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DOE OSTI2026

Multiphysics simulation of TRISO fuel compacts and the effects of homogenization on silver release predictions

This work studies the impact of explicit and homogenized modeling approaches on the multiphysics simulation of TRistructural ISOtropic (TRISO) fuel compacts in prismatic High Temperature Gas Reactors (HTGRs) and the silver release predictions. TRISO fuel compacts exhibit complex double heterogeneity that significantly affects heat conduction, neutron transport, and fission products release. In this work, we use Cardinal, a multiphysics tool based on the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework, to couple neutron transport and heat conduction. OpenMC is used for neutron transport and the MOOSE heat transfer module is used for the heat conduction. Then, we use BISON for the silver release predictions. Two different modeling approaches—explicit modeling of individual TRISO particles and homogenized representation using effective thermal properties—are compared at high TRISO packing fractions (20% and 40%) across varying power densities. Results demonstrate that homogenization significantly under-predicts peak temperatures, for the case of high power/TRISO, there is a difference of 83.73 K in the maximum temperature. Additionally, homogenization underestimates the silver release predictions compared to explicit modeling. Specifically, the temperature and power density differences lead to significant differences in silver release predictions. This work demonstrates the importance of accurately modeling heterogeneity of the TRISO particles to reliably predict fission product release and assess reactor safety margins.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2020

Analysis of multi-electron, multi-step homogeneous catalysis by rotating disc electrode voltammetry: theory, application, and obstacles

Rotating disc electrode (RDE) voltammetry has been widely adopted for the study of heterogenized molecular electrocatalysts for multi-step fuel-forming reactions but this tool has never been comprehensively applied to their homogeneous analogues. Here, the utility and limitations of RDE techniques for mechanistic and kinetic analysis of homogeneous molecular catalysts that mediate multi-electron, multi-substrate redox transformations are explored. Using the ECEC' reaction mechanism as a case study, two theoretical models are derived based on the Nernst diffusion layer model and the Hale transformation. Current–potential curves generated by these computational strategies are compared under a variety of limiting conditions to identify conditions under which the more minimalist Nernst Diffusion Layer approach can be applied. Based on this theoretical treatment, strategies for extracting kinetic information from the plateau current and the foot of the catalytic wave are derived. RDEV is applied to a cobaloxime hydrogen evolution reaction (HER) catalyst under non-aqueous conditions in order to experimentally validate this theoretical framework and explore the feasibility of RDE as a tool for studying homogeneous catalysts. Importantly, analysis of the foot-of-the-wave via this theoretical framework provides rate constants for elementary reaction steps that agree with those extracted from stationary voltammetric methods, supporting the application of RDE to study homogeneous fuel-forming catalysts. Lastly, obstacles encountered during the kinetic analysis of cobaloxime, along with the voltammetric signatures used to diagnose this reactivity, are discussed with the goal of guiding groups working to improve RDE set-ups and help researchers avoid misinterpretation of RDE data.

08 HYDROGEN↗

DOE OSTI2011

Beam Homogeneity Dependence on the Magnetic Filter Field at the IPP Test Facility MANITU

The homogeneity of the extracted current density from the large RF driven negative hydrogen ion sources of the ITER neutral beam system is a critical issue for the transmission of the negative ion beam through the accelerator and the beamline components. As a first test, the beam homogeneity at the IPP long pulse test facility MANITU is measured by means of the divergence and the stripping profiles obtained with a spatially resolved Doppler-shift spectroscopy system. Since MANITU is typically operating below the optimum perveance, an increase in the divergence corresponds to a lower local extracted negative ion current density if the extraction voltage is constant. The beam H{sub {alpha}} Doppler-shift spectroscopy is a rather simple tool, as no absolute calibration - both for the wavelength and the emission - is necessary. Even no relative calibration of the different used lines of sight is necessary for divergence and stripping profiles as these quantities can be obtained by the line broadening of the Doppler-shifted peak and the ratio of the integral of the stripping peak to the integral of the Doppler-shifted peak, respectively. The paper describes the H{sub {alpha}} MANITU Doppler-shift spectroscopy system which is now operating routinely and the evaluation methods of the divergence and the stripping profiles. Beam homogeneity measurements are presented for different extraction areas and magnetic filter field configurations both for Hydrogen and Deuterium operation; the results are compared with homogeneity measurements of the source plasma. The stripping loss measurements are compared with model calculations.

43 PARTICLE ACCELERATORS↗

DOE OSTI2015

Molecular simulation of homogeneous nucleation of crystals of an ionic liquid from the melt

The homogeneous nucleation of crystals of the ionic liquid [dmim{sup +}][Cl{sup −}] from its supercooled liquid phase in the bulk (P = 1 bar, T = 340 K, representing a supercooling of 58 K) was studied using molecular simulations. The string method in collective variables [Maragliano et al., J. Chem. Phys. 125, 024106 (2006)] was used in combination with Markovian milestoning with Voronoi tessellations [Maragliano et al., J. Chem. Theory Comput. 5, 2589–2594 (2009)] and order parameters for molecular crystals [E. E. Santiso and B. L. Trout, J. Chem. Phys. 134, 064109 (2011)] to sketch a minimum free energy path connecting the supercooled liquid and the monoclinic crystal phases, and to determine the free energy and the rates involved in the homogeneous nucleation process. The physical significance of the configurations found along this minimum free energy path is discussed with the help of calculations based on classical nucleation theory and with additional simulation results obtained for a larger system. Our results indicate that, at a supercooling of 58 K, the liquid has to overcome a free energy barrier of the order of 60 kcal/mol and to form a critical nucleus with an average size of about 3.6 nm, before it reaches the thermodynamically stable crystal phase. A simulated homogeneous nucleation rate of 5.0 × 10{sup 10} cm{sup −3} s{sup −1} was obtained for our system, which is in reasonable agreement with experimental and simulation rates for homogeneous nucleation of ice at similar degrees of supercooling. This study represents our first step in a series of studies aimed at understanding the nucleation and growth of crystals of organic salts near surfaces and inside nanopores.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2013

Invariant distributions on compact homogeneous spaces

In this paper, we study distributions on compact homogeneous spaces, including invariant distributions and also distributions admitting a sub-Riemannian structure. We first consider distributions of dimension 1 and 2 on compact homogeneous spaces. After this, we study the cases of compact homogeneous spaces of dimension 2, 3, and 4 in detail. Invariant distributions on simply connected compact homogeneous spaces are also treated. Bibliography: 18 titles.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Homogenized halides and alkali cation segregation in alloyed organic-inorganic perovskites

The role of the alkali metal cations in halide perovskite solar cells is not well understood. Using synchrotron-based nano–x-ray fluorescence and complementary measurements, we found that the halide distribution becomes homogenized upon addition of cesium iodide, either alone or with rubidium iodide, for substoichiometric, stoichiometric, and overstoichiometric preparations, where the lead halide is varied with respect to organic halide precursors. Halide homogenization coincides with long-lived charge carrier decays, spatially homogeneous carrier dynamics (as visualized by ultrafast microscopy), and improved photovoltaic device performance. We found that rubidium and potassium phase-segregate in highly concentrated clusters. Alkali metals are beneficial at low concentrations, where they homogenize the halide distribution, but at higher concentrations, they form recombination-active second-phase clusters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Can the angular scale of cosmic homogeneity be used as a cosmological test?

Abstract In standard cosmology, the cosmic homogeneity scale is the transition scale above which the patterns arising from non-uniformities – such as groups and clusters of galaxies, voids, and filaments – become indistinguishable from a random distribution of sources. Recently, different groups have investigated the feasibility of using such a scale as a cosmological test and arrived at different conclusions. In this paper, we complement and extend these studies by exploring the evolution of the spatial ( $$R_{\textrm{H}}$$ R H ) and angular ( $$\theta _{\textrm{H}}$$ θ H ) homogeneity scales with redshift, assuming a spatially flat, $$\varLambda $$ Λ -Cold Dark Matter universe and linear cosmological perturbation theory. We confirm previous results concerning the non-monotonicity of $$R_{\textrm{H}}$$ R H with the matter density parameter $$\varOmega _{\textrm{m0}}$$ Ω m0 but also show that it exhibits a monotonical behavior with the Hubble constant $$H_{0}$$ H 0 within a large redshift interval. More importantly, we find that, for $$z \gtrsim 0.6$$ z ≳ 0.6 , $$\theta _{\textrm{H}}$$ θ H presents a monotonical behavior with $$\varOmega _{\textrm{m0}}$$ Ω m0 , as well as for $$H_0$$ H 0 the entire redshift interval analyzed. We find also that the angular homogeneity scale is sensitive to $$H_{0}$$ H 0 , especially at higher redshifts. Using the currently available $$\theta _{\textrm{H}}$$ θ H measurements, we illustrate the constraints on the $$\varOmega _{\textrm{m0}}$$ Ω m0 – $$H_{0}$$ H 0 plane through a MCMC analysis and show the feasibility of using the angular homogeneity scale as a new, model-independent way to constrain cosmological parameters.

Physics↗

DOE OSTI2018

Theoretical Analysis of Liquid–Ice Interaction in the Unsaturated Environment with Application to the Problem of Homogeneous Mixing

Abstract The process of ice–liquid water interaction in the unsaturated environment is explored both analytically and with the help of a numerical simulation. Ice–liquid water interaction via the condensation–evaporation mechanism is considered in relation to the problem of homogeneous mixing in an unmovable air volume. The process is separated into three stages: the homogenization stage, during which the rapid alignment of thermodynamic and microphysical parameters in the mixing volume takes place; the glaciation stage, during which the liquid droplets evaporate; and the ice stage, which leads to attaining a thermodynamic equilibrium. Depending on the initial temperature, humidity, and mixing ratios of liquid water and of ice water, the third stage may result in two outcomes: existence of ice particles under zero supersaturation with respect to ice or a complete disappearance of ice particles. Three characteristic times are associated with the microphysical stages: the phase relaxation time associated with droplets, the glaciation time determined by the Wegener–Bergeron–Findeisen process, and the phase relaxation time associated with ice. Since the duration of the second and third microphysical stages may be of the same order as the homogenization time or even longer, the homogeneous mixing scenario is more probable in mixed-phase clouds than in liquid clouds. It is shown that mixing of a mixed-phase cloud with a dry environment accelerates cloud glaciation, leading to a decrease in the glaciation time by more than 2 times. The conditions of fast ice particles’ disappearance due to sublimation are analyzed as well.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2011

Development of K-Basin High-Strength Homogeneous Sludge Simulants and Correlations Between Unconfined Compressive Strength and Shear Strength

K-Basin sludge will be stored in the Sludge Transport and Storage Containers (STSCs) at an interim storage location on Central Plateau before being treated and packaged for disposal. During the storage period, sludge in the STSCs may consolidate/agglomerate, potentially resulting in high-shear-strength material. The Sludge Treatment Project (STP) plans to use water jets to retrieve K-Basin sludge after the interim storage. STP has identified shear strength to be a key parameter that should be bounded to verify the operability and performance of sludge retrieval systems. Determining the range of sludge shear strength is important to gain high confidence that a water-jet retrieval system can mobilize stored K-Basin sludge from the STSCs. The shear strength measurements will provide a basis for bounding sludge properties for mobilization and erosion. Thus, it is also important to develop potential simulants to investigate these phenomena. Long-term sludge storage tests conducted by Pacific Northwest National Laboratory (PNNL) show that high-uranium-content K-Basin sludge can self-cement and form a strong sludge with a bulk shear strength of up to 65 kPa. Some of this sludge has 'paste' and 'chunks' with shear strengths of approximately 3-5 kPa and 380-770 kPa, respectively. High-uranium-content sludge samples subjected to hydrothermal testing (e.g., 185 C, 10 hours) have been observed to form agglomerates with a shear strength up to 170 kPa. These high values were estimated by measured unconfined compressive strength (UCS) obtained with a pocket penetrometer. Due to its ease of use, it is anticipated that a pocket penetrometer will be used to acquire additional shear strength data from archived K-Basin sludge samples stored at the PNNL Radiochemical Processing Laboratory (RPL) hot cells. It is uncertain whether the pocket penetrometer provides accurate shear strength measurements of the material. To assess the bounding material strength and potential for erosion, it is important to compare the measured shear strength to penetrometer measurements and to develop a correlation (or correlations) between UCS measured by a pocket penetrometer and direct shear strength measurements for various homogeneous and heterogeneous simulants. This study developed 11 homogeneous simulants, whose shear strengths vary from 4 to 170 kPa. With these simulants, we developed correlations between UCS measured by a Geotest E-280 pocket penetrometer and shear strength values measured by a Geonor H-60 hand-held vane tester and a more sophisticated bench-top unit, the Haake M5 rheometer. This was achieved with side-by-side measurements of the shear strength and UCS of the homogeneous simulants. The homogeneous simulants developed under this study consist of kaolin clay, plaster of Paris, and amorphous alumina CP-5 with water. The simulants also include modeling clay. The shear strength of most of these simulants is sensitive to various factors, including the simulant size, the intensity of mixing, and the curing time, even with given concentrations of simulant components. Table S.1 summarizes these 11 simulants and their shear strengths.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2017

Effect of Microstructure Constraints on the Homogenized Elastic Constants of Elastomeric Sylgard/GMB Syntactic Foam.

Previous numerical studies of Sylgard filled with glass microballoons (GMB) have relied on various microstructure idealizations to achieve a large range of volume fractions with high mesh quality. This study investigates how different microstructure idealizations and constraints affect the apparent homogenized elastic constants in the virgin state of the material, in which all GMBs are intact and perfectly bonded to the Sylgard matrix, and in the fully damaged state of the material in which all GMBs are destroyed. In the latter state, the material behaves as an elastomeric foam. Four microstructure idealizations are considered relating to how GMBs are packed into a representative volume element (RVE): (1) no boundary penetration nor GMB-GMB overlap, (2) GMB-GMB overlap, (3) boundary penetration, and (4) boundary penetration and GMB-GMB overlap. First order computational homogenization with kinematically uniform displacement boundary conditions (KUBCs) was employed to determine the homogenized (apparent) bulk and shear moduli for the four microstructure idealizations in the intact and fully broken GMB material states. It was found that boundary penetration has a significant effect on the shear modulus for microstructures with intact GMBs, but that neither boundary penetration nor GMB overlap have a significant effect on homogenized properties for microstructures with fully broken GMBs. The primary conclusion of the study is that future investigations into Sylgard/GMB micromechanics should either force GMBs to stay within the RVE fully and/or use periodic BCs (PBCs) to eliminate the boundary penetration issues. The implementation of PBCs requires the improvement of existing tools in Sandia’s Sierra/SM code.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Large-scale homogeneity in the distribution of quasars in the Hercules-Corona Borealis Great Wall region

In light of recent debates on the existence of a gigaparsec-scale structure traced by gamma-ray bursts, namely the Hercules-Corona Borealis Great Wall (HCBGW), we revisit large-scale homogeneity in the spatial distribution of quasars. Our volume-limited sample of quasars in the redshift range 1:6 < z ≤ 2:1, which is constructed from the data release 7 of the Sloan Digital Sky Survey quasar catalogue, covers about half of the suspected HCBGW region. We analyze the sample in two complementary ways: fractal analysis of determining the average scale of homogeneity and friends- of-friends analysis of identifying specific large-scale structures. The quasar distribution on average reaches homogeneity at rh = 136 ± 38h-1 Mpc and the richness and comoving size frequencies of large (> ~ 150h-1 Mpc) quasar groups are consistent with the prediction of homogeneous distribution. These results put constraints on the spatial extent of the HCBGW but do not contradict its existence since our quasar sample does not cover the entire HCBGW region.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

Theoretical investigation of mixing in warm clouds – Part 2: Homogeneous mixing

Evolution of monodisperse and polydisperse droplet size distributions (DSD) during homogeneous mixing is analyzed. Time-dependent universal analytical expressions for supersaturation and liquid water content are derived. For an initial monodisperse DSD, these quantities are shown to depend on a sole non-dimensional parameter. The evolution of moments and moment-related functions in the course of homogeneous evaporation of polydisperse DSD is analyzed using a parcel model. It is shown that the classic conceptual scheme, according to which homogeneous mixing leads to a decrease in droplet mass at constant droplet concentration, is valid only in cases of monodisperse or initially very narrow polydisperse DSD. In cases of wide polydisperse DSD, mixing and successive evaporation lead to a decrease of both mass and concentration, so the characteristic droplet sizes remain nearly constant. As this feature is typically associated with inhomogeneous mixing, we conclude that in cases of an initially wide DSD at cloud top, homogeneous mixing is nearly indistinguishable from inhomogeneous mixing.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Method and composition for reducing nitrates, nitrites, and/or hydroxylamine in water using a homogeneous reduced copper tetra-substituted fluorinated pinacolate ligand catalyst complex

A method for reducing nitrates, nitrites, and/or hydroxylamine in water using a homogeneous reduced copper tetra-substituted fluorinated pinacolate ligand catalyst complex. The method includes dissolving a copper(II) tetra-substituted fluorinated pinacolate ligand pre-catalyst complex in water having an excess amount of nitrates, nitrites, and/or hydroxylamine therein. The dissolved copper(II) tetra-substituted fluorinated pinacolate ligand pre-catalyst complex in the water is subjected to electrochemical reduction to form a homogeneous reduced copper tetra-substituted fluorinated pinacolate ligand catalyst complex. The homogeneous reduced copper tetra-substituted fluorinated pinacolate ligand catalyst complex reduces the nitrates, nitrites, and/or hydroxylamine in the water to compounds with nitrogen in a lower oxidation state with the homogeneous reduced copper tetra-substituted fluorinated pinacolate ligand catalyst complex.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2012

Spatial homogenization of thermal feedback regions in Monte Carlo reactor calculations

An integrated thermal-hydraulic feedback module has previously been developed for the Monte Carlo transport solver, MC21. The module incorporates a flexible input format that allows the user to describe heat transfer and coolant flow paths within the geometric model at any level of spatial detail desired. The effect that the varying levels of spatial homogenization of thermal regions has on the accuracy of the Monte Carlo simulations is examined in this study. Six thermal feedback mappings are constructed from the same geometric model of the Calvert Cliffs core. The spatial homogenization of the thermal regions is varied, giving each scheme a different level of detail, and the adequacy of the spatial homogenization is determined based on the eigenvalue produced by each Monte Carlo calculation. The purpose of these numerical experiments is to determine the level of detail necessarily to accurately capture the thermal feedback effect on reactivity. Several different core models are considered: axial-flow only, axial and lateral flow, asymmetry due to control rod insertion, and fuel heating (temperature -dependent cross sections). The thermal results generated by the MC21 thermal feedback module are consistent with expectations. Based upon the numerical experiments conducted it is concluded that the amount of spatial detail necessary to accurately capture the feedback effect on reactivity is relatively small. Homogenization at the assembly level for the Calvert Cliffs PWR model results in a similar power defect to that calculated with individual pin-cells modeled as explicit thermal regions. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2016

Multigroup Transport Equations Derived via Homogeneity and Isotropy Restoration Theory

The multigroup neutron transport calculation at a cell-level or assembly-level is a key step in conventional deterministic reactor analysis. As the computing power grows, it is contemplated that the multigroup transport equation itself be used in whole-core calculation. While the continuous-energy transport equation is derived straightforwardly and rigorously, the multigroup transport equation currently in use involves several approximations during its derivation. Recently, we proposed the Homogeneity and Isotropy Restoration (HIRE) theory in a preliminary form for deriving a multigroup transport equation that maintains angle-independence in the total cross section and homogeneity in the material region (originally each material region is usually homogeneous by design). As a byproduct, only the isotropic scattering term remained, which also relieved the computational burden significantly. In the Homogeneity and Isotropy Restoration (HIRE) theory, we introduced a discontinuity factor in the form of partial current discontinuity factor (PCDF) at the material interface. In this paper, we elaborate on the HIRE theory and apply it to several typical pin-cell problems. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

Surface heterogeneity propagation and homogenization for pouch cell-scale Li metal anodes

Li metal anode is a promising candidate for next-generation energy storage systems and is widely explored in Li-ion and solid-state batteries. Despite its potential, Li metal anodes face instabilities during long-term cycling, especially when paired with NMC or sulfur-based cathodes, where Li is cycled at high capacities of 6-8 mAh/cm2, equivalent to a thickness of 30-40 µm. During such extensive utilization, degradation mechanisms such as excessive solid electrolyte interphase (SEI), dendrites, and dead Li emerge, and ultimately lead to sudden failure and reduced cycle life. The origin of the degradation mechanisms stem from surface heterogeneities introduced during Li foil manufacturing and storage [1, 2]. As cycling progresses, the local heterogeneities propagate, resulting in uneven Li utilization and degradation-prone regions across the electrode [3], which consequently induce performance variations at the cell level. This heterogeneity propagation is particularly pronounced in large-format pouch cells in practical applications, where the surface effects are magnified. Without a clear understanding of the multi-scale heterogeneities and the development of surface homogenization methods, the performance consistency will be compromised, hindering the commercialization of Li metal batteries. In this presentation, we investigate the evolution of surface heterogeneity propagation on commercially available Li foils. We discover that inhomogeneous Li utilization appears as early as the first half-cycle of formation, manifesting as localized clusters and pits. In pouch cell configurations, these features exhibit areal density variations across the electrode on a scale of millimeters. To improve Li utilization homogeneity, a scalable mechanical brushing method is introduced to remove the chemically heterogeneous surface passivation layer. Furtherore, the influence of utilization homogeneity on cell-to-cell consistency is evaluated using 32 Li-NMC811 pouch cells divided into as-received and brushed Li groups. On the brushed Li, clusters and pits are no longer observable, and the cells exhibit significantly improved consistency in discharge capacity trajectories and cycle lifetime. Overall, this study highlights the role of Li surface utilization homogeneity on long-term cycling performance. Our research provides a pathway for improving large-area electrode uniformity and establishing evaluation methods for cell-to-cell consistency, both are key steps toward the commercialization of Li metal batteries and beyond. [1] Otto, Svenja-K., et al. "In-depth characterization of lithium-metal surfaces with XPS and ToF-SIMS: toward better understanding of the passivation layer." Chemistry of Materials 33.3 (2021): 859-867. [2] Hatzell, Kelsey, et al. "Aligning lithium metal battery research and development across academia and industry." Joule (2024). [3] Kim, Sangwook, et al. "Calendar life of lithium metal batteries: Accelerated aging and failure analysis." Energy Storage Materials 65 (2024): 103147.

25 - ENERGY STORAGE↗

DOE OSTI2012

Homogenization and Upscaling for Diffusion, Heat Conduction, and Wave Propagation in Heterogeneous Materials

We present a general homogenization method for diffusion, heat conduction, and wave propagation in a periodic heterogeneous material with piecewise constants. The method is relevant to the frequently encountered upscaling issues for heterogeneous materials. The dispersion relation for each problem is first expressed in the general form where the frequency w (or wavenumber k) is expanded in terms of the wavenumber k (or frequency w). A general homogenization model can be directly obtained with any given dispersion relation. Next step we study the unit cell of the heterogeneous material and derive the exact dispersion relation. The final homogenized equations include both leading order terms (effective properties) and high order contributions that represent the effect of the microscopic heterogeneity on the macroscopic behavior. That effect can be lumped into a single dimensionless heterogeneity parameter, which is bounded between -1/12 less than or equal to less than or equal to 0 and has a universal expression for all three problems. Numerical examples validate the proposed method and demonstrate a significant computational saving.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2019

Hybrid super homogenization and discontinuity factor method for continuous finite element diffusion

This paper presents a novel homogenization equivalence technique aiming to simultaneously leveragethe simplicity of the Super Homogenization (SPH) method to reproduce reference reaction rates andthe ability to preserve reference leakage rates at desired surfaces through Discontinuity Factors (DF).The need for this new class of methods arises from the inability of the current state-of-the-art SPH technology to properly reproduce the reactor multiplication factor for problems with significant leakage. This work shows that this defect lies in the use of normalization factors in the SPH algorithm: while they are necessary with purely reflecting problems to ensure uniqueness of the solution, they introduce homogenization inconsistencies if at least one vacuum boundary condition is present. Two solutions to this problem are presented in this work: (i) to simply remove the normalization factor or (ii) to introduce additional degrees of freedom in the form of DFs in such a way that the normalization factors can still constrain the problem. While the former clearly offers unrivaled simplicity and can lead to very satisfactory results for leakage-dominated cores or if spatial restriction of the SPH regions is applied – as demonstrated for the High Temperature Test Reactor, the latter is more robust and does not require to scale the fission terms with the reference eigenvalue.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗