18
1 Introduction
known to obey classical hydrodynamics, but slow and dense flows pose a considerable
challenge to theorists, due to many-body interactions and non-thermal fluctuations
[43]. The underlying physical mechanism of dense granular flow is far from fully
understood.
To verify the feasibility of the two-region pebble bed, an experimental facility was
built by scaled down of a prototypic pebble-bed reactor [61]. The existence of the
stagnant region was validated via phenomenological experiments [119]. The particle
flow in the bed is very slow and dense, and the characteristic of pebble bed is much
different from the conventional granular system [60].
Many attempts have been made to evaluate the properties of the pebble bed through
experimental, theoretical, and numerical studies [48, 149, 156, 177]. Numerical
approaches can simulate pebble flows under various fabricating and operating conditions that are difficult to simulate in real experiments. Over the past 50 years, many
mathematical models have been proposed for the pebble flow, such as continuum
approach [129, 164], void model [165, 166], spot model [167], discrete element
method [170, 178], and so on. However, a generally accepted theoretical model is
still lacking. Among these models, DEM might be more appropriate and adaptable
for dense granular flow by comparison. It can be utilized to study some complex
characteristics of granular materials, like velocity profiles [127, 154], recirculation
flow rates [123, 179], non-spherical pebble flow [31, 32], optimal bed structure [146,
180], which can be beneficial for the design and efficiency of the granular system.
However, the DEM method has still been doubted on the quantitative accuracy,
especially about the arbitrarily shaped particles, although its qualitative accuracy has
been widely accepted. So a majority of the investigation on the pebble flow in the
dynamic core still depends on experimental works, e.g., those of AVR in Germany
[181], PBMR in South Africa [111], MPBR in the USA [108, 110], and HTR-PM in
China, but they are still not sufficient. DEM simulations of PBR have been reported
by MIT group for their own designed PBR [126]; meanwhile, an experimental study
has been carried out [110]. In their inventive works, a new method called Spot Model
has been developed [182, 183]. The computational speed of the spot model is much
faster than the DEM. However, DEM seems more reliable and predictive. Yang et
al. [61] and Jiang et al. [119] conducted both experimental and numerical studies to
verify the stable establishment of the two-region arrangement and the applicability
of DEM was validated.
As for experimental studies, early in Germany, Bendenig et al. [181], performed
experiments to study the characteristics of pebble flow, principally aiming at determining the paths followed by the fuels in the core and the velocity distribution, in
support of AVR operation and the THTR design. Researchers in South Africa, studied
pebble flow to guide the design of PBMR [111]. Kadak et al. [184] conducted specific
experiments to investigate the study pebble flow in the conceptually designed MPBR
in the USA [108]. These studies were to support the design of HTR-PM developed
in China. On the other hand, an attempt was made to find the general characteristics
of pebble flow to support the further development of advanced pebble-bed HTGRs.
For the specific application of HTGR design, the main task is to control and limit
the mixing degree between fuel pebbles and graphite pebbles, since a better pebble
1 Introduction
known to obey classical hydrodynamics, but slow and dense flows pose a considerable
challenge to theorists, due to many-body interactions and non-thermal fluctuations
[43]. The underlying physical mechanism of dense granular flow is far from fully
understood.
To verify the feasibility of the two-region pebble bed, an experimental facility was
built by scaled down of a prototypic pebble-bed reactor [61]. The existence of the
stagnant region was validated via phenomenological experiments [119]. The particle
flow in the bed is very slow and dense, and the characteristic of pebble bed is much
different from the conventional granular system [60].
Many attempts have been made to evaluate the properties of the pebble bed through
experimental, theoretical, and numerical studies [48, 149, 156, 177]. Numerical
approaches can simulate pebble flows under various fabricating and operating conditions that are difficult to simulate in real experiments. Over the past 50 years, many
mathematical models have been proposed for the pebble flow, such as continuum
approach [129, 164], void model [165, 166], spot model [167], discrete element
method [170, 178], and so on. However, a generally accepted theoretical model is
still lacking. Among these models, DEM might be more appropriate and adaptable
for dense granular flow by comparison. It can be utilized to study some complex
characteristics of granular materials, like velocity profiles [127, 154], recirculation
flow rates [123, 179], non-spherical pebble flow [31, 32], optimal bed structure [146,
180], which can be beneficial for the design and efficiency of the granular system.
However, the DEM method has still been doubted on the quantitative accuracy,
especially about the arbitrarily shaped particles, although its qualitative accuracy has
been widely accepted. So a majority of the investigation on the pebble flow in the
dynamic core still depends on experimental works, e.g., those of AVR in Germany
[181], PBMR in South Africa [111], MPBR in the USA [108, 110], and HTR-PM in
China, but they are still not sufficient. DEM simulations of PBR have been reported
by MIT group for their own designed PBR [126]; meanwhile, an experimental study
has been carried out [110]. In their inventive works, a new method called Spot Model
has been developed [182, 183]. The computational speed of the spot model is much
faster than the DEM. However, DEM seems more reliable and predictive. Yang et
al. [61] and Jiang et al. [119] conducted both experimental and numerical studies to
verify the stable establishment of the two-region arrangement and the applicability
of DEM was validated.
As for experimental studies, early in Germany, Bendenig et al. [181], performed
experiments to study the characteristics of pebble flow, principally aiming at determining the paths followed by the fuels in the core and the velocity distribution, in
support of AVR operation and the THTR design. Researchers in South Africa, studied
pebble flow to guide the design of PBMR [111]. Kadak et al. [184] conducted specific
experiments to investigate the study pebble flow in the conceptually designed MPBR
in the USA [108]. These studies were to support the design of HTR-PM developed
in China. On the other hand, an attempt was made to find the general characteristics
of pebble flow to support the further development of advanced pebble-bed HTGRs.
For the specific application of HTGR design, the main task is to control and limit
the mixing degree between fuel pebbles and graphite pebbles, since a better pebble