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Multigroup Examination of Nickel-Reflected HEU System

Critical configurations of HEU-MET-FAST-003 (HMF-003) from the International Criticality Safety Benchmark Evaluation Project Handbook were modeled for addition into the Verified, Archived Library of Inputs and Data maintained at Oak Ridge National Laboratory. HMF-003 contains models of a highly enriched uranium sphere with a spherical metal reflector of natural uranium, tungsten carbide, or nickel. For these simple models, good agreement is expected between the k eff calculated with continuous-energy (CE) and multigroup (MG) transport. However, using the CSAS5 sequence of the SCALE 6.2.4 package, the 8 in. thick nickel reflector model resulted in a difference of around 1.2 % Δ k . Results presented a clear indication of poor performance for the SCALE 252-group based on ENDF/B-VII.1 cross section library for this model. The bias was investigated over a range of nickel thickness and then compared with other MG libraries available in SCALE 6.2.4. As the nickel thickness increases, the MG k eff deviates from the CE result, confirming a performance issue with the MG calculation. Additionally, the reactions were compared between the two libraries to help determine the cause of k eff bias. Finally, additional MG libraries within SCALE 6.3 and based on ENDF/B-VII.1 and ENDF/B-VIII were reviewed. The 302-group and 1597-group result in significant improvements compared with the 252-group library. Nickel cross sections were modified from ENDF/B-VII.1 to ENDF/B-VIII. For the ENDF/B-VIII library, the deviation between the CE libraries and MG libraries is less pronounced than for ENDF/VII.1, except for the 1597-group. This examination clearly indicates the importance of validating calculations with applicable benchmark experiments and caution when using MG libraries.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Performing k eff Validation of As-Loaded Criticality Safety Calculations Using UNF-ST&DARDS: Sensitivity Calculations

The general method for performing validation of as loaded criticality safety calculations using UNF ST&DARDS is presented in a paper by Clarity, which includes a description of the UNF-ST&DARDS system. Proof-of-principle analyses were performed in the summer of 2019 for MPC-32 dual purpose canisters (DPCs) containing pressurized water reactor (PWR) fuel assemblies. Summaries of these results are presented in this and a companion paper for this conference. The current paper describes the TSUNAMI-3D calculations performed to generate sensitivity data, and the companion paper discusses the selection of critical experiments applicable for validation of the 11 MPC-32 DPCs considered. The generation of sensitivity data for as-loaded spent nuclear fuel (SNF) DPCs is a challenge given the detailed model of the fuel compositions generated by UNF ST&DARDS. Each fuel assembly is modeled with its own irradiation history in 18 axial nodes, unless the fuel assembly is damaged and thus considered as fresh by design basis. This results in a set of 576 fuel compositions, each of which must be processed separately in a multigroup (MG) calculation. Therefore, a continuous-energy (CE) TSUNAMI-3D method was chosen to alleviate this challenge. Two CE TSUNAMI-3D methods are available in SCALE 6.2.3: the iterated fission probability (IFP) and contribution-linked eigenvalue sensitivity/uncertainty estimation via track-length importance characterization (CLUTCH). Since the IFP method is not feasible because of memory requirements associated with its implementation in SCALE, the CLUTCH method was selected for these calculations. CLUTCH has been implemented in SCALE in parallel, allowing long calculations to be performed in reasonable timeframes. The two primary user inputs necessary for CLUTCH calculations are the F*(r) mesh and the number of latent generations used in determining the F*(r) function. This F*(r) function is used as the importance function for fission chains originating in a given volume element (voxel), and it is calculated using the IFP method in the skipped generations. A large number of skipped generations is thus required to ensure accurate calculation of this importance function. In these calculations, 500 generations were used to calculate the F*(r) function. For more information regarding the calculation of F*(r), see Jones [4]. The remainder of this paper is focused on the selection of the F*(r) mesh and the number of latent generations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

SCALE capabilities for high temperature gas-cooled reactor analysis

The SCALE code system’s ability to address stochastic distributions of fuel particles within a graphite matrix has been revisited in both multigroup (MG) features and continuous-energy (CE) Monte Carlo methods. Furthermore, this paper describes current and emergent SCALE capabilities within the CSAS sequence to address double-heterogeneous systems and presents verification and validation studies of these methods and data. Good agreement was obtained for a high temperature gas-cooled reactor (HTGR) fuel pebble model between CSAS MG eigenvalue calculations and corresponding CE reference solutions. Code-to-code comparisons for this HTGR pebble model showed good agreement of CSAS-KENO and CSAS-Shift CE calculations and the Serpent and MCNP codes in terms of eigenvalues and reaction rate ratios. Validation studies based on two HTGR experiments resulted in good agreement between MG and CE results, as well as between experiment and calculation, although the level of agreement was significantly influenced by the applied ENDF/B nuclear data library.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Sensitivity Calculations for Systems with Polyethylene Reflector Materials Using CLUTCH

The SCALE 6.2.4 code package contains four sequences for calculating $k_{eff}$ sensitivity coefficients. Two of these sequences use deterministic transport solvers: a one-dimensional (1D) capability based on XSDRN, and a two-dimensional (2D) capability based on NEWT. These sequences are restricted to the multigroup (MG) treatment of neutron energy. The three-dimensional (3D) sequences use the KENO V.a or KENO-VI Monte Carlo transport codes and can be used to calculate sensitivity coefficients with either MG or continuous-energy (CE) transport. The 3D sensitivities are ultimately reported in an MG structure, regardless of the method used in the transport calculations. If desired, the sensitivity coefficients can be reported with very fine energy resolution from a CE calculation, but they are calculated only in the MG library structure in the MG mode. CE TSUNAMI methods are available in SCALE starting in SCALE version 6.2. Sensitivity coefficients were generated using the 3D sequences as part of the generation of the SCALE 6.2.2 Validation Report; difficulties encountered when using the CLUTCH method for thick, fissionable-material reflectors were discussed and investigated as documented in a previous paper. This paper discusses the difficulties encountered in generating accurate sensitivity coefficients using the CLUTCH technique for polyethylene reflectors for two fast spectrum benchmarks. Direct perturbation (DP) calculations were performed to confirm the accuracy of the total sensitivity coefficient for important isotopes with large sensitivities in the system. Discrepancies were detected for CLUTCH-calculated sensitivity coefficients in the reflector of a critical experiment with a radial polyethylene reflector. A simple polyethylene-reflected plutonium sphere was then used to further investigate the discrepancy. Calculations performed using the iterated fission probability (IFP) method generated accurate sensitivity coefficients in both cases. The results of this study emphasize the need to confirm CLUTCH sensitivity results with DP calculations. IFP calculations are generally less efficient but more reliable than CLUTCH calculations. Improvements to the CLUTCH methodology that retain the greater efficiency but address identified difficulties are therefore potentially useful to analysts.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Performance of the Initial Implementation of the Shift Monte Carlo Code in SCALE 6.3

The Shift Monte Carlo code will be introduced in SCALE 6.3 as an alternative to the KENO V.a, KENO-VI, and Monaco codes. Calculations were performed to establish the performance of Shift for criticality safety analyses within the criticality safety analyses sequence (CSAS) based on models in the Verified, Archived Library of Inputs and Data (VALID). This test suite contains over 600 critical experiment models covering a broad range of fissile materials and neutron energy spectra. The comparisons presented include calculated k eff values and runtime performance for serial calculations and a selection of parallel calculations. Comparisons are presented for multigroup (MG) and continuous-energy (CE) calculations for KENO V.a and KENO-VI models. Results generated with a beta version of SCALE 6.3 indicate excellent agreement in k eff values between KENO and Shift. The largest differences in the average k eff value calculated for the 15 categories of KENO V.a models are 0.00020 ± 0.00011 Δ k for MG calculations and 0.00011 ± 0.00005 Δ k for CE calculations. Similar comparisons in three categories using KENO-VI result in the largest differences for MG calculations: as 0.00004 ± 0.00003 Δ k , and -0.00002 ± 0.00003 Δ k for CE. The preliminary results also indicate that Shift is faster than KENO on a per particle basis, especially for fast spectrum systems. The uncertainty per history is also higher, however, so the Monte Carlo figure of merit is higher for KENO for thermal and intermediate spectrum systems. As expected, Shift generally has better speedup than KENO for parallel calculations, regardless of neutron energy spectrum.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Analysis of SCALE Criticality and Sensitivity Calculations for Reflected HEU Cylinders

The SCALE code package offers multiple nuclear data libraries and sensitivity and uncertainty (S/U) methods supporting and derived from Monte Carlo (MC) transport. The CSAS and TSUNAMI-3D sequences use KENO MC, utilizing either continuous-energy (CE) cross sections or multigroup (MG) cross section libraries. TSUNAMI-3D has two CE calculational methods: the iterated fission probability (IFP) method, and the Contribution-Linked eigenvalue sensitivity/Uncertainty estimation via Tracklength importance CHaracterization (CLUTCH) method. Previous work has shown poor agreement between CLUTCH and confirmatory direct perturbation calculations in specific applications (e.g., fissionable and polyethylene reflectors). The HEU-MET-FAST-084 (HMF-084) International Criticality Safety Benchmark Evaluation Project evaluation consists of 27 cylindrical highly enriched uranium metal cores with 14 unique reflector materials of 0.5 and 1 in. thicknesses. Included in this list of reflector materials are natural uranium and polyethylene. This work utilized SCALE 6.2.4 models of the HMF-084 evaluation, with additional non-physical configurations to test both the MG bias and CLUTCH functionality across a variety of reflector material thicknesses. The evaluation’s use of concentric cylinders allowed for examination of several MG self-shielding methods: infinite homogenous, cylindrical, and spherical. The results indicate that the use of polyethylene reflectors with CLUTCH is not fundamentally impossible but sensitive to geometry. The poor performance of CLUTCH with fissionable reflectors was reaffirmed. The 2 in. and greater polyethylene-reflected calculations demonstrate the necessity of using the 302-group library for fast systems. The nickel MG bias was substantial, as discussed in a companion paper, as were cobalt and iron.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

SCALE Code System

The SCALE Code System is a widely used modeling and simulation suite for nuclear safety analysis and design that is developed, maintained, tested, and managed by the Reactor and Nuclear Systems Division (RNSD) of Oak Ridge National Laboratory (ORNL). SCALE provides a comprehensive, verified and validated, user-friendly tool set for criticality safety, reactor and lattice physics, radiation shielding, spent fuel and radioactive source term characterization, and sensitivity and uncertainty analysis. Since 1980, regulators, licensees, and research institutions around the world have used SCALE for safety analysis and design. SCALE provides an integrated framework with dozens of computational modules, including three deterministic and three Monte Carlo radiation transport solvers that are selected based on the desired solution strategy. SCALE includes current nuclear data libraries and problem-dependent processing tools for continuous-energy (CE) and multigroup (MG) neutronics and coupled neutron-gamma calculations, as well as activation, depletion, and decay calculations. SCALE includes unique capabilities for automated variance reduction for shielding calculations, as well as sensitivity and uncertainty analysis. SCALE’s graphical user interfaces assist with accurate system modeling, visualization of nuclear data, and convenient access to desired results.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

SCALE 6.2 Lattice Physics Performance Assessment

The US Nuclear Regulatory Commission relies on the lattice physics analysis capabilities of the SCALE code system to perform confirmatory licensing analyses. Either SCALE lattice physics code—TRITON/NEWT or Polaris—can be used to generate cross section data used by the PARCS nodal core simulator for full-core neutronics calculations. This report presents an assessment of the accuracy of SCALE lattice physics codes for preparation of lattice physics data that are used to support simulator codes such as the NRC’s PARCS, for UO 2 -mixed oxide (MOX)/Zr fueled light water reactor (LWR) analyses. Due to the nature of lattice physics calculations, critical reactor experiment benchmarks cannot be modeled in explicit detail in a lattice physics code. However, this limitation does not mean that these measurement data are not usable for lattice physics studies. Therefore, either geometry approximations or axial buckling must be implemented to determine the critical water height. These modeling limitations have led to development of a three-phase assessment strategy. In the first phase, selected critical experiment benchmarks are modeled using the SCALE 3D continuous-energy (CE) Monte Carlo (MC) code KENO, which is the most rigorous neutron transport method available in SCALE, with no approximations in the spatial, angle, or energy treatments. Biases and statistical uncertainties in quantities of interest such as k eff and pin power distributions are determined by comparing CE KENO results to experimental data. This first phase in the accuracy assessment is to demonstrate and establish the use of CE KENO as a reference solution for the second phase. In the second phase, 14 numerical test suites are used to compare SCALE lattice physics calculations with CE KENO as a reference solution. In the third phase, SCALE lattice physics depletion calculations are performed, and the spent fuel isotopic results are compared with available radiochemical assay measurements. Isotopic measurement comparisons provide quantitative assessment of isotopic density distribution predictions with the depletion models in SCALE lattice physics codes. This report documents results for all test suites. The assessment was performed using standard production techniques unless otherwise noted. Both TRITON/NEWT and Polaris exhibited acceptable accuracy for most test cases. For the few test cases in which acceptable accuracy criteria were not met, further code and data development are planned. The computer codes used in this assessment are as follows: SCALE 6.2 rev19189 (pre-release of 6.2.1) was used for CE KENO, TRITON/NEWT and Polaris (PWR only) calculations; SCALE 6.2.2 was used for Polaris calculations to address several updates in support of support boiling water reactor (BWR) lattice geometries. For this work, there is no difference between SCALE 6.2.1 and SCALE 6.2.2 beyond the inclusion of the Polaris BWR analysis capability; The ENDF/B-VII.1 continuous energy and 252 group libraries deployed in SCALE 6.2 were generated with AMPX 6.2 that is distributed with SCALE.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Analysis of SCALE Criticality and Sensitivity Calculations for Reflected HEU Cylinders [Abstract]

The SCALE code package offers several nuclear data libraries to support Monte Carlo (MC) transport, as well as MC-based derivation of $\kappa$ eff sensitivity and uncertainty (S/U) data. The CSAS sequence using the KENO MC code can utilize continuous-energy (CE) cross sections, or pre-generated multigroup (MG) cross section libraries. The use of MG libraries introduces bias into calculations in exchange for faster transport solutions. The TSUNAMI-3D sequence also utilizes KENO MC calculations. TSUNAMI-3D has two CE calculational methods: the Iterated Fission Probability (IFP) method, and the Contribution-Linked eigenvalue sensitivity/Uncertainty estimation via Tracklength importance CHaracterization (CLUTCH) method. Previous work has shown poor agreement between CLUTCH and confirmatory direct perturbation calculations in specific applications, e.g., fissionable and polyethylene reflectors

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Deterministic-Monte Carlo Hybrid Methods for Eigenvalue Sensitivity Coefficient Calculations

The TSUNAMI suite within the SCALE code package includes several methods for generating sensitivity data, including multigroup (MG) and continuous-energy (CE) capabilities. For generating sensitivities with CE data, three methods are available in SCALE 6.3.0: (1) the iterated fission probability (IFP) method with the KENO Monte Carlo transport solver, (2) IFP with the Shift Monte Carlo transport solver, and (3) the Contributon-Linked eigenvalue sensitivity/Uncertainty estimation via Tracklength importance Characterization (CLUTCH) with the KENO Monte Carlo transport solver. Currently, it is difficult to generate accurate sensitivities with large reflectors when using the CLUTCH method, specifically with fissionable and hydrogenous materials. To address this issue, the work presented herein examines a methodology to calculate the adjoint flux externally with the 3D deterministic SN transport code DENOVO in SCALE; the result is then read directly into the CLUTCH-TSUNAMI sequence. This hybridization method replaces the Monte Carlo F*(r) calculation in CLUTCH while still utilizing the forward calculation. The critical benchmark HEU-MET-FAST-028-001 is used to generate sensitivities based on the inability of CLUTCH to generate accurate sensitivities. Results from the hybrid method appear to generate sensitivity values that are in excellent agreement with direct perturbations. Although further testing is needed, the method provides promising results for the development and utility of a hybrid method for use in TSUNAMI.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Automated Direct Perturbation Calculations with SCALE TSUNAMI [Abstract]

In nuclear criticality safety analysis, the sensitivity of the eigenvalue keff to uncertainties in nuclear data and its evaluation are crucial. The TSUNAMI sequences within the SCALE code system offer users various options with both multigroup (MG) and continuous-energy (CE) 3D Monte Carlo (MC) transport capabilities for calculating keff sensitivity coefficients and storing them in a sensitivity data file (SDF). Each methodology available in TSUNAMI offers distinct advantages and limitations, and its effectiveness can vary based on the specific problem being solved. As a best practice, practitioners typically use the direct perturbation (DP) method as a confirmatory step alongside their sensitivity calculations to verify the accuracy of the sensitivity data generated. In this process, DP calculations are usually performed on select nuclides, those considered most important for validating their total sensitivities. However, because of code limitations, analysts use a workaround method when conducting DP calculations for a single nuclide: rather than perturbing the nuclide's microscopic cross section, an equivalent number density for this nuclide is calculated to reflect the effect of a change in the macroscopic cross section due to a perturbation in the microscopic cross section. The current approach requires rerunning the CSAS criticality calculation several times with model changes. Although this method can yield results with acceptable accuracy, it is labor-intensive and prone to errors.

AZURE: SAMMY↗