Bubbler LNTR

Bubbler LNTRs pass the propellant through the molten fuel body in order to transfer heat from the fuel to the propellant.

A bubbler has the advantage that it is able to use an incredible amount of surface area for heat transfer from the fuel to the propellant, with the surface area being inversely proportional to the size of the individual bubbles: smaller bubbles, more surface area, more heat transfer, greater theoretical power density in the active region of the reactor. They also have the advantage of being able to regeneratively cool the entire length of the fuel element’s outside surface as a natural consequence of the way the propellant is fed into the fuel, rather than using specialized regenerative cooling systems in the fuel element canister and reactor body. However, bubblers also have a couple problems: first, the reactor will not be operating continuously, so on shutdown the fuel will solidify, and the bubbling mechnaism will become clogged with frozen nuclear fuel; second, the breaching of the bubbles to the surface can fling molten fuel into the fast-moving propellant stream, causing fuel to be lost; finally, the bubbles increase mixing of the fuel, which is mostly good but can also lead to certain chemical components of the fuel being carried at a greater rate by either vaporizing and being absorbed into the bubbles or becoming entrained in the fuel and outgassing when the bubble breaches the surface. In a way, it’s sort of like boiling pasta sauce: the water boils, and the bubbles mix the sauce while they move up, but some chemical compounds diffuse into the water vapor along the way (which ones depend on what’s in the sauce), and unless there’s a lid on the pot the sauce splatters across the stove, again depending on the other components of the sauce that you’re cooking. (the obvious problem with this metaphor is that, rather than the gaseous component being a part of the initial solution they’re externally introduced).

For more information about the bubbler-type LNTR, click here.

Radiator LNTR

Radiators avoid many of the problems of a bubbler, but not all, by treating the fuel almost like a solid mass when its under centrifugal force: the propellant enters from the ship end, through the central void in the fuel element, and then out the aft end to enter the nozzle through an outlet plenum. This makes fuel retention a far simpler problem overall, but fuel will still be lost through vaporization into the propellant stream (more on this later). Another issue with radiators is that without the propellant passing all the way through the fuel from the outer to inner diameter, the thermal emissions will not only go into the propellant, but also into the fuel canister and the reactor itself – more efficiently, actually, since H2 isn’t especially good at capturing heat,k and conduction is more efficient than radiation. This requires regenerative cooling both for the fuel canister and the reactor as well most of the time – which while doable also requires a more complex plumbing setup within the reactor body to maintain material thermal limits on even relatively high temperature materials, much less hydrides (which are good low-volume, low-mass moderators for compact reactors, but incredibly thermally sensitive).

For more information about radiator LNTRs, click here.

Design and Physics Considerations

Fuel Materials

One fundamental question for any LNTR fuel is the maximum theoretical isp of a design, which is a direct function of the critical temperature (when the fuel boils) and at what rate the fuel would vaporize from where the fuel and propellant interact. Pretty much every material has a range of temperature and pressure values where either sublimation (in a solid) or vaporization (in a liquid) will occur, and these characteristics were not well understood at the time.

This is actually one of the major tradeoffs in bubbler vs radiator designs. In a bubbler, you get the propellant and the maximum fuel temperature to be the same, but you also effectively saturate the fuel with any available vapor. The actual vapor concentrations are… well, as far as I can tell, it’s only ever been modeled with 1960s methods, and those interactions are far beyond what I’m either qualified or comfortable to assess, but I suspect that while the problem may be able to be slightly mitigated it won’t be able to be completely avoided.

However, there are general constraints on the fuels available for use, and the choice of every LNTR has been UC2, usually with a majority of the fuel mass being either ZrC or NbC as the dilutent. Other options are available, potentially, such as 184W-U or U-Si metals, but they have not been explored in depth.

Vapor Pressure Considerations

A study on the vapor pressure of uranium was conducted in 1953 by Rauh et al at Argonne NL, which determined an approximate function of the vapor pressure of “pure” uranium metal (some discussion about the inhibiting effects of oxygen, which would not be present in an NTR to any great degree, and also tantalum contamination of the uranium, were needed based on the experimental setup), but this was based on solid U, so was only useful as a starting point.

W Louis Barret Jr. conducted another study in 1963 on the implications of fuel composition for a bubbler-type LNTR, and the constraints on the potential specific impulse of this type of reactor. The author examined many different fissile fuel matrices in their paper, including Pu and Th compounds:

From this, and assuming a propellant pressure of 10^3 psi, a maximum theoretical isp was calculated for each type of fuel:

Additional studies were carried out on uranium metal and carbon compounds – mostly Zr-C-U, Nb-C-U and 184W-C-U, in various concentrations – in 1965 and 66 by Kaufman and Peters of MANLABS for NASA Lewis Research Center (the center of LNTR development at the time), conducted at 100 atmospheres and ~4500 to ~5500 K. These were low atomic mass fraction systems (0.001-0.02), which may be too low for some designs, but will minimize fissile fuel loss to the propellant flow. Other candidate materials considered were Mo-C-U, B-C-U, and Me-C-U, but not studied at the time.

Number of Fuel Elements

The number of fuel elements in an LNTR is a trade-off.

• Advantages to increasing the number of fuel elements
  • The total surface area available in the fuel/propellant boundary increases, increasing thrust for a given specific impulse
  • The core becomes more homogeneous, making a more idealized neutronic environment (there’s a limit to this, including using interstitial moderating blocks between the fuel elements to further thermalize the reactor, but is a good rule of thumb in most cases)
• Advantages to minimizing the number of fuel elements
  • The more fuel elements, the more manufacturing headache in making the fuel element canisters and elements themselves, as well as the support equipment for maintaining the rotation of the fuel elements;
    • depending on the complexity of the manufacturing process, this could be a significant hurdle,
    • Electronic motors don’t do well in a high neutron flux, generally requiring driveshaft penetration of at least part of the shadow shield, and turbines to drive the system can be so complex that this is often not considered an option in NTRs (to be fair, it’s rare that they would be needed)
  • The less angular velocity is needed for each fuel element to have the same centrifugal force, due to the larger radius of the fuel element
  • For a variety of reasons the fuel thickness increases to maintain the same critical mass in the reactor – NOTE: this is a benefit for bubbler-type LNTRs, but either neutral or detrimental to streamer-type NTRs.

Another major area of trade-off is propellant mass flow rates. These are fundamentally limited in bubbler LNTRs (something we’ll discuss in the next post), since the bubbles can’t be allowed to combine (or splattering and free droplets will occur), the more bubbles the more the fuel expands (causing headaches for fuel containment), and other issues will present themselves. On the other hand, for radiator – and to a lesser extent the bubbler – type LNTRs, the major limitation is thermal uptake in the propellant (too much mass flow means that the exhaust velocity will drop), which can be somewhat addressed by propellant seeding (to be addressed in the future).

LNTR Proposals

The First LNTR: McCarthy LNTR

The first proposal for an LNTR was by J. McCarthy in 1954, in his “Nuclear Reactors for Rockets.” This design used a single, large cylinder, spun around the long axis, as both the reactor and fuel element. The fuel was fed into the void in the cylinder radially, bubbling through the fuel mass, which was made of uranium carbide (UC2). This design, as any first design, had a number of problems, but showed sufficient promise for the design to be re-examined, tweaked, and further researched to make it more practical. While I don’t have access to this paper, a subsequent study of the design placed the maximum specific impulse of this type of NTR in the range of 1200-1400 seconds.

Bubbler LNTR

Princeton LNTR

This led to the first significant research program into the LNTR, carried out by Nelson et al at the Princeton Aeronautical Engineering Laboratory in 1963. This design changed the single large rotating cylinder into several smaller ones, each rotating independently, while keeping the same bubbler architecture of the McCarthy design. This ended up improving the thrust to weight ratio, specific impulse, power density, and other key characteristics. The study also enumerated many of the challenges of both the LNTR in general, and the bubbler in specific, for the first time in a detailed and systematic fashion, but between the lack of information on the materials involved, as well as lack of both computational theory and modeling capability, this study was hampered by many assumptions of convenience. Despite these challenges (which would continue to be addressed over time in smaller studies and other designs), the Princeton LNTR became the benchmark for most LNTR designs of both types that followed. The final design chosen by the team has a vacuum specific impulse of 1250 s, a chamber pressure of 10 atm, and a thrust-to-weight ratio of about 2:1, with a reactor mass of approximately 100 metric tons.

More info about the Princeton LNTR can be found here.

Radiator LNTR

Lewis Research Center LNTR

Work on the radiator concept began in 1964, and was conducted by a team headed by R Ragsdale, one of the leading NTR designers ar Lewis Research Center. To mitigate the vapor losses of the bubbler type, the question was asked if the propellant actually had to pass through the fuel, or if radiant heating would suffice to thermalize the hydrogen propellant while minimizing the fuel loss from the liquid/gas interaction zone. The answer was a definite yes, although the fuel temperature would have to be higher, and the propellant would likely need to be seeded with some particulate or vapor to increase its thermal absorption. While the overall efficiency would be slightly lower, only a minimal loss of specific impulse would occur, and the thrust to weight ratio could be increased due to higher propellant flow (only so much propellant can pass through a given volume of bubbler-type fuel before unacceptable splattering and other difficulties would arise). This seems to have reached its conclusion in 1967, the last date that any of the papers or reports that I’ve been able to find, with a final compromise design achieving 1400 s of isp, a thrust-to-core-weight-ratio of 4:1, at a core temperature of 5060 K and a reactor pressure of 200 atm (2020 N/m^2).

For more information about the Lewis RC LNTR, click here.

Liquid Annular Reactor System (LARS)

This concept, presented by J Powell of Brookhaven National Lab, was the Liquid Annular Reactor System. Compared to the Lewis and Princeton designs, it was a simple reactor, with only seven fuel elements, These would be spaced in a cylinder of Be/H moderator, and would use a twice-through coolant/propellant system: each cylinder was regeneratively cooled from nozzle-end to ship-end, and then the propellant, seeded with W microparticles, would then pass through the central void and out the nozzle. Interestingly enough, this design did not seem to reference the work done by either Princeton or Lewis RC, so there’s a possibility that this was a new design from first principles (other designs presented at the conference made extensive use of legacy data and modeling). This reactor was only conceptually sketched out in the documentation I’ve found, operated at higher temperatures (~6000 K) and lower pressures (~10 atm) than the previous designs to dissociate virtually all of the hydrogen propellant, and no estimated thrust-to-core-weight ratios.

For more info about the LARS, click here.

Conclusion

Liquid fueled NTRs (LNTRs) show great promise as a stepping stone to advanced NTR development in both their variations, the bubbler and radiator variants. The high specific impulse, as well as potentially high thrust-to-weight ratio, offer benefits for many interplanetary missions, both crewed and uncrewed.

However, there are numerous challenges in the way of developing these systems. Of all the NTR types, they are some of the least researched, with only a handful of studies conducted in the 1960s, and a single project in the 1990s. These projects have focused on a single family of fuels, and those have not been able to be tested under fission power for various neutronic and reactor physics behaviors necessary for the proper modeling of these systems.

Additionally, the interactions between the fuel and propellant in these systems is far more complex than it is in most other fuel types. Only two other types of NTR (the droplet/colloid core and open cycle gas core NTRs) face the same level of challenge in fissile fuel retention and fuel element mass entrainment that the LNTR faces, especially in the bubbler variation.

Finally, they are some of the least well-known variations of NTR in both popular and technical literature, with only a few papers ever being published and only short blurbs on popular websites due to the difficulty in finding the technical source material.