7.5 Friction Optimization
491
particle–wall friction small enough to ensure mass flow in a pebble bed contributes
to the elimination of a stagnant zone.
7.5.4.2 Vertical Standard Deviation— D v
In the previous subsection, pre-filled stripes were employed to highlight the vertical
movement of the pebble flow. In this part, features of a horizontal pebble-stripe can
be used to reflect the radial flow uniformity. One stripe of differently colored pebbles
was tracked from the beginning, and their location data over the simulation time were
collected. Analysis of vertical coordinates of pebbles belonging to a horizontal stripe
indicates the pebble dispersion in the vertical direction, and it is also a reflection of
the flow uniformity along the radius. For instance, in a radially uniform flow field,
one initially located pebble-stripe can remain horizontal and concentrate in a thin
layer during the running process like mass flow pattern, as shown in Fig. 7.33a.
However, in a flow field with a bad radial uniformity, a pebble-stripe would curve
and disperse because of varying vertical velocity along the radius, as shown in Fig.
7.33c. The standard deviation of the pebble-stripe’s vertical coordinates, (D v ) which
reflects the extent of dispersion in the vertical direction, can be regarded as the
indication of radial uniformity. The uniform field can keep D v as small as its initial
value even when a labeled pebble-stripe enters the lower bin. However, the value
of D v will increase sharply in the non-uniform field, and the non-constant vertical
velocity profile, especially in the lower bin (refer to Fig. 7.34, is responsible for the
significant vertical dispersion.
Curves of varying D v over the simulation time in pebble beds with different friction
settings are illustrated in Fig. 7.39, and these curves represent pebble-stripes located
at 70–75cm (namely the top stripes in Fig. 7.33) in six cases. Particle–wall friction
poses a significant impact on the radial uniformity of pebble flow by determining flow
patterns in a pebble bed. Typical funnel flows in beds with considerable particle–wall
friction (“μ p−w = 0.6, μ p− p = 0.5” and “μ p−w = 0.3, μ p− p = 0.5”) experience a sharp
rise of D v , while in smooth beds (“μ p−w = 0.1, μ p− p = 0.5” and “μ p−w = 0.01, μ p− p
= 0.5”) which form mass flow, D v remains at a bottom level and even sees a very
slight decrease. In funnel flow, central pebbles have apparent advantages over side
pebbles in flowing downward. The side pebbles would find it more difficult to catch
up with the central flow if they have to overcome extra particle–wall friction. This
is the reason for the pebble-stripe bending downward at the center (refer to Figs.
7.33c) and 7.33d) and the rise of D v value. By contrast, mass flows in “μ p−w = 0.1,
μ p− p = 0.5” and “μ p−w = 0.01, μ p− p = 0.5” enable all the pebbles to move as an
entirety with the same vertical velocity. The pebble-stripes can remain horizontal
and concentrated during the circulating process, which maintains the small D v as a
verification of the radial uniformity. The slight decrease of D v results from pebbles
getting more compacted while moving downward.
The impact of particle–particle friction on the radial flow uniformity is also significant. Less friction among pebbles is beneficial to radial flow uniformity. Particle–
particle friction is the connection between the near-wall region and the bulk region
491
particle–wall friction small enough to ensure mass flow in a pebble bed contributes
to the elimination of a stagnant zone.
7.5.4.2 Vertical Standard Deviation— D v
In the previous subsection, pre-filled stripes were employed to highlight the vertical
movement of the pebble flow. In this part, features of a horizontal pebble-stripe can
be used to reflect the radial flow uniformity. One stripe of differently colored pebbles
was tracked from the beginning, and their location data over the simulation time were
collected. Analysis of vertical coordinates of pebbles belonging to a horizontal stripe
indicates the pebble dispersion in the vertical direction, and it is also a reflection of
the flow uniformity along the radius. For instance, in a radially uniform flow field,
one initially located pebble-stripe can remain horizontal and concentrate in a thin
layer during the running process like mass flow pattern, as shown in Fig. 7.33a.
However, in a flow field with a bad radial uniformity, a pebble-stripe would curve
and disperse because of varying vertical velocity along the radius, as shown in Fig.
7.33c. The standard deviation of the pebble-stripe’s vertical coordinates, (D v ) which
reflects the extent of dispersion in the vertical direction, can be regarded as the
indication of radial uniformity. The uniform field can keep D v as small as its initial
value even when a labeled pebble-stripe enters the lower bin. However, the value
of D v will increase sharply in the non-uniform field, and the non-constant vertical
velocity profile, especially in the lower bin (refer to Fig. 7.34, is responsible for the
significant vertical dispersion.
Curves of varying D v over the simulation time in pebble beds with different friction
settings are illustrated in Fig. 7.39, and these curves represent pebble-stripes located
at 70–75cm (namely the top stripes in Fig. 7.33) in six cases. Particle–wall friction
poses a significant impact on the radial uniformity of pebble flow by determining flow
patterns in a pebble bed. Typical funnel flows in beds with considerable particle–wall
friction (“μ p−w = 0.6, μ p− p = 0.5” and “μ p−w = 0.3, μ p− p = 0.5”) experience a sharp
rise of D v , while in smooth beds (“μ p−w = 0.1, μ p− p = 0.5” and “μ p−w = 0.01, μ p− p
= 0.5”) which form mass flow, D v remains at a bottom level and even sees a very
slight decrease. In funnel flow, central pebbles have apparent advantages over side
pebbles in flowing downward. The side pebbles would find it more difficult to catch
up with the central flow if they have to overcome extra particle–wall friction. This
is the reason for the pebble-stripe bending downward at the center (refer to Figs.
7.33c) and 7.33d) and the rise of D v value. By contrast, mass flows in “μ p−w = 0.1,
μ p− p = 0.5” and “μ p−w = 0.01, μ p− p = 0.5” enable all the pebbles to move as an
entirety with the same vertical velocity. The pebble-stripes can remain horizontal
and concentrated during the circulating process, which maintains the small D v as a
verification of the radial uniformity. The slight decrease of D v results from pebbles
getting more compacted while moving downward.
The impact of particle–particle friction on the radial flow uniformity is also significant. Less friction among pebbles is beneficial to radial flow uniformity. Particle–
particle friction is the connection between the near-wall region and the bulk region