Study of heat transfer by using DEM–CFD method in a randomly packed pebble-bed reactor

  • Qiang Niu
  • Na-Xiu WangEmail author


The pebble-bed reactor is one of the most promising designs for the nuclear energy industry. In this paper, a discrete element method–computational fluid dynamics (DEM–CFD) approach that includes thermal conduction, radiation, and natural convection mechanisms was proposed to simulate the thermal-fluid phenomena after the failure of forced circulation cooling system in a pebble-bed core. The whole large-scale packed bed was created using the DEM technique, and the calculated radial porosity of the bed was validated with empirical correlations reported by researchers. To reduce computational costs, a segment of the bed was extracted, which served as a good representative of the large-scale packed bed for CFD calculation. The temperature distributions simulated with two different fluids in this DEM–CFD approach were in good agreement with SANA experimental data. The influence of the natural convection mechanism on heat transfer must be taken into account for coolants with strong convective capacity. The proposed DEM–CFD methodology offers a computationally efficient and widely applied method for understanding the heat transfer process in a pebble-bed core. The method can also be easily extended to assess the passive safety features of newly designed fluoride-salt-cooled pebble-bed reactors.


Discrete element method Computational fluid dynamics Pebble bed Heat transfer Natural convection 


  1. 1.
    F. Gou, Y. Liu, F.B. Chen et al., Thermal behavior of the HTR-10 under combined PLOFC and ATWS condition initiated by unscrammed control rod withdrawal. Nucl. Sci. Tech. 29, 123 (2018). CrossRefGoogle Scholar
  2. 2.
    J.J. Lee, G.C. Park, K.Y. Kim et al., Numerical treatment of pebble contact in the flow and heat transfer analysis of a pebble bed reactor core. Nucl. Eng. Des. 237, 2183–2196 (2007). CrossRefGoogle Scholar
  3. 3.
    W.J. van Rooyen, D.L.W. Krueger, E.H. Mathews et al., Simulation and optimisation of gas storage tanks filled with heat sink. Nucl. Eng. Des. 236, 156–163 (2006). CrossRefGoogle Scholar
  4. 4.
    C.G. Toit, P.G. Rousseau, G.P. Greyvenstein et al., A systems CFD model of a packed bed high temperature gas-cooled nuclear reactor. Int. J. Therm. Sci. 45, 70–85 (2006). CrossRefGoogle Scholar
  5. 5.
    J. Baggemann, D. Shi, S. Kasselmann et al., Use of SANA experimental data for validation and verification of MGT-3D and a CFD porous media model for V application. Nucl. Eng. Des. 305, 678–687 (2016). CrossRefGoogle Scholar
  6. 6.
    H.P.A. Calis, J. Nijenhuis, B.C. Paikert et al., CFD modelling and experimental validation of pressure drop and flow profile in a novel structured catalytic reactor packing. Chem. Eng. Sci. 56, 1713–1720 (2001). CrossRefGoogle Scholar
  7. 7.
    A.G. Dixon, M. Nijemeisland, E. Hugh Stitt, Systematic mesh development for 3D CFD simulation of fixed beds: contact points study. Comput. Chem. Eng. 48, 135–153 (2013). CrossRefGoogle Scholar
  8. 8.
    Y.M. Ferng, K.Y. Lin, Investigating effects of BCC and FCC arrangements on flow and heat transfer characteristics in pebbles through CFD methodology. Nucl. Eng. Des. 258, 66–75 (2013). CrossRefGoogle Scholar
  9. 9.
    S.X. Song, X.Z. Cai, Y.F. Liu et al., Pore scale thermal hydraulics investigations of molten salt cooled pebble bed high temperature reactor with BCC and FCC configurations. Sci. Technol. Nucl. Install. 2014, 589895 (2014). CrossRefGoogle Scholar
  10. 10.
    A.A. Merrikh, J.L. Lage, Natural convection in an enclosure with disconnected and conducting solid blocks. Int. J. Heat Mass Transf. 48, 1361–1372 (2005). CrossRefzbMATHGoogle Scholar
  11. 11.
    X. Zhao, T. Montgomery, S. Zhang, Modeling stationary and moving pebbles in a pebble bed reactor. Ann. Nucl. Energy 80, 52–61 (2015). CrossRefGoogle Scholar
  12. 12.
    R. Mohanty, S. Mohanty, B.K. Mishra, Study of flow through a packed bed using discrete element method and computational fluid dynamics. J. Taiwan Inst. Chem. E 63, 71–80 (2016). CrossRefGoogle Scholar
  13. 13.
    A. Singhal, S. Cloete, S. Radi et al., Heat transfer to a gas from densely packed beds of monodisperse spherical particles. Chem. Eng. J. 314, 27–37 (2017). CrossRefGoogle Scholar
  14. 14.
    B.N. Stocker, H.F. Niessen, Data sets of the SANA experiment 1994–1996. JUEL-3409, Forschungszentrum Julich (1997). Accessed 26 Dec 2017
  15. 15.
    P.A. Cundall, O.D.L. Strack, A discrete numerical model for granular assemblies. Gotechnique 29, 47–65 (1979). CrossRefGoogle Scholar
  16. 16.
    Itasca Consulting Group, PFC3D-Particle Flow Code in 3 Dimensions, Version 3.1 User’s Manual, Minneapolis (2005)Google Scholar
  17. 17.
    International Atomic Energy Agency, Heat Transport and Afterheat Removal for Gas Cooled Reactors Under Accident Conditions, IAEA-TECDOC-1163, IAEA, Vienna (2001)Google Scholar
  18. 18.
    T. Atmakidis, E.Y. Kenig, CFD-based analysis of the wall effect on the pressure drop in packed beds with moderate tube/particle diameter ratios in the laminar flow regime. Chem. Eng. J. 155, 404–410 (2009). CrossRefGoogle Scholar
  19. 19.
    S.K.M. Ookawara, D. Street, K. Ogawa, High-fidelity DEM–CFD modeling of packed bed reactors for process intensification, in Proceedings of European Congress of Chemical Engineering-6 (2007)Google Scholar
  20. 20.
    S.W. Churchill, Comprehensive, theoretically based, correlating equations for free convection from isothermal spheres. Chem. Eng. Commun. 24, 339–3523 (1983). CrossRefGoogle Scholar
  21. 21.
    ANSYS Inc, ANSYS FLUENT Theory Guide, Release 16.0, (2015)Google Scholar
  22. 22.
    C.G. du Toit, Radial variation in porosity in annular packed beds. Nucl. Eng. Des. 238, 3073–3079 (2008). CrossRefGoogle Scholar
  23. 23.
    A. de Klerk, Voidage variation in packed beds at small column to particle diameter ratio. AIChe J. 49, 2022–2029 (2003). CrossRefGoogle Scholar
  24. 24.
    C.G. du Toit, W. van Antwerpen, P.G. Rousseau, Analysis of the porous structure of an annular pebble bed reactor, in International Congress on Advanced in Nuclear Power Plants, Tokyo, Japan, 10–14 May (2009)Google Scholar
  25. 25.
    W. van Antwerpen, P.G. Rousseau, C.G. du Toit, Multi-sphere unit cell model to calculate the effective thermal conductivity in packed pebble beds of mono-sized spheres. Nucl. Eng. Des. 247, 183–201 (2012). CrossRefGoogle Scholar
  26. 26.
    W. van Antwerpen, C.G. du Toit, P.G. Rousseau, A review of correlations to model the packing structure and effective thermal conductivity in packed beds of mono-sized spherical particles. Nucl. Eng. Des. 240, 1803–1818 (2010). CrossRefGoogle Scholar
  27. 27.
    W.W.M. Siu, S.H.-K. Lee, Effective conductivity computation of a packed bed using constriction resistance and contact angle effects. Int. J. Heat Mass Transf. 43, 3917–3924 (2000). CrossRefzbMATHGoogle Scholar
  28. 28.
    C.T. Hsu, P. Cheng, K.W. Wong, A lumped-parameter model for stagnant thermal conductivity of spatially periodic porous media. J. Heat Transf. 117, 264–269 (1995). CrossRefGoogle Scholar

Copyright information

© China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, Chinese Nuclear Society and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Shanghai Institute of Applied PhysicsChinese Academy of SciencesShanghaiChina
  2. 2.CAS Innovative Academies in TMSR Energy SystemChinese Academy of SciencesShanghaiChina
  3. 3.University of Chinese Academy of SciencesBeijingChina

Personalised recommendations