1200 psi, velocity at valve closure ~ 570 fps, pressure ~ 1160 psi, speed of sound ~ 1180 fps
Now let's use a stock transfer port diameter of 0.140", and calculate the port velocity.... The port area is 41.6% of the bore area, so we divide the velocity at valve closure by 0.416....
2000 psi, (430 / 0.416) = 1034 fps (not choked)
1700 psi, (500 / 0.416) = 1202 fps (nearly choked)
1200 psi, (570 / 0.416) = 1370 fps (choked)
We can see that even in the best case scenario, the stock transfer port in a Disco will be sonically choked below about 1700 psi.... I would expect that to lower the efficiency below that pressure, to an even greater degree than would be otherwise predicted from the later valve closure.... Additionally, if you increase the port size, there would be less possibility of sonic choking occurring.... A common port size for a modded Disco is 0.162", which is 55.7% of the bore area.... Looking at the 1200 psi case, we have (570 / 0.557) = 1023 fps, and since the speed of sound at 1160 psi is about 1180 fps, we would expect no more sonic choking.... It is possible this at least partially explains why increasing the port size increases the efficiency at low pressures, and also moves the peak of the shot string bell-curve to lower pressures as well, even when the dwell remains unchanged.... I realize I didn't take into account the roughly 4% increase in muzzle velocity that occurs with drilling the port to that size on a stock Disco.... but even so, we would expect the port velocity to remain subsonic to possibly as low as 1000 psi....
My records indicate that my .22 cal Disco went from 25 shots at 22.5 FPE (a total of 563 FPE) peaking at ~ 1680 psi.... to 24 shots at 24.4 FPE (a total of 586 FPE) peaking at ~ 1620 psi.... when I drilled the ports to 0.162".... In other words, the efficiency increased enough to gain 1 shot within a 4% ES (563 FPE / 24.4 = 23 shots expected).... There could well be other factors involved in this.... but normally as power increases, or pressure drops, or the valve stays open longer (because of the lower pressure), the efficiency goes down, not up.... It is possible that just the decrease in resistance to flow because of the larger ports is the sole reason for the increase in efficiency.... It is also possible, however, that if the ports are no longer subject to (or subject to reduced) sonic choking.... that could be (one of) the reason(s)....
Bob
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I think you might be getting close to explaining why Sean's .30 cal is so efficient with that big valve!
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I've been thinking about this thread and how it relates to my "What Makes Sense for PCPs" thread.... http://www.gatewaytoairguns.org/GTA/index.php?topic=57828.0 (http://www.gatewaytoairguns.org/GTA/index.php?topic=57828.0)
I started that thread with one of the two criteria being to avoid Sonic Choking, but I was using Steve in NC's formula based on muzzle velocity.... In this thread I presented the argument for using the velocity at the moment the valve closes, and of course that changes the relative dimensions for the ports I used in the other thread.... As this thread developed, it became apparent that the important pressure to look at was the regulated pressure, or the pressure at the bottom of the shot string for an unregulated gun.... This is because as the pressure drops, so does the speed of sound, and also for a given state of tune the velocity at the moment the valve closes increases....
The relationship between the velocity at valve closure and the muzzle velocity is closely related to the basic efficiency of the tune.... The sooner the valve closes, for the most part, the more efficient the shot, as the air in the barrel at that moment continues to expand, adding energy to the projectile.... Once the valve is open for more than 50% of the barrel length, the efficiency is very poor, as the additional air being released by the valve after that point adds little to the acceleration of the projectile.... Steve in NC has his theory about the "Sonic Horizon", and while I don't agree with his use of the speed of sound in his calculations (I think the molecular velocity is more important), it does predict a fall off in efficiency as the valve is open longer and the velocity increases.... He calls this the "point of valve ineffectiveness", and while he says it is a precise point beyond which any additional air released from the valve can have NO effect on the projectile, the drastic drop in efficiency predicted by straight F=ma calculations does predict a similar, if not abrupt, result....
Perhaps we should explore port size, and sonic choking, based on the idea that the valve should be closed at 50% of the barrel length or before.... and that the muzzle velocity should be 950 fps, as pushing past that loses efficiency outside the barrel from excess bullet drag due to transonic effects.... I ran various combinations through Lloyd's Internal Ballistics Spreadsheet, and got an interesting result.... To achieve a muzzle velocity of 950 fps, and have the valve close at 50% of the barrel length, the projectile is going about 770 fps at the point of valve closure.... This appears to be the case over a wide range of calibers, bullet weights, barrel lengths, and efficiency factors when using air... I didn't try CO2 or Helium, but it gives us a starting point for this "thought experiment".... If the valve closes sooner, the velocity is lower....
Now we need to look at the Speed of Sound in air at high pressures, from this thread.... http://www.gatewaytoairguns.org/GTA/index.php?topic=66866.0 (http://www.gatewaytoairguns.org/GTA/index.php?topic=66866.0) .... I'll give you a few examples....
1000 psi : ~ 1170 fps
1500 psi : ~ 1200 fps
2000 psi : ~ 1260 fps
2500 psi : ~ 1310 fps
3000 psi : ~ 1360 fps
3500 psi : ~ 1420 fps
If we take our above air column velocity of 770 fps and compare it to those pressures, we can calculate the port diameter, relative to bore size, at which the air velocity through the port would equal the speed of sound at that pressure.... The port diameters, as a percentage of bore size, are:
1000 psi : 81%
1500 psi : 80%
2000 psi : 78%
2500 psi : 77%
3000 psi : 75%
3500 psi : 74%
This would represent the minimum port diameter to prevent Sonic Choking in a PCP using HPA, where the valve is closing at 50% of the barrel length.... Note that it is a pretty narrow range.... I didn't go above 3500 psi as remember you have to look at the LOWEST (or regulated) pressure in the shot string.... I also didn't take into account any transonic effects such as we see outside the barrel on the drag curve of a projectile.... They are likely to occur, and they would require even larger porting to reduce the air velocity through the port below the speed of sound.... However, to me it says that if you are after ~ 950 fps with reasonable efficiency, you need ports that are 75-80% of the bore diameter.... Since that is the largest round port you can drill in a barrel without creating loading problems, it gives a pretty good indication of where you need to be....
I have used ports larger than 80%, right up to bore size in area, but that requires an oblong barrel port.... The potential power DOES increase beyond the 80% port diameter, and I can only attribute that to reduced friction and possible elimination of transonic effects.... For a high performance PCP, it means that 75-80% of bore diameter is a good design point unless you are trying to drive heavy bullets at maximum FPE, in which case you need to explore oblong barrel ports and correspondingly larger transfer and exhaust ports and valve throats....
Bob
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Just one final thought about port size.... If you are using pellets, even the heaviest pellets available for the caliber, you can probably stay with a round, drilled barrel port of 75% of the boresize and a transfer and exhaust port to match.... I don't think it is necessary to go to the trouble of making a oblong barrel port and increasing the other porting to take advantage of that like you need to do to get maximum performance with heavy bullets where you are pushing the SD towards the maximum for the caliber at whatever pressure you are running....
One of the reasons for this is that when you get the gun running efficiently with the pellets, in that mid 900 fps range, and assuming you have enough pressure and barrel length to drive them efficiently at that speed, you will be closing the valve much sooner than 50% of the barrel travel, more like 25-33%.... That reduces the velocity of the air through the ports even further, making the possibility of Sonic Choking even more remote.... The exception would be if you want to build a Carbine or run quite a low pressure, when you might benefit from the larger ports....
Bob
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Bob,
I am still working on another response to your valve lift modeling thread but I ran across this treasure trove of NASA information ;D ,
http://www.grc.nasa.gov/WWW/BGH/shorth.html (http://www.grc.nasa.gov/WWW/BGH/shorth.html)
including one section on sonic choking! :o
http://www.grc.nasa.gov/WWW/BGH/mflchk.html (http://www.grc.nasa.gov/WWW/BGH/mflchk.html)
Very cool stuff for the pathetically geeky crowd!
The math is rather intimidating, but at least understandable, and I unfortunately have not been able to get the java calculator app to work yet.
But the very exciting thing that I see is that it specifically states that the mass flow through a nozzle (yes, it might be a bit of slight mis-application to call our application a "nozzle") is at its MAXIMUM at mach 1. In other words, the mass of the compressible gas flowing through the nozzle (the product of its density and velocity) increases as mach 1 is approached, reaches a maximum at mach 1, and then starts to decrease as mach 1 is exceeded. It appears that there is no sharp "shut off" of air flow through the nozzle or port. This would certainly help explain some of the very high pellet velocities that have been obtained in experimental situations. Some number crunching is needed to see how significant the mass flow drop-off rate is, but at the velocities we are talking about, it might not be that significant.
I think this could be another light bulb.
Lloyd
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OK :D Now you have me trying to visualize the shock waves in the porting, and trying to figure out how to utilize them. I do love those light bulbs, especially the 1KW ones. ;D ;D
One thing that just came to mind is boundary layer effects. How would that play into the equation? I know they play hob when turning corners, which is why blending the throat pays big time.
Anybody have a good Fluid Dynamics program? ::) ;D
Try Taco corporation they build circulator pumps and have a complete program available for flow characteristics on line and free I still need to go back to school to keep up with you geeks
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HI Lloyd, and nice to see you back, BTW.... I am aware of "converging-diverging" nozzles and their application in rocket exhaust, where they are designed for Mach 1 to occur at the narrowest point and then the gas continues to accelerate in the diverging portion.... They seem to be a very specific shape, and I would be surprised if we "accidently" managed to get that just right....
I'm not suggesting that the flow STOPS when it passes Mach 1.... only that there is an additional restriction caused by the formation of shockwaves.... ie drag on the flow.... Your finding that flow maxes out at Mach 1 CONFIRMS that.... I'm certainly not an expert (although Steve in NC did/does work at JPL).... The main point of this thread was the using the muzzle velocity (as he did) was, IMO, flawed, because the maximum velocity through the PORTS occurs just as the valve shuts....
One good example of how your discovery that the maximum MASS flow through a "nozzle" occurs at Mach 1 would be what is happening as the valve closes.... As the area decreases, the velocity should increase, until it reaches Mach 1.... At that point, then the amount of air mass moving through the valve would start to decrease, and as the valve continues to close, I would think it decreases so rapidly that it effectively stops before the poppet hits the seat.... Well, not really stops, but the amount of flow decreases much faster than the area does, "clipping" the last part of the valve cycle.... The closer the flow is to Mach 1 just before the valve lift drops below the "curtain limit" (1/4 of it's diameter) then the sooner and more abruptly in the shot cycle the flow drops precipitously.... That's how I visualize it, anyway....
I found this quote in the NASA article on choking we need to ponder.... "Choked" is defined as Mach 1 at the prevailing conditions of temperature and pressure for the gas in question....
If we have a tube with changing area, like the nozzle shown on the slide, the maximum mass flow rate through the system occurs when the flow is choked at the smallest area.
Bob
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I have been looking at the basic equation for Mass Flow Rate on that NASA website, and it's actually quite simple....
MFR = r V A
MFR = mass flow rate (the number of molecules of air moved per second)
r = air density at whatever pressure and temperature you have
V = velocity of the airflow
A = area of the tube or port where that velocity is occurring
For an ideal gas (and air is pretty close below 3000 psi and within 9% of ideal at 4500), then the density (for a given gas) is proportional to the pressure P, so although the units are wrong, we can use this proportionality:
MFR ~ P V A
The mass flow rate must be a constant throughout the system (conservation of mass), so if we hold any one variable constant, the other two become inversely proportional.... Therefore:
for constant pressure P.... MFR ~ V A.... or V ~ 1/A within the system....
for constant area A.... MFR ~ P V.... or P ~ 1/V within the system....
for constant velocity.... MFR ~ P A.... or P ~ 1/A within the system....
So the mass flow rate reaches a maximum at Mach 1 at the port (assuming that is the most restricted point).... and we have a pretty good idea of what that velocity is, based on the temperature and pressure of the gas.... At that point the gun is operating "sonically choked", but does NOT mean that is the maximum velocity for the pellet.... The velocity downstream (ie in the barrel) can exceed Mach 1 if there is a pressure drop across the port.... As long as that pressure is still high enough to accelerate the pellet, it will continue to accelerate down the bore.... For the same mass flow rate, and a given area, the velocity can still increase, but the density (ie pressure) must drop.... so in practical terms, what happens when the port becomes sonically choked, the pressure available downstream (ie at the pellet) will be less than the pressure on the valve side of the port.... IMO, this shows up as a loss of efficiency, compared to what was occurring before the sonic choking occurred.... Once the port becomes sonically choked, the pressure in the barrel begins to drop, even though the valve is still open....
If we consider that the potential maximum power of the gun will occur when the mass flow rate peaks (most molecules of air flowing per second).... then for peak power, I would propose that there be no restrictions below boresize in the system.... The power will then be dependent on the pressure and the area (caliber).... Since no point of the system is smaller than any other point, the mass flow rate is not artificially choked until limited by the boresize.... Increasing the pressure increases the density, and hence increases the mass flow, and hence the potential power.... I'm not, however, suggesting that all airguns require boresize porting.... If the velocity is subsonic, and the valve closes relatively early in the pellet travel down the bore, much smaller ports can be used.... However, if you try and push those smaller ports past the point of sonic choking, then larger ports will show more power....
What about Helium, which has lower density?.... Shouldn't that have less power?.... No, because the speed of sound is much higher, so sonic choking doesn't occur until a much higher velocity is reached.... In addition, because it is less dense, I also think it flows easier through the ports and barrel, and can therefore maintain more pressure at the pellet, but I can't prove it.... Certainly the relationship between pressure (which is what accelerates the pellet) and mass flow rate is different for Helium than for air.... it has more pressure for the same mass....
Bob
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Bob,
I think your next to the last paragraph sums it up pretty well. If I may paraphrase: When high power and/or high velocity are the goal, making all the porting the same size as the bore is probably a good idea.
But in addition to that, I feel that large, contoured ports probably have as much to do with achieving smooth, non-turbulent air flow as they do in avoiding restricted airflow caused by exceeding Mach 1 in the passage.
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Amen to that!!!
Bob
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I'm a mechanical engineer, and have 30 years of design experience under my belt - machines, power transmission, high performance hydraulics, pnuematic system, and other stuff like machine dynamics, and industrial process modeling are all areas I played in daily.
Bob and I have been having an email conversation regarding a design, and we got into the subject of sonic choking. Chunks of that email are posted below, in italics.
Wiki has a pretty good explanation of "Choked flow", (can't post an external link, go here - wikipedia.org/wiki/Choked_flow)
but you can just skim the middle bit, and cut to the chase.
The good bit is the last half, and especially the diagram on the lower-right (copied below).
If you go to the Wiki page, you can actually read the diagram. (Fixed it with photobucket)
(http://i15.photobucket.com/albums/a362/Jim_Hbar/Flowpatterns.gif)
If the pressure (absolute) on the upstream side of a restriction is greater than 1.893 times the down stream pressure (absolute), the flow is choked somewhere..
Period, Full Stop.
ALL the way down to about 14 psig at ambient..
(deleted)
When the flow is choked, that restriction determines the mass flow rate of the system, until the pressure ratio is reached.
(deleted)
When the ports are big enough - What this calculated mass flow rate will do, is put an upper limit on the acceleration possible from the pellet - and that's how I likely will use it.
That's all - pretty small potatoes..
Thinking through it a bit more and crunching a few numbers, I agree that the choke has very little practical effect at the velocities we are talking about, if the ports are reasonable. If they are too small, I'm sure it does have some effect.
And of course, it applies after the pellet leaves the barrel, but that's not interesting - jokes over by then!
A dump shot should be affected by the choked flow if the barrel is long enough, but perhaps not as much some would think.
If you look at the last four panels on that Wiki diagram, the velocity downstream of the orfice is super-sonic in what could be considered the barrel. Intuitively, people under stand case A & B, and perhaps will go as far as C & D, but rarely E, and the fact that the flow can be super-sonic well beyond the nozzle as in F & G just goes beyond intuition.
Especially when considering that the flow is only sonic at the restriction.
To go through an orfice and then speed up?
But that's what happens, and the flow is choked.
BTW, as upstream pressure is increased relative to the downstream pressure, the flow regimes move down that chart.
The standing waves shown at the outlet (in the last panel), are related to the shock diamonds in the outlet of a jet or rocket engine. See wikipedia.org/wiki/Shock_diamond
That's enough for now.
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;D This thread needs a large disclaimer " Caution do not read before second cup of morning coffee"
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sfttailrider46
It had better be high test coffee ( maybe a couple red bull chasers?? ) cause I've had 3 cups "unleaded" and I feel like I need a handful of aspirin trying to keep up
Brian
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Since supersonic flow after choke point is possible, shouldn't we introduce the choke point at the pellet probe then? That would then cause a supersonic flow in the barrel if transfer port can be considered as the chamber. If the choke point is earlier in the flow path the supersonic flow may have trouble reaching the barrel due to additional choke points and turns in the path.
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Since supersonic flow after choke point is possible, shouldn't we introduce the choke point at the pellet probe then? That would then cause a supersonic flow in the barrel if transfer port can be considered as the chamber. If the choke point is earlier in the flow path the supersonic flow may have trouble reaching the barrel due to additional choke points and turns in the path.
I see it as convergence at the probe or restrictor and divergence beyond so we use the speedy air forward of the probe/restrictor to help scavenge the air through the porting. I use the probe as a choke on bolt actions and the Transfer port restrictor on the Thumb in guns. As long as you create a reasonable flow patch at the redirections those will not create the flow restrictions a Port restrictor or Probe head will. It is a good idea to create the Choke point rather than let the system use the chaos of corner flow to be the throttle.
The reason we do extended bolt probes the way we do is to seat the pellet fully and create the Flow dynamics that work to our advantage to put the choke where it creates the best flow profile.
TimmyMac1
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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.
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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
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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 (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)
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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
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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.
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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.
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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
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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
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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 (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.
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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
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A graphical isothermal portrayal of the regions around choked flow would be fun if anyone comes across such tid-bits"
I've been looking,
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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/ (http://www.thermopedia.com/content/659/)
The stagnant regions defining the effective shape
A lot would depend on the poppet valve flow shaping.
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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.
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That maybe so.... but I repeat, to what benefit?....
Bob
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understanding
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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
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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.
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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.
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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
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I suspect that with an elegant enough implementation one could employ choking to influence barrel harmonics.
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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..
Bob
Bob
I read that there may be some misinterpretation. My comments are not in forming choked flow for any purpose, but rather, I'm going under the impression that at some point in the valve operation, choked flow is inevitable. And so, best understood.
And on that theme, A thought passed through (pretty much empty space ;-)
IF the pellet were retained from first movement, until the pressure drop across the valve opening was small enough to inhibit choked flow, then any "disturbance" attributed to the choked flow on opening event would be immaterial. Thus eliminating 1/2 of the possible difficulty. Playing with break away factor, much like adjusting the neck size on a cartridge or throat dimensions on a barrel in order to manipulate chamber pressure.
Perhaps not easily accomplished in a controlled manner, but it could just be a matter of size and fits. Smooth twist style barrels may have advantages in testing.
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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
Douglas
The Evanix AR6/Renegade design has no port to squeeze into any transfer sleeve.... A design trade off I suppose ;-)
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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
Bingo,
Reduced striker force translates to high variability so we don't like that direction as it makes it shoot like it has a HDD(not accurate). I'd rather stand on nthe spring and fly the hammer fast and back the power down at the Restrictor. A lot of people go for pure FPE output but the level of power that exhibits the best accuracy is normally also where it is efficient. So why choke it!. It is the best way to back the power down to where the system is getting efficient. Where we see the accuracy is optimal is so often the best efficiency as well it is the way we get the best of both worlds. The Really good 12 FPE guns get 150-160 shots per fill from a 13 CI. That is a bunch of FPE per didly. When we see a gun that makes big or little power and doesn't do it with reckless disregard to the practice of matching valve timing with barrel timing, we get what we want. GOLD!
Lots of folks focus on FPE while my practice of focusing on the Accuracy has led me to the practice of choking the flow.
As you turn a port restrictor in (that is the choke point) it will get a loud gun a lot more quiet (and accurate)before it ever drops velocity. If you see that as much as I have you get the picture.
A huge amount of what I do is pragmatic. Mistakes are valuable because as you explore you learn more. I made some big improvements to stuff I did not understand why till later. Why doesn't matter to me. Like 885. Some stuff works so often it is your security blanket. Getting the best use of your air has always worked (short of increased striker drag) ON TARGET! ALL MY GAMES HAVE POWER LIMITS. Shooting harder is not an option unless there is no power limit like the EBR. Even then, efficiency ruled. I think it always will with pellets.
What works for Drag stabilized pellets may not work for SLUGS. That is a whole different discussion(I'm clueless on that). Getting mileage is a lot like getting the best accuracy because you are sipping fluid, not gulpin'. Fluid dynamics is a hugely interesting subject I have involved myself with for my entire life. I've never had the lab to get it done proper so we focus on the ACCURACY. 950 would not be accurate.
Backed down guns WIN! Turning pellets sideways will never work on Target. WE are playing with lead shuttlecocks and she wants to turn when you blow up the girls skirt. Accuracy and BC suffer when the air timing doesn't match the Barrel timing. You audibly sense the extended duration that ruins BC and makes guns shoot 3 times the groups at the Paper.
Loud is Waste!
TimmyMac1
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Cal, I think that having choked flow on both ends of the shot (flow) cycle is beneficial.... I was aware of the sonic choking at the closing part of the cycle, which "squares off" the pressure pulse at the end as the poppet approaches the seat.... What I was not aware of until Jim brought it up was that there was a "pressure choking" (if I may use that term) which occurs at the beginning of the shot cycle as well, until the pressure difference across the seat drops below 1.893:1.... I had read that there was little flow that occurred until the valve was open a few thou, and perhaps that is the reason for that?.... In any case, the theoretical lift to dwell curve, which is a parabola, can not only get clipped across the top, from the "curtain limit" (when the lift exceeds 1/4 the throat diameter flow no longer increases), but also on both ends, on opening from pressure differential, and on closing from sonic choking.... This effect helps us approach the ideal "square wave" pressure pulse that we are striving for....
Having said that, any restriction in the flow path downstream of the valve (but ahead of the pellet) MAY cause sonic choking to occur prematurely.... If the goal is maximum power, IMO this is a bad thing.... However, at Tim@Mac1 points out, it can be used to great benefit to tune a PCP to a desired velocity while allowing full pressure fills.... The mechanism is that of sonic choking limiting the mass flow once Mach 1 is reached at the port restriction....
Bob
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I did up some diagrams that may help you visualize the flow through a "strike-open" valve in a PCP.... I started with the Lift to Dwell curve which from Physics should be a parabola (assuming a constant closing force).... Then I limited the flow to that allowed by a curtain height of 1/4 the throat diameter.... Next I added choking from the pressure differential as the valve opens and from sonic choking as the valve closes.... Lastly I showed what would happen if the port downstream of the valve was restricted so that sonic choking occurred to limit the mass flow....
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/ValveFlow1_zps5a9bbe8d.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/ValveFlow1_zps5a9bbe8d.jpg.html)
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/ValveFlow2_zps5540b52d.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/ValveFlow2_zps5540b52d.jpg.html)
I used a dwell of 2 milliseconds for the horizontal axis, which is typical.... The vertical axis numbers are only relative, with 100 being the maximum flow through the throat diameter at the pressure being used.... These are not necessarily to scale, but just presented as a visual aid to display what we have been discussing above....
Bob
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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
That raises a good question.
When does the dynamic pressure of density X velocity X are become static pressure that is based on reservoir pressure and is used in the F=ma quantification?
The stagnation point being the base of the pell, which is under constant deceleration with respect to the air flow.
Hmmm. makes a fellow wonder.
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I think Jim would be a good guy to ask that.... I assume you are asking if there is a difference (and how much) between the pressure seen on the walls of the barrel compared to on the base of the (moving) pellet?.... Since pressure is nothing more than the collision of air molecules with the container (barrel), and the random motion of said molecules (in every direction) at room temperature is ~ 1650 fps RMS (with some much faster and some slower, near zero), I would think that much below that velocity there would be no (or little) difference.... at least until you approach it very closely.... During the valve open phase, you are continually adding air from the reservoir, of course.... only after the valve shuts is the air expanding to any noticeable degree.... so my guess is those two conditions are quite different as well....
The airflow is accelerating along with the pellet all the time the valve is open, as I see it.... That is why the FPE lost in accelerating the air mass is such a large percentage of the losses we see.... and one reason why Helium has less such loss, and hence develops more power....
Bob
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Air has mass so when it expands in a barrel it is directional and has momentum. Consequently it acts as an unrestrained spring loaded energy force than can generate much greater flow speed when suddenly constricted. The mass flow momentum is modulated/controlled @ restrictor/restriction to create the moment of valve closure via Sonic Choke. It can be done at the Bolt probe OR it will be choked at the redirection if that is the Max Restriction. There will always be some point where it is the bottleneck. If that point has adjustability it is best. That way you can set all your Striker settings to Optimize the best pressure map and power adjustments DON'T affect your map other than to cut the top of your curve off to benefit shot count. All good. Air Flow is very dynamic and you must consider both the flow as well as the pressure as the closing forces you can manipulate to get the best valve flow profile.
Sonic choking takes the violence out of the valve closure and the resulting Pressure Pulse created with the air mass reversing direction. The Pressure/mass wave moves things and often it moves things too much. Most structure shakes unless it is adequate. The Ping says the air was what you could move. Structurally it means to Me I have achieved adequate or better. We build guns with massive Billets for structural integrity and then still try to minimize the Jolt. I think it is one of the reasons Wide Open never shows well in Competition even when there are no limits. Physical limits will always exist whether you can see them or not. Team Wide Open will always exist but it is a frustrating path. I like watching people venture there. It is where you get experience meaning you don't get what you want downrange.
TimmyMac1
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I assume you are asking if there is a difference (and how much) between the pressure seen on the walls of the barrel compared to on the base of the (moving) pellet?
In a non-dynamic, constant cross-section application, we all know that there has to be a pressure gradient down the barrel, otherwise the air would not flow. But make it the dynamic situation that we are interested in, and it very quickly becomes exceedingly complex, and I suspect, virtually impossible to generalize across the wide range of applications we are visualizing. Of course Bernoulli is ever present, but once it get's beyond the First Law of Thermodynamics, all the rest of the mumbo-jumbo comes into play. :o And that is exactly where this discussion is heading! That's the deep end of the pool, and over my head. I'll sit on the edge of the pool and dangle my feet in the water. 8)
To model what happens at the level being discussed here, could be done by a CFD geek, I would expect - If the software was up to the challenge. And the model would still need to be validated by comparing to actual data, and tweaking it to match actual results.
For practical purposes, the way I understand Loyd's model works, by qualifying the model to match field data through the use of an "efficiency" factor, is exactly the way I would do it. And is effectively what happens in a model of any complex system, regardless of the modeling method.
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.
A sonic choke is anything but isothermal - adiabatic is closer, but I fear the 2nd and 3rd law apply.
Unless this was a joke on the newby, then Ha Ha Ha..
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A sonic choke is anything but isothermal - adiabatic is closer, but I fear the 2nd and 3rd law apply.
Unless this was a joke on the newby, then Ha Ha Ha..
[/quote]
Jim
I agree, real computation would be overly tedious. Fudge factors answer for most purposes, based on observations. I'm impressed that the presented algorithms perform so well!
As to "iso thermal", it is perhaps a confusion of terms in common usage. My intent is "lines of equal temperature" . i.e. iso- thermals. A map.
http://dictionary.reference.com/browse/isothermal+line (http://dictionary.reference.com/browse/isothermal+line)
adiabatic has nothing in common
ps
I would bet there are some interesting avenues of development along these lines.
http://en.wikipedia.org/wiki/Ludwieg_tube (http://en.wikipedia.org/wiki/Ludwieg_tube)
I've always wondered what performance would be obtained if launching a projectile with a fixed volume of compressed air filling the entire system, and a rupture disk at the muzzle.
Not practical, but may give insight into harnessing shock wave energy for certain purposes.
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Cal:
Isothermal and Adiabatic processes have very precise and specific meanings in thermodynamics/engineering. Check Wiki for "Isothermal Process". The first paragraph of that page does a fair job.
Isothermal and Adiabatic processes describe the two ends of a possible range of real processes. Isothermal processes (constant temperature) are slow, and adiabatic processes (constant energy) very fast. Reality is usually somewhere in between.
"Isotherm" is the word for used for the lines of constant temperature in this area of study.
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When I'm doing my calculations, I use Isothermal while the valve is open, and usually afterwards as well, even though it makes sense for the expansion phase (after the valve closes) to be Adiabatic, or nearly so.... Isothermal has an exponent of 1.0, Adiabatic of 1.4, and as Jim says, you can use something in between, such as 1.2 for after the valve closes.... However, using Lloyd's spreadsheet all that happens if you use Adiabatic is that you have to change the Efficiency "fudge factor" to a higher value.... I find his Model matches reality better using Isothermal, so I use that as my default.... If you used Adiabatic for the entire shot cycle the Efficiency factor gets too close to 100% to be realistic, IMO....
Bob
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Cal:
Isothermal and Adiabatic processes have very precise and specific meanings in thermodynamics/engineering. Check Wiki for "Isothermal Process". The first paragraph of that page does a fair job.
Isothermal and Adiabatic processes describe the two ends of a possible range of real processes. Isothermal processes (constant temperature) are slow, and adiabatic processes (constant energy) very fast. Reality is usually somewhere in between.
"Isotherm" is the word for used for the lines of constant temperature in this area of study.
For your reference, I attach the link again
http://dictionary.reference.com/browse/isothermal+line (http://dictionary.reference.com/browse/isothermal+line)
And restate. adiabatic nor isothermal processes have anything to do with my interest in an isothermal line graph of a gas flow in a choked state.
If you come across such an image, please let me know of it. I'm curious.
cheers
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hey Bob have you ever heard of modeling eddies with fractal dimensions... ;)
I have heard of renormalizing and it seems it would be similar
I have not the concentration for math any more myself... ::) :-[
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Heard of it, know nothing about it....
Bob
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Cal, I think that having choked flow on both ends of the shot (flow) cycle is beneficial.... I was aware of the sonic choking at the closing part of the cycle, which "squares off" the pressure pulse at the end as the poppet approaches the seat.... What I was not aware of until Jim brought it up was that there was a "pressure choking" (if I may use that term) which occurs at the beginning of the shot cycle as well, until the pressure difference across the seat drops below 1.893:1.... I had read that there was little flow that occurred until the valve was open a few thou, and perhaps that is the reason for that?.... In any case, the theoretical lift to dwell curve, which is a parabola, can not only get clipped across the top, from the "curtain limit" (when the lift exceeds 1/4 the throat diameter flow no longer increases), but also on both ends, on opening from pressure differential, and on closing from sonic choking.... This effect helps us approach the ideal "square wave" pressure pulse that we are striving for....
Having said that, any restriction in the flow path downstream of the valve (but ahead of the pellet) MAY cause sonic choking to occur prematurely.... If the goal is maximum power, IMO this is a bad thing.... However, at Tim@Mac1 points out, it can be used to great benefit to tune a PCP to a desired velocity while allowing full pressure fills.... The mechanism is that of sonic choking limiting the mass flow once Mach 1 is reached at the port restriction....
Bob
I was just reading through past threads/ posts on this forum. ('sort of forgot how recently it started ;-)
In reading, one post by you, Bob, mentioned a detail that is very likely true for most considerations. That is, during the period of time the valve is open, the entire event is pretty much a constant pressure event. (Considering a usefully large reservoir and not a "big bore" with two shots per fill ;-)
With valve closing while the projectile remains in the beginning half of the barrel volume, this detail may very likely be the case. After the valve closes, expansion rules.
For this discussion, IF we assume an "almost constant pressure", though polytropic event, sonic choking on valve closing is highly unlikely when applying the 1.9 : 1 pressure ratio rule of thumb. Can we envision the propelling pressure drooping that low with the pell not yet half way out the barrel? Perhaps....., in a spacial isolation, such as at the valve sealing face. But the effect must be of very short duration.
Perhaps this is included in the data that produced displayed plots. I did not catch it if so.
With that, If the choke effect might be minimized on valve opening by sufficient projectile break away requirements, and choking may be suppressed on valve closing due to insufficient pressure differential, this topic may reduce to only a thought problem.
Perhaps it comes down to a question , "what pressure differential projections and data were used to describe choking conditions?".
It would be beneficial to know the pressure profile in our air guns under any and all conditions ;-)
Regards
Cal
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As I said, there can be no choking due to exceeding Mach 1 on the opening part of the cycle, that would be due to the pressure difference, hence why I coined the term "pressure choking"..... On closing, the velocity of the airstream is at it's highest, and as the valve closes it speeds up locally through the (ever reducing) gap (curtain area) under the poppet, until reaching Mach 1 when the curtain area is small enough.... That is true "sonic choking", and limits the mass flow through the valve after it occurs.... and it WILL occur at some point as the poppet approaches the seat....
Steve in NC did an excellent analysis on Sonic Choking and the port sizes it occurs at, but he used muzzle velocity, not the velocity of the pellet (and airflow) at the instant before the valve closes.... Muzzle velocity has nothing to do with it, otherwise his chart was right on, just substitute the velocity at valve closure.... The velocity through the ports at that instant is the inverse ratio of the areas.... Go right back to the beginning of this thread for that argument, modified later in the thread by the increase in Mach 1 at high pressures.... However, even if the ports are big enough not to suffer sonic choking the throat (curtain area) of the valve MUST just before it shuts....
The best model I have seen of the pressure profile is the one produced by Lloyd's spreadsheet on Internal Ballistics....
Bob
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Bob\
I'm in complete agreement with the flow velocity on a closing valve. Velocity should be at it's highest unless the crest of the flow wave has passed, and molecules are stacking up. What is less certain is the required 2:1 pressure ratio. The sonic flow must pass into a region of low pressure. (1.89:1) That is not logical to me. With the pell still in the barrel and accelerating, there must still be high pressure all the way back to the valve.
Where do you feel the pressure difference would come from. Is there a way to justify the projectile acceleration and velocity using only 1/2 of the reservoir pressure at witnessed volumes?
On valve opening, we do have the required 2:1 pressure differential. I feel Mach speed is pretty much instantaneous. But can it be described as flow? The gas molecules are already moving with that average velocity, they just need someplace to stretch their legs. The opening valve is the gate. (the disparity may be only terms ;-)
This may lead back to the dynamic vs static pressure determination.
Just to be sure we are discussing the same subject, I C&P the description of choked flow from wiki. I'm not clear on your coined "pressure choking".
clip
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 rate will not increase with a further decrease in the downstream pressure environment while upstream pressure is fixed. end clip
I'll summarize my views on the details here in a few lines.
1) The valve port of our airguns is surely the venturi. There may be others throughout the port geometry.
2) The establishment of a "flowing fluid" might need clarification. At least in the early portions of the valve event.
3) The "flow" in the reservoir upstream of the valve is subsonic prior to valve opening, (there is none), with the gas in the region adjacent to the valve developing flow as the valve event matures.
4)IF the flow into and out of any region between the valve port and the pell establishes the required 1.9:1 pressure differential, we may see the static pressure/ density decrease that is the defining condition for choked flow. i.e. constant mass flow across a restriction.
Help me understand the graph models you have posted. The sections of the plots associated with the valve in the near closed position? Are the curve profiles of "choked flow" based on open area X constant mass/unit area flow? As opposed to open area X (what?)
Your description
clip, Next I added choking from the pressure differential as the valve opens and from sonic choking as the valve closes.... Lastly I showed what would happen if the port downstream of the valve was restricted so that sonic choking occurred to limit the mass flow....end clip.
If I have it correctly, the last plots project models of flow across the open valve WHEN the absolute mass flow of the system is being determined by flow conditions determined by elements down stream of the valve and prior to the pellet base.
An added comment
I suppose one could use the MV for estimation if one were wedded to the sonic horizon theory. For all the same reasons. Namely, events happening "back there" no longer matter. That is a different topic.
eta
The plot on post #14 of this thread would suggest full pressure behind the pell at the get go, with no significant let off until the valve closes .
http://www.gatewaytoairguns.org/GTA/index.php?topic=75341.msg717558#msg717558 (http://www.gatewaytoairguns.org/GTA/index.php?topic=75341.msg717558#msg717558)
With that, if the acceleration force follows Bernoulli's equation Both Static and dynamic forces need be summed. Ps+ (density X Velocity^2 X 1/2) to determine the total pressure.
There seem to be ample guess-timation in this investigation ;-)
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I think the point is that we should use ports larger enough to avoid the problem, IMO....
Bob
Data point
The transfer port drillings for the Evanix AR6 in .22 measures 4.55-4.6mm diameter , the same for the .177 caliber rifle (likely only the barrel and mag differ)
So, "full bore" in the one example, and 80% in the other. There are two 90 degree corners however ;-)
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The sonic flow must pass into a region of low pressure. (1.89:1)
Where are you getting that from?.... Jim said that choking will occur at that pressure ratio, regardless of velocity, I didn't see where he stated that the reverse is required.... Nowhere do I see a "requirement" for a 1.9:1 pressure differential for choking to occur.... In point of fact, if the venturi restriction is only 10% in area and the flow velocity pre-choke is Mach 0.95, the flow will choke at the venturi, but the pressure will only drop ~10% through the venturi....
Jim, is there a REQUIREMENT for a 1.9:1 pressure differential for choking to occur?.... if so, what am I missing here?....
Bob
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The sonic flow must pass into a region of low pressure. (1.89:1)
Where are you getting that from?.... Jim said that choking will occur at that pressure ratio, regardless of velocity, I didn't see where he stated that the reverse is required.... Nowhere do I see a "requirement" for a 1.9:1 pressure differential for choking to occur.... In point of fact, if the venturi restriction is only 10% in area and the flow velocity pre-choke is Mach 0.95, the flow will choke at the venturi, but the pressure will only drop ~10% through the venturi....
Jim, is there a REQUIREMENT for a 1.9:1 pressure differential for choking to occur?.... if so, what am I missing here?....
Bob
http://en.wikipedia.org/wiki/Choked_flow (http://en.wikipedia.org/wiki/Choked_flow)
scroll down to "Minimum pressure ratio required for choked flow to occur".
Perhaps there are some gaps missing in our understanding of this condition.
The salient point regarding choked flow is that NO REDUCTION IN THE DOWN STREAM PRESSURE CAN INCREASE MASS FLOW THROUGH THE RESTRICTION.
Increasing pressure above the restriction WILL send more mass through. i.e. density will increase. The Mach is "almost" irrelevant, as the gas velocity after the pinch in a CD nozzle can easily be "super sonic" into unrestricted flow)
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Assuming that Wiki article is accurate (and you never know, certainly I don't) then the only time choked flow could occur would be for a brief instant when the valve is opening, before the pressure in the exhaust port reaches ~50% of the reservoir pressure.... That might occur before the pellet even starts to move.... I can't see the pressure anywhere in the system ever having a 1.9: 1 pressure gradient after that point, or there would not be enough force to accelerate the pellet at the rates achieved.... IF that is true, then Steve in NC's whole idea of Sonic Choking is wrong....
I'll let you go over to the Green and tell him....
In the meantime, I'll wait for Jim to chime in again before making up my mind.... For one thing, I need to know if the ~1.9:1 pressure ratio is the ratio of upstream pressure to downstream pressure.... or the ratio of upstream pressure to the pressure at the orifice (venturi).... as that Wiki article says both, which makes no sense to me....
Bob
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As mentioned:
There may be gaps in our understanding....
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Assuming that Wiki article is accurate (and you never know, certainly I don't) then the only time choked flow could occur would be for a brief instant when the valve is opening, before the pressure in the exhaust port reaches ~50% of the reservoir pressure.... That might occur before the pellet even starts to move.... I can't see the pressure anywhere in the system ever having a 1.9: 1 pressure gradient after that point, or there would not be enough force to accelerate the pellet at the rates achieved.... IF that is true, then Steve in NC's whole idea of Sonic Choking is wrong....
I'll let you go over to the Green and tell him....
In the meantime, I'll wait for Jim to chime in again before making up my mind.... For one thing, I need to know if the ~1.9:1 pressure ratio is the ratio of upstream pressure to downstream pressure.... or the ratio of upstream pressure to the pressure at the orifice (venturi).... as that Wiki article says both, which makes no sense to me....
Bob
If we may use reason to form our positions. think a bit
If the pressure differential across a restriction is Zero, would you expect any limits? .........I would not. No.
Again, If the pressure differential across a restriction were infinite, if there were limits, would those limits be imposed? YES!
So if the limit is at the ratio of 1.9: 1 for air, would that not stand a test of reason? YES
Though I concede, the actual number may be in question due to many variables, but certainly in the ball park!
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I think the issue is whether the ~1.9:1 ratio is across the entire system (ie from reservoir to pellet).... or if it is from the reservoir to the choke point?.... for those are surely VERY different answers.... As I said, Wiki contradicts itself within one paragraph, at least the way I read it.... I can easily see the pressure at the choke point having to be less than 53% of the upstream pressure to reach Mach 1 at the choke point.... but as I understand it, what happens downstream of the nozzle is the pressure again increases as the port expands and the flow slows.... I'm hoping Jim can shed some light on this....
Bob
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It only is an issue of the pressure differential across the restriction.
If a flat plate orifice, or a CD nozzle, makes no difference. Choking may occur at the muzzle, as the exhausted air exits to atmosphere. (with attendant pressure wave phenomena.)
Down stream matters, if it effects the upstream pressure but that is only logical.
eta
I'll not comment on the Carolinian. We diverge on our rational thinking...;-)
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I am recalling a reason for avoiding compressible flow courses...LOL and now there is discovered a use for them. Just discovered another thing to do with the Time Machine; give self kick in the tucchus.
cheers,
Douglas
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;D Every time I read these threads I regret some of the decisions of my mis spent youth and reaffirm my decision to begin taking classes again now that I will have the needed time.
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Use this dandy calculator
http://www.grc.nasa.gov/WWW/k-12/airplane/isentrop.html (http://www.grc.nasa.gov/WWW/k-12/airplane/isentrop.html)
and play with the p/pt value. Notice the status of the subsonic/supersonic display when the value is juggled between 5 and 6 ;-)
Playing with the other conditions gives insight as well.
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Okay, I'm now back in captivity! Had to go check on our "other" place, and traverse the "Big Smoke" twice.. -
It only is an issue of the pressure differential across the restriction.
If a flat plate orifice, or a CD nozzle, makes no difference.
I agree 100%.
Choking may occur at the muzzle, as the exhausted air exits to atmosphere. (with attendant pressure wave phenomena.)
There may a sonic wave, but that may not be a sonic choke. See case #D in the diagram in post 14. (copied below)
Down stream matters, if it effects the upstream pressure but that is only logical.
Downstream pressure cannot affect the upstream pressure IF the flow is choked. That's the fundamental property of the choke.
(http://i15.photobucket.com/albums/a362/Jim_Hbar/Flowpatterns.gif)
I think the issue is whether the ~1.9:1 ratio is across the entire system (ie from reservoir to pellet)....
That is the minimum condition that needs to exists for a choke to exist. If the pressure drops across the various restrictions do not the meet the 1.9:1 ratio, at those restrictions, then a choke doesn't form at that point.
or if it is from the reservoir to the choke point?.... for those are surely VERY different answers....
Whenever that ratio of pressures (across the choke point) is reached, the flow sonically chokes. I suspect that any chokes are exceedingly transient at any point (other than perhaps the main restriction), in our application.
As I said, Wiki contradicts itself within one paragraph, at least the way I read it.... I can easily see the pressure at the choke point having to be less than 53% of the upstream pressure to reach Mach 1 at the choke point.... but as I understand it, what happens downstream of the nozzle is the pressure again increases as the port expands and the flow slows....
Whether the flow decelerates or accelerates is a function of the end conditions, and the geometry of system..
I'll have to let my mind fester on this point, before I put my foot in my mouth...
Like I stated before, I suspect that sonic chokes are likely not significant in the "normal" conditions that we are interested in here.
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Thanks for the clarification, Jim.... I was totally out to lunch, I thought the ratio of areas dictated the velocity at the restriction.... Since the only time we can have a 1.9:1 pressure differential between the reservoir and the base of the pellet is a very brief transient period while the valve is opening, then the whole premise of this thread is WRONG !!!....
I based the thread on what I viewed to be a correction (using velocity at valve closing instead of muzzle velocity) of a post made by Steve in NC over on the Green.... He had a lovely chart and all the calculations that showed what port sizes would sonically choke, based on the port diameter, caliber, and muzzle velocity.... Here is the chart and the formula he used to insure that the port did not sonically choke....
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/OptimumPort_zps47d215e6.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/OptimumPort_zps47d215e6.jpg.html)
It made sense to me, once corrected to use the velocity at the instant the valve closed, which is the moment when the flow through the valve would have the highest velocity (so I thought).... My reasoning was that initially there was no velocity, and as the pellet accelerated, so did the airflow behind it.... At some point, it seemed perfectly reasonable that if the port was smaller than the caliber, then the flow would reach Mach 1 at the restriction, limiting any further mass flow, and therefore limiting the power.... After all, that idea agreed with observed facts, that restricting transfer ports reduced velocity and energy....
Apparently the entire premise is flawed, and once the pellet has started to move, NO choking can occur after that, because the pressure differential is never large enough.... Therefore, we must look elsewhere for the observed effectiveness of restricting the transfer port in limiting the velocity of the pellet.... We KNOW that it works, but if the process is entirely REVERSIBLE (subsonic flow is, only choked flow isn't correct?) then making the transfer port smaller should have NO effect, because the flow simply speeds up to cram more air through the venturi (at lower pressure) but then slows down and goes back to the original pressure and velocity after the restriction (ie in the barrel).... It seems counter-intuitive to me that unless the pressure drop is there across the entire system there can be no choking, and therefore no possibility of IRREVERSIBLE losses from restricting the transfer port....
I wonder, then, what the explanation is for a known fact and tuning method that we use all the time in PCPs?.... As always, a little knowledge is a dangerous thing, and I apologize for spreading a myth in this thread....
Bob
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I thought about starting a new thread to discuss what is happening when you restrict a transfer port and the velocity and energy of a PCP is reduced, but perhaps it would be better done here, as much of the background is already in this thread, albeit incorrectly (again, my apologies).... Here is a simple diagram, just so that we can all use the same variables....
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/PortRestriction_zpse384e340.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/PortRestriction_zpse384e340.jpg.html)
The idea is to start with a PCP having boresize porting throughout.... so that once the valve is open more than 1/4 the throat diameter (ie the curtain height flow limit) the area would be A straight through from throat to pellet.... Then we start reducing the area at the transfer port, area B, until the velocity and energy of the pellet decreases significantly.... I want to understand WHY that reduction is taking place....
First let's look at no restriction, and subsonic flow.... That's pretty obvious....
Area: A = B = A
Velocity: X = Z = V
Pressure: U = P = D
Now let's look at low subsonic flow (so that Z<<Mach 1), and set area B = A/2.... and velocity of the airstream entering the barrel is V.... As I understand it....
Since upstream and downstream areas are the same (A), and in subsonic flow the conditions are reversible, upstream and downstream values are (virtually) identical....
Pressure: U = D
Velocity: X = V
Can somebody help me out here with the Pressure and Velocity at the Port?.... That is where I'm having a problem.... If the ratio of areas is 2:1 what is the pressure and velocity in the port?.... I found a Bernoulli Calculator online, and it appears that the velocity is inversely proportional to the area for incompressible flow....
Velocity: Z = V (A/B) .... and since A/B = 2.... Z = 2V
The pressure is a lot more complicated, however.... Sorry I was editing this post when you posted.... *oops*
Bob
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I am no physician but I don't think your statement about speed Velocity: Z = V (B/A) is correct.
If B/A is 100 I don't think Z will increase by Hundred times.
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Ups.
I am too slow.
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I agree, but that is where choking comes in.... Here is the Bernoulli Calculator I have been playing with.... http://hyperphysics.phy-astr.gsu.edu/hbase/pber.html (http://hyperphysics.phy-astr.gsu.edu/hbase/pber.html)
The first section allows you to input different flow rates and air density, inlet pressure, inlet area and venturi diameter.... and gives you the velocity in the venturi.... I have tried a huge range of those values, and if the areas are 2:1, the velocities are as well.... This seems to be independent of air density, flow rate, or areas, it is only the ratio of areas that dictates the ratio of velocities.... However, changing those values, does make a big change in the pressure at the venturi.... I would assume the calculator breaks down once the flow becomes compressible (near Mach 1)....
Bob
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Bob:
(Bob and others posted while I was typing - this is in response to post #70)
I'm certain that sonic choking must come into play when one goes super-sonic with the pellet.
And it could very well be a factor if one wants to hit a velocity that is significantly less than Mach1.
Otherwise, I suspect that choking just clips the corner like you show back in the third diagram of post #44
Also, just because a port is not exactly "sonically choked" does not mean that it is not the main "throttle" point in the system. I view the sonic choke value as the potential upper limit of the mass flow that can be pushed through the port/system. Flow resistances add in an air circuit, just like electrical resistances add in an electrical circuit. So, like Tim points out, it's best to have low resistance everywhere but at your tuning point.
I can see reasons why the chart in post #70 has validity. Yes, it probably over simplifies the situation, but simple tools promote better understanding - then we can add sectional density of the pellet, barrel length etc. into the game.
Re: Post #71..
To directly answer your question, Bernoulli is your man. And Bernoulli is just a special case of First Law (conservation of energy).
If A=B=A, and U=P=D, then X=Z=D that is correct - however in reality it is the null case where X= Z = D = 0
I was hoping to skirt this topic.
This is where you have to understand that your conversing with a jaded engineer on this end :o, not a bright-eyed eager young theoretical scientist.
I think in terms of "stagnation" pressure, not static pressure and dynamic pressure. In a constant mass flow situation, the energy available in the fluid is proportional to the stagnation pressure. And there cannot be any fluid flow without an associated pressure drop. (Loss of energy) (Basically Second law).
Here's how I think about it.
Consider fluid as incompressible
So if A= 2B = A, then D=U-deltaP and X=V check if 2X<< Mach 1 - if that condition is true, then close enough!
IF 2X ~= or> Mach1 - oops!!! Make the port bigger!!
Here are some documents I found.
3w.therebreathersite.nl/04_Links/Downloads/Choked.pdf
3w.thermopedia.com/content/267 - Figure 2 is of interest..
If I still had my text books at hand, I could find one very similar to this.
Need to go do something.......
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HI Jim....
Thanks for that explanation.... I think!.... I guess my question is this:
WHERE is the pressure difference (~1.9:1) that is required for choking to occur measured?.... Is it from the upstream side to the lowest pressure in the system (somewhere around the vernturi).... If so, then it seems perfectly reasonable that we can get choked flow even though the downstream pressure is a large percentage of the upstream pressure.... On the other hand, if the pressure well downstream of the restriction is where the pressure must be less than ~53% of the upstream pressure then we can't be dealing with choked flow at any time after the (subsonic) pellet moves....
My confusion is this.... On the one hand, we have the statement:
I think the issue is whether the ~1.9:1 ratio is across the entire system (ie from reservoir to pellet)....
That is the minimum condition that needs to exists for a choke to exist.
which I take to mean that the ~1.9:1 ratio must be across the whole system.... and then we have the second statement:
or if it is from the reservoir to the choke point?.... for those are surely VERY different answers....
Whenever that ratio of pressures (across the choke point) is reached, the flow sonically chokes.
and then:
Downstream pressure cannot affect the upstream pressure IF the flow is choked. That's the fundamental property of the choke.
Further, here is the quote from Wikipedia....
The minimum pressure ratio may be understood as the ratio between the upstream pressure and the pressure at the nozzle throat when the gas is traveling at Mach 1; if the upstream pressure is too low compared to the downstream pressure, sonic flow cannot occur at the throat.
The two parts in bold say different things in a single sentence.... Trying to reconcile these (in my mind) conflicting statements leaves me beating my head against my keyboard....
If I may postulate what I think occurs in a PCP where there is a single significant choke point (eg. a restricted transfer port) for this example half the bore area....
1. The valve opens, the pressure differential across the seat is very large, the flow is choked at the seat (only)....
2. The valve opens enough that the pressure differential across the seat drops to less than critical (~1.9:1) and the flow is no longer choked....
3. The pellet starts to move, either before or after #2, it doesn't really matter....
4. The air flows and the pellet accelerates, along with the airflow behind it....
5. Initially, the airflow through the restriction is approximately double the pellet velocity (minus friction and other losses)....
6. At some time point, the airflow just downstream of the restriction approaches Mach/2, and the velocity at the restriction approaches Mach 1.... Compressibility becomes an issue....
7. At some later time, with compressibility increasing, the lowest pressure at the restriction drops below 53% of the upstream pressure, and the flow chokes....
8. The rate of mass flow can never be higher than at that moment....
9. The pressure downstream of the restriction will be higher than the pressure at the restriction, I think still a significant percentage of the upstream pressure....
10. This condition continues as the pellet continues to accelerate and the downstream airflow with it, but at a lower rate than if no restriction was present, because of less flow....
11. The valve approaches the seat, and when the area at the seat is smaller than that of the restriction, the flow chokes at the seat....
12. It no longers matters what is happening at the transfer port, the rapidly decreasing area at the seat is shutting off the mass flow very rapidly....
13. The valve is fully closed, and the air in the ports and barrel now expands to finish accelerating the pellet to the final muzzle velocity....
14. During this expansion phase, the flow velocity at the original restriction is virtually zero, the air is only expanding, so there is no longer any choke there....
If I may be so bold as to suggest, the flow IS choked at the restriction because the ~1.9:1 pressure differential DOES occur between the upstream pressure and the lowest pressure in the restriction.... I would further suggest that as a rough estimate, the chart by Steve in NC is valid, once you substitute the velocity at the moment the valve close for the muzzle velocity, and the speed of sound at the ambient pressure for that at atmospheric.... I accept that fact I could be wrong, but I would like to know where, and why....
Bob
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;D Ouch I have just enough understanding of where this thread has gone and is going to say that it makes sense but I'm totally lost at this point . Now I will leave it alone until my mind is fresh probably tomorrow after the second cup of coffee
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A choke exists IF the pressure up stream (absolute) of the particular restriction/orifice/nozzle is greater than that 1.9 times the absolute downstream pressure.....
I probably should have put more emphasis on the word MINIMUM in the first text you quoted above.... Another way to phrase that statement is "If the pressure behind "the pellet" is more than 53% of the reservoir pressure, there isn't a "Sonic" choke in the system". Sorry for any confusion.
I think about it in terms of energy (stagnation pressure) and pressure drops - not the instantaneous "static" pressure at any point.
1. The valve opens, the pressure differential across the seat is very large, the flow is choked at the seat (only).... 100%
2. The valve opens enough that the pressure differential across the seat drops to less than critical (~1.9:1) and the flow is no longer choked....100%
3. The pellet starts to move, either before or after #2, it doesn't really matter....100%
4. The air flows and the pellet accelerates, along with the airflow behind it....100%
5. Initially, the airflow through the restriction is approximately double the pellet velocity (minus friction and other losses)....Not sure where this comes from, but is likely very close if the port is small relative to the caliber
6. At some time point, the airflow just downstream of the restriction approaches Mach/2, and the velocity at the restriction approaches Mach 1.... Compressibility becomes an issue.... Not the normal way to think about it - I believe it's valid
7. At some later time, with compressibility increasing, the lowest pressure at the restriction drops below 53% of the upstream pressure, and the flow chokes.... It's not the static pressure at the restriction that causes the sonic choke, it's the deltaP across the restriction. If the supply is 200 bar(a), when the barrel pressure drops below 106 bar(a), it's choked at the restriction
8. The rate of mass flow can never be higher than at that moment.... 100%
9. The pressure downstream of the restriction will be higher than the pressure at the restriction, I think still a significant percentage of the upstream pressure....Static pressure, Yes - Stagnation Pressure? No. Energy is lost across the restriction, so the stagnation pressure is lower, otherwise the air would not flow in that direction.
10. This condition continues as the pellet continues to accelerate and the downstream airflow with it, but at a lower rate than if no restriction was present, because of less flow....100%
11. The valve approaches the seat, and when the area at the seat is smaller than that of the restriction, the flow chokes at the seat.... probably not - the pressure in the transfer port would have to drop from 200 bar to below 106 bar as the valve closes from that opening, for a choke to form.
12. It no longers matters what is happening at the transfer port, the rapidly decreasing area at the seat is shutting off the mass flow very rapidly....100%
13. The valve is fully closed, and the air in the ports and barrel now expands to finish accelerating the pellet to the final muzzle velocity....100%
14. During this expansion phase, the flow velocity at the original restriction is virtually zero, the air is only expanding, so there is no longer any choke there.... 100% - it disappeared at step 11
If I may be so bold as to suggest, the flow IS choked at the restriction because the ~1.9:1 pressure differential DOES occur between the upstream pressure and the lowest pressure in the restriction.... It's the pressure drop across the restriction, that results in the choke.
I suspect that a choke forms as the valve opens and it quickly travels down the port to the pellet, at a speed somewhat less than Mach1 (the air behind it is sub-sonic). From there on in, other than for a super-sonic dump shot, I doubt that any choke reforms in any normal shot sequence. To do so would waste some energy, compared to just shutting the valve, and chopping the flow.
BTW, you're keeping me away from my drafting! ;D
The trigger is proving to be challenging! :-X
Jim
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;D Jim thanks for your insight you clarified this a great deal. It is a rare talent when an expert can break the information down enough for a "lay" person understand them and you just did that for me .
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Jim I understand your points... one final question.... Which comes first, the chicken or the egg?.... Does the downstream pressure have to drop to 53% of upstream before the flow chokes?.... Or can the flow through the restriction accelerate to Mach 1, causing the choke and at that moment, simultaneously, the pressure drops so that the downstream pressure is 53% of the upstream?.... In the first instance, the choking can ONLY occur if the downstream pressure drops below 53% (and it will never do that).... In the second case, they occur simultaneously, brought about by the increasing velocity at the restriction as the airflow accelerates....
I realize this may look like grasping at straws, but I see the difference as critical.... I am now visualizing the flow at the restriction accelerating until it reaches Mach 1.... and as the compressibility at the restriction increases the pressure downstream of the restriction drops.... At the moment the velocity reaches Mach 1, the pressure downstream also reaches 53% of the upstream pressure.... To me, this mechanism explains why reducing the transfer port size reduces the power.... The pressure accelerating the pellet is reservoir pressure until the port chokes.... After that, it is 53% of reservoir pressure.... A smaller port chokes sooner, at a lower barrel flow (pellet) velocity, shortening the time at full pressure and increasing the time at 53% pressure.... and consequently lowering the power of the gun....
Am I all wet, here?.... If I'm not, this could be added to Lloyd's spreadsheet, allowing the transfer port diameter as a variable to "shift gears" to the 53% pressure at a precise, known point, based on the velocity of the pellet.... (or at least approximately known).... Your final quote....
It's the pressure drop across the restriction, that results in the choke.
Could it be that the choke causes the pressure drop across the restriction?.... or that they happen simultaneously and could be triggered by the velocity at the restriction approaching Mach 1?....
Bob
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Comments
To add to the statements of downstream pressure having any effect on upstream conditions,
and I feel this has direct bearing on Bob's questioning regarding local or general pressure ratios.
If the downstream pressure increases such as to upset the differential requirement that establishes
choked conditions, those conditions will be upset, and choked flow will cease, regardless of velocity. And to reiterate, no REDUCTION of downstream pressure can increase the constant mass flow through a choked condition
It is not "chicken or egg", the pressure ratio MUST have been sufficient to begin, or choked conditions will never be initiated.
On the Idea of the usefulness of Bernoulli's work in these airgun considerations. The complete absence of steady state "smooth" flow completely devalues any calculations that may be applied, or information derived. The airflow though an airgun port is nothing if not turbulent and chaotic. Bernoulli avoided these uncertainties entirely by decree. There may be some insight to be gained there, but only in broadest of generalities.
Perhaps there is a possibility to shed light on the events of this thread purely on the examination of timing.
What is the condition of the pellet during the "time" that is shared while the reservoir passes it's compressed gas molecules into the volume between valve and pell base? (
Also, Let us not loose perspective. We might frequently return our consideration to how and why the rifle is being pressed back into our shoulder with each shot let go. There is no magic held by the gas molecules entrained in any high or low speed flow. The flow is completely the workings of pressure differences. As is the acceleration of the rifle mass and the pellet.
It can be difficult to distinguish between cause and effect, or effect and result.
I like to solve a puzzle in a paragraph before working through unfamiliar mathematics. In the case of the events between poppet valve and pellet base, there is much to be uncertain about. Numerical manipulations can give the sense of exactitude,while all the while failing in reality.
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eta
It would be instructive to explore the impetus given in acceleration of any projectile as related to static and dynamic pressures. For it is surely the sum of these doing the work.
Jim's mention of stagnation being the key word.
This is already a healthy discussion! imo
cheers
Cal
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Bob
This line from a post above caught my attention
We KNOW that it works, but if the process is entirely REVERSIBLE (subsonic flow is, only choked flow isn't correct?) then making the transfer port smaller should have NO effect, because the flow simply speeds up to cram more air through the venturi (at lower pressure) but then slows down and goes back to the original pressure and velocity after the restriction (ie in the barrel).... It seems counter-intuitive to me that unless the pressure drop is there across the entire system there can be no choking, and therefore no possibility of IRREVERSIBLE losses from restricting the transfer port....[end]
I'm turned to thoughts regarding density of the working fluid.
For in my mind, a restriction can only impede the number of molecules passing per unit time.
Then, as your statement reads, the only way fewer members could again obtain equal velocity and pressure, would be by the addition of heat.
just a point to ponder.
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It is not "chicken or egg", the pressure ratio MUST have been sufficient to begin, or choked conditions will never be initiated.
Cal, if that statement is true (and the whole purpose of me asking Jim was because he was trained in and works with that subject, I don't know your credentials, with all due respect).... then if you have air at 1 atmosphere flowing in a parallel tube that is miles long and could accelerate the flow to past Mach 1, then no choking would ever occur because all the air in the tube was at the same pressure.... Supersonic flow without any choking.... Even when the air exited the tube there would be no reduction in pressure to 53% of the pressure in the tube, it was, after all, at 1 atmosphere.... I simply want to know if accelerating the air to Mach 1 causes such a Compressibility Effect that the increase in pressure created by the air reaching Mach CREATES the pressure differential required to cause the choked flow to initiate.... I ask because I do not know and wish to.... It is, after all, called Compressibility, and occurs as you approach Mach 1....
Bob
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I do dislike to answer a question with a question,
But what could induce the air to flow down the long tube besides a pressure differential?
And in our exploration. what differential might be sufficient to accelerate any mass to the mach?
Basics, It is not the velocity that causes the pressure differential, it is the differential that causes the velocity.
regarding compressibility, I have not considered that aspect any greater than to compare real gasses with the concept of an ideal gas, for which air compares closely' even up to 200 bar pressures (within 80%). Except perhaps in respect to viscosity or temperature changes, at this moment, I do not see local and temporal density changes as defining aspects, though it does complicate exact knowing of what is taking place during the fluid transfer. Another fudge factor? To respond to the question, supersonic flow is NOT SUFFICIENT to establish choked conditions nor pressure differentials. The pressure change must be from physical "obstructions". (even friction)
Is it not a puzzle that a simple blow pipe can send a dart along at velocities near 400fps on only 1 psi pressure difference.
1psi being about the maximum pressure attainable with human lungs during exhale. We can draw in twice that or more, such is life's urgency.
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To sfttailrdr46 - Thanks, but this topic is causing me to dredge the recess's of my memory from the late 70's - when I did coursework in fluid mechanics and fluid dynamics. Since then this knowledge base has been used designing industrial pnuematic systems, where one just makes sure the air doesn't choke, except perhaps at a flow control.
Caveats:
When I say pressure, I mean "stagnation pressure", unless I state otherwise.
When I'm typing fast, I tend to drop non-essential words, and the message comes across as snappy, argumentative, and exceedingly direct. That is NOT how I intend the following to be read.
Which comes first, the chicken or the egg?.... Actually, the dinosaur came first ;D
In the second case, they occur simultaneously, brought about by the increasing velocity at the restriction as the airflow accelerates....
The two results are symptoms of the same phenomena - they happen together
I am now visualizing the flow at the restriction accelerating until it reaches Mach 1.... and as the compressibility at the restriction increases the pressure downstream of the restriction drops.... At the moment the velocity reaches Mach 1, the pressure downstream also reaches 53% of the upstream pressure.... Exactly - I totally agree, the two must happen for the choke to form
To me, this mechanism explains why reducing the transfer port size reduces the power.... The pressure accelerating the pellet is reservoir pressure until the port chokes.... After that, it is 53% of reservoir pressure.... A smaller port chokes sooner, at a lower barrel flow (pellet) velocity, shortening the time at full pressure and increasing the time at 53% pressure.... and consequently lowering the power of the gun....
I have to switch to "engineer speak" here - it's too hard to translate, and takes too long to type.
It's not a step function - the pellet will see "most" of reservoir pressure (Pr) at the start (we will ignore the loss to the restriction), and this pellet pressure (Pp) will drop as the pellet accelerates. let's call this pressure drop across the restriction "delta P" or dP.
So Pr-dP=Pp.
But dP is a function of the velocity of the air (Va) through the restriction, which is a function of the velocity of the pellet Vp.
Therefore it follows that Pp=Pr-F(Vp) and when Va = mach 1, Pr/Pp = 1.893, and Va doesn't change after that, even with increasing Pr/Pp
Am I all wet, here?.... If I'm not, this could be added to Lloyd's spreadsheet, allowing the transfer port diameter as a variable to "shift gears" to the 53% pressure at a precise, known point, based on the velocity of the pellet.... (or at least approximately known).... Your final quote....
It's the pressure drop across the restriction, that results in the choke.
Could it be that the choke causes the pressure drop across the restriction?.... or that they happen simultaneously and could be triggered by the velocity at the restriction approaching Mach 1?....
This is where my bias of thinking in terms of stagnation pressure (energy), and trying to express it in English instead of formulae turns around and bites me. To me, the air velocity and static pressures are just output numbers that result from the energy flow in the system. I visualize the system in terms of stagnation pressures and pressure drops, and once the system is described that way, the fluid velocities and static pressure numbers can be calculated if one wants them.
If the downstream pressure increases such as to upset the differential requirement that establishes
choked conditions, those conditions will be upset, and choked flow will cease, 100%
regardless of velocity. Depends on what velocity we are referencing - Port, Pellet, or Air in the barrel.
And to reiterate, no REDUCTION of downstream pressure can increase the constant mass flow through a choked condition
It is not "chicken or egg", the pressure ratio MUST have been sufficient to begin, or choked conditions will never be initiated.100%
On the Idea of the usefulness of Bernoulli's work in these airgun considerations. The complete absence of steady state "smooth" flow completely devalues any calculations that may be applied, or information derived. The airflow though an airgun port is nothing if not turbulent and chaotic. Bernoulli avoided these uncertainties entirely by decree. There may be some insight to be gained there, but only in broadest of generalities.
Perhaps there is a possibility to shed light on the events of this thread purely on the examination of timing.
What is the condition of the pellet during the "time" that is shared while the reservoir passes it's compressed gas molecules into the volume between valve and pell base? Agreed, Bernoulli tells you something after the system is described in energy terms
Also, Let us not loose perspective. We might frequently return our consideration to how and why the rifle is being pressed back into our shoulder with each shot let go. There is no magic held by the gas molecules entrained in any high or low speed flow. The flow is completely the workings of pressure differences. As is the acceleration of the rifle mass and the pellet. I would use conservation of momentum and energy to describe the recoil, not pressure - but stagnation pressure is essentially energy anyway, so largely semantics
It can be difficult to distinguish between cause and effect, or effect and result.
I like to solve a puzzle in a paragraph before working through unfamiliar mathematics. In the case of the events between poppet valve and pellet base, there is much to be uncertain about. Numerical manipulations can give the sense of exactitude,while all the while failing in reality. That's where thinking in Second Law terms is important. BTW, I went through engineering school right at the transition from slide rules to electronic calculators, and the old slide-rule quickly teaches the importance of significant figures. This is something that recent graduates need to have pounded into their heads.
if you have air at 1 atmosphere flowing in a parallel tube that is miles long and could accelerate the flow to past Mach 1, then no choking would ever occur because all the air in the tube was at the same pressure.... Supersonic flow without any choking.... Even when the air exited the tube there would be no reduction in pressure to 53% of the pressure in the tube, it was, after all, at 1 atmosphere.... I simply want to know if accelerating the air to Mach 1 causes such a Compressibility Effect that the increase in pressure created by the air reaching Mach CREATES the pressure differential required to cause the choked flow to initiate....
This is how I think about this.
1) If it's 1 Atm absolute, the air won't flow if there isn't a pressure drop...
2) If it's 1 Atm(gauge) then the Pr/Pa = 2/1 since 2>1.893, the flow will choke.... :-[
3) Let's start with something easier ;) - We have a tank that's at 10psig, with a ball valve and 50 ft of 3/8 hose. We open the ballvalve - what happens? Pr/Pa = 24.7/14.7 = 1.68, 1.68<1.893, so the flow doesn't choke. The initial 10psi is lost in pressure drop through the hose, so, by the time the air reaches the end, the static pressure of the air is at ambient, and all energy has been converted to kinetic energy, frictional heat, and noise. The mass flow rate is such that the frictional losses are exactly balanced by the available pressure.
Measure the stagnation pressure along the hose, and there will be a steady decrease.
I'll address the #2 question later.
Got to go!
Jim
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;D So I will sit back and let the dust settle and continue to enjoy becoming better educated in the sub world of high performance modding of AG's
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The two results are symptoms of the same phenomena - they happen together
I totally agree, the two must happen for the choke to form
Jim, first of all, thanks for putting up with my persistence, which as I understand it, has paid off.... It seems to me that what I was postulating is, in fact, what happens as the air velocity at the restriction approaches Mach 1.... The increased air resistance (friction, compressibility, whatever) causes the DeltaP across the restriction to increase.... This would not, of course, be a linear function, but greatly concentrated in the last bit of velocity increase just before Mach 1 is reached.... We are all familiar with the huge increase in drag as an object approaches Mach 1.... This same phenomenon occurs in a tube as well, particularly if there is a point where the diameter is smaller.... Across that restriction, as the velocity approaches Mach 1, the DeltaP approaches the critical value.... When the velocity reaches Mach 1 (or slightly before), the DeltaP reaches 1.893:1, and the flow chokes.... THAT is exactly what I have been so persistant in trying to point out.... I initially didn't explain it very well, but you clarified above that is indeed what happens where there is a restriction to the flow and the flow is accelerating through it, as happens in a PCP while the valve is open....
If the restriction is abrupt, turbulent, turning, partially obstructed, or any combination of the above, then it is likely that the pressure drop across it will become greater than ~1.9:1 before the flow reaches Mach 1, in which case the flow will choke earlier than predicted by Bernoulli.... His prediction, based on the ratio of areas, is the best case scenario for laminar flow, I realize that.... In reality, the flow will choke before it would as predicted by the ratio of areas.... However, using the ratio of areas give us a LAST POSSIBLE moment when choking will occur.... Therefore, the chart offered by Steve in NC, modified by using the pellet velocity at the instant the valve closes (instead of the muzzle velocity), and the value of Mach 1 at pressure (since it does rise at high pressures) would predict the smallest possible port that would not choke under those circumstances....
Further, by using the above simple ratios of areas, we can predict a 47% (minimum) loss in the pressure at the base of the pellet at a given time in the shot cycle, that being the instant when the particular port size in question chokes.... Will it be perfectly accurate, of course not, it will likely occur earlier, as all the model can do is predict the best case scenario.... I am going to take a short break before continuing as I want to look at Lloyd's Internal Ballistics spreadsheet to see what happens when this idea is incorporated.... I hope to post my ideas about that later today....
Bob
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To carry on my thoughts from above, here is a graph showing roughly what happens inside a .22 cal. Disco at the beginning, middle, and end of the shot string.... at pressures of 2000, 1600, and 1200 psi....
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/DiscoPressures_zps03cb3e61.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/DiscoPressures_zps03cb3e61.jpg.html)
Note that even in the lowest pressure case, the valve is closing before the pellet reaches 600 fps, and the assumption is that the transfer port is large enough that the flow does not choke at the port.... Now let's see what might happen if the port is reduced to the point that the flow chokes when the pellet (and the airstream behind it) reaches 400 fps.... Here are the changes I am postulating.... Note I have put a "step" in the pressure (purple) curve showing the pressure dropping to 53% of the pre-choked pressure when the pellet reaches 400 fps.... Then on the velocity (green) curve I lowered the acceleration after 400 fps.... Please note that these are crude assumptions, just for the purpose of visualizing what I think may occur when you install a smaller transfer port....
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/DiscoPressures400fps_zpsa7ba9ce0.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/DiscoPressures400fps_zpsa7ba9ce0.jpg.html)
We all know that the velocity is reduced.... What I'm trying to do is propose a change to the model to represent that.... I'm going to PM Lloyd to have a look and see if he thinks this might be worthwhile.... In the meantime, I would invite your comments, in particular Jim's thoughts, on the validity of this approach.... Remember that this represents the "best case" scenario, the choking may occur sooner, and the pressure drop across the transfer port may be greater.... but just as in many other parts of the Model, those will end up in the "Efficiency fudge factor" to balance the spreadsheet results with reality.... Let me know what you think....
Bob
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SWMBO had us to run to Kamloops this afternoon, (and thus the hurry in my previous post) but all is good since I scored an 8Lb jug of IMR4350!!!
I believe we are on the same page - The only thing I would like to clarify/add is IF the restriction is sufficient to form a sonic choke, it causes the volume of air that passes through the choke to loose a bunch of energy - in an efficient design, that condition should be avoided. It is better to use a larger port, and chop the flow/volume early, and stay away from the chaos.
Regarding your long pipe question:
Quote from: rsterne on December 11, 2014, 11:17:57 PM
if you have air at 1 atmosphere flowing in a parallel tube that is miles long and could accelerate the flow to past Mach 1, then no choking would ever occur because all the air in the tube was at the same pressure.... Supersonic flow without any choking.... Even when the air exited the tube there would be no reduction in pressure to 53% of the pressure in the tube, it was, after all, at 1 atmosphere....
The "choked flow" applies to nozzles and orfices, and wouldn't actually apply to this problem. As indicated before, the air would not flow if there wasn't a pressure gradient along the length of the pipe. If the high pressure side was 1 Atmosphere (gauge) (2Atm(absolute)) venting to 1 Atmosphere (absolute), then the pipe would stabilize at a constant mass flow rate such that the friction losses down the pipe exactly match the available deltaP.... The air would go in at 29.4Psia, and exit the pipe at 14.7Psia..
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HI Jim.... Yeah, I realized my long pipe example was a pile of smelly stuff.... *LOL*....
I agree that it SHOULD be better to use larger ports and chop the flow off early.... Unfortunately, on an unregulated PCP, doing that by reducing the hammer spring preload ends up dropping the fill and refill pressure, at least it does with any I have seen.... Let's say you have a 22 cal Disco, which is a 2000 psi fill and 22 FPE.... You can reduce the power down to about 17 FPE and still use the 2000 psi fill, but try and get it down to 12 FPE and you can only fill to about 1600 psi.... On the other hand, if you leave the hammer strike alone, set for that 2000 psi fill, and strangle up the transfer port, all sorts of good things happen.... The smaller port flattens out the string, knocking more off the top (where the flow is maxed) and less off the ends.... Although the valve is still open for (roughly) the same amount of time, less air escapes into the barrel before it shuts, so you get more shots.... The net result is more shots at higher efficiency while still using the full pressure range (maybe even more range at the low end)....
There is one alternative method that works, called the bstaley mod.... It consists of an O-ring buffer between the hammer and the valve that limits the lift (and therefore the dwell) without having to dial back the hammer energy with the preload.... It also flattens the shot string and lengthens it, by acting like a very stiff, progressive rate valve spring.... Providing you are dialing the power back a long ways, it tends to very good efficiency, and can be better than found by restricting the transfer port.... so in fact is what you are suggesting, big ports and short dwell....
Now that I've got you agreeing that the increasing velocity through the restriction, through friction/backpressure/compressibility could cause that ~1.9:1 pressure differential and therefore kick the system into being choked.... I'm beginning to have second thoughts.... *LOL*.... If I look at it in tiny time increments, until the velocity at the restriction approaches Mach 1, the pressure upstream (reservoir) and downstream (ie between the restriction and the pellet) are similar.... The pellet is moving down the barrel, increasing in velocity, but the volume between it and the restriction (which for this example is the transfer port) is increasing.... When the flow velocity at the restriction is, say, Mach 0.8, there is hardly any compressibility effect, so there is little DeltaP across the restriction.... However, there is now significant volume of high pressure air between the restriction and the pellet.... The larger the restriction, the more volume at that Mach 0.8, but a typical case where the port is about 75% of bore diameter (56% area) would see the pellet going roughly 500 fps when the velocity at the restriction reaches Mach 0.8 (900 fps).... In the charts above, the pellet has moved 3-5", so the volume is already 2-3 cc at nearly reservoir pressure.... If the flow suddenly choked, and the pressure on the immediate downstream side of the restriction dropped to 53% of reservoir pressure, then the flow would reverse, instantly bringing the pressure back to nearly reservoir pressure - no more choke.... I can visualize this continuing in tiny increments as the pellet goes faster and further down the barrel, and the restriction never getting enough DeltaP to choke.... So, even though the velocity of the air through the restriction eventually exceeds Mach 1, the flow can't choke because the DeltaP never reaches ~1.9:1.... My question now is, how can these two facts be resolved.... The pellet, and the airflow behind it, can go supersonic, and yet the flow doesn't choke?....
I am now wondering if the size of the restriction (or the caliber, if there is no restriction) simply ends up being a mass flow limit.... and if that is the case, how can that be calculated and used?....
Bob
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I am jumping back into this thread rather late, but have read the various recent posts. A lot of good ideas and information. The internal ballistics spreadsheet/simulation has gone through numerous improvements and revisions over the years, but has never taken into account a flow restriction orifice or venturi, whether it be the T-port or valve exhaust port, or barrel port. Flow has always been calculated as if all passages were full bore diameter, which obviously is not the case. Part of the original thinking was that the pellet is acting like a cork in the barrel and will always keep a very significant percentage of the reservoir pressure directly behind it.
Even though flow restriction is not part of the spreadsheet, it really should be and I am adding "something" to the spreadsheet right now. That "something" is based on the inputs from this thread. Some of the factors that are already taken into account in the spreadsheet are: reservoir volume, reservoir starting pressure, initial dead volume between the valve and the pellet, barrel length, caliber, pellet weight, pellet break-away force, barrel friction, mass of the volume of air (adjusted for pressure) accelerating behind the pellet (BTW, the mass of the air is significant), valve closure point/time, residual pressure after valve closing, isothermal and adiabatic phases (which I am unsure of exactly how to apply), etc. There are variables I didn't mention, and probably some necessary variables that I am totally ignorant of.
But, even with all those variables in place, a "system efficiency factor" (fudge factor), has always been needed to reconcile the differences between predicted performance and empirical data. That factor varies, with low velocity big heavy bullets running as high as 95%, but light weight high vel pellets needing a factor as inefficient as 60%. The "system efficiency," (not to be confused with the efficiency of actual air usage vs fpe output) has always suffered more and more as the velocity went higher and higher. Maybe this sonic choking, or some velocity dependent phenomenon is a predictable impediment to achieving higher velocities.
Thinking about it more, with the pellet acting as a cork in the barrel, I doubt delta P across the T-port will ever be great enough to cause choking (but I could be wrong). However, the possibility of the air reaching Mach 1 in the T-port is certainly real. Then a couple of questions come to mind: After reaching Mach 1, how much is the flow reduced? Or does it almost stop? Is there a gradient approaching Mach 1? If some air continues to flow through the port, what variables control the calc of that flow? Others?
I'll try adding some version of the T-port vel dependent flow restriction to the spreadsheet. I am very curious to see if it brings the calculation closer to the empirical data.
Note- Even though the spreadsheet is an exercise in forcing the math to agree with the data, for me, the geek factor challenge is enough to give it value. I am lucky to be among people who "understand" that perverse need, LOL.
Lloyd
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HI Lloyd, and welcome back, your insight and input has been sorely missed.... I think it is clear that once the flow through the restriction reaches Mach 1, the mass flow limit is reached at that pressure, and even though the downstream velocity may exceed Mach 1, you will never get more air going through the restriction unless you increase the upstream pressure.... From what I read, the mass flow limit is directly proportional to the upstream pressure, and (neglecting friction) proportional to the area of the restriction (the square of the diameter)....
Perhaps the easiest way to approach this may be to modify the spreadsheet in some way so that the pressure/flow/something downstream of the restriction is degraded by the ratio of areas, relative to the way it is now which assumes bore-size porting.... and to apply that reduction only once the predicted velocity through the restriction reaches Mach 1.... I have no idea how to relate mass flow to the pressure at the base of the pellet, and ultimately that is the number you use to do all the calculations for velocity and energy.... but perhaps Jim may have a suggestion on how to work this concept into the spreadsheet.... The initial idea I proposed above, dropping the pressure to roughly half at the moment of choking (as in the graphs above) isn't the way, I already know that from preliminary looks at the numbers.... We need a mechanism/formula to "cap" the mass flow through the barrel, based on reservoir pressure and caliber.... and then degrade that based on any restriction placed on the mass flow from a smaller diameter between the reservoir and the pellet....
I have been playing around with calculations in a spreadsheet using the product of the transfer port diameter and the caliber to predict the RELATIVE FPE as you restrict the porting, and it seems to agree with the real world results to a high degree.... The other variables in the calculation are pressure and barrel length.... It is pretty crude in concept, but the results are surprising consistent with empirical data.... At the limit, with bore-size porting, the product is the caliber squared, of course.... My spreadsheet doesn't take into account any "timing" caused by the reduction in port diameter, it assumes the reduction is happening all the time.... If you introduced a timing element, having the reduction in power only happen after the velocity at the restriction approached Mach 1, the function would likely be proportional to the area, not the diameter.... just a thought....
Your spreadsheet Model is simply amazing.... I use it daily, and every time I do, I marvel at how accurate the predictions are for even large changes of caliber, bullet weight, pressure, and barrel length.... Once the basic Efficiency fudge-factor is found to make the model agree with the velocity and FPE/CI of the gun you are working from, how far you can go from that in terms of pressures, volumes, calibers, weights, and all the other variables amazes me.... Surely this is a test of just how good a Model it really is.... If we can add the diameter of the transfer port into the model, which at the same time I think will add a degrading of efficiency for supersonic velocities, it will be even better....
Bob
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Here is what I am thinking may be what is happening.... The basic layout is like Lloyd's graphs above, with the black being pressure in the barrel and the red being the velocity.... The green line is what I imagine the mass flow to look like with the flow everywhere subsonic.... Since the pressure is relatively constant, and the airflow is accelerating as the pellet accelerates, I think the mass flow is increasing until the valve closes, when it drops basically to zero and the expansion phase begins....
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/MassFlow1_zpsb2da5dc0.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/MassFlow1_zpsb2da5dc0.jpg.html)
If we insert a restriction into the system that limits the mass flow (ie approaching the limit which a choke would create), we get the blue line, which goes horizontal (constant value) after the port (restriction) gets near Mach 1.... This (somehow) lowers the acceleration felt by the pellet during the time the flow through the restriction is limited, resulting in the reduced velocity shown by the orange line.... What I don't know is how to relate the difference between the blue line and the green line into what happens to the pellet....
Jim?.... Lloyd?.... any ideas?....
Bob
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The following is a reply to Bob's post 91, and of course Bob has posted twice since then and Lloyd once, but I have so much into the reply, I'm posting it anyways, and will catch up to the others later. We have a Christmas dinner to go to tonight, so I won't get back here until tomorrow!
My question now is, how can these two facts be resolved.... The pellet, and the airflow behind it, can go supersonic, and yet the flow doesn't choke?....
There are two concepts regarding compressible flow that I've wanted to bring forward since I jumped in here, but the conversation has never swung around to the direction needed to really discuss them. I touched on both of them in post #69, but I'm not sure the implications of what they mean is totally understood. And they apply to Bob's question above, and which IS the point where I believe sonic "chokes" apply in PCP's. (Other than that case, I see them as being exceedingly transient events)
Firstly, is the nature of the sonic choke/sonic barrier. If Mach 1 has been reached in the restriction/nozzle, pressure events on the downstream (low pressure) side cannot influence what is happening up-stream... The downstream pressure can only influence the upstream pressure if the sonic barrier is not there - eg. - the flow is sub-sonic.
The analogous situation occurs when a super-sonic jet is approaching you - you cannot hear it until it has passed, due to the fact that the pressure waves in the air (which we hear as sound) cannot travel faster than the speed of sound in the ambient air, but the plane is traveling faster than that.
To understand what is happening with that, leads us into the second point I want to bring forward now. It's related to my favorite diagram on this topic, here it is again, for easy reference.
(http://i15.photobucket.com/albums/a362/Jim_Hbar/Flowpatterns.gif)
What is implied in the diagram, but has not been explicitly stated so far in this discussion (or what I recall from the Wiki article I stole it from), are the basic premises behind that diagram. If you followed along this far, you all probably intuitively realize what is going on, (and the conditions expressed in the diagram were undoubtedly stated in the text that Wiki stole the diagram from), but some less than obvious facts can be gleaned from the diagrams.
In general, the conditions of the diagram would be stated in the text of article, and for this one it would be a given that the chamber volume should be considered to be infinite, such that the supply pressure is constant (but different) in each figure. The ambient volume that the nozzle vents into would also be infinite, such that the air flow into it would not cause an increase in pressure. Also, the diagrammed flow would be established such that transient acceleration effects have disappeared.
The diagrams show a series of increasing mass flows, as the pressure differential increases across the nozzle. Let's call that deltaP nozzle, or dPn. Pressure of the chamber is Pc, and ambient pressure is Pa = 1. Pressure at the outlet of the nozzle = Po.
All pressures discussed here are stagnation pressures, and absolute, unless noted otherwise.
Fig. A shows subsonic flow. Pc/Pa<1.893 for air Po=Pa dPn=Pc-Pa
Fig. B shows choke just formed. Pc/Pa=1.893 for air Po=Pa this condition would not be very stable. dPn=.893 (plus the frictional loss in the outlet section) The sonic shock occurs at the choke.
Fig. C shows the choke, and the shock in the nozzle. Pc/Pa>=1.893, Po=Pa - Supersonic flow exists between choke and shock. The dPn has increased due to frictional drag at supersonic velocities.
Fig. D shows the choke at the outlet Pc/Pa>1.893, Po=Pa - Supersonic flow exists between choke and shock. dPn has increased.
Fig. E is overexpanded - Po<Pa, Insufficient back pressure, Chaos at nozzle - transonic velocity at outlet
Fig. F is just right Po=Pa again - exit velocity is supersonic, at ambient pressure
Fig. G Po>Pa, standing shock waves at outlet - exit velocity is supersonic/hypersonic.
The flow cannot go super-sonic without a "choke"/"barrier" (or sonic boom in aircraft terms). And there will be a corresponding shock wave, as the super-sonic flow collapses. So the flow travels up and down those diagrams, as the flow rate increases and decreases, and pressures build and fall in the outlet.
The above are discussions about the ideal nozzle, and then we go and put a pellet in front of it, and extend the heck out of the nozzle and call it a barrel! One thing we do know is, you can't have sub-sonic flow upstream of the barrel, and supersonic flow downstream of a point in the barrel, without the air passing through a sonic barrier with the corresponding 47% pressure drop. For the pellet to go super-sonic, the flow model has to get to to a flow regime as shown in Fig. D, or higher. The air immediately in front of the pellet must also be super-sonic, so the sonic shock MUST pass the pellet in the barrel.
And that is where all the energy and efficiencies go as the pellet velocity goes transonic.
One other little tidbit - Bob stated above
If the restriction is abrupt, turbulent, turning, partially obstructed, or any combination of the above, then it is likely that the pressure drop across it will become greater than ~1.9:1 before the flow reaches Mach 1, in which case the flow will choke earlier than predicted by Bernoulli.... His prediction, based on the ratio of areas, is the best case scenario for laminar flow, I realize that.... In reality, the flow will choke before it would as predicted by the ratio of areas....
And it is an important point to keep at the front of the mind.
We are beating up theories based on mathematical models developed in labs under ideal circumstances. And sharp edged orfices behave somewhat like the c/d nozzle I have been using as an illustration point, but the correctly shaped sharp edged orfice (with the back side relieved) tends to act more restrictive to higher deltaP's, and effectively throttle the flow, and reduce the effective area of the orfice as the dP's increase. And that is why nice relieved holes and gentle transitions flow better than the sharp edged ports. Just visualize the streamlines. BUT- a sharp edged orfice can be used to good effect, and apply some "pressure compensation" if you will.
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OK, so the important thing I got out of that is that for the pellet to go supersonic, there must be a choke formed behind it.... That choke caused the DeltaP to be at least 1.9:1, and then after that point, although the pressure is less than the reservoir pressure (by at least 47%) the velocity of the airflow and the pellet, can be supersonic, just as in diagram D or later.... This means that to go supersonic, even in a PCP with bore-size porting, the pressure accelerating the pellet must be 53% of the reservoir pressure or less, once the pellet exceeds Mach 1 (or maybe before), correct?.... No wonder the efficiency drops like a stone !!!
I assume the speed of Mach 1 inside the barrel is the speed at pressure (eg. ~ 1250 fps @ 2000 psi).... but would you use the pressure before or after the choke point to determine the speed of sound.... ie the velocity where the pressure drops by 47%.... Just for reference, the speed of sound in air is ~1130 fps @ 0 psig, ~1170 @ 1000 psig, ~1250 @ 2000 psig, ~1360 @ 3000 psig, and ~1490 fps @ 4000 psig....
Bob
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The Mach1 speed and the density at the "choke" would be determined by the upstream pressure. The logical test is, as the air approaches and is going Mach .99, it will be at upstream pressure and density.
Yes, there is an increase in mach1 with increasing density in air, but personally I would just pick a number in the middle of the range expected, and run with that. It's my opinion that this stuff really only applies as one attempts to hit transonic (Mach .9ish) or faster pellet speeds..
It's important to understand that the actual energy available to push the pellet will always be less than what is calculated by a model, due to turbulence, and other non-quantified effects, so the density and pressure available will be less than a simple calculation might predict. Using "fudge factors" covers off those things that are not easily quantified, as I understand Lloyd has done in his model, and that is a very reasonable and practical approach unless one is doing a technical thesis for a post graduate physics degree.
Jim
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;D Some of us need to go back and complete our Bachelors first then maybe I will understand what I need to know to comprehend what you guys are disseminating here ??? ;D
All kidding aside I have really enjoyed trying to follow along on this thread and I'm actually planning to attend the spring semester at my local SUNY
for some refresher math and mechanical engineering classes on fluid dynamics
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Work is progressing on the mod to the spreadsheet, but already there are some interesting, and I think significant observations.
As I stated previously, my model has always assumed full bore dia passages throughout the air circuit downstream of the valve head. And based on that, the column of air behind the pellet was a homogeneous, full pressure, mass. For the big bore work this spreadsheet was initially used for, that makes sense. But for PCPs with restrictive T-ports, maybe not.
Checking T-port vel in a medium powered PCP, it appears that with a T-port that is 3/4 the bore dia, Mach 1 might be reached in the T-port when the pellet is about 5" down the barrel. Bob has already stated this, and for many PCPs the valve is closing at about the same time the T-port hits Mach 1. I think that is a good thing. But if we drop the T-port to 1/2 the bore dia, M-1 is reached in the T-port when the pellet is only one inch down the barrel ! Yikes ! So what happens then if the valve is still open for 4 more inches of pellet travel?
The flow choking and the accompanying big delta P across the T-port ! I think the important point/question here is: "How much longer does the valve remain open AFTER M1 is reached in the T-port. I am trying to get the conditional statements and the math in place for what "might" be happening, but consider this (already stated by others in various ways): 1) the valve is still fully open and the reservoir is trying to force air thru the t-port, 2) the flow is now choked such that (with a 1/2 bore dia port) the barrel is now filling at 1/4 the rate it was before M1 was reached. (I think that is correct, but please correct me if I am wrong.) So for the next 4" of travel, the air is dribbling thru the T-port at 1/4 the original rate and adding minimal usable power to the pellet. We have always worked hard to achieve that "square wave" valve sequence, but now this flow choke is sabotaging all of our hard work. We don't see a severe drop in efficiency because we are only loosing air at 1/4 the rate, but still, the air isn't doing much to accelerate the pellet. It probably would have been better if the valve closed just as M1 was reached.
So back to the spread sheet. After M1 is reached in the t-port, the air will continue to flow thru the T-port as if the bore size has been reduced to the same dia as the t-port. So the rate of pressure drop in the reservoir is now 1/4 what it had been (with a 1/2 bore dia port) so not much additional air is being used, but now, the fill rate behind the pellet in the barrel is now 1/4, and therefore, the pressure (actually the force) on the pellet is starting to drop noticeably (note- I am not sure about this... at the very least, the rate of increase is dropping) before the valve starts to close. Pellet acceleration is dropping way down.
This will take a little time to work out, but, the sun came up about 30 minutes ago, and it is a pretty day out side with projects that can only be done on a day like today. The fresh air calls!
Lloyd
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;D Some of us need to go back and complete our Bachelors first then maybe I will understand what I need to know to comprehend what you guys are disseminating here ??? ;D
All kidding aside I have really enjoyed trying to follow along on this thread and I'm actually planning to attend the spring semester at my local SUNY
for some refresher math and mechanical engineering classes on fluid dynamics
Don, more power to you! Learning something new is about as healthy as it gets! But at my age, I think going back of school school would be torture, LOL, so my hat is off to you. Still, if I don't learn something new every day, I feel like I missed an opportunity.
With a lot of this stuff, after you sift through what is presented, it boils down to common sense. At least in hind-sight, LOL. I am glad we have so many smart contributors and people asking questions. The free flow of information is great. I worked the last half of my career at a place that designed, built, and tested, high end inertial navigation systems. I was fortunate enough t work with some REALLY smart people and whatever I needed to know, somebody there could help me.
Lloyd
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Lloyd, as always I am impressed by your ability to cut to the chase!.... It doesn't really matter if the transfer port is actually choked because the 1.9:1 DeltaP is reached or not, once the velocity reaches Mach 0.99, the flow rate through it flattens out at nearly the same value as if the port was choked, and can never exceed that value.... I also observed that with a 75% of bore transfer and barrel port, which is about as big as you can go without resulting to oval barrel porting or an axial flow design, that the transfer port velocity approaches Mach 1 at roughly the 5" point, which is a good point for the valve to close to maintain good efficiency.... It is interesting, however, how small an increase in port diameter is needed to push that distance much further down the barrel, and of course with bore-sized porting, you should never approach a choked condition even with the valve open to the muzzle if you keep the muzzle velocity in the mid 900s....
I'm going to do up a couple of diagrams showing where the velocity should, in theory, get to Mach 1 with some different size transfer ports so that everyone can compare them to the ones I already posted on the previous page.... That post compared WFO to choking occurring at 400 fps, which for a .22 cal Disco would require a smaller than stock transfer port of 1/8".... That value comes from: (0.125/0.217)^2 x 1207 fps = 400 fps.... I used 1207 as the average value for Mach 1 for a Disco because that is the speed of sound in air at 1500 psi.... Here are the graphs for a stock .22 cal Disco transfer port of 0.140", which would in theory choke at (0.140/0.217)^2 x 1207 = 502 fps....
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/DiscoPressures502fps_zpsf14653a5.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/DiscoPressures502fps_zpsf14653a5.jpg.html)
You will notice that at 2000 psi, the valve closes before the pellet reaches 502 fps.... At 1600 psi, any choke would form just as the valve is closing.... but at 1200 psi, at least in theory, the choke would exist for about 1" of barrel travel.... I don't know how to properly represent what happens to the pressure in the barrel after the valve closes, but the flow through the port essentially stops at that point and all that is happening is that the air in the ports and barrel, between the valve seat and the pellet, expands to continue accelerating the pellet.... All the diagram represents is the time between a possible choke forming and the valve closing, and it would seem that during that time period (and possibly afterwards?) we have reduced acceleration occurring....
One other thing I just thought about.... A stock .22 cal Disco gets significantly louder about half way through the shot string.... Is it possible that increase in noise is partly the "sonic boom" from a choking event.... or is it just the increased residual muzzle pressure we are hearing?....
Bob
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Here is another way of thinking about the importance of the transfer port size.... I am going to be adding several examples to this post as I draw the graphs, for some typical PCPs, and will put a title above the graph and comments below it for each graph I add.... I'm going to start with a regulated .30 cal PCP designed for 90 FPE and using a 90 cc plenum with a 2000 psi setpoint, where the valve is closing at 50% of the 24" barrel....
.30 cal Regulated - 50% Closing point - 950 fps MV
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/ChokingvsPortSize50_zpscbb4b1c8.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/ChokingvsPortSize50_zpscbb4b1c8.jpg.html)
The vertical green lines represent the theoretical point in the barrel where a choke would form at the transfer port for the sizes given (as % or boresize).... Note that an 80% or larger port should not choke in this gun....
.30 cal Regulated - 33% Closing point - 909 fps MV
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/ChokingvsPortSize33_zps0b1356f1.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/ChokingvsPortSize33_zps0b1356f1.jpg.html)
Reducing the dwell so that the valve closes at 33% of barrel length loses 41 fps, but now a 75% transfer port shouldn't choke.... This would probably be somewhere on the "knee" of the curve for this gun, and a pretty efficient tune, showing why the 75% transfer port is a good number for much of what we do....
.30 cal Regulated - 25% Closing point - 870 fps MV
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/ChokingvsPortSize25_zpsc75da6e9.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/ChokingvsPortSize25_zpsc75da6e9.jpg.html)
Reducing the dwell further, so that the valve closes at 25% of barrel length, drops another 39 fps off the velocity, and now a 70% of boresize transfer port should be OK....
.30 cal Regulated - 100% Closing point - 979 fps MV
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/ChokingvsPortSize100_zps278e1ffb.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/ChokingvsPortSize100_zps278e1ffb.jpg.html)
Going the other way, and keeping the valve open until the pellet has just left the barrel, only gains 29 fps, and would need a 90% transfer port to not choke.... Incidently, this tune uses about 75% more air than the 50% tune to produce that 29 fps gain.... an increase in FPE of just 6%....
I'm going to shift now to a .257 cal at 3000 psi with a 28" barrel, and the baseline will be a 72 gr. bullet at 960 fps with the valve closing at 50% of barrel length....
.257 cal 72 gr. - 50% Closing point - 960 fps MV
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Choking257cal72gr50_zps43c638bb.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Choking257cal72gr50_zps43c638bb.jpg.html)
The higher pressure has increased the speed of sound to 1360 fps, allowing a 75% port to nearly remain unchoked at the point the valve closes (in theory).... Now, instead of changing the dwell, I'm going to change the bullet weight (a lot) to change the velocity, which because the bullet is moving faster or slower will change where the bullet is when the valve closes.... Added NOTE: Even though this gun is a lot different than the one above, with the valve closing at 50%, the diameter of the port when the choke occurs at the moment the valve closes is within a pretty narrow range (76-79%).... If the same velocity was used for the speed of sound in both examples, that difference would have disappeared....
.257 cal 116 gr. - 33% Closing point - 750 fps MV
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Choking257cal116gr33_zpsfa50be3e.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Choking257cal116gr33_zpsfa50be3e.jpg.html)
Notice that because the velocity is so much lower, we shouldn't see choking even with a much smaller transfer port.... That doesn't mean that we wouldn't lose power by putting in a smaller port, only that choking is no longer an issue....
.257 cal 36 gr. - 84% Closing point - 1230 fps MV
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Choking257cal36gr84_zps55597fd3.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Choking257cal36gr84_zps55597fd3.jpg.html)
Still the same valve dwell, but with half the bullet weight we started with, the gun is now shooting supersonic.... and the valve is open nearly until the bullet leaves the muzzle.... It now takes a 95% transfer port to avoid choking.... Wait a minute, we said the bullet was supersonic, how come the barrel isn't choked?.... That's because (in theory) the speed of sound in the 3000 psi air is 1360 fps....
I think that is enough examples, this was really only a side trip to look at what minimum transfer ports make sense.... and the discussion has moved on.... Added NOTE: It would appear that the primary factors in determining what size port is required to not choke are the muzzle velocity and the point in the barrel where the valve closes.... Of secondary importance is the operating pressure of the system, which is determined by both the starting reservoir pressure and it's volume, which determine the pressure in the barrel, and hence the speed of sound, at the moment the valve closes....
COMMENT: After perusing the above and trying some more examples, I have realized that one generic chart stands out as a point of interest....
Muzzle Velocity 950 fps - Valve closing at 33% - Port diameter 75% of boresize
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Choking33Closure75Port_zps9da36bc5.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Choking33Closure75Port_zps9da36bc5.jpg.html)
While not exact for every gun, depending on the operating pressure and smoothness of flow, there is one useful piece of information to be had from this chart.... With the commonly used transfer and barrel port size of 75% of the caliber, any dwell over 33% of the barrel length will take a hit on efficiency in a gun shooting at 950 fps....
Bob
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the barrel is now filling at 1/4 the rate it was before M1 was reached. (I think that is correct, but please correct me if I am wrong.)
If upstream pressure is constant, the restriction determines what the maximum mass flow rate through the port can be.. As the velocity through the restriction increases, the delta P across the restriction also increases, and the mass flow rate through the port increases to the value given by density, mach1 and the port area. It can never be higher, theoretically. (Btw, when people say theoretically, they usually really mean "simplistically - but that's another discussion.)
The stagnation pressure downstream (and thus the energy in the air) has been decreasing rapidly as the maximum mass flow rate approaches.
From my very first post in this thread!
When the flow is choked, that restriction determines the mass flow rate of the system, until the pressure ratio is reached.
(deleted)
When the ports are big enough - What this calculated mass flow rate will do, is put an upper limit on the acceleration possible from the pellet - and that's how I likely will use it.
That's all - pretty small potatoes..
Thinking through it a bit more and crunching a few numbers, I agree that the choke has very little practical effect at the velocities we are talking about, if the ports are reasonable. If they are too small, I'm sure it does have some effect.
And of course, it applies after the pellet leaves the barrel, but that's not interesting - jokes over by then!
A dump shot should be affected by the choked flow if the barrel is long enough, but perhaps not as much some would think.
If you look at the last four panels on that Wiki diagram, the velocity downstream of the orfice is super-sonic in what could be considered the barrel. Intuitively, people under stand case A & B, and perhaps will go as far as C & D, but rarely E, and the fact that the flow can be super-sonic well beyond the nozzle as in F & G just goes beyond intuition.
Especially when considering that the flow is only sonic at the restriction.
To go through an orfice and then speed up?
But that's what happens, and the flow is choked.
BTW, as upstream pressure is increased relative to the downstream pressure, the flow regimes move down that chart.
The standing waves shown at the outlet (in the last panel), are related to the shock diamonds in the outlet of a jet or rocket engine.
Lloyd, the way I would use all this "choke" information, is calculate what the maximum mass flow rate (Mmax) into the barrel can be, as determined by the restriction area, or the caliber of the barrel.
Then I would go through the time iterations/numerical method calculations, and calculate the massflow rate (Mr) at the restriction/barrel entrance. Once Mach "C" is reached in the port (a tweak point, start at perhaps .85??), assume that the calculated mass makes it through the restriction, but the pressure drop across the port is increasing by a linear function of the velocity in the port.
Say (Pu-Pd)=(1-.53)(Vn-C)/(1-C)
Where Pu = Pressure Upstream, Pd = Pressure downstream, Vn is velocity in the nozzle expressed as Mach#, C is the Mach number to be tweeked where things start to get messy.
Once Vn = 1, Pu = 1.893Pd, Mr = Mmax there on out..
Jim
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Jim, thanks for confirming that the mass flow rate limit is the governing factor, and even more thanks for suggesting a way to predict the downstream pressure once Mach is approached....
This begs the question, how do we calculate the maximum mass flow rate?.... I assume the critical factors are the reservoir pressure and the area of the restriction?.... Other than environmental factors (temperature/others?) likely the molecular weight of the gas (eg. He, N2, Air would be different) and/or the speed of sound for that gas at the pressure used?....
And then, of course, the other question is what happens to the pressure in the barrel after the valve closes.... I assume it then simply expands, starting from the last value used before the valve closed, as the pellet continues towards the muzzle?....
Bob
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Bob - For the maximum mass flow rate, I would just start with reservoir pressure, air density at that pressure, Mach 1 at that pressure, and the area of the restriction. Mass flow simply = density x velocity x area x (some constants to make the units work out) Then de-rate that mass flow by 5 or 10% or so to account for pressure drops to the restriction, sharp edge orifice effects, boundary layers, etc...
It's going to be very close!
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the barrel is now filling at 1/4 the rate it was before M1 was reached. (I think that is correct, but please correct me if I am wrong.)
If upstream pressure is constant, the restriction determines what the maximum mass flow rate through the port can be.. As the velocity through the restriction increases, the delta P across the restriction also increases, and the mass flow rate through the port increases to the value given by density, mach1 and the port area. It can never be higher, theoretically.........
/quote]
Lloyd, the way I would use all this "choke" information, is calculate what the maximum mass flow rate (Mmax) into the barrel can be, as determined by the restriction area, or the caliber of the barrel.
Then I would go through the time iterations/numerical method calculations, and calculate the massflow rate (Mr) at the restriction/barrel entrance. Once Mach "C" is reached in the port (a tweak point, start at perhaps .85??), assume that the calculated mass makes it through the restriction, but the pressure drop across the port is increasing by a linear function of the velocity in the port.
Say (Pu-Pd)=(1-.53)(Vn-C)/(1-C)
Where Pu = Pressure Upstream, Pd = Pressure downstream, Vn is velocity in the nozzle expressed as Mach#, C is the Mach number to be tweeked where things start to get messy.
Once Vn = 1, Pu = 1.893Pd, Mr = Mmax there on out..
Jim
Jim,
Thanks for the insight you have provided! Your statement that the max mass flow is dependent upon density, Mach 1, and the port area is very helpful in explaining the rapidly decreasing efficiencies of high velocity shots. I was a bit surprised at how quickly Mach1 could be reached in the T-port.
I am having a little trouble with the concept of Pu/Pd=1.893. I could see where this might be true in an open system, but the PCPs we are working with are closed systems. Does the Pu/Pd=1.893 apply for closed systems as well as open systems? In a closed system, the application might be different. Here is my reasoning. Until the pellet leaves the barrel, the PCP airgun is a closed by the pellet in the barrel. The flow of the air that is released by the valve is basically pushing against a cork in the barrel. That cork consists of the friction of the bullet along the barrel walls, the inertia of the bullet, and the steadily increasing inertia of the column of air that is accelerating behind the pellet. It should be noted that the mass of the air column can be significant percentage of the weight of the pellet and must be included in the calculation.
As the air vel in the T-port approaches M1, Pu/Pd = 1, and delta P is close to zero. Even when M1 is first reached, delta P =0. And as the mass air flow stays at the steady, pressure dependent maximum rate, the bullet keeps the air from expanding to much. The amount of "make-up" passing into the barrel can be calculated, and its expansion against the restriction of the bullet can also be calculated. I think the ration of Pu/Pd will be closer to 1 than to 1.893, but I could be wrong. Could that be the case?
Lloyd
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OK, well using the Metric system that looks pretty easy.... Density in kg/m^3.... Velocity in m/sec.... Area in m^2.... multiply them all together and you get kg/sec.... So at 2000 psi, the air density is 164.4 kg/m^3, the speed of sound is 1252 fps (381.6 m/sec), and let's use a 1" diameter, which gives an area of 5.067 cm^2.... and there are 10,000 cm^2 in one m^2.... so we have....
164.4 x 381.6 x 5.067 / 10,000 = 31.79 kg/sec.... That is the mass flow limit at 2000 psi through a 1" diameter.... Did I get the math right (other than the derating)?....
Assuming I did, then multiplying that number by the caliber squared (in inches) should give the mass flow limit at 2000 psi.... so for a .250" cal (or port) you would have.... 31.79 x 0.250 x 0.250 =1.987 kg/sec at 2000 psi....
Bob
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the barrel is now filling at 1/4 the rate it was before M1 was reached. (I think that is correct, but please correct me if I am wrong.)
If upstream pressure is constant, the restriction determines what the maximum mass flow rate through the port can be.. As the velocity through the restriction increases, the delta P across the restriction also increases, and the mass flow rate through the port increases to the value given by density, mach1 and the port area. It can never be higher, theoretically.........
/quote]
Lloyd, the way I would use all this "choke" information, is calculate what the maximum mass flow rate (Mmax) into the barrel can be, as determined by the restriction area, or the caliber of the barrel.
Then I would go through the time iterations/numerical method calculations, and calculate the massflow rate (Mr) at the restriction/barrel entrance. Once Mach "C" is reached in the port (a tweak point, start at perhaps .85??), assume that the calculated mass makes it through the restriction, but the pressure drop across the port is increasing by a linear function of the velocity in the port.
Say (Pu-Pd)=(1-.53)(Vn-C)/(1-C)
Where Pu = Pressure Upstream, Pd = Pressure downstream, Vn is velocity in the nozzle expressed as Mach#, C is the Mach number to be tweeked where things start to get messy.
Once Vn = 1, Pu = 1.893Pd, Mr = Mmax there on out..
Jim
Jim,
Thanks for the insight you have provided! Your statement that the max mass flow is dependent upon density, Mach 1, and the port area is very helpful in explaining the rapidly decreasing efficiencies of high velocity shots. I was a bit surprised at how quickly Mach1 could be reached in the T-port.
I am having a little trouble with the concept of Pu/Pd=1.893. I could see where this might be true in an open system, but the PCPs we are working with are closed systems. Does the Pu/Pd=1.893 apply for closed systems as well as open systems? In a closed system, the application might be different. Here is my reasoning. Until the pellet leaves the barrel, the PCP airgun is a closed by the pellet in the barrel. The flow of the air that is released by the valve is basically pushing against a cork in the barrel. That cork consists of the friction of the bullet along the barrel walls, the inertia of the bullet, and the steadily increasing inertia of the column of air that is accelerating behind the pellet. It should be noted that the mass of the air column can be significant percentage of the weight of the pellet and must be included in the calculation.
As the air vel in the T-port approaches M1, Pu/Pd = 1, and delta P is close to zero. Even when M1 is first reached, delta P =0. And as the mass air flow stays at the steady, pressure dependent maximum rate, the bullet keeps the air from expanding to much. The amount of "make-up" passing into the barrel can be calculated, and its expansion against the restriction of the bullet can also be calculated. I think the ration of Pu/Pd will be closer to 1 than to 1.893, but I could be wrong. Could that be the case?
Lloyd
Great contributions!
It is difficult to pull the important details from the possibilities.
The pell must see pressure at it's base in order to satisfy acceleration equations. Propellent velocity does no good.
Have you ever seen an internal ballistics calculation for PB based on propellent velocity?
F=ma and all that.....
Still, The concept of "choking", seems to mean different things to different people in this discussion.
If the mass flow is set by "choked conditions", what effect will that have if the pell velocity is a function of propellant velocity?
Can you see the disconnect?
Why do light gasses propel with more velocity? because they show up with higher pressures more rapidly!
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Lloyd:
The air won't flow without a pressure drop (speaking in stagnation pressure terms, as I always do) - in other words, there is a constant loss of energy, (or work done by the air), to pass from the high pressure area to the low(er) pressure area. If there is no pressure drop, there is no flow.... The greater the flow, the greater the pressure drop required to sustain that flow, everything else being equal. Until you hit the wall and can't push any more through the hole......
Here's a web page to look at (http://www.womackmachine.com/engineering-toolbox/design-data-sheets/cv-%28flow-factors%29-for-compressed-air.aspx) - for simplicity sake, they use the value of 2 instead of 1.893, (and 50% instead of 53%)... Cv is measure of the flow capacity of a valve or component in a system, and is how industrial pneumatic flow capacities are rated.
But the chart illustrates the point I'm be-laboring.
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First off, I want to thank everyone for their patience with me on this. I know it is a pain when someone comes late to the discussion and then presents ideas and questions that have already been flogged to death. My apologies.
I am sure that I am misapplying some terms and that I have some semantics issues, but my guess is that we are not as far apart as it seems.
Cal, yes, I realize that pellet velocity (or pellet acceleration) is dependent on the force from the pressure on its cross sectional area, and not the velocity of the air behind it. I might not have stated that very clearly. BTW, where I live, the VT at the bottom of your posts can only mean Virginia Tech. Is that by any chance the case?
Jim, My background is more straight mechanical so the fluid mechanics are a little less intuitive to me and I am sure my terminology is a bit off, so I appreciate your persistence and patience. I am familiar with the C sub V factor (at least for solenoids), but, like in calculus, there is a difference in being able to work the problems and actually "understanding" the concepts. I can fumble through the problems, but you understand what is happening.
Let me try another slightly different explanation of my visualization of what is happening as the air reaches M1 in the T-port. Let me know where I am going off course. Thank you in advance for the help.
For simplicity sake and to help me better understand what is happening I would like to use some real numbers. Let's assume a reservoir of infinite volume filled to 1000 psi. The T-port is the main restriction and is one half the diameter of the barrel. The pellet is light enough to achieve high velocity at this pressure.
1) After the valve opens, and the pellet starts accelerating, the velocity of the moving column of air quadruples as it passes through the T-port, and then drops back down on the pellet side of the T-port. As long as the vel through the T-port stays below M1, the reservoir is able to keep the barrel filled behind the pellet such that the barrel and reservoir are essentially the same pressure.
(Is that explanation correct?)
2) As the pellet continues to accelerate, the air passing through the T-Port continues to fill the barrel faster and faster, and quickly reaches M1 and thus its mass flow limit. This is where I am getting hung up. Just before reaching M1, the pressure on either side of the T-port is close to being the same. (Correct??)
3) When M1 is reached the air flow doesn't stop, but continues to fill the barrel at a constant rate equal to the mass flow limit. (Correct?)
4) The pellet continues to accelerate, but because the fill rate is now a constant and cannot keep the barrel filled to 1000psi, the pressure in the barrel starts to drop. But the pressure drop is gradual and doesn't just plummet to 53%, or 530psi. (Correct?)
5) Or, does the air flow through the T-port basically stop until the pellet has moved far enough to let the barrel pressure drop to 530psi?
I am confused. Please help! Thanks,
Lloyd
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;D Lloyd let me say that your confusion and hard work with Cal and Bob working to clarify it is helping me to finally grasp what the significance of the thread and you guys goals achieve. Scarily it is beginning to make sense to me and the Impact on High performance tuning of our favorite toys ;D ;D
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I'm going to be busy for the next couple of days, except in the evening. Have an appointment in an hour, so this is going to blunt, with little explanation.
1) After the valve opens, and the pellet starts accelerating, the velocity of the moving column of air quadruples as it passes through the T-port, and then drops back down on the pellet side of the T-port. As long as the vel through the T-port stays below M1, the reservoir is able to keep the barrel filled behind the pellet such that the barrel and reservoir are essentially the same pressure.
(Is that explanation correct?) No - intially 1000 psi gets there quickly, as there is no flow, but starts dropping as flow increases
2) As the pellet continues to accelerate, the air passing through the T-Port continues to fill the barrel faster and faster, and loose more and more pressure and quickly reaches M1 and thus its mass flow limit. This is when the pressure downstream of the port is 530 psi I am getting hung up. Just before reaching M1, the pressure on either side of the T-port is close to being the same. (Correct??) No
3) When M1 is reached the air flow doesn't stop, but continues to fill the barrel at a constant rate equal to the mass flow limit. (Correct?) Yes And there will actually be a pressure drop from the port to the pellet, if the pellet is a significant distance down the barrel.
4) The pellet continues to accelerate, but because the fill rate is now a constant and cannot keep the barrel filled to 530psi, the pressure in the barrel starts to drop even more. But the pressure drop is gradual (and doesn't just plummet to 53%, or 530psi.Correct?) It was already at that level at step 3
Study the page and the table I linked to in my last post - It just happens to be the first table that popped up in a Google, that had the info I was looking for - I'll look for a better explanation/link tonight.
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Lloyd, you are struggling with EXACTLY the same problems I have (and still am).... I agree 100% with your first point, and most of the second, right up to the point where you say the pressure downstream of the restricition is basically equal to the upstream pressure right up to the velocity at the restriction reaching Mach 1.... That seems inconsistent with the requirement post choke for it to (suddenly) be only 53% of the upstream pressure (sudden discontinuous change in pressure seems unrealistic).... I agree 100% with your point 3, and I would love to believe that point 4 is what happens, but I think Jim will shoot it down as the 53% drop across the restriction is apparently a condition of the velocity reaching Mach 1.... Your point 5 seems unrealistic as well, of course, not only counter-intuitive, but involves stopping and starting the flow of a large mass of air....
Cal, I likewise realize that the propellant velocity is NOT what drives the pellet, it is pressure at the base of the pellet that does that, (which in the end is just rapidly, and mostly randomly, moving air molecules bouncing around), and the applicable formula is indeed F=ma.... That is EXACTLY where the disconnect in our reasoning is.... I think we can all grasp (and agree with) the concept of the mass flow reaching a limit when the flow at the restriction reaches Mach 1.... What Lloyd and I are having trouble with is the huge and sudden drop in pressure that accompanies that.... As I stated in one of my earlier posts, if that drop was sudden, like turning off a switch, then at that instant, the volume of air at the original pressure between the restriction and the pellet would simply expand (backwards) until the pressure was equalized.... and that would instantly cancel the choke.... Yet the choke must occur once the velocity reaches Mach 1....
Jim, once again thanks for your input.... in particular this sentence in response to Lloyd's point 1....
No - intially 1000 psi gets there quickly, as there is no flow, but starts dropping as flow increases
Reading this, to me, was the lightbulb moment.... At the instant the valve opens, but the pellet is stationary, there is virtually NO flow, those randomly bouncing around air molecules are just raising the pressure between the valve and the pellet until it starts to move, reaching 1000 psi very quickly.... Then the pellet begins to accelerate down the barrel, expanding the volume behind it, and the air from the reservoir keeps that volume full, but with enough pressure gradient to keep the air flowing through the barrel and ports as fast as the pellet is moving away from the valve.... When we place a restriction between the valve and the pellet, we begin to generate an additional pressure gradient across that restriction, which we call DeltaP.... This pressure gradient increases as the velocity through the restriction approaches Mach 1, eventually reaching 1.893:1 when the velocity reaches Mach 1, and the flow is then fully choked.... I add the word "fully" because this has been an exponential process, becoming noticeable at about Mach 0.8 (where the transonic region begins) and quickly building from there to Mach 1, when the flow is officially "choked"....
I do have a question, and that is in regards to the statement that the pressure at the pellet will be even lower than 530 psi.... IIRC, you stated previously that it is the DeltaP over the entire system that must be >1.893:1, so if that is the case, would not the pressure at the pellet be 530 psi when the choke first occurs?.... As the pellet continues to accelerate, and with constant mass flow input, why does it have to drop further?.... There is still air being supplied by the valve, in abundance, and the downstream pressure has no affect over the flow rate in a choked port.... Could not the pressure just downstream of the restriction be, say, 600 psi at the moment the choke forms, and increasing to, say, 650 psi as the pellet moves away from it, to keep the pressure gradient in the barrel, and yet maintain the DeltaP across the system because the air at the pellet is still only 530 psi?.... I know this is probably insignificant, but I want to understand as it is important that we can calculate the pressure, hence the force, accelerating the pellet....
Bob
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I had a look at the page that Jim linked to, and the chart clearly shows the mass flow (SCFM) limit when the outlet pressure drops below half the inlet pressure.... The formula given intrigues me, however....
Q = 0.6875 x (P1-P2)^0.5 x (P1-P2)^0.5.... which simplifies to Q= 0.6875 x (P1-P2).... which doesn't agree with the chart, as any difference of pressure of (for example) 10 psi should have the same flow in SCFM.... I therefore believe that equation must have been misprinted.... If the correct formula can be found, then would it be possible, using a mass flow calculation, to work it in reverse and calculate the pressure difference across the restriction as the velocity increases?.... We need to get a feel for how the DeltaP builds as the flow through the restriction approaches Mach 1.... Linear?, Exponential? (and to what power?)....
Bob
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Bob,
I noticed that problem with the formula, too.
Jim,
Thank you for the answers. They are tremendously helpful. The understanding that the entire air circuit is a continuum of pressure gradients that vary based on air velocity and air volume and passage and port shape, etc, etc, is the lightbulb moment for me. Very helpful, now I just need to apply it.
For what its worth, a single shot from a .22 pcp might use 22 cuin of air at std pressure, delivered in 0.002 seconds of valve open-time. (The pellet might stay int he barrel for .004 seconds, though.) That converts to about 390 scfm. And a valve or orifice in the circuit might have a Cv of 0.2 (big guess). Maybe a pressure drop of 300 psi is fully acceptable. I do not know if that pressure drop is reasonable or achievable.
Lloyd
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Since nobody disputed my formula for the Mass Flow Limit in Post #107 above, I decided to work with it and came up with the following.... First, a repeat of the Speed of Sound chart I came up with earlier in this thread.... http://www.gatewaytoairguns.org/GTA/index.php?topic=66866.0 (http://www.gatewaytoairguns.org/GTA/index.php?topic=66866.0) .... Note that the values for Air were extrapolated using the geometric average for N2 an O2 in the ratio 78:21....
(http://i378.photobucket.com/albums/oo221/rsterne/Important/SpeedofSound_zpsbe789913.jpg) (http://s378.photobucket.com/user/rsterne/media/Important/SpeedofSound_zpsbe789913.jpg.html)
Next, using the same calculator at http://www.peacesoftware.de/einigewerte/einigewerte_e.html (http://www.peacesoftware.de/einigewerte/einigewerte_e.html) I determined and graphed the Density at 20*C vs. Pressure as follows....
(http://i378.photobucket.com/albums/oo221/rsterne/Important/Density_zps156bc1dc.jpg) (http://s378.photobucket.com/user/rsterne/media/Important/Density_zps156bc1dc.jpg.html)
I then used the formula in Post #107 above to calculate the Mass Flow Limit through a 1" diameter and plotted it vs. Pressure as follows....
(http://i378.photobucket.com/albums/oo221/rsterne/Important/MassFlowLimit_zps44b7a9cd.jpg) (http://s378.photobucket.com/user/rsterne/media/Important/MassFlowLimit_zps44b7a9cd.jpg.html)
What a nice surprise that it turned out to be so close to a linear function that we can consider it as such, particularly since we will have to derate the value slighty to allow for turbulence, etc., which will induce a greater uncertainty than any non-linearity.... We can now safely state that for our purposes the Mass Flow Limit through any given orifice is directly proportional to the upstream pressure.... I took this one step further, and divided the Mass Flow Limit by the Pressure and converted to grams instead of kg. and came up with the following chart to show the slight variation in the value of the "constant"....
(http://i378.photobucket.com/albums/oo221/rsterne/Important/MassFlowConstant_zps0932cc24.jpg) (http://s378.photobucket.com/user/rsterne/media/Important/MassFlowConstant_zps0932cc24.jpg.html)
Over the range of interest (1K-4K) it varies from 15 to 17.4, with an average value over that range of 16.3.... If we derate that by 8%, we get a value of 15 g/sec/psi, in other words the Mass Flow Limit is 15 grams/second for each psi of upstream pressure on a 1" orifice.... I think that should be a usable value for further calculations, unless somebody can blow a hole in my math....
ADDITION: Using that figure, at 2000 psi, in a time of 1 millisecond in a .22 caliber barrel, we would see about....
15 g/sec/psi x 2000 psi x 0.001 sec. x (0.22")^2 = 15 x 2 x 0.0484 = 1.45 grams/millisecond for the MAXIMUM flow rate possible....
Using Lloyd's example above, 22CI of air at std. pressure is 360 cc, and has a mass of 360 x 0.001204 = 0.433 grams spread over 2 milliseconds, for an AVERAGE flow rate of 0.22 grams/millisecond.... It certainly seems possible to reconcile these two figures....
Bob
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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 (http://www.aerospaceweb.org/question/propulsion/q0224.shtml)
cheers,
Douglas
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The understanding that the entire air circuit is a continuum of pressure gradients that vary based on air velocity and air volume and passage and port shape, etc, etc,
That's a very good description! I wish I would of thought to express it like that earlier.
Bob - I wouldn't trust that link I put up. It's just the first table that I found that demonstrated the point I was trying to make at the time.... It makes no sense to express a formula in that form (two square roots of the same term multiplied together?) , and therefore, I suspect it must be in error..... The 40PSIG Column also has goofy numbers, btw. It was copyrighted in 1990, so you would think they would had gotten around to fixing the boo-boos by now.
Unfortunately, any books that I may have still are at our other place, so I can't even go looking for information..
I used to rely on a particular binder of information from a certain manufacturer for my calculations, however, they now have converted that approach and information to an application that is sold for a price..
Try this one (http://www.generant.com/downloads/Cv_Calculator_Explanation.pdf) for formulas - it looks better. And it is the explanation for this calculator http://www.generant.com/cvcalc.aspx (http://www.generant.com/cvcalc.aspx)
And here's another to read http://www.swagelok.com/downloads/webcatalogs/EN/MS-06-84.PDF (http://www.swagelok.com/downloads/webcatalogs/EN/MS-06-84.PDF)
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Jim,
That Swagelock tech bulletin is pulling it all together for me. Thank you!
Lloyd
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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 - https://www.youtube.com/watch?v=CnAEwDQxeKo (https://www.youtube.com/watch?v=CnAEwDQxeKo) - 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 (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..
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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....
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Disco1600TheoryvsActual_zps06df1feb.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Disco1600TheoryvsActual_zps06df1feb.jpg.html)
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
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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....
(http://i378.photobucket.com/albums/oo221/rsterne/PCP%20Internal%20Ballistics/Disco1600MassFlowLimit_zps5a8dfa0e.jpg) (http://s378.photobucket.com/user/rsterne/media/PCP%20Internal%20Ballistics/Disco1600MassFlowLimit_zps5a8dfa0e.jpg.html)
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
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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
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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
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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 (http://www.aerospaceweb.org/question/propulsion/q0224.shtml)
cheers,
Douglas
Though not quite the same mechanism, this visual and narrative is interesting.
https://www.youtube.com/watch?v=cp5gdUHFGIQ (https://www.youtube.com/watch?v=cp5gdUHFGIQ)
It highlights the element of flows captive within the directed stream.
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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
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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
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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
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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
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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.
(http://i920.photobucket.com/albums/ad47/abbababbaccc/comparison_zpsa5d8d52f.jpg) (http://s920.photobucket.com/user/abbababbaccc/media/comparison_zpsa5d8d52f.jpg.html)
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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,
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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)
(http://i15.photobucket.com/albums/a362/Jim_Hbar/MassFlowvsPressuredrop-1.jpg)
The second is the same equation flipped around, with Mass flow as the independent variable, and Outlet Pressure as the dependent.
(http://i15.photobucket.com/albums/a362/Jim_Hbar/Outlet_vs_Mflow-1.jpg)
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 )
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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
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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! ;D ;D 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.........
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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
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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..... :o :o :o :-X :-X
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...
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.. 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?
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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
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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
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Curiously, While watching the hockey game, I was also doodling with port designs that include multiple tangential drillings that would allow vastly increased port area without pellet problems. (Two stroke piston port technology in play ;-)
I wonder about situations where the poppet valve face is the dominant feature in the gas flow equation. Small poppets, light springs, long travel/dwell etc.
At present, Typical designs seem to focus on the probe and port interface. Should that just "go away"?
I could see a time when tuning is accomplished with valve face inserts to control port area, and/or travel limiters (Lift) With everything down stream dictated by bore size. Not to disregard reservoir pressures of course.
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The multiple port designs I have seen are inferior to the single, larger port.... In the RWS 850 you drill out the bottom barrel port if you want it to flow.... In the Hatsan with their 6-port valve outlet, plug 5 of them and enlarge the one that lines up with the flow and you gain efficiency.... Just my observations on what HAS been done, not that some other alternative can't be made to work....
If you want maximum power, make all the ports bore-size or a bit larger, and make the valve throat area about 10% larger than the bore area.... After that, I don't think it matters where you decide to throttle the flow, or how.... You can reduce the FPE by using a smaller transfer port, barrel port, larger probe, smaller valve exhaust port, choking one of the ports off with a screw, or as I did on my probeless, retractable bolt, prevent it from drawing clear of the barrel port... Any of those work to reduce the flow, be it by choking, adding resistance, whatever the method.... You can also reduce the FPE by reducing the valve lift and/or dwell, and you can do that by backing off on the hammer strike, adding more valve spring, or an O-ring buffer (which is really a very stiff, progressive valve spring), or by physically limiting the lift with a hammer stop... You can also cut the power by using less pressure, and a few other ways I've forgotten to mention or I'm not aware of.... I guess it boils down to what is the easiest way to shed power without giving up too much efficiency (or even by gaining it).... Some of these methods will work on regulated guns (eg. lift limiting like on a Korean PCP), but if you use them on an unregulated PCP they don't work well because you are taking away the valve's ability to self-regulate.... Others will work equally well on unregulated PCPs.... Some of them hurt the efficiency, and some help....
My opinion is that having everything as unrestricted as possible (including valve lift >1/4 throat diameter) and varying the amount of air released by the valve is the best from an efficiency point of view.... Trying to do that on an unregulated gun is VERY complicated, much less so if regulated, because you are just working with one variable, the dwell.... For a given pressure, barrel length and caliber, the dwell then represents the balance between power and efficiency.... more of one, less of the other, pure and simple.... Want more power, increase any of the above (no replacement for displacement).... I think of the product of the pressure (turbo boost) and the barrel volume (length x area = displacement) as the potential the gun has to produce power.... Fix those quantities, and the heavier you make the pellet, the more dwell you can stand (and need) to get more FPE from that heavier pellet.... The limiting factor on weight is when the SD of the bullet overcomes the pressure's ability to produce the velocity you want in the barrel length you have.... but I'm getting wayyyyyyyyyyyy off track here....
Given a choice, I would have wide open porting, on a regulated PCP.... To vary the power, I would change the setpoint pressure, and then find the best hammer strike to operate the gun so that the valve is closing at about 25-33% of barrel length (the knee of the curve).... Then we can forget all about choking....
Bob
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Bob
You always catch me with comments like "then we can forget all about choking"
And yet it is one of the very first phenomena that comes to play on valve opening.
But, perhaps it is insignificant in the over all scheme..... Time wise any way.
It would be interesting to make use of flow inertia in the quest for efficiency. The cooling of the reservoir must offer some energy to exchange "somewhere".
Are you aware that normally aspirated I.C. engines can have volumetric fill ratios greater than 100%? All due to "tuned port" inertia. I bet you did ;-)
If this same utilization of energy can be applied to air guns, We should get more shots/fpe from the same fills. The examples you have mentioned in testimony of the theme.
Yes, Porting that did not raise more questions than knowns would be a real boon.
Have you ever played with a flow bench? Amazing what a 8mm diameter ball on a stick can do to the flow through a 30 mm tube.
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Yes, Cal, you're 100% correct, the valve is choked from the moment it opens until the pressure in the exhaust port reaches 53% of the reservoir pressure.... How long does that take, 0.00001 seconds?.... How much flow would you lose compared to if the valve was not choked during that time period?.... So there you go, you're right, OK, we can't get away from choking, it's part of a PCP....
but we CAN forget about the effect it (valve choking on opening) has on the operation of the gun, IMO.... better?.... The CONTEXT of my statement was regarding using bore size porting to eliminate choking in the part of the valve cycle that is actually DOING anything....
Never had the opportunity to play with a flow bench, but porting and polishing cylinder heads and all the accompanying tricks are quite familiar to me.... and also the multi-transfer ports in 2-strokes from the (wide open) crankcase.... and the use of tract length tuning (intake and exhaust).... quite a bit different than what takes place in an airgun.... again IMO.... YMMV....
Bob
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Yes, Cal, you're 100% correct, the valve is choked from the moment it opens until the pressure in the exhaust port reaches 53% of the reservoir pressure.... How long does that take, 0.00001 seconds?.... How much flow would you lose compared to if the valve was not choked during that time period?.... So there you go, you're right, OK, we can't get away from choking, it's part of a PCP....
but we CAN forget about the effect it (valve choking on opening) has on the operation of the gun, IMO.... better?.... The CONTEXT of my statement was regarding using bore size porting to eliminate choking in the part of the valve cycle that is actually DOING anything....
Never had the opportunity to play with a flow bench, but porting and polishing cylinder heads and all the accompanying tricks are quite familiar to me.... and also the multi-transfer ports in 2-strokes from the (wide open) crankcase.... and the use of tract length tuning (intake and exhaust).... quite a bit different than what takes place in an airgun.... again IMO.... YMMV....
Bob
Are you going to tell Steve in NC? ;-)
ps, piston port two strokes at 10K rpm, everything happens in .006 seconds, power stroke in .003! Not far off from air gun internals. A volume and flow, BMEP comparison might be in order. hmmmm Another day.......? ;-)
pss I always stuffed the crankcases. makes for higher compression, and better flow ;-)
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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?
What poppet valve?? 8) 8)
:-X
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Or do you mean.... what valve?.... as I assume whatever it is, there would still be a greater than 2:1 pressure ratio across it when closed.... but now I'm being silly as like you said, Jim, other than a transient on valve opening, just keep the ports boresize and the velocity subsonic and we can disregard (better word than forget) choking....
Bob
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Ok guys the deal is to use a convergent cone to feed the barrel Bore size from behind the pellet and to used sonic choking to produce sonic packing....
as the pellet travels down the barrel after a certain point it becomes a faux de laval/C.D. nozzle and flow does go super sonic and the shock waves cause sonic packing of the charge behind the pellet which is already accelerating...
the charge behind the shock wave fall back to subsonic as it travels up the column of air but packs it in front till the shock wave hits the back of the pellet...
post # 123 (instead of copy and paste) http://www.gatewaytoairguns.org/GTA/index.php?topic=94054.msg994804#new (http://www.gatewaytoairguns.org/GTA/index.php?topic=94054.msg994804#new)
?
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I have never heard of "sonic packing".... can you please supply a reference to it?.... Google returned zero hits....
Bob
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well that's my term for the compression of a gas in front of the shock wave...
scroll down to in supersonic flows.
https://en.wikipedia.org/wiki/Shock_wave
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The interesting thing I got from that reference is that the length of the shockwave is about 200 nm.... or about 0.00001".... Not much "packing" can be done in that length, IMO....
Bob
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a nitrogen molecule is .3 nm so the scale is 200mn pushing .3nm... and I think (?) I read using grams law oxy molecules are smaller...
the sky is blue because the molecules are in tenths of nanometers, smaller than the wavelengths of visible light...
edit*
I looked here and 0-two has a molecular weight slightly higher than N-two...
http://www.engineeringtoolbox.com/molecular-weight-gas-vapor-d_1156.html (http://www.engineeringtoolbox.com/molecular-weight-gas-vapor-d_1156.html)
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so scaled to inches that is 50' and .9"
?
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and compared to the size of the pellet, or the length of the barrel?.... I guess I just have no idea what you are suggesting.... Perhaps if you can show me where something like this has been measured, or the real effect of a shockwave in a barrel, as opposed to just expanding gasses, I will understand better.... but at the moment I am completely in the dark.... Sorry....
Bob
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https://en.wikipedia.org/wiki/Blast_wave
https://en.wikipedia.org/wiki/Shock_tube
thanks for the patience...
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Unless I misunderstood those two articles, we do not have any conditions inside a PCP which could even come close to creating a blast wave.... In fact, I do not think even a conventional firearm would have such conditions, as the propellant gas is created by rapid combustion, not detonation, which is required to produce a blast wave.... Even the gas-driven shock tube requires a rupture disc to allow a very short rise time for the pressure, I would think orders of magnitude faster than we get by opening a valve....
In Lloyd's experiment, there is NO rapid rise I pressure, only a simple "uncorking" of the high pressure by releasing the bullet.... and so far that is producing the highest velocities we have been able to attain.... These conditions are just about as far from a blast wave as you can get, IMO....
Bob
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Sonic choking, sonic packing, sonic horizon...
Why? So far, conventional mechanical engineering principals have been used to model and predict PCP velocities of >1700fps. If they hold to 2000fps, then all this talk of "sonic ????" is needless.
The diminishing returns build quickly at the levels we are seeing. I think we will see 2000fps, but not much more. Unless we want to go the great length (20 foot long barrels, and carbon fiber pellets).
The phenomenon being referred to as "sonic packing" is the radial velocity gradient resulting from fluid friction.
Maybe a CD nozzle would serve to promote the gradient sooner, but it will happen on it's own, even with a straight inlet.
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Sonic choking, sonic packing, sonic horizon...
Why? So far, conventional mechanical engineering principals have been used to model and predict PCP velocities of >1700fps. If they hold to 2000fps, then all this talk of "sonic ????" is needless.
The diminishing returns build quickly at the levels we are seeing. I think we will see 2000fps, but not much more. Unless we want to go the great length (20 foot long barrels, and carbon fiber pellets).
The phenomenon being referred to as "sonic packing" is the radial velocity gradient resulting from fluid friction.
Maybe a CD nozzle would serve to promote the gradient sooner, but it will happen on it's own, even with a straight inlet.
It matters because the design can be tuned and it matters where the shock wave occurs to possibly tune to a Mach Stem formation...
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"Unless I misunderstood those two articles, we do not have any conditions inside a PCP which could even come close to creating a blast wave...."
for a pellet to exit the barrel at super sonic speed there has to be super sonic flow right?
super sonic flow itself causes a shock wave..... It does not matter what is moving thru the air it can be a column of air or a plane wing... as soon as it hits supersonic it causes a shock wave...
ok so how does a shock wave become a blast wave..? right?
A blast wave is simply a sharply peaked shock wave.
so
How does the supersonic shockwave become sharply peaked?
it is in a focusing device called a barrel quoting the article "Blast waves cause damage by a combination of the significant compression of the air in front of the wave (forming a shock front)"
for the pellet to beat the speed of sound of the starting pressure 4500 psi means there is a blast wave/shock wave...
in fact it has to cause the pressure to rise behind the pellet to accelerate the charge to the pellets MV 1750 fps...
how can that happen..?
The pressure has to rise the point that the speed of sound is 1750 fps in the charge...
but pressure drops by the time the pellet is near the muzzle because of Boyles law... so pressure should be way down... ???
I can see your statement about the first shockwave not being strong enough to cause that rise... with your chart in the other thread that ends at 5000psi I make the guess it needs the charge to be about 5500-6000 psi or so... a 20-25% rise
but if it becomes stronger then maybe
that is why I wanted you to see is the bit about Mach stem formation and constructive interference cause that could be one of the things happening...
Quoting the article again " Anything in this area experiences peak pressures that can be several times higher than the peak pressure of the original shock front."
with your help we could find about when super sonic flow happens it has to be about the time the pellet is at high trans sonic near supersonic fps for the psi in the barrel/reservoir
but the pellet is a ways down the barrel which you can chart with your spreadsheet... velocity at barrel length
and the shock wave is near the nozzle which is also near the closed end of the tube...
so what happens when the reflected shock wave catches up to the shock wave headed to the pellet...
constructive interference/Mach stem...
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Well, as usual, a little knowledge is a dangerous thing.... I have never heard of a "Mach Stem", so when I Googled it and the very first (and in fact most of the) results talked about Nuclear explosions I immediately know I was in wayyyyyyyyyyyyyy over my head.... I have no intention of going back to University to learn about this stuff, and I definitely won't understand enough to intelligently discuss it any other way.... Therefore I will just have to stumble along with good ol' Newtonian Physics as I understand it.... and let those much more capable and knowledgeable than I debate the intricacies that may (or may not) be happening inside a PCP barrel....
Mach Stems?.... Blast Waves?.... Sonic Packing?.... Sorry, not a snowball's chance in H E double hockey sticks I will live long enough to understand them completely enough to apply them to a PCP....
Bob
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I will, however, toss out this idea....
We have all seen the beautiful photos of Shock Waves forming around the nose of a jet fighter, or bullet.... where we have an object penetrating a mass of (relatively) still air....
We have also seen diagrams of the velocity gradient that takes place in a pipe, where the air near the wall is slower than the air in the middle....
We know that at room temperature, the RMS velocity of air molecules is 1650 fps.... but that some are stationary and some moving many times faster....
Is it possible that with nothing to "hit" but other air molecules (and the back of the pellet).... that there is no collision to create a shock wave inside a barrel?.... I am thinking of each layer of air in the barrel (pipe) moving slightly faster than the one outside it.... Each air molecule has nothing to hit at Mach 1 to create a shock wave.... Not another air molecule, not even the back of the pellet, because it is moving away from the molecules at (in our case) 1700+ fps..... Since the molecules near the wall of the barrel are moving slower than the ones in the middle, even THEY are not hitting the barrel, as a group, fast enough to cause a shockwave....
Yeah, I know there is such a thing as a CD nozzle.... and I know that IF the FLOW VELOCITY reaches Mach 1 there (which at 4500 psi is ~1550 fps) then the flow is choked.... However, is it possible that the only place the FLOW (as a whole) is reaching 1550 fps is momentarily, just before the pellet reaches the muzzle?.... Perhaps without the CONVERGING part of the CD nozzle, to strip away the outer, slower layers of air, there is no Shock formed at the narrowest part, because there IS no narrowest part.... and no molecules are hitting the walls fast enough to trigger a shockwave and choking.... I don't know, I'm just throwing the idea out there.... Or, perhaps any "choking" that does occur is so far down the barrel that most of the acceleration has already taken place?.... Food for thought?....
Bob
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We had some light rain last night and this morning, and were expecting heavy downpours this afternoon, so in prep for that I was up on a ladder :( cleaning out the gutters. Half round gutters, half full of water, with big wads of leaves and twigs here and there blocking the flow. So, just like any normal airgun techno-geek, what I was REALLY seeing was a cross section of a barrel with a pellet in it. Wow, is that pathetic or what ! :-[ Opening the blockage at the exit end, the water flowed out nice and easy. But trying to push the water along with my hand to Force the leaves to the exit end, there the waves were :o , striking the leaves and then bouncing back upstream in the gutter, and then reflecting back down stream again. Wave theory...... I don't think I have enough brain cells to really embrace and learn about this. K.O. and Bill G have been talking about it and are obviously visualizing something that I am just not able to. Like listening to music and not having a clue as to what the notes are. That's probably part of the reason why I am so stubbornly resistant to all the wave and sonic theory talk. My apologies if I am a little pig headed about it sometimes. :-X I know there is something there, but it totally baffles me. :-\
Lloyd
P.S. Bill G and K.O., you guys are explaining it fine, but for me, its like a cow taking a leak on a flat rock, it all just bounces off. ;)
P.P.S. Bob, sure I will say that that is one explanation of what is happening, and just as good as any of them. ;)
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LLoyd,
first this has become obsessive for me too...I was looking for answers in my sleep... I actually dreamed another unlikely but (in dream) possible... so first because some particles are heavier they as the tank sat stratified....gravity ya know... so tank stored nozzle down it gave a slightly more oxy rich mix... then as the projectile was wizzin down the barrel the oring was leaving petro based molecules behind... this mix then ignites producing part of the 25% boost...
crazy huh...
but the other obsessive I reread the whole thread trying to get the gist of the bases of the statements...see if they fit 2-d or 3d modele and such to see what is being suggested...
or the boundry conditions and how those system are being thought of...(me I think Chaos theory/fractal generations, Might work)... Navier -stokes and etc... etc....
Point is so much food for thought been working hard with stuff I barely remember and have to look up again and talk with my son (shared hobby tryin to understand Q-physics)... mostly self taught...not much of the math per say (understand some) but understanding principals/theories the math is founded on...
been a good few days forcing myself to concentrate tiring but loving it... small contribution t 20 will on the way for the cause.
between the 1st-5th thanks for your work already done...
Bob,
Sonic stuffing came from my teenage interest in 2 stroke dirt bikes and how they use the size and shape of a expansion chamber to help widen or narrow the power band
the wave theory came because of being in the army at 17 I got hold of subcourse en 0053(still have it my daughter used it to scribble in/on when 3 but its still readable)... and that lead to wanting to understand about shaped charges a bit better... then at 19 or so had some informal tutoring from an E.O.D. specialist... that was when I learned about Mach stems...
Ok Bob Now You are Going to need patience with me... q-physics but it lets it be possible both you and I be right...and just may set up conditions in my part of the system for a kind of quantum tunneling... ;)
I was about to respond to your above post with part of the first law of thermodynamics... Bob it just does not make sense the conservation of energy says--- that the total energy of an isolated system is constant; energy can be transformed from one form to another, but cannot be created or destroyed.---
Well Bob I have a ton of respect for you so I decided to hold off and think for a day longer...
so then I remembered two things... the rest of the rule( energy can change state)...
and that some one told me (can not remember who) if you can't explain a systems behavior at the 100nm scale or about then use the Quantum scale... .3nm molecules... bingo...look at it from quantum field theory...
So a closed dynamic quantum field (the pressure vessel)with a bit of leakage/expansion to a larger system(entropy)...transferring heat...
and that fields state is 4500 psi med high supersonic-perturbed...half the molecules are going double the Mean fps and half are going half the mean fps
ok now add the next variable the forth dimension... space/time (can simplify to just time for our purposes)...
and a bit of and perturbation theory(closed dynamic systems tend to seek balance)
http://www.scholarpedia.org/article/Perturbation_theory_(dynamical_systems) (http://www.scholarpedia.org/article/Perturbation_theory_(dynamical_systems))
So state1 ( 4500 psi@cc perturb supersonic)-entropy(time at state) + time = (4500psi@cc more balanced state(same average energy but less deviation from average fps))- entropy(time at state)
There is a reason I started with 4500psi perturbed supersonic not 4500 psi perturbed 1550fps but will save explanation of that for a bit but there is a reason it is at that state...
Care to take a swing at the reason or are you thinking... is he bs-ing or... May not be right but serious theory....or Gooblygook...
I then have a theory about why the more unbalanced beginning state may be beneficial to the work of pushing the pellet to velocity...
not fully developed but logical....
But may not understand the theories as well as I think I do even though I did some re reading...
Bob some thing cool is they just figure out that space just stretched/shrank solar system using kilometers long lasers and mirrors that become misaligned...
and two stations one near here and one in Louisiana... gravity waves just proved... ;D... some theories really seem to work...
Well anyways feel free to call me crazy(gently PLEASE).... ::) 8) 8) 8) ??? :-[ ;)
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but yep 4500 psi is not 4500 psi...
it is 4500 psi@STATE
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And Bob I think with decently high certainty if the sonic choke is occurring it is happening near and maybe even in the psi reservoir...
Super Sonic flow in a pipe :
"
shock wave appears when supersonic flow is decelerated...
In this case the gas ahead of the shock is supersonic (in the laboratory frame), and the gas behind the shock system is either supersonic (oblique shocks) or subsonic (a normal shock) (Although for some oblique shocks very close to the deflection angle limit, the downstream Mach number is subsonic.) The shock is the result of the deceleration of the gas by a converging duct, or by the growth of the boundary layer on the wall of a parallel duct.
"
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Oh I left a gap in my explanation of the mechanism that accounts for the change of state....
basically a slower traveling molecule gets hit by a faster molecule what happens..? the slower molecule speeds up and has it's trajectory changed...
and the faster molecule slows down with it's trajectory changed.... and still has near the same average velocity within the charge as before... some heating of the molecule that's why near... but that also tend to balance across the charge...
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As soon as you started talking Quantum Physics, my eyes glazed over.... I hated it when I was in University, never understood it, still hate it and still don't understand it....
So, I will have you let you enjoy your theories.... as I simply can't understand them, let alone debate them.... while I take Shroedinger's cat for a walk (or a drag).... depending on if it's alive or dead....
Bob
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As soon as you started talking Quantum Physics, my eyes glazed over.... I hated it when I was in University, never understood it, still hate it and still don't understand it....
So, I will have you let you enjoy your theories.... as I simply can't understand them, let alone debate them.... while I take Shroedinger's cat for a walk (or a drag).... depending on if it's alive or dead....
Bob
;) ;D Finally I gt to sit back and enjoy the show Bob now you know how I feel at times when I read your stuff It usually takes a couple of reads and some Aleve before the light comes on
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Bob that was pseudo science but good enough particle thought, to help look at how to get to 1750 fps in different ways... hobby level not deep understanding... I do know quantum tunneling is how we get the electron microscope...any the theory some...
Statistically the some molecules faster theory getting the pellet to 1750 is not probable... the sheer # of collisions tends to balance things very quickly...
1500 fps for a very short time and ~ (50-60 diameters wrong will corect) ~-18nm bang , and then same again and etc....
Recognizing what's happening... and below is not... but could happen... but trying to simplify the above... which was just another way of looking
there are a whole range of ways to get 4500 psi so first 4500 psi is actually "4500 psi @ state/temp" and there are some differ
so lets call 4500 @ 70F cool/ or state one ok then there is 4500 psi state two which is 4050 psi excited from 70F to 130f at 10% kelvin rise...
this concept is what I want to call a hot fill (After scuba term)... it will heat up the charge... if you have never heard the term link next
http://hawaiiscubaadventures.com/tag/hot-fill/ (http://hawaiiscubaadventures.com/tag/hot-fill/)
But I do not think this is what is happening in this case for two reasons first it is unsafe and Lloyd would not fill that way, second we are talking about a ~ 26cc/1.6ci chamber not enough work done to heat it much...
Did the same concept another way(heated the fill to gain psi) to raise pressure in a MK177 and boosted a 7.9g CPHP from 905fps to 1024 fps... that's right 18.5 fpe from pumping a plastic toy with a 16.25" barrel 22 times... ;)
unsafe sort of (* .17ci valve and sturdy ::) ) way and set the MK 177 on a oil filled heater to warm the pump cup to soften it to get it to set to the pump wall...
This raised the valves temp to about 130F... I then pumped 22 times (1300-1500 psi) so psi then rose to 1430-1650 psi... pow 1024 fps...
so same with 1.5 ci to take it from 4050psi to 4500 psi not a good idea also Very Unsafe
point is there are ways to get to psi @ temp... but again not how Llyod would do it...
but the Two states have differing property's
the hot fill has 10% faster messengers of info, but less of them having the same number of collisions further apart, the speed of sound is 10% higher than the ~1550 of the cool 4500 psi...1700 fps...
Now some molecules will be traveling faster and slower but not enough to matter because it is a closed dynamic system that wants to reach balance with time...
The collisions are the mechanism and I think it happens pretty quick because of the number of collisions happening.... link below to # of average number of molecules in a meter3 at sea level...
http://spacemath.gsfc.nasa.gov/earth/RBSP9.pdf (http://spacemath.gsfc.nasa.gov/earth/RBSP9.pdf)
MFP = Mean Free Path (between collisions) with a .3nm(3 angstrom)(near oxy and nitro)
AMS = Average Molecule Separation (freeze frame at any given time)
NMPcc = 112,500,000,000,000,000,000,000,000,000 (112.5 octillion short scale) Numbers of Molecules Per cc of 4500 psi air at sea level @70F (see below*)
250,000,000,000,000,000,000,000 =( 2.5 x 1023 ) = SLADA= Sea Level Average Density of molecules cc3 (nocked off two zeros to convert to cc from m3) Now multiply by 4500 and that is the number of molecules in 1cc of 4500 psi air at ~70f)... 25 x 45 = 1125 so see above
the above in bold is wrong will fix...
4500@~70f/294Kelvin 4500@~122f/323Kelvin
MFP ~.32755 x 10-9 meters (~ 1.09 diameters) ~.39968 x 10-9 meters (~ 1.3322 diameters)
.0000000003275 meters .00000000039968 meters
AMS ~ .507845 x 10-9 meters (~ .64499 diameters) ~.542676 X10-9 meters (~.7365 diameters)
NMPcc ~ ~
_________________________________________________________________________________________________________________
~10 % or so slower top speed thus messengers are slower 10% faster messengers and top speed because molecules
total charge is 10% heavier and last 10% longer... themselves are at a higher energy state and bounce of each other
and containment with more force...
takes 10% more barrel to reach top speed faster charge needs 10% or so less barrel...
so why is the speed of sound the speed limit not because of choking it is because that is as fast as the messengers can exchange info/force with the pellet for a given psi @ temp/state...
so how did Lloyd hit 1700+ fps:
simple he did not use 400% of barrel volume with which would have gone slower than it did using 200%...
200% in this case(barrel length) is more beneficial for what it allows to happen... ;)
If I am right in how it works and I am pretty sure it does the more I think and re study... and the pellet after it has traveled a ways givin back to create a short leg convergent cone with long divergent cone in a ways...thus creating supersonic flow with a pop for good measure...
prob not super clear and I have not proof read but gotta go for now... should be more understandable though... but Triggered by a serious look
at it all and it does seem to be pointing the shock/stem direction, it fits very well...
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Hope I am not driving you all nuts... ;)
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Don't worry, it's a (very) short trip... *LOL*....
BTW, cc to M^3 is a factor of 100^3 = 1 million cc's in a cubic metre.... In addition, 4500 psi is only 310 bar, so that would be the mulitplier.... but maybe you have so many zeros it doesn't matter anyway.... *grin*....
Bob
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;D OK I confess I am clueless at this point that math is way beyond my college algebra
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Mine too....
Bob
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Bout that time, when was doing was the # of zeros did seem was almost irrelevant...and the two days in the rabbit hole was getting to me... besides I knew if I goofed you would catch it.
it is much harder now than when was young... I tend to remember the concepts and then re look up the math some I can still understand/do, some I struggle...
But I have a secret weapon who just gave me a grandson...just finishing a her B.A. in math and her 6'5" (smarter and taller than me *^**#@) Beau on his way to PhD... Both more into pure math than application...
This time in my search for the equation I got lucky and found an app... ;) saved me from having to set up a spreadsheet...
heck for me now it is just hard making sure you are using the right units of measurements...
But yep now I have to remember the concepts and terminology then dive into the rabbit hole and try to put interrelationships together... with help...
like there are so many molecules in a cc of air that putting 4500 times as many in that same space only reduces the mean free path from about ~68nm to ~18nm... :o
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OK, so if your argument is that the mean free path is so short that the RMS velocity of air (1650 fps @ 70*F) is the limiting factor.... how come Lloyd managed 1745?.... The temperature during expansion would be lower, not higher....
BTW, did you see the note in the PCP gate about the chap who did 2043 fps with a tinfoil ball in a PCP at 250 bar?.... http://www.gatewaytoairguns.org/GTA/index.php?topic=104752.20 (http://www.gatewaytoairguns.org/GTA/index.php?topic=104752.20)
Bob
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like there are so many molecules in a cc of air that putting 4500 times as many in that same space only reduces the mean free path from about ~68nm to ~18nm... :o
should have read
like there are so many molecules and they are so small ... in a cc of air that putting 4500 times as many in that same space only reduces the mean free path from about ~68nm to ~18nm... :o
Bob for now have to discount the 2000 fps just to many unknowns... also may be same thing happening and if so showing this help prove that shot... I know in my heart and Lloyds data is solid...99.9999999999999%....
now the rabbit hole gets into ordered flow and the attractive-repulsive properties of the gas molecule and what that may do and other such stuff...
mow am trying to get it all put in shape to present, hopefully tomorrow get into the how as best I can...
"The temperature during expansion would be lower, not higher...."
should only effect timing of events and pretty minor effect at that... I think/gut feel...working mainly on how the mainly field acts as an ordered flow and the other events...
more detail on Lloyds chamber would be useful but not totally necessary to explain but would help accuracy and maybe fine tuning in future.
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more detail on Lloyds chamber would be useful but not totally necessary to explain but would help accuracy and maybe fine tuning in future.
Kirby,
Below is a photo of the Version 1 design, and, a sketch of the Version 2 design that I am in the process of building. The version one had a forcing cone 1" in dia x 1" long, and the reservoir volume continued as a 1" dia cylinder. In the Version one, there were black Delrin disks (5/8" dia) to restrict the flow. The 1745 shots used a disk with .22 dia tapered entry. I hope that is the info you were asking about.
Lloyd
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/MV-1_zpsvgywmatf.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/MV-1_zpsvgywmatf.jpg.html)
(http://i226.photobucket.com/albums/dd79/loyd500/MaxVel%20Test%20Gun/Ver2-Mech-a_zps9stx8ygc.jpg) (http://s226.photobucket.com/user/loyd500/media/MaxVel%20Test%20Gun/Ver2-Mech-a_zps9stx8ygc.jpg.html)
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like there are so many molecules in a cc of air that putting 4500 times as many in that same space only reduces the mean free path from about ~68nm to ~18nm...
Do you mean 300 times as many? 4500 psi is about 300 ATM I think? Did I miss something there?
If I missed something-just ignore-
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Yep, I mentioned the same thing above.... 4500 psi = 310 bar.... In fact it will be less than 300x the molecules because of the VanDeerWaal's correction factor at that high a pressure.... because air is no longer an ideal gas.... Air at 4500 psi is roughly 280 times more dense than at 1 atmosphere....
Bob
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you guys are right and what is worse is there is a worse mistake... while I was trying to do it son had energetic old friends over and I was researching other stuff added to my concentration probs that I suffer...
so disregard above numbers above but the concept still does show I put in psi for mmhg.... had converted got interrupted and the put in 4500 instead of 232717.197 mmhg.... :-[ :-[ :-[ ::)
so will go back and edit my above post to reflect the changes in magnitude....
:-[ :-[ :-[
like I said I do remember the concepts just have a hard time remembering to make sure of units of measurement needed.....
that's why I need your guys help... and I do think I could be wrong about the mechanisms and events that got to 1745 fps...
have been studying up on molecular beams as best I can.....
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here is a link to the calculator I miss- used...
it also has a link to frequency of collisions...
http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/menfre.html#c3 (http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/menfre.html#c3)