5.2 Continuum Modeling of Pebble Radiation
241
Fig. 5.1 Conductive effective thermal conductivity with porosity of nuclear pebble bed
For the nuclear pebble bed filled with graphite spheres, the packing parameters are
α f = 0.39 and d = 60 mm. Based on [14, 15], the ETC of the conduction of a pebble
bed with interstitial helium gas is about 2.3 W/(m·K) at 300 K and R i j = 8.1 K/W.
When porosities range from 0.3 to 0.8, the conductive ETC given by Eq. (5.14) in
the current continuum model is in general agreement with the existing correlations
(see in Fig. 5.1).
For the radiative heat transfer in a nuclear pebble bed, the Short-range Radiation
Model (SRM) is used here, which considers only Voronoï neighboring pairs [5]. For
the FCC lattice, the RDF for the Voronoï neighbors is given as
g SRM (r i j ) = 12
δ(r i j − L 0 )
ρ 0 · 4πr
2
i j
(5.17)
where L 0 is the distance between two Voronoï neighboring centers. When d ≤ L 0 ,
its relationship with porosity is
α f = 1 −
√
2π d
3
6L
3
0
(5.18)
With Eqs. (5.11)–(5.12), the radiative ETC of the SRM is formulated as
k r,FCC = 4σ T
3
(1 − α f )
L
2
0
d
= 4σ T
3 d(1 − α f )
1
3
√
2π
6
2
3
(5.19)