This page is about a particular type of liquid fueled nuclear thermal rocket. For more information about nuclear thermal rockets (NTRs) in general, click here. For more information about liquid fueled NTRs (LNTRs), click here.

The second round of liquid fueled nuclear thermal rocket (LNTR) development addressed the problem of fuel vaporization that the initial bubbler-type LNTRs faced. This was what I call the radiator-type LNTR, and was kind of an in-between design between the solid-fueled NTR concepts, where fuel-propellant interactions were relatively minimal, and the advantage of the higher temperatures of molten nuclear fuel.

Rather than passing the propellant directly through the molten fuel, in this system the propellant would pass through the central void of the fuel element, becoming heated primarily through radiation (although some convection within the propellant flow would occur, overall it was a minor effect), hence the name.

This concept had been mentioned in previous works on bubbler-type LNTRs, and initial studies on the thermalization behavior of the propellant, and conversely fuel cooling behavior, were conducted during the early 1960s, but the first major study wouldn’t occur until 1966. However, it would also extend into the 1990s in its development, meaning that it was a far longer-lived design.

While there is a thermodynamically appealing symmetry to homogenizing your fuel and propellant temperatures (the primary advantage of the bubbler LNTR, discussed here), this isn’t actually necessary, is it? The fuel elements are already annular in shape, after all, so why not use them as a more traditional fuel element for an NTR? The lower surface area would mean that there’s less chance for the inconveniently high vapor pressure of the fuel would be mitigated by the fact that the majority of the propellant wouldn’t come in contact with the fuel (or even the layer of propellant that does interact with the fuel), meaning that the overall propellant molecular mass would be kept low… right?

The problem is that this means that the only method of heating the propellant becomes radiation (there’s a small amount of convection, but it’s so negligible that it can be ignored)… which isn’t that great in hydrogen, especially in the UV spectrum that most of the photons from the nuclear reaction are emitted in. The possibility of using either microparticles or vapors which would absorb the UV and re-emit it in a lower wavelength, which would be more easily absorbed by the hydrogen, was already being investigated in relation to gas core NTRs (which have the same problem, but in a completely different order of magnitude), and offered promise, but was also a compromise: this deliberately increases the molar mass of the propellant one way to minimize the molar mass a different way. This was a design possibility that needed to be carefully studied before it could be considered more feasible than the bubbler LNTR.

If you’re interested in the particular reactors which have been proposed in this paradigm, they each have their own pages, available here:

Lewis Research Center LNTR

Liquid Annular Reactor System (LARS)

Initial Feasibility Studies: Lewis Research Center

As with any design, the first question was the basics of reactor configuration. The LRC team never looked at a single-tube LNTR, for a variety of reasons, and instead focused their efforts on a multi-tube design, but the number and diameter of the tubes was one of the major questions to be addressed in initial studies. Because of this, and the particular characteristics of the heat transfer required, the reactor would have many fuel elements with a diameter of between 1 and 4 inches, but which diameter was best would be a matter of quite some study.

Another question for the study team was what the fuel element temperature would be. As in every NTR design, the hotter the propellant, the higher the isp (all other things being equal), but as we saw in the bubbler design, higher temperatures also mean higher vapor pressure, meaning that mass is lost more easily into the propellant – which increases the propellant mass and reduces the isp, and at some point even cost more specific impulse due to higher mass than is gained with the higher temperature. Because the propellant and the fuel would only interact on the surface of the fuel element, the surface temperature of the fuel was the overriding consideration, and was also explored, in the range of 5000 to 6100 K.

Effect of Reactor Pressure on T/W Ratio and U mass loss ratio in H, Ragsdale 1967

The final consideration which was optimized in this design was engine operating pressures. Because this design wasn’t fundamentally limited by the bubble velocity and void fraction of the molten fuel, the chamber pressure could be increased significantly, leading to both more thrust and a higher thrust-to-weight ratio. However, the trade-off here is that at some point the propellant isn’t being completely thermalized, resulting in a lower specific impulse.

For more information about the NTR design that resulted from these studies, check out the LRC LNTR page, here.

Wall Construction

Both the LRC and later LARS (more info here) LNTRs ended up with similar fuel element configurations: a high temperature material, with coolant tubes traveling the length of the fuel element walls to regeneratively cool the walls. This material would have to withstand not only the temperature of the fuel element, but also resist chemical attack by the hydrogen used for the regenerative cooling, as well as being able to withstand the mechanical strain of not only the spinning fuel, but also the torque from whatever drive system is used to spin the fuel element to maintain the centripetal force used to contain the fuel element.

Another constant concern is the temperature of the wall. While high temperature loadings can be handled using regenerative cooling, the more heat is removed from the fuel during the regenerative cooling step, but it reduces the specific impulse of the engine. Here’s a table from the LRC study that examines the implications of wall cooling ratio vs specific impulse in that design, which will also apply as a general rule of thumb for LARS:

However, from there, the two designs differed significantly. The LARS design is far simpler: a can of beryllium, with a total of 20% of the volume being the regenerative cooling channel. As mentioned previously, the fuel didn’t become completely molten, but remained solid (and mostly containing the ZrC/NbC component, with very little U). Surrounding the outside of the fuel element can itself was another coolant gap. This would then be mounted to the reactor body with a drive system at the ship end, and a bearing at the hot end. This would then be mounted in the stationary moderator which made up the majority of the internal volume of the reactor core, which was shielded from the heat in the fuel element in a very heterogeneous temperature profile.

The LRC concept on the other hand, was far more complex in some ways. Rather than using a metal can, the LRC design used graphite, which maintains its strength far better than many metals at high temperatures. A number of options were considered to maintain the wall of the can, due not only to the fuel mixture potentially attacking the graphite (as the carbon could be dissolved into the carbide of the fuel element), as well as attack from the hydrogen in the coolant channels (which would be able to be addressed in a similar way to how NERVA fuel elements used refractory metal coatings to prevent the same erosive effects).

The LRC design, since the fuel would be completely molten across the entire volume of the fuel element, was a more complex challenge. A number of options were considered to minimize the wall heating of the fuel element, including:

This set of options offer a trade-off: either a simpler option, which sets hard limits on the fuel element temperature in order to ensure the phase gradient in the fuel element (the LARS concept), or the fully liquid, more complex-behaving LRC design which has better power distribution, and a higher theoretical fuel element temperature – only limited by the vapor pressure increase and fuel loss rates in the fuel element, rather than the wall heating temperature limits of the LARS design.

Anyone designing a new radiator LNTR has much work that they can draw from, but other than the dynamics of the actual fuel behavior (which have never gone through a criticality test), the fuel element can design will be perhaps the largest set of engineering challenges in this type of system (although simpler than the bubbler-type LNTR).

Propellant Thermalization

The major change between the bubbler and radiator-type LNTRs is the difference in the thermalization behavior of the propellant: in a bubbler-type LNTR, assuming the propellant can be fed through the fuel, the two components reach thermal equilibrium, so the only thing needed is to direct it out of the nozzle; a radiator on the other hand has a similar flow path to the Rover-type NTRs, once through from nozzle to ship side for regenerative cooling, then a final thermalization pass through the central void of the fuel element.

This is a problem for hydrogen propellant, which is largely transparent to the EM radiation coming off the reactor. This thermal transfer accounted for all but 10% of the thermalization effects in the LARS design, and in many of the LRC studies this was completely ignored as negligible, with the convective effects in the propellant mainly being a concern in terms of fuel mass loss and propellant mass increase.

While the fuel mass loss would increase the opacity of the gas (making it absorb more heat), a far better option was available: adding a material in microparticle form to the propellant flow as it goes through the final thermalization cycle. The preferred material for the vast majority of these applications, which we’ll see in the gas cycle NTRs as well, is microparticles of tungsten.

This has been studied in a host of different applications, and will be something that I’ll discuss in depth on a section of the propellant webpage in the future (which I’ll link to here once it’s done), but for the LRC design the target goal for increasing the opacity of the H2 was to achieve between 10,000 and 20,000 cm^2/gm, for a reduction in single-digit percentage of specific impulse due to the higher mass. They pointed out that the simplified calculations used for the fuel mass loss behavior could lead to an error that they were unable to properly address, and which could either increase or decrease the amount of additive used.

The LARS concept used tungsten microparticles as well, and their absorption actually was the defining factor in the two designs they proposed: the emissivity and reflectivity of the fuel in terms of the absorption of the wall and the propellant.

Two other options are available for increasing the opacity of the hydrogen gas.

The first is to use a metal vapor deliberately, as was the paradigm in Soviet gas core design. Here, they used either NaK or Li vapor, both of which have small neutron absorption cross-sections and high thermal capacity. This has the advantage of being more easily mixed with the turbulent propellant stream, as well as being far lower mass than the W that is often used in US designs, but may be less opaque to the EM frequencies being emitted by the fuel’s surface in an LNTR design. I’m still trying to track down a more thorough writeup of the use of these vapors in NTR design at the moment (a common problem in both Soviet and Russian astronuclear literature is a lack of translations), but when I do I’ll discuss it in far more depth, since it’s an idea that doesn’t seem to have translated into the American NTR design paradigm.

The Future of the Forgotten Reactor

While often referenced in passing in any general presentation on nuclear thermal rockets, the liquid core NTR seems to be the least studied of the different NTR types, and also the least covered. While the bubbler offers distinct advantages from a purely thermodynamic point of view, the radiator offers far more promise from a functional perspective.

Sadly, while both solid and gas core NTRs have been studied into the 20th century, the liquid core has been largely forgotten, and the radiator in particular seems to have gone through a reinvention of the wheel, as it were, between the 1960s NASA design and the 1990s DOE design, with few of the lessons learned from the LRC concept being applied to the BNL design as far as vapor dynamics, thermal transfer, and the like.

This doesn’t mean that the design is without promise, though, or that the challenges that the reactor faces are insurmountable. A number of hurdles in testing need to be overcome for this design to work – but many of the problems that there simply isn’t any data for can be solved with a simple set of criticality and reactor physics tests, something well within the capabilities of most research nuclear programs with the capability to test NTRs.

With the advances in nuclear and two-phase flow modeling, a body of research that doesn’t seem to have been examined in depth for over two decades, and the possibility of a high-isp, moderate-to-high thrust engine without the complications of a gas core NTR (a subject that we’ll be covering soon), the LNTR, and the radiator in particular, offer a combination of promise and ability to develop advanced NTRs as low hanging fruit that few systems are able to offer.

References

ANALYSES OF VAPORIZATION IN LIQUID URANIUM BEARING SYSTEMS AT VERY HIGH TEMPERATURES, Kaufman and Peters 1965 https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19660002967.pdf

ANALYSIS OF VAPORIZATION OF LIQUID URANIUM, METAL, AND CARBON SYSTEMS AT 9000” AND 10,000” R Kaufman and Peters 1966 https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19660025363.pdf

Fundamental Material Limitations in Heat-Exchanger Nuclear Rockets, Kane and Wells, Jr. 1965 https://www.osti.gov/servlets/purl/4610034/

VAPOR-PRESSURE DATA EXTRAPOLATED TO 1000 ATMOSPHERES (1.01~108 N/m2) FOR 13 REFRACTORY MATERIALS WITH LOW THERMAL ABSORPTION CROSS SECTIONS Masser 1967 https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19670030361.pdf

PERFORMANCE POTENTIAL OF A RADIANT-HEAT-TRANSFER LIQUID-CORE NUCLEAR ROCKET ENGINE, Ragsdale 1967 https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19670030774.pdf

HEAT- AND MASS-TRANSFER CHARACTERISTICS OF AN AXIAL-FLOW LIQUID-CORE NUCLEAR ROCKET EMPLOYING RADIATION HEAT TRANSFER, Ragsdale et al 1967 https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19670024548.pdf

FEASIBILITY OF SUPPORTING LIQUID FUEL ON A SOLID WALL IN A RADIATING LIQUID-CORE NUCLEAR ROCKET CONCEPT, Putre and Kasack 1968 https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19680007624.pdf

[Paywall] Conceptual Design of a LARS Based Propulsion System, Ludewig et al 1991 https://arc.aiaa.org/doi/abs/10.2514/6.1991-3515

The Liquid Annular Reactor System (LARS) Propulsion, Powell et al 1991 https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19910012832.pdf

LIQUID ANNULUS, Ludewig 1992 https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19920001886.pdf

[Paywall] The liquid annular reactor system (LARS) for deep space exploration, Maise et al 1999 https://www.sciencedirect.com/science/article/abs/pii/S0094576599000442