Hello, and welcome back to Beyond NERVA! Today, we’re finishing (for now) our in-depth look at liquid fueled nuclear thermal rockets, by looking at the second major type of liquid NTR (LNTR): the radiator-type LNTR. If you’re just joining us, make sure to check out the introduction (available here) and the bubbler post (available here) for some important context to understand how this design got here.
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.
Let’s begin by looking at the differences between the bubbler and radiator designs, and why the radiator offers an attractive trade-off compared to the bubbler.
The Vapor Problem, or Is Homogenization of Propellant/Fuel Temp Worth It?
Liquid fuels offer many advantages for an NTR, including the fact that the fuel will distribute its heat evenly across the volume of the fuel element, the fact that the effective temperature of the fuel can be quite high, and that the fuel is able to be reasonably well contained with minimal theoretical challenges.
The bubbler design had an additional advantage: by passing the propellant directly through the fuel, in discrete enough bundles (the bubbles themselves) that the fuel and the propellant would have the same temperature.
Sadly, there are significant challenges to making this sort of nuclear reactor into a rocket, the biggest one being propellant mass. These types of NTRs still use hydrogen propellant, the problem occurs in the fuel mass itself. As the bubbles move through the zirconium/niobium-uranium carbide fuel, it heats up rapidly, and the pressure drops significantly during this process. This means that all of the components of the fuel (the Zr/Nb, C, and U) end up vaporizing into the bubbles, to the point that the bubble is completely saturated by a mix of these elements in vapor form by the time it exits the fuel body. This is called vapor entrainment.
This is a major problem, because it means that the propellant leaving the nozzle has a far higher mass than the hydrogen that was originally input into the system. While there’s the possibility that a different propellant could be used which would not entrain as much of the fuel mass, but would also be higher molecular mass to start – to the point that the gains might likely outweigh the losses (if you feel like exploring this trade-off on a more technical footing, please let me know! I’d love to explore this more), and it wouldn’t eliminate the entrainment problem.
This led people to wonder if you have to pass the propellant through the fuel in the first place. After all, while there is a thermodynamically appealing symmetry to homogenizing your fuel and propellant temperatures, 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.
The leader of the effort to study this trade-off was one of the best-known fluid fueled NTR designers on the NASA side: Robert Ragsdale at Lewis Research Center (LRC, and we’ll come back to Ragsdale in gas core NTR design as well). There were a collection of studies around a particular design, beginning with a study looking at reactor geometry and fuel element size optimization to not only maximize the thrust and specific impulse, but also to minimize the uranium loss rates of the reactor.
This study concluded that there were many advantages to the radiator-type LNTR over the bubbler-type. The first consideration, minimizing the vapor entrainment problem that was laguing the bubbler, was minimized, but not completely eliminated, in the radiator design. The next conclusion is that the specific impulse of the negine could be maintained, or increased, to 1400 s isp or more. Finally, one of th emost striking was in thrust-to-core-weight ratio, which went from about 1:1 in the Nelson/Princeton design that we discussed in the last post all the way up to 19:1 (potentially)! This is because the propellant flow rate isn’t limited y the bubble velocity moving through the fuel (for more detail on this problem, and the other related constraints, check out the last blog post, here).
These conclusions led to NASA gathering a team of researchers, including Ragsdale, Kasack, Donovan, Putre, and others ti develop the Lewis LNTR reactor.
Lewis LNTR: The First of the Line
Once the basic feasibility of the radiator LNTR was demonstrated, a number of studies were conducted to determine the performance characteristics, as well as the basic engineering challenges, facing this type of NTR. They were conducted in 1967/68, and showed distinct promise, for the desired 2000 to 5000 MWt power range (similar to the Phoebus 2 reactor’s power goal, which remains the most powerful nuclear reactor ever tested at 3500 MWt).
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.
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. This final consideration was explored in the range of 200 to 1000 atm (2020-10100 N/cm2).
The three primary goals were: to maximize specific impulse, maximize thrust-to-weight ratio, and minimize uranium mass loss. They quickly discovered that they couldn’t have their cake and eat it, too: higher temperatures, and therefore higher isp, led to faster U mass loss rates, increasing T/W ratio reduced the specific impulse, and minimizing the U loss rate hurt both T/W and isp. They could improve any one (or often two) of these characteristics, but always at the cost of the third characteristic.
We’ll look at many of the design characteristics and engineering considerations of the LRC work in the next section on general design challenges and considerations for the radiator LNTR, but for now we’ll look at their final compromise reactor.
The reactor itself would be made up of several (oddly, never specified) fuel elements, in a beryllium structure, with each fuel element being made up of Be as well. These would be cooled by cryogenic hydrogen moving from the nozzle end to the spacecraft end of the reactor, before flowing back into the central void of the fuel element. As it was fed through the central annulus, it would be seeded with tungsten microparticles to increase the amount of heat the propellant would absorb. Finally, it would be exhausted through a standard De Laval nozzle to provide thrust.
The final fuel that they settled on was a liquid ternary carbide design, with the majority of the fuel being niobium carbide (although ZrC was also considered), with a molar mass fraction of 0.02 being UC2. This compromise offered good power density for the reactor while minimizing the vaporization rate of the fuel mass. This would be held in 2 inch diameter, 5 foot long fuel element tubes, with a fuel surface temperature of 5060 K. The propellant would be pressurized to 200 atm in the reactor.
This led to a design that struck a compromise between isp, T/W, and U mass loss which was not only acceptable, but impressive: 1400 s isp (on par with some forms of electric propulsion), a T/W ratio (of the core alone) of 4, and a hydrogen-to-uranium flow rate ratio of 50.
They did observe that none of these characteristics were as high as they could be, especially in terms of T/W ratio (which they calculated could go as high as 19!), or isp (with a theoretical maximum of 1660), and the uranium loss was twice the theoretical minimum, but sadly the cost of maximizing any of these characteristics was so high from an engineering point of view that it wasn’t feasible.
Sadly, I haven’t been able to find any documentation on this reactor design – and very few references to it – after February 1968. The exact time of the cancellation, and the reasons why, are a mystery to me. If someone is able to help me find that information it would be greatly appreciated.
LARS: The Brookhaven Design
The radiator LNTR would remain dormant for decades, as astronuclear funding was scarce and focused on particular, well-characterized systems (most of which were electric powerplant concepts), until the start of the Space Exploration Initiative. In 1991, a conference was held to explore the use of various types of NTR in future crewed space missions. This led to many proposals, including one from the Department of Energy’s Brookhaven National Laboratory in New York. This was the Liquid Annular Reactor System, or LARS.
A team of physicists and engineers, including Powell, Ludewig, Lazareth, and Maise decided to revisit the radiator LNTR design, but as far as I can tell didn’t use any of the research done by the LRC team. Due to the different design philosophies, lack of references, and also the general compartmentalization of knowledge within the different parts of the astronuclear community, I can only conclude that they began this design from scratch (if this is incorrect, and anyone has knowledge of this program, please get in contact with me!).
LARS was a very different design than the LRC concept, and seems to have gone through two distinct iterations. Rather than the high-pressure system that the LRC team investigated, this was a low-pressure, low-thrust design, which optimized a different characteristic: hydrogen dissociation. This maximizes the specific impulse of the NTR by reducing the mass of the propellant to the lowest theoretically possible mass while maintaining the temperature of the propellant (up to 1600 s, according to the BNL team). The other main distinction from the LRC design was the power level: rather than having a very powerful reactor (3000 to 5000 MWt), this was a modest reactor of only 200 MWt. This leads to a very different set of design tradeoffs, but many of the engineering and materials challenges remain the same.
LARS would continue to us NbC diluted with UC2, but the fuel would not completely melt in the fuel element, leaving a solid layer against the walls of the beryllium fuel element tube. This in turn would be regeneratively cooled with hydrogen flowing through a number of channels in the durm, as well as a gap surrounding the body of the fuel element which would also be filled with cold hydrogen. A drive system would be attached on the cold end of the tube to spin it at an appropriate rate (which was not detailed in the papers). The main changes were in the fuel element configuration, size, and number.
The first iteration of LARS was an interesting concept, using a folded-flow system. This used many small fuel element tubes, arranged in a similar manner to the flow channels in the Dumbo reactor, with the propellant moving from the center of the reactor to the outer circumference, before being ejected out of the nozzle of the reactor. Each layer of fuel elements contained eleven individual tubes, with between 1 and 10 layers of fuel elements in the reactor. As the number of layers increased, the length and radius of the fuel elements decreased.
One of the important notes that was made by the team at this early design date was that the perpendicular fuel element orientation would minimize the amount of fission products that would be ejected from the rocket. I’m unable to determine how this was done, other than if they were solids which would stick to the outside of the propellant flue, however.
Unfortunately, I haven’t been able to discover exactly why this design was abandoned for a more traditional LNTR architecture, but the need to cool the entire exterior of the reactor to keep it from melting seems to possibly be a concern. Reversing the flow, with the hot propellant being in the center of the reactor rather than the external circumference, seems like an easy fix if this was the primary concern, but the discussions of reactor architecture after this seem to pretty much ignore this early iteration. Another complication would be the complexity of the reactor architecture. Whether with dedicated motors, or with a geared system allowing one motor to spin multiple fuel elements, a complex system is needed to spin the fuel elements, which would not only be something which would potentially break down more, but also require far more mass than a simpler system.
The second version of LARS kept the same type of fuel, power output, and low pressure operation, but rather than using the folded flow concept it went with seven fuel elements in a beryllium body. The propellant would be used to cool first the nozzle of the rocket, then the rotating beryllium drum which contained the fuel element, before entering the main propellant channel. The final thermalization of the propellant would be facilitated by the use of tungsten microparticles in the H2, necessary due to the low partial pressure and high transparency of pure H2 (while the vapor pressure issues of any LNTR were acknowledged, the effect that this would have on the thermalization seems to have not been considered a significant factor in the seeding necessity) Two versions, defined by the emissivity of the fuel element, were proposed.
This design was targeted to reach up to 2000 s isp, but due to uncertainties in U loss rates (as well as C and Nb), the overall mass of the propellant upon exiting the reactor was uncertain, so the authors used a range of 1600-2000 s. The thrust of the engine was approximately 20,000 N, which would result in a T/W ratio of about 1;1 when including a shadow shield (one author points out that without the shield the ratio would be about 3-4/1.
I have been unable to find the research reports themselves for this program (unlike the LRC design), so the specifics of the reactor physics tradeoffs, engineering compromises, actual years of research and the like aren’t something that I’m able to discuss. The majority of my sources are conference papers and journal articles, which occurred in 1991 and 1992, but there was one paper from 1999, so it was at least under discussion through the 1990s (interestingly, that paper discussed using LARS for the 550 AU mission concept, which later got remade into the FOCAL gravitational lens mission: https://www.centauri-dreams.org/2010/11/15/a-focal-mission-into-the-oort-cloud/ ).
This seems to be the last time that LARS has been mentioned in the technical literature, so while it is mentioned as the “baseline” liquid core concept in places such as Atomic Rockets (http://www.projectrho.com/public_html/rocket/enginelist2.php#id–Nuclear_Thermal–Liquid_Core–LARS) it has not been explored in depth since.
Lessons Learned, Lessons to Learn: The Challenges of LNTR
In many ways, the apparent dual genesis of radiator LNTRs offers the ability to look into two particular thought processes in what the challenges are with radiator-type LNTRs. One example of this is what’s discussed more in the “fundamental challenges” sections of the introductory section of the reports: for the LRC team they focus on vapor entrainment minimization, whereas in the BNL presentations it seems quite important to point out that “yes, containing a refractory in a spinning, gas cooled drum is relatively trivial.” This juxtaposition of foci is interesting to me, as an examination of the different engineering philosophies of the two teams, and the priorities of the times.
Both the LRC and LARS 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:
- Selective fuel loading
- A common strategy in solid fuel elements, this creates hotter and cooler zones in the fuel element
- Neutron heating will distribute the radiative heating past U distribution
- Convection and fuel mixing will end up distributing the fuel over time
- May be able to be limited by affecting the temperature and viscosity of the fuel for the life of the reactor
- A common strategy in solid fuel elements, this creates hotter and cooler zones in the fuel element
- Multiple fluids in fuel
- Step beyond selective loading, a different material may be used as the outer layer of the fuel body, resisting mixing and reducing thermal load on the wall
- Vapor insulation along exterior of fuel body
- Using thermally opaque vapor to insulate the fuel element wall from the fuel body
- Significantly reduces the heating on the outer wall
- Two options for maintaining vapor wall:
- Ablative coating on inner wall of fuel element can
- Porous wall in can (similar to a low-flow version of a bubbler fuel element) pumping vapor into gap between fuel and can
- Maximum stable vapor-layer thickness based on vapor bubble force balance vs centripetal force of liquid fuel
- Two phase flow dynamics needed to maintain the vapor layer would be complex
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).
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.
As I said, this is a concept that I’m going to cover more in depth in both the gas core and general propellant pages, so with one final – and fascinating – note, we’ll move on to the conclusion.
An Interesting Proposal
The final option is something that Cavan Stone mentioned to me on Facebook a while ago: the use of lithium deuteride (LiD) as a propellant or additive in this design. This is an interesting concept, since Li7 is a fissile material, and is reasonably opaque to the frequencies being discussed in these reactors. The use of deuterium rather than protium also increases the neutron moderation of the propellant, which can in turn increase fissile efficiency of the reactor. The Li will harden the neutron spectrum overall, while the D and Be (in the fuel element can/reactor body) will thermalize the spectrum.
There was a discussion of using LiD as a propellant in NTRs in the 1960s [https://www.osti.gov/biblio/4764043-nuclear-effect-using-lithium-hydride-propellant-nuclear-rocket-reactor-thesis], but sadly I can’t find it anywhere online. If someone is able to help me find it, please let me know. This is a fascinating concept, and one that I’m very glad Cavan brought up to me, but also one that is complex enough that I really need to see an in-depth study by someone far more knowledgeable than me to be able to intelligently discuss the implications of.
Conclusion, or 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.
With that, we’re leaving the realm of liquid fueled NTRs for now. This is a fascinating field, and one that I haven’t seen much discussion of outside the original technical papers, so I hope you enjoyed it! I’m going to work on getting these posts into a more easily-referenced form on the website proper, and will make a note of that in my blog (and on my social media) when I do! If anyone is aware of any additional references pertaining to the LNTR, as well as its thermophysical behavior, fuel materials options, or anything else relating to these desgins, please let me know, either in the comments or by sending me a message to beyondnerva at gmail dot com.
Our next blog post will be on droplet and vapor core NTRs, and will be covered by a good friend of mine and fellow astronuclear enthusiast: Calixto Lopez. These reactors have fascinated him since he was in school many moons ago, and he’s taught me the majority of what I know about them, so I asked him if he was willing to write that post.
After that, we’re going to move on to the closed cycle gas core NTR, which I’ve already begun research on. There’s lots of fascinating tidbits about this reactor type that I’ve already uncovered, so this may end up being another multiple part blog series.
Finally, to wrap up our discussion of advanced NTRs, we’re going to do a series on the open cycle gas core NTR types. This is going to be a long, complex series on not only the basic physics challenges, but the design evolution of the engine type, as well as discussion on various engineering methods to mitigate the major fuel loss and energy waste issues involved in this type of engine. There may be a delay between the closed and open cycle NTR posts due to the sheer amount of research necessary to do open cycles justice, but rest assured I’m already doing research on them.
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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
Radiator-Specific LNTR References
Lewis Research Center LNTR
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
Liquid Annular Reactor System (LARS)
[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