Christopher M. Perfetti

SCALE Continuous-Energy Eigenvalue Sensitivity Coefficient Calculations

Abstract The need to model geometrically complex systems with improved ease of use and fidelity and the desire to extend the Tools for Sensitivity and UNcertainty Analysis Methodology Implementation (TSUNAMI) analysis to advanced applications have 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 Track length 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 CE Monte Carlo methods. This paper provides a detailed description of the theory behind the CLUTCH method and describes in detail its implementation. This work also explores the improvements in eigenvalue sensitivity coefficient accuracy that can be gained through use of CE sensitivity methods and compares several sensitivity methods in terms of computational efficiency and memory requirements. The IFP and CLUTCH methods produced sensitivity coefficient estimates that matched, and in some cases exceeded, the accuracy of those produced using the multigroup TSUNAMI-3D approach. The CLUTCH method was found to calculate sensitivity coefficients with the highest degree of efficiency and the lowest computational memory footprint for the problems examined.

Development of a Generalized Perturbation Theory Method for Sensitivity Analysis Using Continuous-Energy Monte Carlo Methods

Abstract The sensitivity and uncertainty analysis tools of the Oak Ridge National Laboratory 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 with realistic three-dimensional Monte Carlo simulations but currently can only quantify the uncertainty in important neutronic parameters such as multigroup cross sections, fuel fission rates, activation rates, and neutron fluence rates with one- or two-dimensional models. A more complete understanding of the sources of uncertainty in these design-limiting parameters using high-fidelity models could lead to improvements in process optimization and reactor safety and help inform regulators when setting operational safety margins. A novel approach for calculating eigenvalue sensitivity coefficients, known as the CLUTCH (Contributon-Linked eigenvalue sensitivity/Uncertainty estimation via Track length importance CHaracterization) 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 an extension of the CLUTCH method, known as the GEneralized Adjoint Responses in Monte Carlo (GEARMC) method, that enables the calculation of sensitivity coefficients and uncertainty analysis for a generalized set of neutronic responses using high-fidelity continuous-energy Monte Carlo calculations. Several criticality safety systems were examined to demonstrate proof of principle for the GEAR-MC method, and GEAR-MC produced response sensitivity coefficients that agreed well with reference direct perturbation sensitivity coefficients.

Adjoint-based sensitivity and uncertainty analysis for density and composition: A user's guide

Abstract The evaluation of uncertainties is essential for criticality safety. This paper deals with material density and composition uncertainties and provides guidance on how traditional first-order sensitivity methods can be used to predict their effects. Unlike problems that deal with traditional cross-section uncertainty analysis, material density and composition-related problems are often characterized by constraints that do not allow arbitrary and independent variations of the input parameters. Their proper handling requires constrained sensitivities that take into account the interdependence of the inputs. This paper discusses how traditional unconstrained isotopic density sensitivities can be calculated using the adjoint sensitivity capabilities of the popular Monte Carlo codes MCNP6 and SCALE 6.2, and we also present the equations to be used when forward and adjoint flux distributions are available. Subsequently, we show how the constrained sensitivities can be computed using the unconstrained (adjoint-based) sensitivities as well as by applying central differences directly. Three distinct procedures are presented for enforcing the constraint on the input variables, each leading to different constrained sensitivities. As a guide, the sensitivity and uncertainty formulas for several frequently encountered specific cases involving densities and compositions are given. An analytic k∞ example highlights the relationship between constrained sensitivity formulas and central differences, and a more realistic numerical problem reveals similarities among the computer codes used and differences among the three methods of enforcing the constraint.

Diagnosing Undersampling Biases in Monte Carlo Eigenvalue and Flux Tally Estimates

This study focuses on understanding the phenomena in Monte Carlo simulations known as undersampling, in which Monte Carlo tally estimates may not encounter a sufficient number of particles during each generation to obtain unbiased tally estimates. Steady-state Monte Carlo simulations were performed using the KENO Monte Carlo tools within the SCALE code system for models of several burnup credit applications with varying degrees of spatial and isotopic complexities, and the incidence and impact of undersampling on eigenvalue and flux estimates were examined. Using an inadequate number of particle histories in each generation was found to produce a maximum bias of ∼100 pcm in eigenvalue estimates and biases that exceeded 10% in fuel pin flux tally estimates. Having quantified the potential magnitude of undersampling biases in eigenvalue and flux tally estimates in these systems, this study then investigated whether Markov Chain Monte Carlo convergence metrics could be integrated into Monte Carlo simulations to predict the onset and magnitude of undersampling biases. Five potential metrics for identifying undersampling biases were implemented in the SCALE code system and evaluated for their ability to predict undersampling biases by comparing the test metric scores with the observed undersampling biases. Of the five convergence metrics that were investigated, three (the Heidelberger-Welch relative half-width, the Gelman-Rubin diagnostic, and tally entropy) showed the potential to accurately predict the behavior of undersampling biases in the responses examined.