1.3 Pebble Flows
7
have essential engineering applications. For example, the efficiency and safety of the
pebble-bed nuclear reactor depend on the degree of mixing [35–37].
The process of silo discharge can be considered an example of the complexity
of granular flows. Lots of experimental and simulation studies have been carried
out over the past decades. Usually, the orifice is opened at the bottom of the silo
filled with grains. The effects of the orifice size on the flow characteristics have been
widely studied. In general, bigger orifices may result in more homogeneous pebble
flow, while smaller orifices can develop pebble flow intermittencies [38]. The flowrate oscillations caused by different sizes of orifice seem not to be dominated by any
particular frequency. Moreover, the flow of granular materials inside a quasi-twodimensional silo was measured and compared with some existing models, including
the kinematic model, void model, and the spot model [39].
The basic mechanism of granule flow has not been fully understood yet, especially
this specific pebble flow in a reactor core. However, the flow field characteristic is
vital to the efficiency and safety of HTGR. The behavior of the pebbles should be
ensured to fulfill thermal-hydraulic rules and radiation safety requirements.
Experimental and numerical studies have shown features of variously shaped
particles flowing through silos with different geometries. Still, those cases all belong
to free outflow and more focus on the prediction of outflow rate [40–42].
The law governing the pebble flow is an important topic and crucial for the design
of the pebble-bed reactor. It is an attractively simple and yet surprisingly complex
subject. Fast, dilute flows are known to obey classical hydrodynamics, but slow
and dense flows pose a considerable challenge to theorists [43], due to many-body
interactions and non-thermal fluctuations. The underlying physical mechanism of
dense granular flow is far from fully understood, although it is very familiar to us,
e.g., sand in an hourglass [43].
1.3.2 Very Slow Pebble Flow in HTGR
The pebble flow characteristics are the basis of geometrical design, neutronic design
and nuclear fuel cycle of the pebble bed reactor core. The reactor physics, thermal
engineering, and nuclear fuel cycle designs all depend on the pebble flow. Therefore,
the pebble flow plays a fundamental role in the design improvement and thermal
safety analysis of the pebble-bed high-temperature gas-cooled reactor [44].
The pebble flow in pebble-bed reactors is a unique particle flow or granular flow.
In contrast to conventional reactors, there are no structured fuel and reflector assemblies in the pebble-bed HTGR. Discrete baseball-size graphite-coated fuel pebbles
instead of the structured fuel rods are used to form the pebble-bed HTGR core. The
stochastically and densely accumulated hundreds of thousands of fuel pebbles flow
downward very slowly through the core of the pebble-bed reactor driven by gravity.
This a very slow particle flow is called a pebble flow. The pebbles are loaded from
the top of the reactor core and discharged from the bottom. The pebble-bed HTGRs
run in a circulating mode with fresh fuel pebbles loaded from bed top and used fuel
7
have essential engineering applications. For example, the efficiency and safety of the
pebble-bed nuclear reactor depend on the degree of mixing [35–37].
The process of silo discharge can be considered an example of the complexity
of granular flows. Lots of experimental and simulation studies have been carried
out over the past decades. Usually, the orifice is opened at the bottom of the silo
filled with grains. The effects of the orifice size on the flow characteristics have been
widely studied. In general, bigger orifices may result in more homogeneous pebble
flow, while smaller orifices can develop pebble flow intermittencies [38]. The flowrate oscillations caused by different sizes of orifice seem not to be dominated by any
particular frequency. Moreover, the flow of granular materials inside a quasi-twodimensional silo was measured and compared with some existing models, including
the kinematic model, void model, and the spot model [39].
The basic mechanism of granule flow has not been fully understood yet, especially
this specific pebble flow in a reactor core. However, the flow field characteristic is
vital to the efficiency and safety of HTGR. The behavior of the pebbles should be
ensured to fulfill thermal-hydraulic rules and radiation safety requirements.
Experimental and numerical studies have shown features of variously shaped
particles flowing through silos with different geometries. Still, those cases all belong
to free outflow and more focus on the prediction of outflow rate [40–42].
The law governing the pebble flow is an important topic and crucial for the design
of the pebble-bed reactor. It is an attractively simple and yet surprisingly complex
subject. Fast, dilute flows are known to obey classical hydrodynamics, but slow
and dense flows pose a considerable challenge to theorists [43], due to many-body
interactions and non-thermal fluctuations. The underlying physical mechanism of
dense granular flow is far from fully understood, although it is very familiar to us,
e.g., sand in an hourglass [43].
1.3.2 Very Slow Pebble Flow in HTGR
The pebble flow characteristics are the basis of geometrical design, neutronic design
and nuclear fuel cycle of the pebble bed reactor core. The reactor physics, thermal
engineering, and nuclear fuel cycle designs all depend on the pebble flow. Therefore,
the pebble flow plays a fundamental role in the design improvement and thermal
safety analysis of the pebble-bed high-temperature gas-cooled reactor [44].
The pebble flow in pebble-bed reactors is a unique particle flow or granular flow.
In contrast to conventional reactors, there are no structured fuel and reflector assemblies in the pebble-bed HTGR. Discrete baseball-size graphite-coated fuel pebbles
instead of the structured fuel rods are used to form the pebble-bed HTGR core. The
stochastically and densely accumulated hundreds of thousands of fuel pebbles flow
downward very slowly through the core of the pebble-bed reactor driven by gravity.
This a very slow particle flow is called a pebble flow. The pebbles are loaded from
the top of the reactor core and discharged from the bottom. The pebble-bed HTGRs
run in a circulating mode with fresh fuel pebbles loaded from bed top and used fuel