304
5 Numerical Models for Pebble-Bed Heat Transfer
Fig. 5.57 The structure of the pebble bed of the HTR-10 (a) and the initial heat source distribution
at 5% full power (b)
pled with the open DEM code LIGGGHTS with the python interface. The explicit
scheme was applied to updating the particle position, velocity, and angular velocity by calculating the contact forces and torques to surrounding ones. Then, the
particle conductive and radiative flux were computed to update all particles’ temperatures. The time step is much less than the Rayleigh time to make sure that the
iteration is convergent. All physical walls are adiabatic, and the initial temperature
of the inserted particles in the top region is set at 300
◦ C. The emissivity is 0.81 and
k c = 2.0 W/(m·
◦ C) in Eq. (5.140). The particle discharge rate n p is 1,000 particles/s,
and the time step is Δt = 10
−5 s in the simulation. Thus, a particle at the bottom is
reset on the top every 100 steps.
The non-dimensional time τ is defined as the number of discharged particles at the
bottom at physical time t, i.e., τ = n p · t. There are 27,000 pebbles in the bed, and
an average discharged number of all pebbles is 2.0 at τ = 5.4 × 10
4 . The numerical
results at τ = 0, τ = 10
4 , τ = 3 × 10
4 , and τ = 6 × 10
4 are shown in Fig. 5.58.
The transient temperature distribution in the pebble bed is significantly related to
the particle velocity profile. The velocity on the x = 0 plane is shown in Fig. 5.59a.
The particle velocities near the bottom and top are much higher than those of others.
Five points (O, A, B, C, D) marked in Fig. 5.57a are selected, and the local point
temperature is the average of the particle temperatures at a distance of 0.1 m. The
temporal responses of the five points are given in Fig. 5.59b. It is found that the
temperature distribution becomes a quasi-steady state at τ = 6 × 10
4 . In the axial
direction (points, A, B, O, and C), the particle temperature increases with the flow
direction. Even though the heat source on point D is much less than that on other
5 Numerical Models for Pebble-Bed Heat Transfer
Fig. 5.57 The structure of the pebble bed of the HTR-10 (a) and the initial heat source distribution
at 5% full power (b)
pled with the open DEM code LIGGGHTS with the python interface. The explicit
scheme was applied to updating the particle position, velocity, and angular velocity by calculating the contact forces and torques to surrounding ones. Then, the
particle conductive and radiative flux were computed to update all particles’ temperatures. The time step is much less than the Rayleigh time to make sure that the
iteration is convergent. All physical walls are adiabatic, and the initial temperature
of the inserted particles in the top region is set at 300
◦ C. The emissivity is 0.81 and
k c = 2.0 W/(m·
◦ C) in Eq. (5.140). The particle discharge rate n p is 1,000 particles/s,
and the time step is Δt = 10
−5 s in the simulation. Thus, a particle at the bottom is
reset on the top every 100 steps.
The non-dimensional time τ is defined as the number of discharged particles at the
bottom at physical time t, i.e., τ = n p · t. There are 27,000 pebbles in the bed, and
an average discharged number of all pebbles is 2.0 at τ = 5.4 × 10
4 . The numerical
results at τ = 0, τ = 10
4 , τ = 3 × 10
4 , and τ = 6 × 10
4 are shown in Fig. 5.58.
The transient temperature distribution in the pebble bed is significantly related to
the particle velocity profile. The velocity on the x = 0 plane is shown in Fig. 5.59a.
The particle velocities near the bottom and top are much higher than those of others.
Five points (O, A, B, C, D) marked in Fig. 5.57a are selected, and the local point
temperature is the average of the particle temperatures at a distance of 0.1 m. The
temporal responses of the five points are given in Fig. 5.59b. It is found that the
temperature distribution becomes a quasi-steady state at τ = 6 × 10
4 . In the axial
direction (points, A, B, O, and C), the particle temperature increases with the flow
direction. Even though the heat source on point D is much less than that on other