14
1 Introduction
For Pebble Flow Characteristics
A new application field of granule flow has recently been developed in nuclear
engineering because of the development of pebble-bed high-temperature gas-cooled
reactors (HTGR).
The pebble flow in pebble-bed reactors is a unique particle flow or granular flow.
It is estimated that the flow velocity through the core under gravity is about 10
−4 –
10
−3 m/h. Such a small velocity in the pebble bed is due to the low circulating rate
in practical reactors, like 125 fuel pebbles per day for HTR-10, which results in
phenomena and characteristics quite different from common fast particle flow. In
addition, the pebble flows can be interrupted by different sizes of pebble avalanches
happening at random locations and time points, and this is called flow intermittency.
The discharge process of the reactor setup is controlled by a discharging facility,
which is used to remove the bottom pebbles one by one at a certain rate. In this way, the
discharge process would be kept steady and consistent, different from common free
outflow in other industrial applications. Controlled and constant discharge process
is the direct engineering reason leading to the very slow pebble flow in pebble-bed
HTGRs.
Granule flow has not been well understood, and some basic mechanisms still
remain to be explained. Very slow pebble flow with the discharge-controlled process
is even less familiar. Lots of studies of pebble flows or similar granular flows have
been carried out in the past decades, contributing to various relevant aspects of the
pebble flow, such as velocity profiles [113, 130], phenomenological analysis [112],
two-region design [136], diffusion and mixing [114], as well as numerical simulations
[128, 137–141], and detailed analysis [48], etc.
Both experimental and numerical studies have been done to illustrate underlying
physics of granule flow in silos, discussions like silo shapes [42], friction effect on
flow pattern [41, 142], force analysis of clogging arches [143], and prediction for
discharge rate [38, 40]. All of these works offered helpful insights for the pebble flow
optimization and the design of the pebble bed. However, the applications running with
free outflow and fluctuating discharge rate did not meet the discharge-controlled process in a reactor; furthermore, most studies focused on qualitative discussion. Mass
flow Index (MFI) was introduced as a quantitative value to evaluate flow uniformity,
but MFI is not fine enough [144]. For pebble-bed reactors, modifying the geometry
of bed through adjusting base cone angle [145] and bottom shape [63], has been
validated to be effective measures. Moreover, introducing reasonably designed wall
structures is helpful in avoiding a large area of near-wall pebble caking [104].
Although its construction project of HTR-PM will be finished, the details of threedimensional 1:1 scale pebble flow in the reactor core of HTGR is not well understood.
It would be much helpful if we can predict the real-scale three-dimensional pebble
flow characteristics of HTR-PM or related bed configurations. Therefore, the pebble flow in such a prototypic reactor is very important and interesting for nuclear
engineering.
Various methods have already been proposed to model the pebble flow in pebble
bed reactors. In general, there are two main categories. The one category is the
1 Introduction
For Pebble Flow Characteristics
A new application field of granule flow has recently been developed in nuclear
engineering because of the development of pebble-bed high-temperature gas-cooled
reactors (HTGR).
The pebble flow in pebble-bed reactors is a unique particle flow or granular flow.
It is estimated that the flow velocity through the core under gravity is about 10
−4 –
10
−3 m/h. Such a small velocity in the pebble bed is due to the low circulating rate
in practical reactors, like 125 fuel pebbles per day for HTR-10, which results in
phenomena and characteristics quite different from common fast particle flow. In
addition, the pebble flows can be interrupted by different sizes of pebble avalanches
happening at random locations and time points, and this is called flow intermittency.
The discharge process of the reactor setup is controlled by a discharging facility,
which is used to remove the bottom pebbles one by one at a certain rate. In this way, the
discharge process would be kept steady and consistent, different from common free
outflow in other industrial applications. Controlled and constant discharge process
is the direct engineering reason leading to the very slow pebble flow in pebble-bed
HTGRs.
Granule flow has not been well understood, and some basic mechanisms still
remain to be explained. Very slow pebble flow with the discharge-controlled process
is even less familiar. Lots of studies of pebble flows or similar granular flows have
been carried out in the past decades, contributing to various relevant aspects of the
pebble flow, such as velocity profiles [113, 130], phenomenological analysis [112],
two-region design [136], diffusion and mixing [114], as well as numerical simulations
[128, 137–141], and detailed analysis [48], etc.
Both experimental and numerical studies have been done to illustrate underlying
physics of granule flow in silos, discussions like silo shapes [42], friction effect on
flow pattern [41, 142], force analysis of clogging arches [143], and prediction for
discharge rate [38, 40]. All of these works offered helpful insights for the pebble flow
optimization and the design of the pebble bed. However, the applications running with
free outflow and fluctuating discharge rate did not meet the discharge-controlled process in a reactor; furthermore, most studies focused on qualitative discussion. Mass
flow Index (MFI) was introduced as a quantitative value to evaluate flow uniformity,
but MFI is not fine enough [144]. For pebble-bed reactors, modifying the geometry
of bed through adjusting base cone angle [145] and bottom shape [63], has been
validated to be effective measures. Moreover, introducing reasonably designed wall
structures is helpful in avoiding a large area of near-wall pebble caking [104].
Although its construction project of HTR-PM will be finished, the details of threedimensional 1:1 scale pebble flow in the reactor core of HTGR is not well understood.
It would be much helpful if we can predict the real-scale three-dimensional pebble
flow characteristics of HTR-PM or related bed configurations. Therefore, the pebble flow in such a prototypic reactor is very important and interesting for nuclear
engineering.
Various methods have already been proposed to model the pebble flow in pebble
bed reactors. In general, there are two main categories. The one category is the