472
7 Applications: Pebble Flow Optimizations
Fig. 7.25 Sketch of bed
configuration
Table 7.4 Parameters used in simulation
Dimension of pebble bed D x × D y × D x (mm) 800 × 1200 × 12
Diameter of outlet D out (mm)
120
Base cone angle α ( ◦ )
30
Pebble diameter d p (mm)
12
Pebble number N p (mm)
7345
Pebble density ρ p (kg/m 3 )
1700
Pebble friction coefficient μ p
0.3
Pebble restitution coefficient e p
0.95
Pebble stiffness factor K n (N/m)
10 4
Time step δt (s)
5 × 10 −4
Total simulated time t T (s)
150
Drainage rate of pebbles r c (s −1 )
100
demonstration. Otherwise, a real three-dimensional simulation is another problem
that would be left for future study.
For showing the effect of the bed configuration on the pebble flow, especially
the contraction configuration at the bottom, some arc-shaped configurations are
employed. As shown in Fig. 7.25, there are four arc-shapes, i.e., (1) A straight line
with length e s , or an arc shape (named R ∞ ) with an infinite radius R ∞ ; (2) An arc
shape (named R 1 ) with a radius R 1 =
e s
√
3
for the circumcircle of the equilateral triangle which has an edge of the inclined straight line e s ; (3) An arc shape (named
R 2 ) with a radius R 2 equal to the edge of the equilateral triangle, i.e., R 2 = e s ; and
(4) An arc shape (name R 3 ) on a circle with a radius R 3 . The distance between the
7 Applications: Pebble Flow Optimizations
Fig. 7.25 Sketch of bed
configuration
Table 7.4 Parameters used in simulation
Dimension of pebble bed D x × D y × D x (mm) 800 × 1200 × 12
Diameter of outlet D out (mm)
120
Base cone angle α ( ◦ )
30
Pebble diameter d p (mm)
12
Pebble number N p (mm)
7345
Pebble density ρ p (kg/m 3 )
1700
Pebble friction coefficient μ p
0.3
Pebble restitution coefficient e p
0.95
Pebble stiffness factor K n (N/m)
10 4
Time step δt (s)
5 × 10 −4
Total simulated time t T (s)
150
Drainage rate of pebbles r c (s −1 )
100
demonstration. Otherwise, a real three-dimensional simulation is another problem
that would be left for future study.
For showing the effect of the bed configuration on the pebble flow, especially
the contraction configuration at the bottom, some arc-shaped configurations are
employed. As shown in Fig. 7.25, there are four arc-shapes, i.e., (1) A straight line
with length e s , or an arc shape (named R ∞ ) with an infinite radius R ∞ ; (2) An arc
shape (named R 1 ) with a radius R 1 =
e s
√
3
for the circumcircle of the equilateral triangle which has an edge of the inclined straight line e s ; (3) An arc shape (named
R 2 ) with a radius R 2 equal to the edge of the equilateral triangle, i.e., R 2 = e s ; and
(4) An arc shape (name R 3 ) on a circle with a radius R 3 . The distance between the