10
1 Introduction
To date, several fundamental problems about slow and dense granular flow have
not been resolved, including the velocity fluctuations on the trajectories [70], and the
distinct “motion events” in dense granular Couette flow [52]. The cross-correlation
between velocity and density fluctuations in a vibrated granular monolayer was discussed by Olafsen [71]. The shear localization and fluctuations were also studied
by Refs. [72, 73]. Measurement [74], showed that there could be a “granular temperature” in the absence of a shear gradient. The local velocity fluctuations and the
coordination number of sand flow in a hopper were also analyzed by Ref. [75]. However, it is still expected to find out more details of the relationship between velocity
fluctuations and internal particle structures in the slow and dense pebble flow through
experiments.
Much attention was paid to the arching phenomenon of granular materials [40, 76,
77]. Arches are collective internal structures in which particles rely on each other for
mutual stability. Early theoretical efforts have incorporated the definition of free-fall
arch to explain the constant mass flow rate observed in granular material. Lots of
studies have been conducted on the free-fall arch, e.g., the correlation between the
fluctuation of discharging flow rate (or jamming events) and size of free-fall arch
[78]. Some systematic experiments were performed on the relationship between silo
orifice size and the jamming events or intermittencies [53]. The particle contacts
created the network of force chains and arches, which influenced the particle flow
[79, 80]. It was found that a quasi-static deformation in pure shear-induced anisotropy
and created long correlations along with the forces chains.
Some investigations of the bulk arch were done by using the pseudo-dynamic
model [81], the molecular dynamic-type simulation [82], and the discrete element
methods [83], on the arch size distribution, coordination number, and so on. Bulk
arches could form at any place inside the packing structures, while the blocking arch
[84], usually appeared near the outlet of the hopper. Both arches were shown to be
responsible for strong fluctuations of the discharging flow rate and density waves
[85–87]. In a real typical packing, up to 70% of the particles are part of the bulk
arch configurations [88]. However, few studies were reported to the free-fall arch or
blocking arch in the slow and dense granular flows in the silo bed. Moreover, few
references were focused on the experimental measurements of the bulk arches [81].
Much more work is needed to explore the details of the bulk arches in the particle
packing and the connection between arches and velocity fluctuations.
For the mechanical study of the dynamics of discrete particles, the local packing
structure and equivalent stress-tensor may be of the most importance. The packing
structure is needed for either the design optimization or safety assessment, such as the
packing density, radial distribution function, and coordination number distribution
[89]. The packing factor is also crucial since it affects the mechanical behavior [90],
void distribution and coolant flow drag and pressure drop, especially for multi-sized
pebble bed [91]. For example, the mechanical behavior of mixed fusion pebble beds
may have essential features related to the stiffness between the softer-solid system
and stiffer-solids system, which is dependent on both solid material and the loadingunloading cycle numbers [90]. On the other hand, the packing factors for pebbles a
1 Introduction
To date, several fundamental problems about slow and dense granular flow have
not been resolved, including the velocity fluctuations on the trajectories [70], and the
distinct “motion events” in dense granular Couette flow [52]. The cross-correlation
between velocity and density fluctuations in a vibrated granular monolayer was discussed by Olafsen [71]. The shear localization and fluctuations were also studied
by Refs. [72, 73]. Measurement [74], showed that there could be a “granular temperature” in the absence of a shear gradient. The local velocity fluctuations and the
coordination number of sand flow in a hopper were also analyzed by Ref. [75]. However, it is still expected to find out more details of the relationship between velocity
fluctuations and internal particle structures in the slow and dense pebble flow through
experiments.
Much attention was paid to the arching phenomenon of granular materials [40, 76,
77]. Arches are collective internal structures in which particles rely on each other for
mutual stability. Early theoretical efforts have incorporated the definition of free-fall
arch to explain the constant mass flow rate observed in granular material. Lots of
studies have been conducted on the free-fall arch, e.g., the correlation between the
fluctuation of discharging flow rate (or jamming events) and size of free-fall arch
[78]. Some systematic experiments were performed on the relationship between silo
orifice size and the jamming events or intermittencies [53]. The particle contacts
created the network of force chains and arches, which influenced the particle flow
[79, 80]. It was found that a quasi-static deformation in pure shear-induced anisotropy
and created long correlations along with the forces chains.
Some investigations of the bulk arch were done by using the pseudo-dynamic
model [81], the molecular dynamic-type simulation [82], and the discrete element
methods [83], on the arch size distribution, coordination number, and so on. Bulk
arches could form at any place inside the packing structures, while the blocking arch
[84], usually appeared near the outlet of the hopper. Both arches were shown to be
responsible for strong fluctuations of the discharging flow rate and density waves
[85–87]. In a real typical packing, up to 70% of the particles are part of the bulk
arch configurations [88]. However, few studies were reported to the free-fall arch or
blocking arch in the slow and dense granular flows in the silo bed. Moreover, few
references were focused on the experimental measurements of the bulk arches [81].
Much more work is needed to explore the details of the bulk arches in the particle
packing and the connection between arches and velocity fluctuations.
For the mechanical study of the dynamics of discrete particles, the local packing
structure and equivalent stress-tensor may be of the most importance. The packing
structure is needed for either the design optimization or safety assessment, such as the
packing density, radial distribution function, and coordination number distribution
[89]. The packing factor is also crucial since it affects the mechanical behavior [90],
void distribution and coolant flow drag and pressure drop, especially for multi-sized
pebble bed [91]. For example, the mechanical behavior of mixed fusion pebble beds
may have essential features related to the stiffness between the softer-solid system
and stiffer-solids system, which is dependent on both solid material and the loadingunloading cycle numbers [90]. On the other hand, the packing factors for pebbles a