The windowed multipole formalism and applications to uncertainty quantification

Abstract

In the safety oriented nuclear engineering world, managing uncertainties on fundamental parameters is crucial. Large uncertainties in the neutron cross sections of materials used in these systems propagate through the modeling process and result in large uncertainties in the predicted behavior of the system. Without reducing the uncertainties on the input neutron cross sections by evaluating new experimental data, the only solution to the safety concern of the large uncertainties is to provide large safety margins. The practice of over designing is economically wasteful and adds to the already high cost of nuclear reactors. On the other hand, investing the funds in better nuclear data would result in less uncertainty in the predicted behavior of the system. The high cost of cross section experiments and evaluations requires a procedure to best allocate the funds by proposing experiments that can have the biggest impact on reducing the uncertainties that directly impact the operation and safety of nuclear systems.This work develops a novel method based on first order sensitivity analysis that propagates the nuclear cross section uncertainty to uncertainties in calculated quantities, such as keff, reactivity coefficients, multigroup cross sections, and reaction rate ratios. The method developed here improves on existing methods by fully accounting for temperature effects, and by providing a natural, physics-inspired strategy for binning the sensitivity coefficient which aids in the statistical convergence of the sensitivity tallies. These benefits are achieved by using the windowed multipole cross section representation.As part of the development of the framework, several individual capabilities were developed. First, an algorithm for calculating the sensitivity coefficients to the windowed multipole parameters based on the CLUTCH-FM method is developed and implemented in OpenMC. Second, a process for converting the existing resonance parameter uncertainties to uncertainties in the windowed multipole parameters is introduced. Finally, an analytical benchmark is developed for the purposes of validating the framework, as well as the implementation. This analytical benchmark consists of a solution to the forward and adjoint neutron transport equations.The windowed multipole covariance matrix is obtained for three nuclides; 23Na, 157Gd, and 238U. The framework is used to calculate the uncertainties for two criticality safety benchmarks, and a beginning-of-life PWR model. The uncertainty of several reaction rate ratios due to the uncertainty in the 157Gd cross section is also calculated for the PWR model. The resonances of 238U and 157Gd that have the largest contribution to the uncertainty are identified for the criticality safety benchmarks.