Much better to run a high temp differential Stirling engine off solar input. A polished 3 M dish can melt steel in seconds at the focus. A pretty small Stirling engine can deliver a lot of power if you compress the working fluid, and use either Helium or Hydrogen, instead of air. There are tricks (called the Heylandt crown) to keep the hot gas off the seals, so all the seals run at modest temperature. Then you can use teflon-bearing seal material for piston rings, and put sealed ball bearings on the mains and rods. This allows you to have no liquid lube in the engine, so oil mist won't coke up in the heater tubes. You want to run the heater tubes as hot as your materials can stand, like 600 -800 C.
You can build a hermetic machine, and put a little brushless PM alternator inside the crankcase. Drive whatever you want with the electrical output.
But...but...if the object is a cooler, it's SO much simpler to build the Stirling as a cooler rather than as an engine. No lube problems, no material problems, and they run well on air if you aren't going for cryocooling.
Of course, you need a way to drive it, and if you aren't going to use an electric motor, and if you're really ambitious, you could use a Stirling motor. But what you're describing is a WHOLE lot more hassle than a small Stirling cooler.
My calculations for a conventional compressor assumed the efficiency of a
10 SEER air conditioner, which also has the losses of the electrical motor and the air handler fan to overcome to get to that 10 SEER, which the beer can chiller doesn't. I don't know if scaling things down makes them more or less efficient, or how much so.
Those darned things still confuse me. I've never looked closely enough to figure out how they really work, aside from the simple expansion of air and its consequent absorption of heat. But there's more to it, I think.
Anyway, without knowing anything about their thermodynamic efficiency, yes, they sure look appealing from a simplicity standpoint.
Note that there are two ends to it, and cold air comes out one end, and hot air out the other.
Essentially, compressed air is fed in tangentially around a point just past the junction of a disk and a large diameter tube. In the center of the disk is a smaller hole, going off to a tube in the other direction. The larger tube has an obstruction at a distance so the total area is similar to the smaller tube (and I think ideally the larger tube has twice the area of the smaller tube).
The tangential feed causes the air to form a spinning disc at that point. Hotter air has molecules in faster motion than colder air, so the hotter molecules tend to (on average) collect around the OD of the spinning disc of air, and the colder molecules migrate to the center. Since there is only one direction the hotter molecules can go (down the larger tube) and while there are two directions the colder air can go, most of the hotter air from the compressor is going down the larger tube, so the pressure is a bit higher there, and the colder air mostly goes down the smaller diameter tube. (It might be possible to make it more efficient by putting a blocking disc near the center on the hot side so the colder air can't go that way readily.
I made one of these a long time ago, using mostly plumbing fittings and a bit of turned and machined brass after seeing one in a demo of the things one of the other labs in the area was developing. (The air from the cold side was piped into the helmets of tank crew, especially those who are trapped down inside the tank during normal operation.)
What I made was terribly inefficient -- it took a lot of compressed air to get a reasonable separation between hot and cold output -- but the hot side pipe was uncomfortable to hold, and the cold side was quite pleasant in mid summer. I understand that the main things against them are the noise output and the relatively poor efficiency. But in a tank, there is energy to spare, and an already noisy environment, so the cooling is quite welcome.
That was a valiant effort, but I think I need a diagram. I'll put it on my short list of things to look into. As you describe it, it does sound intriguing.
It appears from that description that there is some controversy about the best way to describe it. That sounds like the controversy over the Bernoulli Principle and the lift on an aircraft wing. You just pick the explanation that works for you.
I'll have to dig further. Again, I appreciate the link.
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