View factors in high-temperature pebble beds based on the ray tracing theory
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摘要: 在高温颗粒球床堆芯辐射换热过程中，角系数是辐射换热计算的关键参数。传统数值计算角系数的方法需进行复杂积分运算，且不同几何形状的积分公式各异，计算难度较大。为降低球床颗粒间角系数的计算难度，提出了一种基于光线追踪理论并结合颗粒辐射特性的角系数计算模型。该模型无需对颗粒进行建模做离散分析，仅需获取颗粒的坐标信息和半径即可进行计算，极大地简化了计算过程。通过在颗粒相切情况下对比光线追踪与数值结果，当光线密度达到特定值时，二者结果相对误差在1%内。颗粒间辐射主要以中心连线为辐射能量最强处，向四周减少，其变化趋势呈余弦函数。在球床颗粒随机堆积情况下，选取单个颗粒进行分析，发现辐射范围以2倍直径内为主，此时角系数累积超过0.98，颗粒数量在100个以内；在3倍直径范围内，累积角系数超过0.99。Abstract:
Background In high-temperature pebble bed cores, radiative heat transfer plays a crucial role, where the view factor is a key parameter in determining radiative exchange between particles. Traditional methods for calculating view factors rely on complex integration, which varies with geometric configurations and is computationally intensive.Purpose This study aims to accurately calculate view factors in randomly packed pebble beds. It proposes a ray tracing model based on thermal radiation mechanisms to simplify the calculation of view factors between particles in complex packing structures.Methods Firstly, the particle surface is discretized to generate uniformly distributed ray origin points. Secondly, ray directions are determined based on the characteristics of thermal emission. Thirdly, rays defined in local coordinates are transformed into global space and traced for intersections with target particles. Finally, the view factor is computed as the ratio of rays that collide with target particles to the total number of emitted rays.Results The results show that inter-particle radiation is mainly concentrated at the center line and decays towards the periphery, showing a clear cosine distribution. The radiation range of a single particle is mainly concentrated within twice the particle diameter, at which point the view factor exceeds 0.98 and the number of particles is less than 100. Within three times the diameter, the cumulative view factor exceeds 0.99.Conclusions The proposed quasi-Monte Carlo ray tracing model provides an accurate and efficient method for computing view factors in dense particle systems. It effectively captures the anisotropic nature of radiative transfer in randomly packed beds and offers a practical tool for analysing thermal radiation in high-temperature pebble beds.-
Key words:
- high-temperature pebble beds /
- radiation heat exchange /
- ray tracing /
- view factor /
- numerical method
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图 6 光线追踪模型与数值解角系数对比
Figure 6. Comparison of view factors between ray tracing model and numerical solution
图 7 辐射平均传递距离和辐射平均传递角度
Figure 7. Average radiation transmission distance and average radiation transmission angle
图 8 颗粒间距离和遮挡颗粒位置对角系数的影响
Figure 8. Impact of interparticle distance and obstructive particle position on the view factors
图 10 不同直径范围内的颗粒角系数变化
Figure 10. Variation of the particle view factors within different diameter ranges
表 1 光线行进距离和光线偏移角度的变化趋势
Table 1. The trend of changes in the distance traveled by light and the angle of light deviation
particle center
distance/Hray tracing/10-2 numerical metho/10-2 average distance of
heat radiationaverage angle of
thermal radiation2 7.573 7.558 0.358 30.05 3 2.964 2.959 1.494 18.25 4 1.605 1.615 2.620 13.35 5 1.017 1.021 3.621 10.51 6 0.698 0.704 4.597 8.73 
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