Abstract Thermal radiation in pebble bed is very hard to compute accurately and efficiently since it occurs between the surfaces no matter how far they are. Herein, radiative heat flux and effective thermal conductivity were derived mathematically by a matrix model to present the thermal radiation between particles in pebble beds. For structured packing, the transient radiative heat transfer is proven to be similar to thermal diffusion. This study proposed a correlation to predict the radiation exchange factor under different porosity. Radiative effective thermal conductivity was found to grow slightly with void fractions. For random pebble beds, a regression model of the multi-layer neural network was trained by large datasets to compute the view factor matrix efficiently. With the trained model and GPU acceleration, it is feasible to perform real-time-simulation of full-range radiations inside large-scale pebble beds, even for real reactors (e.g. HTR-PM). A thermal radiation simulation of the decay heat removal of a real reactor adopted this model as a demonstrative application and showed that the highest temperature is still within the design limitation of the packed bed.

中文翻译：

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结构化和随机填充球床中颗粒尺度辐射传热的矩阵模型

摘要 球床中的热辐射很难准确有效地计算，因为它发生在表面之间，无论距离多远。在这里，辐射热通量和有效热导率是通过矩阵模型数学推导出来的，以呈现卵石层中颗粒之间的热辐射。对于规整填料，瞬态辐射传热被证明类似于热扩散。本研究提出了一种相关性来预测不同孔隙度下的辐射交换因子。发现辐射有效热导率随着空隙率的增加而略微增加。对于随机卵石床，多层神经网络的回归模型由大型数据集训练，以有效计算视角因子矩阵。借助经过训练的模型和 GPU 加速，即使对于真实的反应堆（例如 HTR-PM），在大型卵石床内进行全范围辐射的实时模拟也是可行的。实际反应器衰变热去除的热辐射模拟采用该模型作为示范应用，表明最高温度仍在填充床的设计限制范围内。