2.4 Pebble Flow Mechanism Analysis
65
the neighbor pebbles. Figure 2.14 shows that if pebbles close to the base slope are
arranged with the pattern of part D of Fig. 2.14 and small displacement to a pebble
of No. 0 is given, the No. 1 and No. 8 will move; however, among Nos. 5, 2, 10,
and No. 9, which will firstly move is uncertain. Similarly, in part B, if No. 7 and
No. 8 move down, No. 1, or No. 2 to occupy the space above No. 4 and No. 5 is
random. This is a so-called competition mechanism of pebble flow, in which the tiny
difference will lead to greatly different results. The competition mechanism exists
all over the pebble packing. For example, in the experiment vessel, it can be found
that the arrangement of pebbles in part C is just right, similar to that in part D.
The pebble of No. 5 in part D receives the forces, including the friction force
from base wall, component of its gravity along the base slope, the driving force
from the pebble that is at the back of it, e.g., No. 6 and the normal and tangential
force from No. 2 and No. 1. Whether No. 5 or No. 2 is possible to move firstly is
determined not only by the base cone angle and friction coefficient but also by the
mode of discharging pebbles. Herein the mode of discharging pebbles means either
the quasi-static flow of being discharged one by one or the steady flow of being
quickly discharged. If the pebble of No. 1 is quickly removed, it is possible that No.
5 moves ahead of No. 2 due to the tiny difference of the arrangement between No.
2 and No. 5; otherwise, if No. 1 moves very slowly, e.g., in quasi-static pebble flow,
it is possible that No. 2 moves prior to No. 5, even the pebbles of No. 3 and No. 4
are ahead of the pebble of No. 5. Hence, a layer of pebbles close to the base wall
become the slow flow pebbles. For the same reason, in a quasi-static pebble flow, if
the pebble of No. 10 is ahead of No. 2 and No. 5, two layers of pebbles will be the
slow flow pebbles. In this way, the slow flow zone emerges nearby the slope of the
base cone and next to the drainage hole. This is called a competitive block caused by
the competition mechanism between pebbles. Similarly, such a mechanism will give
rise to the mixing of pebbles located in different regions, e.g., differently colored
regions, and then produce the mixing zone between the different regions. This is
called competitive diffusion. Thus, it can be seen that the competition mechanism is
one of the essential reasons to cause resistance and diffusion between pebbles.
Furthermore, pebbles in the slow flow zone significantly block the flow of pebbles
that are located behind them and cause a much slower flow of pebbles. Further away
from the orifice, the flow of pebbles is more gradual to form a more substantial area
with slower flowing pebbles, namely a stagnant zone, as shown in the lower right
corner of Fig. 2.14. The slow flow zone is one section of the stagnant zone, which is
located in the front. The stagnant zone plays a vital role in the overall flow field of
the pebble packing.
The experimental studies have already proved that the average flow of the pebble packing is a smooth streamline; however, the actual trajectory of pebbles is not
smooth but rough and waved. This means the actual interface between the stagnant
zone and the outer zone is not smooth, as shown by the waved line in Fig. 2.14.
The force between the stagnant zone and the outer zone includes the normal force
and the tangential force, namely the friction force when the relative motion happens.
Because the actual trajectory of pebbles is not smooth, the normal force between pebbles can offer a great blocking to the movement of the neighbor pebbles in the outer
65
the neighbor pebbles. Figure 2.14 shows that if pebbles close to the base slope are
arranged with the pattern of part D of Fig. 2.14 and small displacement to a pebble
of No. 0 is given, the No. 1 and No. 8 will move; however, among Nos. 5, 2, 10,
and No. 9, which will firstly move is uncertain. Similarly, in part B, if No. 7 and
No. 8 move down, No. 1, or No. 2 to occupy the space above No. 4 and No. 5 is
random. This is a so-called competition mechanism of pebble flow, in which the tiny
difference will lead to greatly different results. The competition mechanism exists
all over the pebble packing. For example, in the experiment vessel, it can be found
that the arrangement of pebbles in part C is just right, similar to that in part D.
The pebble of No. 5 in part D receives the forces, including the friction force
from base wall, component of its gravity along the base slope, the driving force
from the pebble that is at the back of it, e.g., No. 6 and the normal and tangential
force from No. 2 and No. 1. Whether No. 5 or No. 2 is possible to move firstly is
determined not only by the base cone angle and friction coefficient but also by the
mode of discharging pebbles. Herein the mode of discharging pebbles means either
the quasi-static flow of being discharged one by one or the steady flow of being
quickly discharged. If the pebble of No. 1 is quickly removed, it is possible that No.
5 moves ahead of No. 2 due to the tiny difference of the arrangement between No.
2 and No. 5; otherwise, if No. 1 moves very slowly, e.g., in quasi-static pebble flow,
it is possible that No. 2 moves prior to No. 5, even the pebbles of No. 3 and No. 4
are ahead of the pebble of No. 5. Hence, a layer of pebbles close to the base wall
become the slow flow pebbles. For the same reason, in a quasi-static pebble flow, if
the pebble of No. 10 is ahead of No. 2 and No. 5, two layers of pebbles will be the
slow flow pebbles. In this way, the slow flow zone emerges nearby the slope of the
base cone and next to the drainage hole. This is called a competitive block caused by
the competition mechanism between pebbles. Similarly, such a mechanism will give
rise to the mixing of pebbles located in different regions, e.g., differently colored
regions, and then produce the mixing zone between the different regions. This is
called competitive diffusion. Thus, it can be seen that the competition mechanism is
one of the essential reasons to cause resistance and diffusion between pebbles.
Furthermore, pebbles in the slow flow zone significantly block the flow of pebbles
that are located behind them and cause a much slower flow of pebbles. Further away
from the orifice, the flow of pebbles is more gradual to form a more substantial area
with slower flowing pebbles, namely a stagnant zone, as shown in the lower right
corner of Fig. 2.14. The slow flow zone is one section of the stagnant zone, which is
located in the front. The stagnant zone plays a vital role in the overall flow field of
the pebble packing.
The experimental studies have already proved that the average flow of the pebble packing is a smooth streamline; however, the actual trajectory of pebbles is not
smooth but rough and waved. This means the actual interface between the stagnant
zone and the outer zone is not smooth, as shown by the waved line in Fig. 2.14.
The force between the stagnant zone and the outer zone includes the normal force
and the tangential force, namely the friction force when the relative motion happens.
Because the actual trajectory of pebbles is not smooth, the normal force between pebbles can offer a great blocking to the movement of the neighbor pebbles in the outer