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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

POLCA8 - modelling of cross section variations inside hexagonal assemblies

This paper presents the POLCA8 approach for modelling non-constant cross section distributions inside hexagonal fuel assemblies. The multigroup diffusion equation is modified to account for intranodal cross section variations. The obtained equation is solved in a node-wise manner based on the Fourier expansion method. As a result of varying cross sections, the solution includes a particular part additionally to the homogeneous one. A method for obtaining the particular solution is derived. Numerical tests on a VVER-1000 core are presented showing the impact of cross-section variations to some key parameters for reactor operation. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2019

Nuclear Data and Benchmarking Program: Nuclear Data Performance Assessment for Advanced Reactors

Over the last several Evaluated Nuclear Data File (ENDF)/B releases, many updates have been introduced to the nuclear data libraries that can significantly change computational results. These changes can be particularly important for advanced reactor concepts, which are not as thoroughly investigated as those used in light water reactor (LWR) systems. Therefore, a performance assessment of the ENDF/B libraries using the SCALE 6.2.3 code package was conducted under the auspices of the U.S., Department of Energy Office of Nuclear Energy (DOE-NE). The following systems relevant to the advanced reactor community were chosen as subject for investigation in this report: sodium cooled fast reactor systems, graphite moderated high temperature gas-cooled reactors, and several molten salt reactor models. At first, the similarity of the integral performance of the ENDF/B-VII.1 and ENDF/B-VIII.0 nuclear data libraries caused by compensating errors in important differential data was demonstrated. In calculations for a shipping container of high-assay low enriched uranium, the data of individual isotopes were systematically swapped between the two ENDF/B libraries. An eigenvalue difference of up to 450 pcm was found due to the use of 235 U and 238 U from one library and 1 H and 16 O from the other library. This clearly demonstrates a cross-correlation between reaction data sets of different isotopes within a library that should be reported in the evaluations. For sodium-cooled fast reactor (SFR) fuel assemblies, significant eigenvalue (k inf ) differences (200– 450 pcm) were found between calculations using the 2011 ENDF/B-VII.1 data and 2018 ENDF/B-VIII.0 data. These differences were mainly caused by updates of 238 U and 239 Pu neutron cross sections. Results from the multigroup (MG) calculations further revealed that the group structure of the applied MG library strongly influences the MG bias due to the importance of an appropriate energy resolution of the resonances in higher energy ranges. The application of previously used MG libraries requires new verification for advanced reactor simulation in comparisons with reference continuous-energy calculations. Nuclear data uncertainty analyses of these SFR systems resulted in eigenvalue uncertainties between 1,400 and 1,800 pcm, which are three to four times higher than corresponding uncertainties in light water reactor (LWR) systems. The main contributor to this uncertainty was found to be inelastic scattering on 238 U, which shows an uncertainty of up to 50% in the fast energy range. Other important contributors are the scattering reactions of 56 Fe and 23 Na which have so far not appeared in LWR analysis. Since the largest contribution to the eigenvalue uncertainty of SFR systems is coming from scattering reactions, it is expected that uncertainties in the angular scattering distributions also have a significant impact. Those uncertainties are, however, not available for the majority of nuclides, and the capabilities to determine sensitivities to this data are currently underdeveloped. For two graphite moderated high temperature gas-cooled reactor (HTGR) benchmarks, only the ENDF/BVII. 1 calculations resulted in consistent eigenvalues (k eff ) with the corresponding experimental measurements. Eigenvalue differences of about 1,000 pcm were found between the 2006 ENDF/B-VII.0 data and the 2011 ENDF/B-VII.1 data, primarily due to an updated carbon capture cross section in the thermal energy range in the later ENDF/B release. The ENDF/B-VIII.0 eigenvalue was larger than the ENDF/B-VII.1 eigenvalue by about 300 pcm mainly due to updates in multiple 235 U neutron cross sections, with offsetting updates in the 238 U cross sections. With ENDF/B-VIII.0, graphite can be modeled as perfect crystal or with two different porosities. The choice of the graphite evaluation can have a significant influence of the eigenvalue. For a HTGR benchmark, maximum eigenvalue differences as high as 650 pcm due to different porosities were observed. More detailed studies of the impact of the porosity are necessary while considering that the graphite porosity can vary between the used materials and changes as a function of neutron fluence. xii The uncertainty of the HTGR eigenvalues due to nuclear data uncertainties was found between 500 and 600 pcm, with the top contributor being the neutron multiplicity of 235 U. A gap in the form of missing uncertainties in graphite thermal scattering data, that might have significant impact on HTGR reactors, was identified. This gap is being investigated by the DOE-NE Nuclear Data and Benchmarking Program, as documented in a separate report The fast spectrum molten salt reactor calculations revealed similar comparisons as for the SFR assemblies. The eigenvalue uncertainties were significantly influenced by inelastic scattering on 238 U, while the impact of angular scattering distributions is unknown. For the graphite and zirconium hydride moderated system, eigenvalue uncertainties of up to 700 pcm were observed, requiring in depth analyses of the cross sections and corresponding uncertainties of the included materials. In general, it was observed that the flux spectra of the various molten salt reactor systems show significant differences, even between a fresh state and a depleted state. The choice of the energy group structure of MG calculations is therefore highly relevant; the applicability of previously used MG libraries needs to be verified. Due the unavailability of pin power measurements of advanced reactor systems, pin power calculations with both ENDF/B-VII.1 and VIII.0 data were performed for a light water reactor and compared to corresponding measurements. Both calculations show good agreement with the measurements. A comparison between the ENDF/B-VII.1 and VIII.0 results revealed small differences, mostly in the range of about 0.2%.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2020

(U) Preliminary Notes on Bondarenko Self-Shielded Cross Section Sensitivities

The Bondarenko method for resonance self-shielding was recently implemented in the PARTISN multigroup discrete ordinates code. This report derives the sensitivities of self-shielded cross sections with respect to nuclide densities and the subsequent sensitivities of k eff with respect to nuclide densities. Numerical results are presented for two test problems.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2022

Importance of 3-D S{sub N} depletion in non-proliferation using BSOLVE

We present a single Pressurized Water Reactor (PWR) 3-D fuel rod design for depletion analysis using BSOLVE, our newly developed Runge-Kutta-Fehlberg based depletion code. BSOLVE is coupled with the deterministic 3-D S{sub N} particle transport code, PENTRAN, applied here with a 4-neutron energy group comparison to Continuous Energy (C/E) SERPENT2 Monte Carlo results. Differences are expected, as PENTRAN+BSOLVE retains full (multi-group) energy information for reactions, nuclide specific fission contributions, and energy dependent fission yields, using the latest available ENDF-BVIII data, important to retain accurate burned fuel inventories; SERPENT2 collapses burnup reactions to a single energy value. For depletion times up to ∼ 700 days and typical PWR power densities, relative differences between multigroup 3-D S{sub N} with full energy data and Monte Carlo one group burnup for trans-uranium nuclide concentrations and fission products are up to ∼20%. System eigenvalues are consistent, but with differences early and late in the cycle attributed to multigroup vs. C/E Monte Carlo cross sections. This work highlights the importance of low variance transport driven burnup for non-proliferation concerns, since plutonium quality varies significantly along axial lengths, and is more challenging to converge using Monte Carlo; details of depletion steps with spatial/zone dependent plutonium quality are provided. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

(U) A Code System for Cross-Section Uncertainty Propagation for PARTISN

A rudimentary code system has been developed for propagating neutron cross-section uncertainties to response uncertainties using the PARTISN multigroup discrete-ordinates neutron transport code. The code system uses the first-order sandwich rule with sensitivities computed using SENSMG and covariances computed using NJOY. Databases of reaction cross sections and covariances using ENDF/B-VIII.0 data in the LANL standard 30-group structure have been precalculated. The final uncertainty in a k eff example problem compares well with the result from TOFFEE, a similar code that propagates neutron cross-section uncertainties to response uncertainties using the MCNP6 Monte Carlo neutron transport code. Presently, neither code system propagates uncertainties in $\overline{v}$, $\overline{μ}$, or χ, and neither code system propagates nuclide-nuclide covariances

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1973

Transport analysis of measured neutron leakage spectra from spheres as tests of evaluated high energy cross sections

Integral tests of evaluated ENDF/B high-energy cross sections have been made by comparing measured and calculated neutron leakage flux spectra from spheres of various materials. An Am-Be (alpha,n) source was used to provide fast neutrons at the center of the test spheres of Be, CH2, Pb, Nb, Mo, Ta, and W. The absolute leakage flux spectra were measured in the energy range 0.5 to 12 MeV using a calibrated NE213 liquid scintillator neutron spectrometer. Absolute calculations of the spectra were made using version 3 ENDF/B cross sections and an S sub n discrete ordinates multigroup transport code. Generally excellent agreement was obtained for Be, CH2, Pb, and Mo, and good agreement was observed for Nb although discrepancies were observed for some energy ranges. Poor comparative results, obtained for Ta and W, are attributed to unsatisfactory nonelastic cross sections. The experimental sphere leakage flux spectra are tabulated and serve as possible benchmarks for these elements against which reevaluated cross sections may be tested.

Bogart, D. D.↗
DOE OSTI2022

A new approach for resonance treatment of doubly heterogeneous fuel using the RSE method

A new resonance calculation method for the doubly-heterogeneous (DH) fuels such as high- temperature gas-cooled reactor fuel is proposed based on the resonance calculation based on Spectral Expansion (RSE) method. The concept of pointwise disadvantage factor for fuel grain is taken into account to treat the DH fuels. The verification calculation is carried out for simplified single fuel cell and fuel compact consisting of five fuel cells and graphite moderator. The calculation results indicate that the present method can appropriately handle the space- dependent self-shielding effect for DH fuels. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Fission Product Yield Data Adjustment in a Prototype Version of TSURFER

The TSURFER (Tool for Sensitivity/Uncertainty analysis of Response Functionals using Experimental Results) module of Oak Ridge National Laboratory’s (ORNL’s) SCALE code system has been updated to perform nuclear data adjustments for fixed-source irradiation/depletion problems. TSURFER uses a generalized linear least squares (GLLS) approach to consolidate a prior set of measured responses and corresponding calculated values to create the most self-consistent set of nuclear data. Traditionally, TSURFER adjustments have been performed for multigroup nuclear data such as reaction cross sections. In this work, TSURFER is expanded to perform adjustments to independent fission product yields and branching ratios that need equality constraints. To preserve equality constraints after the data adjustment procedure, an updated GLLS formulation includes a new Lagrange multiplier that forces data adjustment to sum to 0 for a given fission yield/branching ratio parent. A test problem illustrates that the newly updated TSURFER module satisfies the required constraint that adjustments for fission yield data sum to 0.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1969

GAMBIT program

GAMBIT computer program provides multigroup flux and current averaged neutron cross sections for input to transport programs. The fast neutron compilation includes P/0/ and P/1/ elastic scattering transfer matrices, inelastic scattering matrices, n,2n cross section matrices, absorption and fission cross sections for all isotopes.

Collier, G.↗
DOE OSTI2017

Open Source Release of NJOY2016 and NJOY21

NJOY has been the standard for nuclear data processing for many decades. NJOY is a comprehensive computer code used to produce point-wise and multigroup nuclear data application libraries from cross sections and related quantities obtained from evaluated nuclear data in the Evaluated Nuclear Data Format (ENDF). NJOY was first publicly released in 1977 and distributed by what is now the Radiation Safety Information Computational Center (RSICC) at Oak Ridge National Laboratory and the National Energy Software Center (NESC) at Argonne National Laboratory. From that time until the release of NJOY2012, NJOY has been distributed by RSICC and made available to researchers outside the United States by agreements between RSICC and the NEA Databank. NJOY2012 was distributed by the Feynman Center at Los Alamos National Laboratory which did not have agreements with the NEA Databank, thus making it more difficult for non US citizens to obtain copies of NJOY2012. Furthermore, NJOY has had export control restrictions preventing some researchers from obtaining NJOY at all. Two new versions of NJOY have been released, NJOY2016 and NJOY21, in January of 2017. Both NJOY2016 and NJOY21 have been released with no export control restrictions and are distributed with an open-source license. This is a big departure from previous releases and impacts not only who has access to NJOY, but also how updates are made available to users and how collaboration is facilitated among interested developers. In addition to distributing NJOY2016 and NJOY21 with an open-source license, these two new versions provide new capabilities for NJOY which will maintain NJOY as the standard for nuclear data processing into the foreseeable future. We report in this summary about the changes that come with these two new versions of NJOY and how this impacts the users and long-time contributors to NJOY.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

(U) Average Scattering Angle Cosine Sensitivities

The Evaluated Nuclear Data File (ENDF) provides covariances of the average scattering angle cosine $\overline{μ}$ for 117 nuclides, and the NJOY nuclear data processing code can process these covariances. To propagate them to the uncertainty of a response due to uncertainties in $\overline{μ}$ requires sensitivities of the response with respect to $\overline{μ}$. This report uses NJOY’s definition of $\overline{μ}$ and derives a relationship between the sensitivity of a response to $\overline{μ}$ and the sensitivity of the response to the anisotropic P 1 elastic scattering cross section. This relationship has been implemented in the multigroup neutron sensitivity code SENSMG, which relies on the discrete ordinates code PARTISN for the neutron transport calculations. Kodeli has also calculated sensitivities with respect to $\overline{μ}$ and associated uncertainties. However, the formal derivation of this paper shows that the definition of the sensitivity with respect to $\overline{μ}$ is ambiguous because there are multiple ways to change $\overline{μ}$ by changing scattering cross sections. Here we derive two such ways. Both are implemented in SENSMG. This report is organized as follows. Section II discusses $\overline{μ}$ and its significance. Section III presents the equations used for the sensitivity of a response with respect to $\overline{μ}$, and Section IV discusses how to compute these sensitivities with SENSMG and MCNP6.3. Section V is a fast-spectrum test problem, and Sec. VI is a thermal-spectrum problem. Section VII is a summary. The example problem inputs are listed in the appendix.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

(U) Energy-Dependent Perturbations of Scattering Cross Sections Using the PERT Card in MCNP6.2

The PERT card is used for first- and second-order perturbations of material densities, isotope densities, and isotope cross sections in the MCNP6.2 Monte Carlo code. Using the PERT card for firstand second-order sensitivities is straightforward. Reference 2 only looked at density perturbations with no energy dependence. This report looks at the sensitivity of a response to scattering cross sections as a function of energy and finds that there is a bug in the PERT capability. The SENSMG multigroup neutron sensitivity code was recently given the capability of computing sensitivities to user-specified reactions whose cross sections are available in a user-supplied NJOY output file. SENSMG uses the PARTISN multigroup discrete ordinates code for the transport. The NJOY-reaction capability is similar to that of SUSD3D, which also uses PARTISN for the multigroup transport. The PERT bug was identified by comparing MCNP6.2 outputs with SENSMG outputs. The next section of this report describes the test problem. Section III presents the MCNP6.2 PERT bug and proposes a solution. Section IV is a summary and conclusions. The SENSMG and MCNP input files are listed in the appendix.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2019

Problem Description

Gobstopper.inp is a test problem that is designed to be a nice middle-of-the-road problem that balances work done in tracking and collisions. It is domain decomposed to stress particle communication between domains while in the tracking phase. This is an eigenvalue problem that is forced to run for 25 cycles with 10,000 particles per cycle. The final eigenvalue (keff) should be around 0.998 with some uncertainty reported. The cross sections are stored in a 230 energy multigroup fashion, but the collisions use continuous energy physics. The geometry is 1,000 nested spheres made of random materials from the list of materials found in a reactor. The shells are uniformly spaced up to 10 centimeters. However, 80% of the shells are made of highly enriched uranium found in the Godiva criticality experiment. This was to push the criticality eigenvalue (keff) closer to 1.0. The material compositions may be found in the material section. The densities are all the same for each material and can be found in the cell description. The geometry is further decomposed into 64 (4 X 4 X 4) cube domains. The problem is initially sourced in the first cycle with particles uniformly over a 10 cm sphere. Their energy spectrum is represented by the outgoing fission spectrum from U-235 nucleus hit by a 1.5 MeV neutron. The tallies are mostly turned off except for the balance, eigenvalue and spectrum tallies. The spectrum and eigenvalue tallies are written out to the .plt file. The balance and eigenvalue tallies are written to the .out file.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2017

A Comparison of Monte Carlo and Deterministic Solvers for keff and Sensitivity Calculations

Verification and validation of our solutions for calculating the neutron reactivity for nuclear materials is a key issue to address for many applications, including criticality safety, research reactors, power reactors, and nuclear security. Neutronics codes solve variations of the Boltzmann transport equation. The two main variants are Monte Carlo versus deterministic solutions, e.g. the MCNP [1] versus PARTISN [2] codes, respectively. There have been many studies over the decades that examined the accuracy of such solvers and the general conclusion is that when the problems are well-posed, either solver can produce accurate results. However, the devil is always in the details. The current study examines the issue of self-shielding and the stress it puts on deterministic solvers. Most Monte Carlo neutronics codes use continuous-energy descriptions of the neutron interaction data that are not subject to this effect. The issue of self-shielding occurs because of the discretisation of data used by the deterministic solutions. Multigroup data used in these solvers are the average cross section and scattering parameters over an energy range. Resonances in cross sections can occur that change the likelihood of interaction by one to three orders of magnitude over a small energy range. Self-shielding is the numerical effect that the average cross section in groups with strong resonances can be strongly affected as neutrons within that material are preferentially absorbed or scattered out of the resonance energies. This affects both the average cross section and the scattering matrix.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2018

Criticality Safety Validation of SCALE 6.2.2

The computational bias of criticality safety computer codes must be established through the validation of the codes to critical experiments. A large collection of suitable experiments has been vetted by the International Criticality Safety Benchmark Evaluation Project (ICSBEP) and made available in the International Handbook of Evaluated Criticality Safety Benchmark Experiments (ICSBEP Handbook). More than 600 cases from this handbook ha ve been prepared and reviewed within the Verified, Archived Library of Inputs and Data (VALID) , which is maintained by the Reactor and Nuclear Systems Division at Oak Ridge National Laboratory. The performance of the KENO V.a and KENO-VI Monte Carlo codes within the SCALE 6.2.2 code system is assessed using the VALID models of benchmark experiments. A range of nuclear cross section libraries based on both ENDF/B-VII.1 and ENDF/B-VII.0 in both multigroup (MG) and continuous energy (CE) formats is considered. The TSUNAMI tools for sensitivity and uncertainty analysis are used to examine some systems further to try to identify potential causes of unexpected results.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Impact of Increased Latent Generations on Sensitivity Calculations with SCALE

Analyses of cross section sensitivity data from systems with fissile material allow analysts to associate an importance for each material, nuclide, reaction, and neutron energy by simulating real world criticality scenarios. Although criticality safety validation efforts can be guided by the cross-section sensitivity and uncertainty data generated for a particular system, these calculations can often be computationally expensive and sometimes cumbersome without proper guidance. The TSUNAMI suite within the SCALE code package has several methods for generating sensitivity data, including multigroup and continuous energy (CE) capabilities. The release of SCALE 6.3 has three different CE methods for generating cross section sensitivity data: (1) the Iterated Fission Probability (IFP) method with the KENO Monte Carlo transport solver, (2) the IFP method with the Shift Monte Carlo transport solver, and (3) the Contributon-Linked eigenvalue sensitivity/Uncertainty estimation via Tracklength importance CHaracterization (CLUTCH) method with the KENO Monte Carlo transport solver. Although the CLUTCH method has additional parameters for generating sensitivity data files relative to the IFP method, all three methods use latent generations, which are the generations between an event (i.e., fission) and the assessment of importance based on the asymptotic population of progeny neutrons. Increasing the number of latent generations in a calculation leads to increased discrimination of the sensitivity coefficients but at the cost of the increased uncertainty associated with those generated values. Analysts must balance the accuracy of the sensitivity calculations and its uncertainty with the associated computational cost involved in generating the values. This paper discusses the impact of adjusting the latent generation parameter for a range of sensitivity values and how these changes compare with the direct perturbation values obtained from a change of ±0.5% Δ k in both benchmark and safety application models. Two benchmarks from the International Handbook of Evaluated Criticality Safety Benchmark Experiments and the MPC-32 dual purpose canister for spent nuclear fuel are used for analysis.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Data reduction in deterministic neutron transport calculations using machine learning

Neutron cross section matrices for fission and scattering data are required for each material, temperature, and enrichment level to calculate the neutron transport equation accurately. Here, this information can be a limiting factor when using the multigroup discrete ordinates (S N ) method when the number of energy groups is large. Machine Learning (ML) can be used to replace the need for the cross section matrices by reproducing the function that maps the scalar flux to the scattering and fission sources. Through the use of autoencoders and Deep Jointly-Informed Neural Networks (DJINN), the data storage requirements are reduced by 94% of the original data for a 618 group problem. This is accomplished while preserving the scalar flux, maintaining generality, and decreasing wall clock times.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗