1.3 Pebble Flows
9
of the probability distribution of the real-valued random variables, regarded as an
intermittent index [56]. The theories of fractals and chaos have also been employed
in particle flow study.
Similarly, the Multiplicative Cascade Method (MCM) is introduced [57], to characterize the self-similarity and scale invariance—the typical property of fractals of
the measured flow signals. Besides, Silbert [54], showed the prevalence of the intermittency in granular flows down an inclined plane. He found that the characteristic
time scale τ c associated with the intermittent structural events obeys a power-law
relation with the difference between the slope and the repose angle. Benza et al. [58]
and Fishcher et al. [59] observed the intermittency with spontaneous erratic switches
and the hysteresis cycles by modeling the dynamics of avalanches between intermittent and continuous flow regimes in the rotating drum granular flow. Recently, the
discrete element method was used to analyze the flow characteristics of a gravitydriven dense granular flow in a silo bed [60]. The time variations and derivatives of the
mean forces and velocities, as well as their respective correlations, were analyzed
quantitatively to depict the characteristics of granular flow, including intermittent
characteristics.
The underlying mechanism of granular flow has not been fully understood yet,
especially for the specific pebble flow in the 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 and radiation safety requirements [61]. In the reactor core of HTR-PM [62], the pebble flow driven by gravity
is very slow which is termed as a quasi-static flow regime. The particles are dumped
from the outlet at the bottom, and reloaded at the top of the reactor core, forming a
recirculation mode of operation. In this recirculation process, the velocities of particles throughout the bed are varied significantly, depending on the bed configurations,
loading method, and etc. In common, particles flow fast in the central part and slowly
near the wall. The uniformity of pebble flow is of crucial importance for the performance and safety of reactor operation, which should be focused on reactor core
design work [63].
Although the direct visualization of the particle trajectories suggests a correlation in the particle velocities, their correlations have seldom been directly measured
or characterized in experiments, and their effects on the overall flow behavior are
unknown [64]. For the rapid granular flows at low and moderate solid fractions, the
autocorrelation functions used by many investigators [65–67], are found to follow the
exponentially decaying curves. This corresponds with the memory loss of the rapid
pebble collisions as the collisions with their neighbors are random [68]. However,
for slow granular flows, the collisions are characterized by long-lasting, frictional
contacts between pebbles, and the stress magnitudes independent of the rate of deformation. Furthermore, the mechanism on how the microscopic feature at the particle
scale affects the macroscopic flow behavior is still not fully understood. In addition,
although a number of experiments [69], have been carried out about the average
macroscopic properties of slow, the lack of a complete experimental description of
the pebble system, especially at the microscopic scale, has so far severely prevented
the rigorous confirmation of any of the approaches [64].
9
of the probability distribution of the real-valued random variables, regarded as an
intermittent index [56]. The theories of fractals and chaos have also been employed
in particle flow study.
Similarly, the Multiplicative Cascade Method (MCM) is introduced [57], to characterize the self-similarity and scale invariance—the typical property of fractals of
the measured flow signals. Besides, Silbert [54], showed the prevalence of the intermittency in granular flows down an inclined plane. He found that the characteristic
time scale τ c associated with the intermittent structural events obeys a power-law
relation with the difference between the slope and the repose angle. Benza et al. [58]
and Fishcher et al. [59] observed the intermittency with spontaneous erratic switches
and the hysteresis cycles by modeling the dynamics of avalanches between intermittent and continuous flow regimes in the rotating drum granular flow. Recently, the
discrete element method was used to analyze the flow characteristics of a gravitydriven dense granular flow in a silo bed [60]. The time variations and derivatives of the
mean forces and velocities, as well as their respective correlations, were analyzed
quantitatively to depict the characteristics of granular flow, including intermittent
characteristics.
The underlying mechanism of granular flow has not been fully understood yet,
especially for the specific pebble flow in the 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 and radiation safety requirements [61]. In the reactor core of HTR-PM [62], the pebble flow driven by gravity
is very slow which is termed as a quasi-static flow regime. The particles are dumped
from the outlet at the bottom, and reloaded at the top of the reactor core, forming a
recirculation mode of operation. In this recirculation process, the velocities of particles throughout the bed are varied significantly, depending on the bed configurations,
loading method, and etc. In common, particles flow fast in the central part and slowly
near the wall. The uniformity of pebble flow is of crucial importance for the performance and safety of reactor operation, which should be focused on reactor core
design work [63].
Although the direct visualization of the particle trajectories suggests a correlation in the particle velocities, their correlations have seldom been directly measured
or characterized in experiments, and their effects on the overall flow behavior are
unknown [64]. For the rapid granular flows at low and moderate solid fractions, the
autocorrelation functions used by many investigators [65–67], are found to follow the
exponentially decaying curves. This corresponds with the memory loss of the rapid
pebble collisions as the collisions with their neighbors are random [68]. However,
for slow granular flows, the collisions are characterized by long-lasting, frictional
contacts between pebbles, and the stress magnitudes independent of the rate of deformation. Furthermore, the mechanism on how the microscopic feature at the particle
scale affects the macroscopic flow behavior is still not fully understood. In addition,
although a number of experiments [69], have been carried out about the average
macroscopic properties of slow, the lack of a complete experimental description of
the pebble system, especially at the microscopic scale, has so far severely prevented
the rigorous confirmation of any of the approaches [64].