Compressible flow and Destin Sandlin's 1050-MPH baseball cannon 2

[JoeFrickinFriday]

You've probably seen this by now, but just in case, last fall Destin Sandlin uploaded a video about a pneumatic baseball cannon he and some friends built that can launch baseballs at well over 1,000 MPH. There's a 23-minute video in which they describe the design, constructions, and early tests of it:

https://www.youtube.com/watch?v=cqidD7kVnxY

Destin uploaded a companion video a few months later, in which he and his fellows fire baseballs through a variety of items through which you should not be able to fire a baseball:

https://www.youtube.com/watch?v=4I-p8vjQ95s

My question concerns the first video. at 2:48, we see a 2-D CAD printout showing a critical flow venturi in the barrel just upstream of where the baseball begins its journey. This made sense to me, as it seems like a CFV would be needed to accelerate the driving gas past sonic velocity. Without a CFV, ISTM the tank and barrel together would form a CFV with an exit-to-throat ratio of 1 (so I guess something akin to a critical flow orifice), making it impossible to go faster than the local sonic velocity. But a little while later at 3:30, we see a SolidWorks model that shows no CFV in the barrel. So what gives? I asked this question in the comment section, but got no response (no hurt feelings on my parts, he's got a lot of videos with a lot of comments and can't respond to all of them).

So I'm wondering what the collective here has to say. Is a CFV necessary for achieving supersonic muzzle velocity in a pneumatic cannon like this, or am I missing something about compressible flow?

Thanks...

 

[3DDave]

I calculated at each step where the gas pressure in the tank doubles - which means that half the gas is from the external source. Then at each step I take the average temp and calculate from that the temperature after compressing it to fit the accumulator volume and iterate to around 500 psi. Note that the constant enthalpy curve rises as the outlet pressure rises; it's not much and makes little difference, but I estimated the effect.

Then I looked at the ratio of the speed of sound at that temp to the speed at roughly standard conditions. That gets a result that the outlet should be M1.2 from a temp of 420K ; they were getting M1.35 which should require a temp of 520K. Perhaps that comes from heat picked up between the bottles and the accumulator (a small amount?).

Here's the picture -

Maybe part is that N2 is less dense than average air (28 g/mole vs 29 g/mole -> another 3% bump)? Maybe the gas heats a little more or the bottles were hotter than 80F from being in the sunshine? Possibly friction losses in the lines from the bottles to the accumulator? It seems like 410K-520K is a big jump, but perhaps it's from a bunch of little additions.

Correcting for the changing temp from the nitrogen bottles makes a tiny difference; it's not -80C.

 

[SwinnyGG]

When 2000 PSI hydraulic fluid is dropped to 500 PSI through an orifice or restriction it gets incredibly hot. But not when it's another fluid?

Hydraulic fluid is a non-compressible liquid. Nitrogen gas is a highly compressible... gas. The viscosity of these two media are different by more than three orders of magnitude... so yes, they're going to behave very differently when being drive through an orifice under pressure.

Then at each step I take the average temp and calculate from that the temperature after compressing it to fit the accumulator volume and iterate to around 500 psi.

Now re-calculate, and include the (very large) reduction in temperature in the N2 feed gas due to the initial expansion from ~140 atm to 1 atm.

The initial temperature of the nitrogen entering the tank is not 80F. It is very, very cold.

You seem to be laser focused on finding some way for the speed of sound in the gas in the tank to be equal to the speed of sound they achieved with their projectile. The two are not related.

 

[3DDave]

While those observations are correct - that's not an answer to "why."

 

[3DDave]

Sorry Swinney - I used the enthalpy chart, not an off-the cuff guess for temperature. The nitrogen in the tanks is a compressed gas, not very cold.

For clarification - tank = where the 2000 psi nitrogen is. accumulator = what is being pressurized. If you can correct your answer to reflect that it would make more sense as to why it's wrong.

As for "the two are not related," how can the projectile outrun the speed of the molecules in the gas?

 

[SwinnyGG]

not very cold.

It isn't cold when it's in the tank - but it becomes very cold when it is expanded from 140 atm to 1 atm, which you are neglecting.

From an energy standpoint what you are saying is that I can pump water uphill using gravity alone... it just doesn't work.

As for "the two are not related," how can the projectile outrun the speed of the molecules in the gas?

It can't - but the gas driving the ball is not a 1-D volume undergoing flow without a pressure change. It is flowing and expanding at the same time. The leading edge of that volume of gas can exceed mach 1 without a shock wave forming because the volume of gas in which waves are traveling is itself moving.

 

[3DDave]

You are neglecting that work was done to compress the gas in the bottles. Some work is lost as heat, but much of it remains as pressure. If both the tank and the accumulator lose temperature then you have discovered a way to destroy energy. I say that energy is conserved and heats the compressed gas in the accumulator and I used the enthalpy chart for nitrogen to track that.

 

[SwinnyGG]

I say that energy is conserved

This is part of the issue at hand. This isn't an isentropic process.

 

[3DDave]

You have just failed the class. Energy is always conserved in Newtonian physics. If it's rejected as heat - where did it go?

 

[SwinnyGG]

You must be a professor, based on your ability to condescend AND ignore the real world at the same time.

Again. Not adiabatic. Not isentropic.

 

[SwinnyGG]

I'm not here to teach you physics. Your failure to analyze is your own.

If you can't figure out why a real world process is non-isentropic and non-adiabatic, and that you can't heat something by extracting work from itself, there is literally no reference or insight I can provide which will enlighten you.

Best of luck.

 

[3DDave]

Look up stagnation temperature and stagnation temperature for compressive heating. It's what causes meteors and de-orbiting spacecraft to heat. If you are going to toss expertise about, show some.

 

[SwinnyGG]

If you are going to toss expertise about, show some.

Again, best of luck.

 

[danschwind]

Upon a second thought, I now do agree the temperature on the cylinder will increase (if completely insulated). I will need to do some thermo/math work later though to check this with 100% certainty.

But at first it seems that because the cylinder is getting an accumulation, its change in internal energy will be a function of the incoming mass flow rate and its associated enthalpy, which are always positive values, therefore the net change will be positive. Will later check this in more details.

It is not insulated though, so the overall kinematics are way more complicated.


Keep civil guys, the discussion is good

Daniel
Rio de Janeiro - Brazil

 

[3DDave]

The problem that Swinny was trying to get at is that if the process continues until the pressure equalizes wouldn't my explanation of this leave the accumulator at a higher temp than the tank? Obviously not, if for no reason other that the process slows to a crawl as the pressure approaches equalization, so the amount of gas transferred dwindles.

The process is adiabatic - no heat is necessarily added or removed to get the gas to change location. It is also roughly isentropic. The gas isn't changed by the process, such as combustion might do.

 

[TugboatEng]

Can I leave this here?

In the third case, the temperature increases, therefore mach number, as the exit of the nozzle is reached.

Do we know the bore of the gun is straight or is it nozzle shaped?

 

[SwinnyGG]

The bore is straight.

 

[TugboatEng]

Not entirely, that vent box thing at the end isn't much different than than an expansion.

 

[SwinnyGG]

I'm going to go ahead and argue that 20 feet of constant diameter pipe with a little hole in the end is much closer to 20 feet of constant diameter pipe than it is to a 20 foot long tapered nozzle.

That little expansion volume does not do what a tapered cross section would do- I'd bet it actually does the opposite. The whole point of the shape of a supersonic nozzle is to provide gradual expansion and prevent a stepwise change in volume anywhere, which would create a shock wave. A long straight barrel with a single stepwise dimension change (ie a hole into another volume) does the exact opposite of that.

The problem that Swinny was trying to get at is that if the process continues until the pressure equalizes wouldn't my explanation of this leave the accumulator at a higher temp than the tank? Obviously not, if for no reason other that the process slows to a crawl as the pressure approaches equalization, so the amount of gas transferred dwindles.

This isn't actually what I was getting at at all. But, since you brought it up, good point. Your algorithm for finding a solution provides no mechanism for the temperature increase to ever stop. And I suspect you know this already, because dragging your equations down two more rows is pretty easy. Look:

This means I've got gas at the same pressure, and thus the same volume, but at a much higher temperature. This very large enthalpy change, according to your algorithm, happened without any external work being applied.

What I was actually getting at is that you're neglecting the source of the work being performed on the gas, which is the internal energy of the gas itself.

Internal energy in an ideal gas has no relationship with pressure at all; in a real gas the relationship is very very weak, to the point where it can be disregarded. What you're describing in your algorithm is a situation where the total internal energy of the gas in the system (including the gas in the bottles) is increasing over time, without any additional external applied work. A system that works as you've described is a perpetual motion machine.

 

[3DDave]

Did both the tank and the accumulator lose energy and there was no heat produced. The potential energy of the compressed gas just went into nothing?

 

[rb1957]

this is more fun than a Climate Change thread ...

another day in paradise, or is paradise one day closer ?