5.5 Further Issues
349
Fig. 5.92 The particle temperature profile (a) and the radial distribution (b) of the black radiation
model in the packed pebble bed
Table 5.6 The radiation exchange factor in dense packed bed of black surface
Model
F at ε r = 1.0
References
Argo correlation
1.0
[27]
Wakao correlation
1.15
[73]
Vortmeyer correlation
1.12
[88]
Nasr correlation
1.0
[15]
Two flux model
1.11
[19]
Sub-cell radiation model
1.14
[9]
Present black radiation model 1.03
–
that the radial temperature distribution T (r ) in the bed was linear to r
2 approximately. The effective thermal conductivity k r was obtained by the linear fitting of
Eq. (5.196) under different temperatures (as shown in Fig. 5.92), and it was found
that k r is directly proportional to T
3 . Thus, the radiation exchange factor F in dense
granular systems of mono-sized spheres is defined as (Eq. (5.72), [77])
F =
k r
4σ d p T 3
(5.197)
where d p is the particle diameter of the pebble bed. As shown in Fig. 5.93, F is
1.03 for the pebble bed of HTR-10 computed by the current black radiation model.
It is also shown in Table 5.6 that the black radiation model agrees with existing
correlations and models for the black surfaces, including the Argo correlation [27],
the Wakao correlation [73], the Vortmeyer correlation [88], the Nasr correlation [15],
the two-flux model [19], and the sub-cell radiation model [9].