GEEK Alert - Sonic Choking!

[rsterne]

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....



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

[Big Bore Bart]

  OK    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.

   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? 

[rsterne]

I think the point is that we should use ports larger enough to avoid the problem, IMO....

Bob

[PakProtector]

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

[rsterne]

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....



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

[rsterne]

With reference to the Speed of Sound in HPA, as noted in this thread:  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

[rjorge]

I think you might be getting close to explaining why Sean's .30 cal is so efficient with that big valve!

[rsterne]

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

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 .... 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

[rsterne]

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

[lloyd-ss]

Bob,
I am still working on another response to your valve lift modeling thread but I ran across this treasure trove of NASA information  ,
http://www.grc.nasa.gov/WWW/BGH/shorth.html
 including one section on sonic choking! 
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

[Sfttailrdr46]

  OK    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.

   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? 

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

[rsterne]

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

[rsterne]

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

[lloyd-ss]

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.

[rsterne]

Amen to that!!!

Bob

[Jim_Hbar]

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)


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.

[Sfttailrdr46]

  This thread needs a large disclaimer " Caution do not read before second cup of morning coffee"

[au hunter]

     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

[rkr]

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.

[TimmyMac1]

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