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: In this paper, view factors are crucial for radiative heat transfer calculation in high-temperature pebble beds. Traditional numerical calculation of view factors demands complex integration, and different formulas are needed for various geometries, leading to high computational complexity. To address this issue, we proposed a view factors model based on ray tracing and combined with particle radiation characteristics. This model eliminates the need for discrete analysis in particle modeling; it only requires particle coordinates and radii for computation. When comparing the results of ray tracing and the numerical method for tangent particles, we found that when the optical density reaches a certain value, the relative error between the two results is within 1%. particle-particle radiation mainly concentrates along the center line, and its intensity decreases in all directions following a cosine function. When we analyzed a single particle from the randomly accumulated pebble bed particles, we determined that the radiation range was mainly within twice the diameter. This was accompanied by a cumulative angular coefficient exceeding 0.98 and the number of particles is within 100. When examining the radiation range within three times the diameter of the particles, we discovered that when the cumulative angular coefficient surpassed 0.99. This paper presents a simpler method for calculating the view factor of complex pebble beds, providing technical support for analyzing the heat radiation transfer characteristics in high-temperature pebble beds.
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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 (H)ray tracing
($ \times {10}^{-2} $)numerical method
($ \times {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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