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At least 883 records · Page 49

Analysis of Using a Hybrid ZIRCEX Process to Generate High-Assay Low-Enriched Uranium (HALEU) - 20158

Idaho National Lab (INL) is investigating the feasibility of providing High-Assay Low Enriched Uranium (HALEU) by recovering Highly Enriched Uranium (HEU) from spent nuclear fuel (SNF) and downblending the HEU with natural, low-enriched, or depleted uranium (NU, LEU, or DU). That investigation identified that significant quantities of HALEU could be produced with a Hybrid ZIRCEX process to further advanced reactor research while reducing INL's environmental liability. Many new advanced reactor designs are being developed with improved safety, efficiency, and economics. Most require nuclear fuel with U-235 enrichment between 5% and 20%, which is defined as HALEU. Although technically feasible, there is no current domestic capability to make HALEU in the US. While it is anticipated that industry will provide HALEU through commercial enrichment once advanced reactors mature, until a market is established, an interim source of HALEU is needed to enable research and demonstration. An interim source of HALEU could be provided by recovering the HEU in some DOE-managed SNF and downblending it to between 5% and 20% using the Hybrid ZIRCEX Process. ZIRCEX is a dry head-end process to remove cladding (zirconium or aluminum) from SNF. Drying of the SNF is needed prior to introduction to ZIRCEX. After cladding removal, uranium and fission products in the bed material are oxidized and elutriated. In a Hybrid ZIRCEX process, the HEU process stream is sent to a very compact, modular solvent extraction process for uranium purification. The uranyl nitrate from solvent extraction is denitrated and calcined to produce a HALEU product ready for fuel fabrication. The long-lived fission products from solvent extraction are immobilized in glass using a small in-can melt. By removing the cladding before dissolution, the volume of glass waste is reduced by a factor of up to 300 times (when compared to not removing the cladding from the fuel). Other radioactive wastes from the process could be disposed of as Class A or Class B low-level waste. In addition to producing HALEU for advanced reactors, consumption of SNF would reduce DoE's environmental liability. Incorporating low-enriched spent fuel (versus exclusive use of LEU, DU, or NU) into the downblending scheme could reduce the SNF inventory even further. Several downblending and enrichment scenarios using INL fuels were investigated in this study. The results of this analysis show that the Hybrid ZIRCEX process could make a significant contribution to needed HALEU feedstock and reduce the environmental liability of managing SNF at INL. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Experimental investigation of turbulent wake flows in a helically wrapped rod bundle in presence of localized blockages

In nuclear sodium fast reactors, bundles of rods are tightly packed into a triangular lattice, enclosed in a hexagonal duct, and each pin is spirally wrapped with a thin wire. Flow blockages can potentially impact the local flow characteristics and heat transfer mechanisms in the bundle due to its small subchannel size. The effects of the blockage on the flow structures and heat transfer mechanisms are important aspects that require an accurate investigation. In this study, the flow-field characteristics in the vicinity of a blockage located in the exterior subchannel of rod bundles with helically wrapped wires were experimentally investigated. The velocity fields in the exterior subchannel were acquired by applying matched-index-of-refraction and time-resolved particle image velocimetry (TR-PIV) techniques for Reynolds numbers of Re 1 = 4000 and Re 2 = 17 000, i.e., equivalent to Rew 1 = 19 600 and Rew 2 = 83 200, respectively, based on the blockage width. The results from the TR-PIV measurements revealed an arch-shaped vortex with a large flow recirculation and a pair of counter-rotating vortices in the wake region downstream of the blockage, which is commonly observed in the wake flow of bluff bodies. The relative lateral distance and angle between the two vortices decreased when the Reynolds numbers increased. Profiles of maximum turbulence intensity along the shear layers illustrated the transition process including the growth, peak, and decay along the flow direction. From the spectral analysis of the turbulent velocities extracted at points along the shear layer, the Strouhal numbers ( St ) representing the vortex shedding frequency were found to be St = 0.25 and St = 0.56 for the left and right shear layers, respectively. Characteristics of shear layers generated by the blockage in the exterior subchannel were investigated via the two-point cross correlation of fluctuating velocities. The patiotemporal cross correlations of turbulent velocities, computed at points in the region where the left shear layer exhibited rolling effects and vortex breakdowns, were considerably wider and longer. The convection velocity U c was estimated to be ~0.82 U m to 0.93 U m . Proper orthogonal decomposition (POD) analysis was applied to the instantaneous velocity fields to extract the statistically dominant flow structures. It was found that POD modes 2–3 and 4–5 formed the pair modes when the corresponding POD temporal coefficients depicted sinusoidal shapes and exhibited nearly circular orbits in the phase space. Spectral analysis of the POD temporal coefficients confirmed the vortex shedding frequencies detected in the analysis of turbulent velocities.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

SPC-70525 Rev 2 Beryllium Metal Procurement Specification

Idaho National Laboratory (INL) is developing a microreactor to produce electrical power utilizing a small nuclear core under the Microreactor Application Research Validation and Evaluation (MARVEL) program. Key to this design are neutron reflector components constructed of Beryllium Metal (S-65) which is a structural grade of hot-pressed beryllium block. MARVEL will be located at the Transient Reactor Test (TREAT) facility. Any conflict between this specification and referenced Codes and Standards, or any supplementary specifications in the procurement documents requires written clarification from the Contractor prior to proceeding with any work. Any deviation from the procurement documents requires approval by the Contractor with the change request process.

21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗

The Fast Modular Reactor (FMR) - Development Plan of a New 50 MWe Gas-cooled Fast Reactor

General Atomics Electromagnetic Systems (GA-EMS) will be developing a new 50-megawatt electric (MWe) fast modular reactor (FMR), under the Department of Energy’s (DOE’s) Advanced Reactor Demonstration Program (ARDP), Advanced Reactor Concepts 2020 (ARC-20) development pathway, that provides safe, carbon free electricity, capable of incremental capacity additions. A modular design allows it to be factory-built and assembled on-site to keep the cost of capital low, while the dry-cooling facilitates siting to complement renewables in nearly any location. GA-EMS is committed to commercialization of the proposed reactor, with a demonstration by 2030, and deployment by the mid-2030s. The ultimate goal of the design is to develop flexible and dispatchable carbon-free power source for the 2035 US electricity market. The GAEMS- led team will verify that simplified characteristics (e.g., inert helium gas coolant, pellet-loaded fuel rod, installation-free of heat sink requirements, small and passive heat removal systems) of the FMR will result in a safe, maintainable, cost-effective, distributed, nuclear energygenerating station. Three key specific project objectives for the next three years include: Development of the conceptual design of the 50- MWe FMR plant, Achievement of Technology Readiness Level (TRL) 4 for key system and component technologies through in-pile tests, out-of-pile tests, and numerical experiments; and Development of robust techno-economic analysis (TEA) and pre-application licensing approach necessary for timely demonstration and eventual commercialization.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

UN-SiC TRISO Post Irradiation Examination Developmental Work

As part of efforts to strengthen INL?s post irradiation analysis capabilities with non-Advanced Gas Reactor (AGR) tristructural isotropic (TRISO) fuels, two developmental activities were conducted. The first activity was to determine how best to analyze uranium nitride TRISO fuel kernels using electron probe microanalysis, while the second activity focused on developing a method to deconsolidate TRISO fuel particles that have been encased in a silicon carbide matrix. Because these two activities were unrelated, they have been presented separately in this report. Initial EPMA analyses showed nitrogen contents that far exceeded the concentration expected for UN--a line compound. Further examination showed that current literature values for the mass absorption coefficient (MAC) for the N ka X-ray absorbed by U ranged from approximately 1600 to 9500, with most values tending toward 9500. Measuring UN with five different progressively increasing accelerating voltages followed by using the modeling program xMAC suggests the actual MAC is approximately 2115. Additional MAC modifications were required to produce reasonable analytical results. Because of the inaccuracies of necessary MAC coefficients, UN analysis via scanning electron microscopy (SEM) is likely to produce inaccurate results. This is because SEM software does not typically allow the user to alter MACs. Tests have been performed to examine the feasibility of an electrochemical technique to liberate irradiated TRISO fuel from a SiC matrix without damaging the outer pyrolytic carbon layer of the fuel particle. The method is performed by electrochemically exposing the SiC to magnesium metal forming Mg2Si and C. Following exposure, the small SiC samples showed slight mass increases with no evidence of conversion to Mg2Si and C nor obvious degradation of the SiC samples.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Fascinating physics at the edge of magnetic fusion devices

Abstract The physics of the processes at the edge of magnetic fusion devices is multifaceted and exhibits complex, nonlinear synergistic effects. Even though this region occupies only a small portion of the whole device, it plays a crucial role in overall plasma confinement, heat exhaust, and plasma–wall interactions. The latter affects not only the performance but also the lifetime of plasma-facing components and therefore remains an outstanding challenge for future fusion reactors. At the edge of fusion devices, researchers are dealing with phenomena including classical and anomalous plasma transport, atomic physics effects, and physics of plasma-facing material under strong irradiation by particle and energy fluxes. The diversity of edge physics makes it particularly attractive for young scientists. Working in this field, they can find endless possibilities to demonstrate their talents and creativity. This short review describes just some of the basic scrape-off layer and divertor plasma phenomena including divertor plasma detachment, intermittent bursts of anomalous cross-field plasma transport, plasma–material interactions, and dust in fusion plasmas, which are of particular interest in relation to fusion reactors.

Physics↗

Corrigendum: Simulations of stand-off runaway electron beam termination by tungsten particulates for tokamak disruption mitigation (2024 Nucl. Fusion 64 056019)

In the original article, we inadvertently omitted a reference which previously introduced the concept of tungsten injection for 'Disruption Mitigation in Tokamak Reactor via Reducing the Seed Electrons of Avalanche.' In that reference, the authors have proposed injection of a tungsten cylinder of 80 mm by 8 mm dimensions, by rail guns, to absorb the runaway seed population. This can be contrasted with another interesting idea of using small tungsten pellets coated with a low Z material for depleting the runaway seeds as an option for upgrade of the ITER Disruption Mitigation System. Interested readers are referred to those two papers on the tungsten injection for runaway seed removal/reduction, and the related issue of not shortening the current quench excessively. The application focus of was not on reducing the runaway seeds in the initial Ohmic-to-runaway current conversion phase, but on safe termination of a fully formed and likely decaying runaway beam that is about to scrape off against the first wall, which can be accelerated by vertical displacement events. This scheme thus serves as a last line of defense against potential wall damage. The choice here is locally released tungsten particulates, similar to the previous idea of using tungsten particulates as a dust shield for the divertor. The most significant finding of is that strong pitch angle scattering, in addition to energy attenuation and absorption, of high-energy runaways by tungsten particulates, provides a transport mechanism by which runaways damage of the first wall can be mitigated by reducing and spreading the runaway wall load. We regret the omission in the original article, and thank the authors of the cited article for bringing this matter to our attention. We also find the possibility of using the injected tungsten rod from to terminate the runaways, as opposed to the cloud of tungsten particulates in intriguing. In that context, it is of interest to mention another possibility of a retractable tungsten metal arm that can be swung out for deployment in runaway termination, which would remove the need for post-mitigation recovery of tungsten debris in injection schemes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Modeling a High-Temperature Electrochemically Driven Water-Gas-Shift Process Using a Mixed-Conducting Membrane without External Electrical Power

This paper develops a model to predict and interpret the performance of an elevated-temperature, electrochemical, membrane-assisted, water-gas-shift process. The process uses separated feed streams of H 2 O and CO to produce separated streams of H 2 and CO 2 , without an external electrical power source. The dense ceramic membrane is mixed ionic-electronic-conducting (MIEC) gadolinium-doped ceria (GDC) and the porous composite electrodes are Ni-YSZ. At elevated temperature, GDC conducts both oxygen ions and small polarons. The present process uses chemical potential to drive the process. Electrochemical oxidation of CO proceeds within the composite anode and H 2 O reduction proceeds within the composite cathode. At high temperature (e.g., T > 700 °C), GDC has significant electronic leakage in the form of a reduced-cerium small polaron, which supports the charge-transfer reactions. In a typical electrolyzer or fuel cell, this leakage is significantly problematic. However, the present process depends on the leakage current to complete the electrochemical circuit. Model development and validation is based on measured material properties and reactor performance. Potential applications include using CO-rich blast-furnace off gases in steel processing, producing separated streams of H 2 and CO 2 .

Zhu, Huayang↗

Management of the Three Mile Island Unit 2 Accident Corium and Severely Damaged Fuel Debris (Rev. 2)

The Three Mile Island, Unit Two (TMI-2) pressurized water reactor core underwent a significant meltdown in 1979 due to an untimely combination of maintenance problems that led to a loss of feedwater, followed by a series of operational misunderstandings and errors. Primary coolant discharging through a malfunctioning valve represented what was analyzed as a “small-break” loss-of-coolant accident (LOCA) and ultimately became a full core meltdown. The melted core recovery process required the development of a wide array of tools. After approximately three years of water management and other cleanup actions, the first views of the core revealed a much higher degree of damage than previously expected. Approximately 62 metric tons of the core had melted, leaving only 42 of the 177 fuel assemblies standing with fuel rods intact. The core to be recovered was composed of loose, gravel-like and granular particulate material and a central solidified mass of formerly molten fuel. Molten fuel had also penetrated some of the pressure vessel internals and resolidified below the main core support structure. Robotic tools that had been designed for the task were of limited effectiveness due to the range of material types and phases.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Management of the Three Mile Island Unit 2 Accident Corium and Severely Damaged Fuel Debris (Rev. 2)

The Three Mile Island, Unit Two (TMI-2) pressurized water reactor core underwent a significant meltdown in 1979 due to an untimely combination of maintenance problems that led to a loss of feedwater, followed by a series of operational misunderstandings and errors. Primary coolant discharging through a malfunctioning valve represented what was analyzed as a “small-break” loss-of-coolant accident (LOCA) and ultimately became a full core meltdown. The melted core recovery process required the development of a wide array of tools. After approximately three years of water management and other cleanup actions, the first views of the core revealed a much higher degree of damage than previously expected. Approximately 62 metric tons of the core had melted, leaving only 42 of the 177 fuel assemblies standing with fuel rods intact. The core to be recovered was composed of loose, gravel-like and granular particulate material and a central solidified mass of formerly molten fuel. Molten fuel had also penetrated some of the pressure vessel internals and resolidified below the main core support structure. Robotic tools that had been designed for the task were of limited effectiveness due to the range of material types and phases.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Modeling Functional Organic Chemistry in Arctic Rivers: An Idealized Siberian System

Rivers of the Arctic will become ever more important for the global climate, since they carry a majority of continental dissolved organic carbon flux into the rapidly changing polar ocean. Aqueous organics comprise a wide array of functional groups, several of which are likely to impact coastal and open water biophysical properties. Light attenuation, interfacial films, aerosol formation, gas release and momentum exchange can all be cited. We performed Lagrangian kinetic modeling for the evolution of riverine organic chemistry as the molecules in question make their way from the highlands to Arctic outlets. Classes as diverse as the proteins, sugars, lipids, re-condensates, humics, bio-tracers and small volatiles are all included. Our reduced framework constitutes an idealized northward flow driving a major hydrological discharge rate and primarily representing the Russian Lena. Mountainous, high solute and tundra sources are all simulated, and they meet up at several points between soil and delta process reactors. Turnover rates are parameterized beginning with extrapolated coastal values imposed along a limited tributary network, with connections between different terrestrial sub-ecologies. Temporal variation of our total dissolved matter most closely resembles the observations when we focus on the restricted removal and low initial carbon loads, suggesting relatively slow transformation along the water course. Thus, channel combinations and mixing must play a dominant role. Nevertheless, microbial and photochemical losses help determine the final concentrations for most species. Chemical evolution is distinct for the various functionalities, with special contributions from pre- and post-reactivity in soil and delta waters. Several functions are combined linearly to represent the collective chromophoric dissolved matter, characterized here by its absorption. Tributaries carry the signature of lignin phenols to segregate tundra versus taiga sources, and special attention is paid to the early then marine behaviors of low molecular weight volatiles. Heteropolycondensates comprise the largest percentage of reactive carbon in our simulations due to recombination/accumulation, and they tend to be preeminent at the mouth. Outlet concentrations of individual structures such as amino acids and absorbers lie above threshold values for biophysical influence, on the monolayer and light attenuation. The extent of coastal spreading is examined through targeted regional box modeling, relying on salinity and color for calibration. In some cases, plumes reach the scale of peripheral arctic seas, and amplification is expected during upcoming decades. Conclusions are mapped from the Lena to other boreal discharges, and future research questions are outlined regarding the bonding type versus mass release as permafrost degrades. Dynamic aqueous organic coupling is recommended for polar system models, from headwaters to coastal diluent.

54 ENVIRONMENTAL SCIENCES↗

Particle orbits in a rotating liquid

The motion of small spherical particles under gravity, in a viscous fluid rotating uniformly about a horizontal axis, is investigated. Formulations and solutions are obtained for the particle orbit problem and the rotation rate optimization problem. It was found that the rotation rate which maximizes the fraction of the reactor cross-section area containing particles that will not spiral out to the wall in the experimental time (for heavy particles), or that have spiraled inward without hitting the wall (for light particles) is close to 1 rpm.

Roberts, Glyn O.↗

Monolithic Continuous-Flow Bioreactors

Monolithic ceramic matrices containing many small flow passages useful as continuous-flow bioreactors. Ceramic matrix containing passages made by extruding and firing suitable ceramic. Pores in matrix provide attachment medium for film of cells and allow free movement of solution. Material one not toxic to micro-organisms grown in reactor. In reactor, liquid nutrients flow over, and liquid reaction products flow from, cell culture immobilized in one set of channels while oxygen flows to, and gaseous reaction products flow from, culture in adjacent set of passages. Cells live on inner surfaces containing flowing nutrient and in pores of walls of passages. Ready access to nutrients and oxygen in channels. They generate continuous high yield characteristic of immobilized cells, without large expenditure of energy otherwise incurred if necessary to pump nutrient solution through dense biomass as in bioreactors of other types.

Stephanopoulos, Gregory↗

Study of alkaline carbonate cooling to mitigate Ex-Vessel molten corium accidents

To mitigate adverse effects from molten corium following a reactor pressure vessel failure (RPVF), some new reactor designs employ a core catcher and a sacrificial material (SM), such as ceramic or concrete, to stabilize the molten corium and avoid containment breach. Existing reactors cannot easily be modified to include these SMs but could be modified to allow injectable cooling materials. Current reactor designs are limited to using water to stabilize the corium, but this can create other issues such as reaction of water with the concrete forming hydrogen gas. Here the novel SM proposed is a granular carbonate mineral that can be used in existing light water reactor plants. The granular carbonate will decompose when exposed to heat, inducing an endothermic reaction to quickly solidify the corium in place and producing a mineral oxide and carbon dioxide. Corium spreading is a complex process strongly influenced by coupled chemical reactions, including decay heat from the corium, phase change, and reactions between the concrete containment and available water. A recently completed Sandia National Laboratories laboratory directed research and development (LDRD) project focused on two research areas: experiments to demonstrate the feasibility of the novel SM concept, and modeling activities to determine the potential applications of the concept to actual nuclear plants. Small-scale experiments using lead oxide (PbO) as a surrogate for molten corium demonstrate that the reaction of the SM with molten PbO results in a fast solidification of the melt due to the endothermic carbonate decomposition reaction and the formation of open pore structures in the solidified PbO from CO 2 released during the decomposition. A simplified carbonate decomposition model was developed to predict thermal decomposition of carbonate mineral in contact with corium. This model was incorporated into MELCOR, a severe accident nuclear reactor code. A full-plant MELCOR simulation suggests that by the introduction of SM to the reactor cavity prior to RPVF ex-vessel accident progression, e.g., core-concrete interaction and core spreading on the containment floor, could be delayed by at least 15 h; this may be enough for additional accident management to be implemented to alleviate the situation.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Corrosion of 316H Stainless Steel Specimens in Two FLiBe (LiF-BeF 2 ) Salt Batches

This milestone was originally envisioned for completion in FY21 and was delayed due to the COVID-19 response and difficulties in fabricating fluoride salts. To complete the milestone, commercial FLiBe was compared to a batch of FLiBe produced by the conventional hydrofluorination process. However, the batch was stopped early due to an HF leak and the salt did not undergo the final H2 sparging. Subsequent static compatibility testing of 316H specimens in 316H capsules resulted in small mass losses for the commercial FLiBe and much larger mass losses for the 2nd batch of FLiBe.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

No ball milling needed: Alternative ODS steel manufacturing with gas atomization reaction synthesis (GARS) and friction-based processing

Oxide dispersion strengthened (ODS) steels are promising structural materials for future fusion reactors. The high-density (~10 23 /m 3 ) of highly stable Y-(Ti)-O nano-oxides provide high sink strength for radiation resistance and high-temperature (> 650 °C) creep strength. Concomitantly, helium management is enabled by trapping high density (~10 23 /m 3 ) of small (< 3 nm) helium bubbles in the vicinity of nano-oxides. However, conventional route of making ODS steels involves prolonged ball milling, canning, degassing, and laborious thermo-mechanical processing (TMP). Such route, especially the batch-by-batch ball milling step, faces persistent challenge with scalability and high costs. Gas atomization reaction synthesis (GARS) method has demonstrated the potential of making precursor ODS steel powders without ball milling, but the nano-oxide density was around 10 21 /m 3 in the final consolidated form by conventional TMP. Taking advantage of GARS precursor powder, we use friction-based processing, including friction consolidation and extrusion, to manufacture ODS steel with further improved nano-oxide characteristics. Here, preliminary results showed that Y/Ti/O species were intimately mixed and rapidly reacted to form nano-oxides with a number density of ~10 22 /m 3 .

36 MATERIALS SCIENCE↗

Mechanistic Insights into Nonoxidative Ethanol Dehydrogenation on NiCu Single-Atom Alloys

Ethanol dehydrogenation presents a promising pathway towards the production of acetaldehyde, a valuable building block in chemicals production. Under non-oxidative conditions, the reaction is facilitated by supported Cu nanoparticles which afford reasonable activity and high selectivity. The stability issues associated with Cu nanoparticle sintering can be addressed by the addition of small amounts of Ni, which further boost reactivity while retaining selectivity. Despite the promise of NiCu single-atom alloys for non-oxidative ethanol dehydrogenation, little is known about the role of each component and the pathway of this mechanistically complex process. Herein, kinetic investigations from reactor tests identify C-H bond scission as the rate limiting step, while 1-hydroxyethyl is detected as the intermediate via IR spectroscopy. Temperature program desorption studies are employed to examine the effect of Ni coverage and to demonstrate that Ni atoms activate ethanol selectively at lower temperatures, resulting in higher acetaldehyde yield than pure Cu. Temperature program desorption experiments also reveal the spillover of intermediates from the Ni atom to neighboring Cu sites as a relevant step in the reaction pathway. Density functional theory calculations are used to investigate the 2 reaction energetics and to confirm that C-H bond scission is the initial reaction step, while a clear effect of H 2 partial pressure on the reaction pathway is realized. Further, counter to the expected behavior that all reaction steps take place on the Ni atoms, our degree of rate control analysis reveals that a mechanism involving spillover of the 1-hydroxyethyl intermediate from the Ni atom to the Cu surface, where it will dehydrogenate further, is more likely. Furthermore, our combined kinetic, spectroscopic, and theoretical approach sheds light on this complex reaction mechanism and represents a promising method for the understanding and designing of highly active, selective, and stable single-atom alloys for other multistep catalytic processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Monte Carlo techniques for solving transport problems

The Monte Carlo procedure is a model sampling technique. A model is established, and the behavior of sample units in this model is followed. A sufficient number of sample units are followed to obtain a statistical average or macroscopic quantities, which are the quantities of interest. This technique was used in crude form by Fermi in connection with the building of the first atomic pile. Later, Von Neumann and Ulam developed and used the Monte Carlo procedure extensively in developing the atomic bomb. Since then this technique has gained considerable use in nuclear reactor problems (refs. 1 and 2), and we at the Lewis Research Center have been extending it to thermal radiation (refs. 3 and 4), rarefied gas flows, and plasma flow problems (ref. 5). This technique, which requires a large number of sample histories to obtain solutions with small variances, is receiving greater use because of the development of the high-speed electronic computers.

SAMPLED DATA SYSTEM↗