7.2 Wall Structure Optimization
451
flow in the near-wall region as well. Therefore, to get a better result, proper intervals
between structures should be set to balance these contradicting effects.
7.2.4 Mean Kinematic Energy and Eulerian Velocity
This section shows the flow mechanisms in the near-wall region by measuring pebbles’ kinematic energy and velocity. The near-wall region in the simulations refers to
locations with x-coordinate less than 0.15 m or greater than 0.65 m (the bed is 0.8m
wide, ranging 0–0.8 m in the x-direction).
The mean kinematic energy, E m (m
2 /s
2 ), is a temporal–spatial averaged parameter
which aims to measure pebbles’ activity level
E m =
1
t − t 0
t
t 0
1
N
N
i=1
v(i, t)
2
2
dt,
(7.2)
where N represents the number of near-wall pebbles. The mass of each pebble is
ignored in the calculations. Near-wall pebbles in a normal bed and modified beds
with wall structures have quite different behaviors. In the normal bed, pebbles get
stuck or crystallized easily, so they would stay at rest for a longer time, resulting in
smaller E m . On the other hand, pebbles flowing against wall structures tend to be
more active because they are less likely to form blocking or crystallization. They can
keep moving down or moving toward the axis, presenting a relatively larger E m . The
pebble beds are expected to be energetic in the near-wall region.
A comparison of the activity level of the near-wall region in different bed configurations can be observed in Fig. 7.7. All modified beds except “arc_12_10” have more
active near-wall regions than a normal bed, and especially “triangle_12_20”, “triangle_12_10”, and “arc_12_20” have E m increased by more than 50%. It is believed
that in the abovementioned pebble beds, fewer stagnant pebbles, smaller stagnant
regions, and less possibility of forming crystallization would occur. This finding
coincides with the recommended bed configurations in Sect. 7.2.3, which demonstrates that E m of the near-wall region differentiates the ability of wall structures in
preventing stagnant regions and crystallization.
In the Discrete Element Method (DEM) simulation, all the particles are traced
in the Lagrangian frame, but the mean velocities of pebbles during 150 s in several
specific locations are calculated by using the Eulerian method to reveal more details
in the near-wall region. Nine measurement points of velocity have been set on a
vertical line located at 0.02m away from the wall, which is very close to the wall and
assures capturing the wall-sticking velocity in the pebble flow field.
Figure 7.8 describes the profiles of wall-sticking velocity in the bed from top to
bottom. In most elevated locations, “triangle_12_20” ranks first, followed by “sawtooth_12” and “triangle_12_10”. However, in the lowest elevated location, “sawtooth_12” surpasses others, becoming the leading one.
451
flow in the near-wall region as well. Therefore, to get a better result, proper intervals
between structures should be set to balance these contradicting effects.
7.2.4 Mean Kinematic Energy and Eulerian Velocity
This section shows the flow mechanisms in the near-wall region by measuring pebbles’ kinematic energy and velocity. The near-wall region in the simulations refers to
locations with x-coordinate less than 0.15 m or greater than 0.65 m (the bed is 0.8m
wide, ranging 0–0.8 m in the x-direction).
The mean kinematic energy, E m (m
2 /s
2 ), is a temporal–spatial averaged parameter
which aims to measure pebbles’ activity level
E m =
1
t − t 0
t
t 0
1
N
N
i=1
v(i, t)
2
2
dt,
(7.2)
where N represents the number of near-wall pebbles. The mass of each pebble is
ignored in the calculations. Near-wall pebbles in a normal bed and modified beds
with wall structures have quite different behaviors. In the normal bed, pebbles get
stuck or crystallized easily, so they would stay at rest for a longer time, resulting in
smaller E m . On the other hand, pebbles flowing against wall structures tend to be
more active because they are less likely to form blocking or crystallization. They can
keep moving down or moving toward the axis, presenting a relatively larger E m . The
pebble beds are expected to be energetic in the near-wall region.
A comparison of the activity level of the near-wall region in different bed configurations can be observed in Fig. 7.7. All modified beds except “arc_12_10” have more
active near-wall regions than a normal bed, and especially “triangle_12_20”, “triangle_12_10”, and “arc_12_20” have E m increased by more than 50%. It is believed
that in the abovementioned pebble beds, fewer stagnant pebbles, smaller stagnant
regions, and less possibility of forming crystallization would occur. This finding
coincides with the recommended bed configurations in Sect. 7.2.3, which demonstrates that E m of the near-wall region differentiates the ability of wall structures in
preventing stagnant regions and crystallization.
In the Discrete Element Method (DEM) simulation, all the particles are traced
in the Lagrangian frame, but the mean velocities of pebbles during 150 s in several
specific locations are calculated by using the Eulerian method to reveal more details
in the near-wall region. Nine measurement points of velocity have been set on a
vertical line located at 0.02m away from the wall, which is very close to the wall and
assures capturing the wall-sticking velocity in the pebble flow field.
Figure 7.8 describes the profiles of wall-sticking velocity in the bed from top to
bottom. In most elevated locations, “triangle_12_20” ranks first, followed by “sawtooth_12” and “triangle_12_10”. However, in the lowest elevated location, “sawtooth_12” surpasses others, becoming the leading one.