GEEK Alert - Sonic Choking!

[rsterne]

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

[Cal]

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.
 

[Cal]

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

[Cal]

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.

[rsterne]

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

[Cal]

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.

[Jim_Hbar]

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 

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

[Sfttailrdr46]

  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

[rsterne]

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

[rsterne]

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....



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....



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

[Jim_Hbar]

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..

[rsterne]

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

[lloyd-ss]

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

[rsterne]

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

[rsterne]

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....



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

[Jim_Hbar]

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.


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.

[rsterne]

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

[Jim_Hbar]

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 

[Sfttailrdr46]

  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 
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

[lloyd-ss]

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