Abstract

Thermal stratification (TS) is a thermal-fluid phenomenon that can introduce large uncertainties to nuclear reactor safety. The stratified layers caused by TS can lead to temperature oscillations in the reactor core. They can also result in damages to both the reactor vessel and in-vessel components due to the growth of thermal fatigue cracks. More importantly, TS can impede the establishment of natural circulation, which is widely used for passive cooling and ensures the inherent safety of numerous reactor designs. A fast-running one-dimensional (1-D) model was recently developed in our research group to predict the TS phenomenon in pool-type sodium-cooled fast reactors. The efficient 1-D model provided reasonable temperature predictions for the test conditions investigated, but nonnegligible discrepancies between the 1-D predictions and the experimental temperature measurements were observed. These discrepancies are attributed to the model uncertainties (also known as model bias or errors) in the 1-D model and the parameter uncertainties in the input parameters.

In this study, we first recognized through a forward uncertainty analysis that the observed discrepancies between the computational predictions and the experimental temperature measurements could not be explained solely by input uncertainty propagation. We then performed an inverse uncertainty quantification (UQ) study to reduce the model uncertainties of the 1-D model using a modular Bayesian approach based on experimental data. Inverse UQ serves as a data assimilation process to simultaneously minimize the mismatches between the predictions and experimental measurements, while quantifying the associated parameter uncertainties. The solutions of the modular Bayesian approach were in the form of posterior probability density functions, which were explored by rigorous Markov Chain Monte Carlo sampling. Results showed that the quantified parameters obtained from the inverse UQ effectively improved the predictive capability of the 1-D TS model.

摘要

热分层（TS）是一种热流体现象，会给核反应堆安全性带来很大的不确定性。TS引起的分层可能导致反应堆堆芯中的温度振荡。由于热疲劳裂纹的增长，它们还可能导致对反应堆容器和容器内组件的损坏。更重要的是，TS会阻碍自然循环的建立，自然循环被广泛用于被动冷却并确保了众多反应堆设计的固有安全性。我们的研究小组最近开发了一种快速运行的一维（1-D）模型，以预测池型钠冷快堆中的TS现象。高效的一维模型为所研究的测试条件提供了合理的温度预测，但观察到的一维预测与实验温度测量值之间的差异不可忽略。这些差异归因于一维模型中的模型不确定性（也称为模型偏差或误差）和输入参数中的参数不确定性。

在这项研究中，我们首先通过正向不确定性分析认识到，计算预测和实验温度测量值之间观察到的差异不能仅通过输入不确定性传播来解释。然后，我们基于实验数据，使用模块化贝叶斯方法进行了逆不确定性量化（UQ）研究，以减少一维模型的模型不确定性。逆UQ用作数据同化过程，以同时最小化预测值和实验测量值之间的失配，同时量化相关的参数不确定性。模块化贝叶斯方法的解采用后验概率密度函数的形式，这是通过严格的马尔可夫链蒙特卡洛采样法进行探索的。