2.6 Summary
115
The bed configurations are compared and analyzed in several aspects. From the
point of vertical velocity, two parameters including the mass flow level (α) and
flow uniformity (σ ) are proposed to estimate the flow pattern and flow uniformity
quantitatively in the pebble flow. In light of the resultant movement of the pebble
flow, the angle θ in of the vector sum (v sum ) of the velocities of the whole particles in
the pebble bed is introduced and the distribution of the Δθ (angle difference between
the individual particle velocity and v sum ) is also calculated to estimate the resultant
motion consistency level. Moreover, for each bed configuration, the thickness of
displacement is analyzed to measure the funnel flow zone based on the boundary
layer theory.
The sequence of levels of each estimation criterion is obtained for all bed configurations. The results demonstrate that the pebble flow under the contraction configuration with a base angle of 60
◦ is the best, for both the flow patterns and field
characteristics analyses. A larger base angle always means the more desired flow
behavior by comparing bed configuration series with infinite radius. In the series
of R 1 , R 2 , R 3 , and R (∞,30 ◦ ) cases, the R 2 bed configuration usually does better
because the smooth transition region makes the streamlines of the funnel flow zone
smoother. Finally, the arc shapes with finite radius (R 2 , R 3 ) show a smaller difference of δ
between the cylinder and wedged sections than those with infinite radius
(R (∞,30 circ ) ,R (∞,45 circ ) ) for their smoother transition region.
In addition, the proposed criteria can also be applied and adopted in testing other
geometry designs of pebble beds. In this section, the R (∞,60 circ ) bed configuration is
strongly suggested to be used for a pebble-bed reactor design.
The enhanced PTV method can be regarded as a combination of the Relaxation
Method and the Voronoï diagram to detect singular particle movement. The velocity
fluctuations and arching characteristics in the very slow dense pebble flow in a
pebble-bed reactor are analyzed. The conclusion and summary are summarized as
follows:
• The particles in the packing can form bulk arches with different sizes. Arch size
spans from two to six in the detection window with 8d width and 6d height. The
arch size distribution obeys the second-order polynomial distribution in the semilogarithmic scale for all cases.
• The horizontal spans of arches are analyzed to measure the geometrical characteristics of the bulk arches. It shows the difference in the transverse direction of the
horizontal distribution. The near-wall region has clearly ordered arches while the
central region has disordered states. However, the difference in the vertical direction is not very clear. The probability distribution of successive angles between the
neighbors of the arching particles is a good indicator of the stability of the arches.
Besides, the relationship between arch breaking and contact network changing has
been demonstrated with the cross-correlation method.
• The cross-correlation of the mean velocity of arching particles (non-arching particles) and total particles are discussed where the number of arching particles is
nearly equal to non-arching particles. The characteristic lifetime of arches and
the autocorrelation time of fluctuation velocity present a positive correlation. The
115
The bed configurations are compared and analyzed in several aspects. From the
point of vertical velocity, two parameters including the mass flow level (α) and
flow uniformity (σ ) are proposed to estimate the flow pattern and flow uniformity
quantitatively in the pebble flow. In light of the resultant movement of the pebble
flow, the angle θ in of the vector sum (v sum ) of the velocities of the whole particles in
the pebble bed is introduced and the distribution of the Δθ (angle difference between
the individual particle velocity and v sum ) is also calculated to estimate the resultant
motion consistency level. Moreover, for each bed configuration, the thickness of
displacement is analyzed to measure the funnel flow zone based on the boundary
layer theory.
The sequence of levels of each estimation criterion is obtained for all bed configurations. The results demonstrate that the pebble flow under the contraction configuration with a base angle of 60
◦ is the best, for both the flow patterns and field
characteristics analyses. A larger base angle always means the more desired flow
behavior by comparing bed configuration series with infinite radius. In the series
of R 1 , R 2 , R 3 , and R (∞,30 ◦ ) cases, the R 2 bed configuration usually does better
because the smooth transition region makes the streamlines of the funnel flow zone
smoother. Finally, the arc shapes with finite radius (R 2 , R 3 ) show a smaller difference of δ
between the cylinder and wedged sections than those with infinite radius
(R (∞,30 circ ) ,R (∞,45 circ ) ) for their smoother transition region.
In addition, the proposed criteria can also be applied and adopted in testing other
geometry designs of pebble beds. In this section, the R (∞,60 circ ) bed configuration is
strongly suggested to be used for a pebble-bed reactor design.
The enhanced PTV method can be regarded as a combination of the Relaxation
Method and the Voronoï diagram to detect singular particle movement. The velocity
fluctuations and arching characteristics in the very slow dense pebble flow in a
pebble-bed reactor are analyzed. The conclusion and summary are summarized as
follows:
• The particles in the packing can form bulk arches with different sizes. Arch size
spans from two to six in the detection window with 8d width and 6d height. The
arch size distribution obeys the second-order polynomial distribution in the semilogarithmic scale for all cases.
• The horizontal spans of arches are analyzed to measure the geometrical characteristics of the bulk arches. It shows the difference in the transverse direction of the
horizontal distribution. The near-wall region has clearly ordered arches while the
central region has disordered states. However, the difference in the vertical direction is not very clear. The probability distribution of successive angles between the
neighbors of the arching particles is a good indicator of the stability of the arches.
Besides, the relationship between arch breaking and contact network changing has
been demonstrated with the cross-correlation method.
• The cross-correlation of the mean velocity of arching particles (non-arching particles) and total particles are discussed where the number of arching particles is
nearly equal to non-arching particles. The characteristic lifetime of arches and
the autocorrelation time of fluctuation velocity present a positive correlation. The