2.5 Particle Velocimetry Measurements
91
a significant decrease from 90% at h = 75d to 40% at h = 15d on average except
the situation R (∞,45 ◦ ) and R (∞,60 ◦ ) . The poor flow uniformity in the radial direction
makes the mass flow region narrower in the lower part of the cylinder section. In the
wedged section, it presents a rising profile of L m from 55% at 30d to 95% at 1d for
the R (∞,45 ◦ ) case, and from 40% at 15d to 80% at 1d for the R (∞,30 ◦ ) case. The main
reason for this is that the contraction of the bed base keeps the width of the vessel
declining more significantly than the width of mass flow region. For R 2 and R 3 , the
L m goes up after dropping from h = 15d to h = 5d. Notably, there is a continuous
fall of L m from 30% at h = 15d to 5% at h = 1d for R 1 bed configuration since that
the vessel width seems not to show apparent decreasing from h = 15d to h = 1d.
In conclusion, the total mass flow level can be calculated by average all L m at
each height. Table 2.2 shows the total mass flow level for all bed configurations. All
the values indicate the following sequence of total mass level:
R (∞,60 ◦ ) > R (∞,45 ◦ ) > R 2 > (R 3 or R (∞,30 ◦ ) ) > R 1 .
(2.15)
The combination (σ -α) of mass flow level and the flow uniformity in the radial
direction can be used to estimate the flow pattern and flow uniformity quantitatively
in the pebble flow.
2.5.3.15 Resultant Movement Estimation
Although the vertical velocity field was discussed in the previous section, the resultant
velocity field is also indispensable when estimating the whole flow field in the real
pebble-bed reactor. As is known, in the pebble bed, directions of resultant velocity
vector for pebbles with different locations are various, and their distribution can be
regarded as an excellent indicator to evaluate the consequent movement for the whole
pebble flow.
To estimate the relationship between vertical and transverse movements and flow
characteristics of the resultant flow, the tilted (or inclined) angle θ in is defined as
the average of the angles between the resultant velocities and the radial directions
for all particles in the vessel during the experiment time firstly. The tangent value of
θ in can be calculated as the ratio of the vertical to transverse average displacement
magnitude of the whole particles as follows:
θ in = arctan
¯
s y
¯
s x
,
(2.16)
where
¯
s y
¯
s x
is the average of transverse (vertical) displacement magnitude of all particles.
As shown in Table 2.2, the growing up of base angle (from 30
◦ to 60
◦ ) indicates the
dropping of θ in (from 75.6
◦ to 66.4
◦ ) for the arc shapes with infinite radius. As shown
in Fig. 2.27, the R (∞,60 ◦ ) bed configuration presents a higher transverse velocity field
than other situations. Thus, the average transverse displacement magnitude ¯
s x for
91
a significant decrease from 90% at h = 75d to 40% at h = 15d on average except
the situation R (∞,45 ◦ ) and R (∞,60 ◦ ) . The poor flow uniformity in the radial direction
makes the mass flow region narrower in the lower part of the cylinder section. In the
wedged section, it presents a rising profile of L m from 55% at 30d to 95% at 1d for
the R (∞,45 ◦ ) case, and from 40% at 15d to 80% at 1d for the R (∞,30 ◦ ) case. The main
reason for this is that the contraction of the bed base keeps the width of the vessel
declining more significantly than the width of mass flow region. For R 2 and R 3 , the
L m goes up after dropping from h = 15d to h = 5d. Notably, there is a continuous
fall of L m from 30% at h = 15d to 5% at h = 1d for R 1 bed configuration since that
the vessel width seems not to show apparent decreasing from h = 15d to h = 1d.
In conclusion, the total mass flow level can be calculated by average all L m at
each height. Table 2.2 shows the total mass flow level for all bed configurations. All
the values indicate the following sequence of total mass level:
R (∞,60 ◦ ) > R (∞,45 ◦ ) > R 2 > (R 3 or R (∞,30 ◦ ) ) > R 1 .
(2.15)
The combination (σ -α) of mass flow level and the flow uniformity in the radial
direction can be used to estimate the flow pattern and flow uniformity quantitatively
in the pebble flow.
2.5.3.15 Resultant Movement Estimation
Although the vertical velocity field was discussed in the previous section, the resultant
velocity field is also indispensable when estimating the whole flow field in the real
pebble-bed reactor. As is known, in the pebble bed, directions of resultant velocity
vector for pebbles with different locations are various, and their distribution can be
regarded as an excellent indicator to evaluate the consequent movement for the whole
pebble flow.
To estimate the relationship between vertical and transverse movements and flow
characteristics of the resultant flow, the tilted (or inclined) angle θ in is defined as
the average of the angles between the resultant velocities and the radial directions
for all particles in the vessel during the experiment time firstly. The tangent value of
θ in can be calculated as the ratio of the vertical to transverse average displacement
magnitude of the whole particles as follows:
θ in = arctan
¯
s y
¯
s x
,
(2.16)
where
¯
s y
¯
s x
is the average of transverse (vertical) displacement magnitude of all particles.
As shown in Table 2.2, the growing up of base angle (from 30
◦ to 60
◦ ) indicates the
dropping of θ in (from 75.6
◦ to 66.4
◦ ) for the arc shapes with infinite radius. As shown
in Fig. 2.27, the R (∞,60 ◦ ) bed configuration presents a higher transverse velocity field
than other situations. Thus, the average transverse displacement magnitude ¯
s x for