4.3 Three-Dimensional Pebble Flow
219
Table 4.13 Parameters used in simulation
Bed diameter D B , (m)
3
Bed height H B , (m)
11
Silo diameter D S , (m)
0.6
Silo height H S , (m)
0.5
Angle of conical base θ to horizon, ( ◦ )
30 (named “A30”), 45 (“A45”), 60 (“A60”)
Number of particles N p
420000
Particle diameter d p , (mm)
60
Particle density ρ p , (kg/m 3 )
1750
Stiffness factor k c (N/m)
10 5
Poisson ratio ν
0.3
Restitution coefficient e
0.30
Friction coefficient μ
0.15, 0.3, 0.5, 0.8
Time step δt (s)
10 −4
Time for recirculating a pebble t S (ms)
0.3 (in “Fa” mode), 1 (“Me”), 2 (“Sl”)
Simulation time T s , (s)
126, 420, 840, respectively
that the pebble flow patterns in the HTR-PM reactor would be considerably uniform.
The stagnant region will not be formed in HTR-PM.
On the other side, Figure 4.34, shows the pebble spindles within the beds of base
angles θ = 30
◦ (a), θ = 45
◦ (b), θ = 60
◦ (c). Each pebble spindle is composed of a
bundle of pebble trajectories which are all originated from a local region centered
on the origination of x
0
i , (i = 1, . . . , 28, see Fig. 4.34d). Herein the local region is a
spherical region bounded by |x − x
0
i | =
d p
2
, (Fig. 4.34d). The pebble spindles look
like perfectly straight in the main cylindrical body of the bed. In the conical base,
the pebble spindles curve toward the central discharge silo with a little bit larger
horizontal diffusion than in the cylindrical body.
On Diffusion in Pebble Spindles
The probability density function f N (r), defined as
f N (r) =
n i (r)
δr
N
i=1 n i (r)
(4.39)
is used here to quantify the horizontal diffusion of pebbles in the pebble spindles,
where n i (r) is the number of data points located within (r −
δr
2
, r +
δr
2
).
Taking the beds of base angle θ = 30
◦ as an example, f N (r) on the heights from
H = 1.0 − 8.0 m are shown in Fig. 4.35. f N (r) has peak shapes around the pebble
spindle locations. As the pebble spindle is perfectly straight, the locations of the peak
219
Table 4.13 Parameters used in simulation
Bed diameter D B , (m)
3
Bed height H B , (m)
11
Silo diameter D S , (m)
0.6
Silo height H S , (m)
0.5
Angle of conical base θ to horizon, ( ◦ )
30 (named “A30”), 45 (“A45”), 60 (“A60”)
Number of particles N p
420000
Particle diameter d p , (mm)
60
Particle density ρ p , (kg/m 3 )
1750
Stiffness factor k c (N/m)
10 5
Poisson ratio ν
0.3
Restitution coefficient e
0.30
Friction coefficient μ
0.15, 0.3, 0.5, 0.8
Time step δt (s)
10 −4
Time for recirculating a pebble t S (ms)
0.3 (in “Fa” mode), 1 (“Me”), 2 (“Sl”)
Simulation time T s , (s)
126, 420, 840, respectively
that the pebble flow patterns in the HTR-PM reactor would be considerably uniform.
The stagnant region will not be formed in HTR-PM.
On the other side, Figure 4.34, shows the pebble spindles within the beds of base
angles θ = 30
◦ (a), θ = 45
◦ (b), θ = 60
◦ (c). Each pebble spindle is composed of a
bundle of pebble trajectories which are all originated from a local region centered
on the origination of x
0
i , (i = 1, . . . , 28, see Fig. 4.34d). Herein the local region is a
spherical region bounded by |x − x
0
i | =
d p
2
, (Fig. 4.34d). The pebble spindles look
like perfectly straight in the main cylindrical body of the bed. In the conical base,
the pebble spindles curve toward the central discharge silo with a little bit larger
horizontal diffusion than in the cylindrical body.
On Diffusion in Pebble Spindles
The probability density function f N (r), defined as
f N (r) =
n i (r)
δr
N
i=1 n i (r)
(4.39)
is used here to quantify the horizontal diffusion of pebbles in the pebble spindles,
where n i (r) is the number of data points located within (r −
δr
2
, r +
δr
2
).
Taking the beds of base angle θ = 30
◦ as an example, f N (r) on the heights from
H = 1.0 − 8.0 m are shown in Fig. 4.35. f N (r) has peak shapes around the pebble
spindle locations. As the pebble spindle is perfectly straight, the locations of the peak