90
2 Experiments in Pebble Flows
Fig. 2.29 The mass flow
level α (dots) for several
horizontal-stripe layers and
the relative size L m (lines) of
mass flow region at each
height for various bed
configurations
to mass flow patterns always occupy the middle part of the pebble bed, leaving the
funnel flow particles in the near-wall region. The mass flow level can be expressed
as the ratio (α) of the number of mass flow particles to the total number of particles
in a given horizontal-stripe layer. As aforementioned, the line is plotted in Fig. 2.27
to identify the mass flow region in the middle part where R CV > 0.3 at each height.
By comparison, the relative size (L m ) of the mass flow region is also defined as the
ratio of the width of the mass flow zone to the width of the experiment vessel at a
certain height.
Several horizontal-stripe layers are chosen to calculate the mass flow level during
the experiment time of 3300 seconds. Figure 2.29 shows the dependence of the mass
flow level (α) and relative size (L m ) of the mass flow region on the height. On the
one hand, α and L m hold almost the same values at each level. For the R (∞,60 ◦ ) bed
configuration, all particles in the vessel can flow with the mass flow pattern. That
is, the number of mass flow particles is equal to the total number of particles in a
horizontal-stripe layer. The width of the mass flow region and the experiment vessel
is also the same in size. There is no doubt that α and L m retain the same value of 1
for the situation R (∞,60 ◦ ) . On the other hand, the L m shows a little bit lower than α in
the cases of mixed-pattern flow apart from the R (∞,60 ◦ ) bed configuration. The void
fraction in the middle part is always higher than that in the side part when pebbles
keep flowing, which has been studied with a simulation by Yang, et al. [46]. Thus,
there are fewer particles per unit area in the central region than that for the near-wall
region, which makes the α smaller.
However, the difference between α and L m is small since the void fraction does
not change much along the radius at the same height when the speed of pebbles is
low enough. The mass flow level can also be studied by focusing on the relation
between L m and height instead. At each height in the cylinder section of the vessel,
there are not large differences of L m among the bed configurations except R (∞,60 ◦ ) .
This difference usually remains around 10%. For instance, L m arranges from 80%
for R 1 to 90% for R 2 at the height of 75d. In the cylinder section, L m experiences
2 Experiments in Pebble Flows
Fig. 2.29 The mass flow
level α (dots) for several
horizontal-stripe layers and
the relative size L m (lines) of
mass flow region at each
height for various bed
configurations
to mass flow patterns always occupy the middle part of the pebble bed, leaving the
funnel flow particles in the near-wall region. The mass flow level can be expressed
as the ratio (α) of the number of mass flow particles to the total number of particles
in a given horizontal-stripe layer. As aforementioned, the line is plotted in Fig. 2.27
to identify the mass flow region in the middle part where R CV > 0.3 at each height.
By comparison, the relative size (L m ) of the mass flow region is also defined as the
ratio of the width of the mass flow zone to the width of the experiment vessel at a
certain height.
Several horizontal-stripe layers are chosen to calculate the mass flow level during
the experiment time of 3300 seconds. Figure 2.29 shows the dependence of the mass
flow level (α) and relative size (L m ) of the mass flow region on the height. On the
one hand, α and L m hold almost the same values at each level. For the R (∞,60 ◦ ) bed
configuration, all particles in the vessel can flow with the mass flow pattern. That
is, the number of mass flow particles is equal to the total number of particles in a
horizontal-stripe layer. The width of the mass flow region and the experiment vessel
is also the same in size. There is no doubt that α and L m retain the same value of 1
for the situation R (∞,60 ◦ ) . On the other hand, the L m shows a little bit lower than α in
the cases of mixed-pattern flow apart from the R (∞,60 ◦ ) bed configuration. The void
fraction in the middle part is always higher than that in the side part when pebbles
keep flowing, which has been studied with a simulation by Yang, et al. [46]. Thus,
there are fewer particles per unit area in the central region than that for the near-wall
region, which makes the α smaller.
However, the difference between α and L m is small since the void fraction does
not change much along the radius at the same height when the speed of pebbles is
low enough. The mass flow level can also be studied by focusing on the relation
between L m and height instead. At each height in the cylinder section of the vessel,
there are not large differences of L m among the bed configurations except R (∞,60 ◦ ) .
This difference usually remains around 10%. For instance, L m arranges from 80%
for R 1 to 90% for R 2 at the height of 75d. In the cylinder section, L m experiences