View factors in high-temperature pebble beds based on the ray tracing theory

Zhao Peng; Wu Hao

doi:10.11884/HPLPB202537.240438

Article Contents

Article Navigation > High Power Laser and Particle Beams > 2025 > Accepted Manuscript

Zhao Peng, Wu Hao. View factors in high-temperature pebble beds based on the ray tracing theory[J]. High Power Laser and Particle Beams. doi: 10.11884/HPLPB202537.240438

Citation:

Zhao Peng, Wu Hao. View factors in high-temperature pebble beds based on the ray tracing theory[J]. High Power Laser and Particle Beams. doi: 10.11884/HPLPB202537.240438

Zhao Peng, Wu Hao. View factors in high-temperature pebble beds based on the ray tracing theory[J]. High Power Laser and Particle Beams. doi: 10.11884/HPLPB202537.240438

Citation:

Zhao Peng, Wu Hao. View factors in high-temperature pebble beds based on the ray tracing theory[J]. High Power Laser and Particle Beams. doi: 10.11884/HPLPB202537.240438

PDF( 4428 KB)

View factors in high-temperature pebble beds based on the ray tracing theory

doi: 10.11884/HPLPB202537.240438

Zhao Peng,
Wu Hao^,

School of Nuclear Science and Engineering, North China Electric Power University, Beijing 102206, China

Received Date: 2024-12-24
Accepted Date: 2025-05-30
Rev Recd Date: 2025-03-12

Available Online: 2025-07-16

Abstract

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.
- high-temperature pebble beds,
- radiation heat exchange,
- ray tracing,
- view factor,
- numerical method

FullText(HTML)

References(24)

References

[1]	游战洪. 世界首座模块式球床高温气冷堆[J]. 科学, 2016, 68(1):24-28 You Zhanhong. The world first pebble-bed modular high temperature gas cooled reactor[J]. Science, 2016, 68(1): 24-28
[2]	Wu Yongyong, Ren Cheng, Yang Xingtuan, et al. Repeatable experimental measurements of effective thermal diffusivity and conductivity of pebble bed under vacuum and helium conditions[J]. International Journal of Heat and Mass Transfer, 2019, 141: 204-216. doi: 10.1016/j.ijheatmasstransfer.2019.06.071
[3]	姜胜耀, 桂南, 杨星团, 等. 球床式高温气冷堆球流及球床辐射的理论与实验研究进展[J]. 原子能科学技术, 2019, 53(10):1918-1929 Jiang Shengyao, Gui Nan, Yang Xingtuan, et al. Theoretical and experimental research progress on pebble flow and effective thermal conductivity in pebble-type HTGR[J]. Atomic Energy Science and Technology, 2019, 53(10): 1918-1929
[4]	吴浩, 桂南, 杨星团, 等. 高温球床辐射换热机理研究[J]. 核动力工程, 2016, 37(2):32-37 Wu Hao, Gui Nan, Yang Xingtuan, et al. Study on mechanism of radiation heat exchange for high temperature pebble beds[J]. Nuclear Power Engineering, 2016, 37(2): 32-37
[5]	郑艳华, 夏冰, 解衡, 等. HTR-10超高温运行的初步物理热工设计[J]. 中国基础科学, 2021, 23(3):16-20 Zheng Yanhua, Xia Bing, Xie Heng, et al. Preliminary physical design and thermal hydraulic design on HTR-10 operating in higher outlet temperature[J]. China Basic Science, 2021, 23(3): 16-20
[6]	包涛, 高若晗, 谭援强. 基于斐波那契数积分计算非等径颗粒视角系数[J]. 计算力学学报, 2022, 39(3):389-396 doi: 10.7511/jslxCMGM202216 Bao Tao, Gao Ruohan, Tan Yuanqiang. Fibonacci integration for evaluating view factors coefficient of non-equal-diameter particles[J]. Chinese Journal of Computational Mechanics, 2022, 39(3): 389-396 doi: 10.7511/jslxCMGM202216
[7]	王宪礴, 赵富龙, 谢林, 等. 氦氙气冷小堆燃料棒辐射散热特性分析[J]. 原子能科学技术, 2024, 58(5):1060-1068 Wang Xianbo, Zhao Fulong, Xie Lin, et al. Analysis of radiation heat dissipation characteristics of helium-xenon gas cooled small reactor fuel rod[J]. Atomic Energy Science and Technology, 2024, 58(5): 1060-1068
[8]	Rousseau P G, du Toit C G, van Antwerpen W, et al. Separate effects tests to determine the effective thermal conductivity in the PBMR HTTU test facility[J]. Nuclear Engineering and Design, 2014, 271: 444-458. doi: 10.1016/j.nucengdes.2013.12.015
[9]	De Beer M, Du Toit C G, Rousseau P G. A methodology to investigate the contribution of conduction and radiation heat transfer to the effective thermal conductivity of packed graphite pebble beds, including the wall effect[J]. Nuclear Engineering and Design, 2017, 314: 67-81. doi: 10.1016/j.nucengdes.2017.01.010
[10]	Nassar Y F. Analytical-numerical computation of view factor for several arrangements of two rectangular surfaces with non-common edge[J]. International Journal of Heat and Mass Transfer, 2020, 159: 120130. doi: 10.1016/j.ijheatmasstransfer.2020.120130
[11]	Howell J R, Daun K J. The past and future of the Monte Carlo method in thermal radiation transfer[J]. Journal of Heat Transfer, 2021, 143: 100801. doi: 10.1115/1.4050719
[12]	Mirhosseini M, Saboonchi A. View factor calculation using the Monte Carlo method for a 3D strip element to circular cylinder[J]. International Communications in Heat and Mass Transfer, 2011, 38(6): 821-826. doi: 10.1016/j.icheatmasstransfer.2011.03.022
[13]	Gupta M K, Bumtariya K J, Shukla H, et al. Methods for evaluation of radiation view factor: a review[J]. Materials Today: Proceedings, 2017, 4(2): 1236-1243. doi: 10.1016/j.matpr.2017.01.143
[14]	杨星团, 刘志勇, 胡文平, 等. HTR-10堆芯球流运动的唯象学DEM模拟[J]. 原子能科学技术, 2013, 47(12):2231-2237 Yang Xingtuan, Liu Zhiyong, Hu Wenping, et al. DEM simulation of pebble flow in HTR-10 core by phenomenological method[J]. Atomic Energy Science and Technology, 2013, 47(12): 2231-2237
[15]	Sobol’ I M, Asotsky D, Kreinin A, et al. Construction and comparison of high-dimensional sobol’ generators[J]. Wilmott, 2011, 2011(56): 64-79. doi: 10.1002/wilm.10056
[16]	Jarc A, Pers J, Rogelj P, et al. Efficient sampling for the evaluation protocol for 2-D rigid registration[J]. Informacije MIDEM, 2009, 39(1): 1-8.
[17]	Todorov V, Georgiev S. A Hammersley and Van Der Corput sequences comparison for multidimensional sensitivity analysis[J]. AIP Conference Proceedings, 2023, 2953: 090008.
[18]	Howell J R, Menguc M P, Daun K, et al. Thermal radiation heat transfer[M]. 7th ed. Boca Raton: CRC Press, 2020.
[19]	Feng Yuntian, Han K. An accurate evaluation of geometric view factors for modelling radiative heat transfer in randomly packed beds of equally sized spheres[J]. International Journal of Heat and Mass Transfer, 2012, 55(23/24): 6374-6383.
[20]	Smith N A, Tromble R W. Sampling uniformly from the unit simplex[R]. Baltimore: Johns Hopkins University, 2004: 29.
[21]	埃里克·海恩斯, 托马斯·艾科奈-莫勒. 光线追踪精粹—基于DXR及其他API的高质量实时渲染[M]. 张静, 黄琦, 张鹏飞, 译. 北京: 科学出版社, 2021 Haines E, Akenine-Möller T. Ray tracing gems: high-quality and real-time rendering with DXR and other APIs[M]. Zhang Jing, Huang Qi, Zhang Pengfei, trans. Beijing: Science Press, 2021
[22]	Walker T, Xue Shicheng, Barton G W. A robust Monte Carlo based ray-tracing approach for the calculation of view factors in arbitrary 3D geometries[C]//Proceedings of the CHT-12. ICHMT International Symposium on Advances in Computational Heat Transfer. 2012.
[23]	程云阶, 李一波, 丛伟. 光线追踪求交算法的研究及其实现[J]. 沈阳航空工业学院学报, 2000, 17(2):9-13 Cheng Yunjie, Li Yibo, Cong Wei. Research on ray tracking cap[J]. Journal of Shenyang Institute of Aeronautical Engineering, 2000, 17(2): 9-13
[24]	Frank A, Heidemann W, Spindler K. Modeling of the surface-to-surface radiation exchange using a Monte Carlo method[J]. Journal of Physics: Conference Series, 2016, 745: 032143. doi: 10.1088/1742-6596/745/3/032143