Heat Transfer Modeling of Spent Nuclear Fuel Using Uncertainty Quantification and Polynomial Chaos Expansion

Abstract

A novel method that incorporates uncertainty quantification (UQ) into numerical simulations of heat transfer for a 9 × 9 square array of spent nuclear fuel (SNF) assemblies in a boiling water reactor (BWR) is presented in this paper. The results predict the maximum mean temperature at the center of the 9 × 9 BWR fuel assembly to be 462 K using a range of fuel burn-up power. Current related modeling techniques used to predict the heat transfer and the maximum temperature inside SNF assemblies rely on commercial codes and address the uncertainty in the input parameters by running separate simulations for different input parameters. The utility of leveraging polynomial chaos expansion (PCE) to develop a surrogate model that permits the efficient evaluation of the distribution of temperature and heat transfer while accounting for all uncertain input parameters to the model is explored and validated for a complex case of heat transfer that could be substituted with other problems of intricacy. UQ computational methods generated results that are encompassing continuous ranges of variable parameters that also served to conduct sensitivity analysis on heat transfer simulations of SNF assemblies with respect to physically relevant parameters. A two-dimensional (2D) model is used to describe the physical processes within the fuel assembly, and a second-order PCE is used to characterize the dependence of center temperature on ten input parameters.

Quantification of Uncertainties on the Critical Buckling Load of Columns under Axial Compression with Uncertain Random Materials

“…Monte Carlo method has been largely used as a very powerful stochastic solver in various domains of science, especially for uncertainty quantification [47,48]. Stochastic analysis involving Monte Carlo simulations as a stochastic solver has been reported in many works, for example, for structural dynamics [49,50,51], in vascular mechanics [52,53,54], for composite materials [15,55,56,57,58], for model reduction [59,60], for concrete structures [61,62], for hyper-elastic materials [26,63], and for heat transfer problems [64]. Such techniques, based on statistically independent sampling, are extremely efficient and powerful for calculating the statistical quantities that measure the propagation of the uncertainty of input parameters on the output results.…”