276
5 Numerical Models for Pebble-Bed Heat Transfer
Fig. 5.30 Cell-to-particle
area ratio of different
packings
The factor γ is very close 1 (about 0.9–1.1), and for the SC, BCC, and FCC, it is
given by
γ SC =
η SC
η T
=
3
4Γ (
5
3 )
6
π
1
3
= 1.0308,
(5.96)
γ BCC =
η BCC
η T
=
3(2
√
3+1)
4πΓ (
5
3 )
√
3π
8
2
3 = 0.9130,
(5.97)
γ FCC =
η FCC
η T
=
9
√
2
4πΓ (
5
3 )
√
2π
6
2
3 = 0.9183.
(5.98)
5.3.8.2 SRM Solution (For Comparison)
The solid conductivity of the particle material plays an vital role in particle thermal
radiation [46]. In the packed pebble beds, the solid conductivity acts as an inner thermal resistance. When it is neglected, the particle radiation flux will be overestimated
significantly, especially at high temperatures. For the graphite pebbles of HTGR, if
the solid conductivity is neglected, the effect of the overestimation of heat flux of the
particle radiation is canceled out in general by cutting off of the long-range radiation
parts in the short-range radiation model when the operating temperature is about
550–1,262
◦ C [5, 7]. Thus, the short-range radiation by only considering radiation
between adjacent Voronoï pairs provides a good prediction of the particle radiation.
Using SRM, the radiation heat flux between two neighboring cells can be solved by
Eq. (5.69) [5].
For the cube of SC and rhombic dodecahedron of the FCC, the view factors are
V i, j =
1
6
, and V i, j =
1
12
, respectively. Combining Eq. (5.91) and Eq. (5.69), in which