This study explored the impact of undersampling on the accuracy of tally estimates in Monte Carlo (MC) calculations. Steady-state MC simulations were performed for models of several critical systems with varying degrees of spatial and isotopic complexity, and the impact of undersampling on eigenvalue and fuel pin flux/fission estimates was examined. This study observed biases in MC eigenvalue estimates as large as several percent and biases in fuel pin flux/fission tally estimates that exceeded tens, and in some cases hundreds, of percent. This study also investigated five statistical metrics for predicting the occurrence of undersampling biases in MC simulations. Three of the metrics (the Heidelberger-Welch RHW, the Geweke Z-Score, and the Gelman-Rubin diagnostics) are commonly used for diagnosing the convergence of Markov chains, and two of the methods (the Contributing Particles per Generation and Tally Entropy) are new convergence metrics developed in the course of this study. These metrics were implemented in the KENO MC code within the SCALE code system and were evaluated for their reliability at predicting the onset and magnitude of undersampling biases in MC eigenvalue and flux tally estimates in two of the critical models. Of the five methods investigated, the Heidelberger-Welch RHW, the Gelman-Rubin diagnostics, and Tally Entropy produced test metrics that correlated strongly to the size of the observed undersampling biases, indicating their potential to effectively predict the size and prevalence of undersampling biases in MC simulations.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

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 OSTI2014

Monte Carlo Capabilities of the SCALE Code System

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Rearden, Bradley T↗

DOE OSTI2014

CONTINUOUS-ENERGY MONTE CARLO METHODS FOR CALCULATING GENERALIZED RESPONSE SENSITIVITIES USING TSUNAMI-3D

This work introduces a new approach for calculating sensitivity coefficients for generalized neutronic responses to nuclear data uncertainties using continuous-energy Monte Carlo methods. The approach presented in this paper, known as the GEAR-MC method, allows for the calculation of generalized sensitivity coefficients for multiple responses in a single Monte Carlo calculation with no nuclear data perturbations or knowledge of nuclear covariance data. The theory behind the GEAR-MC method is presented here, and proof of principle is demonstrated by using the GEAR-MC method to calculate sensitivity coefficients for responses in several 3D, continuous-energy Monte Carlo applications.

CLUTCH↗

DOE OSTI2014

Quantifying the Effect of Undersampling in Monte Carlo Simulations Using SCALE

This study explores the effect of undersampling in Monte Carlo calculations on tally estimates and tally variance estimates for burnup credit applications. Steady-state Monte Carlo simulations were performed for models of several critical systems with varying degrees of spatial and isotopic complexity and the impact of undersampling on eigenvalue and flux estimates was examined. Using an inadequate number of particle histories in each generation was found to produce an approximately 100 pcm bias in the eigenvalue estimates, and biases that exceeded 10% in fuel pin flux estimates.

bias↗

DOE OSTI2014

Enhancements in Continuous-Energy Monte Carlo Capabilities for SCALE 6.2

SCALE is a widely used suite of tools for nuclear systems modeling and simulation that provides comprehensive, verified and validated, user-friendly capabilities for criticality safety, reactor physics, radiation shielding, and sensitivity and uncertainty analysis. For more than 30 years, regulators, industry, and research institutions around the world have used SCALE for nuclear safety analysis and design. SCALE provides a plug-and-play framework that includes three deterministic and three Monte Carlo radiation transport solvers that are selected based on the desired solution. SCALE includes the latest nuclear data libraries for continuous-energy and multigroup radiation transport as well as activation, depletion, and decay calculations. SCALE s graphical user interfaces assist with accurate system modeling, visualization, and convenient access to desired results. SCALE 6.2 provides several new capabilities and significant improvements in many existing features, especially with expanded continuous-energy Monte Carlo capabilities for criticality safety, shielding, depletion, sensitivity and uncertainty analysis, and improved fidelity in nuclear data libraries. A brief overview of SCALE capabilities is provided with emphasis on new features for SCALE 6.2.

Continuous-Energy↗

DOE OSTI2014

Performance Enhancements to the SCALE TSUNAMI-3D Generalized Response Sensitivity Capability

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Perfetti, Christopher M↗