在高温气冷堆（high-temperature gas-cooled reactor，HTGR）堆芯球床中，燃料球间的辐射换热是重要的传热模式，与堆芯固有安全特性密切相关。该文利用机器学习方法提出了球床颗粒间辐射角系数智能预测方案，其中基础计算模型基于角系数显式解析表达式，合理描述了球床热辐射特性随球心距变化规律和周围颗粒球平均阻挡作用，用于快速计算球床堆中辐射角系数的核心主导部分。利用高温气冷堆示范项目（HTR-PM）球床堆积结构和光线追踪方法，建立了高温堆球床高精度角系数大数据集，共包含1.66×107条角系数工况，覆盖了球床各种局部结构。利用大数据训练后的梯度提升决策树模型有效提升了角系数预测精度，综合基础计算模型后角系数回归系数超过0.999。该文成果为高温气冷堆球流传热研究、堆芯优化和热工流体分析提供了高效的辐射传热计算方法。
Abstract
[Objective] In high-temperature gas-cooled reactors (HTGR), experimental results show that thermal radiation plays a significant role in the heat transfer process and it is highly related to the inherent safety of the nuclear reactor. The HTGR core is a dense pebble bed of single-sized fuel spheres. It is a fundamental and very challenging task to discuss the particle-scale radiative heat transfer in a pebble bed. In this study, using a machine learning approach, an artificial intelligent regression model is developed and trained on a large dataset to predict the obstructed view factor between fuel spheres in a nuclear pebble bed.[Methods] Comparing the numerical and experimental results, the radiative transfer equation (RTE) method significantly underestimates the radiative heat flux in dense pebble beds. The Lagrangian discrete element method (DEM) is often applied in pebble flow simulations. Thus, particle-particle interactions in the DEM framework are used in this present study. The view factor in the base model is calculated using an explicit analytical expression with the elliptic integral function. The model reasonably describes the effect of the distance between spheres and the average obstruction contribution of the surroundings. The obstruction function is proposed by fitting the numerical results. The analytical base model is used to efficiently obtain the dominant parts of the view factor. Furthermore, for the machine learning model, a large dataset of the view factor is established by the particle-scale DEM packing of the HTR-PM, an HTGR demonstration plant, and the thermal ray tracing method. Following preprocessing, the dataset contains a total of 16.6 million records under various conditions in a pebble bed. The gradient boosting decision tree (GBDT) model is used to learn the rules for view factor regression. The model input is the Cartesian coordinates of the sphere and its surrounding ones. The model output is the difference between the ground truth of the view factor and the analytical base model's prediction. 80% of the dataset is used for training, and 20% is left for validation. The mean square error (MSE) and coefficient of determination are selected to evaluate the machine learning model. The GBDT model was trained using the open-source software LightGBM, and the hyperparameter tuning was performed in the FLAML platform to find the best model parameters.[Results] The MSE of the trained machine learning model decreases gradually as the model complexity increases. The analytical base model provides a generally satisfactory forecast of the view factor in the pebble bed, and the gradient boosting decision tree model trained by big data greatly improved the prediction accuracy. With the base model, the coefficients of determination of the trained machine learning model are greater than 0.999.[Conclusions] This study presents an efficient artificial intelligent model for obstructed view factor prediction for heat transfer research, parameter optimization, and thermal hydraulic analysis of the nuclear pebble bed. The trained machine learning model can also be used in effective thermal conductivity analysis, and it is feasible to be coupled with the CFD-DEM simulations of conduction and heat convection in large-scale nuclear pebble beds.
关键词
高温气冷堆 /
球床 /
热辐射 /
颗粒尺度 /
角系数 /
梯度提升决策树 /
机器学习
Key words
high-temperature gas-cooled reactor /
pebble bed /
thermal radiation /
particle scale /
obstructed view factor /
gradient boosting decision tree /
machine learning
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基金
国家自然科学基金资助项目（12105101，12027813）；核反应堆系统设计技术重点实验室基金资助项目（KFKT-05-FW-HT-20220010）
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