2.5 Particle Velocimetry Measurements
87
Fig. 2.27 Flow profiles in the pebble beds with different bed configurations. The transverse velocity profiles are given in the left half. The zones characterized by different vertical velocity ranges
are shown in the right half. The line R CV =0.3 is plotted (if it exists) in each case. a R (∞,30 ◦ ) configuration. b R (∞,45 ◦ ) configuration. c R (∞,60 ◦ ) configuration. d R 1 configuration. e R 2 configuration.
f R 3 configuration
pebble bed. The vertical velocity in the near-wall region is the lowest, which provides
less space for particles close to the wall to move toward the wall. The particles in
the top part exhibit the plug flow behavior where the difference between the vertical
velocity magnitude in the central and near-wall regions is small.
Based on the detailed velocity field data discussed above, the flow channel boundary is defined as the interface between mass flow and funnel flow (Johanson 1964;
Watson and Rotter 1996). A Ratio of Critical Velocity (R CV ) is introduced as a criterion to delineate the boundary between the “flowing” particles from the “stationary”
ones: R CV =
v
v
0
. The v
denotes the vertical velocity of a particle at a given position;
v
0 is the vertical velocity of the particle at the central position of the corresponding
level that stands for the highest vertical velocity at the same level. Generally, values
of R CV < 0.3 are indicative of funnel flow while those of R CV > 0.3 are typical mass
flow. The overall flow pattern for the silo is determined by the change in R CV over
the height of the silo. The R CV line is depicted (Fig. 2.27) except for the case with
the base angle equal to 60
◦ , which means that no particles belong to the funnel flow
regime.
In addition, the cases with different bed configurations will be discussed by comparing the velocity profiles. For the R (∞,30 ◦ ) configuration, the pebbles move nearly
uniformly in the central part of the bed, except the near-wall regions. Some pebbles
are stagnant near the wall, moving fairly slowly and then stay around the bottom
87
Fig. 2.27 Flow profiles in the pebble beds with different bed configurations. The transverse velocity profiles are given in the left half. The zones characterized by different vertical velocity ranges
are shown in the right half. The line R CV =0.3 is plotted (if it exists) in each case. a R (∞,30 ◦ ) configuration. b R (∞,45 ◦ ) configuration. c R (∞,60 ◦ ) configuration. d R 1 configuration. e R 2 configuration.
f R 3 configuration
pebble bed. The vertical velocity in the near-wall region is the lowest, which provides
less space for particles close to the wall to move toward the wall. The particles in
the top part exhibit the plug flow behavior where the difference between the vertical
velocity magnitude in the central and near-wall regions is small.
Based on the detailed velocity field data discussed above, the flow channel boundary is defined as the interface between mass flow and funnel flow (Johanson 1964;
Watson and Rotter 1996). A Ratio of Critical Velocity (R CV ) is introduced as a criterion to delineate the boundary between the “flowing” particles from the “stationary”
ones: R CV =
v
v
0
. The v
denotes the vertical velocity of a particle at a given position;
v
0 is the vertical velocity of the particle at the central position of the corresponding
level that stands for the highest vertical velocity at the same level. Generally, values
of R CV < 0.3 are indicative of funnel flow while those of R CV > 0.3 are typical mass
flow. The overall flow pattern for the silo is determined by the change in R CV over
the height of the silo. The R CV line is depicted (Fig. 2.27) except for the case with
the base angle equal to 60
◦ , which means that no particles belong to the funnel flow
regime.
In addition, the cases with different bed configurations will be discussed by comparing the velocity profiles. For the R (∞,30 ◦ ) configuration, the pebbles move nearly
uniformly in the central part of the bed, except the near-wall regions. Some pebbles
are stagnant near the wall, moving fairly slowly and then stay around the bottom