Abstract
Uncertainty analyses of fission product yields are indispensable in evaluating reactor burnup and decay heat calculation credibility. Compared with neutron cross section, there are fewer uncertainty analyses conducted and it has been a controversial topic by lack of properly estimated covariance matrix as well as adequate sampling method. Specifically, the conventional normal-based sampling method in sampling large uncertainty independent fission yields could inevitably generate nonphysical negative samples. Cutting off these samples would introduce bias into uncertainty results. Here, we evaluate thermal neutron-induced U-235 independent fission yields covariance matrix by the Bayesian updating method, and then we use lognormal-based sampling method to overcome the negative fission yields samples issue. Fission yields uncertainty contribution to effective multiplication factor and several fission products’ atomic densities at equilibrium core of pebble-bed HTGR are quantified and investigated. The results show that the lognormal-based sampling method could prevent generating negative yields samples and maintain the skewness of fission yields distribution. Compared with the zero cut-off normal-based sampling method, the lognormal-based sampling method evaluates the uncertainty of effective multiplication factor and atomic densities are larger. This implies that zero cut-off effect in the normal-based sampling method would underestimate the fission yields uncertainty contribution. Therefore, adopting the lognormal-based sampling method is crucial for providing reliable uncertainty analysis results in fission product yields uncertainty analysis.
Highlights
Reactor design and safety analysis rely on accurate calculations of system responses with properly evaluated uncertainties. ere has been an increasing need for evaluating the credibility of reactor safety
Uncertainty Analysis of the Effective Multiplication Factor at Equilibrium Core. e unperturbed burnup calculation is conducted with V.S.O.P. built-in fission yields library and ENDF/B-VII.1 posterior fission yields
Effective multiplication factor calculated from ENDF/B-VII.1 posterior fission yields is compared with that calculated from V.S.O.P. built-in fission yields and the total discrepancy at equilibrium core state is lower than 50 pcm which is small enough for the following fission product yields uncertainty propagation analysis. e comparison between ENDF/B-VII.1 posterior fission yields predicated keff and builtin yields predicted keff are shown in Figure 18(b). is discrepancy is within the sampling distribution of keff
Summary
Reactor design and safety analysis rely on accurate calculations of system responses with properly evaluated uncertainties. ere has been an increasing need for evaluating the credibility of reactor safety. As the fission yields’ covariances in current releases of evaluated nuclear data libraries are still absent, e.g., ENDF/B-VII., many methods are developed to estimate these covariances information based on the imposed physical constraints. Based on the provided independent and cumulative fission yields uncertainties information in ENDF/B-VII., this work adopts the Bayesian updating method to estimate the independent fission yields covariances. Sampling-based methods for uncertainty analysis or stochastic UQ methods [17] require properly perturbed samples to provide reliable uncertainty analysis results of QoI As it is observed from the evaluated nuclear data library, independent fission yields generally have larger uncertainties. Random sampling on these yields under normal distribution could generate nonphysical negative samples.
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