FLONE's question redux

Just starting to spud and wonder how long your barrel should be? Want to know how to build a better cannon? This is just the place! If you think your question is one of a newcomer, please post it in here. If your question is posted elsewhere, and it's a newcomer's type question, it will be moved in here.

Postby jimmy » Mon Dec 04, 2006 1:31 pm

Boiling: You are right about the problem with when the apple starts to move. In the graph on my page with label "apple starts to move" is clearly wrong. That was one of the first analyses of the raw data and I was trying to figure out what all the transitions are. If you look at the later analysis on the page those labels are removed since I really can't tell when the apple starts to move. That particular gun fires at 330 FPS with a 30" barrel. So the actual transit time is about (30")(1'/12")(2/330FPS)=15mS (assuming constant acceleration which probably isn't quite true). That value is very close to the "14mS" you have on your graph for the projectile transit time. If you look at my Pressure vs. Time graphs and measure back 15mS from the barrel exit point (probably the only part of the graph that I am 100% sure about, well that and the "click" of the igniter) you get the spud starting to move at about the time the pressure peaks. This is not to say that the gun is working perfectly, i.e., "the apple moves once peak pressure is reached" but rather that once the apple starts to move the total chamber volume increases faster than the combustion process.

In a graph of dP/dT for laminar burning I would expect there to be several discontinuities (spikes, humps, etc.);

1. When the burn radius exceeds the chamber radius the flame front transitions from a spherical ball to two "domed shaped" fronts. When the flame front is spherical its surface area is increasing as the square of its radius (also the square of the flame propagation speed). Once the flame front reaches the nearest chamber wall the flame front surface area becomes essentially constant for the rest of the burn (or until point 2 below). Here is a ASCII graph of how the flame front area changes versus time in a cylindrical chamber (laminar burning, constant pressure);
<pre> |
| **************************
| *
| *
| *
Flame | *
Front | *
Area | *
| *
| *
| *
|*----------------------------------------
Time</pre>
Of course, in a closed chamber the pressure and temperature rises so you don't get a plateau in pressure even though you get a plateau in flame front area.

2. When one of the flame fronts reaches the end of the chamber (or the spud's butt) you get a transition where the flame front area is suddenly divided by two. This will be noticeable only when the spark is not at the front-to-back center of the chamber.

3. When the spud starts to move you get a non-zero dV/dT which affects the dP/dT.

Regarding your second point concerning turbulent flow and its affect on combustion rate. First of all, are you sure the fluxuation in your (Latke's) data is real? There seems to be a lot of noise in the data based on the complexity of the curves and the size of the error bars.

Secondly, how do you arrive at "combustion in the extremely turbulent barrel flow"? Why would this combustion be so turbulent? Granted we are forcing gases past the reducer but is that enough to cause turbulent flow? My data is for a 3"ID chamber and 2"ID barrel, Latke's data is for a 3/4"ID barrel so perhaps there is more turbulence in Latke's data. But, for the early part of the projectiles movement relatively little gases are being moved into the barrel, indeed for the first few milliseconds of movement only a very small amount of gas has to move into the barrel. At low flow the flow may not be turbulent. As the projectile moves farther, and faster, more gas has to move but how do you know it is ever really turbulent? Or, how do you know the flame front is actually in the turbulent part of the air flow? The volume of unburnt gases directly behind the spud would be moving but not necessarily be turbulent even if air flow at the reducer is turbulent. The combustion front is only in the vicinity of the reducer for part of the combustion process.

I don't know enough about turbulent flow to be able to tell if it applies to the area around the reducer or to the volume that is burning at a particular time. If there is turbulent flow then the burn rate may indeed increase rapidly since a turbulent burning front burns much faster the a laminar (smooth) flame front.

Regardless of the above, you may be right about the second spike, it could have something to do with turbulence and its affect on combustion in the barrel. Clearly it is not caused by the start of movement of the spud.

How fast do the gases have to be moving though the reducer to get turbulence? For a 3"ID chamber to 2"ID barrel isn't the maximum speed of glass flow through the reducer only about (muzzle velocity)(1/2)(2<sup>2</sup>/3<sup>2</sup>)=73 FPS for a 330 FPS muzzle velocity? (The factor of 1/2 is for a 1:1 C:B ratio.) And this flow rate starts at zero when the spud starts to move and only reaches 73 FPS at the instant the spud leaves the barrel. Is that enough to cause significant turbulance?

Edit: removed "goes" from second to last sentence.
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Postby boilingleadbath » Mon Dec 04, 2006 6:27 pm

330 fps, hu? Bit faster than I was expecting... how much does this apple weigh?

Yeah, I question the accuracy of my data... but the error bars arn't worth anything. Shite, I don't even know much about error bars. To me, they just look pretty. (not quite...)

Anyways, the gexcon gas explosion handbook has graphs of flame velocity vs. time in pipes, showing that it increases with time.
They explain this as a positive feedback cycle; higer velocities cause more turbulence in the flow, which causes faster combustion, and ect.
(<a href="http://www.gexcon.com/index.php?src=handbook/GEXHBchap9.htm">Gexcon's handbook</a> - see diagram 9.4 and 9.5)

My point being that these pipes have no interior bumps or obstructions, and thus that our fast air collum in the pipe has turbulence throughout (although their data starts at ~60fps, a tad faster then latke's breach flow (see next paragraph))

As to hard numbers, the flow velocity at the breach when the pressure curve starts acting up is about 40 fps, with the projectile (and thus fastest fuel-air mixture) moving at about 130 fps. This is a steep difference; such a steep difference will cause a rapid increase in burn rate once it gets started... and we notice that in your pressure graph.
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Postby jimmy » Tue Dec 05, 2006 7:53 pm

Boiling: An apple in a 2" barrel is about 80g, versus say 100g for a 1/2 spud.

Gexcon's handbook does have a lot of interesting stuff in it. But, I'm not sure how relevant figure 9.5 is to a spud gun or its barrel.

1. Their pipe is huge, 1.6m (4.6 feet) diameter
2. Their pipe is long, the first value is at 2.5m (8 feet) and goes out to 40m (131 feet).
3. Which trace are you looking at? The two for pipes with open ends are not relevant to a spud gun barrel. The trace for the closed pipe is just weird.

Do you really need to invoke turbulence to explain the increase in the flame speed for the closed end pipe? Closed chambers in general give an increasing flame speed as the combustion progress. In a spherical chamber with a central ignition the flame front speed goes up <b>a lot</b> even though the flame front never interacts with the chamber walls (well, not until it burns out anyway).

The flame front in a closed chamber would be expected to accelerate. Mostly because of the rising temperature of the gases. (Curiously, the flame front speed decreases as the pressure increase.) I came across a handy formula for calculating the laminar (no turbulence) flame speed as a function of temperature and pressure in the chamber:
S<sub>i</sub>=S<sub>0</sub>(T<sub>i</sub>/T<sub>0</sub>)<sup>alpha</sup> (P<sub>i</sub>/P<sub>0</sub>)<sup>beta</sup>
Where the i sub$cripts refer to a particular T and P pair and the 0 sub$cripts refer to a reference state, usually STP. For propane in air S<sub>0</sub>=0.43m/s, alpha=2.13 and beta=-0.17.

The rising then <u>falling</u> then rising flame front speeds in 9.5 are just weird. Is the chamber resonating?

So I'm not sure how relevant turbulence is to a typical spud gun. It just doesn't seem to me like the gases are ever moving fast enough to cause much turbulence. Or, that by the time the gases are moving fast enough for turbulence to start the reaction is so close to being done that it doesn't make much difference. Or, some of the gases are moving fast enough to cause turbulence but the turbulence is not at the flame front.

Just a thought, DR and others have fallen in love with the little "camping fans" as chamber fans. They are cheap, readily available and easy to install. Claims have been made that they boost muzzle velocities if the fan is running when the gun is fired. Turbulence in the chamber could certainly increase the burn speed of the fuel, perhaps enough to get a significantly faster pressure rise and a resulting increase in muzzle velocities. Unfortunately, I haven't seen any muzzle velocity data. So far it has only been anecdotal results.
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Postby boilingleadbath » Tue Dec 05, 2006 9:08 pm

Bah, 12% error in my values... EVBEC is predicting 290 fps.

Anyway... reynolds number equation....

(2(.0198 m)(~4.5 kg/m^3)(13 m/s))/(.000018 Pa*s) = 129,000
That (the barrel flow) is turbulent.

(I interpret the rising/falling flame speeds in 9.5 as evidence of multiple compeating effects - although I won't try to enumerate them.)
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Postby SpudBlaster15 » Tue Dec 05, 2006 9:28 pm

<blockquote id="quote"><font size="1" face="tahoma,verdana,arial" id="quote">quote:<hr height="1" noshade id="quote">Originally posted by jimmy
Unfortunately, I haven't seen any muzzle velocity data. So far it has only been anecdotal results.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

Since I use one of those camping fans, I will test the effects of turbulence along with the spark gap quantity/placement tests I plan to do this weekend. 5 shots in which the fan is off, 5 shots in which the fan is on. The fan will be run for 5 seconds before each shot to properly atomize the fuel.
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Postby boilingleadbath » Wed Dec 06, 2006 9:16 am

The velocity deviation with spuds is pretty huge, so it'd be nice if we could get 8 shots or so.
You know, more accurate data, that type of stuff... unless you are using a golfball/gasket slug/such, in which case 5 shots should be plenty.
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Postby SpudBlaster15 » Wed Dec 06, 2006 6:50 pm

I plan to use homemade slugs of wood, each with a bolt ran through the center to increase density.
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Postby jimmy » Thu Dec 07, 2006 11:53 am

<blockquote id="quote"><font size="1" face="tahoma,verdana,arial" id="quote">quote:<hr height="1" noshade id="quote">Originally posted by boilingleadbath
[br]Anyway... reynolds number equation....

(2(.0198 m)(~4.5 kg/m^3)(13 m/s))/(.000018 Pa*s) = 129,000
That (the barrel flow) is turbulent.
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

I havn't used the Reynold's equation in years. I think I get most of the values you used. But shouldn't the density of the gas be ~0.6kg/m^3, half the density of air (1.2kg/m^3) since the mass of the gases is unchanged but the volume nearly doubles at spud exit (c:b=1). Where does the 13 m/s come from? Shouldn't the velocity of the gas range from zero to ~100m/s at spud exit?

It seems to me that there are a couple of issues, (1) early in the combustion process the gas velocity is low and the flow will be laminar. (2) Late in the combustion process the gas flow will be higher but the turbulent flow only matters if it is in the vicinity of the flame front. And, (3) only the forward (nearest the barrel) flame front would be turbulent. The rear flame front is in gases that are moving very little and would still be laminar.
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Postby boilingleadbath » Thu Dec 07, 2006 5:40 pm

I stated the density of the gas as 4.5g/l because, at the time the supposed barrel combustion is occuring, the chamber pressure is about 30 PSIG - so the compressed fuel-air mixture in the barrel is at 3 times it's normal density.

The 13 m/s is the velocity of latke's gas flow at the begining of the barrel, as presented in my post at the top of this page. (starts with "330 fps, hu?")
...of course, I have no clue why the number is so low, with the projectile going 130 fps... shouldn't it be more on the order of 130*(4/5)=104 fps? (with 4:1 being the C:used_barrel ratio at the time)
...so the reynolds number maybe be closer to 300,000. (also turbulent)

...again, I'm only applying the reynold's calculation to the flow in the barrel.
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Postby jimmy » Fri Dec 08, 2006 10:40 am

<blockquote id="quote"><font size="1" face="tahoma,verdana,arial" id="quote">quote:<hr height="1" noshade id="quote">Originally posted by boilingleadbath
[br]I stated the density of the gas as 4.5g/l because, at the time the supposed barrel combustion is occuring, the chamber pressure is about 30 PSIG - so the compressed fuel-air mixture in the barrel is at 3 times it's normal density.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
That is not correct. The density of the gasses in the chamber is independent of the pressure in the chamber. If you start with 1g of gas it still weighs 1g when combustion is complete (in non-nuclear chemistry mass is always conserved). If the volume of the chamber doesn't change (i.e., a closed chamber) then the density of the gas is constant throughout the combustion process.

If the volume of the chamber is not constant (i.e., a spud gun) then the density will decrease as the volume increases but the mass of the gas doesn't change. So, if the C:B is 1 the volume doubles as the spud goes from its starting point to the muzzle, the density drops by a factor of two but the mass of the gas is constant.

The increase in pressure in the chamber as combustion proceeds is caused by the temperature rising from 300K to >2000K, not because the mass, or density, of the gas is changing.
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