The sub would be about the size of:
- the Sōryū class, which displaces 4200 tonnes (implying about 4200m³ volume) and has a 6000kW propulsion system
- the Oyashio class, which displaces 4000 tonnes (implying about 4000m³ volume) and has a 5780kW propulsion system
- On the smaller side: Collins Class, 3407 tonnes displaced, 4200kW
Nuclear tech is not available in this world.
They could fuel up on hydrogen from bases, and I might go that route if the answer to this is a hard no, but I would prefer to keep them autonomous. Even this anti-hydrogen-economy article concedes that submarines might be a good niche application for hydrogen: https://phys.org/news/2006-12-hydrogen-economy-doesnt.html
The question is: can such a sub harvest enough energy from the currents, chemistry, and thermal gradients of the sea around it to run??
Reduce power demand
Of the above, Sōryū demands 1.428kW/tonne, Oyashio 1.445kW/tonne, Collins 1.23kW/tonne.
Note that the bigger they are, the more energy they use proportionally. Is this an absolute law? Something to do with drag, or some square-cube law? Are smaller subs always gonna be more efficient? (If so I may make all the subs in my world smaller.) Or is it just because bigger subs are fancier and have more gizmos?
This trend continues in a more pronounced way if we consider really small subs: the DSRV-1 Mystic displaces 37 tonnes with 11.2 kW for a score of 0.3027kW/tonne, and this one 61 tonnes with 50 kW for a score of 1.02kW/tonne
Can the efficiencies of large subs be brought down to something like 0.3027kW/tonne? Because that would be amazing. Or is it impossible? What's the physics here?
It does seem that with aircraft size is bad for efficiency: https://web.archive.org/web/20180302044700/https://theicct.org/blog/staff/size-matters-for-aircraft-fuel-efficiency
PS: I see now that the DSRV-1 Mystic, as well as using about a-fifth the energy, achieves about a-fifth the top speed, so maybe speed rather than size is the issue.
PPS: There's some debate over whether pump-jets are more efficient than propellers (all the subs detailed here use propellers). Here's an article on the side of that debate against pump-jets, but it does seem to accept that they'd be better at high speeds. (It also says "the square law for drag means that the energy required for propulsion becomes extremely small at very low speeds", which is good news for this thread.) Certainly the drag is proportional to the square of the speed, so halving the speed means only one-quarter as much drag, and drag is a large part of energy consumption though not all.
PPPS: Some comments on increasing efficiency by those guys who got defeated by a flock of emus – https://apps.dtic.mil/sti/pdfs/ADA428039.pdf – including the interesting proposal of coating the surface with some sort of polymer to make the flow laminar rather than turbulent on the first few meters of the nose.
Generating from ocean currents
Let's say we don't get the efficiency way down, and our heroes need 6000kW to go.
Energy can be harvested from ocean currents. This can be done with turbines, but this tech trumps all - https://minesto.com/our-technology - because it claims "Small in size and lightweight. Up to 15 times less per MW than competing technologies." Its compact size makes it perfect for our purposes of a generator the sub can carry. This is credible tech, with government partners, not some scammy website, and it is something like an underwater kite carrying turbines.
Could this tech be scaled up to 6000kW? I think it would weigh 70 tonnes then (3MW version weighs 35 tonnes, the 250kW version, one-twelfth the capacity, weighs 3 tonnes, so I guess the weight scales up proportionately with the capacity?) What sort of wingspan would be needed? I see no reason not to make the wings foldable/collapsible.
Other power sources
Anærobic digestion of the crew's waste? Assume 23 submariners; how many watts could be generated?
Electrically-active microbes in the sea - https://tos.org/oceanography/assets/docs/25-1_girguis.pdf - how much could be generated here?
OTEC - https://www.nrel.gov/docs/legosti/old/254.pdf envisions a unit generating 32kW or 50% more with advanced materials. The dimensions aren't given, but the figure on page 19 shows it about six feet tall, but I don't think the weight is mentioned. How would this scale up? What size OTEC unit would the sub need to deploy to approach 6MW?
Several people have brought up that fish, whales, dolphins do what I'm talking about: swim around on ocean energy by using bio-energy. Whales and dolphins do this while also supporting a warm-blooded metabolism. Technology can often do things much more efficiently than biology, so could we ingest biochemicals from the water, digest them more efficiently than an animal, and use them for an efficient propeller?