Analysis of Statistical Uncertainties in Monte Carlo Functional Expansion Tallies

Abstract

Functional expansion tallies (FETs) have been investigated as an alternative approach to improve the fidelity of light water reactor (LWR) multi-physics (MP) simulations. Although FETs have been implemented in some Monte Carlo (MC) codes, the statistical properties have not been studied for use in core neutronics analysis. This work examines the convergence and statistical properties of FETs used in a two-dimensional (2D) and three-dimensional (3D) LWR fuel pin and compares the sample, apparent and real standard deviation (STD) of mesh-based volume-integrated power FET with those of the histogram-based tallies. Inter-cycle correlation, autocorrelation coefficients (ACC), convergence rate, and sensitivity of the FET statistical uncertainty to the expansion order, size and number of tally regions are investigated. We show that for the 2D pin, the real STD of the Zernike-based radial power FET is lower compared to the zeroth-order tally (offering a kind of variance reduction). The inter-cycle correlation is low at all lags and negative for the high order coefficients. For the Legendre FET of axial power in the 3D pin, the coefficients have high inter-cycle correlation at lag 1. In addition, the real variance is underestimated. However, variance reduction can also be achieved depending on the size of the tally region.