Bubbler LNTR

This page is about a particular subset of liquid fueled nuclear thermal rockets. For more information about nuclear thermal rockets in general, check out the NTR page here. For information about liquid fueled NTRs, see this page.

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.

Bubbles passing through fuel, Nelson 1963

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.

There was only one minor and one major effort to study this type of reactor, a proposal by J McCarthy in 1954, and a study at Princeton University headed by Nelson. While I don’t have much info about the McCarthy proposal (and so I’ll cover everything here), there is much more information available about the Nelson program, which has its own page available here.

McCarthy, 1954

Image from Barrett, Jr 1964

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:

  1. 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
  2. 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
  3. The behavior of the hydrogen as it passes through, and also out of, the liquid fuel was not well understood in practice, and
  4. 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.\

Princeton LNTR

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 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”).

For more information about this reactor, check out its page here.

Bubbler Challenges and Constraints

Because of the unique configuration of this design, while many of the normal considerations for an NTR are present, such as the relationship between temperature and propellant mass determining specific impulse, thrust-to-weight considerations, and ensuring as much energy is deposited in the propellant as possible, there are also a number of unique challenges, which will be covered here.

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.

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.

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.

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.

McGuirk 1972

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.

Bubble Dynamics

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:

  1. 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.
  2. 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.
  3. 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,
  4. 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.

References

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

[PAYWALL] Specific Impulse of a Liquid Core Nuclear Rocket, Barrett Jr 1963 https://arc.aiaa.org/doi/abs/10.2514/3.2141?journalCode=aiaaj

[PAYWALL] 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