448
7 Applications: Pebble Flow Optimizations
pebbles form a structured packing, they may get stuck and stay at rest. If the structured
packing happens in bulk flow, it would be destructed probably due to movements of
bottom and surrounding pebbles, returning to ordinary flow in a short time. However,
structured packing formed in the near-wall region has less chance to be disturbed due
to the lack of motivation from neighbors. This kind of packing would turn larger and
more stable as time goes on, and finally becoming crystallization of pebbles (refer
to the region along the right wall in the normal bed in Fig. 7.4).
The crystallization of pebbles along the wall is much less severe in the bed with
wall structures, as illustrated in Fig. 7.4. In the modified bed, most aged pebbles,
namely red pebbles, concentrate around corners as a result of contraction configuration of the bottom bed, which has been studied through numerical simulations as well
[2] and is not the critical point of this analysis. It is easy to understand the impact of
the wall structure by comparing the near-wall region in the two beds. Wall structures
prohibit pebbles from packing in order along the wall, which is similar to the effect of
producing flow disturbance in conventional fluid rules. Therefore, structured packing cannot survive in the near-wall region, and the probability of crystallization is
minimized. The wall structure effect is related to its shape, size, etc., which would
be discussed in the next sections.
From the above analysis, the behavior of the near-wall pebbles plays an essential
role in determining the overall flow field in the pebble bed, so it is focused on
these pebbles’ behavior. For accelerating the simulation, the operating mode with a
circulating rate of 40 pebbles per second is adopted to shorten the simulation time
to 150 s. From now on, the results are obtained through the simulations with the
condition mentioned above.
The motion of the near-wall pebbles throughout the time is described in Fig. 7.5.
The overall trend of red pebbles’ movement in the two beds is similar. Gravity drives
all the pebbles down, and red pebbles have a tendency of diffusing into the bulk flow
because of pebbles’ random dispersion and the contracted configuration of the bottom
bed. Nevertheless, near-wall pebbles in the two beds encounter different resistances
when they flow down. In the normal bed, smooth internal walls provide suitable conditions for structured packing, which could be observed at t = 50 s where red pebbles
begin to form a steady structure, especially around the left wall. This situation did
not change significantly in the following 100 s: red pebbles still stick to the left wall
up to about 0.55 m height at time t = 150 s. The straight wall cannot produce enough
driving force to destruct crystallized pebbles. By contrast, red pebbles in the modified
bed seem to be more active. The pebble motion observed around the structured wall
looks similar to a porous structure full of voids, rather than a stable blocking structure
around the straight wall. It is this fragile structure that contributes to the strengthened
dispersion and motions, for it is not strong enough to last long and would form and collapse repeatedly. This mechanism makes it easier for red pebbles to maintain kinetic
energy and flow down smoothly. At the final stage, red pebbles in the modified bed fall
to below 0.4 m at time t = 150 s, and new blue pebbles occupy the near-wall region.
Figure 7.5 shows snapshots of near-wall pebbles’ motion at different time points.
Crystallization in a pebble flow happens completely randomly, and it is unpredictable in terms of time, location, and behavior. Randomness is the reason why
7 Applications: Pebble Flow Optimizations
pebbles form a structured packing, they may get stuck and stay at rest. If the structured
packing happens in bulk flow, it would be destructed probably due to movements of
bottom and surrounding pebbles, returning to ordinary flow in a short time. However,
structured packing formed in the near-wall region has less chance to be disturbed due
to the lack of motivation from neighbors. This kind of packing would turn larger and
more stable as time goes on, and finally becoming crystallization of pebbles (refer
to the region along the right wall in the normal bed in Fig. 7.4).
The crystallization of pebbles along the wall is much less severe in the bed with
wall structures, as illustrated in Fig. 7.4. In the modified bed, most aged pebbles,
namely red pebbles, concentrate around corners as a result of contraction configuration of the bottom bed, which has been studied through numerical simulations as well
[2] and is not the critical point of this analysis. It is easy to understand the impact of
the wall structure by comparing the near-wall region in the two beds. Wall structures
prohibit pebbles from packing in order along the wall, which is similar to the effect of
producing flow disturbance in conventional fluid rules. Therefore, structured packing cannot survive in the near-wall region, and the probability of crystallization is
minimized. The wall structure effect is related to its shape, size, etc., which would
be discussed in the next sections.
From the above analysis, the behavior of the near-wall pebbles plays an essential
role in determining the overall flow field in the pebble bed, so it is focused on
these pebbles’ behavior. For accelerating the simulation, the operating mode with a
circulating rate of 40 pebbles per second is adopted to shorten the simulation time
to 150 s. From now on, the results are obtained through the simulations with the
condition mentioned above.
The motion of the near-wall pebbles throughout the time is described in Fig. 7.5.
The overall trend of red pebbles’ movement in the two beds is similar. Gravity drives
all the pebbles down, and red pebbles have a tendency of diffusing into the bulk flow
because of pebbles’ random dispersion and the contracted configuration of the bottom
bed. Nevertheless, near-wall pebbles in the two beds encounter different resistances
when they flow down. In the normal bed, smooth internal walls provide suitable conditions for structured packing, which could be observed at t = 50 s where red pebbles
begin to form a steady structure, especially around the left wall. This situation did
not change significantly in the following 100 s: red pebbles still stick to the left wall
up to about 0.55 m height at time t = 150 s. The straight wall cannot produce enough
driving force to destruct crystallized pebbles. By contrast, red pebbles in the modified
bed seem to be more active. The pebble motion observed around the structured wall
looks similar to a porous structure full of voids, rather than a stable blocking structure
around the straight wall. It is this fragile structure that contributes to the strengthened
dispersion and motions, for it is not strong enough to last long and would form and collapse repeatedly. This mechanism makes it easier for red pebbles to maintain kinetic
energy and flow down smoothly. At the final stage, red pebbles in the modified bed fall
to below 0.4 m at time t = 150 s, and new blue pebbles occupy the near-wall region.
Figure 7.5 shows snapshots of near-wall pebbles’ motion at different time points.
Crystallization in a pebble flow happens completely randomly, and it is unpredictable in terms of time, location, and behavior. Randomness is the reason why