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...

 

[mc5w]

A convergent divergent nozzle is needed to achieve hypersonic fluid flow. I do not know who came up with that idea but every liquid fueled rocket has that. Otherwise, it would not be possible to achieve orbit or escape velocity.

Sounds a lot like a cannon that the US Air Force has that fires dead chickens at airplane windshields that are under test at about 600 MPH. By the time I finished high school every airplane windshield that Uncle Sam had tested could not withstand a 600 MPH chicken. This is no joke. A flock of geese took out both engines of a jet plane that was taking off in New York City had to ditch the plane in the Hudson River.

One time when I was driving on a country road north of Marysville, Ohio a little bird flew into the front grill of my pickup truck when I was under way. In this case the little bird lost grille won. If it had been a Canadian goose it would have damaged my pickup truck and died. Usdually birds take off when a motor vehicle is coming.

 

[JStephen]

I'm not sure I understand the issue, but are you not also saying that firearms cannot exceed the speed of sound?

 

[3DDave]

Firearms are different. The speed of sound is generally a reflection of the temperature of the gas. In a firearm that temperature is higher than typical for the surrounding conditions.

Choking requires exceeding a pressure ratio. The usual case is a combination of a restriction and a down-stream pressure, such as an orifice plate. In this case the flow into the barrel is subsonic and there is no pressure ratio as the source of that is friction, which has no opportunity to develop at the inlet. As the gas expands with the movement of the ball, the gas at the ball continues to accelerate, but at every step along the way there is no step in the friction for which there is a downstream flow condition - the ball prevents that.

So I see that the first place for the flow to choke is when the gas reaches the exit after the ball has left the barrel.

It seems reasonable to predict the ball isn't quite supersonic in the barrel.

However. A lot of energy went into compressing that gas. It's possible the temperature and therefore the speed of sound from that hot compressed gas is higher than in the ambient air of the firing range.

One thing they could have done is to add a heater to increase the temperature of the reservoir and therefore the speed of sound at the stagnation condition. It would also be interesting to use helium instead of air.

 

[JoeFrickinFriday]

> A convergent divergent nozzle is needed to achieve hypersonic fluid flow. I do not know who came up with that idea but every liquid fueled rocket has that.

They are sometimes called de Laval nozzles:

https://en.wikipedia.org/wiki/De_Laval_nozzle

> So I see that the first place for the flow to choke is when the gas reaches the exit after the ball has left the barrel.

But if the barrel is constant-diameter along its entire length, wouldn't the choke point be back at the transition from the reservoir to the barrel, with constant-speed flow for the entire length of the barrel after that? If that's true, then assuming the reservoir gas is at room temperature before firing, the speed of sound at the resulting choke point would be about 720 MPH, which would mean the ball is picking up another 330 MPH of speed after it leaves the barrel. This seems implausible. The very reason CFVs have an expansion after the choke point is to accelerate the flow to supersonic velocity. If the driving gas is sonic as it leaves the barrel, it's already pressure-matched to atmospheric at that point; it's not going to accelerate to a higher velocity, and so neither is the ball.

> However. A lot of energy went into compressing that gas. It's possible the temperature and therefore the speed of sound from that hot compressed gas is higher than in the ambient air of the firing range.

I suspect the reservoir gas is well below ambient when they fire. At 12:07 in the first video, you can see a rack of gas bottles in the background, which is probably what they're charging the reservoir from. They're outdoors at a field testing site, so it's unlikely they've got a high-pressure compressor nearby. With room temperature gas bottles supplying nitrogen at ~2000 psi and filling the reservoir to ~700 psi, the reservoir would be at -65F when filled to capacity. The reservoir appears to be made from pretty hefty steel, so the gas won't stay that cold for very long, but I doubt it's getting close to room temperature before they fire.

 

[rb1957]

don't forget that the gas is compressible, so a higher density at the throat allows the gas to expand (and accelerate) and maintain mass flow rate.

The aerodynamics of this thing are very interesting. I was surprised that they got 1000 ft/sec, but they certainly did. You could look into the energy in the compressed gas, but you'd need to include the pressure recovery over the throat. I'm surprised that the throat is so critical ... I'd've thought it was the flow into the tube from the tank was the critical shock ... flow around the annulus formed by the "plug" gate valve.

I'm surprised that they put so much effort into putting a vacuum ahead of the ball. This only gives an additional 14psi pressure (on top of the gas pressure they have and somewhat neutralised when the seal at the end ruptures and allows the external air into the tube (a flow against the intended flow).

What'd happen if you vented the N2 tanks into the tube ... drive the ball with 2000psi pressure ? Maybe have a "sabot" upstream of the ball so the pressure doesn't crush the ball, although you can see the cover getting peeled (flayed ?) off already with something like 500psi pressure driving the ball.

I wonder how the length of the tube affects things ? longer barrel gives more time for the gas pressure to accelerate the ball ?

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

 

[3DDave]

They got Mach 1.35, confirmed by the Schleiren and high-speed camera timing.

The vacuum is required to remove the mass of the air that would otherwise also need to be accelerated.

Still, the flow into the tube cannot be sonic until the ball is sonic.

I'll need to find what happens when high pressure gas flows into a control volume - typical experience says that the source drops in temperature, so it would suggest that a great deal of kinetic energy would have to vanish in compressing gas in the reservoir for the target vessel to also cool?

My experience is that pressurizing a tank causes the air temp to go up.

 

[EdStainless]

With air (nitrogen) compression results in heating and expansion in cooling. If the pressure drops are high enough you get a lot of cooling. Enough so that if the air is moist you get condensation.
Now He or H2 will heat on expansion.
Used He in a precharged air rifle once. Muzzle velocity went from 1200ft/sec to about 1800ft/sec.

= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, consulting work welcomed

 

[SwinnyGG]

This isn't a simple flow problem; remember that the gas in the 'tank' is at very high pressure, 35+ atm. The gas in the barrel, on both sides of the ball at the moment the valve is opened, is at much lower pressure.

Once gas has moved into the barrel behind the ball, and the ball has moved, there is a volume of gas inside the barrel which is not going through a 'nozzle' - it is expanding to fill a control volume of constant diameter and changing length. This gas can reach supersonic velocities inside the barrel, without having supersonic flow at the inlet between the tank and barrel, because there is a very significant density change happening in the barrel at the same time

It's simpler to imagine the tank and barrel as separate control volumes, than to imagine them as a control volume with a nozzle on the end.

Another way to think of the system is to imagine that the barrel is just the narrow section of a delaval nozzle which is extremely long. Supersonic flow can happen in the barrel, and the flow becomes subsonic at the exit to the mass atmosphere.

 

[rb1957]

I think the discharge from the tank into the tube (upstream of the delaval nozzle) is critical to understanding the flow.

How neat of a fit is the ball in the tube ? I assume there is leakage around the baseball, to allow the vacuum to enter the other side of the ball.

Would it help to put "wadding" (a la 18th century naval guns) on the pressure side ? To reduce the amount of leakage around the ball, at the cost of some friction ?

At the end of the day, with more than enough tank pressure (500+psi) we can make a baseball go supersonic.
I wonder how much energy is being used (in the gas in the tank) for how much "useful" work done (if you can call making a baseball go supersonic useful) ?

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

 

[3DDave]

They used a ram-rod to fit the ball into the tube, so the leakage is already minor.

I'd guess that less than 5% of the energy expended in getting that tank pressurized is seen in the baseball. That said, that's a lot of energy in that baseball.

 

[rb1957]

so when they evacuate the tube, they're only doing it to one side of the ball ?

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

 

[3DDave]

I am pretty certain I did not indicate that to be the case. Under the high pressure the ball is self-obturating as the ball will tend to expand from the pressure delta vs the inertia of the ball. Leakage under vacuum is helpful but at some point any air behind the ball during evacuation will either leak by during that lengthy process or the ball will move from the pressure difference until the force of friction resists the resultant air pressure.

 

[danschwind]

This is an interesting topic that got me thinking. It is a highly transient phenomena that I don't think we can apply our typical concepts of 1-D compressible pipe flow to it.

During the initial phases of the ball's movement (still inside the cannon), a shock wave will develop upstream of it, will it not? If by definition, AFAIK, a shock wave travels at supersonic speeds, then maybe this has something to do with it provided there is not enough resistance to movement (in this case, for the expanding control volume) to dissipate this energy?

Also regarding the nozzle, it is a fact that a De Laval nozzle is needed to sustain supersonic flows. Keyword 'sustain'. During a rapid transient, isn't possible to have supersonic flow that quickly dissipates?

Only throwing some ideas around. Would love to see other's thoughts on it!

Daniel
Rio de Janeiro - Brazil

 

[MechinNC]

A convergent/divergent nozzle has the benefit of creating a supersonic flow in the divergent section through expansion, even with the upstream pressure being not that high. So for rocket propulsion, it makes it much more efficient. Combustion pressure need not be that high.

On the baseball rig they can absolutely get supersonic speeds just by using gobs of pressure. Efficiency be damned.

Similar to dynamics in a gun barrel.

I did a similar thing with a spud gun with a yellow onion. Blew a nice hole in 5/16" plywood.

 

[3DDave]

The puzzle isn't the pressure - the puzzle is the sonic or supersonic performance. The spud gun does a lot because the fuel-air mixture raises the pressure and raises the temperature - the speed of sound in a gas is governed by the temperature, not the pressure.

 

[rb1957]

I would have thought that the flow through the valve (that isolates the tank from the tube) would be where the flow goes supersonic ... well, wants to be supersonic ... I suspect it is choked with a strong shock and lots of pressure loss.

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

 

[kjoiner]

Now I want to see his 250MPH baseball bat setup go up against the 1050MPH baseball cannon!

Kyle

 

[SwinnyGG]

The speed of sound in the gas doesn't matter all that much when the pressure ratio is more than 100:1.

 

[MechinNC]

Flow will be choked at the valve admitting N2 from the tank into the barrel. But once inside the barrel that N2 is going to be expanding at a rapid rate. 590psi N2 has a lot of energy!!

While the the choked flow rate/velocity restrictions would exist at the admission valve, once in the barrel I don't think rate of expansion and thus speed of the ball is limited to the temperature based limit on supersonic velocity.

But then again it has been 35yrs since I studied this stuff!!

And if you can believe the two measuring techniques used to determine velocity, it DID go supersonic, so there is that. I tend to trust their measurements, no reason for them to BS there. I think.

I wish they figured out why the vacuum in the barrel was decaying off, I think it must be a tiny leak in the admission valve. Vac did not decay much until tank pressure got high. Need to lap that valve!!! Not sure what effect the decayed vac would have on the speed of the ball, but probably not too much as the air (n2) mass ahead of the ball would not be that much.