| Research Article |
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Machine learning model of radiation heat transfer in the high-temperature nuclear pebble bed |
| WU Hao, NIU Fenglei |
| School of Nuclear Science and Engineering, North China Electric Power University, Beijing 102206, China |
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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.
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| Keywords
high-temperature gas-cooled reactor
pebble bed
thermal radiation
particle scale
obstructed view factor
gradient boosting decision tree
machine learning
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Issue Date: 22 July 2023
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2023,
Vol. 63
