88
2 Experiments in Pebble Flows
corner of the bed. As mentioned above, the formation of stagnant zones will not
benefit the real reactors, although the pebbles may be discharged from the outlet
after a sufficiently long time at last. By comparison, the stagnant zone is smaller for
the R (∞,45 ◦ ) configuration, and it even disappears for the R (∞,60 ◦ ) configuration.
The case of the R 1 configuration seems to be much worse than the situation of
R (∞,30 ◦ ) . A larger stagnant region consisting of stagnant pebbles is noticed clearly
around the corner. The main reason for this would be that a flatter bottom promotes
the formation of the stagnant region. When the pebbles reach the flat bottom, the
driven force of gravity is resisted and the particles have to flow horizontally until
they arrive at the outlet region. The velocity profile of R 3 configuration is quite
similar to that of the R (∞,30 ◦ ) configuration since the arc curve in R 3 configuration
is quite near the straight line edge in R (∞,30 ◦ ) configuration. The R 2 case appears to
be better than R 1 and R 3 situations.
2.5.3.13 Flow Uniformity in Radial Direction
In the previous section, a contour map was employed to highlight the vertical movement of the pebble flow. In this section, the features of the pebbles on the same levels
are used to reflect the radial flow uniformity. Horizontal layer-like regions with 4d
height (68-72d, 28-32d, etc.) are selected, and then the vertical velocity of all pebbles
within each region is calculated during the whole experiment time. For example, in
a radially uniform flow layer, it takes almost the same time for the particles on the
same level to flow out of this layer, which shows a mass flow pattern. However, in a
flow field with poor radial uniformity, the pebbles in the central part will flow out of
the layer earlier than the particles in the near-wall region at the same height, as shown
in Fig. 2.27. That is, the particles near the wall move down with the flow pattern of
a first-in and last-out type. The standard deviation σ of all vertical velocities within
the same layer can reflect the extent of dispersion in the vertical direction, which
would be a good indication of the radial uniformity. In the mass flow region, the σ
can retain smaller values even at the lower part of the experiment vessel. In contrast,
the magnitude of σ will increase significantly in the non-uniform field, especially in
the lower section which presents significant vertical dispersion.
As depicted in Fig. 2.28, there are similar tendencies among various bed configurations on the values of σ in the horizontal-stripe layers on several levels. The middle
part of the layer belonging to the dominating central flow moves down faster in the
lower section of the setup. On the other hand, the side part has to move slower by
overcoming additional friction force against the wall. Consequently, the near-wall
particles move down slowly and form structured packing in the stagnant or dead
region. This leads to the loss of uniformity and the increase of σ for the pebble flow
in the lower layers. The upper bed gets a less significant vertical dispersion than that
in the bottom, which is caused by the more uniform velocity distribution along the
radius. For the layers with high levels, vertical velocities of the particles increase
slowly with a reduction of height because of the constant width of the vessel. However, in the wedged part of the pebble bed, the particle velocity in the middle region
2 Experiments in Pebble Flows
corner of the bed. As mentioned above, the formation of stagnant zones will not
benefit the real reactors, although the pebbles may be discharged from the outlet
after a sufficiently long time at last. By comparison, the stagnant zone is smaller for
the R (∞,45 ◦ ) configuration, and it even disappears for the R (∞,60 ◦ ) configuration.
The case of the R 1 configuration seems to be much worse than the situation of
R (∞,30 ◦ ) . A larger stagnant region consisting of stagnant pebbles is noticed clearly
around the corner. The main reason for this would be that a flatter bottom promotes
the formation of the stagnant region. When the pebbles reach the flat bottom, the
driven force of gravity is resisted and the particles have to flow horizontally until
they arrive at the outlet region. The velocity profile of R 3 configuration is quite
similar to that of the R (∞,30 ◦ ) configuration since the arc curve in R 3 configuration
is quite near the straight line edge in R (∞,30 ◦ ) configuration. The R 2 case appears to
be better than R 1 and R 3 situations.
2.5.3.13 Flow Uniformity in Radial Direction
In the previous section, a contour map was employed to highlight the vertical movement of the pebble flow. In this section, the features of the pebbles on the same levels
are used to reflect the radial flow uniformity. Horizontal layer-like regions with 4d
height (68-72d, 28-32d, etc.) are selected, and then the vertical velocity of all pebbles
within each region is calculated during the whole experiment time. For example, in
a radially uniform flow layer, it takes almost the same time for the particles on the
same level to flow out of this layer, which shows a mass flow pattern. However, in a
flow field with poor radial uniformity, the pebbles in the central part will flow out of
the layer earlier than the particles in the near-wall region at the same height, as shown
in Fig. 2.27. That is, the particles near the wall move down with the flow pattern of
a first-in and last-out type. The standard deviation σ of all vertical velocities within
the same layer can reflect the extent of dispersion in the vertical direction, which
would be a good indication of the radial uniformity. In the mass flow region, the σ
can retain smaller values even at the lower part of the experiment vessel. In contrast,
the magnitude of σ will increase significantly in the non-uniform field, especially in
the lower section which presents significant vertical dispersion.
As depicted in Fig. 2.28, there are similar tendencies among various bed configurations on the values of σ in the horizontal-stripe layers on several levels. The middle
part of the layer belonging to the dominating central flow moves down faster in the
lower section of the setup. On the other hand, the side part has to move slower by
overcoming additional friction force against the wall. Consequently, the near-wall
particles move down slowly and form structured packing in the stagnant or dead
region. This leads to the loss of uniformity and the increase of σ for the pebble flow
in the lower layers. The upper bed gets a less significant vertical dispersion than that
in the bottom, which is caused by the more uniform velocity distribution along the
radius. For the layers with high levels, vertical velocities of the particles increase
slowly with a reduction of height because of the constant width of the vessel. However, in the wedged part of the pebble bed, the particle velocity in the middle region