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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 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 OSTI2023

Impact of Thermal Scattering Law on Similarity Assessment in Light-Water or Polyethylene-Moderated Systems

A collaborative effort between Pacific Northwest National Laboratory (PNNL) and Oak Ridge National Laboratory (ORNL) is underway to provide a technical basis and methodology for the criticality safety community to use the sum of fractions (SoF) method for generating limits for mixtures of “selected actinide nuclides” included in the ANSI/ANS 8.15 standard. The PNNL scope in this project is to define a range of mixtures of 233 U, 235 U, and 239 Pu moderated with either light water or polyethylene and to examine the critical masses for these mixtures. The ORNL scope is primarily to provide validation support for these studies. More complete discussion of the project and its validation aspects will be presented at the upcoming International Conference on Nuclear Criticality Safety (ICNC) this Fall in Sendai, Japan. Clear differences in benchmark similarity to application systems as assessed by the integral parameter ck are noted in the validation studies performed as part of this project as a function of moderator. The c k value is a correlation coefficient that represents that amount of shared uncertainty in k eff due to cross sections between two systems. Individual nuclide-reaction contributions between the two systems can be simply summed to arrive at the total c k value. Specifically, the c k values for light-water–moderated solution experiments are higher for a water-moderated application than for a polyethylene-moderated application. This result is neither totally unexpected nor surprising, but the magnitude of the difference was difficult to anticipate. The TSUNAMI sequence, in the SCALE 6.2.4 code package developed by ORNL, was used to generate eigenvalues and reactivity effects with perturbation-theory based approach through sensitivity coefficients for all nuclides in the system with all reactions and energy groups. The TSUNAMI-Indices and Parameters (IP) sequence then uses the sensitivity data generated through TSUNAMI to generate relational parameters (i.e., c k ) to determine the degree of similarity between systems. One detail of the SCALE material and data implementation must be discussed at this point. Several thermal scattering laws (TSLs) are available for 1 H. SCALE uses a different nuclide ID number for each TSL; essentially, each version of 1 H is treated as a unique nuclide. For example, 1 H bound in water ( 1 H-H2O) is assigned the nuclide ID 1001, whereas 1 H bound in polyethylene (h-poly) is assigned the nuclide ID 9001001. The same cross section data are used for all reactions in 1 H, regardless of TSL, except for scattering below the TSL cutoff energy. TSUNAMI-IP treats different nuclide IDs as different nuclides; thus, no uncertainty is shared between 1 H-H2O and h-poly, despite much of the same data, including covariance data, being used for both nuclides. This presents a question: how much of the difference in assessed similarity between water- and polyethylene-moderated systems is due to the moderators, and how much is caused by the treatment of 1 H-H2O and h poly with cross section and covariance data. The extended edits generated by TSUANMI-IP allow for an investigation of this issue specifically, as well as a demonstration of the general techniques available within TSUNAMI to understand the results of the similarity assessment. This paper presents and analyzes the similarity assessment of both water- and polyethylene-moderated systems for a single benchmark: PST-002-001.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Deep Learning for Multigroup Cross-Section Representation in Two-Step Core Calculations

Here we investigate using deep learning, a type of machine-learning algorithm employing multiple layers of artificial neurons, for the mathematical representation of multigroup cross sections for use in the Griffin reactor multiphysics code for two-step deterministic neutronics calculations. A three-dimensional fuel element typical of a high-temperature gas reactor as well as a two-dimensional sodium-cooled fast reactor lattice are modeled using the Serpent Monte Carlo code, and multigroup macroscopic cross sections are generated for various state parameters to produce a training data set and a separate validation data set. A fully connected, feedforward neural network is trained using the open-source PyTorch machine-learning framework, and its accuracy is compared against the standard piecewise linear interpolation model. Additionally, we provide in this work a generic technique for propagating the cross-section model errors up to the k eff using sensitivity coefficients with the first-order uncertainty propagation rule. Quantifying the eigenvalue error due to the cross-section regression errors is especially practical for appropriately selecting the mathematical representation of the cross sections. We demonstrate that the artificial neural network model produces lower errors and therefore enables better accuracy relative to the piecewise linear model when the cross sections exhibit nonlinear dependencies; especially when a coarse grid is employed, where the errors can be halved by the artificial neural network. However, for linearly dependent multigroup cross sections as found for the sodium-cooled fast reactor case, a simpler linear regression outperforms deeper networks.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2016

CE TSUNAMI-3D Algorithm Improvements in SCALE 6.2

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 continuous-energy (CE) TSUNAMI-3D code is a new tool included in SCALE 6.2 that allows for eigenvalue and generalized response sensitivity calculations using high-fidelity CE Monte Carlo methods. This paper describes several improvements to CE TSUNAMI-3D beyond those previously published. These improvements primarily consist of - A multi-response capability for the CE TSUNAMI generalized response sensitivity calculation mode; and - Efficiency improvements in CE TSUNAMI's Iterated Fission Probability (IFP)-based algorithms. This paper documents several improvements to the CE TSUNAMI-3D sensitivity algorithms included in the SCALE 6.2 release. These improvements have enabled the simulation of multiple GPT responses within a single CE TSUNAMI simulation, a feature that increases the memory footprint of the simulations by approximately 1-3% per response and the runtime by approximately 1-2%, per response. These algorithmic improvements have also significantly improved the computational efficiency of CE TSUNAMI IFP-based sensitivity calculations, reducing the memory footprints approximately by a factor of 3 and the simulation runtimes by 10-70%. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗