Uncertainty Propagation Analysis for PWR Burnup Pin-Cell Benchmark by Monte Carlo Code McCARD

Ho Jin Park,Chang Hyo Kim,Hyung Jin Shim

doi:10.1155/2012/616253

Ho Jin Park, Chang Hyo Kim + Show 1 more

Open Access

https://doi.org/10.1155/2012/616253

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Abstract

In the Monte Carlo (MC) burnup analyses, the uncertainty of a tally estimate at a burnup step may be induced from four sources: the statistical uncertainty caused by a finite number of simulations, the nuclear covariance data, uncertainties of number densities, and cross-correlations between the nuclear data and the number densities. In this paper, the uncertainties ofkinf, reaction rates, and number densities for a PWR pin-cell benchmark problem are quantified by an uncertainty propagation formulation in the MC burnup calculations. The required sensitivities of tallied parameters to the microscopic cross-sections and the number densities are estimated by the MC differential operator sampling method accompanied by the fission source perturbation. The uncertainty propagation analyses are conducted with two nuclear covariance data—ENDF/B-VII.1 and SCALE6.1/COVA libraries—and the numerical results are compared with each other.

Highlights

Monte Carlo (MC) burnup analysis codes [1,2,3,4,5] have been successfully applied for the neutronics design and analysis of advanced nuclear systems with increasing computing power
Since Takeda et al [6] first proposed a formulation to evaluate the uncertainty propagation of number densities in the MC burnup analysis using the sensitivities of the burnup matrix to cross-sections and number densities, several studies [7,8,9,10,11] on the uncertainty propagation of MC burnup analysis followed with different uncertainty quantification formulations
The uncertainty quantification of a nuclear parameter, such as keff, reaction rates, and number densities, in the MC burnup analysis is currently conducted by two different approaches: the sensitivity and uncertainty (S/U) analysis [12] and the direct stochastic sampling methods

Summary

Introduction

Monte Carlo (MC) burnup analysis codes [1,2,3,4,5] have been successfully applied for the neutronics design and analysis of advanced nuclear systems with increasing computing power. The uncertainty quantification of a nuclear parameter, such as keff, reaction rates, and number densities, in the MC burnup analysis is currently conducted by two different approaches: the sensitivity and uncertainty (S/U) analysis [12] and the direct stochastic sampling methods. The direct stochastic sampling methods can produce output distributions from a number of MC calculations each with different input data set sampled. This approach is easy to implement by running existing MC neutronics analysis codes with different input data sets but at the expense of high computational costs. The numerical results with ENDF/B-VII. covariance data are compared with those from the SCALE6.1/COVA covariance libraries

McCARD Uncertainty Propagation Methodology

UAM PWR Pin-Cell Burnup Benchmark

Conclusion