That's not the reason submarine reactors are so small for their power output. The actual reason they're so powerful for their size is due to their insane enrichment. Commercial reactors are enriched to roughly 5% U235. US Navy reactors are enriched beyond bomb grade, to a minimum of 93% U235.
The primary function of an atomic pile is to produce heat energy, which is then used to drive some kind of reciprocating or rotating motion, to spool up dynamos which then power the more efficient electric motors to be used to turn the propellers on the final drive.
Most nuclear submarines use steam turbines with direct drive for propulsion. I've never heard of reciprocating steam engines on a submarine. I think that went away by World War 1 when battleships converted to turbines.
Of course there are turbine generator sets on all nuclear submarines, but they aren't for propulsion with the exception of a few one-off subs like the USS Tullibee and the USS Lipscomb. Those are the only two turbo-electric USN subs, but I believe the new Columbia class might be turbo-electric as well.
Steam is often the medium used to carry the energy to the mechanism, be it a turbine, or a swashplate, or even an older design of a reciprocating piston-driven multi-cylinder engine. It is a matter of harnessing the heat energy for the most efficient means of recovering the maximum that can be extracted before releasing the excess heat to the environment.
Thorium-fueled Molten Salt reactors are an even more adaptable design that is highly scalable, and which produce virtually no long-lived isotopes as a result of operation, and are inherently impossible to fail due to a runaway reaction and overheating, causing the “China Syndrome”, which was always a possibility with the older uranium-fueled Light Water reactors.
I don't know much about thorium reactors, but most PWR's won't runaway either due to their negative temperature coefficient of reactivity. The hotter the coolant and moderator get, the fewer reactions occur.
Meltdowns occur when coolant is removed, but that's not a runaway reaction. The fuel is just hotter than the melting point of the cladding.
Do your comments for nuclear submarines apply to nuclear aircraft carriers?
Just curious.
For some reason the power discussion also reminds me of the way modern diesel-electric locomotives operate.
Propelled by electric motors that are powered by generators that are fueled by diesel fuel.
When someone speaks of a Thorium 232 reactor, they often fail to mention that it is the breeding of Uranium 233 from the Thorium, which provides a fissionable fuel.
As said by many, our stockpile of used fuel rods retain about 95% of their initial energy content. Processed to fuel a salt coolant based reactor, this fuel reserve could power the grid for the better part of a century.