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Related: Is there some fundamental limitation that would prevent steam-powered rockets from reaching space?

Thermal rockets, including nuclear thermal rockets, work best with minimal molecular weight propellant gases. This is because, for a constant temperature or a constant amount of thermalized kinetic energy per unit mass, low molecular weight leads to a higher velocity of the particles and therefore a higher exhaust velocity.

The effect is, inconveniently, strong enough that there is almost no point in using anything but hydrogen as propellant for a solid-core NTR, and many common volatiles such as water manage the impressive feat of being worse than even low-performance chemfuel.

Are there methods that can be used to improve the issue or get good performance out of non-LH2 propellant or to operate nuclear thermal rockets with good performance on higher density propellants?

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    $\begingroup$ Seems doubtful that you'd find anything that wouldn't also make the performance of an H2 NTR proportionally better. The solution is probably "don't use an NTR". $\endgroup$ – Starfish Prime Feb 26 '20 at 20:33
  • $\begingroup$ What else would you use? There's not much else we can build anytime soon that has both high thrust and Isp over 500. $\endgroup$ – ikrase Feb 26 '20 at 20:37
  • $\begingroup$ Use for what, though? An NTR isn't going to give you a useful SSTO for use on Earth, and whilst it might be high-thrust it is still no torchship handwave engine so it isn't going to whisk you across the solar system in a blink of an eye. $\endgroup$ – Starfish Prime Feb 26 '20 at 20:44
  • $\begingroup$ (that said though, there are some interesting modified NTR designs out there. I've just been reading about the Scorpion, which I particularly like, or for more handwavium there are pulsed NTRs... both will get the highest Isp with the lightest propellant molecules though cos that's just how physics rolls) $\endgroup$ – Starfish Prime Feb 26 '20 at 20:48
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    $\begingroup$ The truth is, you're probably better off using the same fissionables to build a power reactor for propellant production. Using a NTR (with hydrogen) roughly doubles your available delta-v...so does refueling at your destination. One of these options requires hauling a lot of radiation shielding around and has you periodically doing maintenance on a highly radioactive engine. A NTR also ties up those fissionables for its working lifetime while only making very intermittent use of them. $\endgroup$ – Christopher James Huff Feb 27 '20 at 0:56
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To copy the key part of this answer (and this related earlier answer)... an important figure of merit in a rocket engine is the "characteristic velocity":

$$c_* \propto \sqrt{\frac{T_t}{M_w}}$$

where $T_t$ can be taken to be the exhaust temperature, and $M_w$ is the molecular weight of the gas species in the exhaust.

(The "proportional" bit is doing some work here as not all exhaust species are created equal... the heat capacity ratio is an important factor that the author of the older answer mentioned, and I don't doubt there are others).

The operating temperature of the reactor puts an upper limit of $T_t$, above which your fuel elements melt and you (briefly) get a liquid core NTR. Again, not all exhaust species will be created equal here, because their various chemistries at ~3000K±500K require various different protective covers around the fuel elements to prevent (or at least limit) corrosion, and those protective layers will have different melting points and thermal properties and so on.

That just leaves you with $M_w$, and which ever way you slice it, water molecules are going to be about 10 times heavier than plain old H2, and when your exhaust gasses are at the same temperature that water is just going to be travelling slower and hence the rocket's Isp is going to be lower.

This 1990 paper by Zubrin lists some other potential NTR fuels and their expected specific impulses at various core temperatures, and you can see these tally reasonably well with the above relation.

Temp  C02 H20 CH4 CO  Ar
2800K 283 370 606 253 165
3000K 310 393 625 264 172 
3200K 337 418 644 274 178 
3500K 381 458 671 289 187

But to counter your main complaint:

there is almost no point in using anything but hydrogen as propellant for a solid-core NTR... common volatiles such as water [are] worse than even low-performance chemfuel.

The universe in general, and the outer solar system in particular, is just absolutely chock full of water, just lying around, ready for the taking. More or less. It is commonplace, energetically easy to harvest, relatively straightfoward to store, given its density and the lack of need for compression or refridgeration or worries about tiny molecules escaping your grasp (sure, you've got to keep it liquid, but you do have a nuclear reactor on your spaceship). And just because the Isp is low, that doesn't mean that the engine power is low too... the same number of watts are going into the exhaust, and that means high thrust. Its a different use-case to an H2-fuelled NTR, to be sure, but it is still a very handy one.

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