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I've been doing some reading on propane flame propogation rate.
On his website Jimmy101 has some experimental data (sort of) as well as an equation that I presume corresponds to *initial* flame rate in quiescent conditions.
I've also done other reading in other areas(*), but I've never seen much treatment of closed vessels and flame rate progressions that are anything other than empirical.
In other words.... Does anybody have any ideas as to a set of assumptions/equations to model combustion for our purposes? It doesn't have to be perfect, mind you, just reasonable. I know there are a zillion variables, but ya gotta start somewhere, yada yada yada.
Now, to inspire ya'll, the reason I'm asking.... see pic.
(*) Been reading a document on "Flame Propogation In Industrial Scale Piping." Ya'll may be glad to hear that while DDT is very real, it appears that as long as you stick to aspect ratios less than 30 you'll never see it.
OK.... With nobody answering as yet (so I'm impatient!).
Initial burn rate can be obtained via the equation on Jimmy's webpage (forgive me for not remembering it).
At 15.7:1 compression ratio, burn rate can be assumed to be sonic at 540 C (813 K).
Between those two points.... I'm thinking a 2nd order polynomial with a 1st order negation. IE, Rate = a + b*P^2
This would have to be calculated on the fly, but that shouldn't be a big deal.
I think that talk of many equations and calculations just puts off alot of the members who just come here for fun. Looking good though, so this is all for your 19" hybrid? The idea is awesome.
Perhaps it would be worth your time to get a length of polycarb tube and a high-speed camera to conduct experiments. I don't think we have enough data to make any solid equations because no one has really observed propagation directly.
With controlled conditions you should probably be able to see patterns emerging that you can put into numbers.
I second _Fnord's idea. I really know only the absolute basics of combustion dynamics, so I can't be of a whole lot of help here. No one here but you really has the resources to directly observe and record flame propagation in propane.
Spudfiles' resident expert on all things that sail through the air at improbable speeds, trailing an incandescent wake of ionized air, dissociated polymers and metal oxides.
I spent a fair amount of time trying to come up with a model for combustion spud guns. You might take a look at the archives of my posts in Spudtech.
Intro: Towards a mathematical model of combustion spud guns
http://www.spudfiles.com/spudtech_archi ... hp?t=15477
Part I: Towards a model of combustion spud gun
http://www.spudfiles.com/spudtech_archi ... hp?t=15478
Part II: Combustion / Compressed Air gun performance disconnect
http://www.spudfiles.com/spudtech_archi ... hp?t=15498
Part III: How efficient can a combustion gun be?
http://www.spudfiles.com/spudtech_archi ... hp?t=15526
Part IV: Modeling closed combustion chamber
http://www.spudfiles.com/spudtech_archi ... hp?t=15557
Part V: Adiabatic Gun Model
Alternate title: The Spud Finally moves!
It ain't easy. Not to belittle GGDT or anything, but a combustion gun is a lot more complex than a compressed air gun.
You would think that a since a combustion spud gun is basically an internal combustion engine (and a hybrid gun is identical to an ICE) that there would be a large number of models, equations etc. developed for ICEs that would be directly applicable to combustion spudguns.
Near as I can tell, this is not the case. Numeric models for ICEs are very complex. Full blown simulations are so complex that the code is either proprietary or only available if you shell out big $$$$. Google "flamelet model combustion".
A couple flamelet papers (abstracts only, even the reprint costs are too much for me); one, two
(D_Hall, this is why I asked if you had access to a decent technical library, I'll bet that you can get the full papers for free.)
I vaguely recall that NASA (or some other gov't agency) has a free simulation program but I've never tried it.
There are several challenges to modeling the combustion process;
1. The form function. Exactly analogous to solid propellants, it is just the shape of the flame front. Not really all that difficult as long as the flame front is laminar. Turbulence makes things not only complex but chaotic.
2. The flame front speed; laminar isn't to bad, turbulent is very difficult.
3. It is possible to model the flame front speed if you know the temperature and pressure but, what is the temperature of the gas 1/4" from the flame front? Bulk (average) values are fairly easy to get, but they are very crude approximations to what is happening in the vicinity of the flame front, which is what matters.
4. Heat loss is significant, a heck of a lot of energy is lost as heat transfer to the gun.
With my combustion model I can predict several of the "oddities" of combustion spud guns, in particular the gross burn rate, peak pressure and the maximum efficiency at a CB of ~0.8. That last one is the real oddball of spud gunning and is, I think, the most interesting test of a combustion model.
I've done some rough calculations on D_Halls big-ass-gun. My model doesn't handle multiple sparks or hybrid ratios or approaching the speed of sound (which is actually pretty irrelevant to the internal ballistics)...
For a chamber 1/6th the size proposed (this was done to model a single spark gap), with a barrel scaled in area to 1/6th the real barrel (30' long), burst disk set to just a hair under the theoretical peak pressure of 1X propane + air, 1Kg projectile with 10 pounds dynamic friction, the model's treatment of heat loss turned off... insert a bunch more caveats here.
Burn time of the fuel: 380mS (a typical sized 1X gun burns in ~50mS)
Peak pressure: 121.6 PSIG
Total fuel energy: ~4.6MJ (this result is trivial, based on the HOC of propane in air and chamber volume)
Projectile muzzle velocity: 1370 FPS
Projectile exits at: 420mS after ignition
Exit Temp: 2562K
Exit Pressure: 107.3 PSIG
Actual CB ratio: 11.2:1
Optimal CB ratio: 0.23:1 (heat loss is turned off so the model pretty much acts like a pneumatic model in terms of CB)
Optimal barrel length: 1450 feet
Projectile velocity at optimal CB: 4500 FPS
Turning on heat loss (and making a wild ass guess at the thermal characteristics of a gun this big) gives;
Burn time of the fuel: no change
Peak pressure: 112.7 PSIG (dropped by 9 PSIG)
Total fuel energy: ~4.6MJ (no change)
Projectile muzzle velocity: 1270 FPS (dropped by 100 FPS)
Projectile exits at: 427mS after ignition (increased by 7mS)
Exit Temp: 2466K (dropped by ~100K)
Exit Pressure: 89 PSIG (dropped by 20 PSIG)
Efficiency: 1.6% (dropped by 0.3)
Actual CB ratio: 11.2:1 (same)
Optimal CB ratio: 0.81:1 (heat loss is turned on)
Optimal barrel length: 411 feet (dropped by 1000')
Projectile velocity at optimal CB: 2830 FPS (dropped by ~2x)
Interesting reading. I can see that you and I have gone over much of the same ground and apparently we went over it almost at the same time (that screen capture I posted? 90% of that code was written in Nov '06). Looks like my big oversite so far is that I was/am still modeling an adiabatic system although I've not made it to the point of actual projectile motion.
Also very interesting to see your simplified combustion assumptions. And here I've been trying to come up with some sort of "transition to turbulence" model that scales worth a damn (and failing miserably at it, I might add!).
So is there any more of your lecture series?
I noticed that (per the research cited in the Gexcon Gas Explosion Handbook) that the run-up distance of hydrocarbon-air detonations is roughly inversely proportional to pipe diameter; 4" pipe requires twice the length distance to undergo DDT compared to 2".
If one accepts the premise that DDT is facilitated via turbulent flow (how else do you get sonic flame fronts?) this suggests that turbulence proceeds in a scalable and repeatable manner...
However, such research might not be useful with the aspect ratios of our pipes, which have a large portion of their flame prorogation take place before interaction with the wall of the pipe becomes important.
And, per my understanding, flame modeling in open spaces is a nasty problem: all the complexity of turbulent CFD, plus the implications of chaos theory.
Ya, that is about where I kind of got stumped. With a little real gun data I could deal with the heat loss problem (though how well I'm not sure).
It is the transition from a laminar to turbulent flame front that finally stopped me. In my model, to match my "standard gun", I have to start with a laminar speed about twice as fast as it should be (0.8m/s vs. 0.4m/s) and use that faster initial speed to grossly account for the faster flame front when turbulent. Overall not a bad approach and it may be possible to tweak the correction further if there is sufficient real world data. I figured that what happens during the laminar phase is a pretty minor part of the total combustion process, the interesting part is the high speed (turbulent) combustion phase so you might as well just model that.
That is why I posted earlier about the possible coupling between the combustion process and the projectile's movement. Inital thoughts would suggest that once the projectile starts to move the temp and pressure drops and the combustion process slows down. (In most combustion guns the ammo starts to move when a fairly small, 10~30%, amount of the fuel has been burned.) However, if the movement of the ammo causes sufficient movement of the gases then the laminar to turbulent transition may more than make up for the affect of dropping Temp.
I've wondered if this kind of an affect might be part of the explanation of the "0.8 CB ratio rule". The chamber volume and the barrel volume plus the projectile's movement are all working togther to give the burn speed. An oversized barrel doesn't have enough fuel left when the gas velocities cause the laminar to turbulent transition. An undersized barrel causes the ammo to exit before the transition can occur. The optimum gun balances all these affects.
I wonder if you could use a Reynold's type calculation, along with the flame speed and gas movement speed, to get a rough estimate of laminar to turbulent timing. Something along the line of "If flow through the system at the flame front location is turbulent (by Reynold's number) then multiply the calculated laminar speed for the current Temp & Pressure conditions by 5X~10X (or whatever seems suitable)".
Yeah, I've been toying with the Reynold's number idea. Figured a cheap and dirty way to deal with that might be simply adding 1 to the burn rate exponent or something when it's decided that the flow has gone turbulent.
And I must confess that I'm somewhat at a disadvantage here. My combustion studies have always centered around solid rocket motors. In rocket motors, the burn rate is dominated by pressure; not temperature as your stated models indicate. It took me a bit to wrap my head around that one but I think I understand why the mechanism is different now.
That said... I'm a bit confused by your equation. You indicate flame rate as being dependent upon temperature.... But WHAT temperature. The adiabatic flame temperature is obviously not the right temp to use as to do so would result in a step function increase that doesn't make much sense in the real world. I tried using the unburned gas temperature (assuming it's being heated by adiabatic compression throughout the burn), but it doesn't seem to accelerate nearly fast enough with that approach. Are you using the bulk average temperature?
Well, the good news for the Pipe Dream is that virtually any flow is going to be turbulent. The bad news for folks around here is that with a 2" diameter it looks like the flow goes turbulent at about 0.75 m/s so clearly there WILL be a transition for smaller systems.
Sorry to sidetrack the discussion of the model, but I'm not so sure the projectile starts to move early on in the launch sequence...
Initial accelerations in combustion launchers is HIGH.
<a href="http://img.photobucket.com/albums/v611/car2/pressvspos.png">Old graph</a>
Ignore the pink line, the "14ms", and the error bars - respectively, those are a model, a time estimate, and made up.
This might explain why fans <i>only</i> improve performance as much as they do. Which sometimes seems small, considering the long list of benefits they provide - some of those benefits are irrelevant.
Well, your "HIGH" is a relative term. Looking at the pink line on the graph (and assuming I'm reading it correctly) the projectile starts to move at about 50 PSI. That corresponds to about 50/120 = 42% combustion. So, when is "early"? Certainly 10% would be earlier, and 90% would be late, but ~40% is in the range where movement of the ammo will affect the burning of more than half the fuel. I would think that could be significant and qualifies as "early".
Isn't the estimate of the pressure at the start of ammo movement basically a measure of the static friction in the system? Or perhaps it would be the difference beteeen the static and dynamic friction.
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