Any theories for Latke's data collapse?

[jimmy101]

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?

Specific heat is the heat capacity per unit mass of material. Heat capacity is for an object. The relationship between the two is that the heat capacity = specific heat X mass of object.

So, when you compare say PVC with steel and you want to calculate the final temperatures you need to know the specific heats and the two masses.

<table border="1"><tr><td>Material</td><td>Specific Heat
Capacity
(cal/g/C)</td><td>Density
(g/cc)</td></tr> <tr><td>PVC</td><td>0.25</td><td>1.4</td></tr> <tr><td>steel</td><td>0.4-0.5</td><td>7.8</td></tr> <tr><td> aluminum </td><td>0.96</td><td>2.7</td></tr> <tr><td>air (C_v) </td><td>~0.3</td><td>~0.0013</td></tr></table>
Air and PVC have very similar specific heats. But the large difference in density means that in a typical gun there is a large swing in the temperature of the gases as they cool but only a minor change in the temperature of the PVC.

Of course, this is all steady state (equilibrium) stuff. The problem is that this isn't steady state, it is a dynamic process and that makes things much more comlex.

[boilingleadbath]

Eh, jimmy, it heats up 170k if the temperature difference is 1000k. That's a 17% difference in heat transfer rate.

If we are correct about the... shortness... of the latke curve being primarily due to heat loss, that's a significant difference.

That said, there are two main differences between PVC and steel/copper/aluminum:

1) The metal contains significantly less energy per unit volume.
2) The metal conducts the heat away from the gas-pipe boundary much faster.

Playing around with my simulating spreadsheet, we find that #1 isn't very important when it comes to how fast the skin gets hot or how hot it gets.

However, the high thermal conductivity of the metals is significant. The metal 'feels' cold to the gas. The PVC... not quite so cold.

[jimmy101]

Eh, jimmy, it heats up 170k if the temperature difference is 1000k. That's a 17% difference in heat transfer rate.

Actually, wouldn't that be a (1000K-300K) vs (1000K-470K) difference? A 24% change? Of course, at 2000K it's back down to a ~10% change.

Regardless of 14% or 24% or 10%, I don't think that difference is nearly enough to explain the "knee".

I agree with your points about plastic vs. steel. Latke's data is for PVC. A steel (or Al) gun might be expected to have an even worse "knee".

[boilingleadbath]

Jimmy, I think you are missing a point: if the gas temperature is higher, the heat is transfered into the pipe wall faster, so the wall gets hotter. I suspect Wall-temp vs gas temp is roughly linear.

Is it?

Temp change at T + .025 seconds : Temp differential
55:100
110:200
274:500
550:1000

Yes, at least according to my spreadsheet, it is.
*********

Now, this discussion has gotten slightly off topic: we aren't just discussing heat transfer, we are discussing heat transfer as it relates to the graph's 'knee'.

Perhaps the difference between cold-wall and hot-wall heat transfer is responsible for an increase in total heat-transfer rate, causing the knee?

Especially considering that the mean gas temperature at .8:1 is only about 670k, the cold (extra barrel length) will conduct nearly twice as fast...
Actually, more than that, considering that:
1) The gas near the projectile is moving faster (and heat conduction is linear with Reynolds number, ergo gas velocity)
2)

If this is a real effect wouldn't actually be surprised if the metal pipe had LESS of a knee; the steel pipe STAYS cold.

[jimmy101]

BoilingLB

Yep, i agree (i think). As the projectile moves down the barrel several things contibute to an increase in heat loss;

1. The surface area increases. More surface=more heat loss.

2. The gases are moving through the barrel. The closer to the ammo the faster they are moving. The further the ammo has moved the faster it is moving. Faster gas movement = faster heat loss. More heat is lost to the barrel near the ammo than the barrel near the chamber or to the chamber itself.

3. At some point in time, and position in the barrel, gas flow through the barrel switches from laminar to turbulent. The turbulent flow moves hot gases from the center of the barrel to the barrel wall significantly increasing heat loss. (In laminar flow the stagnant gases near the wall will act as a thermal insulator, air is an excellent thermal insulator as long as it isn't moving.)

All of this suggests that a long skinny barrel would be really bad. To much surface area, too high a gas velocity, turbulent flow at relatively low projectile velocities ...

A short fat barrel of the same volume should have much less heat loss.

Back to the "knee" in the velocity versus CB plot. The knee isn't caused by a phase change, there aren't any in a typical combustion or hybrid gun. Water condensation is too small an affect to cause the knee.

The knee is caused by a switch in the dominant mechanism of energy loss as the projectile moves through the barrel. At short barrel lengths heat loss is relatively constant and a lot of energy goes into the ammo. As the barrel gets longer heat loss increases exponentially overwhelming the energy transfered to the ammo. The faster the ammo moves the faster heat is lost to the walls of the gun.

Especially considering that the mean gas temperature at .8:1 is only about 670k, the cold (extra barrel length) will conduct nearly twice as fast...

I don't think you can use the mean gas temperature. The peak temp is ~2500K. A small volume of just burned fuel is at ~2500K, not the mean gas temp. The difference between heat transfer from a 2500K object to a 300K or 470K object is going to be pretty small.

[boilingleadbath]

Well, I dunno the velocity-weighted mean gas temperature in the barrel... but I'd expect that it's below the average temperature in the gun.