Lunar nuclear power system - how can hydrogen generated on the Moon be liquefied?

Question

In September 2020, NASA asked for proposals for a lunar nuclear power system.

The 10-kW water electrolysis system can create 5-10 tons of hydrogen in a week from the Moon’s surface ice.

How would you cool and liquefy this hydrogen on the Moon?

Answer 1

How would you cool and liquefy this hydrogen on the Moon?

I guess one would have to do a serious study to find out for sure which way is more suitable in a given scenario, but I think passive cooling by exposure to space is a competitive alternative to active refrigeration for making liquid hydrogen (LH₂).

All you need is some good multilayer thin metallized film insulation the kind you see all over the place in spaceflight. The mathematics and principle is covered in the article.

At night the surface temperature of the Moon anywhere drops below 100 Kelvin and at the poles (where the water and therefore hydrogen will be) it's substantially colder.

Use of multilayer insulation is common in liquid helium (LHe, 4.2 Kelvin) systems and where possible separates it from surfaces cooled by much cheaper liquid nitrogen (LN₂) at 77 Kelvin.

Here hydrogen at 1 atmosphere will liquefy all by itself at 20 Kelvin when simply allowed to radiate to space (the ultimate free refrigerator!) during the roughly two weeks of lunar night, assuming you're not too close to the poles, or at least in a crater shielded from the Sun.

Compare passive radiative refrigeration to active refrigeration

There are LHe refrigerators on the JWST that are believed to be so reliable that there is no current plan (or way) to service them out in a Sun-Earth L2 halo orbit. While hydrogen is a much more pesky material to handle and especially store than helium (due to its propensity to diffuse through and make brittle many solid materials), I don't think there's any reason to try to go out of one's way to avoid a few compressors other than mass.

In passive cooling you use pretty large areas of insulation and radiators to space to dump your heat. For active refrigeration you can also use radiation, but it will be a much smaller area because radiation scales as T⁴ and so if the hot end is 100 Kelvin it will need 600 times less area than a 20 Kelvin passive condenser for LH₂.

And of course if it's hot enough -- hotter than the 50 to 100 Kelvin surface of the Moon at night -- you can dump the heat directly into the lunar surface as well, meaning you either don't even need to insulate between your radiators and the surface, or you can run pipes into the surface and dump it into the "ground" the way heat pumps on Earth sometimes work.

Of course, dusty lunar regolith has low heat capacity and low heat conductivity, so then you've probably got to start drilling, so maybe radiation is the only practical way here.

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From LRO DIVINER Lunar Radiometer Experiment

(See also Williams et al. 2017 The global surface temperatures of the Moon as measured by the Diviner Lunar Radiometer Experiment (paywalled, also found here and here))

Equator Average Temperature:

• 390K at noon
• ~95K at midnight

Polar Average Temperature:

• ~98K (outside of shadow)

Minimum Temperature:

• ~25K (Hermite Crater)

Thermal model calculations of monthly and annual lunar surface temperature variations at various latitudes.

Animation showing measured Diviner-measured monthly global bolometric lunar surface temperatures (one frame of the 2.8 MB GIF, too large to upload here)

Answer 2

Cryogenic cooling typically works by cooling pressurised gas, releasing the pressure to reach even lower temperatures. The cooling itself uses boiling of some other gas with a higher boiling point (typically nitrogen), and you chain these stages together until you can start at ambient temperature. The lower the desired final temperature, the lower the yield due to the higher number of stages needed.

None of this requires an atmosphere or even gravity, it all happens inside pipes and tanks.

The only issue with doing this on the Moon is getting an appropriate heat sink at the beginning of the chain. On Earth, you can just have a river running through the factory for cooling, or have cooling towers for air cooling.

The only practical initial cooling source on the Moon is radiators, having some appropriate cooling medium inside them.

The whole cooling process also requires a fair amount of power for the compressors (and so does the electrolysis), so I imagine nuclear power is absolutely required to supply all of this. This would also require radiators.

So: Radiators, lots of radiators. And then a compressor/boiling chain.