Uncertainty and sensitivity analysis of core flow distribution optimization using Monte-Carlo method and Wilks' formula

The core flow distribution optimization is of great significance in enhancing reactor performance and safety. However, the use of uncertainty quantification and sensitivity analysis to assess the reliability of flow distribution optimization schemes is rare. Previous uncertainty studies mainly focus on safety-related reactor parameters. In this paper, the optimization objectives (the maximum-to minimum and the maximum-to-average temperature difference at the core outlet) and the safety constraint (MDNBR) for flow distribution were considered as the system outputs of interest. Taking twelve input uncertain parameters into account, Monte Carlo method and Wilks' method were utilized to quantify the output uncertainty of the optimized system. The results showed that, even under the most restrictive conditions, the optimized system still significantly outperformed the unoptimized state, with MDNBR remaining well above the safety limit. Therefore, the credibility of the optimization scheme was confirmed. Furthermore, through adjusting the order of the Wilks’ statistics and multiple trials, we compared the performance of the two uncertainty analysis methods. Lastly, sensitivity analysis based on Monte Carlo results was performed using Pearson, Spearman, Kendall, and partial rank correlation coefficients. The most influential parameter on core outlet temperature nonuniformity and the hottest channel temperature was the radial power distribution. On the other hand, axial power distribution, system flow, core power, and radial power distribution exhibit significant correlations with MDNBR.