204
4 Numerical Methods and Simulation for Pebble Flows
It is reported that the radial void fraction profile of a pebble bed fluctuates near
the wall [54]. The oscillating trend of void fraction shows an asymptotical value of
0.39, which is the average value observed in experiments [55]. Although this type
of oscillation of packing fraction does not affect the average reactor parameters, it
may influence local flow properties and thermodynamic and reaction characteristics.
For example, it can cause near-wall channeling of the coolant flow [56]. du Toit [57–
59] showed a very extensive compilation of recent investigations of void fraction,
including comparisons of experimental data. It is concluded that most of the studies
and analyses of void fraction already available in the literature are based on the
radial/annual or longitudinal distributions of void fraction in packed beds[54–63] .
On the other hand, the void fraction distribution is determined by pebble packing
characteristics. Up to now, many controversies exist in analytical and numerical data
on the descriptions of radial variation of void fractions near the wall, i.e., fluctuated
(oscillatory correlations observed in experiments) [54–59] or not fluctuated (exponential correlations, usually using the concept of implicit sphere and averaged void
fraction) [61–63], radial porosity in packed beds. It is difficult and controversial to
determine the near-wall coordination numbers of the packed bed. The structure of
packing arrangement, such as simple cubic, body center cubic, face center cubic,
etc., may affect the quantification of void fraction in both the internal and near-wall
regions. Thus, it can affect the bulk thermo-physics of the packed beds, e.g., effective thermal conductivity, etc. The arrangement structure can affect the flow and
thermo-physics characteristics in the pebble-discharging bed similarly.
Moreover, it is mentioned that the packing factor can be influenced by the movement of pebbles in the reactor. As a result, the void fraction should be time-dependent.
In other words, the results obtained from the stationary packed bed cannot be directly
used for estimating void fractions in the pebble-discharging bed, since there is a fundamental difference between the slowly moving pebble flows and the stationary
packed beds.
In conclusion, a full description of the void fraction characteristics, both in radial
and axial directions, is critical in the packed and discharging bed. A detailed and
accurate study and analysis of the three-dimensional and dynamical characteristics
of the void fractions in pebble-discharging beds are studied here, corresponding to
the real test facility of HTR-10 in Tsinghua university.
4.3.1.1 Simulation Setup
The parameters used in the current simulation are listed in Table 4.11. The normal
stiffness factor is softened to 10
4 to reduce the computational cost for the simulation of a three-dimensional bed with 27000 particles. The softened stiffness factor
or reduced Young’s modulus is intrinsic modifications for the soft-sphere approach
of the discrete element method, and it has been commonly used in many studies
[8, 58]. The disadvantage is that it can result in additional deformations caused
by reduced repulsive force between the pebbles, which can slightly decrease void
fractions throughout the bed uniformly. However, this disadvantage is of secondary
4 Numerical Methods and Simulation for Pebble Flows
It is reported that the radial void fraction profile of a pebble bed fluctuates near
the wall [54]. The oscillating trend of void fraction shows an asymptotical value of
0.39, which is the average value observed in experiments [55]. Although this type
of oscillation of packing fraction does not affect the average reactor parameters, it
may influence local flow properties and thermodynamic and reaction characteristics.
For example, it can cause near-wall channeling of the coolant flow [56]. du Toit [57–
59] showed a very extensive compilation of recent investigations of void fraction,
including comparisons of experimental data. It is concluded that most of the studies
and analyses of void fraction already available in the literature are based on the
radial/annual or longitudinal distributions of void fraction in packed beds[54–63] .
On the other hand, the void fraction distribution is determined by pebble packing
characteristics. Up to now, many controversies exist in analytical and numerical data
on the descriptions of radial variation of void fractions near the wall, i.e., fluctuated
(oscillatory correlations observed in experiments) [54–59] or not fluctuated (exponential correlations, usually using the concept of implicit sphere and averaged void
fraction) [61–63], radial porosity in packed beds. It is difficult and controversial to
determine the near-wall coordination numbers of the packed bed. The structure of
packing arrangement, such as simple cubic, body center cubic, face center cubic,
etc., may affect the quantification of void fraction in both the internal and near-wall
regions. Thus, it can affect the bulk thermo-physics of the packed beds, e.g., effective thermal conductivity, etc. The arrangement structure can affect the flow and
thermo-physics characteristics in the pebble-discharging bed similarly.
Moreover, it is mentioned that the packing factor can be influenced by the movement of pebbles in the reactor. As a result, the void fraction should be time-dependent.
In other words, the results obtained from the stationary packed bed cannot be directly
used for estimating void fractions in the pebble-discharging bed, since there is a fundamental difference between the slowly moving pebble flows and the stationary
packed beds.
In conclusion, a full description of the void fraction characteristics, both in radial
and axial directions, is critical in the packed and discharging bed. A detailed and
accurate study and analysis of the three-dimensional and dynamical characteristics
of the void fractions in pebble-discharging beds are studied here, corresponding to
the real test facility of HTR-10 in Tsinghua university.
4.3.1.1 Simulation Setup
The parameters used in the current simulation are listed in Table 4.11. The normal
stiffness factor is softened to 10
4 to reduce the computational cost for the simulation of a three-dimensional bed with 27000 particles. The softened stiffness factor
or reduced Young’s modulus is intrinsic modifications for the soft-sphere approach
of the discrete element method, and it has been commonly used in many studies
[8, 58]. The disadvantage is that it can result in additional deformations caused
by reduced repulsive force between the pebbles, which can slightly decrease void
fractions throughout the bed uniformly. However, this disadvantage is of secondary