290
5 Numerical Models for Pebble-Bed Heat Transfer
Fig. 5.44 Experimental results and particle-scale simulation of the transient heat transfer processes
of TF-PBEC at half height
wall in the radial direction. The particle temperatures increase gradually and reach
a steady state at 140 h.
5.3.9.5 Multi-component Polydisperse Beds
The discrete heat transfer model is still applicable to the polydisperse beds of multicomponent pebbles. The different packing and Voronoï tessellations of random packing (α f = 0.39) are shown in Fig. 5.45, the geometry of which is based on the HTTU
[21]. At a steady state of the packed pebble beds without a heat source, the radial
Effective Thermal Conductivity (ETC) k eff can be calculated by
k eff =
Q
2π L(T i − T o )
ln
r o
r i
,
(5.130)
where T i and T o are the temperatures of inner and outer walls, which are fixed at
given values. Only particle radiation is discussed and k c = 0. The total ETC also
can also be evaluated by the Sub-Cell radiation Model (SCM). The effective particle
diameter of the weighted harmonic mean [76, 77] is defined as
1
d p
=
n
i=1
x i
d i
=
x 1
d 1
+
x 2
d 2
+ · · · +
x n
d n
(5.131)