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At least 541 records · Page 30
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

3D modelling of MHD mixed convection flow in a vertical duct with transverse magnetic field and volumetric or surface heating

Understanding phenomena associated with the multiple effects/interactions of the fusion nuclear environment on liquid metal flow is required to correctly design liquid metal (LM) blankets for fusion facilities. These effects are investigated in the present work by numerically simulating 3D LM MHD flow. The simulated geometry consists of a straight, vertical duct which runs perpendicular to a strong, fringing applied magnetic field. There is also a region of applied heating as the primary goal is to explore buoyancy effects in MHD duct flows. Results are presented for both buoyancy assisted (upwards) and buoyancy opposed (downwards) flows in conducting and insulating ducts for a range of Hartmann numbers (Ha) up to 100, Reynolds numbers (Re) from 10 3 to 10 4 and Grashof (Gr) numbers from 10 7 to 10 8 . While increasing Gr or decreasing Re increases buoyancy effects, increasing Ha was shown to increase maximum temperature through turbulence reduction. The extent to which the MHD mixed convection flows are quasi-2D is analyzed and buoyant effects, in competition with electromagnetic forces, are shown to bring about 3D flow features not seen in purely MHD flows. Volumetric nuclear heating with steep gradients is applied to the vertical MHD flows for comparison to flows with surface heating only. Finally, surface heating generates stronger buoyancy effects than volumetric heating of the same total power; however, many of the same phenomena occur. Therefore, surface heating, the only option for lab experiments, can provide indication of the effects of volumetric heating in MHD flows.

42 ENGINEERING↗
DOE OSTI2020

Thermodynamic properties of Ca–Pb electrodes determined by electromotive force measurements

Thermodynamic properties of Ca–Pb alloys are investigated by electromotive force (emf) measurements to determine equilibrium cell potentials and phase properties for their application in energy storage systems such as liquid metal batteries. Using the electrochemical cell Ca(s) | CaF 2 (s) | Ca(in Pb) at 700–1060 K, cell emf is measured for thirteen Ca–Pb alloys at mole fractions, x Ca = 0.06–0.80. At 873 K, the equilibrium potentials of liquid Ca–Pb alloys are 0.57–0.62 V versus Ca and the activity values are as low as a Ca = 6.2 × 10 -8 at x Ca = 0.06. In addition, the emf values as a function of temperature provide partial molar quantities (entropy and enthalpy) as well as phase transitions which are corroborated by determining transition temperatures and phase constituents using differential scanning calorimetry (DSC) and powder X-ray diffraction (XRD). This study establishes the fundamental data necessary for the design of Pb-containing liquid metal electrodes through the integration of electrochemical, thermal, and structural properties of Ca–Pb electrodes.

25 ENERGY STORAGE↗
NASA NTRS1984

Liquid droplet radiator performance studies

By making use of droplets rather than solid surfaces to radiate waste heat in space, the liquid-droplet radiator (LDR) achieves a radiating area/mass much larger than that of conventional radiators which use fins or heat pipes. The light-weight potential of the LDR is shown to be limited primarily by the radiative properties of the droplets. The requirement that the LDR heat-transfer fluid have a very low vapor pressure limits the choice of fluids to relatively few several liquid metals and a silicone fluid are the only suitable candidates so far identified. An experimental determination of the emittance of submillimeter droplets of the silicon fluid indicates that an LDR using this fluid at temperatures of 275-335 K would be about 10 times lighter than the lightest solid-surface radiators. Although several liquid metals appear to offer excellent performance in LDR applications at temperatures between 200 and 975 K, experimental determination of liquid-metal emissivities is needed for a conclusive assessment.

Mattick, A. T.↗
DOE OSTI2022

FFTF Acceptance and Startup Testing for GAIN

The Fast Flux Test Facility (FFTF) is the most recent liquid metal reactor (LMR) to be designed, constructed, and operated by the U.S. Department of Energy (DOE). The 400-MWt sodium-cooled, fast-neutron flux reactor plant was designed for irradiation testing of nuclear reactor fuels and materials for liquid metal fast breeder reactors. Following the demise of the breeder reactor program in the United States, FFTF continued to play a key role in providing a test bed for demonstrating performance of advanced fuel designs and demonstrating operation, maintenance, and safety of advanced liquid metal reactors. FFTF operations ceased in April 1992 after a determination by DOE that no combination of proposed missions was financially feasible over a ten-year period. The reactor is currently deactivated and in a long-term surveillance and maintenance (S&M) mode. This report provides information on the extensive and rigorous process that was used to conduct turnover from construction followed by acceptance and startup testing of the FFTF. This paper is in support of the Gateway for Accelerated Innovation in Nuclear (GAIN), which provides the nuclear energy community with access to the technical, regulatory, and financial support necessary to move new or advanced nuclear reactor designs toward commercialization while ensuring the continued safe, reliable, and economic operation of the existing nuclear fleet. The information obtained from the design, startup, and operation of the FFTF provides valuable insight for follow-on reactor projects, such as the Versatile Test Reactor (VTR), in the areas of plant system and component design, component fabrication, fuel design and performance, prototype testing, site construction, reactor startup and operations, and reactor deactivation and decommissioning (D&D). The focus of this report is on the process used to startup the FFTF and to ensure that operations could be conducted efficiently and safely. A reference section is provided of documents detailing the successful turnover and testing process implemented for startup of the reactor and its supporting systems. The documents listed can be retrieved upon request and are believed useful for future reactor startup endeavors.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2025

Laser-spectroscopy testbed for impurity monitoring in liquid metal-cooled fast reactors

A significant challenge in sodium-cooled fast reactors is controlling impurities, in particular oxygen impurities, within the sodium coolant, as they can accelerate corrosion and indicate leaks. Optical methods offer the potential to rapidly detect small concentrations of both gaseous and metal impurities that accelerate corrosion, plug coolant channels, and lead to increased activation of isotopes in the coolant. We present the design and performance of an apparatus designed to enable the application of multiple optical analytical techniques, such as laser-induced breakdown spectroscopy, to detect elemental impurities in the sodium melt with high sensitivity. Here, we experimentally demonstrate the detection of characteristic sodium and oxygen spectral lines in liquid sodium, which sets the stage for the optimization of its analytical sensitivity. A robust sensor of this type integrated with the sodium cooling loop has the potential to significantly improve the safety and operational efficiency of generation IV nuclear reactors.

47 OTHER INSTRUMENTATION↗
NASA NTRS1987

Microgravity fluid management requirements of advanced solar dynamic power systems

The advanced solar dynamic system (ASDS) program is aimed at developing the technology for highly efficient, lightweight space power systems. The approach is to evaluate Stirling, Brayton and liquid metal Rankine power conversion systems (PCS) over the temperature range of 1025 to 1400K, identify the critical technologies and develop these technologies. Microgravity fluid management technology is required in several areas of this program, namely, thermal energy storage (TES), heat pipe applications and liquid metal, two phase flow Rankine systems. Utilization of the heat of fusion of phase change materials offers potential for smaller, lighter TES systems. The candidate TES materials exhibit large volume change with the phase change. The heat pipe is an energy dense heat transfer device. A high temperature application may transfer heat from the solar receiver to the PCS working fluid and/or TES. A low temperature application may transfer waste heat from the PCS to the radiator. The liquid metal Rankine PCS requires management of the boiling/condensing process typical of two phase flow systems.

Migra, Robert P.↗
DOE OSTI2023

Progress and opportunities in corrosion mitigation in heat transfer fluids for next-generation concentrating solar power

Concentrating solar power (CSP) systems have gained considerable eminence in converting solar thermal energy into electrical power in recent years. According to the U.S. Department of Energy's Gen3 roadmap, the CSP system should operate > 700 °C, as its efficiency depends directly on the operating temperature of the heat transfer fluids (HTFs). A significant challenge, however, is the corrosion of containment materials by the HTFs that is exacerbated at the higher temperatures. A comprehensive review of the high temperature stable HTFs, their properties, corrosion mechanisms on different alloys, and corrosion mitigation measures is of much importance for directing a concerted research and development in the field, which forms the motivation for this compendium. First, molten salt HTFs and their thermophysical properties, along with liquid metals, are introduced. Corrosion of structural materials in different HTFs including molten salts, liquid metals, and supercritical carbon-di-oxide at various temperatures and the corrosion mechanisms are comprehensively reviewed. In addition, several corrosion mitigation methods are discussed. Finally, future directions for HTFs and corrosion mitigation methods in molten salts are proposed. As a result, the holistic review presented here will serve as the foundation for further research addressing relevant challenges and enabling the promise of achieving cost-competitive CSP.

14 SOLAR ENERGY↗
NASA NTRS2016

Two-Step Multi-Physics Analysis of an Annular Linear Induction Pump for Fission Power Systems

One of the key technologies associated with fission power systems (FPS) is the annular linear induction pump (ALIP). ALIPs are used to circulate liquid-metal fluid for transporting thermal energy from the nuclear reactor to the power conversion device. ALIPs designed and built to date for FPS project applications have not performed up to expectations. A unique, two-step approach was taken toward the multi-physics examination of an ALIP using ANSYS Maxwell 3D and Fluent. This multi-physics approach was developed so that engineers could investigate design variations that might improve pump performance. Of interest was to determine if simple geometric modifications could be made to the ALIP components with the goal of increasing the Lorentz forces acting on the liquid-metal fluid, which in turn would increase pumping capacity. The multi-physics model first calculates the Lorentz forces acting on the liquid metal fluid in the ALIP annulus. These forces are then used in a computational fluid dynamics simulation as (a) internal boundary conditions and (b) source functions in the momentum equations within the Navier-Stokes equations. The end result of the two-step analysis is a predicted pump pressure rise that can be compared with experimental data.

Fission Power Systems↗
NASA NTRS2016

Two-Step Multi-Physics Analysis of an Annular Linear Induction Pump for Fission Power Systems

One of the key technologies associated with fission power systems (FPS) is the annular linear induction pump (ALIP). ALIPs are used to circulate liquid-metal fluid for transporting thermal energy from the nuclear reactor to the power conversion device. ALIPs designed and built to date for FPS project applications have not performed up to expectations. A unique, two-step approach was taken toward the multi-physics examination of an ALIP using ANSYS Maxwell 3D and Fluent. This multi-physics approach was developed so that engineers could investigate design variations that might improve pump performance. Of interest was to determine if simple geometric modifications could be made to the ALIP components with the goal of increasing the Lorentz forces acting on the liquid-metal fluid, which in turn would increase pumping capacity. The multi-physics model first calculates the Lorentz forces acting on the liquid metal fluid in the ALIP annulus. These forces are then used in a computational fluid dynamics simulation as (a) internal boundary conditions and (b) source functions in the momentum equations within the Navier-Stokes equations. The end result of the two-step analysis is a predicted pump pressure rise that can be compared with experimental data.

Fission Power Systems↗
NASA NTRS2015

The Combined Strength of Thermodynamics and Comparative Planetology: Application of Activity Models to Core Formation in Terrestrial Bodies

Recent models for accretion of terrestrial bodies involve metal-silicate equilibrium as the metallic core formed during growth. Most elements considered are either refractory or well studied elements for which effects of pressure, temperature, oxygen fugacity, and metallic liquid composition are well known. There are a large number of elements that are both siderophile and volatile, whose fate in such models is unknown, largely due to a lack of data at comparable conditions and com-positions (FeNi core with light elements such as S, C, Si, and O). We have focused on Ge, In, As, Sb and determined the effect of Si and C on metal-silicate partitioning, and developed a thermo-dynamic model that allows application of these new data to a wide range of planetary bodies. New experiments: We have previously carried out experiments with FeSi metallic liquid at C-saturated conditions at 1600 and 1800 C [4]. In a new series of experiments we investigate the effect of Si in carbon-free systems at 1600 C for comparison. Experiments were carried out at 1 GPa in MgO capsules using the same basaltic starting composition as in previous studies. The MgO capsule reacts with the silicate melt to form more MgO-rich liquids that have 22-26 wt% MgO. Experimental met-als and silicates were analyzed using a combination of electron microprobe analysis and laser ablation ICP-MS. Results: The new results can be interpreted by considering Ge as an example, in the simple exchange equilibrium Fe + GeO = FeO + Ge, where the equilibrium constant Kd can be examined as a function of Si content of the metal. The slope of lnKd vs. (1-XSi) for this new series allows derivation of the epsilon interaction parameter for each of these four elements and Si (both C-saturated and C-free).All four elements have positive epsilon values, indicating that Si causes a decrease in the partition coefficients; values are 6.6, 6.5, 27.8 and 25.2 for In, Ge, As, and Sb, respectively, at 1 GPa and 1600 C. As an example of how large the effect of Si can be, these epsilon values correspond to activity coefficients (gamma) for As of 0.01 when XSi = 0, and up to gamma = 23 when XSi = 0.2. Combining these new results with previous determinations [5,6] of epsilon parameters for S and C for these elements allows us calculate activity of Ge, In, As, and Sb in Fe-Ni-Si-S-C-O metallic liquids. We apply this new model to sever-al terrestrial bodies such as Earth (Si-rich core), Mars (S-rich core), Moon (S-, C-, and Si-poor core), and Vesta, and examine the resulting core and mantle concentrations of these elements. Mantle concentrations of these four elements are well explained for Earth and Mars in models that call for mid-mantle equilibration between Si-bearing and S-bearing FeNi cores, respectively. Modeling results for the Moon and Vesta will also be presented.

Righter, K.↗
NASA NTRS2004

Metal-Silicate Segregation in Deforming Dunitic Rocks: Applications to Core Formation in Europa and Ganymede

Core formation is an important event in the evolution of a planetary body, affecting both the geochemical and geophysical properties of the body. Metal-silicate segregation could have proceeded either by settling of liquid metal through a magma ocean or by percolation of liquid metal through a solid silicate mantle. Percolation of metallic melt had previously been excluded as a viable segregation mechanism because metallic melts do not form an interconnected network under hydrostatic conditions, except at high melt fraction (>5 vol%), due to the high dihedral angle between metals and silicates (>60 ). Without an interconnected network, porous flow of metallic melt is impossible, leaving the magma ocean scenario as the only mechanism to form the core. Moment-of-inertia measurements of Europa and Ganymede from the Galileo probe indicate that they are differentiated. This evidence suggests that a method for segregating metals and silicates at temperatures low enough to retain volatile compounds must exist. We have investigated the effect of deformation on the distribution of metallic melts in silicates. We have deformed samples of olivine + 5-9 vol% Fe-S to strains of 2.5 in simple shear and find that the metallic melt segregates into melt-rich planes oriented at 20 to the shear plane. These metallic melt-rich bands are similar in structure to the silicate melt-rich bands reported by Holtzman, indicating that deformation can interconnect isolated metallic melt pockets and allow porous flow of non-wetting melts. Such a core formation process could have occurred in the jovian satellites.

Hustoft, J. W.↗
NASA NTRS1993

Insoluble coatings for Stirling engine heat pipe condenser surfaces

The work done by Thermacore, Inc., Lancaster, Pennsylvania, for the Phase 1, 1992 SBIR National Aeronautics and Space Administration Contract, 'Insoluble Coatings for Stirling Engine Heat Pipe Condenser Surfaces' is described. The work was performed between January 1992 and July 1992. Stirling heat engines are being developed for electrical power generation use on manned and unmanned earth orbital and planetary missions. Dish Stirling solar systems and nuclear reactor Stirling systems are two of the most promising applications of the Stirling engine electrical power generation technology. The sources of thermal energy used to drive the Stirling engine typically are non-uniform in temperature and heat flux. Liquid metal heat pipe receivers are used as thermal transformers and isothermalizers to deliver the thermal energy at a uniform high temperature to the heat input section of the Stirling engine. The use of a heat pipe receiver greatly enhances system efficiency and potential life span. One issue that is raised during the design phase of heat pipe receivers is the potential solubility corrosion of the Stirling engine heat input section by the liquid metal working fluid. This Phase 1 effort initiated a program to evaluate and demonstrate coatings, applied to nickel based Stirling engine heater head materials, that are practically 'insoluble' in sodium, potassium, and NaK. This program initiated a study of nickel aluminide as a coating and developed and demonstrated a heat pipe test vehicle that can be used to test candidate materials and coatings. Nickel 200 and nickel aluminide coated Nickel 200 were tested for 1000 hours at 800 C at a condensation heat flux of 25 W/sq cm. Subsequent analyses of the samples showed no visible sign of solubility corrosion of either coated or uncoated samples. The analysis technique, photomicrographs at 200X, has a resolution of better than 2.5 microns (.0001 in). The results indicate that the heat pipe environment is not directly comparable to liquid metal pumped loop data, that nickel aluminide is still a leading candidate for solubility corrosion protection, and that longer duration tests are required to reach a definitive conclusion whether coatings are required at all. Should further testing be required, the test vehicle and analytical tools were developed.

Dussinger, Peter M.↗
DOE OSTI2023

First-principles study of grain-boundary wetting in Fe-Σ5(013)[100] tilt boundary

Here, we report an ab-initio study of grain-boundary wetting (GBW) in three systems (Fe/Zn, Fe/Pb & Fe/Bi) on a Σ5(013)[100] tilt grain boundary. An energy-based approach is pursued and adapted to the study of liquid-metal/solid-metal interfaces. We provide a sound calculation of the wettability parameter S (i.e., defined as the minimum energy difference between the unbroken initial state and final state with liquid-metal/solid-metal interfaces). Solid/liquid interfaces are modelled by ab-initio molecular dynamics, also allowing a study of structural effects in the liquid phase near the solid interface. We show how surface energies for solid-metal/liquid-metal interfaces need a special treatment for the liquid-metal chemical potential due to the change in crystallinity near the interface. The computation of the wettability criterion for the three systems correctly predicts the GBW trend known experimentally for these systems. The computations are compared with small-scale TEM experiments on GBW of two systems (Fe/Pb and Fe/Bi) and it is shown to provide reasonable results. This approach offers new perspectives in predicting GBW trends across various systems.

36 MATERIALS SCIENCE↗
DOE OSTI2022

NIOWAVE Oxygen Control Status Report, July 2022

The following is a summary of the status report: Oxygen concentration in liquid metal measurement; Literature search on oxygen control in liquid metal coolant in nuclear installation; Possible oxygen control in vacuum system are getter materials and cold trap; and, Initial ideas on implementation of these two methods

43 PARTICLE ACCELERATORS↗
DOE OSTI2023

Transition from wall modes to multimodality in liquid gallium magnetoconvection

Coupled laboratory-numerical experiments of Rayleigh-Bénard convection in liquid gallium subject to a vertical magnetic field are presented. The experiments are carried out in two cylindrical containers with diameter-to-height aspect ratio Γ = 1.0 and 2.0 at varying thermal forcing (Rayleigh numbers 10 5 ≲ Ra ≲ 10 8 ) and magnetic field strength (Chandrasekhar numbers 0 ≲ Ch ≲ 3 × 10 5 ). Laboratory measurements and numerical simulations confirm that magnetoconvection in our finite cylindrical tanks onsets via nondrifting wall-attached modes, in good agreement with asymptotic predictions for a semi-infinite domain. With increasing supercriticality, the experimental and numerical thermal measurements and the numerical velocity data reveal transitions between wall mode states with different azimuthal mode numbers and between wall-dominated convection to wall and interior multimodality. These transitions are also reflected in the heat transfer data, which combined with previous studies connect onset to supercritical turbulent behaviors in liquid metal magnetoconvection over a large parameter space. The gross heat transfer behaviors between magnetoconvection and rotating convection in liquid metals are compared and discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Activity model for 36 elements in Fe-Ni-Si-S-C liquids with application to terrestrial planet accretion and mantle geochemistry: New data for Ru, Re, Pt, Os, Ti, Nb, and Ta

Understanding siderophile element partitioning between metal and silicate melts under diverse conditions can be used to place important constraints on the materials and conditions of planetary accretion and core formation, as well as post core formation processes. However, the effects of Si on the partitioning and activity coefficients for these elements are not well known, despite Si likely being one of the dominant light elements in Earth’s core. To address this gap in understanding, we have undertaken a systematic study of the highly siderophile elements Re, Pt, Os, and Ru, and the refractory lithophile elements Nb, Ta and Ti at 1600 °C and 1 GPa, to derive epsilon interaction parameters for these elements in FeSi metallic liquids. Positive epsilon interaction parameters were measured for Nb, Ta, Ti, Ru, Re, Pt, and Os, indicating that dissolved Si in Fe liquids causes a decrease in their metal/silicate partition coefficients (or ‘silicophobic’ behavior). Furthermore, ε$_{Re, Os, or Ru}^{Si}$ > ε$_{Re, Os, or Ru}^{S}$ which means Si causes a larger decrease in D(metal/silicate) than S, and the chalcophile behavior expected from some elements will be completely masked by the presence of Si in a metallic liquid. The new parameters are used to update an activity model that now includes 36 siderophile elements in Fe-Ni-Si-S-C liquids (27 trace elements considered here). Systematic assessment of these 27 elements shows which have the strongest affinity for Si, C, and S, and also how activity coefficients for these elements would vary during accretion and core formation in Earth, Mars, and Mercury of widely differing fO 2 and core compositional conditions. The activity model is combined with new partitioning expressions for Mo, W, Cr, Re Ru, Pt, and Os and applied to aspects of post core formation mantle geochemistry of Earth, Mars, and Mercury. Our updated expressions show that the BSE Mo/W ratio can easily be achieved with metal/silicate partitioning during growth of the Earth, whereas Re, Os and Ru become lower than and highly fractionated compared with BSE values during core formation and accretion, and thus nearly 99% of their BSE abundances are likely contributed by late accretion. Ru isotopes should be a very good indicator of the source material for the late accretion. The high Pt/Os and Re/Os developed in a deepening magma ocean during the growth of the Earth, indicates 186 Os and 187 Os isotopes could be coupled if this ancient material remained isolated and subsequently became entrained in mantle plumes and measured in surficial lavas. The extent to which this occurred will be limited by the low Os content of this ancient material, thus requiring mixing as a major component in plume sources. Martian mantle Hf/W ratio stays low during accretion and core formation modelling, suggesting that W isotope anomalies are more likely due to solid/liquid silicate fractionation than to core formation. Finally, Ti contents measured by MESSENGER at Mercury’s surface can be explained by segregation of either a metallic core (IW-6 to -8) or metallic core + sulfide (IW-4 to -7.5) followed by mantle melting.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
NASA NTRS1991

Heat transfer and core neutronics considerations of the heat pipe cooled thermionic reactor

The authors summarize the results of detailed neutronic and thermal-hydraulic evaluations of the heat pipe cooled thermionic (HPTI) reactor design, identify its key design attributes, and quantify its performance characteristics. The HPTI core uses modular, liquid-metal core heat transfer assemblies to replace the liquid-metal heat transport loop employed by in-core thermionic reactor designs of the past. The nuclear fuel, power conversion, heat transport, and heat rejection functions are all combined into a single modular unit. The reactor/converter assembly uses UN fuel pins to obtain a critical core configuration with in-core safety rods and reflector controls added to complete the subassembly. By thermally bonding the core heat transfer assemblies during the reactor core is coupled neutronically, thermally, and electrically into a modular assembly of individual power sources with cross-tied architecture. A forward-facing heat pipe radiator assembly extends from the reactor head in the shape of a frustum of a cone on the opposite side of the power system from the payload. Important virtues of the concept are the absence of any single-point failures and the ability of the core to effectively transfer the TFE waste heat load laterally to other in-core heat transfer assemblies in the event of multiple failures in either in-core and radiator heat pipes.

Determan, W. R.↗
NASA NTRS2010

Status of Kilowatt-Class Stirling Power Conversion Using a Pumped NaK Loop for Thermal Input

Free-piston Stirling power conversion has been identified as a viable option for potential Fission Surface Power (FSP) systems on the Moon and Mars. Proposed systems consist of two or more Stirling convertors, in a dual-opposed configuration, coupled to a low-temperature uranium-dioxide-fueled, liquid-metal-cooled reactor. To reduce developmental risks associated with liquid-metal loop integration, a test rig has been built to evaluate the performance of a pair of 1-kW free-piston Stirling convertors using a pumped sodium-potassium (NaK) loop for thermal energy input. Baseline performance maps have been generated at the Glenn Research Center (GRC) for these 1-kW convertors operating with an electric heat source. Each convertor was then retrofitted with a custom-made NaK heater head and integrated into a pumped NaK system at the Marshall Space Flight Center (MSFC). This paper documents baseline testing at GRC as well as the progress made in integrating the Stirling convertors into the pumped NaK loop.

Briggs, Maxwell H.↗