1.3 Pebble Flows
19
mixing is detrimental to the safety of the nuclear reactor. Choosing different pebble
sizes and region widths are of the basic approaches to control the mixing degree. To
date, although some studies on the two-region pebble bed have been carried out, they
are mainly based on the phenomenological analysis of the mixing region. There are
still lacking quantitative and statistical data of the two-region pebble beds, especially
for the analyses on the effects of multi-sized particles and different widths of regions.
To get a comprehensive understanding of the mixing zone of the two-region pebble bed, it is also essential to quantify the degree of mixing process mathematically.
However, although some mixing indices have been proposed [185, 186], the universality and adaptability of the indices for the pebble bed still need to be investigated in
detail. Generally, there are three categories of the mixing index: (1) The mean index
that is related to the average particle position [187], or similarly, the segregation index
based on the average percentage of contact numbers between different types of particles [188]. The mean index is straightforward and fast to evaluate multiple mixtures.
(2) The macroscopic mixing index, where the container is divided into finite cubic
sample cells [189, 190]. The macroscopic index may change slightly with different
grid sizes and the sampling methods. (3) The particle-scale index [191]. As an example, it was used to study the vertically-shafted bladed mixer (a mixer having a blade
or blades on the walls or axis) and showed that the particle diameter and material
density jointly determine the degree of mixing [192].
Furthermore, the influence of the loading ratio of fuel pebbles to graphite pebbles
and their densities on the flow pattern is also essential for the design of two-region
pebble bed. It will significantly affect the boundary of the central region and the flow
characteristics of pebbles. It is proved by many researchers that the particle size and
shape have great significance on the flow pattern [193, 194]. However, there is still
little research focusing on the pebble density, which is also a crucial non-negligible
factor for the flow patterns and spatial distribution. Wu et al. [195] investigated the
mixing flow of different density pebbles in a circulating packed bed and found many
unique flow characteristics such as pushing and segregation phenomenon. But the
influence of density difference on the pebble flow in a two-region-designed dynamic
core is still unknown. Also, the loading ratio of fuel pebbles directly affects the sizes
of the central region and the core configuration, and thus should be considered as
well.
1.4 Pebble Bed Heat Transfer
The core of the high-temperature gas-cooled reactor (HTGR) is a densely packed
pebble bed with large-sized fuel spheres operated in high-temperatures. The energy
generated from large quantities of mono-sized fuel elements is transported to a steam
generator by forced convection under high-pressure [21]. Numerical simulations
of the flow and heat transfer of the coolant and pebbles are indispensable for the
engineering design and nuclear safety analysis of HTGR.
19
mixing is detrimental to the safety of the nuclear reactor. Choosing different pebble
sizes and region widths are of the basic approaches to control the mixing degree. To
date, although some studies on the two-region pebble bed have been carried out, they
are mainly based on the phenomenological analysis of the mixing region. There are
still lacking quantitative and statistical data of the two-region pebble beds, especially
for the analyses on the effects of multi-sized particles and different widths of regions.
To get a comprehensive understanding of the mixing zone of the two-region pebble bed, it is also essential to quantify the degree of mixing process mathematically.
However, although some mixing indices have been proposed [185, 186], the universality and adaptability of the indices for the pebble bed still need to be investigated in
detail. Generally, there are three categories of the mixing index: (1) The mean index
that is related to the average particle position [187], or similarly, the segregation index
based on the average percentage of contact numbers between different types of particles [188]. The mean index is straightforward and fast to evaluate multiple mixtures.
(2) The macroscopic mixing index, where the container is divided into finite cubic
sample cells [189, 190]. The macroscopic index may change slightly with different
grid sizes and the sampling methods. (3) The particle-scale index [191]. As an example, it was used to study the vertically-shafted bladed mixer (a mixer having a blade
or blades on the walls or axis) and showed that the particle diameter and material
density jointly determine the degree of mixing [192].
Furthermore, the influence of the loading ratio of fuel pebbles to graphite pebbles
and their densities on the flow pattern is also essential for the design of two-region
pebble bed. It will significantly affect the boundary of the central region and the flow
characteristics of pebbles. It is proved by many researchers that the particle size and
shape have great significance on the flow pattern [193, 194]. However, there is still
little research focusing on the pebble density, which is also a crucial non-negligible
factor for the flow patterns and spatial distribution. Wu et al. [195] investigated the
mixing flow of different density pebbles in a circulating packed bed and found many
unique flow characteristics such as pushing and segregation phenomenon. But the
influence of density difference on the pebble flow in a two-region-designed dynamic
core is still unknown. Also, the loading ratio of fuel pebbles directly affects the sizes
of the central region and the core configuration, and thus should be considered as
well.
1.4 Pebble Bed Heat Transfer
The core of the high-temperature gas-cooled reactor (HTGR) is a densely packed
pebble bed with large-sized fuel spheres operated in high-temperatures. The energy
generated from large quantities of mono-sized fuel elements is transported to a steam
generator by forced convection under high-pressure [21]. Numerical simulations
of the flow and heat transfer of the coolant and pebbles are indispensable for the
engineering design and nuclear safety analysis of HTGR.