Skip to main content
Log in

A review of recent study on the characteristics and applications of pebble flows in nuclear engineering

  • Review Article
  • Published:
Experimental and Computational Multiphase Flow Aims and scope Submit manuscript

Abstract

This paper reviews the recent three-year progress on the investigations of pebble bed flows in nuclear engineering. Both the application of pebble beds in the fission reactors and the fusion reactors are included. The fundamental characteristics of packing, flows, conduction, convection, radiation, and the effective thermal conductivity of pebble beds are reviewed. The important issues on the design of the pebble beds as well as that related to the reactor safety are also introduced. In addition, the advances in measurement techniques and numerical coupled methods for exploring the pebble flow characteristics are categorized and summarized too.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Ahmed, F., Ara, N., Deshpande, V., Mollah, A. S., Bhowmik, P. K. 2021. CFD validation with optimized mesh using benchmarking data of pebble-bed high-temperature reactor. Progress in Nuclear Energy, 134: 103653.

    Article  Google Scholar 

  • Avramenko, A. A., Dmitrenko, N. P., Shevchuk, I. V., Tyrinov, A. I., Kovetskaya, M. M. 2021. Heat transfer and fluid flow of helium coolant in a model of the core zone of a pebble-bed nuclear reactor. Nuclear Engineering and Design, 377: 111148.

    Article  Google Scholar 

  • Bester, P. M., du Toit, C. G., Potgieter, M. C. 2021. A numerical analysis of the porosity of the HTR-10 packed pebble bed. Nuclear Engineering and Design, 383: 111438.

    Article  Google Scholar 

  • Bu, S., Chen, B., Li, Z., Jiang, J., Chen, D. 2021. An explicit expression of empirical parameter in ZBS model for predicting pebble bed effective thermal conductivity. Nuclear Engineering and Design, 376: 111106.

    Article  Google Scholar 

  • Bu, S., Wang, J., Sun, W., Ma, Z., Zhang, L., Pan, L. 2020. Numerical and experimental study of stagnant effective thermal conductivity of a graphite pebble bed with high solid to fluid thermal conductivity ratios. Applied Thermal Engineering, 164: 114511.

    Article  Google Scholar 

  • Chen, L., Lee, J. 2020a. Effect of pebble diameters on the heat transfer characteristics of a structured pebble bed in an HTGR. Energy, 212: 118642.

    Article  Google Scholar 

  • Chen, L., Lee, J. 2020b. Effects of inserted sphere on thermal field and heat-transfer characteristics of face-centered-cubic-structured pebble bed. Applied Thermal Engineering, 172: 115151.

    Article  Google Scholar 

  • Chen, X., Dai, Y., Yan, R., Mei, M., Zhang, J., Zou, Y., Cai, X. 2020. Experimental study on the vibration behavior of the pebble bed in PB-FHR. Annals of Nuclear Energy, 139: 107193.

    Article  Google Scholar 

  • Choi, D., Park, S., Han, J., Ahn, M. Y., Lee, Y., Park, Y. H., Cho, S., Sohn, D. 2019. A DEM-CFD study of the effects of size distributions and packing fractions of pebbles on purge gas flow through pebble beds. Fusion Engineering and Design, 143: 24–34.

    Article  Google Scholar 

  • Cui, X., Gui, N., Yang, X., Tu, J., Jiang, S. 2021a. Analysis of particle shape effect on the discharging of non-spherical particles in HTR-10 reactor core. Nuclear Engineering and Design, 371: 110934.

    Article  Google Scholar 

  • Cui, X., Liu, X., Gui, N., Yang, X., Tu, J., Jiang, S. 2021b. DEM study of flow characteristics of wet cohesive particles in packed bed. Annals of Nuclear Energy, 163: 108538.

    Article  Google Scholar 

  • Feng, Y., Gong, B., Cheng, H., Luo, X., Wang, L., Wang, X. 2021a. Effects of bed dimension, friction coefficient and pebble size distribution on the packing structures of the pebble bed for solid tritium breeder blanket. Fusion Engineering and Design, 163: 112156.

    Article  Google Scholar 

  • Feng, Y., Gong, B., Cheng, H., Wang, L., Wang, X. 2021b. Effects of fixed wall and pebble size ratio on packing properties and contact force distribution in binary-sized pebble mixed beds at the maximum packing efficiency state. Powder Technology, 390: 504–520.

    Article  Google Scholar 

  • Gámez Rodríguez, A., Rojas Mazaira, L. Y., García Hernández, C. R., Sanchez Dominguez, D., Brayner de Oliveira Lira, C. A. 2021. An integral 3D full-scale steady-state thermohydraulic calculation of the high temperature pebble bed gas-cooled reactor HTR-10. Nuclear Engineering and Design, 373: 111011.

    Article  Google Scholar 

  • Gui, N., Huang, X., Yang, X., Tu, J., Jiang, S. 2020. HTR-PM-based 3D pebble flow simulation on the effects of base angle, recirculation mode and coefficient of friction. Annals of Nuclear Energy, 143: 107442.

    Article  Google Scholar 

  • Gui, N., Li, Z., Zhang, Z., Yang, X., Tu, J., Jiang, S. 2019. Numerical study of pebble recirculation in a two-dimensional pebble bed of stationary atmosphere using LB-IB-DEM coupled method. Annals of Nuclear Energy, 124: 58–68.

    Article  Google Scholar 

  • Hu, G., Zhang, H., Liu, Q. 2022. Design optimization on characteristics of packed-bed thermal energy storage system coupled with high temperature gas-cooled reactor pebble-bed module. Energy Conversion and Management, 257: 115434.

    Article  Google Scholar 

  • Kile, R. F., Bostelmann, F., Skutnik, S. E., Wieselquist, W. A., Brown, N. R. 2022. Assessment of SCALE and MELCOR for a generic pebble bed fluoride high-temperature reactor. Annals of Nuclear Energy, 173: 109107.

    Article  Google Scholar 

  • Kim, D. O., Hwang, S. P., Sohn, D. 2021. DEM study of packing and connectivity of binary-sized pebbles according to their size and mixing ratios under vibration conditions. Fusion Engineering and Design, 168: 112648.

    Article  Google Scholar 

  • Kumar, P., Thakur, A., Saha, S. K., Sharma, A., Sharma, D., Chaudhuri, P. 2021. CFD investigation of helium gas flow in sphere packed (pebble bed) in a rectangular canister using OpenFOAM. Fusion Engineering and Design, 172: 112858.

    Article  Google Scholar 

  • Lee, Y., Choi, D., Hwang, S. P., Ahn, M. Y., Park, Y. H., Cho, S., Sohn, D. 2020. Numerical investigation of purge gas flow through binary-sized pebble beds using discrete element method and computational fluid dynamics. Fusion Engineering and Design, 158: 111704.

    Article  Google Scholar 

  • Li, B., Gui, N., Wu, H., Yang, X., Tu, J., Jiang, S. 2021. Effects of the 3-D wall structures on the flow and mixing characteristics of pebbles in pebble beds in HTR-10. Annals of Nuclear Energy, 164: 108607.

    Article  Google Scholar 

  • Lin, M., Li, Y. 2020. Analysis of the interactions between spent fuel pebble bed and storage canister under impact loading. Nuclear Engineering and Design, 361: 110548.

    Article  Google Scholar 

  • Liu, L., Deng, J., Zhang, D., Wang, C., Qiu, S., Su, G. H. 2020. Experimental analysis of flow and convective heat transfer in the water-cooled packed pebble bed nuclear reactor core. Progress in Nuclear Energy, 122: 103298.

    Article  Google Scholar 

  • Liu, Y., Liu, X., Peng, S., Gui, N., Yang, X., Tu, J., Jiang, S. 2022a. A fast region homogenization method based on experimental data for pebble flow. Powder Technology, 396: 542–554.

    Article  Google Scholar 

  • Liu, Y., Marquardt, J., Peng, S., Ge, L., Gui, N., Yang, X. T., Tu, J. Y., Jiang, S. Y., Kim, S. 2022b. Neural network prediction of residence time distribution for quasi-2D pebble flow. Chemical Engineering Science, 250: 117363.

    Article  Google Scholar 

  • Liu, Y., Peng, S., Gui, N., Yang, X., Tu, J., Jiang, S. 2021. An improved high accuracy PTV algorithm for pebble flow. Powder Technology, 387: 227–238.

    Article  Google Scholar 

  • Mardus-Hall, R., Ho, M., Pastrello, A., Yeoh, G. 2020. 3-Way coupled thermohydraulic-discrete element-neutronic simulation of solid fuel, molten salt reactor. Annals of Nuclear Energy, 135: 106973.

    Article  Google Scholar 

  • Novak, A. J., Schunert, S., Carlsen, R. W., Balestra, P., Slaybaugh, R. N., Martineau, R. C. 2021. Multiscale thermal-hydraulic modeling of the pebble bed fluoride-salt-cooled high-temperature reactor. Annals of Nuclear Energy, 154: 107968.

    Article  Google Scholar 

  • Panchal, M., Saraswat, A., Chaudhuri, P. 2020a. Experimental measurements of gas pressure drop of packed pebble beds. Fusion Engineering and Design, 160: 111836.

    Article  Google Scholar 

  • Panchal, M., Saraswat, A., Verma, S., Chaudhuri, P. 2020b. Measurement of effective thermal conductivity of lithium metatitanate pebble bed by transient hot-wire technique. Fusion Engineering and Design, 158: 111718.

    Article  Google Scholar 

  • Patel, H., Panchal, M., Saraswat, A., Patel, N., Chaudhuri, P. 2021. Simultaneous measurement of effective thermal conductivity and effective thermal diffusivity of Li2TiO3 pebble bed using transient hot-wire technique. Fusion Engineering and Design, 171: 112564.

    Article  Google Scholar 

  • Qi, H., Gui, N., Yang, X., Tu, J., Jiang, S. 2020. Effects of restitution coefficient on pebble motion in a thin pebble bed - Lagrangian analysis. Annals of Nuclear Energy, 145: 107549.

    Article  Google Scholar 

  • Satvat, N., Sarikurt, F., Johnson, K., Kolaja, I., Fratoni, M., Haugh, B., Blandford, E. 2021. Neutronics, thermal-hydraulics, and multiphysics benchmark models for a generic pebble-bed fluoride-salt-cooled high temperature reactor (FHR). Nuclear Engineering and Design, 384: 111461.

    Article  Google Scholar 

  • Sedani, C., Panchal, M., Chaudhuri, P. 2021. Simulation and experimental analysis of purge gas flow characteristic for pebble bed. Fusion Engineering and Design, 172: 112778.

    Article  Google Scholar 

  • Sharma, A., Thakur, A., Saha, S. K., Sharma, A., Sharma, D., Chaudhuri, P. 2020. Thermal-hydraulic characteristics of purge gas in a rectangular packed pebble bed of a fusion reactor using DEM-CFD and porous medium analyses. Fusion Engineering and Design, 160: 111848.

    Article  Google Scholar 

  • Shi, L., Zhao, J. Q., Liu, B., Li, X. W., Luo, X. W., Zhang, Z. M., Zhang, P., Sun, L. B., Wu, X. X. 2021. Development strategy of key materials technology for the high temperature gas-cooled reactor. Journal of Tsinghua University (Science and Technology), 61(4): 270–278.

    Google Scholar 

  • Tang, Y., Zhang, L., Guo, Q., Xia, B., Yin, Z., Cao, J., Tong, J., Rycroft, C. H. 2019. Analysis of the pebble burnup profile in a pebble-bed nuclear reactor. Nuclear Engineering and Design, 345: 233–251.

    Article  Google Scholar 

  • Wakao, N., Kaguei, S., Funazkri, T. 1979. Effect of fluid dispersion coefficients on particle-to-fluid heat transfer coefficients in packed beds: Correlation of nusselt numbers. Chemical Engineering Science, 34: 325–336.

    Article  Google Scholar 

  • Wang, C., Chen, L., Liu, S. 2019. A DEM-CFD numerical model for the prediction of the effective thermal conductivity of pebble beds with contact conduction. Fusion Engineering and Design, 147: 111257.

    Article  Google Scholar 

  • Wang, C., Chen, L., Liu, S. 2020a. Experimental measurements for the effective thermal conductivity of pebble beds with uncertainty analysis. Fusion Engineering and Design, 156: 111707.

    Article  Google Scholar 

  • Wang, J., Lei, M. Z., Yang, H., Xu, S. L., Xu, K., Yin, Z., Li, C., Zhao, P. H., Song, Y. 2021a. Study on the packing characteristics of a special “J” shape ceramic packed pebble bed based on discrete element modeling. Powder Technology, 379: 362–372.

    Article  Google Scholar 

  • Wang, J., Lei, M., Yang, H., Xu, K., Xu, S., Zhao, P., Song, Y. 2021b. Effects of coefficient of friction and coefficient of restitution on static packing characteristics of polydisperse spherical pebble bed. Particuology, 57: 1–9.

    Article  Google Scholar 

  • Wang, J., Li, Z., Guo, Z., Ding, M. 2022a. Application of a new OpenFOAM-based neutron diffusion kinetics solver to pebble-type VHTRs. Annals of Nuclear Energy, 170: 108976.

    Article  Google Scholar 

  • Wang, Q., Gui, N., Liu, Y., Peng, S., Yang, X., Tu, J., Jiang, S. 2020b. A morphological image processing method for simultaneous scrutinization of particle position and velocity in pebble flow. Annals of Nuclear Energy, 148: 107704.

    Article  Google Scholar 

  • Wang, S. W., Zhou, C., Cai, C. X., Zhu, H. H., Wang, N. X., Zou, Y. 2022b. Experimental research on convective heat transfer characteristics of molten salt in a pebble bed channel with internal heat source. Nuclear Engineering and Design, 387: 111619.

    Article  Google Scholar 

  • Wang, S., Wang, S., Wu, B., Lu, Y., Zhang, K., Chen, H. 2021c. Effect of packing structure on anisotropic effective thermal conductivity of thin ceramic pebble bed. Nuclear Engineering and Technology, 53: 2174–2183.

    Article  Google Scholar 

  • Wongkham, J., Wen, T., Lu, B., Cui, L., Xu, J., Liu, X. 2020. Particle-resolved simulation of randomly packed pebble beds with a novel fluid-solid coupling method. Fusion Engineering and Design, 161: 111953.

    Article  Google Scholar 

  • Wu, H., Gui, N., Yang, X., Tu, J., Jiang, S. 2020a. A matrix model of particle-scale radiative heat transfer in structured and randomly packed pebble bed. International Journal of Thermal Sciences, 153: 106334.

    Article  Google Scholar 

  • Wu, H., Gui, N., Yang, X., Tu, J., Jiang, S. 2020b. Analysis and evaluations of four models of thermal radiation for densely packed granular systems. Chemical Engineering Science, 211: 115309.

    Article  Google Scholar 

  • Wu, H., Gui, N., Yang, X., Tu, J., Jiang, S. 2020c. Analysis of clumped-pebble shape on thermal radiation and conduction in nuclear beds by subcell radiation model. Journal of Heat Transfer, 142: 032101.

    Article  Google Scholar 

  • Wu, H., Hao, S., Niu, F., Tu, J., Jiang, S. 2022a. A data-driven deep learning model of radiative heat transfer in dense granular systems. Annals of Nuclear Energy, 167: 108855.

    Article  Google Scholar 

  • Wu, M., Gui, N., Liu, X., Yang, X., Tu, J., Jiang, S. 2022b. Numerical analysis of the effects of different outlet sizes on pebble flows in HTR-10 pebble beds. Nuclear Engineering and Design, 387: 111620.

    Article  Google Scholar 

  • Wu, M., Gui, N., Wu, H., Yang, X., Tu, J., Jiang, S. 2019a. Effects of density difference and loading ratio on pebble flow in a three-dimensional two-region-designed pebble bed. Annals of Nuclear Energy, 133: 924–936.

    Article  Google Scholar 

  • Wu, M., Gui, N., Wu, H., Yang, X., Tu, J., Jiang, S. 2019b. Numerical study of mixing pebble flow with different density in circulating packed bed. Annals of Nuclear Energy, 130: 483–492.

    Article  Google Scholar 

  • Wu, M., Gui, N., Yang, X., Tu, J., Jiang, S. 2021. Effects of 3D contraction on pebble flow uniformity and stagnation in pebble beds. Nuclear Engineering and Technology, 53: 1416–1428.

    Article  Google Scholar 

  • Wu, Q., Lei, M., Wang, J., Xu, K., Xu, S. 2022c. Packing characteristics of pebble beds for fusion reactors under different friction coefficients. Fusion Engineering and Design, 176: 113051.

    Article  Google Scholar 

  • Wu, Y., Ren, C., Yang, X., Tu, J., Jiang, S. 2019c. Repeatable experimental measurements of effective thermal diffusivity and conductivity of pebble bed under vacuum and helium conditions. International Journal of Heat and Mass Transfer, 141: 204–216.

    Article  Google Scholar 

  • Wu, Z., Wu, Y., Wang, C., Tang, S., Liu, D., Qiu, S., Su, G. H., Tian, W. 2019d. Experimental and numerical study on helium flow characteristics in randomly packed pebble bed. Annals of Nuclear Energy, 128: 268–277.

    Article  Google Scholar 

  • Yang, Q., Gui, N., Huang, X., Zhang, X., Yang, X., Tu, J., Jiang, S. 2022. Effects of the central graphite column dimension and pebble size on power density distribution in annular core pebble-bed HTR. International Journal of Energy Research, 46: 8076–8092.

    Article  Google Scholar 

  • Zhang, Y., Fang, X., Ma, T., Xia, B., Li, C. 2021. Study on on-line temperature measurement technology for core of pebble bed high temperature gas-cooled reactor. Nuclear Engineering and Design, 371: 110944.

    Article  Google Scholar 

  • Zou, L., Hu, G., O’Grady, D., Hu, R. 2022. Explicit modeling of pebble temperature in the porous-media model for pebble-bed reactors. Progress in Nuclear Energy, 146: 104175.

    Article  Google Scholar 

  • Zou, Q., Gui, N., Yang, X., Tu, J., Jiang, S. 2021. Comparative study on the numerical methods for view factor computation for packed pebble beds: Back propagation neural network methods versus Monte Carlo methods. Journal of Heat Transfer, 143: 083301.

    Article  Google Scholar 

Download references

Acknowledgements

The authors are grateful for the support of this research by the National Science and Technology Major Project (Grant No. 2011ZX06901-003), and Funds of Nuclear Power Technology Innovation Centre (Grant Nos. HDLCXZX-2020-HD-022 and HDLCXZX-2021-ZH-024).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Shengyao Jiang.

Ethics declarations

The authors have no competing interests to declare that are relevant to the content of this article.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gui, N., Jiang, S., Yang, X. et al. A review of recent study on the characteristics and applications of pebble flows in nuclear engineering. Exp. Comput. Multiph. Flow 4, 339–349 (2022). https://doi.org/10.1007/s42757-022-0140-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42757-022-0140-z

Keywords

Navigation