Multigroup Libraries Research Articles

Analytic Error Analysis of the Partial Derivatives Cross-Section Model—I: Derivation

Accurate assessment of uncertainties in cross-section data is crucial for reliable nuclear reactor simulations and safety analyses. In this study, we focus on the interpolation procedure of the partial derivatives (PD) cross-section model used to evaluate nodal parameters from pregenerated multigroup libraries. Our primary objective is to develop a systematic methodology that enables prediction of the incurred errors in the cross-section model, leading to the development of optimal case matrices, more efficient cross-section models, and informed case matrix construction for reactor types lacking substantial data and experience. We make progress toward this objective through a rigorous analytic error analysis enabled by the derivation of error expressions and bounds for the PD model based on the discovery that the method is a form of Lagrange interpolation. Our investigations reveal distinct outcomes depending on the chosen cross-section functionalizations, achieved by identifying the sources of error. These error sources are found to include interpolation error, which is always present, and model form error, which is a property of the supplied case matrix. We show that simply increasing grid refinement through the addition of branches may not always lead to decreased cross-section errors, particularly in cases where the model form error predominantly contributes to the total error. We present numerical results and verification in a companion paper, showing these different error characteristics for various cross-section functionalizations. Although applied to current light water reactor environments, our methodology offers a means for advanced reactor analysts to develop case matrices with quantified error levels, advancing the goal of a general methodology for robust two-step reactor analysis. Future work includes exploring different lattice types and functionalizations, extending reactivity bounds to multilattice problems, and investigating historical effects within the macroscopic depletion model.

The fast neutron fluence and the activation monitor activity calculations using fine multigroup and continuous nuclear data

The fast neutron fluence and the activation monitor activities are routinely calculated with TORT deterministic code and BUGLE-B7 nuclear data library with 47 broad energy groups. The objective of the paper is to analyse options to improve reactor dosimetry transport calculations. There are two paths to improve reactor dosimetry calculations. Increasing geometry, angular and energy mesh size is applicable for TORT code while using newer nuclear data libraries is relevant for both deterministic and Monte Carlo codes. Two new calculation options (improved TORT and Monte Carlo MCNP6) were compared with the standard TORT calculation for VVER-440 Dukovany Unit 3 Cycle 31. The fast neutron fluence with 0.5 MeV threshold as well as activity of Fe. Ni, Ti, Cu. Mn and Nb monitors were evaluated. Standard TORT calculations were improved from S16P3 to S30P3 with three times finer axial mesh size. 120° core symmetry r-ϑ mesh size with 0.5° step and fine multigroup libraries VUAMIN-B7 with 199 neutron energy groups and ENDF/B-VH.1 with 200 neutron energy groups. Both ENDFB and IRDFF activation cross sections were used. The drawback of expanded mesh size is raised calculation runtime since TORT deterministic code is not parallelized and one calculation can require multiple weeks of CPU time. An alternative option of using MCNP6 Monte Carlo code with continuous ENDF/B-VH.1 nuclear data with detailed 3-D geometry and pin-wise effective neutron source prepared by MOBY-DICK diffusion code reactor analysis wras explored. It was found that using finer mesh size affects reactor dosimetry’ tallies less than the choice of nuclear data library. BUGLE-B7 and VTTAMIN-B7 produce results typically within 1% difference. ENDF/B-VH.1 calculations with 200 neutron energy’ groups with TORT code are even in better agreement with MCNP6 calculations with continuous nuclear data libraries. The largest differences of around 2% were observed between VTTAMIN-B7 library based onENDFB-VH.O nuclear data and ENDF/B-VH.1 library. Nuclear data library’ has larger impact on the results with up to 7 % difference between all 0.5 MeV fast neutron fluence calculations. The largest intact of nuclear data was observed for Mn(n.2n) monitor.

The multigroup library processing method for coupled neutron and photon heating calculation of fast reactor

To accurately calculate the heating distribution of the fast reactor, a neutron-photon library in MATXS format named Knight-B7.1-1968n × 94γ was processed based on the ENDF/B-VII.1 library for ultrafine groups. The neutron cross-section processing code MGGC2.0 was used to generate few-group neutron cross sections in ISOTXS format. Additionally, the self-developed photon cross-section processing code NGAMMA was utilized to generate photon libraries for neutron-photon coupled heating calculations, including photo-atom cross sections for the ISOTXS format, prompt photon production cross sections, and kinetic energy release in materials (KERMA) factors for neutrons and photons, and the self-shielding effect from the capture and fission cross sections of neutron to photon have been taken into account when the photon source generated by neutron is calculated. The interface code GSORCAL was developed to generate the photon source distribution and interface with the DIF3D code to calculate the neutron-photon coupling heating distribution of the fast reactor core. The neutron-photon coupled heating calculation route was verified using the ZPPR-9 benchmark and the RBEC-M benchmark, and the results of the coupled heating calculations were analyzed in comparison with those obtained from the Monte Carlo code MCNP. The calculations show that the library was accurately processed, and the results of the fast reactor neutron-photon coupled heating calculations agree well with those obtained from MCNP.

Development and Verification of Capability for Processing the Generalised Nuclear Database Structure (GNDS) in Nuclear Data Processing Code NECP-Atlas

The latest evaluated nuclear data libraries, including ENDF/B-VIII.0, TENDL2019, all have two formats, the Evaluated Nuclear Data File (ENDF-6) nuclear data format, and the Generalised Nuclear Database Structure (GNDS) format. The first official public documentation of all of the options for storing data in GNDS was released by the Working Party on International Nuclear Data Evaluation Cooperation (WPEC) of the Nuclear Energy Agency. The generalized derived class is designed to be compatible with ENDF-6 and GNDS in nuclear data processing code NECP-Atlas, and the GNDS-Toolkit is developed in NECP-Atlas to parse and convert GNDS. ACE format library and multi-group library are generated based on GNDS, and they are used in the Monte-Carlo code and deterministic based code to compare with ENDF-6. The numerical results show that GNDS libraries can be processed by NECP-Atlas competently to generate specific format library and the difference in ENDF-6 and GNDS is very small.

Capability of processing the GNDS format evaluated nuclear data in NECP-Atlas for neutronics calculations

The Generalized Nuclear Data Structure (GNDS) has been being designed as the replacement of the conventional ENDF-6 format for the evaluated nuclear data libraries. The specification for the GNDS format was released by OECD/NEA in 2020. And the latest evaluated nuclear data libraries ENDF/B-VIII.0 and TENDL2019 were released in the ENDF-6 format and the GNDS format, simultaneously. The capability of processing the GNDS format evaluated nuclear data libraries is developed in the nuclear data processing code NECP-Atlas. To be compatible with the GNDS and ENDF-6 formats, the memory management method and the data structure in NECP-Atlas are modified to support more data beyond the ENDF-6 format. At the same time, a module called GNDS-Toolkit is developed to read, parse and convert the GNDS/XML format libraries. The ENDF/B-VIII.0 library in GNDS/XML format is processed into ACE format and multi-group libraries, and used in criticality calculations, lattice physics calculations and shielding calculations. The results show that the GNDS format libraries can be exactly processed by NECP-Atlas.

Fission product depletion chain simplification method based on quantitative contribution function

Recently, an advanced neutronics lattice code called Kylin-2 has been developed by Nuclear Power Institute of China. In order to develop multi-group library for Kylin-2, a fission product depletion chain simplification method was proposed in this paper to generate burnup data for the multi-group library. This method constructed two quantitative contribution functions based on the thought of transmutation trajectory analysis (TTA), according to these contribution functions, a code was developed to identify important fission product nuclides and then a simplification depletion chain was reconstructed using these important nuclides. Verification and validation showed that this method successfully identifies important fission product nuclides and improve the depletion accuracy.

Modification of a Dynamic Monte Carlo Technique to Simplify and Accelerate Transient Analysis with Feedback

In this paper, a simpler approach compared to the existing approaches is developed to analyze nuclear reactor dynamics based on the explicit Monte Carlo method. A new population control method is also introduced to prevent neutron population growth and consequent computer memory shortages, which also increases simulation speed. The scheme is applied for time-dependent particle tracking in three-dimensional arbitrary geometries in the presence of feedbacks through a code named MCSP-Explicit. Changes in material density, as well as geometry dimensions, are also considered during simulation. MCSP-Explicit can be run with either continuous or multigroup data libraries, and it is further boosted by parallel processing to speed up simulations. A number of benchmark problems are studied at the end to evaluate the performance of the proposed approach in various situations.

The Effect of the Flux Separability Approximation on Multigroup Neutron Transport

The angular dependence of flux-weighted multigroup cross sections is commonly neglected when generating multigroup libraries. The error of this flux separability approximation is typically not isolated from other error sources due to a lack of availability of library generation and corresponding solvers that cannot relax this approximation. These errors can now be isolated and quantified with the availability of a multigroup Monte Carlo transport and multigroup library-generation capability in the OpenMC Monte Carlo transport code. This work will discuss relevant details of the OpenMC implementation, provide an example case useful for detailing the type of errors one can expect from making the flux separability approximation, and end with more realistic problems which show the impact of the approximation and highlight how it can strongly arise from an energy-dependent resonance absorption effect. Since the angle-dependence is intrinsically linked to the energy group structure, these examples also show that relaxing the flux separability approximation with angle-dependent cross sections could be used to reduce either the fine-tuning required to set a multigroup energy structure for a specific reactor type or the number of energy groups required to obtain a desired level of accuracy for a given problem. This trade-off could increase the costs of generating multigroup cross sections, and has the potential to require more memory for storing the multigroup library during the transport calculations, but it can significantly reduce the computational time required since the runtime of a discrete ordinates or method of characteristics neutron transport solver scales roughly linearly with the number of groups.

Verification of CENDL-3.2 Nuclear Data on VENUS-3 Shielding Benchmark by ARES Transport Code

The recently released CENDL-3.2 nuclear data library is deemed as an important achievement in the field of nuclear data research in China. To verify the applicability of the library to the shielding calculation of PWR and analyze the influence of multigroup cross-section parameters on the shielding calculation, ARES-MACXS module is used to process the MATXS format multigroup library based on CENDL-3.2 to generate multigroup working cross sections for PWR shielding calculation. VENUS-3 experimental facility has a clear and complete geometry. It is often used to test the ability of the advanced transport calculation method of calculating RPV fast neutron flux and to evaluate the accuracy of cross-section library. Different cross-section parameters are chosen for ARES to calculate VENUS-3 benchmark, and equivalent neutron flux of 58Ni(n,p)58Co, 115In(n,n′)115mIn and 27Al(n,α)24Na detectors is calculated according to the data provided by the benchmark report. The numerical results demonstrate that almost all the relative deviations between the calculated results and the experimental results are within 20%, which satisfies the requirement of shielding calculation. CENDL-3.2 is suitable for PWR shielding calculation. The comparison of various cross-section parameters results indicates that multigroup cross-section parameters have large effects on the transport calculation results.

Lattice physics calculations using the embedded self-shielding method in Polaris, Part I: Methods and implementation

Polaris is a 2-dimensional multigroup lattice physics capability in the SCALE code system for the analysis of light water reactor fuel designs. The goal of light water reactor lattice physics codes is to generate few-group homogenized cross sections for downstream full-core nodal diffusion calculations. Lattice physics calculations contain three primary components: the cross section processing calculation, the 2D transport calculation, and the depletion calculation. This paper summarizes the calculational methods and their implementation into Polaris, with an emphasis on implementation of the embedded self-shielding method. The accuracy of the embedded self-shielding method depends on the procedure used to generate self-shielding factors on the multigroup library. Numerical benchmarks calculations reveal that the accuracy of Polaris eigenvalue predictions is enhanced by (1) using heterogeneous unit cell models to generate the self-shielding factors on the library and (2) using self-shielding factors for within-group scattering cross section.

SCALE/AMPX multigroup libraries for sodium-cooled fast reactor systems

New multigroup cross section libraries and associated covariance files that are optimized for the analysis of sodium-cooled fast reactors were generated with the AMPX tools distributed with the SCALE code system. These new libraries account for the fast neutron flux spectrum with sufficient resolution of resonances in the higher energy range to reproduce continuous-energy reference results and to provide the basis for sensitivity and uncertainty analyses of fast spectrum systems with the SCALE code system. The performance of the new libraries was investigated in terms of the eigenvalue, the neutron flux and reaction rates in criticality calculations, and the generation of group constants. A library using 302 energy groups and a fast neutron flux spectrum as the weighting function led to very good agreement with reference continuous-energy results. The performance of the new library was demonstrated in calculations of experiments from the International Criticality Safety Benchmark Evaluation Project handbook.

Method of Performing Uncertainty Analysis Using Neutron Covariance Data for HTGR

The aim of this work is to develop methods for calculating the neutronic parameters of HTGR and to perform uncertainty analysis with the aid of design programs and neutron covariance data. The method and software modules for preparing multigroup libraries of covariance data for individual isotopes based on a 44-group library of covariance data of the SCALE-6 computational complex were improved in the course of this work. Correction factors are introduced to improve the accuracy of the method. The WIMSD-5 code with a 69-group cross-section libraries, created on the basis of ENDF/BVII.0 and ENDF/BVII.1 evaluated nuclear data files, is used for the neutronic calculations. Calculations of the uncertainties of one-group fission and absorption cross sections for the main isotopes of the elements of the MHTGR-350 core as well as the neutron multiplication coefficients for the fuel-compact cells and fuel-block cells of the MHTGR-350 reactor were performed to verify the developed method.

Processing of the multigroup cross-sections for MCNP calculations

Stochastic Monte Carlo (MC) neutron transport codes are widely used in various reactorphysics applications, traditionally related to criticality safety analyses, radiation shielding and validation of deterministic transport codes. The main advantage of Monte Carlo codes lies in their ability to model complex and detail geometries without the need of simplifications. Currently, one of the most accurate and developed stochastic MC code for particle transport simulation is MCNP. To achieve the best real world approximations, continuous-energy (CE) cross-section (XS) libraries are often used. These CE libraries consider the rapid changes of XS in the resonance energy range; however, computing-intensive simulations must be performed to utilize this feature. To broaden ourcomputation abilities for industrial application and partially to allow the comparison withdeterministic codes, the CE cross section library of the MCNP code is replaced by the multigroup (MG) cross-section data. This paper is devoted to the cross-section processing scheme involving modified versions of TRANSX and CRSRD codes. Following this approach, the same data may be used in deterministic and stochastic codes. Moreover, using formerly developed and upgraded crosssection processing scheme, new MG libraries may be tailored to the user specific applications. For demonstration of the proposed cross-section processing scheme, the VVER-440 benchmark devoted to fuel assembly and pip-by-pin power distribution was selected. The obtained results are compared with continues energy MCNP calculation and multigroup KENO-VI calculation.

Error analysis of approximations and treatments commonly made in multi-group library and self-shielding calculation based on NECP-X

Approximations and treatments commonly applied in multi-group library and self-shielding calculation of conventional neutronics calculation codes are analyzed based on a numerical nuclear reactor physics code NECP-X. The numerical results show that the approximations and treatments introducing largest errors for UO2 pin cell problems are narrow resonance (NR) approximation, ignorance of multi-group (MG) equivalence effect, Bondarenko iteration method and using average fission spectra. For MOX pin cell problems, the approximations and treatments introducing largest errors are ignorance of thermal resonance, NR approximation, resonance interference factor method, ignorance of MG equivalence effect and in-flow transport correction. These analysis provide references and help to improve the conventional methods and legacy codes.

A New Approach to Monte Carlo in High Temperature Reactors

In a recent paper, we described the development of a method for calculating exact collision probabilities between different regions (namely, fuel kernels, graphite matrix, moderator, and coolant) of a lattice cell of a high temperature reactor (HTR) of the pebble bed variety. The method was shown to adequately represent the double heterogeneity in such reactors. In the present paper, we use some of the results obtained in that paper to construct a fast Monte Carlo algorithm for treatment of HTRs. This paper discusses the theoretical basis of the Monte Carlo algorithm, its implementation for the case of a lattice cell with the energy variable treated using a multigroup library, and results obtained. The method can be easily extended to full-core calculations using point cross-section data.

SIMMER extension for multigroup energy structure search using genetic algorithm with different fitness functions

Abstract The multigroup transport theory is the basis for many neutronics modules. A significant point of the cross-section (XS) generation procedure is the choice of the energy groups' boundaries in the XS libraries, which must be carefully selected as an unsuitable energy meshing can easily lead to inaccurate results. This decision can require considerable effort and is particularly difficult for the common user, especially if not well-versed in reactor physics. This work investigates a genetic algorithm-based tool which selects an appropriate XS energy structure (ES) specific for the considered problem, to be used for the condensation of a fine multigroup library. The procedure is accelerated by results storage and fitness calculation speed-up and can be easily parallelized. The extension is applied to the coupled code SIMMER and tested on the European Sustainable Nuclear Industrial Initiative (ESNII+) Advanced Sodium Technological Reactor for Industrial Demonstration (ASTRID)-like reactor system with different fitness functions. The results show that, when the libraries are condensed based on the ESs suggested by the algorithm, the code actually returns the correct multiplication factor, in both reference and voided conditions. The computational effort reduction obtained by using the condensed library rather than the fine one is assessed and is much higher than the time required for the ES search.

A genetic algorithm for multigroup energy structure search

The generation of multigroup neutron cross-section libraries is a key issue of the multigroup transport calculations in reactor physics. The correct choice of the boundaries of the energy groups, in particular, is decisive for obtaining reliable results. Knowledge of the reactor physics, general and specific of the studied reactor, along with long and refined analyses are required for finding out a reasonable energy structure, which is specific for the considered reactor and might be unsuitable for other systems. The genetic algorithm presented in this work aims to choose the most appropriate energy structure for the considered system to collapse a fine multigroup library into a few-groups one, usable for transient transport calculations. The user is free to choose the number of energy groups of the final library, which is in direct relation with the precision required and the time available for the simulation. The methodology is coupled with SIMMER-III code and applied to 3 reactor systems: ESNII+ ASTRID, ESFR and MSFR. The results show that the algorithm can find representative energy structures, providing accurate results on the multiplication factor. The results of each test are analyzed, showing how different compositions, geometries and neutron spectra guide the algorithm choices, so demonstrating the effectiveness of the method.

Evaluation of the Pool Critical Assembly Benchmark with Explicitly Modeled Geometry Using MCNP6

Despite being one of the most widely used benchmarks for qualifying light water reactor (LWR) radiation transport methods and data, no benchmark calculation of the Oak Ridge National Laboratory (ORNL) pool critical assembly (PCA) pressure vessel wall benchmark facility (PVWBF) using MCNP6 with explicitly modeled core geometry exists. As such, this paper provides results for such an analysis. First, a criticality calculation is used to construct the fixed source term. Next, ADVANTG-generated variance reduction parameters are used within the final MCNP6 fixed source calculations. These calculations provide unadjusted dosimetry results using three sets of dosimetry reaction cross sections of varying ages (those packaged with MCNP6, from the IRDF-2002 multigroup library, and from the ACE-formatted IRDFF v1.05 library). These results are then compared to two different sets of measured reaction rates. The comparison agrees in an overall sense within 2% and on a specific reaction and dosimetry location basis within 5%. Except for the neptunium dosimetry, the individual foil raw calculation-to-experiment comparisons usually agree within 10% but are typically greater than unity. Finally, in the course of developing these calculations, geometry that has previously not been completely specified is provided herein for the convenience of future analysts.

Analyses of the TIARA 43 MeV Proton Benchmark Shielding Experiments Using the ARES Transport Code

ARES is a multidimensional parallel discrete ordinates particle transport code with arbitrary order anisotropic scattering. It can be applied to a wide variety of radiation shielding calculations and reactor physics analysis. To validate the applicability of the code to accelerator shielding problems, ARES is adopted to simulate a series of accelerator shielding experiments for 43 MeV proton-7Li quasi-monoenergetic neutrons, which is performed at Takasaki Ion Accelerator for Advanced Radiation Application. These experiments on iron and concrete were analyzed using the ARES code with FENDL/MG-3.0 multigroup libraries and compared to direct measurements from the BC501A detector. The simulations show good agreement with the experimental data. The ratios of calculated values to experimental data for integrated neutron flux at peak and continuum energy regions are within 64% and 25% discrepancy for the concrete and iron experiments, respectively. The results demonstrate the accuracy and efficiency of ARES code for accelerator shielding calculation.

Improvement of Modeling HTGR Neutron Physics by Uncertainty Analysis with the Use of Cross-Section Covariance Information

This work is aimed at improvement of HTGR neutron physics design calculations by application of uncertainty analysis with the use of cross-section covariance information. Methodology and codes for preparation of multigroup libraries of covariance information for individual isotopes from the basic 44-group library of SCALE-6 code system were developed. A 69-group library of covariance information in a special format for main isotopes and elements typical for high temperature gas cooled reactors (HTGR) was generated. This library can be used for estimation of uncertainties, associated with nuclear data, in analysis of HTGR neutron physics with design codes. As an example, calculations of one-group cross-section uncertainties for fission and capture reactions for main isotopes of the MHTGR-350 benchmark, as well as uncertainties of the multiplication factor (k∞) for the MHTGR-350 fuel compact cell model and fuel block model were performed. These uncertainties were estimated by the developed technology with the use of WIMS-D code and modules of SCALE-6 code system, namely, by TSUNAMI, KENO-VI and SAMS. Eight most important reactions on isotopes for MHTGR-350 benchmark were identified, namely: 10B(capt), 238U(n,γ), ν5, 235U(n,γ), 238U(el), natC(el), 235U(fiss)-235U(n,γ), 235U(fiss).