Here's the sketch Ron linked to.
This is old stuff, based on patent no. 2030759 but complicates it. My idea is to simplify that idea by Bob Neal (1936, now in public domain) not complicate it.
The patent shows a tank with an intake pipe entering and dumping air into the tank through two check valves. That's all. No explanation of why it should work, but the inventor did show a working model in order to get the patent. This sketch adds hardware to make it maybe seem feasible. I don't know about the jet pump idea though, the compressor in the tank that supplies drive air might have to move a lot of air and I'm saying it can be done very simply.
The general idea of the "Neal tank" is to make a new kind of compressor that doesn't resist the pressure that's in the tank already but puts atmosphere into the tank "somehow" and let's the compression take place by equalization with what is already in the tank. The "somehow" is the question. The energy source is the internal energy or heat of the incoming atmosphere adding to the pool of energy already in the tank.
Info on air brakes is not to be sneezed at, it stops trains so it had better be right. But the reduction to math is not easy to find. I did find it though about 1.5 times. And it's easy math.
PV/T = constant. Roughly. I know air is not an ideal gas but all the books use this for all practical purposes. So if a fixed quantity of air (a certain weight, a fixed number of molecules) has a condition pv/t, then if you change its pressure, volume, and or temperature, the value of pv/t will remain constant. The subnotations used below refer to different conditions with each separate batch of air being a different condition. For example 1 is atmosphere of a certain pressure, volume and temperature. The subnotation 2 is compressed air of a certain pv/t, a different constant. The subnotation 3 is a new condition referring to the new condition of a new batch of air, the mixture of the first two. This assumes complete pressure equalization and thermal equalization.
But if you don't wait for equilibrium then the result is two new conditions. For example if you fill a scuba tank (condition 1) from a higher pressure tank (condition 2), then the result is a hot scuba tank and a slightly cooled source tank. Conditions 3 and 4. Complete equalization is if you have perfect insulation on both tanks, leave the valve open, and wait for thermal effects to spread out through the combined volume of both tanks till all is equal. That doesn't happen (except in Joule's experiment which proves the energy is conserved, there is no external work done), you take your warm tank with you, the scuba filling station doesn't have time to reclaim their lost heat.
So I'm talking about a simple math I learned from air brake manuals because no one else cares about pressure equalization except odd stuff like player pianos and pipe organs and ear doctors. Google it--I'm not exaggerating. Pressure equalization is an ignored aspect of science except for stopping jillions of tons of train. Thermal effects aren't important in that application because large events are being handled by equalizing relatively large volumes with other relatively large volumes through a small pressure differential. My application involves equalizing a relatively large high pressure volume with a relatively small low pressure volume. It is the difference in size and pressure between the two conditions that creates a drastic surge of heat between the two check valves in the tank. The equalizer is suddenly filled with tank air and if it doesn't get super hot than why do we have to fill scuba tanks slowly? Overshooting equilibrium is dangerous, so it has to be done inside the tank.
Here is the math.
Complete equalization (aka free expansion, unbalanced expansion, unresisted expansion, partially unresisted expansion; discovered by Joule and once called "Joule's Law"):
P
1V
1/T
1 + P
2V
2/T
2 = P
3V
3/T
3
Incomplete equalization (call it a surge-driven equalizer):
P
1V
1/T
1 + P
2V
2/T
2 = P
3V
3/T
3 + P
4V
4/T
4
To be perfectly honest, even the air brake manuals didn't have the last equation, since they ignore thermal effects until a pipe bursts, then I guess they have to clean oil out of their pipes so it won't keep happening. I think if the first equation is true then the second one is also correct. When you mix two pv/t conditions, you add them together to get the new condition.
This is derived mathematically from Boyle's Law, Charles Law, and the combined law, nothing mysterious. If you can ignore thermal effects then you just delete all the T's from the equations. My idea is to make the thermal effects do something with a forward surge past equilibrium and then not allow the disturbance to return. There is no time for full equalization; the heat causes all the air between the check valves to blast into the tank and a depression is left behind in the equalizer so that the compressor is only working against very little pressure instead of tank pressure.
Thanks again for any constructive criticism.
Gumpfer