6.2 Size Effects
413
Fig. 6.10a–c, the width of all type-2 particles in the lower half bed decreases when
the size ratio increases, which is caused by the diffusion of different sized particles.
For Case 14 (Fig. 6.10d), the central region (0.4 m in width) is much wider than
the bottom region (0.12m in width). Thus, type-2 particles generated from the top
region will move longer horizontal distance to reach the bottom. Because only a
small fraction of type-1 particles is located near the bottom, type-1 particles are less
likely to be removed from the pebble bed when the region ratio is R L = 2.0. This
phenomenon also happens for Case 13 (R L = 2.0, R D = 1.0) and Case 15 (R L = 2.0,
R D = 2.0). Thus, it is detrimental to the discharge of pebble flow when the region
ratio R L = 2.0, as it makes much more difficult for type 1 particles (fuel spheres) to
be discharged timely if the nuclear fuel inside has already been burned up. Moreover,
by comparing Fig. 6.9d, e, and f, the shape of mixing interface changes from curved
to nearly straight when the region ratio increases.
6.2.3 Shape and Size of Mixing Region
6.2.3.1 Fractal Dimension of Mixing Interface
For comparative analysis, the discharge rate for Case 1∼12 is 100 particles per
second in simulation. From the perspective of designing the two-region pebble bed,
it is essential to control the mixing region, where the particles are usually in contact
with different types of particles. The shape and size of the mixing region are crucial
in the mixing process. Hence, the particles in the mixing region of the steady state
are marked by green (Fig. 6.11a–c), where the red line is the smoothed centerline of
the mixing region, and the borders are colored by blue. By comparing Fig. 6.11a, b,
the centerline of the mixing region will change with different size ratios. The average
width of the mixing region increases remarkably from 3.5D 1 at R D = 1.0 to 5.5D 1
at R D = 2.0. In Fig. 6.11c, there is no guide plate at the initial state; the width also
increases to 5.1D 1 at R D =1.0. Thus, the effect of the guide plate on the mixing is
negligible.
At the same time, the complexity of the shape of the mixing interface will vary
at different particle size ratios and can be described quantitatively by the fractal
theory. The box-counting method [4–6], is used here for analyzing the images of
visualization for the two-region pebble bed. All the images have 768 pixels in height
and 1024 pixels in width. They are covered by mono-sized square boxes with δ
pixels in width. N is the number of boxes containing both the red and blue pixels.
The correlation between N and box size δ shown in Fig. 6.11d, satisfies
N δ ∝ (
1
δ
)
D 0
(6.1)
413
Fig. 6.10a–c, the width of all type-2 particles in the lower half bed decreases when
the size ratio increases, which is caused by the diffusion of different sized particles.
For Case 14 (Fig. 6.10d), the central region (0.4 m in width) is much wider than
the bottom region (0.12m in width). Thus, type-2 particles generated from the top
region will move longer horizontal distance to reach the bottom. Because only a
small fraction of type-1 particles is located near the bottom, type-1 particles are less
likely to be removed from the pebble bed when the region ratio is R L = 2.0. This
phenomenon also happens for Case 13 (R L = 2.0, R D = 1.0) and Case 15 (R L = 2.0,
R D = 2.0). Thus, it is detrimental to the discharge of pebble flow when the region
ratio R L = 2.0, as it makes much more difficult for type 1 particles (fuel spheres) to
be discharged timely if the nuclear fuel inside has already been burned up. Moreover,
by comparing Fig. 6.9d, e, and f, the shape of mixing interface changes from curved
to nearly straight when the region ratio increases.
6.2.3 Shape and Size of Mixing Region
6.2.3.1 Fractal Dimension of Mixing Interface
For comparative analysis, the discharge rate for Case 1∼12 is 100 particles per
second in simulation. From the perspective of designing the two-region pebble bed,
it is essential to control the mixing region, where the particles are usually in contact
with different types of particles. The shape and size of the mixing region are crucial
in the mixing process. Hence, the particles in the mixing region of the steady state
are marked by green (Fig. 6.11a–c), where the red line is the smoothed centerline of
the mixing region, and the borders are colored by blue. By comparing Fig. 6.11a, b,
the centerline of the mixing region will change with different size ratios. The average
width of the mixing region increases remarkably from 3.5D 1 at R D = 1.0 to 5.5D 1
at R D = 2.0. In Fig. 6.11c, there is no guide plate at the initial state; the width also
increases to 5.1D 1 at R D =1.0. Thus, the effect of the guide plate on the mixing is
negligible.
At the same time, the complexity of the shape of the mixing interface will vary
at different particle size ratios and can be described quantitatively by the fractal
theory. The box-counting method [4–6], is used here for analyzing the images of
visualization for the two-region pebble bed. All the images have 768 pixels in height
and 1024 pixels in width. They are covered by mono-sized square boxes with δ
pixels in width. N is the number of boxes containing both the red and blue pixels.
The correlation between N and box size δ shown in Fig. 6.11d, satisfies
N δ ∝ (
1
δ
)
D 0
(6.1)