Chapter 5
Numerical Models for Pebble-Bed Heat
Transfer
5.1 Introduction
Radiative, convective, and conductive heat transfers are evenly crucial in the nuclear
pebble bed. It is a fundamental task to model the Effective Thermal Conductivity
(ETC) of the pebble bed, which considers the convection and radiation in analogous
formulations of the conduction. In particular, the reactor core of High-Temperature
Gas-cooled Reactors (HTGRs) is a densely packed pebble bed filled with many fuel
spheres. The relation is due to the particle-scale pore structure of the packed bed.
The highest operating temperature of the pebbles is about 800
◦ C, and it can reach
1,600
◦ C under nuclear accidents. Therefore, as an advanced type nuclear reactor
with inherent safety [1–3], particle thermal radiation is particularly essential heat
transfer processes for the HTGR.
In this chapter, the effective heat transfer is modeled both in continuum and
discrete frameworks. Various models of radiation have been proposed in different
scales, from the particle or sub-particle scale to the integral scales throughout the
bed. Further deep in issues and mechanisms have been analyzed too.
5.2 Continuum Modeling of Pebble Radiation
In convention, the Radiative Transfer Equation (RTE) was used to model thermal radiation [4]. Surface-to-surface radiation has been extensively discussed in the particlescale radiative model for the packed bed study [5, 6]. Sometimes it was coupled with
CFD-DEM simulations [7, 8] and validated by the experimental measurement [6,
9]. For a large-scale industrial pebble bed, such as the HTR-PM filled with about
420,000 pebbles [3], the computational time may become unacceptable for discrete
particle simulation of the thermal radiation and conduction at contact. Thus, it is
necessary to develop continuum models for computing radiation in the pebble bed.
Moreover, even though many empirical correlations [10] are available to calculate
© Tsinghua University Press 2021
S. Jiang et al., Multiphase Flow and Heat Transfer in Pebble Bed Reactor Core,
https://doi.org/10.1007/978-981-15-9565-3_5
237
Numerical Models for Pebble-Bed Heat
Transfer
5.1 Introduction
Radiative, convective, and conductive heat transfers are evenly crucial in the nuclear
pebble bed. It is a fundamental task to model the Effective Thermal Conductivity
(ETC) of the pebble bed, which considers the convection and radiation in analogous
formulations of the conduction. In particular, the reactor core of High-Temperature
Gas-cooled Reactors (HTGRs) is a densely packed pebble bed filled with many fuel
spheres. The relation is due to the particle-scale pore structure of the packed bed.
The highest operating temperature of the pebbles is about 800
◦ C, and it can reach
1,600
◦ C under nuclear accidents. Therefore, as an advanced type nuclear reactor
with inherent safety [1–3], particle thermal radiation is particularly essential heat
transfer processes for the HTGR.
In this chapter, the effective heat transfer is modeled both in continuum and
discrete frameworks. Various models of radiation have been proposed in different
scales, from the particle or sub-particle scale to the integral scales throughout the
bed. Further deep in issues and mechanisms have been analyzed too.
5.2 Continuum Modeling of Pebble Radiation
In convention, the Radiative Transfer Equation (RTE) was used to model thermal radiation [4]. Surface-to-surface radiation has been extensively discussed in the particlescale radiative model for the packed bed study [5, 6]. Sometimes it was coupled with
CFD-DEM simulations [7, 8] and validated by the experimental measurement [6,
9]. For a large-scale industrial pebble bed, such as the HTR-PM filled with about
420,000 pebbles [3], the computational time may become unacceptable for discrete
particle simulation of the thermal radiation and conduction at contact. Thus, it is
necessary to develop continuum models for computing radiation in the pebble bed.
Moreover, even though many empirical correlations [10] are available to calculate
© Tsinghua University Press 2021
S. Jiang et al., Multiphase Flow and Heat Transfer in Pebble Bed Reactor Core,
https://doi.org/10.1007/978-981-15-9565-3_5
237