GEEK Alert - Sonic Choking!

[Cal]

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

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)

[rsterne]

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

[Cal]

As mentioned:

There may be gaps in our understanding....

[Cal]

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!

[rsterne]

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

[Cal]

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...;-)

[PakProtector]

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

[Sfttailrdr46]

  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.

[Cal]

Use this dandy calculator
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.

[Jim_Hbar]

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.

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.

[rsterne]

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....



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

[rsterne]

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....



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
 

[gabi.nechita]

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.

[gabi.nechita]

Ups.
I am too slow.

[rsterne]

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

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

[Jim_Hbar]

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 , 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.......

[rsterne]

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

[Sfttailrdr46]

  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

[Jim_Hbar]

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! 
The trigger is proving to be challenging!

Jim

[Sfttailrdr46]

  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 .