392
5 Numerical Models for Pebble-Bed Heat Transfer
radiation. The effect of emissivity was handled correctly in the local radiation model
without the uniform assumption. Since the computation cost of the local radiation
model in large-scale granular systems was huge and not applicable to the CFD-DEM
simulation, the particle-scale radiation model is developed to predict the radiation
flux in the DEM. It was shown that the effect of particle emissivity is a separable term
in the radiative heat transfer equation. The particle-scale radiation model provides
a good approximation of the local radiation model and enables the efficient prediction of radiative heat transfer in a densely packed bed. Also, the contact thermal
resistance with stagnant fluid is investigated by modeling the particle–particle and
the particle–wall conduction in a discrete particle simulation. The model predictions
of effective thermal conductivity are compared with various experimental data for
validation. The effect of the conductivity ratio and the void fraction is discussed.
References
1. Gao, Zuying, and Lei Shi. 2002. Thermal hydraulic calculation of the HTR-10 for the initial
and equilibrium core. Nuclear Engineering & Design 218 (1–3): 51–64.
2. Zhang, Zuoyi, Zongxin Wu, Dazhong Wang, Yuanhui Xu, Yuliang Sun, Fu Li, and Yujie
Dong. 2009. Current status and technical description of Chinese 2×250 mwth HTR-PM
demonstration plant. Nuclear Engineering and Design 239 (7): 1212–1219.
3. Zhang, Zuoyi, Yujie Dong, Fu Li, Zhengming Zhang, Haitao Wang, Xiaojin Huang, Hong
Li, Bing Liu, Xinxin Wu, and Hong Wang. 2016. The Shandong Shidao Bay 200 MWe hightemperature gas-cooled reactor pebble-bed module (HTR-PM) demonstration power plant:
an engineering and technological innovation. Engineering.
4. Singh, B.P., and Massoud Kaviany. 1992. Modelling radiative heat transfer in packed beds.
International Journal of Heat & Mass Transfer 35 (6): 1397–1405.
5. Hao, Wu, Nan Gui, Xingtuan Yang, Jiyuan Tu, and Shengyao Jiang. 2016. Effect of scale on
the modeling of radiation heat transfer in packed pebble beds. International Journal of Heat
& Mass Transfer 101: 562–569.
6. Hao, Wu, Nan Gui, Xingtuan Yang, Jiyuan Tu, and Shengyao Jiang. 2017. Modeling effective
thermal conductivity of thermal radiation for nuclear packed pebble beds. Journal of Heat
Transfer 140 (4): 042701.
7. Hao, Wu, Nan Gui, Xingtuan Yang, Jiyuan Tu, and Shengyao Jiang. 2017. Numerical simulation of heat transfer in packed pebble beds: CFD-DEM coupled with particle thermal
radiation. International Journal of Heat & Mass Transfer 110: 393–405.
8. Zhou, Z.Y., A.B. Yu, and P. Zulli. 2009. Particle scale study of heat transfer in packed and
bubbling fluidized beds. AIChE Journal 55 (4): 868–884.
9. Hao, Wu, Nan Gui, Xingtuan Yang, and Jiyuan Tu, and Shengyao Jiang. 2018. Particle-scale
investigation of thermal radiation in nuclear packed pebble beds. Journal of Heat Transfer
140 (9): 092002.
10. Van Antwerpen, W., C.G. Du Toit, and P.G. Rousseau. 2010. A review of correlations to
model the packing structure and effective thermal conductivity in packed beds of mono-sized
spherical particles. Nuclear Engineering & Design 240 (7): 1803–1818.
11. Majid Bahrami, M., Michael Yovanovich, and J. Richard Culham. 2006. Effective thermal
conductivity of rough spherical packed beds. International Journal of Heat & Mass Transfer
49 (19): 3691–3701.
12. Rouhani, Mina, and Majid Bahrami. 2018. Effective thermal conductivity of packed bed
adsorbers: Part 2 - theoretical model. International Journal of Heat and Mass Transfer 123:
1212–1220.
5 Numerical Models for Pebble-Bed Heat Transfer
radiation. The effect of emissivity was handled correctly in the local radiation model
without the uniform assumption. Since the computation cost of the local radiation
model in large-scale granular systems was huge and not applicable to the CFD-DEM
simulation, the particle-scale radiation model is developed to predict the radiation
flux in the DEM. It was shown that the effect of particle emissivity is a separable term
in the radiative heat transfer equation. The particle-scale radiation model provides
a good approximation of the local radiation model and enables the efficient prediction of radiative heat transfer in a densely packed bed. Also, the contact thermal
resistance with stagnant fluid is investigated by modeling the particle–particle and
the particle–wall conduction in a discrete particle simulation. The model predictions
of effective thermal conductivity are compared with various experimental data for
validation. The effect of the conductivity ratio and the void fraction is discussed.
References
1. Gao, Zuying, and Lei Shi. 2002. Thermal hydraulic calculation of the HTR-10 for the initial
and equilibrium core. Nuclear Engineering & Design 218 (1–3): 51–64.
2. Zhang, Zuoyi, Zongxin Wu, Dazhong Wang, Yuanhui Xu, Yuliang Sun, Fu Li, and Yujie
Dong. 2009. Current status and technical description of Chinese 2×250 mwth HTR-PM
demonstration plant. Nuclear Engineering and Design 239 (7): 1212–1219.
3. Zhang, Zuoyi, Yujie Dong, Fu Li, Zhengming Zhang, Haitao Wang, Xiaojin Huang, Hong
Li, Bing Liu, Xinxin Wu, and Hong Wang. 2016. The Shandong Shidao Bay 200 MWe hightemperature gas-cooled reactor pebble-bed module (HTR-PM) demonstration power plant:
an engineering and technological innovation. Engineering.
4. Singh, B.P., and Massoud Kaviany. 1992. Modelling radiative heat transfer in packed beds.
International Journal of Heat & Mass Transfer 35 (6): 1397–1405.
5. Hao, Wu, Nan Gui, Xingtuan Yang, Jiyuan Tu, and Shengyao Jiang. 2016. Effect of scale on
the modeling of radiation heat transfer in packed pebble beds. International Journal of Heat
& Mass Transfer 101: 562–569.
6. Hao, Wu, Nan Gui, Xingtuan Yang, Jiyuan Tu, and Shengyao Jiang. 2017. Modeling effective
thermal conductivity of thermal radiation for nuclear packed pebble beds. Journal of Heat
Transfer 140 (4): 042701.
7. Hao, Wu, Nan Gui, Xingtuan Yang, Jiyuan Tu, and Shengyao Jiang. 2017. Numerical simulation of heat transfer in packed pebble beds: CFD-DEM coupled with particle thermal
radiation. International Journal of Heat & Mass Transfer 110: 393–405.
8. Zhou, Z.Y., A.B. Yu, and P. Zulli. 2009. Particle scale study of heat transfer in packed and
bubbling fluidized beds. AIChE Journal 55 (4): 868–884.
9. Hao, Wu, Nan Gui, Xingtuan Yang, and Jiyuan Tu, and Shengyao Jiang. 2018. Particle-scale
investigation of thermal radiation in nuclear packed pebble beds. Journal of Heat Transfer
140 (9): 092002.
10. Van Antwerpen, W., C.G. Du Toit, and P.G. Rousseau. 2010. A review of correlations to
model the packing structure and effective thermal conductivity in packed beds of mono-sized
spherical particles. Nuclear Engineering & Design 240 (7): 1803–1818.
11. Majid Bahrami, M., Michael Yovanovich, and J. Richard Culham. 2006. Effective thermal
conductivity of rough spherical packed beds. International Journal of Heat & Mass Transfer
49 (19): 3691–3701.
12. Rouhani, Mina, and Majid Bahrami. 2018. Effective thermal conductivity of packed bed
adsorbers: Part 2 - theoretical model. International Journal of Heat and Mass Transfer 123:
1212–1220.