7.5 Friction Optimization
487
With height decreasing, the near-wall velocity drops while the central velocity rises,
which aggravates the velocity non-uniformity. In the pebble bed with μ p−w = 0.1, the
flow fields in the upper and central parts (h = 50 − 55 cm, h = 65 − 70 cm) remain
quite uniform, and even in the lower bin (h = 25 − 30 cm), the near-wall velocity is
high enough to maintain moving pebbles and prohibit stagnant region. However, in
the coarser pebble bed (μ p−w = 0.3), extra particle–wall friction enlarges velocity’s
radial gradient a lot, especially at the half-radius position where the velocity radial
gradient reaches a peak. The gap between central and near-wall velocities is enlarged,
leading to distinct stagnant regions by the wall in the lower bin. Layers of the bed
with particle–wall μ = 0.3 show that the velocity distribution is like a “laminar flow”
pattern with a “flow channel” in the center and a thick “boundary layer” by the wall.
The transition region at the half-radius position for the “boundary layer” switching
to “flow channel” is of the largest radial gradient of the velocity, and it is predicted
that the most intensive particle–particle friction should be there as well.
7.5.3 Particle–Particle Friction
Compared with particle–wall friction, particle–particle friction is regarded as an
internal interactive force that does not impact flow patterns so much as particle–wall
friction does. But it is crucial in some local mechanisms like force chains, packing
structures, and arch collapsing [26]. In this section, to learn the impact of particle–
particle friction on the flow pattern, the particle–particle friction would be set as the
single variable (μ p− p = 0.05, 0.25 and 0.5) with a constant particle–wall friction
coefficient μ = 0.3.
It is noted from Fig. 7.36 that when the particle–particle friction decreases to
1/10 of the original level (from 0.5 to 0.05), the flow field becomes more uniform
significantly. The flow pattern also changes from a mixed flow to a typical mass flow
based on the definition of the MFI value. This means that reducing particle–particle
friction to a minimum level has a positive effect on the improvement of the flow
field. However, the medium level of the particle–particle friction does not relieve the
non-uniformity as expected. Though the central velocity sees a decline, the near-wall
velocity falls as well. The radial gradient of the vertical velocity is still noticeable,
and MFI values even decrease in most of the layers, which indicates the aggravating
non-uniformity in the radial direction. When it turns to the cross-sectional view in
Fig. 7.37, the above findings are reinforced. The case of μ p− p = 0.05 turns out to
be a better flow field with a uniform velocity distribution. The cases of μ p− p = 0.25
and 0.5 have similar patterns. In comparison with the case of μ p− p = 0.5, the nonuniformity is relieved to some extent for the major region of the case of μ p− p =
0.25, but a lagging zone by the wall like a “boundary layer” with a velocity between
0.0006 and 0.001 m/s appears, which results in the smallest MFI value among three
cases.
487
With height decreasing, the near-wall velocity drops while the central velocity rises,
which aggravates the velocity non-uniformity. In the pebble bed with μ p−w = 0.1, the
flow fields in the upper and central parts (h = 50 − 55 cm, h = 65 − 70 cm) remain
quite uniform, and even in the lower bin (h = 25 − 30 cm), the near-wall velocity is
high enough to maintain moving pebbles and prohibit stagnant region. However, in
the coarser pebble bed (μ p−w = 0.3), extra particle–wall friction enlarges velocity’s
radial gradient a lot, especially at the half-radius position where the velocity radial
gradient reaches a peak. The gap between central and near-wall velocities is enlarged,
leading to distinct stagnant regions by the wall in the lower bin. Layers of the bed
with particle–wall μ = 0.3 show that the velocity distribution is like a “laminar flow”
pattern with a “flow channel” in the center and a thick “boundary layer” by the wall.
The transition region at the half-radius position for the “boundary layer” switching
to “flow channel” is of the largest radial gradient of the velocity, and it is predicted
that the most intensive particle–particle friction should be there as well.
7.5.3 Particle–Particle Friction
Compared with particle–wall friction, particle–particle friction is regarded as an
internal interactive force that does not impact flow patterns so much as particle–wall
friction does. But it is crucial in some local mechanisms like force chains, packing
structures, and arch collapsing [26]. In this section, to learn the impact of particle–
particle friction on the flow pattern, the particle–particle friction would be set as the
single variable (μ p− p = 0.05, 0.25 and 0.5) with a constant particle–wall friction
coefficient μ = 0.3.
It is noted from Fig. 7.36 that when the particle–particle friction decreases to
1/10 of the original level (from 0.5 to 0.05), the flow field becomes more uniform
significantly. The flow pattern also changes from a mixed flow to a typical mass flow
based on the definition of the MFI value. This means that reducing particle–particle
friction to a minimum level has a positive effect on the improvement of the flow
field. However, the medium level of the particle–particle friction does not relieve the
non-uniformity as expected. Though the central velocity sees a decline, the near-wall
velocity falls as well. The radial gradient of the vertical velocity is still noticeable,
and MFI values even decrease in most of the layers, which indicates the aggravating
non-uniformity in the radial direction. When it turns to the cross-sectional view in
Fig. 7.37, the above findings are reinforced. The case of μ p− p = 0.05 turns out to
be a better flow field with a uniform velocity distribution. The cases of μ p− p = 0.25
and 0.5 have similar patterns. In comparison with the case of μ p− p = 0.5, the nonuniformity is relieved to some extent for the major region of the case of μ p− p =
0.25, but a lagging zone by the wall like a “boundary layer” with a velocity between
0.0006 and 0.001 m/s appears, which results in the smallest MFI value among three
cases.