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A Case Study in the Application of TSUNAMI-3D - Part 1, Multigroup

The use of the sensitivity and uncertainty tool suite within SCALE, known as the TSUNAMI suite, has grown following its initial introduction more than a decade ago. Proper use of these tools provides a more complete understanding of system responses to perturbations, especially in the area of nuclear cross section uncertainties. Recent advances within TSUNAMI have added generalized perturbation theory to the k{sub eff} sensitivity capability that was included in TSUNAMI originally. The generation of sensitivity data is encouraged in the review process for new critical experiment requests sponsored by the US Department of Energy (DOE) Nuclear Criticality Safety Program (NCSP) to demonstrate that the proposed experiment will satisfy the identified data need. Many individuals participate in this process, but many analysts have not received proper training in the use of the TSUNAMI tools. The adjoint perturbation theory used to calculate sensitivities is not typically included in nuclear engineering curricula, leaving inexperienced engineers particularly at risk for incorrect use of the tools. The first step in the use of the TSUNAMI tools is the generation of a sensitivity data file (SDF), which contains all of the energy-dependent sensitivity data generated for a model. Most often, the SDF is generated from a three-dimensional (3D) model using either the KENO V.a or KENO-VI code within the TSUNAMI-3D sequence. The sensitivity data generated in TSUNAMI-3D must be accurate for correct quantification of system similarity or any other use of the sensitivity data. The sensitivities calculated by TSUNAMI can be affected by many of the input parameters, cross section processing models, and geometry modeling techniques used within the TSUNAMI-3D input. Fortunately, the total sensitivity of the most important nuclides can be confirmed simply by using direct perturbation (DP) calculations. Confirmation of the total sensitivity of these important nuclides provides confidence that the flux and importance function calculated within the TSUNAMI sequence will yield accurate sensitivities for all nuclides, reactions, and energies of interest. This process is essentially identical for the multigroup (MG) methods and the continuous-energy (CE) methods introduced in SCALE 6.2. This paper discusses the use of DP calculations and provides a case study to confirm that accurate sensitivities are generated by TSUNAMI-3D for a particular benchmark experiment. A companion paper provides a similar case study applying the CE TSUNAMI capability to the same critical experiment. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Reduce-Order Modeling of Multigroup Neutron Cross Sections for High-Temperature Gas-cooled Reactors

Deterministic neutronics calculations rely on multigroup neutron cross section libraries, which usually consists of a database of tabulated values, used to calculate the cross sections through multivariate linear interpolation. However, interpolation of the multidimensional cross section data becomes memory inefficient and time consuming as the number of tabulations increases, significantly slowing down the neutronics calculation, especially in the case of micro cross section libraries where every isotope (on the order of hundreds) has its own set of specific reactions and cross sections. To address this challenge, this work constructs efficient and robust reduced-order models (ROMs) of the multi-group cross sections to support the Griffin simulation of high-temperature gas-cooled reactors (HTGRs). The first part of the study investigates the linearity of the multi-group cross section data across isotopes, reaction types and energy groups on pre-generated datasets for the purpose of dimensionality reduction. Secondly, a down-selection of ROM techniques is presented on representative classical machine learning (ML) techniques, including variants of linear regression, kernel-based methods, tree-based algorithms, and artificial neural networks. The selection criteria jointly consider the memory efficiency, predictive accuracy, prediction speed, and scalability in comparison to the multidimensional interpolation. Among all the ML techniques, deep neural networks (DNNs) have proven to be the best selection with sufficient accuracy, high robustness, good memory efficiency, great scalability, and superior flexibility. DNNs for have been trained for all isotopes in this work and systematic Griffin testing is ongoing at this moment to ensure the feasibility of this ROM technique for cross section predictions.

42 - ENGINEERING↗

MENDF71x. Multigroup Neutron Cross Section Data Tables Based upon ENDF/B-VII.1

A new multi-group neutron cross section library has been released along with the release of NDI version 2.0.20. The library is named MENDF71x and is based upon the evaluations released in ENDF/B-VII.1 which was made publicly available in December 2011. ENDF/B-VII.1 consists of 423 evaluations of which ten are excited states evaluations and 413 are ground state evaluations. MENDF71x was created by processing the 423 evaluations into 618-group, downscatter only NDI data tables. The ENDF/B evaluation files were processed using NJOY version 99.393 with the exception of 35 Cl and 233 U. Those two isotopes had unique properties that required that we process the evaluation using NJOY version 2012. The MENDF71x library was only processed to room temperature, i.e., 293.6 K. In the future, we plan on producing a multi-temperature library based on ENDF/B-VII.1 and compatible with MENDF71x.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Development and Testing of the VITAMIN-B7/BUGLE-B7 Coupled Neutron-Gamma Multigroup Cross-Section Libraries

The U.S. Nuclear Regulatory Commission s Regulatory Guide 1.190 states that calculational methods used to estimate reactor pressure vessel (RPV) fluence should use the latest version of the Evaluated Nuclear Data File (ENDF). The VITAMIN-B6 fine-group library and BUGLE-96 broad-group library, which are widely used for RPV fluence calculations, were generated using ENDF/B-VI data, which was the most current data when Regulatory Guide 1.190 was issued. We have developed new fine-group (VITAMIN-B7) and broad-group (BUGLE-B7) libraries based on ENDF/B-VII. These new libraries, which were processed using the AMPX code system, maintain the same group structures as the VITAMIN-B6 and BUGLE-96 libraries. Verification and validation of the new libraries was accomplished using diagnostic checks in AMPX, unit tests for each element in VITAMIN-B7, and a diverse set of benchmark experiments including critical evaluations for fast and thermal systems, a set of experimental benchmarks that are used for SCALE regression tests, and three RPV fluence benchmarks. The benchmark evaluation results demonstrate that VITAMIN-B7 and BUGLE-B7 are appropriate for use in LWR shielding applications, and meet the calculational uncertainty criterion in Regulatory Guide 1.190.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

New technique to reformat multigroup cross-sections for Monte-Carlo calculation

New method to calculate equi-probability bins from Legendre expansion scattering cross-sections is proposed. The method uses correction of equi-probability bins boundaries to provide conservation of the first angular moment. CRSRD-ST code is developed to reformat cross sections from DTF to ACE format using proposed technique. Numerical results show that the proposed method significantly improves agreement between deterministic and Monte-Carlo calculations. (authors)

97 MATHEMATICS AND COMPUTING↗

A multigroup moment-accelerated deterministic particle solver for 1-D time-dependent thermal radiative transfer problems

We introduce an efficient, robust, Lagrangian (characteristic-based) transport solver for 1-D time-dependent thermal radiative transfer (TRT) applications within the context of a moment-accelerated (High-Order/Low-Order, HOLO) algorithm. This novel transport algorithm inherits the best features of both particle methods (e.g., time accuracy, phase-space adaptivity, positivity) and deterministic, grid-based methods (e.g., no stochastic noise). Particles are adapted by the method of characteristics, with a time-dependent weight that accounts for stiff absorption and reemission process self-consistently. As a result, this approach is able to obtain accurate results while employing large time steps and a moderate number of particles (compared to Implicit Monte Carlo).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Analysis of the multigroup model for muon tomography based threat detection

We compare different algorithms for detecting a 5 cm tungsten cube using cosmic ray muon technology. In each case, a simple tomographic technique was used for position reconstruction, but the scattering angles were used differently to obtain a density signal. Receiver operating characteristic curves were used to compare images made using average angle squared, median angle squared, average of the squared angle, and a multi-energy group fit of the angular distributions for scenes with and without a 5 cm tungsten cube. The receiver operating characteristic curves show that the multi-energy group treatment of the scattering angle distributions is the superior method for image reconstruction.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Multigroup Radiation Transport in Supernova Light Curve Calculations

The supernova associated with long duration gamma0ray bursts are always found to be Type Ic supernova (SN). Type Ic SN are observed to have extremely small amounts of He in their spectra. Astrophysicists have been exploring ways to either hide the He in the observations or eject the He prior to the SN. Recent calculations by Patrick Young using new mixing algorithms suggest that many massive stars may burn the He layer to O during its evolution and therefore naturally account for the lack of He in the spectra of the SN. The LANL supernova light curve codes are being used to generate simulated observations of these new models.

79 ASTRONOMY AND ASTROPHYSICS↗

Consistent Multigroup Theory Enabling Accurate Course-Group Simulation of Gen-IV Reactors

The objective of this proposal is the development of a consistent multi-group theory that accurately accounts for the energy-angle coupling associated with collapsed-group cross sections. This will allow for coarse-group transport and diffusion theory calculations that exhibit continuous energy accuracy and implicitly treat cross- section resonances. This is of particular importance when considering the highly heterogeneous and optically thin reactor designs within the Next Generation Nuclear Plant (NGNP) framework. In such reactors, ignoring the influence of anisotropy in the angular flux on the collapsed cross section, especially at the interface between core and reflector near which control rods are located, results in inaccurate estimates of the rod worth, a serious safety concern. The scope of this project will include the development and verification of a new multi-group theory enabling high-fidelity transport and diffusion calculations in coarse groups, as well as a methodology for the implementation of this method in existing codes. This will allow for a higher accuracy solution of reactor problems while using fewer groups and will reduce the computational expense. The proposed research represents a fundamental advancement in the understanding and improvement of multi- group theory for reactor analysis.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Development of the V4.2m5 and V5.0m0 Multigroup Cross Section Libraries for MPACT for PWR and BWR

The MPACT neutronics module of the Consortium for Advanced Simulation of Light Water Reactors (CASL) core simulator is a 3-D whole core transport code being developed for the CASL toolset, Virtual Environment for Reactor Analysis (VERA). Key characteristics of the MPACT code include (1) a subgroup method for resonance selfshielding and (2) a whole-core transport solver with a 2-D/1-D synthesis method. The MPACT code requires a cross section library to support all the MPACT core simulation capabilities which would be the most influencing component for simulation accuracy.

97 MATHEMATICS AND COMPUTING↗