5.3 Discrete Modeling of Pebble Radiation
283
Fig. 5.37 Sub-cell of the FCC packing in particle radiation model
V 12 is the view factor between surface 1 and surface 2, and it can be calculated by
numerical integral under different porosities [6]. Γ (·) is the gamma function, and it
is defined as
Γ (x) =
+∞
0
u
x−1 e
−u du.
(5.113)
The random modification factor is considered in the SCM [6]. The particle in
the Voronoï cell is smaller than the inscribed sphere of the rhombic dodecahedron.
Thus, the particle diameter is d p = βd i and 0 < β < 1, where d i is the diameter of
the inscribed sphere. The relationship between the porosity and the parameter β is
expressed as
α f = 1 −
√
2πβ
3
6
(5.114)
With the scale factor β, the view factor V 12 in SCM can be obtained under different
porosities. From the numerical results, V 12 is 0.3955 at α f = 0.39 (dense packing)
and 0.3561 at α f = 0.44 (loose packing). Solid conductivities k s under different
temperatures in nuclear-packed pebble beds are available from the experimental
measurements [35, 55].
5.3.9.1 Effect of Radial Porosity Distribution
In the previous discussion [35], the only uniform porosity distribution is considered
in the packed pebble bed. However, from the experimental data [21] and numerical
simulations [56, 57], it is shown that the capability of heat transfer in the near-wall
region is different from that in the bulk region. For the cylindrical beds, such as
283
Fig. 5.37 Sub-cell of the FCC packing in particle radiation model
V 12 is the view factor between surface 1 and surface 2, and it can be calculated by
numerical integral under different porosities [6]. Γ (·) is the gamma function, and it
is defined as
Γ (x) =
+∞
0
u
x−1 e
−u du.
(5.113)
The random modification factor is considered in the SCM [6]. The particle in
the Voronoï cell is smaller than the inscribed sphere of the rhombic dodecahedron.
Thus, the particle diameter is d p = βd i and 0 < β < 1, where d i is the diameter of
the inscribed sphere. The relationship between the porosity and the parameter β is
expressed as
α f = 1 −
√
2πβ
3
6
(5.114)
With the scale factor β, the view factor V 12 in SCM can be obtained under different
porosities. From the numerical results, V 12 is 0.3955 at α f = 0.39 (dense packing)
and 0.3561 at α f = 0.44 (loose packing). Solid conductivities k s under different
temperatures in nuclear-packed pebble beds are available from the experimental
measurements [35, 55].
5.3.9.1 Effect of Radial Porosity Distribution
In the previous discussion [35], the only uniform porosity distribution is considered
in the packed pebble bed. However, from the experimental data [21] and numerical
simulations [56, 57], it is shown that the capability of heat transfer in the near-wall
region is different from that in the bulk region. For the cylindrical beds, such as