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DDT Runup Distance Question

Post questions and info about hybrid (compressed gas with fuel) powered cannons here. This includes discussion about fuels, ratios, ignition systems, build types, safety, and anything else relevant.
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DDT Runup Distance Question

Unread postAuthor: DYI » Thu Jan 24, 2008 8:04 pm

My question is, as the title states, on the subject of DDT run up distances.

Specifically, I wanted to know what the DDT run up distance is in a propane/air mix with a pre-ignition pressure of 20 bar, ignited in a 3" tube. Any relevant answers would be greatly appreciated, especially ones that would help me avoid asking a similar topic again.
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Unread postAuthor: Fnord » Thu Jan 24, 2008 8:39 pm

I can give you an answer, but it won't have any hard numbers behind it.

The run-up in normal atmospheric pressure is around 30-35 feet.
Noname supposedly got a DDT in 5 feet, at 6x normal pressure.

See the pattern?

by the same logic, you may get a DDT in as little as ~1.5 feet.
The higher pressure will cause the flame front speed to slow down, but I don't know how much.

If you're trying to cause it sooner, you can try a schelkin spiral.
If you're trying to slow it down, you can try multiple spark gaps or a filler gas.
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Unread postAuthor: Ragnarok » Thu Jan 24, 2008 8:42 pm

Umm, lemme see... I remember reading something about this on the spudtech archives when I was last browsing for information on detonation, and I think this was it:
http://www.spudfiles.com/spudtech_archi ... hp?t=14818

There's not a lot of the topic (it does mention a figure of 12 metres for a 1 atm 4" diameter pipe - but I don't know how the 20x mix will affect that), but the links are worth a try.

As I'm sure you know, detonation occurs when the burn speed becomes over Mach 1 (in the gas), and I'm sure I saw a calculation for working out propane's burn speed somewhere - if I could remember that, I could probably work it out myself.
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Unread postAuthor: SpudBlaster15 » Thu Jan 24, 2008 10:35 pm

Well, it may not be entirely accurate, but you can estimate a propane/air mixture's flame front velocity as a function of pressure and temperature using a power law (modeling propane's combustion mathematically is very complex, so this formula is derived from experimental data);

V<sub>final</sub> = V<sub>initial</sub>*(T<sub>final</sub>/T<sub>initial</sub>)<sup>2.13</sup>*(P<sub>final</sub>/P<sub>initial</sub>)<sup>-0.17</sup>

V<sub>initial</sub> for propane is ~0.43m/s.

GasEQ estimates that T<sub>final</sub> is ~2640K, and P<sub>final</sub> is ~9.322ATM.

At an atmospheric pressure mixture, we get;

V<sub>final</sub> = 0.43(2640/290)<sup>2.13</sup>*(9.22/1)<sup>-0.17</sup>
V<sub>final</sub> = 32.5m/s

So the flame front speed at maximum obtainable temperature and pressure is about 1/30 of the speed of sound in the chamber.

At 20 bar preignition pressure, we get;

V<sub>final</sub> = 0.43(2760/290)<sup>2.13</sup>*(194/20)<sup>-0.17</sup>
V<sub>final</sub> = 35.5m/s

Conclusion: I don't think you will achieve DDT in the chamber. The change in temperature increases the burn rate by a large amount, but the change in pressure decreases the flame front velocity by a substantial amount, and as such, the flame front velocity increases by a relatively small magnitude as the internal pressure climbs.
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Unread postAuthor: DYI » Thu Jan 24, 2008 10:55 pm

As you could probably guess, I don't want to cause DDT in the chamber. If I wanted that I'd use oxygen enriched mixtures with hydrogen as a fuel. I only wanted to see if I would need multiple spark gaps, or if a single one at the back of the chamber would suffice. I've decided that using the multiple kpsi pressures afforded by high mixes outweighs the velocity increase possible by harnessing detonations.

Thanks for the formula Spudblaster, it may prove useful later on. It also leads me to wonder why people were so scared of causing DDT in 3" diameter chambers with mixes as low as 5 or 6x.

If I'm interpreting your data correctly, it means that the burn rate is actually slightly higher overall, even with the high pre-ignition pressure, and that therefore, heat loss shouldn't be much more of a concern than it is in normal hybrid mixes. Is that right?
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Unread postAuthor: SpudBlaster15 » Fri Jan 25, 2008 1:18 am

As you can tell by the exponents corresponding to the T and P terms, chamber temperature (power of 2.13) has a much larger effect on burn rate than chamber pressure (power of -0.17).

I speculate that the burn rate in hybrid launchers should be slightly higher overall than in atmospheric pressure combustions; though it may be lower during the first few (or more, depending upon chamber size) milliseconds after ignition, before the chamber temperature has risen sufficiently to oppose the effects of the internal preignition pressure.

Heat loss shouldn't be any more of an issue than it is with lower mix hybrid launchers, in which case it is usually not an issue, unless your burst disk is designed to rupture extremely close to peak pressure (in which case there may be a delayed rupture).

Just curious, do you plan to use a HPA cylinder as a pressure source?
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Unread postAuthor: DYI » Fri Jan 25, 2008 9:34 am

The whole point of this project is to avoid the need for bottled gases. Also, neither of the compressed gas depots in town carry air cylinders, so I would have to drive to Sudbury (~1.5 hours) to return empties and pick up full cylinders.

For an air pressure source, I plan on using a cheap 120 psi compressor, with a pressure amplifier attached. Initial cost for the whole setup will be high (~$650), but operating costs will be extremely low in comparison to bottled gas, and there will be no refilling or rental costs involved as there would be with HPA. With the 3.8:1 output to input ratio on the amplifier, I should be able to reach ~500 psi with a $100 air compressor, allowing, in theory, mixes slightly over 30x :twisted: .

By doing this, I can power the SCTBDC and the planned hybrid in my back yard for essentially no cost (except electricity, which I don't pay), and reserve the nitrogen tank for portable applications.
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Unread postAuthor: jimmy101 » Fri Jan 25, 2008 1:00 pm

I believe there is more than one way to get to DDT.

As spudblaster said, as the flame front speed approaches the speed of sound in the chamber... This doesn't make much sense to me. The speed of sound in the chamber increases as the temperature of the gases increases. Off hand, I would think the flame front speed can never catch up with the speed of sound. The speed of sound in a generic 1x spudgun rises by about a factor of 3 during firing to ~900m/s.

The flame front speeds spudblaster posted are for laminar fronts. Turbulent fronts can be much faster, "up to 10 times faster" according to a reference I saw way back. A 10x faster flame front speed would put spudblasters speeds in the 320~350m/s range, near the speed of sound at NTP but still well below the speed of sound in the hot gases in the chamber.

The other way to get to DDT is by compressing the unburned fuel to the point where is reaches the autoignition temperature. Basically, the gun diesels if it gets hot enough. Autoignition of gases distal from the flame front occurs and the whole concepts of "flame front" and "flame front speed" becomes irrelevant.

I believe this is why you usually need a long skinny tube to get to DDT. Ignition on one end of the tube compresses/heats the fuel/air at the other end.

Mutliple sparks will avoid / reduce the chances of DDT. As will putting the spark in the center of the chamber instead of near an end.

Also remember that DDT is not necisarily bad or dangerous. When DDT occurs determines how dangerous it is. If you have to burn 95% of the fuel in the chamber to get to DDT the rapid buring of the last 5% of the fuel is not a big deal.

As you can probably tell, I have no frickin idea what causes DDT.
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Unread postAuthor: DYI » Fri Jan 25, 2008 2:59 pm

Spudblaster, I just found an interesting quote in the thread about _Fnord's piston hybrid (v.2).
Increasing the chamber pressure decreases this run up distance, and it is generally accepted that DDT can occur at anything over a 4x mix in a launcher of average size.

Amazing how quickly our opinions can change, isn't it?
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Unread postAuthor: Fnord » Fri Jan 25, 2008 3:10 pm

People actually still read that thread? lol.

Now that I think of it, I need to get out to the hardware store soon and get v2.1 finished up and posted... it's been sitting around for weeks now doing nothing more than adding a few awesome points to whatever room it's in at the time.

That and collecting dust.
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Unread postAuthor: SpudBlaster15 » Sat Jan 26, 2008 1:45 am

DYI wrote:Amazing how quickly our opinions can change, isn't it?


Indeed it is. While my hybrid launcher (which is I guess the new standard in small metal hybrid designs) was mostly designed based on physics and logic, the established mixture limit was the one thing that I assumed to be true, despite the complete lack of physical evidence that showed the limit to be even close to valid. Once I finally came to my senses and actually applied some physics and mathematics to the issue, I realized that the 4x limit was absurd for my chamber (1.38" ID steel pipe, estimated burst pressure of over 3000PSIG), and that DDT was not going to occur under normal circumstances.

_Fnord's attempts to blow up a 2" Sch40 steel pipe with 11x mixes were also influential; though looking back, not exactly surprising, considering he was likely generating about 1/2 of the pipe's cyclic burst pressure; and about 1/4 of the pipe's tensile stress threshold.
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