286
5 Numerical Models for Pebble-Bed Heat Transfer
Fig. 5.39 Volume-based (a) and area-based (b) radial porosity distribution of the packed pebble
bed
Fig. 5.40 Radial Effective Thermal Conductivity (ETC) with area-based (a) and volume-based (b)
porosity distribution
the damped oscillatory ETC of particle radiation emerges in the near-wall region. But
the experimental ETC monotonically decreases when it comes close to the physical
walls. The results of the volume-based White model shown in Fig. 5.40b are in general agreement with the experimental data with the wall effect. Because the Sub-Cell
radiation Model (SCM) is a particle-scale approach, the volume-based porosity in
the particle scale is more appropriate to be applied to the heat transfer simulations.
5.3.9.2 Effect of Surface Emissivity
The surface emissivity is a crucial parameter in the particle radiation calculation and
it is affected by many factors, such as optical properties, temperature [70], surface
roughness [71], and oxidation [72]. When the solid conductivity is far larger than
the ETC of particle radiation (k s k r ) or operated in low temperature, the radiation
exchange factor F is the single-valued function of the surface emissivity for the
packed pebble beds of dense packing, which is defined as
5 Numerical Models for Pebble-Bed Heat Transfer
Fig. 5.39 Volume-based (a) and area-based (b) radial porosity distribution of the packed pebble
bed
Fig. 5.40 Radial Effective Thermal Conductivity (ETC) with area-based (a) and volume-based (b)
porosity distribution
the damped oscillatory ETC of particle radiation emerges in the near-wall region. But
the experimental ETC monotonically decreases when it comes close to the physical
walls. The results of the volume-based White model shown in Fig. 5.40b are in general agreement with the experimental data with the wall effect. Because the Sub-Cell
radiation Model (SCM) is a particle-scale approach, the volume-based porosity in
the particle scale is more appropriate to be applied to the heat transfer simulations.
5.3.9.2 Effect of Surface Emissivity
The surface emissivity is a crucial parameter in the particle radiation calculation and
it is affected by many factors, such as optical properties, temperature [70], surface
roughness [71], and oxidation [72]. When the solid conductivity is far larger than
the ETC of particle radiation (k s k r ) or operated in low temperature, the radiation
exchange factor F is the single-valued function of the surface emissivity for the
packed pebble beds of dense packing, which is defined as