This answer is about doing it as a fission system. The OP mentions Uranium.
As you describe it, there are huge challenges.
There are two basic time scales to nuclear fission. The slow one is critical but not prompt. And the fast one is prompt.
Prompt has a doubling time of a few microseconds, possibly faster depending on the design. That means you can't usefully control the energy output. Any engine is going to have RPM in the few thousand at most. It cannot respond to the power changes. Your machine explodes on the first stroke. Early in the power part of the first stroke.
Critical but not prompt has a doubling time in the milli-second or slower range, again depending on the design. You might hope to make this useful.
The difference between prompt and not-prompt is not large. Power reactors are carefully designed to stay in the not-prompt range, and for it to be difficult to get across that threshold. Chernobyl was an example of passing over to prompt, and that only for a very short time, some few milliseconds. That was long enough to heat the coolant water enough to produce a steam explosion that destroyed the station.
Controlling power through compressing the fuel would be a finicky thing. An extra 1% compression would be more than enough to push you over. A tiny errror in the input fuel pressure or composition and your engine disappears.
There are other problems. To complete the cycle you either have to cool the fuel in place, or pump it out and cool it outside.
For you to cool it in place is tough. I am unaware of any engine that cools the fuel in place. When the fission stops the decay heat is round about 5% of the full power value. After 1 minute it is down to about 1%. These values depend on the design but they are reasonable approxes. So you need to cool your fuel in a useful time, while dealing with the decay heat. In order to get the heat out in a reasonable time you might well require a cooling system that consumed more energy than produced in the pulse.
If you were prepared to have an hour between strokes you might get something. It seems mighty inefficient.
To pump it out you have to keep in mind that only a minute fraction of the total energy is released in one cycle. So you would need to cycle the fuel through the engine many thousands of times. (100's of thousands? Depends on the design.)
You would need a system that is capable of pumping out the gas and pumping in the previously cooled gas. But note that 5% decay heat. Your pumping system has to deal with 5% of the total power coming out as mostly radiation. And it will be cooking everything near the exhaust port of your engine.
Plus you need to remove the fission products. These are usually quite radioactive. Some of them are gas. And several of them are challenges at handling, such as the Tritium that likes to leak through stuff. These are issues that are being solved for molten salt reactors, but using systems that weigh 100s of tonnes. And that cycle the fuel every few hours, not on a cycle of once-per-engine-stroke. It gives a lot of the nastier isotopes time to decay while still in the reactor.
So your working fuel is going to be this tiny fraction of total fuel. The rest of the system will be a 100's of tonnes station that will tend to leak radioactive isotopes at a prodigious rate. And it will have a very tough time avoiding exploding.
And there are already nuclear power station designs on that scale that work far better in every way.