262
5 Numerical Models for Pebble-Bed Heat Transfer
Fig. 5.18 Voronoï tessellation of SANA-I and a single Voronoï element (particle ID = 2562)
Fig. 5.19 View factor from a sphere to polygon (a) and its decomposition (b)
point A is the projection of the sphere center O onto the interface, and line AB is
perpendicular to line BC. The analytical solution of the view factor [37] is
V =
1
4π
arccos
1
3
−
1
8π
arcsin
(1 − B
2
1 )B
2
3 − 2
(1 + B
2
1 )B
2
3
−
1
16
(5.68)
where B 1 = Y/H , B 3 = L/Y .
5.3.2 Short-Range Radiation Model (SRM)
In the Short-range model, the radiant heat flux Q
r
i, j between a pair of Voronoï neighboring spheres (particle i and particle j) can be simplified as follows:
5 Numerical Models for Pebble-Bed Heat Transfer
Fig. 5.18 Voronoï tessellation of SANA-I and a single Voronoï element (particle ID = 2562)
Fig. 5.19 View factor from a sphere to polygon (a) and its decomposition (b)
point A is the projection of the sphere center O onto the interface, and line AB is
perpendicular to line BC. The analytical solution of the view factor [37] is
V =
1
4π
arccos
1
3
−
1
8π
arcsin
(1 − B
2
1 )B
2
3 − 2
(1 + B
2
1 )B
2
3
−
1
16
(5.68)
where B 1 = Y/H , B 3 = L/Y .
5.3.2 Short-Range Radiation Model (SRM)
In the Short-range model, the radiant heat flux Q
r
i, j between a pair of Voronoï neighboring spheres (particle i and particle j) can be simplified as follows: