4.2 Gravity-Driven Flow Regime Characterization
179
Data collected at two heights are selected to validate the radial distribution of
mean vertical velocity: the height of 150 mm that is located at the hopper section,
and the height of 450 mm that falls in the middle bed section. Due to the bottom
configuration of the hopper, central pebbles have advantages over side pebbles in
flowing downward. This is why the velocity at the center is much larger than that at
both sides. From the comparisons, there is a tolerable error on the maximum velocity,
and this error comes from the calibration error of material properties between the
simulation and the experiment. Overall, it is verified that the basic distribution and
values of vertical velocity can be simulated reasonably well.
As mentioned before, the slow gravity-driven fuel-pebble flow in HighTemperature Gas-cooled Reactor (HTGR) is one of the applications of very slow
dense particle flow. The solid concentration of this particle material varies slightly
between 0.62 and 0.65, because the pebbles pack randomly to form the core, and
the local packing structure fluctuates all the time. Concerning the flow parameters, the mean shear rate (γ ) is in the order of the ratio of mean velocity (V ) to
the particle diameter (d p ) : γ = V /d p , and the value of dimensionless stiffness,
k
= k/(ρd
3
γ
2 ),ranges from 10
5 to 10
12 according to the simulation parameters.
Therefore, based on Campbell’s theory (refer to Fig. 4.1), simulated cases in this
section fall into the elastic–quasi-static flow category.
4.2.3.3 Very Slow Dense Particle Flow
The case with the circulating rate of 1 particle per second (mean velocity V =
0.0054d p /s) is set to represent the slow pebble flow in HTGR. The phenomenon of
the pebble avalanche, namely the sign of the flow intermittence is one of the features
that distinguish this slow pebble flow from those smoothly flowing particle materials.
However, despite the occurrence of the flow intermittence in practical engineering
applications, it is not included in the definition of the old elastic–quasi-static regime.
Different sizes of avalanches can be observed easily by the naked eye in the
experimental setup, and simulation helps to illustrate them more carefully. Figure
4.10 depicts the entire process of the avalanche, such as initiating, developing, reaching maximum size, decaying, and final ending. In the contour map, all the particles
are colored by the magnitude of velocity, which makes it easy to note. Figure 4.10
shows two different sets of sequences of avalanche during the simulation, and the
time interval between the two frames is 0.02s.
The motion of particles transmits from the bottom to the top like transmission of
the wave, and it is a “wave” of voids. Particles are drained out from the lowest place
where the voids are created. Then the surrounding particles will fill the voids caused
by the already discharged particles and leave room for upper particles. Upper particles
will collapse and take up the room. The process repeats and continues until it reaches
the top free surface of the particle pile. The occurrence of the avalanche is the result
of void accumulation. When the voids accumulate beyond a certain threshold, an
avalanche can happen. However, due to many random mechanisms determining and
influencing the steps of the avalanche development, the precise time, location, and
179
Data collected at two heights are selected to validate the radial distribution of
mean vertical velocity: the height of 150 mm that is located at the hopper section,
and the height of 450 mm that falls in the middle bed section. Due to the bottom
configuration of the hopper, central pebbles have advantages over side pebbles in
flowing downward. This is why the velocity at the center is much larger than that at
both sides. From the comparisons, there is a tolerable error on the maximum velocity,
and this error comes from the calibration error of material properties between the
simulation and the experiment. Overall, it is verified that the basic distribution and
values of vertical velocity can be simulated reasonably well.
As mentioned before, the slow gravity-driven fuel-pebble flow in HighTemperature Gas-cooled Reactor (HTGR) is one of the applications of very slow
dense particle flow. The solid concentration of this particle material varies slightly
between 0.62 and 0.65, because the pebbles pack randomly to form the core, and
the local packing structure fluctuates all the time. Concerning the flow parameters, the mean shear rate (γ ) is in the order of the ratio of mean velocity (V ) to
the particle diameter (d p ) : γ = V /d p , and the value of dimensionless stiffness,
k
= k/(ρd
3
γ
2 ),ranges from 10
5 to 10
12 according to the simulation parameters.
Therefore, based on Campbell’s theory (refer to Fig. 4.1), simulated cases in this
section fall into the elastic–quasi-static flow category.
4.2.3.3 Very Slow Dense Particle Flow
The case with the circulating rate of 1 particle per second (mean velocity V =
0.0054d p /s) is set to represent the slow pebble flow in HTGR. The phenomenon of
the pebble avalanche, namely the sign of the flow intermittence is one of the features
that distinguish this slow pebble flow from those smoothly flowing particle materials.
However, despite the occurrence of the flow intermittence in practical engineering
applications, it is not included in the definition of the old elastic–quasi-static regime.
Different sizes of avalanches can be observed easily by the naked eye in the
experimental setup, and simulation helps to illustrate them more carefully. Figure
4.10 depicts the entire process of the avalanche, such as initiating, developing, reaching maximum size, decaying, and final ending. In the contour map, all the particles
are colored by the magnitude of velocity, which makes it easy to note. Figure 4.10
shows two different sets of sequences of avalanche during the simulation, and the
time interval between the two frames is 0.02s.
The motion of particles transmits from the bottom to the top like transmission of
the wave, and it is a “wave” of voids. Particles are drained out from the lowest place
where the voids are created. Then the surrounding particles will fill the voids caused
by the already discharged particles and leave room for upper particles. Upper particles
will collapse and take up the room. The process repeats and continues until it reaches
the top free surface of the particle pile. The occurrence of the avalanche is the result
of void accumulation. When the voids accumulate beyond a certain threshold, an
avalanche can happen. However, due to many random mechanisms determining and
influencing the steps of the avalanche development, the precise time, location, and