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At least 199 records · Page 11

Advanced Electrochemical Separations of Actinide/Fission Products via the Control of Nucleation and Growth of Electrodeposits. Final Report

This is the final report to the NEUP regarding the “Advanced Electrochemical Separations of Actinide/Fission products via the Control of Nucleation and Growth of Electrodeposits” project. This report describes the project activities conducted during the period October 01, 2016 through September 30, 2019. The report includes a brief statement of the project objectives and approach, followed by the details of the performed research activities and suggestion for the future work. It is well known that according to current knowledge the pyroprocessing of spent nuclear fuels invariably leads to the dendritic form of electrodeposits, which from technological point of view is undesirable for many reasons. The aim of this research was to study and preclude the formation of electrodeposits with dendritic morphology (of essential importance to FC-1 Program). This project is characterized with four novel study categories: (1) exploring electrodeposit morphology control by controlling the electrochemical deposition reaction rate, (2) the use of rotating disk electrode technique to distinguish the electrodeposition control modes (reaction rate vs. diffusion), (3) morphology studies of lanthanides (La) and actinides (U) in characteristic stages of nucleation and growth, (4) exploring the need for separation of electrochemical cell in compartments for cathodic and anodic reactions. All these study categories were applied on two distinct electrolyte systems (a) high temperature ionic liquids, i.e. molten LiCl-KCl salts, and (b) room temperature ionic liquids (compounds exclusively made of organic cations, and organic/inorganic anions). Because the quality (dense and smooth) of electrodeposits is a direct function of the electrochemical reduction rate (slower the better), the major expectation was that addition of organic molecules would provide the desired slowing down of electroreduction effect, avoiding the undesired dependence on mass transfer. What was learned is summarized in seven key areas.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Computational fluid dynamics analysis of char conversion in Sandia’s pressurized entrained flow reactor

Design and analysis of practical reactors utilizing solid feedstocks rely on reaction rate parameters that are typically generated in lab-scale reactors. Evaluation of the reaction rate information often relies on assumptions of uniform temperature, velocity, and species distributions in the reactor, in lieu of detailed measurements that provide local information. This assumption might be a source of substantial error, since reactor designs can impose significant inhomogeneities, leading to data misinterpretation. Spatially resolved reactor simulations help understand the key processes within the reactor and support the identification of severe variations of temperature, velocity, and species distributions. In this work, Sandia’s pressurized entrained flow reactor is modeled to identify inhomogeneities in the reaction zone. Tracer particles are tracked through the reactor to estimate the residence times and burnout ratio of introduced coal char particles in gasifying environments. The results reveal a complex mixing environment for the cool gas and particles entering the reactor along the centerline and the main high-speed hot gas reactor flow. Furthermore, the computational fluid dynamics (CFD) results show that flow asymmetries are introduced through the use of a horizontal gas pre-heating section that connects to the vertical reactor tube. Computed particle temperatures and residence times in the reactor differ substantially from the idealized plug flow conditions typically evoked in interpreting experimental measurements. Furthermore, experimental measurements and CFD analysis of heat flow through porous refractory insulation suggest that for the investigated conditions (1350 °C, <20 atm), the thermal conductivity of the insulation does not increase substantially with increasing pressure.

47 OTHER INSTRUMENTATION↗

Synthesis of a novel multifunctional organic–inorganic nanocomposite for metal ions and organic dye removals

In this study, we used solvent assisted mechano-synthesis strategies to form multifunctional organic–inorganic nanocomposites capable of removing both organic and inorganic contaminants. A zeolite X (Ze) and activated carbon (AC) composite was synthesized via state-of-the-art mechanical mixing in the presence of few drops of water to form Ze/AC. The second composite (Ze/L/AC) was synthesized in a similar fashion, however this composite had the addition of disodium terephthalate as a linker. Both materials, Ze/AC and Ze/L/AC, were characterized using scanning electron microscope (SEM), energy-dispersive X-ray spectroscopy (EDS), Powdered X-ray diffraction (P-XRD), Fourier-transform infrared spectrometry (FTIR), Accelerated Surface Area and Porosimetry System (ASAP), and thermal gravimetric analysis (TGA). The SEM–EDS displayed the surface structure and composition of each material. The sodium, oxygen and carbon contents increased after linker connected Ze and AC. The P-XRD confirmed the crystallinity of each material as well as the composites, while FTIR indicated the function groups (C=C, O–H) in Ze/L/AC. The contaminant adsorption experiments investigated the effects of pH, temperature, and ionic strength on the adsorption of methylene blue (MB) and Co(II) for each material. In MB adsorption, the first-order reaction rate of Ze/L/AC (0.02 h -1 ) was double that of Ze/AC (0.01 h -1 ). The reaction rate of Ze/L/AC (4.8 h -1 ) was also extraordinarily higher than that of Ze/AC (0.6 h -1 ) in the adsorption of Co(II). Ze/L/AC composite achieved a maximum adsorption capacity of 44.8 mg/g for MB and 66.6 mg/g for Co(II) ions. The MB adsorption of Ze/AC and Ze/L/AC was best fit in Freundlich model with R 2 of 0.96 and 0.97, respectively, which indicated the multilayer adsorption. In the Co(II) adsorption, the data was highly fit in Langmuir model with R 2 of 0.94 and 0.92 which indicated the monolayer adsorption. These results indicated both materials exhibited chemisorption. The activation energy of Ze/L/AC in MB adsorption (34.9 kJ mol -1 ) was higher than that of Ze/L/AC in Co (II) adsorption (26 kJ mol -1 ).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

(U) LNK3DNT Capability in SENSMG Tested with Transport Correction

The SENSMG multigroup neutron sensitivity code can read materials and geometry from redoin and lnk3dnt files written by the PARTISN multigroup discrete ordinates code or the MCNP6 Monte Carlo code. Reference 5 described an initial version of this capability. Reference 6 introduced two important extensions: 1) Reaction-rate ratios are now allowed as responses with redoin/lnk3dnt inputs; and 2) Sensitivities of reaction-rate ratios to mass densities and interface locations are now calculated (for all problems, not just redoin/lnk3dnt problems). In this report, we document the testing of the redoin/lnk3dnt capability when used with transport correction. PARTISN’s transport corrections are described in Ref. 3, and Refs. 7 and 8 discuss the calculation of cross-section sensitivities when transport corrections are applied. References 7 and 8 verify SENSMG for problems with transport correction using central differences. This report verifies the capability with redoin/lnk3dnt inputs by comparison with regular SENSMG inputs. Unlike Refs. 5 and 6, in this report we use a spherical test problem because the sensitivity of the response with respect to the highest-order scattering is zero in cylinders due to the use of flux moments in the inner products.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

First direct measurement of the 13 $\mathrm{N(α, ρ)}$ 16 $\mathrm{O}$ reaction relevant for core-collapse supernovae nucleosynthesis

We report that understanding the explosion mechanism of a core-collapse supernova (CCSN) is important to accurately model CCSN scenarios for different progenitor stars using model-observation comparisons. The uncertainties of various nuclear reaction rates relevant for CCSN scenarios strongly affect the accuracy of these stellar models. Out of these reactions, the 13 N(α, p) 16 O reaction has been found to affect various stages of a CCSN at varying temperatures. This work presents the first direct measurement of the 13 N(α, p) 16 O reaction performed using a 34.6 MeV beam of radioactive 13 N ions and the active-target detector MUSIC (MUlti-Sampling Ionization Chamber) at Argonne National Laboratory. The resulting total 13 N(α, p) 16 O reaction cross sections from this measurement in the center-of-mass energy range of 3.26 - 6.02 MeV are presented and compared with calculations using the Hauser-Feshbach formalism. Uncertainties in the reaction rate have been dramatically reduced at CCSN temperatures.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Electronic parameters in cobalt-based perovskite-type oxides as descriptors for chemocatalytic reactions

Perovskite-type transition metal (TM) oxides are effective catalysts in oxidation and decomposition reactions. Yet, the effect of compositional variation on catalytic efficacy is not well understood. The present analysis of electronic characteristics of B-site substituted LaCoO3 derivatives via in situ X-ray absorption spectroscopy (XAS) establishes correlations of electronic parameters with reaction rates: TM t2g and eg orbital occupancy yield volcano-type or non-linear correlations with NO oxidation, CO oxidation and N2O decomposition rates. Covalent O 2p-TM 3d interaction, in ultra-high vacuum, is a linear descriptor for reaction rates in NO oxidation and CO oxidation, and for N2O decomposition rates in O2 presence. Covalency crucially determines the ability of the catalytically active sites to interact with surface species during the kinetically relevant step of the reaction. The nature of the kinetically relevant step and of surface species involved lead to the vast effect of XAS measurement conditions on the validity of correlations.

Science & Technology - Other Topics↗

High-precision measurements of half-lives for 69 Ge, 73 Se, 83 Sr, 85 mSr, and 63 Zn radionuclides relevant to the astrophysical p-process via photoactivation at the Madison Accelerator Laboratory

The ground state half-lives of 69 Ge, 73 Se, 83 Sr, 63 Zn, and the half-life of the 1/2 - isomer in 85 Sr have been measured with high precision using the photoactivation technique at an unconventional bremsstrahlung facility that features a repurposed medical electron linear accelerator. The γ -ray activity was counted over about 6 half-lives with a high-purity germanium detector, enclosed into an ultra low-background lead shield. The measured half-lives are: T 1/2 ( 69 Ge) = 38.82 ± 0.07 (stat) ± 0.06 (sys) h; T 1/2 ( 73 Se) = 7.18 ± 0.02 (stat) ± 0.004 (sys) h; T 1/2 ( 83 Sr) = 31.87 ± 1.16 (stat) ± 0.42 (sys) h; T 1/2 ( 85m Sr) = 68.24 ± 0.84 (stat) ± 0.11 (sys) min; T 1/2 ( 63 Zn) = 38.71 ± 0.25 (stat) ± 0.10 (sys) min. These high-precision half-life measurements will contribute to a more accurate determination of corresponding ground-state photoneutron reaction rates, which are part of a broader effort of constraining statistical nuclear models needed to calculate stellar nuclear reaction rates relevant for the astrophysical p -process nucleosynthesis.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Combining scaling relationships overcomes rate vs. overpotential tradeoffs in O2 molecular electrocatalysis

The development of advanced chemical-to-electrical energy conversions requires fast and efficient electrocatalysis of multi-electron/multi-proton reactions, such as the oxygen reduction reaction 10 (ORR). Using molecular catalysts, correlations between the reaction rate and energy efficiency have recently been identified. Improved catalysis requires circumventing the rate vs. overpotential tradeoffs implied by such ‘scaling relationships.’ Described here is an ORR system—using a soluble iron-porphyrin and weak acids—with the best reported combination of rate and efficiency for a soluble ORR catalyst. This advance is achieved not by “breaking” scaling relationships but 15 rather by combining two of them. Key to this behavior is a polycationic ligand, which enhances anionic ligand binding and changes the catalyst E1/2. These results show how combining scaling relationships is powerful way towards improved electrocatalysis.

Martin, Daniel J.↗

An a priori evaluation of a principal component and artificial neural network based combustion model in diesel engine conditions

A principal component analysis (PCA) and artificial neural network (ANN) based chemistry tabulation approach is presented. ANNs are used to map the thermochemical state onto a low-dimensional manifold consisting of five control variables that have been identified using PCA. Three canonical configurations are considered to train the PCA-ANN model: a series of homogeneous reactors, a nonpremixed flamelet, and a two-dimensional lifted flame. The performance of the model in predicting the thermochemical manifold of a spatially-developing turbulent jet flame in diesel engine thermochemical conditions is a priori evaluated using direct numerical simulation (DNS) data. The PCA-ANN approach is compared with a conventional tabulation approach (tabulation using ad hoc defined control variables and linear interpolation). The PCA-ANN model provides higher accuracy and requires several orders of magnitude less memory. Here, these observations indicate that the PCA-ANN model is superior for chemistry tabulation, especially for modelling complex chemistries that present multiple combustion modes as observed in diesel combustion. The performance of the PCA-ANN model is then compared to the optimal estimator, i.e. the conditional mean from the DNS. The results indicate that the PCA-ANN model gives high prediction accuracy, comparable to the optimal estimator, especially for major species and the thermophysical properties. Higher errors are observed for the minor species and reaction rate predictions when compared to the optimal estimator. It is shown that the prediction of minor species and reaction rates can be improved by using training data that exhibits a variation of parameters as observed in the turbulent flame. The output of the ANN is analysed to assess mass conservation. It is observed that the ANN incurs a mean absolute error of 0.05% in mass conservation. Furthermore, it is demonstrated that this error can be reduced by modifying the cost function of the ANN to penalise for deviation from mass conservation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Leveraging Triphenylphosphine-Containing Polymers to Explore Design Principles for Protein-Mimetic Catalysts

Complex interactions between noncoordinating residues are significant yet commonly overlooked components of macromolecular catalyst function. While these interactions have been demonstrated to impact binding affinities and catalytic rates in metalloenzymes, the roles of similar structural elements in synthetic polymeric catalysts remain underexplored. Using a model Suzuki–Miyuara cross-coupling reaction, we performed a series of systematic studies to probe the interconnected effects of metal–ligand cross-links, electrostatic interactions, and local rigidity in polymer catalysts. To achieve this, a novel bifunctional triphenylphosphine acrylamide (BisTPPAm) monomer was synthesized and evaluated alongside an analogous monofunctional triphenylphosphine acrylamide (TPPAm). In model copolymer catalysts, increased initial reaction rates were observed for copolymers untethered by Pd complexation (BisTPPAm-containing) compared to Pd-cross-linked catalysts (TPPAm-containing). Further, incorporating local rigidity through secondary structure-like and electrostatic interactions revealed nonmonotonic relationships between composition and the reaction rate, demonstrating the potential for tunable behavior through secondary-sphere interactions. Lastly, through rigorous cheminformatics featurization strategies and statistical modeling, we quantitated relationships between chemical descriptors of the substrate and reaction conditions on catalytic performance. Collectively, these results provide insights into relationships among the composition, structure, and function of protein-mimetic catalytic copolymers.

Catalysts↗

Improved nuclear physics near A = 61 refines urca neutrino luminosities in accreted neutron star crusts

We performed Penning trap mass measurements for 61 Zn at the National Superconducting Cyclotron Laboratory and NuShellX calculations of the 61 Zn and 62 Ga structure using the GXPF1A Hamiltonian to obtain improved estimates of the 61 Zn(p,γ) 62 Ga and 60 Cu(p,γ) 61 Zn reaction rates. Surveying astrophysical conditions for type-I x-ray bursts with the code mesa, implementing our improved reaction rates, and taking into account updated nuclear masses for 61 V and 61 Cr from the recent literature, we refine the neutrino luminosity from the important mass number A = 61 urca cooling source in accreted neutron-star crusts. Furthermore, this improves our understanding of the thermal barrier between deep heating in the crust and the shallow depths where extra heat is needed to explain x-ray superbursts, as well as the expected signature of crust urca neutrino emission in light curves of cooling transients

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Surface Charge Predicts the Presence of Cation Effects in Electrocatalysis

The identity of electrolyte cations has an important influence on the rates of many electrocatalytic reactions, but these effects are not always observed. Recently, we found that the surface charge of the catalyst, quantified by the potential of zero total charge (PZTC), is a useful heuristic for predicting when cation effects will be observed for the oxygen reduction reaction (ORR). Here, we demonstrate that this descriptor allows us to rationalize the observation or absence of cation effects across a range of conditions, reactions (the hydrogen evolution reaction, the ORR, methanol oxidation, ethylene glycol oxidation, glycerol oxidation, and glucose reduction) and metal surfaces (Pt, Pd, Ag, and Au). These results suggest that when the reaction’s operating potential is negative of the metal’s PZTC, electrolyte cations accumulate at the catalyst surface and influence reaction rates. As a result, when reactions occur positive of the PZTC, cation effects are not observed.

Cations↗

Properties of states near 𝐸 𝑥 = 6 MeV in 18 Ne through 17 F +𝑝 scattering

The rate of energy production in the hot-CNO cycle and breakout to the rapid-proton capture process in Type I X-ray bursts is strongly related to the 14 O⁡(𝛼,𝑝)⁢ 17 F reaction rate. The properties of states in 18 Ne near 𝐸 𝑥 = 6.1–6.3 MeV are important for understanding the 14 O⁡(𝛼,𝑝)⁢ 17 F reaction rate. In order to study 18 Ne resonances around this energy region, the RESOLUT radioactive-ion beam facility at Florida State University was used to perform 17 F⁡(𝑝,𝑝)⁢ 17 F elastic scattering on a polypropylene target under inverse kinematics. Scattered protons were detected in a silicon-strip detector array while recoiling 17 F ions were detected in coincidence in a gas ionization detector. An 𝑅-matrix analysis of measured cross sections was conducted along with a reanalysis of data from previous 17 F +𝑝 measurements. All the data analyzed are well described by a consistent set of parameters with a 1 − assignment for a state at 6.14(1) MeV. A second comparable solution is also found with a 3 − assignment for the 6.14(1) MeV state. There is no conclusive evidence supporting one of the two solutions over the other. The rates of the 14 O⁡(𝛼,p)⁢ 17 F reaction that are determined from the two solutions differ by up to an order of magnitude.

6 ≤ A ≤ 19↗

Finite flame thickness effects on Kolmogorov-Petrovsky-Piskunov turbulent burning velocities

KPP (Kolmogorov-Petrovsky-Piskunov) solutions of the reaction-diffusion equation have application in various physical phenomena occurring in biology, ecology, and reacting flows. In particular, these solutions are commonly used in turbulent combustion to scale turbulent burning velocities. Subject to certain conditions on reaction rate profile through the flame brush and turbulent diffusivity, this theory relates the turbulent burning velocity to the derivative of the reaction rate ($\tilde{ω}$) at the leading edge of the flame brush ($d\tilde{ω}$/$d\tilde{c}$ | $\tilde{c} =$0 ). Such waves are often referred to as “pulled fronts.” However, turbulent flames never actually satisfy the KPP conditions for a pulled front, as the turbulent flame brush, parametrized here by the thickness δ t , consists of an ensemble of laminar flamelets of thickness δ, where ε=δ/δ t $\ll$ 1 is very small, but nonzero, and $d\tilde{ω}$ /$d\tilde{c}$ tends to zero at the brush leading edge for high activation energy, combustion-type kinetics. Here, this paper analyzes these effects on KPP wave solutions, parametrized by ε=δ/δ t and Zeldovich number Ze focusing on whether turbulent flames retain their pulled front character and what the correction to the KPP wave speed is. Variational solutions of the reaction-diffusion equation show that the solution can be expanded in powers of 1/|ln⁡ε|. Both numerical and asymptotic results are presented, showing that the wave still exhibits pulled front solutions but with significant corrections to the KPP result. The leading order correction is of the form |ln⁡ε| –2 and independent of Ze. Higher order corrections are function of both ε and Ze. However, the dominant factor influencing the wave speed correction is due to the finite ε, with Ze exhibiting a weaker effect.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Chemical-damage MINE: A database of curated and predicted spontaneous metabolic reactions

Spontaneous reactions between metabolites are often neglected in favor of emphasizing enzyme-catalyzed chemistry because spontaneous reaction rates are assumed to be insignificant under physiological conditions. However, synthetic biology and engineering efforts can raise natural metabolites' levels or introduce unnatural ones, so that previously innocuous or nonexistent spontaneous reactions become an issue. Problems arise when spontaneous reaction rates exceed the capacity of a platform organism to dispose of toxic or chemically active reaction products. While various reliable sources list competing or toxic enzymatic pathways' side-reactions, no corresponding compilation of spontaneous side-reactions exists, nor is it possible to predict their occurrence. We addressed this deficiency by creating the Chemical Damage (CD)-MINE resource. First, we used literature data to construct a comprehensive database of metabolite reactions that occur spontaneously in physiological conditions. We then leveraged this data to construct 148 reaction rules describing the known spontaneous chemistry in a substrate-generic way. We applied these rules to all compounds in the ModelSEED database, predicting 180,891 spontaneous reactions. The resulting (CD)-MINE is available at https://minedatabase.mcs.anl. gov/cdmine/#/home and through developer tools. We also demonstrate how damage-prone intermediates and end products are widely distributed among metabolic pathways, and how predicting spontaneous chemical damage helps rationalize toxicity and carbon loss using examples from published pathways to commercial products. We explain how analyzing damage-prone areas in metabolism helps design effective engineering strategies. Finally, we use the CD-MINE toolset to predict the formation of the novel damage product N-carbamoyl proline, and present mass spectrometric evidence for its presence in Escherichia coli.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Investigation of 31 P levels near the proton threshold with nuclear resonance fluorescence and the impact on the 30 Si (𝑝,𝛾)⁢ 31 P thermonuclear rate

We investigated the nuclear structure of 31 P near the proton threshold using nuclear resonance fluorescence (NRF) to refine the properties of key resonances in the 30 Si (𝑝,𝛾)⁢ 31 P reaction, which is critical for nucleosynthesis in stellar environments. Excitation energies and spin-parities were determined for several states, including two unobserved resonances at 𝐸 𝑟 = 18.7keV and 𝐸 𝑟 = 50.5keV. The angular correlation analysis enabled the first unambiguous determination of the orbital angular momentum transfer for these states. These results provide a significant update to the 30 Si (𝑝,𝛾)⁢ 31 P thermonuclear reaction rate, with direct implications for models of nucleosynthesis in globular clusters and other astrophysical sites. The revised rate is substantially lower than previous estimates at temperatures below 200 MK, affecting predictions for silicon isotopic abundances in stellar environments. Furthermore, our work demonstrates the power of NRF in constraining nuclear properties, and provides a framework for future studies of low-energy resonances relevant to astrophysical reaction rates.

20 ≤ A ≤ 38↗

Ga + -Chabazite Zeolite: A Highly Selective Catalyst for Nonoxidative Propane Dehydrogenation

Ga-chabazite zeolites (Ga-CHA) have been found to efficiently catalyze propane dehydrogenation with high propylene selectivity (96%). In situ FTIR spectroscopy and pulse titrations are employed to determine that upon reduction, surface Ga 2 O 3 is reduced and diffuses into the zeolite pores, displacing the Brønsted acid sites (BAS) and forming extra-framework Ga + sites. This isolated Ga + site reacts reversibly with H 2 to form GaHx (2034 cm -1 ) with an enthalpy of formation of ~ -51.2 kJ·mol -1 , a result supported by Density functional theory (DFT) calculations. The initial C 3 H 6 dehydrogenation rates decrease rapidly (40%) during the first 100 min and then decline slowly afterward, while the C 3 H 6 selectivity is stable at ~ 96%. The reduction in the reaction rate is correlated with the formation of polycyclic aromatics inside the zeolite (using UV-vis spectroscopy) indicating that the accumulation of polycyclic aromatics is the main cause of the deactivation. The carbon species formed can be easily oxidized at 600 °C with complete recovery of the PDH catalytic properties. The correlations between GaH x vs. Ga/Al ratio, and PDH rates vs. Ga/Al ratio show that extra-framework Ga + is the active center catalyzing propane dehydrogenation. The higher reaction rate on Ga + than In + in CHA zeolites, by a factor of 43, is the result of differences in the stabilization of the transition state due to the higher stability of Ga 3+ vs. In 3+ . The uniformity of the Ga + sites in this material makes it an excellent model for the molecular understanding of metal cation exchanged hydrocarbon interactions in zeolites.

10 SYNTHETIC FUELS↗

Particulate Fuel Modeling of MC 2 -3 using Iterative Local Spatial Self-shielding Method

We report a new spatial self-shielding method for particulate fuels has been developed based on disadvantage factors and implemented in the MC 2 -3 code. This method named the iterative local spatial self-shielding (ILSS) method considers the shadowing effect of randomly distributed particles on spatial self-shielding in particles through a homogenized composition region added outside the particle of interest at the center. The self-shielded cross sections of the central particle are determined iteratively since they are used in determining the cross sections of the homogenized composition region. The ILSS method was verified for infinite stochastic medium problems of single and multiple types of particles, VHTR unit cell problems, and HTTR assembly problems. The verification test results show that the ILSS method accurately predicts the stochastic particle shadowing effect and reaction rates in particles, whereas the regular array model and the stochastic collision probability method underpredict the particle shadowing effect and overestimate reaction rates in particles.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗