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All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

SCALE Continuous-Energy Eigenvalue Sensitivity Coefficient Calculations

Sensitivity coefficients describe the fractional change in a system response that is induced by changes to system parameters and nuclear data. The Tools for Sensitivity and UNcertainty Analysis Methodology Implementation (TSUNAMI) code within the SCALE code system makes use of eigenvalue sensitivity coefficients for an extensive number of criticality safety applications, including quantifying the data-induced uncertainty in the eigenvalue of critical systems, assessing the neutronic similarity between different critical systems, and guiding nuclear data adjustment studies. The need to model geometrically complex systems with improved fidelity and the desire to extend TSUNAMI analysis to advanced applications has motivated the development of a methodology for calculating sensitivity coefficients in continuous-energy (CE) Monte Carlo applications. The Contributon-Linked eigenvalue sensitivity/Uncertainty estimation via Tracklength importance CHaracterization (CLUTCH) and Iterated Fission Probability (IFP) eigenvalue sensitivity methods were recently implemented in the CE-KENO framework of the SCALE code system to enable TSUNAMI-3D to perform eigenvalue sensitivity calculations using continuous-energy Monte Carlo methods. This work provides a detailed description of the theory behind the CLUTCH method and describes in detail its implementation. This work explores the improvements in eigenvalue sensitivity coefficient accuracy that can be gained through the use of continuous-energy sensitivity methods and also compares several sensitivity methods in terms of computational efficiency and memory requirements.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

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↗
DOE OSTI2023

Deterministic-Monte Carlo Hybrid Methods for Eigenvalue Sensitivity Coefficient Calculations [Slides]

Hybrid method was developed based on a need to generate accurate sensitivities for specified systems with CLUTCH. This new method provides improved sensitivities with HMF-028-001, specifically with 238 U in the large reflector region. With the importance of each voxel predetermined with the adjoint flux, the hybrid method is able to generate more accurate sensitivities. More testing is needed for other types of systems and materials (i.e., thermal and intermediate energy ranges and different moderators and reflectors). Initial results are very promising and continual development of the new hybrid method is currently in progress.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Hybrid Method for Eigenvalue Sensitivity Coefficient Calculations: Part II [Slides]

The hybrid method stemmed from a need to develop a way for CLUTCH to generate more accurate sensitivity coefficients for systems with large fissionable reflectors (i.e., HMF-028-001). For additional systems, the method has been shown to generate accurate sensitivity coefficients for a variety of systems with different fissile nuclides, fissile forms, and neutron energy spectra.

CLUTCH↗
DOE OSTI2017

Monte Carlo Estimates of Eigenvalue Sensitivity to System Dimensions using Kernel Density Estimators

In the last decade there has been an increasing interest in calculating sensitivity coefficients in order to quantify the impact of uncertainty in material properties and system parameters on quantities of interest. Extensive work has been done developing Monte Carlo methods to estimate eigenvalue sensitivity to material properties. While deterministic methods exist for determining the eigenvalue sensitivity to system dimensions, the use of Monte Carlo methods to efficiently calculate eigenvalue sensitivity coefficients to system dimensions is still an open topic. Current Monte Carlo methods for calculating eigenvalue sensitivity coefficients to system dimensions are inefficient. Direct Monte Carlo perturbations require two additional simulations of high statistical precision in order to determine the eigenvalue sensitivity to the location of a single boundary. If the sensitivity to the location of multiple surfaces are desired, two additional simulations must be run for each surface. Kiedrowski and Favorite extended continuous energy Monte Carlo methods for sensitivities of nuclear cross sections to calculate sensitivities to interface boundaries or system dimensions to create the only current alternative to direct Monte Carlo calculations. However this method relies on the simulation of additional random walks launched at each surface crossing event. The present method extends upon Kiedrowski's work and eliminates the inefficient portions of the calculation through the use of Kernel Density Estimators (KDEs). The new method efficiently estimates eigenvalue sensitivities to the uniform expansion or contraction of material interface boundaries or system dimensions, negligibly impacting the runtime performance of the Monte Carlo code. The new estimator is tested on bare and reflected critical configurations in spherical geometry and is compared to estimates obtained from direct Monte Carlo perturbations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

Development of a generalized perturbation theory method for sensitivity analysis using continuous-energy Monte Carlo methods

The sensitivity and uncertainty analysis tools of the ORNL SCALE nuclear modeling and simulation code system that have been developed over the last decade have proven indispensable for numerous application and design studies for nuclear criticality safety and reactor physics. SCALE contains tools for analyzing the uncertainty in the eigenvalue of critical systems, but cannot quantify uncertainty in important neutronic parameters such as multigroup cross sections, fuel fission rates, activation rates, and neutron fluence rates with realistic three-dimensional Monte Carlo simulations. A more complete understanding of the sources of uncertainty in these design-limiting parameters could lead to improvements in process optimization, reactor safety, and help inform regulators when setting operational safety margins. A novel approach for calculating eigenvalue sensitivity coefficients, known as the CLUTCH method, was recently explored as academic research and has been found to accurately and rapidly calculate sensitivity coefficients in criticality safety applications. The work presented here describes a new method, known as the GEAR-MC method, which extends the CLUTCH theory for calculating eigenvalue sensitivity coefficients to enable sensitivity coefficient calculations and uncertainty analysis for a generalized set of neutronic responses using high-fidelity continuous-energy Monte Carlo calculations. Here, several criticality safety systems were examined to demonstrate proof of principle for the GEAR-MC method, and GEAR-MC was seen to produce response sensitivity coefficients that agreed well with reference direct perturbation sensitivity coefficients.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Adapting CLUTCH methodology to multigroup TSUNAMI-3D for eigenvalue sensitivity calculations

The sensitivity of the eigenvalue to uncertainties in nuclear data and its evaluation are important for nuclear criticality safety. TSUNAMI-3D sequences within the SCALE code system offer several options to the user community for calculating eigenvalue sensitivity coefficients with multigroup (MG) and continuous energy (CE) 3D transport capabilities. TSUNAMI-3D sequences implement the adjoint-based perturbation theory with MG KENO code, the Contributon Linked eigenvalue sensitivity/Uncertainty estimation via Track length importance CHaracterization (CLUTCH) method with CE KENO code, and the Iterated Fission Probability (IFP) method with CE KENO and Shift codes. Each method has benefits and limitations depending on the problem that is run. The work presented here aims to adapt the CLUTCH method, which enables the Contributon method's mesh-free, memory-efficient approach for calculating adjoint-weighted tallies for sensitivity calculations, to the MG TSUNAMI-3D sequence. This application would eliminate the explicit adjoint KENO calculation, as well as the memory-consuming mesh flux moment tallies required by the conventional MG TSUNAMI-3D. Smaller memory footprints in the CLUTCH methodology and relatively shorter runtimes in MG KENO transport can make MG TSUNAMI-3D a viable method for some complex problems. Moreover, this adaptation allows MG sensitivity calculations with Shift, ORNL's next-generation high-performance Monte Carlo transport code, which currently does not offer any sensitivity capabilities with MG particle transport simulations. Initial implementation of the new MG TSUNAMI-3D sequence and its preliminary results with a selected critical benchmark experiment in the Verified, Archived Library of Inputs and Data (VALID) are presented in this study.

KENO↗
DOE OSTI2018

Development of a Library for Conducting Monte Carlo Tallies on Heterogeneous Systems

A library is introduced that enables users to conduct Monte Carlo tallies on heterogeneous computing systems. The library can be built with or linked to a Monte Carlo transport code to provide tally capabilities for the project. The library provides a set of tools and an interface for constructing tallies that can be computed on CPUs or GPUs regardless of where the sample data was generated. The library can be incorporated into existing Monte Carlo transport codes at both the research and production level with minimal intrusion into the transport code. The tally library is capable of computing a variety of tallies including track-length histogram (mesh) tallies, collisionbased kernel density estimators, functional expansion tallies, eigenvalue sensitivity coefficients via iterated fission probability, and sensitivities of reaction rates or adjoint-weighted quantities via differential operator sampling. The parallelization methods are discussed and speedups are shown for 2-D and 3-D problems with comparisons to both the tally library CPU implementations as well as the tally capabilities in the host transport code. Performance results and examples are shown for MCNP, MCATK, and OpenMC.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Analytic Sensitivity Coefficients for General Multigroup Infinite Medium k-Eigenvalue Problems

This work presents a general set of equations that can be used to rapidly generate new benchmarks to verify nuclear data sensitivity calculations. The general multigroup infinite medium k-eigenvalue neutron transport equation is used to derive analytic expressions for the infinite medium k-eigenvalue, the scalar neutron flux and adjoint flux, and the sensitivity of k∞ to perturbations in the multigroup nuclear data of a single species, isotropic and elastic scattering, material. The multigroup nuclear data for U-235 and U-238 is presented along with their corresponding k-eigenvalues, forward flux, adjoint flux, and sensitivity profiles, which include the sensitivity of k∞ to the total, fission, capture, and scattering macroscopic cross sections as well as to the group-to-group scattering cross section matrix, group-wise fission neutron production, and the unconstrained and constrained fission neutron energy distribution.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Analytic Sensitivity Coefficients for General Multigroup Infinite Medium k-Eigenvalue Problems

The general multigroup infinite medium k-eigenvalue neutron transport equation is used to derive analytic expressions for the infinite medium k-eigenvalue, the scalar neutron flux and adjoint, and the sensitivity of $k$ ∞ to perturbations in the multigroup nuclear data of a single species isotropic elastic scattering material. In the appendix, we present the multigroup nuclear data for U-235 and U-238 along with the corresponding k-eigenvalue, flux, adjoint, and sensitivity profiles, which include the sensitivity of $k$ ∞ to the total, fission, capture, and scattering macroscopic cross sections as well as to the group-to-group scattering cross section matrix, group neutron production, and the unconstrained and constrained fission neutron energy distribution.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

SCALE 6.2 Continuous-Energy TSUNAMI-3D Capabilities

The TSUNAMI (Tools for Sensitivity and UNcertainty Analysis Methodology Implementation) capabilities within the SCALE code system make use of sensitivity coefficients for an extensive number of criticality safety applications, such as quantifying the data-induced uncertainty in the eigenvalue of critical systems, assessing the neutronic similarity between different systems, quantifying computational biases, and guiding nuclear data adjustment studies. The need to model geometrically complex systems with improved ease of use and fidelity and the desire to extend TSUNAMI analysis to advanced applications have motivated the development of a SCALE 6.2 module for calculating sensitivity coefficients using three-dimensional (3D) continuous-energy (CE) Monte Carlo methods: CE TSUNAMI-3D. This paper provides an overview of the theory, implementation, and capabilities of the CE TSUNAMI-3D sensitivity analysis methods. CE TSUNAMI contains two methods for calculating sensitivity coefficients in eigenvalue sensitivity applications: (1) the Iterated Fission Probability (IFP) method and (2) the Contributon-Linked eigenvalue sensitivity/Uncertainty estimation via Track length importance CHaracterization (CLUTCH) method. This work also presents the GEneralized Adjoint Response in Monte Carlo method (GEAR-MC), a first-of-its-kind approach for calculating adjoint-weighted, generalized response sensitivity coefficients—such as flux responses or reaction rate ratios—in CE Monte Carlo applications. The accuracy and efficiency of the CE TSUNAMI-3D eigenvalue sensitivity methods are assessed from a user perspective in a companion publication, and the accuracy and features of the CE TSUNAMI-3D GEAR-MC methods are detailed in this paper.

42 ENGINEERING↗
DOE OSTI2015

SCALE 6.2 Continuous-energy Tsunami- 3D capabilities - 14566

The TSUNAMI (Tools for Sensitivity and Uncertainty Analysis Methodology Implementation) capabilities within the SCALE code system make use of sensitivity coefficients for an extensive number of criticality safety applications, such as quantifying the data-induced uncertainty in the eigenvalue of critical systems, assessing the neutronic similarity between different systems, quantifying computational biases, and guiding nuclear data adjustment studies. The need to model geometrically complex systems with improved ease of use and fidelity and the desire to extend TSUNAMI analysis to advanced applications have motivated the development of a SCALE 6.2 module for calculating sensitivity coefficients using three-dimensional (3D) continuous-energy (CE) Monte Carlo methods: CE TSUNAMI-3D. This paper provides an overview of the theory, implementation, and capabilities of the CE TSUNAMI-3D sensitivity analysis methods. CE TSUNAMI contains two methods for calculating sensitivity coefficients in eigenvalue sensitivity applications: (1) the Iterated Fission Probability (IFP) method and (2) the Contribution-Linked eigenvalue sensitivity/Uncertainty estimation via Track length importance Characterization (CLUTCH) method. This work also presents the Generalized Adjoint Response in Monte Carlo method (GEAR-MC), a first-of-its-kind approach for calculating adjoint-weighted, generalized response sensitivity coefficients - such as flux responses or reaction rate ratios - in CE Monte Carlo applications. The accuracy and efficiency of the CE TSUNAMI-3D eigenvalue sensitivity methods are assessed from a user perspective in a companion publication, and the accuracy and features of the CE TSUNAMI-3D GEAR-MC methods are detailed in this paper. (authors)

42 ENGINEERING↗
DOE OSTI2025

Code Coverage Status of the ARC Code PERSENT

The Argonne Reactor Code (ARC) software system supports users in their fast reactor design goals by providing neutronic, thermal-hydraulic, and structural analysis capabilities. PERSENT fulfills the role of generating reactivity coefficients for a given time point of a REBUS calculation usable in a point kinetics based safety analysis capability. PERSENT also provides a sensitivity coefficient capability on eigenvalue, reactivity worth, and several other key coefficients that are used in the follow-on safety analysis. Given a co-variance matrix, PERSENT can carry out the uncertainty quantification to indicate the amount of error in the reactivity coefficients derived from the errors in the cross section measurements. With continued improvement of computational resources, many of the geometry modeling capabilities in DIF3D that were primarily used in low order schemes are not really needed anymore. Today, the diffusion and transport capabilities of DIF3D-VARIANT are primarily used in the reactor design process with some scattered usage of DIF3D-FD and DIF3D-Nodal. PERSENT is part of the ARC code system and is built around DIF3D-VARIANT and the flux solution it provides. The purpose of the present work is to identify a set of test problems for PERSENT and assess the code coverage of PERSENT for those test problems. PERSENT treats the DIF3D executable as an external executable and thus the code coverage considerations only need to focus on the PERSENT source code and only a fraction of the connected modules in the existing ARC software library. The goal is to document what parts of the existing PERSENT code are touched by the set of test problems and which are not. Because the verification work done on PERSENT was focused on the most common uses of PERSENT for fast reactor analysis, the code coverage assessment of those capabilities is the highest priority. This will ensure that nothing is being missed by the existing verification test problems that users of PERSENT rely upon. The code coverage analysis of PERSENT was performed with the Code Coverage Tool of the Intel Fortran compiler which requires modifications to the compilation of PERSENT. The detailed coverage tables are given for each submodule of PERSENT. Most of the uncovered parts/files could be easily ignored because they are either for error message and debugging output or not needed by PERSENT today. Only a few uncovered parts of PERSENT deserve extending the verification test suite.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2017

Review of Early 21st-Century Monte Carlo Perturbation and Sensitivity Techniques for k -Eigenvalue Radiation Transport Calculations

Since the 1960s, Monte Carlo methods have been used to compute the effect of perturbations on system responses and for computing sensitivity coefficients. This review article focuses on 21st-century developments specific to k-eigenvalue calculations. The theory of correlated sampling, differential operator sampling, and adjoint-based approaches and their historical methods from the 20th century are briefly summarized. Specific focus is given to four recent and significant developments: fission source correction using the correlated sampling and differential operator sampling methods, adjoint-based perturbations for the k eigenvalue using the iterated fission probability method, an extension to reaction rate ratios using generalized perturbation theory, and a recent development using a collision history approach allowing for the calculation of sensitivity coefficients of bilinear ratios and generalized responses. Differences and similarities of the four methods are discussed along with a comparison to the 20th-century approaches. A perspective on future developments is also given.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2017

Sensitivity Coefficients for Diffusion Coefficients and Other Reactor Physics Parameters using CE TSUNAMI-3D

The TSUNAMI (Tools for Sensitivity and Uncertainty Analysis Methodology Implementation) capabilities within the SCALE code system leverage sensitivity coefficients for many criticality safety applications, including quantifying the data-induced uncertainty in the eigenvalue of critical systems, quantifying computational biases, and selecting applicable benchmark experiments. TSUNAMI sensitivity and uncertainty analysis tools have traditionally been limited to criticality safety application spaces, but the introduction of Generalized Perturbation Theory (GPT) sensitivity methods by Jessee in 2009 and Perfetti in 2013 has extended the scope of SCALE adjoint-weighted sensitivity and uncertainty analysis to include reactor physics applications. The continuous-energy (CE) TSUNAMI-3D GPT sensitivity analysis methods were originally developed to calculate sensitivity coefficients for a limited number of reaction-rate responses using CE Monte Carlo methods. These tools were recently applied in an Oak Ridge National Laboratory (ORNL)-directed research and development project to improve the efficiency of {sup 252}Cf production in the High Flux Isotope Reactor (HFIR) by understanding the sensitivity of key heavy actinide capture-to- fission ratios to potential system design changes. This work further extends the applicability of the CE TSUNAMI- 3D GPT methods to reactor physics applications by enabling the calculation of sensitivity coefficients for an expanded set of reaction rate responses-including a first-ever capability for conducting sensitivity analysis of neutron diffusion coefficients.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2015

Sensitivity and uncertainty analysis of reactivities for UO2 and MOX fueled PWR cells

The purpose of this paper is to apply our improved method for calculating sensitivities and uncertainties of reactivity responses for UO{sub 2} and MOX fueled pressurized water reactor cells. The improved method has been used to calculate sensitivity coefficients relative to infinite dilution cross-sections, where the self-shielding effect is taken into account. Two types of reactivities are considered: Doppler reactivity and coolant void reactivity, for each type of reactivity, the sensitivities are calculated for small and large perturbations. The results have demonstrated that the reactivity responses have larger relative uncertainty than eigenvalue responses. In addition, the uncertainty of coolant void reactivity is much greater than Doppler reactivity especially for large perturbations. The sensitivity coefficients and uncertainties of both reactivities were verified by comparing with SCALE code results using ENDF/B-VII library and good agreements have been found.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗