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At least 1,063 records · Page 59
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Improvements to a class of hybrid methods for radiation transport: Nyström reconstruction and defect correction methods

In this study, two modifications are introduced for improving the accuracy, versatility, and robustness of a class of hybrid methods for radiation transport. In general, such methods are constructed by splitting the radiative flux into collided and uncollided components to which low- and high-resolution angular approximations are applied, respectively. In this work we focus on discrete ordinates discretizations of high and low order. The first modification we introduce changes the way in which the collided component is mapped into the uncollided component at the end of each time step in a simulation. The new mapping is a Nyström-type reconstruction that is applicable to arbitrary discrete ordinates quadratures, is guaranteed to preserve positivity of the solution provided that all ordinate weights are positive, is significantly more accurate than previous methods, and can be readily extended to other discretizations such as moment methods, finite element methods, and diffusion approximations. The second modification leverages integral deferred correction (IDC) to iteratively correct for the splitting error introduced by the inconsistency in angular discretization between the collided and uncollided components, in addition to improving the accuracy of the low-order temporal error that is treated by traditional IDC methods. Numerical tests in one- and two-dimensional geometries are used to demonstrate the increased accuracy and efficiency of the proposed modifications. It is found that the two techniques combined yield methods with solution accuracy and memory requirements comparable to that of monolithic discrete ordinates methods while reducing runtime by as much as a factor of between two and ten, depending on the problem.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Solution of the Feynman Equation for Time Evolving Fission Chains

The partial differential equation proposed by Feynman describing the time evolution of a fission chain in metal is solved by a method also proposed by Feynman. The partial differential equation is reduced to a transcendental algebraic equation. The solution involves roots of a 7th order polynomial. Both the roots and the transcendental equation are then solved numerically. Two populations are computed from the probability generating function, the internal number of neutrons in time, and the accumulated number of leaked neutrons in time. This same equation also describes a limit of a thermal reactor, where induced fission is totally driven by neutrons that have thermalized and are diffusing in a moderator.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Tandem particle-slurry batch reactors for solar water splitting (Final Scientific/Technical Report)

Economically, particle slurry reactors are projected to be one of the most promising technologies for solar photoelectrochemical hydrogen production, according to a 2009 techno-economic analysis commissioned by the US DOE and performed by Directed Technologies, Inc. The Fuel Cell Technologies Office’s Multi-Year Research, Development and Demonstration (MYRD&D) goals and targets are to reduce the cost of H 2 produced from renewable sources at the plant gate (i.e. not including delivery, dispensing, or storage) to < $2.00/gge, equivalent to ~$2.00/kg H 2 . Research results from our techno-economic modeling research suggest that this target could be met using particle slurry reactors assuming STH efficiencies in the range of 5 – 10%, materials lifetimes of < 1 year, and nanoparticles that cost up to 20 times more than projected costs of TiO 2 -coated Fe 2 O 3 nanoparticles. Although most large worldwide research efforts directed at solar photoelectrochemical hydrogen production focus on wafer-based designs, the projected lower cost for a particle slurry reactor at these disparate projected STH efficiencies clearly suggests that particle slurry reactors could be a scalable and deployable technology, assuming several challenges are overcome. These major technological challenges include the demonstration of a vertically-stacked-vessel architecture that is capable of operating sustainably while mostly relying on diffusion and natural convection to mix the redox shuttles between the vessels, and the demonstration that photocatalyst particles can operate at an overall 1% STH efficiency or larger when incorporated into this two-vessel design. Our research adds to the understanding of photocatalytic reactors for solar water splitting through numerical modeling results and experimental results. Numerical models were developed to simulate relevant device physics including particle and reactor dimensions which affect optical, transport, and rheological properties, electrocatalytic and photovoltaic properties of particles at various temperatures, and properties of redox shuttles and separators. Moreover, theoretical maximum solar-to-hydrogen efficiencies for ensembles of particles like in photocatalyst reactors were modeled and simulated and shown to equal or exceed those of photoelectrochemical designs under most scenarios. These results help determine constraints on the reactor that will enable more optimal designs for future prototypes. In parallel, experiments were performed to identify the most effective redox shuttles and to empirically validate the numerical models and simulations. Toward the latter, state-of-the-art light-absorbing particles and electrocatalysts were synthesized and characterized physically and photoelectrochemically for water electrolysis and redox chemistry with redox shuttles in the form factor of mesoporous electrodes and free-floating particles. The most promising materials candidates were used in a suspension reactor to evaluate performance toward photocatalytic H 2 production and results from the two measurements were compared. Predominantly, state-of-the-art cocatalyst-modified Rh-doped SrTiO 3 and BiVO 4 particles were further characterized to assess for their ability to perform visible-light-driven H 2 and O 2 evolution, respectively, and results were similar to those reported for the state-of-the-art in the peer-reviewed literature. Outcomes from this work inform the public of the effectiveness and promise of solar photocatalytic water splitting for clean and renewable hydrogen production. This work may also help increase research interest and funding for photocatalysis projects, which will accelerate development of a technology that will benefit the public by generating fuel while emitting few greenhouse gases and pollutants.

08 HYDROGEN↗
DOE OSTI2025

Remarks on the thesis of Aitor Bengoechea Fernández: Generalization of Doppler effect processing using S(α,β) thermal diffusion laws

The thesis titled “Generalization of Doppler effect processing using S(α,β) thermal diffusion laws” addresses a critical gap in the modeling of neutron scattering phenomena in nuclear materials, particularly where crystal lattice effects intersect with low-energy resonances. Conducted within the Doctoral School ED 352 at Aix-Marseille Université and hosted at CEA Cadarache, the research presents a theoretical and numerical framework for extending the applicability of Thermal Scattering Laws (TSLs) using higher-order correlation functions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Tracking Radioactive Isotopes in HVAC and Application for Hot Cell Analyses - 20155

In recent years, the surge in the number of isotope production facilities under design has increased the need to analyze isotope migration in facility Heating, Ventilation, and Air Conditioning (HVAC) during normal operations and accident scenarios. These facilities are used to produce isotopes for medical, security, and industrial applications and as such are subject to license and regulatory requirements 10CFR20, 10CFR30, 10CFR50, and 10CFR70. GOTHIC, a general-purpose thermal-hydraulics software package, includes the ability to model isotopic tracers, radioactive decay and isotope migration as well as HEPA and charcoal filters for isotope retention. A GOTHIC model was developed by Zachry Nuclear Engineering (ZNE) to examine the effect of negative room pressure, HEPA filtration, and HVAC fluctuations on radiation areas, hot cells and gloveboxes. Radioactive tracers were used to simulate the concentration of spills within contaminated areas, track the migration of isotopes of interest, and determine the isotopic retention and buildup on facility HEPA filters. A variety of isotopes with concern to dose (e.g., Kr-85, Sr-90, I-131, etc.), including their decay and progeny, are included in the analysis. Negative pressures are maintained in the regions of interest by a representative central HVAC system equipped with a volumetric fan that exhausts to the environment after a series of isolation valves and HEPA filters. GOTHIC is an industry trusted tool for providing engineering solutions for a variety of applications, including fission product tracking, aerosol and particulate transport and ventilation assessments. The software provides an integrated analysis environment that includes a graphical user interface (GUI) for constructing analysis models, a numerical solver that includes parallel processing capabilities and a post-processor for evaluating simulation results. It solves the conservation equations for mass, momentum and energy for multicomponent, multi-phase flow in lumped parameter and multi-dimensional geometries (1, 2, or full 3D), including the effects of turbulence, diffusion and buoyancy. It has been developed and maintained under a Quality Assurance program in compliance with the requirements of 10CFR50 Appendix B and applicable portions of ASME NQA-1 since 1995. GOTHIC has been used for assessing both forced and natural convection conditions for a wide range of applications, including: - Tracking concentration of hazardous gases and chemicals for habitability and safety assessments - Determining ventilation and filtration requirements and optimizing location and arrangement of these systems - Room heat-up, including diverse and Flexible coping strategies for Extended Loss of AC Power (FLEX/ELAP) - Equipment Qualification (EQ) A distinctive feature of GOTHIC is the ability to track many different fields/substances in a simulation, including user defined tracer elements, in the liquid, vapor and droplet fields as well as surfaces and filters. This capability allows GOTHIC to model fission product transport and release or the removal of particulates or harmful toxins from exhaust gases using a spray scrubber or other types of filtration systems. GOTHIC also includes models for engineered equipment, such as fans, filters, charcoal filters, dryers/demisters, dampers, etc. The aerosols and other filtered material are removed or accumulated in these components. The range of aerosol and radiological applications that GOTHIC has been used for includes: - Source Term: Primary Coolant (Equilibrium) Activity; Non-Water Coolant Source/Leakage. - Conditions for Iodine Re-evolution: Sump/Suppression Pool Conditions and pH; - RWST Conditions and pH. - Isotope Removal Mechanisms: Containment Sprayed and Unsprayed Region Mixing; Charcoal Filter Heating due to Iodine decay. - Radionuclide Transport and Decay: Post-LOCA Release in containment; Transport between connected Compartments and vent systems; Groundwater transport of radionuclides. - Non-Newtonian Fluid modeling for sludge, waste tanks, etc. ADAMS ML071581053 (titled 'Best Practice Guidelines for the use of CFD in Nuclear Reactor Safety Applications') poses guidelines for applying single phase CFD codes in nuclear reactor safety problems and GOTHIC is listed as a 'tool for 3D flows' and 'dispersal and deposition of radionuclides.' The Nuclear Quality Assurance (NQA) pedigree of GOTHIC is an important aspect for applications in the nuclear industry. The fundamental tracer models (convective transport, molecular and turbulent diffusion, removal mechanisms, etc.) have been verified using analytical solutions and validated against applicable separate effects tests. Also, GOTHIC has been benchmarked to many integrated effects tests, including Phebus FP (Fission Product). GOTHIC gives good agreement for the buildup and decay of fission products in Phebus Test 3. The model developed by ZNE demonstrates GOTHIC's applicability and acceptability for use in analyzing the migration and retention of radioactive isotopes and their progeny in normal operation and accident scenario analyses for isotope production facilities, hot cells, and gloveboxes. The tracer activities calculated by GOTHIC can then be used in downstream radiation transport and shielding codes like RADTRAD-NAI{sup C}, MCNP{sup R}, and MicroShield{sup R} to determine on-site and of-site doses. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2017

Effects of irradiation on the interface between U-Mo and zirconium diffusion barrier

Irradiated fuel plates were characterized by microscopy that focused on the interface between U–Mo and Zr. Before irradiation, there were three major sub-layers identified in the U–Mo/Zr interface, namely, UZr 2 , Mo 2 Zr, and U with low Mo. The typical total thickness of this U–Mo/Zr interaction is 2–3 microns. The UZr 2 sub-layer formed during fuel fabrication remains stable after irradiation, without large bubbles/porosity accumulation. However, this sub-layer becomes increasingly discontinuous as burnup increases. The low-Mo sub-layer exhibits numerous sub-micron bubbles/porosity at low burnup. Larger, interconnected porosity in this sub-layer was observed in a medium-burnup fuel specimen. However, at higher burnup, regions with the extra-large bubbles/porosity (i.e., larger than 5 ?m) were observed at least 5 microns away from the original location of this sub-layer. The mechanism for the formation of the extra-large bubbles/porosity is still unclear at this time. In general, the U–Mo/Zr interface in monolithic U–Mo fuels is relatively stable after irradiation. As a result, no large detrimental defects, such as large interfacial bubbles or cracks/delamination, were observed in the fuel plates characterized.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2019

Improving Wind Energy Forecasting through Numerical Weather Prediction Model Development

The primary goal of the Second Wind Forecast Improvement Project (WFIP2) is to advance the state-of-the-art of wind energy forecasting in complex terrain. To achieve this goal, a comprehensive 18-month field measurement campaign was conducted in the region of the Columbia River basin. The observations were used to diagnose and quantify systematic forecast errors in the operational High-Resolution Rapid Refresh (HRRR) model during weather events of particular concern to wind energy forecasting. Examples of such events are cold pools, gap flows, thermal troughs/marine pushes, mountain waves, and topographic wakes. WFIP2 model development has focused on the boundary layer and surface-layer schemes, cloud–radiation interaction, the representation of drag associated with subgrid-scale topography, and the representation of wind farms in the HRRR. Additionally, refinements to numerical methods have helped to improve some of the common forecast error modes, especially the high wind speed biases associated with early erosion of mountain–valley cold pools. This study describes the model development and testing undertaken during WFIP2 and demonstrates forecast improvements. Specifically, WFIP2 found that mean absolute errors in rotor-layer wind speed forecasts could be reduced by 5%–20% in winter by improving the turbulent mixing lengths, horizontal diffusion, and gravity wave drag. The model improvements made in WFIP2 are also shown to be applicable to regions outside of complex terrain. Ongoing and future challenges in model development will also be discussed.

17 WIND ENERGY↗
DOE OSTI2015

The iEBE-VISHNU code package for relativistic heavy-ion collisions

The iEBE-VISHNU code package performs event-by-event simulations for relativistic heavy-ion collisions using a hybrid approach based on (2 + 1)-dimensional viscous hydrodynamics coupled to a hadronic cascade model. We present the detailed model implementation, accompanied by some numerical code tests for the package. iEBE-VISHNU forms the core of a general theoretical framework for model-data comparisons through large scale Monte-Carlo simulations. A numerical interface between the hydrodynamically evolving medium and thermal photon radiation is also discussed. Finally, this interface is more generally designed for calculations of all kinds of rare probes that are coupled to the temperature and flow velocity evolution of the bulk medium, such as jet energy loss and heavy quark diffusion.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Numerical investigation of the pressure-dependence of yield sooting indices for n-alkane and aromatic species

The pressure-dependence of the Yield Sooting Index (YSI), as a measure of sooting tendency, is numerically investigated for pressures ranging from 1 atm to 15 atm. Straight-chain alkanes, including ethane, propane, n-hexane, n-heptane, and n-dodecane, and aromatic species, including benzene, toluene, xylene, and ethylbenzene, are selected as test fuels. A detailed chemical mechanism is used for all test fuels considered, and a flamelet-based YSI simulation methodology is employed, where the YSI values are computed based on the Polycyclic Aromatic Hydrocarbon (PAH) dimer production rate at each pressure. It is found that the maximum flame centerline soot volume fraction increases with increasing pressure for all test compounds. However, the pressure dependence of the maximum soot volume fraction is similar for the hydrocarbons within the same class (n-alkane or aromatics). As a consequence, the YSI values computed at pressures up to 15 atm show only small deviations from their values computed and measured at atmospheric pressure. These results suggest that YSI is robust also at elevated pressures, close to those found in practical combustion devices. This study is entirely based on numerical simulations without any experimental measurements available for direct validation. Experimental YSI measurements at high pressures would be required to fully confirm the conclusions reported in this manuscript. Still, our numerical results provide some guidelines for the design of such experiments in the future.

42 ENGINEERING↗
DOE OSTI2018

Fluid age-based analysis of a lifted turbulent DME jet flame DNS [Residence Time-Based Analysis of a Lifted Turbulent DME Jet Flame]

The link between the distribution of fluid residence time and the distribution of reactive scalars is analysed using Direct Numerical Simulation data. Information about the reactive scalar distribution is needed in order to model the reaction terms that appear in Large Eddy and Reynolds-Averaged simulations of turbulent reacting flows. The lifted flame is simulated taking account of multi-step chemistry for dimethyl-ether fuel and differential diffusion. Due to autoignition and flame propagation, the reaction progress increases with residence time. The variation of fluid residence time is evaluated by solving an Eulerian transport equation for the fluid age. The fluid age is a passive scalar with a spatially-uniform source term, meaning that its moments and dissipation rates in turbulent flows can be modelled using closures already established for conserved scalars such as mixture fraction. In combination with the mixture fraction, the fluid age serves as a useful mapping variable to distinguish younger less-reacted fluid near the inlet from older more-reacted fluid downstream. The local fluctuations of mixture fraction and fluid age have strong negative correlation and, building upon established presumed-pdf models for mixture fraction, this feature can be used to construct an accurate presumed-pdf model for the joint mixture fraction/fluid age pdf. It is demonstrated that the double-conditional first-order moment closure combined with the proposed presumed model for the joint pdf of mixture fraction and fluid age gives accurate predictions for unconditional reaction rates – both for pre-ignition radical species produced by low-temperature processes upstream of the flame base, and for major species that are produced at the flame front.

42 ENGINEERING↗
DOE OSTI2015

Study of electron transport in a Hall thruster by axial–radial fully kinetic particle simulation

Electron transport across a magnetic field in a magnetic-layer-type Hall thruster was numerically investigated for the future predictive modeling of Hall thrusters. The discharge of a 1-kW-class magnetic-layer-type Hall thruster designed for high-specific-impulse operation was modeled using an r-z two-dimensional fully kinetic particle code with and without artificial electron-diffusion models. The thruster performance results showed that both electron transport models captured the experimental result within discrepancies less than 20% in thrust and discharge current for all the simulated operation conditions. The electron cross-field transport mechanism of the so-called anomalous diffusion was self-consistently observed in the simulation without artificial diffusion models; the effective electron mobility was two orders of magnitude higher than the value obtained using the classical diffusion theory. To account for the self-consistently observed anomalous transport, the oscillation of plasma properties was speculated. It was suggested that the enhanced random-walk diffusion due to the velocity oscillation of low-frequency electron flow could explain the observed anomalous diffusion within an order of magnitude. The dominant oscillation mode of the electron flow velocity was found to be 20 kHz, which was coupled to electrostatic oscillation excited by global ionization instability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

IRIS Si iv LINE PROFILES: AN INDICATION FOR THE PLASMOID INSTABILITY DURING SMALL-SCALE MAGNETIC RECONNECTION ON THE SUN

Our understanding of the process of fast reconnection has undergone a dramatic change in the last 10 years driven, in part, by the availability of high-resolution numerical simulations that have consistently demonstrated the break-up of current sheets into magnetic islands, with reconnection rates that become independent of Lundquist number, challenging the belief that fast magnetic reconnection in flares proceeds via the Petschek mechanism which invokes pairs of slow-mode shocks connected to a compact diffusion region. The reconnection sites are too small to be resolved with images, but these reconnection mechanisms, Petschek and the plasmoid instability, have reconnection sites with very different density and velocity structures and so can be distinguished by high-resolution line-profile observations. Using IRIS spectroscopic observations we obtain a survey of typical line profiles produced by small-scale events thought to be reconnection sites on the Sun. Slit-jaw images are used to investigate the plasma heating and re-configuration at the sites. A sample of 15 events from 2 active regions is presented. The line profiles are complex with bright cores and broad wings extending to over 300 km s{sup −1}. The profiles can be reproduced with the multiple magnetic islands and acceleration sites that characterize the plasmoid instability but not by bi-directional jets that characterize the Petschek mechanism. This result suggests that if these small-scale events are reconnection sites, then fast reconnection proceeds via the plasmoid instability, rather than the Petschek mechanism during small-scale reconnection on the Sun.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Toward a Greater Understanding of the Reduction of Drift Coefficients in the Presence of Turbulence

Drift effects play a significant role in the transport of charged particles in the heliosphere. A turbulent magnetic field is also known to reduce the effects of particle drifts. The exact nature of this reduction, however, is not clear. This study aims to provide some insight into this reduction and proposes a relatively simple, tractable means of modeling it that provides results in reasonable agreement with numerical simulations of the drift coefficient in a turbulent magnetic field.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Constraints on Populations of Neutrino Sources from Searches in the Directions of IceCube Neutrino Alerts

Beginning in 2016, the IceCube Neutrino Observatory has sent out alerts in real time containing the information of high-energy ($E$ ≳ 100 TeV) neutrino candidate events with moderate to high (≳30%) probability of astrophysical origin. In this work, we use a recent catalog of such alert events, which, in addition to events announced in real time, includes events that were identified retroactively and covers the time period of 2011–2020. We also search for additional, lower-energy neutrinos from the arrival directions of these IceCube alerts. We show how performing such an analysis can constrain the contribution of rare populations of cosmic neutrino sources to the diffuse astrophysical neutrino flux. After searching for neutrino emission coincident with these alert events on various timescales, we find no significant evidence of either minute-scale or day-scale transient neutrino emission or of steady neutrino emission in the direction of these alert events. This study also shows how numerous a population of neutrino sources has to be to account for the complete astrophysical neutrino flux. Assuming that sources have the same luminosity, an $E$ -2.5 neutrino spectrum, and number densities that follow star formation rates, the population of sources has to be more numerous than 7 × 10 -9 Mpc -3 . This number changes to 3 × 10 -7 Mpc -3 if number densities instead have no cosmic evolution.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Hyperbolic Reformulation Approach to Enable Efficient Simulation of Groundwater Flow and Reactive Transport

We apply Cattaneo's relaxation approach to the one-dimensional coupled Boussinesq groundwater flow and advection-diffusion-reaction equations, commonly used in engineering applications to simulate contaminant transport in the subsurface. The diffusion-type governing equations are reformulated as a hyperbolic system, augmented by an equation that can be interpreted as a momentum balance. The hyperbolization enables an efficient unified computation of the primary variable and its gradients, for example piezometric head and unit discharge in the Boussinesq equation. An augmented Roe scheme is used to solve the hyperbolic system. The hyperbolized system of equations is studied in a set of steady state and transient test cases with idealized geometry. These test cases confirm the equivalence of the hyperbolic system to its original formulation. The larger time step size of the hyperbolic equation is verified theoretically by means of a stability analysis and numerically in the test cases. Finally, a reach-scale application of flow and transport across a river meander is considered. This application case shows that the performance of the hyperbolic relaxation approach holds for more realistic groundwater flow and transport problems, relevant to water resources management.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Iterated Discontinuity Factors Based on Reference Outgoing Currents for Discontinuous Finite Element Diffusion

We present a novel formulation for iteratively computing Discontinuity Factors (DF) designed to reproduce reference partial outgoing currents at the interface between macro-regions using Discontinuous Galerkin Finite Elements to solve the multigroup neutron diffusion equation. Similarly, an expression for the boundary coefficients (BCf) is proposed to match the partial outgoing current at vacuum boundaries. Upon convergence, macro-region averaged reaction and leakage rates are preserved. In addition, we consider a source-free steady-state problem depending on the DFs. The existence of a non-trivial solution is due to the non-linearity of the problem. This form greatly simplifies the implementation within Rattlesnake and efficiently converges by updating the DFs and BCfs at every linear iteration of the Preconditioned Jacobian-Free Newton-Krylov solver. The main challenge then lies in determining an appropriate scaling factor to ensure that the initial values for the DFs and BCfs are not too far from their converged value. While this factor does not change the final solution, it has the potential to significantly affect convergence, for purely numerical reasons. An expression based on the reference fission source integral is proposed and satisfying results are presented for problems and compared to Superhomogénéisation (SPH) results with both reflecting and vacuum boundary conditions.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2018

Iterated Discontinuity Factors Based on Reference Outgoing Currents for Discontinuous Finite Element Diffusion

We present a novel formulation for iteratively computing Discontinuity Factors (DF) designed to reproduce reference partial outgoing currents at the interface between macro-regions using Discontinuous Galerkin Finite Elements to solve the multigroup neutron diffusion equation. Similarly, an expression for the boundary coefficients (BCf) is proposed to match the partial outgoing current at vacuum boundaries. Upon convergence, macro-region averaged reaction and leakage rates are preserved. In addition, we consider a source-free steady-state problem depending on the DFs. The existence of a non-trivial solution is due to the non-linearity of the problem. This form greatly simplifies the implementation within Rattlesnake and efficiently converges by updating the DFs and BCfs at every linear iteration of the Preconditioned Jacobian-Free Newton-Krylov solver. The main challenge then lies in determining an appropriate scaling factor to ensure that the initial values for the DFs and BCfs are not too far from their converged value. While this factor does not change the final solution, it has the potential to significantly affect convergence, for purely numerical reasons. An expression based on the reference fission source integral is proposed and satisfying results are presented for problems and compared to Superhomogénéisation (SPH) results with both reflecting and vacuum boundary conditions.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗