Any theories for Latke's data collapse?

[D_Hall]

OK, (yet another) potential breakthrough (Hopefully this one pans out.)....

I've been tinkering around with variable heat transfer coefficients. My thought went something like...

The further/faster the projectile/gases go, the more turbulent the gases are.

The more turbulent the gases, the higher the heat transfer coefficient.

Thus, I was using odd little equations to relate heat transfer coefficients to projectile velocity and/or position. And as reported earlier in this thread, I was getting some rather interesting results. But interesting isn't the same thing as satisfactory. I'd get curves that would start to dive but they just wouldn't just go into freefall like the test data indicates it should.
But I just noticed something... When I crank up the heat transfer to get that knee started.... I *AM* finding low temperatures.

Sounds like we have a phase transform after all.

Of course, somebody pointed out that the worst a phase transform could do is accelerate a vacuum that is already coming so maybe that isn't enough. Plus, what about supercooling the vapor? That's certainly possible and maybe even probable for the timeframes we're dealing with.

Ugh.

I just don't know!

[starman]

Question: Does anybody know where Latke lives? Or more to the point, does anybody know what altitude those tests were run at?

His site mentions an IPLA NW Shootout in Olympia, Wa., would've been some years back now, so I've always assumed he was a west coaster of some sort. His test setup pictures tools like C-stands which are used almost exclusively in the film and theater business..... made me think he would be close to the industry...therefore SoCal. Also had access to a lab environment to perform his "mini" test, so made me feel like he was peforming a research project of some sort, possibly university level.

You may already know this, but for what it's worth, his email is burntlatke@hotmail.com.

[Lentamentalisk]

Ok, all of this speculation has inspired me to go get us more data. My end of the school year science project is coming up, and I decided that this could be an interesting thing to explore. I made a thread on a cannon I am designing to get us more data to work with, with these speculations. check out the thread here

[SpudMonster]

Latke was in Washington, although I cannot remember exactly where. I think he was in the Seattle area.

[boilingleadbath]

Ah, didn't know your heat transfer model ignored the fluid velocity's role in heat transfer rate. Some searching on wikipedia (for lack of good engineering resources around here) indicates that the following might be reasonably applicable:

Total heat transfer = 1/(1/"gas-wall" + 1/"wall-bulk pipe")

And of course we don't use the "heat transfer across pipe wall formula - because that ignores the pipe's thermal momentum.

For the gas-wall interaction...

transfered energy = Time*h*A*TempDifference

h = (k_w/D)N_u

N_u = .023Re_D^4/5Pr^.3

Pr = ~.7-.8

*********************

Now, there are some requirements to use these formulas:
1) Re has to be 10,000-120,000
2) Pr has to be .7+
3) Dittus-Boelter calculates for a point at least 10-50 diameters down the tube. That excludes a sizable portion of our barrel.

There is another problem: typical Reynolds number in our guns is in the millions, if I calculate correctly. That's a little out of range

Are there better formulas do use in these extreme situations? Should we just use these and accept the decreased accuracy?

[D_Hall]

There is, of course, another problem.... Those equations assume steady state flow. We are anything but steady state.

[jimmy101]

Sorry, I'm a couple days behind in following this thread.

I would think that the rapid drop off at low CB (the left side of the original graph, long barrels in Latkes setup) is caused by the combination of at least two affects:

1. Expansion has dropped the pressure below the point where the ammo is still accelerating. This type of behavior is well predicted by GGDT, the barrel volume is so big that the pressure dropped has past the point where pressureXarea behind the ammo is less than (atmosphericXarea+friction).

2. The surface area and gas movementXtime and perhaps turbulent flow through the gun (which increases heat loss) has reached the point where heat loss has become the dominant energy transfer mechanism. Heat loss is using up energy faster than energy is being transfered to the ammo. The ammo just can't get out of the barrel fast enough and a large portion of the energy in the chamber is lost as heat transfer to the gun.

I wouldn't think that water condensation would be much of an affect. Even at exit the temperature of the gases in the gun are still hot enough to keep the water vaporised. But the water vapor doesn't have to be all that hot. 200C should be more than hot enough. But at 200C the gases have lost what 90% of their peak energy? (assuming peak temperature is ~2200C)

Besides, in a 1x gun there really isn't all that much water vapor anyway. Lets see, propane combustion;
C3H8 + 5O2 = 3CO2 + 4H20
For every cubic inch of fuel in the gun we get 4ci of water vapor. Fuel is 4% of the total chamber volume so water vapor is, very roughly, 16% of the gas volume at the end of combustion. If it all condenses then the pressure change is relatively minor (~16%). Offsetting the drop in pressure, as the water condenses it releases a shit load (a high technical description) of heat that will offset the drop in pressure caused by fewer molecules of gas. In a steam engine the kick-ass (another technical description) energy transfer occurs when the steam condenses. If the steam doesn't condense then the energy transfer is very inefficient.

So, I suspect dave and boilingLB et al., are correct. It's heat loss and heat loss is a very non-linear process in a spudgun. Kind of the opposite of pressure versus time for the combustion process, which is an exponential. In a firing spudgun, heat loss is also an exponential function that combines the increasing surface area, and the increased heat loss caused by gas movement, and the increased heat loss caused once the gas flow switches from laminar to turbulent (which in turn is a function of where in the gun you are looking).

A combustion spud gun is a race. You have to get the ammo out of the barrel in a time frame that cannot be adequately predicted assuming it is simply a pressurized gas system. Heat is key in a combustion spudgun and the heat is extremely short lived. The movement of the ammo decreases the energy in the chamber not only becasue of the expansion, but because of the rapid increase in heat loss caused by movement of the ammo.

[Lentamentalisk]

So my Aerogel link could become useful, insulating the barrel so that there is less heat transfer!

[boilingleadbath]

Heh, looks like I may have miscalculated Re. I needed to calculate it again, and this time I'm getting about 36,000

In other news, it looks like treating the pipe wall as always being 300k would be a significant mistake - within a millisecond, the wall reaches 110*C above initial temperature. (stabilizes at about +170*C)
(assuming constant 1300k gas temperature)

I computed a stack of thin PVC layers. The wall-gas boundary is treated using the equations in my above work.
**************

On a more homely note, this means that pipe wall material is pretty much irrelevant unless you use something HIGHLY insulating; aluminum pipe won't change performance much.

Right?

[Antonio]

Looks very interesting. I do aerospace engineering and had aerodynamics last semester. I could do some calculations on this. As I know how to do calcs with air reservoirs, incompressible, compressible flows etc. Could you guys tell me what the C:B ratio actually means? > Is it the volume? I dont know if you guys kept in mind but the diamter of the barrel and the reservoir are really important. Length and diameter cant be expressed in one ratio for different points. I think that might be the problem, but yeah plz comment:)

[boilingleadbath]

C:B ratio is indeed the volume ratio... it'll be a calculated value, not directly measured.

The volume of the latke chambers (what I use as of EVBEC 1.6, anyways) is as follows:
.75" test: 25.3 cubic inch
1.5" test: 176 ci
2.5" test: 194 ci

[Lentamentalisk]

In other news, it looks like treating the pipe wall as always being 300k would be a significant mistake - within a millisecond, the wall reaches 110*C above initial temperature. (stabilizes at about +170*C)
(assuming constant 1300k gas temperature)

I computed a stack of thin PVC layers. The wall-gas boundary is treated using the equations in my above work.
**************

On a more homely note, this means that pipe wall material is pretty much irrelevant unless you use something HIGHLY insulating; aluminum pipe won't change performance much.

Right?

Are you saying that both metal and PVC will absorb the heat at near the same rate, or are you saying that metals will all be about the same?

[boilingleadbath]

I'll explain it like this:

Heat transfer from 1300k gas to 300k (metal) wall = 1 unit/unit of time
And even steel isn't a superconductor of heat, so the wall would be a bit warmer than that.

Heat transfer from 1300k gas to 470k (PVC) wall = .83 unit/unit of time

.83 is fairly close to 1, and that's comparing a superconductor to PVC... but you are correct in that the difference in heat transfer rate between different metals will be even less significant.

[Lentamentalisk]

However, if PVC has a lower specific heat (or is it heat capacity, I get them mixed up,) than the steel, which I'm pretty damn sure it does, it will absorb less energy before it reaches that temperature, even if it reaches that temperature in about the same time it takes steel to heat up.
Am I right about that?

[jimmy101]

In other news, it looks like treating the pipe wall as always being 300k would be a significant mistake - within a millisecond, the wall reaches 110*C above initial temperature. (stabilizes at about +170*C)
(assuming constant 1300k gas temperature)

I computed a stack of thin PVC layers. The wall-gas boundary is treated using the equations in my above work.
**************

On a more homely note, this means that pipe wall material is pretty much irrelevant unless you use something HIGHLY insulating; aluminum pipe won't change performance much.

Right?

But even a 170C rise is really not all that significant if the gas temperature starts at ~2500K (the adiabatic flame temp.). So, I would think it can still be neglected. The other things that we are having problems modeling, like laminar to tubulent transition, are probably much bigger affects than the relatively minor rise from 300K to ~470K of the thin layer of pipe in contact with the gases.

Ultimately, the temperature of the chamber only rises a few degrees for a typical sized PVC combustion gun. My estimate is that for a 100ci closed chamber the temperature rise of the PVC at equilibrium is only about 7C.