Multigroup Cross Sections Research Articles

Theoretical Development of Cross Section Uncertainty Library for Core Simulators

Abstract The current regulatory process allows for the use of models employing realistic assumptions as opposed to conservative bounding approaches, requiring a concerted use of best-estimate modeling and comprehensive estimation of uncertainties, collectively referred to as best-estimate-plus-uncertainty methods. This necessitates access to an integrated and automated procedure for the propagation and understanding of key sources of uncertainties. Focusing on neutronic reactor core simulation, this paper lays the theoretical foundations for an uncertainty characterization framework that is comprehensive, informative, and efficient, implying its ability to propagate all sources of uncertainties and identify key contributors in a computationally efficient manner. This paper represents the overarching objective of our work to propagate multigroup (MG) cross section uncertainties through lattice physics calculations and core-wide simulation. This requires the evaluation of few-group parameters uncertainties in terms of a wide range of local conditions, e.g., burnup, fuel temperature, etc., which results in a very high dimensional uncertainty space. The first strategy employed to compress the few-group uncertainties is the physics-guided coverage mapping (PCM) methodology developed to assess the similarity between the branch and base uncertainties in lattice calculation. To further compress the uncertainty propagated, this paper employs an accuracy-preserving reduced order modeling (ROM) technique relying on the use of range finding algorithms to construct all few-group parameters variations to a very small preset tolerance. In a separate cosubmitted paper, this framework is demonstrated to thermal reactors including both light and heavy water systems using a number of computer codes, including NESTLE-C, SERPENT, SCALE's NEWT, and SAMPLER codes.

Application of Cross Sections Uncertainty Propagation Framework to Light and Heavy Water Reactor Systems

Abstract Uncertainty quantification has been recognized by the community as an essential component of best-estimate reactor analysis simulation because it provides a measure by which the credibility of the simulation can be assessed. In a companion paper, a framework for the propagation of nuclear data uncertainties from the multigroup level through lattice physics and core calculations and ultimately to core responses of interest has been developed. The overarching goal of this framework is to automate the propagation, prioritization, mapping, and reduction of uncertainties for reactor analysis core simulation. This paper employs both heavy and light water reactor systems to exemplify the application of this framework. Specifically, the paper is limited to the propagation of the nuclear data starting with the multigroup cross section covariance matrix and down to core responses, e.g., eigenvalue and power distribution, in steady-state core wide calculations. The goal is to demonstrate how the framework employs reduction techniques to compress the uncertainty space into a very small number of active degrees-of-freedom (DOFs), which renders the overall process computationally feasible for day-to-day engineering evaluations.

Covariance comparisons between ENDF/B-VII.1 and ENDF/B-VIII.0 with application for the UAM-LWR exercises

In this study, the nuclear-data covariance data have been compared between ENDF/B-VII.1 and ENDF/B-VIII.0. Using NJOY2016.34, the multigroup cross-section covariance libraries based on ENDF/B-VII.1 and ENDF/B-VIII.0 have been generated respectively. From the direct comparisons of the covariance data between ENDF/B-VII.1 and ENDF/B-VIII.0, very notable differences can be observed in the uncertainties and correlations. Based on the multigroup cross-section covariance libraries generated from ENDF/B-VII.1 and ENDF/B-VIII.0, our home-developed UNICORN code has been applied for the uncertainty analysis. The exercises proposed by UAM-LWRs in Phase I have been chosen as the analysis exercises, including the UOX fuel pin-cells, UOX fuel assembly and MOX fuel assembly. The relative uncertainties of the eigenvalues, two-group constants and burnup-related parameters have been quantified and compared, quantifying the uncertainty differences of covariance data in ENDF/B-VII.1 and ENDF/B-VIII.0. Through analysis, the conclusions can be given that more reliable, not smaller nuclear-data covariance data can be provided in ENDF/B-VIII.0.

Uncertainty and sensitivity analysis of PWR mini-core transients in the presence of nuclear data uncertainty using non-parametric tolerance limits

The impact of nuclear data uncertainties is studied for the reactor power and the reactivity during control rod withdrawal transients with reactivity insertions of 0.5$ and 0.97$, respectively, for a PWR mini-core model. Multi-group cross sections, the multiplicities of both prompt and delayed neutrons, and fission spectra are varied by the application of the random sampling-based method XSUSA with covariance data of SCALE 6.1 supplemented by JENDL-4.0. The varied multi-group data are used by TRITON/NEWT to generate varied 2-group cross sections, which are then applied in neutron-kinetic/thermal-hydraulic calculations with DYN3D-ATHLET. A significant impact on both the reactivity uncertainty and the power uncertainty is observed. Since the distributional properties of the output time series vary across the problem time, the distribution-free Wilks tolerance limit is applied as a robust uncertainty measure to complex time series patterns. The most contributing nuclide reactions to the power uncertainty are identified via sensitivity analysis.

Nuclear-data uncertainty propagation in transient simulation for the C5G7-TD benchmark problem

In this study, uncertainty analysis has been performed to the time-dependent transient simulation of the C5G7-TD benchmark problem, propagating the nuclear-data uncertainties to the key parameters of interest. The detailed material compositions and geometries of C5G7-TD have been applied for the time-dependent transient simulation. For uncertainty analysis of the transient simulation, multigroup cross-section covariance library has been generated based on ENDF/B-VII.1 using the NJOY code. Our home-developed uncertainty-analysis code named UNICORN has been utilized for the uncertainty analysis, using the statistical sampling method. For the steady-state and transient simulations, our home-developed high-fidelity neutronics code NECP-X has been utilized. The relative uncertainties of the fuel-assembly normalized power and pin-wise power have been quantified as function of time. The numerical results show that the maximum relative uncertainties for the assembly normalized power can up to be about 2.14% and the value for the pin-wise power distributions can be about 3.54%.

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.

Generation of Multigroup Cross Sections with an Improved Monte Carlo Algorithm

We propose an improved algorithm of generating scattering matrices based on the Monte Carlo method. The new algorithm can greatly improve convergence compared to the traditional approach of the collision estimator. The formula for estimating statistical errors in the new algorithm is given. How the new algorithm benefits the convergence without investing large neutron samples is analyzed, and we also point out that with properly partitioned energy groups, the precision of scattering matrices can get close to that of total scattering cross sections. The new algorithm has been implemented in the neutron transport code NPTS and validated with a number of critical benchmark problems.

The investigation and calculation of the transmutation paths for the production of 252cf in fast reactors

The generation and transmutation process of the transplutoniums in the conversion chains for 252cf production is calculated and analyzed. The production and conversion efficiency of the chains with different target nuclides and neutron spectrums including fast, thermal and moderated neutron spectrums is computed. The conversion paths for 252cf under different neutron spectrums and neutron flux levels are analyzed. The multi-group depletion program STEP1.0 based on linear chain method is used to calculate the nuclide densities. The model of the reactor is simulated by the transport-burnup coupling system based on the STEP1.0 and MCMG-II for the detailed description of the target designs in the fast reactor. The differences of the conversion efficiency caused by the neutron spectrums can be qualified more accurately with the multi-group cross section calculations. The higher conversion efficiency than the typical thermal neutron spectrum can be obtained by some moderated spectrum optimized for absorption reaction in fast reactor (CEFR China Experimental Fast Reactor) through the irradiation of some transplutoniums (242Pu, 241Am, 244Cm). The neutron flux of large scale demonstration fast reactor or prototype fast breeder reactor is usually higher than the experimental fast reactor (CEFR) or reactor device. China is also developing the demonstration fast reactor (CFR China Fast Reactor) which will have a maximum neutron flux higher than 5.0E15 n/(cm2·s). Therefore, the 252cf production will be more practical and efficient with CFR.

Second-order adjoint sensitivity analysis of a general ratio of functionals of the forward and adjoint fluxes in a multiplying nuclear system with source

In the present work, the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) is applied to a generic multiplying subcritical nuclear system comprising a non-fission neutron source in order to compute efficiently and exactly all of the 1st- and 2nd-order functional derivatives (“sensitivities”) of a system response with respect to the system’s many parameters. The system response is defined to be a ratio of two general nonlinear functionals of the forward and adjoint particle fluxes, while the system parameters include isotopic number densities, microscopic cross sections, fission spectrum parameters, neutron sources, and detector response functions. Such ratios of functionals represent the most general models for quantities of fundamental importance in reactor physics, including eigenvalues, ratios of reaction rates and forward/adjoint flux-weighted multi-group cross sections. The exact expressions obtained in this work will be used in subsequent works to perform a large-scale sensitivity analysis of a polyethylene-reflected plutonium metal sphere experimental benchmark to the nuclear data characterizing this benchmark, comprising 21,976 first-order sensitivities and 482,944,576 second-order sensitivities.

Research on the on-the-fly homogenization method based on RMC code for criticality calculations

The applications of traditional deterministic lattice codes are limited in certain cases because they cannot treat closely coupled neutron characteristics and peculiar geometry. Therefore, to use the continuous energy Monte Carlo method and full core homogenization to generate multi-group cross sections has attracted growing interests. In this paper, the on-the-fly homogenization method based on the Monte Carlo code RMC, which generates multi-group cross sections in the frame of full core continuous energy Monte Carlo calculation and then use them in the Monte Carlo multi-group calculation to obtain a more convergent solution, is proposed and implemented. Tests and comparisons for the use of such on-the-fly homogenization method in criticality calculations are conducted using Kaist 1A benchmark and a simplified Lead-cooled reactor. The results show that our on-the-fly homogenization method exhibits similar accuracy with continuous energy Monte Carlo calculation that uses the same number of neutron histories and only costs about half of the computational time. With respect to spatial homogenization schemes, the cell homogenization scheme is the best one which can predict the reference solution especially for problems with strong absorbers. Given a tradeoff between efficiency and accuracy, the hybrid Homogenization scheme, which treats strong absorbers with cell homogenization and others with pin homogenization, can take nearly as much time as the pin Homogenization while achieving nearly the same accuracy as the cell Homogenization.

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.

Estimation of Tritium Production in VVER-440 Reactor Core During Normal Operation

Slovakia as one of the world leading countries in the share of nuclear power in electricityproduction and currently operates 2 nuclear power plants, each with 2 VVER-440 units. In addition to these reactors there are 2 VVER-440 units under construction and 2 units in decommissioning. The VVER-440 technology features thermal neutron spectrum, low enriched uranium dioxide fuel and light-water coolant, diluted boric acid and 37 emergency reactivity control assemblies with boron steel absorber. Due to the presence of 10B in the coolant/moderator which has high thermal neutron capture cross-section, the absorption of neutron on these atoms may lead to tritium production. Tritiumstrongly contributes to the level of radioactivity of the primary coolant, therefore the NPP staff must have appropriate knowledge of its production during operation. This paper focuses on the estimation of the tritium production for a specific scenario of the operation of the 3rd unit of Mochovce NPP. For simulations the SCALE6 system is used with the detailed calculation model developed at the B&J NUCLEAR ltd. company. The calculations presented in the paper are performed using self-shielded multi-group cross-section libraries, taking into account the operation conditions of Mochovce unit 3 NPP in the first fuel campaign.

Application of TULIP/STREAM code in 2-D fast reactor core high-fidelity neutronic analysis

Abstract The deterministic MOC code STREAM of the Computational Reactor Physics and Experiment (CORE) laboratory of Ulsan National Institute of Science and Technology (UNIST), was initially designed for the calculation of pressurized water reactor two- and three-dimensional assemblies and cores. Since fast reactors play an important role in the generation-IV concept, it was decided that the code should be upgraded for the analysis of fast neutron spectrum reactors. This paper presents a coupled code - TULIP/STREAM, developed for the fast reactor assembly and core calculations. The TULIP code produces self-shielded multi-group cross-sections using a one-dimensional cylindrical model. The generated cross-section library is used in the STREAM code which solves eigenvalue problems for a two-dimensional assembly and a multi-assembly whole reactor core. Multiplication factors and steady-state power distributions were compared with the reference solutions obtained by the continuous energy Monte-Carlo code MCS. With the developed code, a sensitivity study of the number of energy groups, the order of anisotropic PN scattering, and the multi-group cross-section generation model was performed on the keff and power distribution. The 2D core simulation calculations show that the TULIP/STREAM code gives a keff error smaller than 200 pcm and the root mean square errors of the pin-wise power distributions within 2%.

Development of the multigroup cross section library for the CASL neutronics simulator MPACT: Method and procedure

The MPACT neutronics module of the Consortium for Advanced Simulation of Light Water Reactors (CASL) core simulator is a 3D whole core transport code being developed for the CASL toolset known as the Virtual Environment for Reactor Analysis (VERA). Key characteristics of the MPACT code include a subgroup method for resonance self-shielding and a whole-core transport solver with a 2D/1D synthesis method. The AMPX and SCALE code packages have been significantly improved to include intermediate resonance parameters, as well as new modules to enhance the accuracy of resonance data and scattering matrices for the Bondarenko approach and transport cross sections of hydrogen. In addition, CASL XSTools have been developed to generate the MPACT multigroup cross section library. A simple super-homogenization method for 238U has been developed to resolve reaction rate discrepancy issues caused by angle-dependent total cross sections, poor scattering matrices, and a poor resonance interference model at coarse group structure. Due to the limitation of computing capacity that can occur even in high performance computing, a new 51-group structure has been developed for efficient simulation that is applicable for both pressurized water reactor (PWR) and boiling water reactor (BWR) simulations. A new ENDF/B-VII.1 MPACT 51-group library has been developed using the AMPX/SCALE and XSTools code packages, and it has been verified and validated by performing various benchmark calculations.

The SCALE/AMPX multigroup cross section processing for fast reactor analysis

The SCALE/AMPX multigroup (MG) cross section processing procedure has been updated to minimize reactivity differences for fast reactor designs and boiling water reactors (BWRs) with very high void fractions to provide excellent agreement with continuous-energy reference calculations. SCALE MG calculations are widely applied to thermal spectrum light-water reactor (LWR) systems as well as fast spectrum metallic systems of interest to National Nuclear Security Administration. With growing interest from industry and regulators in applying SCALE for the design of fast spectrum reactors, both sodium and molten salt, and in the licensing of power up rates for BWRs, it is desirable to review the SCALE/AMPX procedure for unresolved resonance self-shielded data and high energy neutron spectra. The data were improved by generating MG unresolved resonance data based on the analytic probability table method with the narrow resonance approximation as well as the use of a very fine group structure typically used in fast system analysis. This study focused on verifying the probability table and the SCALE/AMPX MG cross section processing procedure by performing reaction rate analysis and benchmark calculations for various fast reactor and high void BWR systems. Results indicate that the improved SCALE/AMPX MG cross section processing provides excellent results for the fast reactor analysis.

Development of the multigroup cross section library for the CASL neutronics simulator MPACT: Verification

The MPACT neutronics module of the Consortium for Advanced Simulation of Light Water Reactors (CASL) core simulator is a 3D whole core transport code being developed for the CASL toolset, known as the Virtual Environment for Reactor Analysis (VERA). Key characteristics of the MPACT code include a subgroup method for resonance self-shielding and a whole-core transport solver with a 2D/1D synthesis method. Depletion capability is supported by coupling SCALE-ORIGEN with MPACT. A new ENDF/B-VII.1 MPACT 51-group library has been developed by using the AMPX/SCALE and CASL-XSTools code packages based on the procedure introduced in the companion paper, “Development of the Multigroup Cross Section Library for the CASL Neutronics Simulator MPACT: Method and Procedure.” The cross section library generation procedure, cross section library, and MPACT transport capability have been verified by performing various benchmark calculations and comparing the benchmark results to the continuous-energy (CE) Monte Carlo results. The code-to-code comparison for the benchmarks shows that the CASL neutronics simulator MPACT and its 51-group library are working reasonably.

Neutronic simulations for the FRM II

A new high density fuel element consisting of an alloy of uranium-molybdenum (UMo) is being developed for the conversion of FRM II’s compact core from highly enriched uranium towards lower enriched uranium. Required slight changes of the core geometry demand both neutronic and thermal-hydraulical re-calculations. This will be achieved by coupled calculations of the deterministic neutronic TORT-TD code and the thermal-hydraulic system code ATHLET for transient calculations. The calculations presented here are used to validate the code and model system for FRM II and are using the current U3Si2 fuel. Starting from the well proven full MCNP6 model of FRM II, a substitutional MCNP6 model was developed and validated. Based on this substitutional vertical stack model, a geometrically equivalent and material preserving Serpent 2 model was created. With the validated Serpent 2 model the multi-group cross sections needed for TORT-TD can be calculated. In the next step, the vertical stack model was translated into an r-Φ-z geometry for TORT-TD. It is shown, that the developed system consisting of data processing tools and new models leads to matching results between Monte Carlo and deterministic codes. With that system of models and post-processing tools, high precision neutronic calculations can easily be embedded in transient calculations with possible fuel candidates for FRM II.

Study on the self-shielding and temperature influences on the neutron irradiation damage calculations in reactors

Displacement per Atom (DPA) is conventionally computed using the DPA cross sections in reactor applications. The DPA cross sections can be influenced by temperature through the Primary Knocked-on Atom (PKA) energy and the Doppler broadening of reaction cross sections. The former is shown not important due to the threshold energy of atomic displacement and the small value of thermal kinetic energy. For 56Fe, the Doppler broadening has limited influence on DPA cross sections due to high resonance energies. On the other hand, the self-shielding should be considered in the computation of DPA, which depends not only on the cross sections but also the corresponding recoil energies of the PKA. ECCO 1968-group calculations show that the self-shielding corrections on DPA cross sections are necessary for the computation of atomic displacement. In addition, the total DPA rate calculated by self-shielding corrected total cross sections is smaller than the sum of partial components. The recommended method to compute DPA is the calculation of each reaction, especially for coarse energy structures. The total DPA rate in ASTRID reactor inner core is 25 DPA/year, for which the contributions of the elastic scattering, total inelastic scattering, and disappearance reactions are 81.9%, 18.0%, and 0.1%, respectively. The corresponding relative reductions due to the corrections of multi-group cross sections are 11.3%, 5.9%, and 20.5%, respectively.

Multigroup Cross-Section Generation with the OpenMC Monte Carlo Particle Transport Code

High-fidelity deterministic transport codes require highly accurate multigroup cross sections (MGXS). Monte Carlo is increasingly cited as a reactor-agnostic approach to MGXS generation since it is unconstrained by the engineering-based approximations that limit the applicability of deterministic MGXS generation tools. This paper introduces a new framework that uses the OpenMC Monte Carlo code to generate MGXS for use in multigroup transport codes. The openmc.mgxs module is built atop OpenMC’s Python application programming interface to process tally data output by the OpenMC executable. This paper validates the module to generate MGXS that enable the multigroup OpenMOC transport code to compute eigenvalues to within 50 pcm and fission rates to within 1% of reference solutions for two heterogeneous pressurized water reactor benchmarks.

Modeling and simulation of a TRIGA MARK-II research reactor using WIMSD-5B and CITATION codes

The main objective of this study is to analyse neutronic safety parameters of the Moroccan TRIGA Mark-II research reactor using the WIMSD-5B and CITATION computer codes. New 172-group libraries of multi-group constants for the lattice code WIMSD-5B have been generated for all isotopes presented in the TRIGA reactor core by processing nuclear data from ENDFB-VII.1, JENDL-4.0 and JEFF-3.1.1 using NJOY99. The lattice code WIMSD-5B was employed to generate multi-group cross sections in the suitable format that will be used by the 3-dimensional diffusion code CITATION. This later was used to calculate various neutronic safety parameters of the TRIGA Mark-II research reactor, such as reactivity excess and neutron fluxes profiles. The results of these calculations are compared to the results of Monte Carlo calculation based on MCNP code. A good agreement is achieved and the current computation scheme will be adopted for our further coupling neutronic/thermal-hydraulic study of the Moroccan TRIGA reactor.