The first major design in bubbler-type LNTRs 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.
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.
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.
For more information about bubbler LNTRs, including more about bubble dynamics and design tradeoffs in general, check out the Bubbler LNTR page here.
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