Hello, and welcome back to Beyond NERVA! Today, we continue our look at liquid fueled nuclear thermal rockets (LNTRs), with a deep dive into the first of the two main types: what I call the bubbler LNTR.
This potentially attractive form of advanced NTR is a design that has been largely forgotten in the history of NTR designs outside some minor footnotes. Because of this, I felt that it was a great subject for the blog! All of the sources that I can find on the designs are linked at the end of this post, including a couple that are not available digitally, so if you’re interested in a more technical analysis of the concept please check that out!
What is a Bubbler LNTR?
Every NTR has to heat the (usually hydrogen) propellant in some way, which is usually done through (usually thermal) radiation from the fuel’s surface into the propellant.
This design, though, changes that paradigm by passing the propellant through the liquid fuel (usually a mix of uranium carbide (UC2) and some other carbide – either zirconium (ZrC) or niobium (NbC). This is done by having a porous outer wall which the propellant is injected through. This is known as a “folded flow propellant path,” and is seen in other NTRs as well, notably the Dumbo reactor from the early days of Project Rover.
In order to keep the fuel in place, each fuel element is spun at a high enough rate to keep the fuel in place using centrifugal force. The number of fuel elements is one of the design choices that varies from design to design, and the overall diameter, as well as the thickness of the fuel layer, is a matter of some design flexibility as well, but on average the individual fuel elements range from about 2 to about 6 inches in diameter, with the ratio between the thickness of the fuel layer and the thickness of the central void where the now-hot propellant passes through to the nozzle being roughly 1:1.
This was the first type of LNTR to be proposed, and was a subject of study for over a decade, but seems to have fallen out of favor with NTR designers in the late 1960s/early 1970s due to fuel/propellant interaction complications and engineering challenges related to the physical structures for injecting the propellant (more on that later).
Let’s look at the history of bubbler LNTR in more depth, and see how the proposals have evolved over time.
History of the Bubbler-type LNTR: The First of its Kind
The first proposal for a liquid fueled NTR was in 1954, by J McCarthy in “Nuclear Reactors for Rockets” [ed. Note I have been unable to locate this report in digital form, if anyone is able to help me get ahold of it I would greatly appreciate your assistance; the following summary is based on references to this study in later works]: This design was the first to suggest the centrifugal containment of liquid fuel, and was also the first of the bubbler designs. It used a single fuel element as the entire reactor, with a large central void in the center of the fuel body as the propellant flow channel once it left the fuel itself.
This design was fundamentally limited by three factors:
- A torus is a terrible neutronic structure, and while the hydrogen propellant in the central void of the fuel would provide some neutron moderation, McCarthy found upon running the MCNP calculations that the difference was so negligible that it could be assumed to be a vacuum; and
- Only a certain amount of heat could be removed from the fuel by the propellant based on assumed fuel element geometry, and that cooling the reactor could pose a major challenge at higher reactor powers; and
- The behavior of the hydrogen as it passes through, and also out of, the liquid fuel was not well understood in practice, and
- the vapor pressure of the fuel’s constituent components could lead to fuel being absorbed in the gas as vapor in both the bubbles and exhausting propellant flow, causing both a loss of specific impulse and fissile fuel. This process is called “entrainment,” and is a (if not the) major issue for this type of reactor.
However, despite these problems this design jump started the design of LNTRs, defined the beginnings of the design envelope for this type of engine, and introduced the concept of the bubbler LNTR for the first time.
The Princeton LNTR, 1963
The next major design step was undertaken by Nelson et al at Princeton’s Dept. of Aeronautical Engineering in 1963, under contract by NASA. This was a far more in-depth study than the proposal by McCarthy, and looked to address many of the challenges that the original design faced.
Perhaps the most notable change was the shift from a single large fuel element to multiple smaller ones, arranged in a hexagonal matrix for maximum fuel element packing. This does a couple of things:
- It homogenizes the reactor more. While heterogeneous (mixed-region) reactors work well, for a variety of reasons it’s beneficial to have a more consistent distribution of materials through the core – mainly for neutronic properties and ease of modeling (this is 1963, MCNP in a heterogeneous core using a slide rule sounds… agonizing).
- Given a materially limited, fixed specific impulse (see the Fuel Materials Constraints section for more in-depth discussion on this) NTR, the thrust is proportional to the total surface area of the fuel/propellant interface. By using multiple fuel elements (which they call vortices), the total available surface area increases in the same volume, increasing the thrust without compromising isp (this also implies a greater specific power, another good thing in an NTR).
This was a thermal (0.37 eV) neutron spectrum reactor, fueled by a mix of UC2 and ZrC, varying the dilution level for greater moderation and increased thermal limits. It was surrounded by a 21 cm reflector of beryllium (a “standard reflector”).
From there, the basic geometry of the reactor, from the number of fuel elements and their fueled thickness, to the core diameter and volume (the length was at a fixed ratio compared to the radius), to the shape, velocity, and number of bubbles (as well as vapor entrainment losses of the fuel material) were studied.
This was a fairly limited study, despite its length, due to the limitations of the resources available. Transients and reactor kinetics were specifically excluded from this study, the hydrogen was again replaced with vacuum in calculations, the temperature was assumed to be higher than possible due to vapor entrainment problems (4300 K, instead of 3600 K at 10 atm, 3800 at 30 atm) the chamber pressure was limited to only >1 atm, and age-diffusion theory calculations only give results within an order of magnitude… but it’s still one of the most thorough study of LNTRs I’ve found, and the most researched bubbler architecture. They pointed out the potential benefits of the use of 233U, or a larger but neutronically equivalent volume of 232Th (turning the reactor into a thermal breeder), in order to improve the overall vaporization characteristics, but this was not included in the study.
Barrett LNTR, 1964
The next year, W. Louis Barrett presented a variation of the Princeton LNTR at the AIAA Conference. The main distinction between the two designs was the addition of zirconium hydride in the areas between the fuel elements and the outer reflector, and presented the first results from a study being conducted on the bubble behavior in the fuel (being conducted at Princeton at the time). The UC2/ZrC fuel was the same, as were the number of fuel elements and reactor dimensions. The author concluded that a specific impulse of 1500-1550 seconds was possible, with a T/W of 1 at 100 atm, with thrust not being limited by heat transfer but by available flow area.
Below are the two relevant graphs from his findings: the first is the point at which the fissile fuel itself would end up becoming captured by the passing gas, and the second looks at the maximum specific impulse any particular fissile fuel could theoretically offer. The image for the McCarthy reactor above was from the same paper.
Final Work: Bubbles are Annoying
For this reactor to work, the heat must be adequately transferred from the fuel element to the propellant as it bubbles through the fuel mass radially. The amount of heat that needs to be removed, and the time and distance that it can be removed in, is a function of both the fuel and the bubbles of H2.
Sadly, the most comprehensive study of this has never been digitized, but for anyone who’s able to get documents digitized at Princeton University and would like to help make the mechanics of bubbler-type LNTRs more accessible, here’s the study: Liebherr, J.F., Williams, P.M., and Grey, J., “Bubble Motion Studies for the Liquid Core Nuclear Rocket,” Princeton University Aeronautical Engineering Report No. 673, December 1963. Apparently you can check it out after you can convince the librarians to excavate it, based on their website: https://catalog.princeton.edu/catalog/1534764.
Here, a clear plastic housing was constructed which consisted of two main layers: an outer, solid casing which formed the outer body of the apparatus, and a perforated, inner cylinder, which simulated the fuel element canister. Water was used as the fuel element analog, and the entire apparatus was spun along its long axis to apply centrifugal acceleration to the water at various rotation rates. Pressurized air (again, at various pressures) was used in place of the hydrogen coolant. Stroboscopic photography was used to document bubble size, shape, and behavior, and these behaviors were then used to calculate the potential thermal exchange, vapor entrainment, and other characteristics of the behavior of this system.
One significant finding, based on Gray’s reporting, though, is that there’s a complex relationship between the dimensions, shape, velocity, and transverse momentum of the bubbles and their thermal uptake capacity, as well as their vapor entrainment of fuel element components. However, without being able to read this work, I can only hope someone can make this work accessible to the world at large (and if you’ve got technical knowledge and interest in the subject, and feel like writing about it, let me know: I’m more than happy to have you write a blog post on here on this INSANELY complex topic).
The last reference to a bubbler LNTR I can find is from AIAA’s Engineering Notes from May 1972 by McGuirk and Park, “Propellant Flow Rate through Simulated Liquid-Core Nuclear Rocket Fuel Bed.” This paper brings up a fundamental problem that heretofore had not been addressed in the literature on bubblers, and quite possibly spelled their death knell.
Every study until this point greatly simplified, or ignored, two phase flow thermodynamic interactions. If you’re familiar with thermodynamics, this is… kinda astounding, to be honest. It also leads me to a diversion that could be far longer than the two pages that this report covers, but I won’t indulge myself. In short, two phase flow is used to model the thermal transfer, hydro/gasdynamic properties, and other interactions between (in this case) a liquid and a gas, or a melting or boiling liquid going through a phase change.
This is… a problem, to say the least. Based on the simplified modeling, the fundamental thermal limitation for this sort of reactor was vapor entrainment of the fuel matrix, reducing the specific impulse and changing he proportions of elements in the matrix, causing potential phase change and neutronics complications.
This remains a problem, but is unfortunately not the main thermal limitation of this reactor, rather it was discovered that the amount of thermal rejection available through the bubbling of the propellant through the fuel is not nearly as high as was expected at lower propellant flow rates, and higher flow rates led to splattering of the bubbles bursting, as well as unstable flow in the system. We’ll look at the consequences of this later, but needless to say this was a major hiccup in the development of the bubbler type LNTR.
While there may be further experimentation on the bubbler type LNTR, this paper came out shortly before the cancellation of the vast majority of astronuclear funding in the US, and when research was restarted it appears that the focus had shifted to radiator-type LNTRs, so let’s move on to looking at them.
Fuel Element Thickness and Heat Transfer
One of the biggest considerations in a bubbler LNTR is the thickness of the fuel within each fuel canister. The fundamental trade-off is one of mechanical vs thermodynamic requirements: the smaller the internal radius at the fuel element’s interior surface, the higher the angular velocity has to be to maintain sufficient centrifugal force to contain the fuel, btu also the greater time and distance the bubbles are able to collect heat from the fuel.
In the Princeton study, the total volume within the fuel canister was roughly equally divided between fuel and propellant to achieve a comfortable trade-off between fuel mass, reactor volume, and thermal uptake in the propellant. In this case, they included the volume of the propellant as it passed through the fuel to be part of the central annulus’ volume, which eases the neutronic calculations, but also induces a complication in the actual diameter of the central void: as propellant flow increases, the void diameter decreases, requiring more angular momentum to maintain sufficient centrifugal force.
A thinner fuel element, on the other hand, runs into the challenge of requiring a greater volume of propellant to pass through it to remove the same amount of energy, but an overall lower temperature of the propellant that is used. This, in turn, reduces the propellant’s final velocity, resulting in lower specific impulse but higher thrust. However, another problem is that the fluid mixture of the propellant/fuel can only contain so much gas before major problems develop in the behavior of the mixture. In an unpublished memorandum from 1963 (“Some Considerations on the Liquid Core Reactor Concept,” Mar 23), Bussard speculated that the maximum ratio of gas to fuel would be around 0.3 to 0.4; at this point the walls of the bubbles are likely to merge, converting the fuel into a very liquidy droplet core reactor (a concept that we’ll discuss in a future blog post), as well as leading to excess splattering of the fuel into the central void of the fuel element. While some sort of recapture system may be possible to prevent fuel loss, in a classic bubbler LNTR this is an unacceptable situation, and therefore this type of limitation (which may or may not actually be 0.3-0.4, something for future research to examine) intrinsically ties fuel element thickness to maximum propellant flow rates based on volume.
There are some additional limits here, as well, but we’ll discuss those in the next section. While the propellant will gain some additional power through its passage out of the fuel element and toward the nozzle, as in the radiator type LNTR, this will not be as significant as the propellant is entering along the entire length fuel element.
This is probably the single largest problem that a bubbler faces: the behavior of the bubbles themselves. As this is the primary means of cooling the fuel, as well as thermalizing the propellant, the behavior of these bubbles, and the ability of the propellant stream to control the entirety of the heat generated in the fuel, is of absolutely critical importance. We looked briefly in the last section at the impacts of the thickness of the fuel, but what occurs within that distance is a far more complex topic than it may appear at first glance. With advances in two phase flow modeling (which I’m unable to accurately assess), this problem may not be nearly as daunting as it was when this reactor was being researched, but in all likelihood this set of challenges is perhaps the single largest reason that the bubbler LNTR disappeared from the design literature when it did.
The other effect that the bubbles have on the fuel is that they are the main source of vapor entrainment of fuel element materials in a bubbler, since they are the liquid/gas interface that occurs for the longest, and have the largest relative surface area. We aren’t going to discuss this particular dynamic to any great degree, but the behavior of this interaction compared to inner surface interactions will potentially be significant, both due to the fact that these bubbles are the longest-lived liquid/gas interaction by surface area and are completely encircled by the fuel itself while undergoing heating (and therefore expansion, exacerbated by the decreasing pressure from the centrifugal acceleration gradient). One final note on this behavior: it may be possible that the bubbles may become saturated with vapor during their thermalization, preventing uptake of more material while also increasing the thermal uptake of energy from the fuel (metal vapors were suggested by Soviet NTR designers, including Li and NaK, to deal with the thermal transparency of H2 in advanced NTR designs).
The behavior of the bubbles depends on a number of characteristics:
- Size: The smaller the bubble, the greater the surface area to volume ratio, increasing the amount of heat the can be absorbed in a given time relative to the volume, but also the less thermal energy that can be transported by each bubble. The size of the bubbles will increase as they move through the fuel element, gaining energy though heat, and therefore expanding and becoming less dense.
- Shape: Partially a function of size, shape can have several impacts on the behavior and usefulness of the bubbles. Only the smallest bubbles (how “small” depends on the fluids under consideration) can retain a spherical shape. The other two main shape classifications of bubbles in the LNTR literature are oblate spheroid and spherical cap. In practice, the higher propellant flow rates result in the largest, spherical cap-type bubbles in the fuel, which complicate both thermal transfer and motion modeling. One consequence of this is that the bubbles tend to have a high Reynolds number, leading to more turbulent behavior as they move through the fuel mass. Most standard two-phase modeling equations at the time had a difficult time adequately predicting the behavior of these sorts of bubbles. Another important consideration is that the bubbles will change shape to a certain degree as they pass through the fuel element, due to the higher temperature and lower centrifugal force being experienced on them as they move into the central void of the fuel element.
- Velocity: A function of centrifugal force, viscosity of the fuel, initial injection pressure of the propellant, density of the constituent gas/vapor mix, and other factors, the velocity of a bubble through the fuel element determines how much heat – and vapor – can be absorbed by a bubble of a given size and shape. An increase in velocity also changes the bubble shape, for instance from an oblate spheroid to a spherical cap. One thing to note is that the bubbles don’t move directly along the radius of the fuel element, both oscillation laterally and radially occur as the shape deforms and as centrifugal, convective, and other forces interact with the bubble; whether this effect is significant enough to change the necessary modeling of the system will depend on a number of factors including fuel element thickness, convective and Coriolis behavior in the fuel mass, bubble Reynolds number, and angular velocity of the fuel element,
- Distribution: One concern in a bubbler LNTR is ensuring that the bubbles passing through the fuel mass don’t combine into larger conglomerations, or that the density of bubbles results in a lack of overall cohesion in the fuel mass. This means that the distribution system for the bobbles must balance propellant flow rate, bubble size, velocity, and shape, non-vertical behavior of the bubbles, and the overall gas fraction of the fuel element based on the fuel element design being used.
As mentioned previously, the final paper on the bubbler I was able to find looked at the challenges of bubble dynamics in a simulated LNTR fuel element; in this case using water and compressed air. Several compromises had to be made, leading to unpredictable behavior of the propellant stream and the simulated fuel behavior, which could be due to the challenges of using water to simulate ZrC/UC2, including insufficient propellant pressure, bubble behavior irregularities, and other problems. Perhaps the most major challenge faced in this study is that there were three distinct behavioral regimes in the two phase system: orderly (low prop pressure), disordered (medium prop pressure), and violent (high prop pressure), each of which was a function of the relationship between propellant flow and centrifugal force being applied. As suspected, having too high a void fraction within the fuel mass led to splattering, and therefore fuel mass loss rates that were unacceptably high, but the point that this violent disorder occurred was low enough that it was not assured that the propellant might not be able to completely remove all the thermal energy from the fuel element itself. If the energy level of each fuel element is reduced (by reducing the fissile component of the fuel while maintaining a critical mass, for instance), this can be compensated for, but only by losing power density and engine performance. The alternative, increasing the centrifugal force on the system, leads to greater material and mechanical challenges for the system.
Adequately modeling these characteristics was a major challenge at the time these studies were being conducted, and the number of unique circumstances involved in this type of reactor makes realistic modeling remain non-trivial; advances in both computational and modeling techniques make this set of challenges more accessible than in the 1960s and 70s, though, which may make this sort of LNTR more feasible than it once was, and restarting interest in this unique architecture.
These constraints define many things in a bubbler LNTR, as they form the single largest thermodynamic constraint on the engine. Increasing centrifugal force increases the stringency for both the fuel element canister (with incorporated propellant distribution system), mechanical systems to maintain angular velocity for fuel containment, maximum thrust and isp for a given design, and other considerations.
Suffice to say, until the bubble behavior, and its interactions with the fuel mass, can be adequately modeled and balanced, the bubbler LNTR would require significant basic empirical testing to be able to be developed, and this limitation was probably a significant contributor to the reason that it hasn’t been re-examined since the early-to-mid 1970s.
The “Restart Problem”
The last major issue in a bubbler-type design is the “restart problem”: when the reactor is powered down, there will be a period of time when the fuel is still molten, requiring centrifugal containment, but the reactor being powered down allows for the fuel to be pressed into the pores of the fuel element canister, blocking the propellant passages.
One potential solution for the single fuel element design was proposed by L. Crocco, who suggested that the fuel material is used for the bubbling structure itself. When powered up, the fuel would be completely solid, and would radiate heat in all directions until the fuel becomes molten [ed. Note: according to Crocco, this would occur from the inner surface to the outer one, but I can’t find backup for that assumption of edge power peaking behavior, or how it would translate to a multi-fuel-element design], and propellant would be able to pass through the inner layers of the fuel element once the liquid/solid interface reached the pre-drilled propellant channels in the fuel element.
Another would be to continue to pass the hydrogen propellant through the fuel element until the pressure to continue pumping the H2 reaches a certain threshold pressure, then use a relief valve to vent the system elsewhere while continuing to reject the final waste heat until a suitable wall temperature has been reached. This is going to both make the fuel element less dense, and also result in a lower fuel element density near the wall than at the inner surface of the fuel element. While this could maybe [ed. Note: speculation on my part] make it so that the fuel is more likely to melt from the inner surface to the outer one, the trapped H2 may also be just enough to cause power peaking around the bubbles, allow chemical reactions to occur during startup with unknown consequences, and other complications that I couldn’t even begin to guess at – but the tubes would be kept clear.
Wall Material Constraints
Other than the “restart problem,” additional constraints apply to the wall material. It needs to be able to handle the rotational stresses of the spinning fuel element, be permeable to the propellant, and able to withstand rather extreme thermal gradients: on one side, gaseous hydrogen at near-cryogenic temperatures (the propellant would have already absorbed some heat from the reactor body) to about 6000 K on the inside, where it comes in contact with the molten fuel.
Also, the bearings holding the fuel element will need to be designed with care. Not only do they need to handle the rather large amount of thermal expansion that will occur in all directions during reactor startup, they have to be able to deal with high rotation rates throughout the temperature range.
The Paths Not (Yet?) Taken
Perhaps due to the early time period in which the LNTR was explored, a number of design options don’t seem to have been explored in this sort of reactor.
One option is neutron moderator. Due to the high thermal gradients in this reactor, ZrH and other thermally sensitive moderators could be used to further thermalize the neutron spectrum. While this might not be explicitly required, it may help reduce the fissile requirements of the reactor, and would not be likely to significantly increase reactor mass.
A host of other options are possible as well, if you can think of one, comment below!
The other option was brought up by Michael Turner at Project Persephone, in regards to the vapor entrainment and restart problem issues: what if you get rid of the holes in the walls of the fuel element, and the bubbles through the fuel element, altogether? As we saw when discussing Project Rover, hydrogen gets through EVERYTHING, especially hot metals. This diffusion process is done through individual molecules, not through bubbles, meaning that the possibility of vapor entrainment is eliminated. The down side is that the propellant mass flow will be extremely reduced, resulting in a higher-isp (due to the ability to increase fuel temp because the vapor losses are minimized), much-lower-thrust reactor than those designed before. As he points out, this may be able to be mixed with bubbles for a high-thrust, lower-isp mode, if “shutters” on the fuel element outer frit were able to be engineered. Another possible requirement would be to reduce the fissile component density of the fuel to match the power output to the hydrogen flow rates, or to create a hybrid diffuser/radiator LNTR to balance the propellant flow and thermal output of the reactor.
I have not been able to calculate if this would be feasible or not, and am reasonably skeptical, but found it an intriguing possibility.
The bubbler liquid nuclear thermal rocket is a fascinating concept which has not been explored nearly as much as many other advanced NTR designs. The advantage of being able to fully thermalize the propellant to the highest fuel element temperature while maintaining cryogenic temperatures outside the fuel element is a rarity in NTR design, and offers many options for structures outside the fuel elements themselves. After over a decade of research at Princeton (and other centers), the basic research on the dynamics of this type of reactor has been established, and with the computational and modeling capabilities that were unavailable at the time of these studies, new and promising versions of this concept may come to light if anyone chooses to study the design.
The problems of vapor entrainment, fissile fuel loss, and restarting the reactor are significant, however, and impact many area of the reactor design which have not been addressed in previous studies. Nevertheless, the possibility remains that this drive may one day indeed make a useful stepping stone from the solid-fueled NTRs of tomorrow to the advanced NTRs of the decades ahead.
A Technical Report on the CONCEPTUAL DESIGN – STUDY OF A LIQUID-CORE NUCLEAR ROCKET, Nelson et al 1963 https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19650026954.pdf
The Liquid Core Nuclear Rocket, Grey 1965 (pg 92) https://permalink.lanl.gov/object/tr?what=info:lanl-repo/lareport/LA-03229-MS
Specific Impulse of a Liquid Core Nuclear Rocket, Barrett Jr 1963 https://arc.aiaa.org/doi/abs/10.2514/3.2141?journalCode=aiaaj
Propellant Flow Rate through Simulated Liquid-Core Nuclear Rocket Fuel Bed, McGuirk and Park 1972 https://arc.aiaa.org/doi/abs/10.2514/3.61690?journalCode=jsr