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At least 73 records · Page 4

Numerical simulation of compressible fluid-dynamics in the chamber of inertial fusion energy systems

Here, this paper aims to establish new and innovative modeling capabilities for analyzing chambers in Inertial Fusion Energy (IFE) systems. IFE is emerging as a promising method to achieve fusion power production, but several challenges must be overcome to develop an IFE pilot plant or deploy commercial IFE systems. These challenges are both theoretical and technical, encompassing a deeper understanding of the underlying physical phenomena and the development of new technologies and materials. One of the needs is to develop mathematical models to describe IFE systems and numerical tools to simulate them. This paper contributes to this endeavor by presenting a new OpenFOAM solver for IFE systems, focusing on gas dynamics in their chambers. The analysis and development of chamber designs will play a significant role in the transition from single-shot experiments to high-repetition rates, as there is a need to protect the chamber walls from the intense radiation fields produced by fusion reactions. A promising design option, normally referred to as thick wall chamber design, consists in using lithium or molten salt jet arrays within the chamber. A critical phenomenon is the venting of high-pressure gases from the center to the external part of the chamber, passing through the blanket array. This process involves the propagation and attenuation of strong pressure waves, requiring suitable modeling approaches for compressible fluid-dynamics. The solver proposed in this work implements a multi-material hydrodynamics model tailored to accurately describe the non-linear propagation of pressure waves while avoiding numerical oscillation issues typical of high-velocity compressible simulation. This solver is verified against numerical test cases, validated against experimental data, and applied to the analysis of the High-Yield Lithium-Injection Fusion-Energy (HYLIFE-I) concept. The relevance of this paper is threefold. Firstly, it contributes to developing and testing modeling approaches for compressible fluid-dynamics phenomena, with specific focus on the new and unexplored topic of IFE thick-liquid-wall blanket modeling. Secondly, it marks one of the first applications of the OpenFOAM library in the research field of IFE systems. Finally, the investigated problem is of practical interest for IFE developers, as it provides useful indications about relevant phenomena in pressure wave propagation in the chamber of these systems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

FORGE: Summer Internship Experience

The presentation summarizes my summer internship experience with the Fluids Group at Fermilab. During the internship, I learned about the maintenance and operation of water pumps and other equipment that support important facility systems. I worked alongside fluids technicians and gained hands-on experience with maintaining machinery, installing pipes, refilling water, cleaning RF cavities, and observing new water-pump construction for PIP-II. My projects included repairing an air dryer, learning how heat exchangers cool low-conductivity water, and cleaning the copper cooling rings used in RF cavities. Overall, this experience helped me better understand the work processes of technicians and the importance of practical technical knowledge for engineers.

Uribe, Anthony [Unlisted, US, IL]

EGS Collab Experiment 2: Continuous Active Source Seismic Monitoring (CASSM)

The dataset contains continuous active-source seismic monitoring (CASSM) data collected during EGS Collab Experiment 2, conducted from February to September 2022 at the Sanford Underground Research Facility in Lead, South Dakota. This experiment aimed to investigate enhanced geothermal systems through high-pressure fluid injections at depths of 1200-1500 meters. The seismic monitoring system included 16 three-component piezoelectric accelerometers and 24 hydrophones installed in boreholes around the injection zones, recording signals from piezoelectric seismic sources. Data were acquired using both continuous and triggered recording systems, with sampling rates of up to 100 kHz. The raw data are organized by timestamps and stored in .dat format, with accompanying log files. Calibration certificates for selected accelerometers are provided to aid in correcting sensor responses, though users are advised to consider possible effects of enclosures and installation on sensor performance. Users are strongly advised to consult the accompanying report, which outlines the experimental setup, data acquisition, sensor specifications, and recording systems.

15 GEOTHERMAL ENERGY

Role of Fluid and Temperature in Fracture Mechanics and Coupled THMC Processes for Enhanced Geothermal Systems

The ability to sustain high energy extraction efficiency from Enhanced Geothermal Systems (EGS) is affected by the ability to measure, characterize, and predict the effect of different perturbations that arise from fluid injection rates, fluid temperature, and shut-in conditions on existing and stimulated fracture systems throughout a subsurface reservoir’s lifecycle. The difficulty arises from limited knowledge of the interaction of fluid and temperature driven fractures with frictional interfaces that govern local deformation and frictional behavior in the surrounding rock. Thermo-poro-mechanical coupled processes tend to dominate this interaction and strongly affect the permeability and local stress distributions that impact efficiency and prevent optimal stimulation conditions over multi-decadal time frames.

Pyrak-Nolte, Laura [Purdue Univ., West Lafayette,

EM-Enhanced HyPOR Loop for Fast Fusion Cycles

Vacuum pumps are the heart of a fusion energy facility – fusion power cannot be generated without them. Nevertheless, the vacuum technology needed to operate a viable fuel cycle for a compact fusion power plant does not exist. Commercial vacuum technology offers the best solution to this challenge, but a pump oil recycling and detritiation system is necessary. Conventional oil detritiation processes have only been developed to deal with legacy waste and are too slow and destructive to the oil. Further, post hoc detritiation strategies are intrinsically inefficient. Our approach is to rethink the challenge holistically by designing the pumping fluid and tritium extraction system in an integrated manner to achieve an innovative solution. By selecting an oil for the specific task of pumping tritium and then designing our catalytic system to selectively target the tritium-bearing functional groups, an effective detritiation system (hydrocarbon pump oil recycling, HyPOR, loop) for fusion power plants can be obtained. The project demonstrated a HyPOR loop process that can selectively remove heavier hydrogen isotopes from pump oil, reaching the target of 99.5 % removal, with an uptake of less than 0.01% of tritium throughput, while also purifying the oil of radiation-induced damage. The recycled oil retained its pumping characteristics over 7 recycles and gamma irradiation over 30 MGy. By meeting these targets, the project enable a reduction in pump operational costs from $\$$14.5M/year to $\$$103k/year (>140× reduction), reducing pump electric power consumption from 2.8 MW to 0.25 MW (>10× reduction), and reducing in-process tritium inventory from 2.03 kg to 0.48 kg (>4× reduction).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Dust supply to close binary systems

Binary systems can be born surrounded by circumbinary discs. The gaseous disc around either of the two stellar companions can have its life extended by the supply of mass arriving from the circumbinary disc. The objective of this study is to investigate the gravitational interactions exerted by a compact and eccentric binary system on the circumbinary and circumprimary discs, and the resulting transport of gas and solids between the disc components. We assume that the gas in the system behaves as a fluid, and we model its evolution by means of high-resolution hydrodynamical simulations. Dust grains are modelled as Lagrangian particles that interact with the gas and the stars. Our models indicate that significant fluxes of gas and dust proceed from the circumbinary disc towards the circumprimary disc. For the applied system parameters, grains of certain sizes are segregated outside the tidal gap generated by the stars. Consequently, the size distribution of the transported dust is not continuous, but presents a gap in the millimetre size range. In close binaries, the lifetime of an isolated circumprimary disc is found to be short, ~10 5 years, because of its low mass. However, because of the influx of gas from beyond the tidal gap, the disc around the primary star can survive much longer, ~10 6 years, as long as gas accretion from the circumbinary disc continues. The supply of solids and the extended lifetime of a circumbinary disc also aids in the possible formation of giant planets. Compared to close binary systems without a circumbinary disc, we expect a higher frequency of singleplanet or multiple-planet systems. Additionally, a planetesimal or debris belt can form in the proximity of the truncation radius of the circumprimary disc and/or around the location of the exterior edge of the tidal gap.

79 ASTRONOMY AND ASTROPHYSICS

Power Electronics Thermal Management

The 2017 Electrical and Electronics Technical Team Roadmap [11] proposes aggressive research and development targets aimed at improving power electronics technology to enable the mass-market penetration of electric-drive vehicles. Achieving these aggressive targets will require a decrease in cost (year 2025 cost target: $2.70/kW) and an increase in power density (year 2025 power density target: 100 kW/L) as compared with current on-road technology. Replacing traditional silicon device-based components with more efficient and higher-temperature wide-bandgap (WBG) semiconductor device-based components will enable increased power density. However, meeting the power density target will also require innovative thermal management solutions to increase the heat fluxes dissipated and allow for compact electronics packaging. This project evaluates, designs, and develops thermal management strategies that use dielectric fluid (single-phase heat transfer) as coolants.

ADVANCED PROPULSION SYSTEMS

Hierarchical Network Partitioning for Solution of Potential-Driven, Steady-State Nonlinear Network Flow Equations

The solution of potential-driven steady-state flow in large networks is a task which manifests in various engineering applications, such as transport of natural gas or water through pipeline networks. The resultant system of nonlinear equations depends on the network topology, and in general, there is no numerical algorithm that offers guaranteed convergence to the solution (assuming a solution exists). Some methods offer guarantees in cases where the network topology satisfies certain assumptions, but these methods fail for larger networks. On the other hand, the Newton-Raphson algorithm offers a convergence guarantee if the starting point lies close to the (unknown) solution. It would be advantageous to compute the solution of the large nonlinear system through the solution of smaller nonlinear sub-systems wherein the solution algorithms (Newton-Raphson or otherwise) are more likely to succeed. Here, this letter proposes and describes such a procedure, a hierarchical network partitioning algorithm that enables the solution of large nonlinear systems corresponding to potential-driven steady-state network flow equations.

42 ENGINEERING

Shape-anisotropy inverses the behavior of emergent vortices in active chiral fluids

Active colloidal fluids exhibit spontaneous emergence of correlated states, characterized by complex collective dynamics and self-organization. In geometrically confined systems, activity modulations trigger robust polar state reversals of a macroscopic vortex formed by colloidal rollers. Here, we reveal that the shape anisotropy of dielectric rollers transforms the system into a chiral active fluid comprised of rollers of arbitrary handedness. The chiral rollers self-assemble into multiple freestanding vortices with a spontaneously selected sense of rotation. We demonstrate that upon reactivation of the system after a complete cessation of activity beyond all relevant timescales, the vortices simultaneously restore their previous chiral states in striking contrast to the chiral state reversals demonstrated by spherical rollers. The analysis reveals that shape-anisotropy modifies the collective state memory of the ensemble. The findings provide insights into the emergence of complex collective behavior in chiral colloidal fluids governed by an interplay between shape anisotropy, chiral motion, and activity modulations.

Colloids

Combined TDLAS and chemiluminescence imaging in a flat flame burner operated with NH3/H2 blends

Ammonia is a promising hydrogen carrier due to its favorable storage and transport characteristics. However, its direct use in combustion systems is limited by low flammability and potential for high nitrogen oxide emissions. To better understand ammonia combustion, researchers conducted experiments using a flat flame burner and measured species profiles using tunable-diode-laser-absorption-spectroscopy and chemiluminescence imaging. They tested three flame conditions with different ammonia-hydrogen blends and oxygen levels. The results were compared to simulations using various kinetic mechanisms, including one that accounts for excited species chemistry. The goal is to provide direct information about species profiles in a simple system, isolating chemical kinetics from fluid dynamic effects, which can inform the development of more efficient and low-emission combustion systems using ammonia.

ammonia combustion

Critical fluid dynamics in two and three dimensions

We describe a numerical method for simulating stochastic fluid dynamics near a critical point in the Ising universality class. This theory is known as model H, and is expected to govern the nonequilibrium dynamics of quantum chromodynamics (QCD) near a possible critical endpoint of the phase transition between a hadron liquid and the quark-gluon plasma. The numerical algorithm is based on a Metropolis scheme, and automatically ensures that the distribution function of the hydrodynamic variables in equilibrium is independent of the transport coefficients and only governed by the microscopic free energy. We verify dynamic scaling near the critical point of a two and three-dimensional fluid and extract the associated critical exponent z. Here, we find z≃3 in three dimensions, and z≃2 for a two-dimensional fluid. In a finite system, we observe a crossover between the mean field value z=4 and the true critical exponent z≃3 (z≃2 in d=2). This crossover is governed by the values of the correlation length and the renormalized shear viscosity.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Multiphysics Co-Optimization Design and Analysis of Double-Side Cooled Silicon Carbide-Based Power Module: Preprint

With the rapid growth of Electric Vehicles (EVs) and Hybrid Electric Vehicles (HEVs), much more rigorous design targets have been set for automotive power electronics, including high power density, high reliability, and low cost. Novel power module and inverter technologies based on wide bandgap (WEG) semiconductors have been developed to meet these design targets, while providing optimal power semiconductor operating temperature and promising thermomechanical performance. Compared with conventional cooling techniques which are normally applied only on one side of power module, double-side cooling approach is now believed to be the solution to enable high power density and low thermal resistance of WEG semiconductor-based power electronics. In this work, we develop a three-phase power module that is double-sided cooled using dielectric fluid jet impingement. In each phase, four silicon carbide (SiC) power semiconductors are bonded to copper busbars without electrical insulation layers. A finite element analysis (FEA) model is created for thermal and thermomechanical analysis. Based on FEA modeling results, we select particular dimensions for a parametric study to optimize thermal and mechanical performance. Using a multi-objective genetic algorithm (MOGA)-based optimization method, we have minimized the maximum junction temperature and thermal stresses within the power module. The multiphysics co-optimization approach has enabled an efficient design process of power modules with greatly reduced computational cost, as compared to conventional processes that rely on exhaustive numerical simulations and iterations.

ADVANCED PROPULSION SYSTEMS

Historical and Future Windstorms in the Northeastern United States

Large-scale windstorms represent an important atmospheric hazard in the Northeastern US (NE) and are associated with substantial socioeconomic losses. Regional simulations performed with the Weather Research and Forecasting (WRF) model using lateral boundary conditions from three Earth System Models (ESMs: Geophysical Fluid Dynamics Laboratory (GFDL), Hadley Centre Global Environment Model (HadGEM) and Max Planck Institute (MPI)) are used to quantify possible future changes in windstorm characteristics and/or changes in the parent cyclone types responsible for windstorms. WRF nested within MPI ESM best represents important aspects of historical windstorms and the cyclone types responsible for generating windstorms compared with a reference simulation performed with the ERA-Interim reanalysis for the historical climate. The spatial scale and frequency of the largest windstorms in each simulation defined using the greatest extent of exceedance of local 99.9th percentile wind speeds (U > U999) plus 50-year return period wind speeds (U50,RP) do not exhibit secular trends. Projections of extreme wind speeds and windstorm intensity/frequency/geolocation and dominant parent cyclone type associated with windstorms vary markedly across the simulations. Only the MPI nested simulations indicate statistically significant differences in windstorm spatial scale, frequency and intensity over the NE in the future and historical periods. This model chain, which also exhibits the highest fidelity in the historical climate, yields evidence of future increases in 99.9th percentile 10 m height wind speeds, the frequency of simultaneous U > U999 over a substantial fraction (5–25%) of the NE and the frequency of maximum wind speeds above 22.5 ms−1. These geophysical changes, coupled with a projected doubling of population, leads to a projected tripling of a socioeconomic loss index, and hence risk to human systems, from future windstorms.

Pryor, Sara C. (ORCID:0000000348473440)

The solubility and speciation of REE phosphate endmembers (CePO 4 and YPO 4 ) in Cl-rich aqueous fluids from 350 to 450 °C and implications for natural systems

The rare earth elements (REE) are important metals used increasingly in advanced technologies. Within the crust, the elements Ce and Y are commonly more abundant compared to other lanthanides and comprise important end-member constituents of REE-bearing minerals. Specifically, Ce is part of the light (L) REE which have larger ionic radii than the heavy (H) REE, which are grouped together with Y. These differences in ionic radius can lead to important physico-chemical trends within the lanthanide group. Despite a recent increase in experimental and thermodynamic data for the REE at high temperature and pressure, there is still a significant lack of these data at supercritical conditions. In this study we conducted batch-type experiments to measure the solubility of REE phosphates (CePO 4 and YPO 4 ) at varying starting pH (1.5–10), and salinity (0.01–1.4 mol/kg NaCl) at 350 and P sat , and from 400 to 450 °C at 700 bar. Results show that the solubility of Ce (33–0.14 ppb) is generally higher than Y (13–0.13 ppb) and that Ce complexes more strongly with both chloride and hydroxyl ligands compared to Y. The solubilities of both REE phosphates are highly pH-dependent and, to a lesser extent, depend on salinity at the studied conditions. The solubility data from this study were implemented into the GEMSFITS program to optimize the thermodynamic properties of Ce and Y hydroxyl and chloride species. The updated standard partial molal Gibbs energies of formation (Δ f G 0 T,P ) are used within the experimental temperature and pressure range to accurately predict the CePO 4 and YPO 4 solubility and Ce and Y speciation behavior. Based on the updated thermodynamic properties we also provide formation constants (log β n Cl,OH ) for Ce and Y hydroxyl and chloride species. Updated thermodynamic properties are applied to model REE-apatite dissolution and REE mobility based on the Pea Ridge iron oxide apatite deposit in Missouri, USA. The apatite dissolution model replicates natural observations including the replacement of monazite and xenotime after apatite and is an example of the utility of the new thermodynamic constants applied to supercritical crustal fluids. Furthermore, the findings of this study advance the predictive capabilities of geochemical models, our understanding of the behavior of individual REE, and permit modeling the overarching fractionation trends between LREE and HREE in supercritical crustal fluids.

58 GEOSCIENCES

Development of a Method for Shape Optimization for a Gas Turbine Fuel Injector Design Using Metal-Additive Manufacturing

Adjoint shape optimization has enabled physics-based optimal designs for aerodynamic surfaces. Additive manufacturing (AM) makes it possible to manufacture complex shapes. However, there has been a gap between optimal and manufacturable surfaces due to the inherent limitations of commercial computational fluid dynamics (CFD) codes to implement geometric constraints during adjoint computation. In such cases, the design sensitivities are exported and used to perform constrained shape modifications using parametric information stored in computer aided design (CAD) files to satisfy manufacturability constraints. However, modifying the design using adjoint methods in CFD solvers and performing constrained shape modification in CAD can lead to inconsistencies due to different shape parameterization schemes. This paper describes a method to enable the simultaneous optimization of the fluid domain and impose AM manufacturability constraints, resolving one of the key issues of geometry definition for isogeometric analysis. Similar to a grid convergence study, the proposed method verifies the consistencies between shape parameterization techniques present within commercial CAD and CFD software during mesh movement as a part of the adjoint shape optimization routine. By identifying the appropriate parameters essential to a shape optimization study, the error metric between the different parameterization techniques converges to demonstrate sufficient consistencies for justifiable exchange of data between CAD and CFD. For the identified shape optimization parameters, the error metric to measure the deviation between the two parameterization schemes lies within the AM laser-powder bed fusion (L-PBF) process tolerance. Additionally, comparison for subsequent objective function calculations between iterations of the optimization loop showed acceptable differences within 1% variation between the modified geometries obtained using the two parameterization schemes. This method provides justification for the use of multiphysics guided adjoint design sensitivities computed in CFD software to perform shape modifications in CAD to incorporate AM manufacturability constraints during the shape optimization loop such that optimal designs are also additively manufacturable.

33 ADVANCED PROPULSION SYSTEMS

Hydrothermal solubility of Dy hydroxide as a function of pH and stability of Dy hydroxyl aqueous complexes from 25 to 250 °C

The rare earth elements (REE) have important applications in green energy technologies. The formation of mineral deposits in geologic systems commonly involves hydrothermal fluids which can mobilize the REE. However, the REE speciation is not well known as a function of pH. The thermodynamic properties of REE hydroxyl complexes used in geochemical models are based on the Helgeson-Kirkham-Flowers (HKF) equation of state parameters which were derived by extrapolation of low temperature experimental and estimated data. In this study, Dy hydroxide solubility experiments are combined with available literature data to improve these models from 25 to 250 °C and optimize the thermodynamic properties of Dy 3+ and Dy hydroxyl complexes using GEMSFITS. Batch-type solubility experiments were conducted from 150 to 250 °C and at saturated water vapor pressure in perchloric acid solutions with initial pH values of 2 to 5 in 0.5 pH unit increments. The measured solubility of Dy hydroxide is retrograde with temperature and decreases with pH. The logarithm of total dissolved Dy molality ranges from –2.3 to –5.3 at 150 °C (pH 4.7–5.5), from –2.4 to –5.6 at 200 °C (pH 3.9–5.1), and from –3.7 to –6.9 at 250 °C (pH of 3.4 and 5.0). The optimized standard partial molal Gibbs energies of formation (Δ f G° T ) derived for Dy 3+ and DyOH 2+ display a close to linear relationship with temperature, fitting with previous optimizations based on DyPO 4 solubility data in the literature. A comparison of the optimized ΔfG°T values for aqueous Dy species with predictions from available HKF parameters indicates significant differences ranging from +11 to –26 kJ/mol between 25 and 250 °C. The experimental fits are used to derive the Dy hydroxide solubility products (K s0 ) and formation constants for the hydrolysis of Dy (β n with n = 1 to 3; Dy 3+ + nOH – = DyOH n 3-n ) as a function of temperature. The optimization method presented yields accurate thermodynamic properties for the Dy 3+ aqua ions and the DyOH 2+ species at the acidic to mildly acidic pH studied whereas more experimental work is needed at near-neutral and alkaline conditions to better constrain the other hydroxyl complexes. Furthermore, the optimized thermodynamic data have a significant impact on geochemical modeling of the mobility and solubility of REE minerals in acidic hydrothermal fluids.

58 GEOSCIENCES

Computational Thermal Hydraulics of a High-Performance Low-Enriched-Uranium Annular Target for HFIR Irradiation

Molybdenum-99 has historically been generated via isolation from fissioned highly enriched uranium (HEU) targets. Here, this isotope is in high demand due to its daily use across the world in radiopharmaceutical medical procedures. The primary objective of this work was to design and analyze an experimental target assembly containing one low-enriched-uranium (LEU) annular target for irradiation at the High Flux Isotope Reactor (HFIR). Efforts included incorporating spatially dependent energy sources from neutron and gamma interactions, quantifying thermal contact conductance at material interfaces, performing grid-independent studies, comparing turbulence models, and simulating various steady-state and transient scenarios relevant for irradiation qualification and eventual insertion. These models provide velocity, pressure, and temperature distributions in both space and time. Such results enable the selection of an appropriate irradiation location, fission rate density, and flow-limiting orifice size and demonstrate compliance with HFIR safety requirements such that insertion into the reactor can be approved. This analysis shows that across all scenarios, wetted surface temperatures remain below the coolant saturation temperature with no net vapor formation in the coolant. In every scenario, all components stay below 30% of the aluminum 6061 melting temperature. Computational fluid dynamics and system-level models predict peak target temperatures that agree within 4%, though the predicted axial location of the peak differs by about 10% of the heated length due to differences in flow development length. These results de-risk the irradiation of LEU (annular targets) and strengthen a domestic, HEU-independent 99 Mo supply by providing important fuel performance data to form the foundation for a robust licensing basis.

Molybdenum-99

Report on Initial Sodium Testing on the Thermal Hydraulic Experimental Test Article (THETA) (Fiscal Year 2024 Final Report)

The Thermal Hydraulic Experimental Test Article (THETA) is a facility that is used to develop sodium components and instrumentation as well as to acquire experimental data for validation of reactor thermal hydraulic and safety analysis codes. The facility simulates nominal thermal hydraulic conditions as well as protected/unprotected loss of flow accidents in a sodium-cooled fast reactor (SFR). High fidelity distributed temperature profiles of the developed flow field may be acquired with Rayleigh backscatter based optical fiber temperature sensors. The facility was designed in partnership with systems code experts to tailor the experiment to ensure the most relevant and highest quality data for code validation. THETA is comprised of a traditional primary coolant and secondary coolant system. The primary system is submerged in the pool of sodium and consists of a pump, electrically heated core, intermediate heat exchanger, and connected piping and thermal barriers (redan). The secondary system, located outside of the sodium pool, consists of a pump, sodium to air heat exchanger, and connected piping and valves. In fiscal year 2023, thermal stratification tests were completed with the primary system online, while the secondary system was being constructed [1]. These tests had shown that the core barrel and intermediate heat exchanger (IHX) outlet required increased thermal insulation. The THETA primary system was removed from METL, cleaned, thermal insulators installed, and then inserted into METL Test Vessel 4. At the time of this writing the THETA primary and secondary system are operational. During this fiscal year 100+ hours of testing was completed to characterize thermal hydraulic phenomena associated with steady state and transient conditions in a pool type liquid metal cooled reactor. A majority of the testing campaign was completed to satisfy the experimental data acquisition requirements for the GAIN Voucher with Oklo, CRADA 2021-21121. THETA is still operational at the time of this publication and future testing is planned for fiscal year 2025. Work is underway to publish existing and future data to an online database to facilitate collaboration with SFR engineers looking to validate their systems code or computational fluid dynamics models.

22 GENERAL STUDIES OF NUCLEAR REACTORS