242
5 Numerical Models for Pebble-Bed Heat Transfer
Fig. 5.2 Radial distribution function in nuclear pebble bed at α f = 0.39
at ε r = 1. This expression is the same as the analytical result in [6] for the FCC of
black radiation.
For a random packing structure at α f = 0.39, the radial distribution function of
all possible pairs is shown in Fig. 5.2, which is solved by the hyper-netted chain
equation [16]. The radiation exchange factor is about 1.0, and it is approximately
F =
k r
4σ dT 3 = ε r [6, 15, 17]. The view factor in the pebble bed at distance r i j is
formulated by the following form
X (r i j ) = A exp
−B
r i j
d
,
(5.20)
where A and B are the shape parameters. Solving Eqs. (5.11), (5.13), and (5.20), the
numerical results at α f = 0.39 are A = 37.0 and B = 3.54 for random packing.
5.2.1.2 Uniform Framework of Continuum Model
From Eqs. (5.5)–(5.6), the governing energy equation of a nuclear pebble bed composed of mono-sized spheres can be written in a uniform framework as
R 3
K (|x − x
|)T
n (x
)dx
dy
dz
− T
n (x)
R 3
K (|x − x
|)dx
dy
dz
+ Q v (x) = 0
(5.21)