## 2 Numerical Methodology  
The particle packing is a complex process involving a large number of multi-body collisions and particle interactions. The discrete element method can simulate well the interaction between each particle and obtain the closest state to that of the actual physical particle packing, which have been demonstrated in a large number of studies in the literature [5; 23; 24; 25; 26; 27], particularly on the use of DEM to simulate a particle packing process. In addition, it is well known that CFD calculations can simulate the flow behavior of fluids and obtain detailed information about fluid behaviors, such as pressure distribution and velocity distribution.  
Firstly, DEM modeling is used to simulate the particle random packing process and establish a fixed pebble bed model with random packing of pebbles. Then, by transferring the pebble bed data and reconstructing the physical geometry, the CFD model can be built. Finally, the gas flow characteristics inside the pebble bed can be obtained by using the CFD solution. By combining the two methods, DEM and CFD, it is possible to obtain the characteristics of the fluid flow behavior in the internal pores of the pebble bed that are closest to the real particle packing state. It provides an excellent way to evaluate the detailed flow characteristics of the purge gas helium inside the tritium breeder pebble bed of a fusion blanket. In addition, this approach of using a combination of DEM and CFD to study gas flow within a fixed bed of particles has been used in a large number of applications in other chemical industries [15; 22; 28; 29; 30; 31].  
Therefore, in this study, a one-way coupling of DEM and CFD is utilized to model the pebble packing process and solve the helium gas flow behaviors in the porous of randomly packed pebble beds. Figure 1 shows the flowchart of the simulation process, as follows:  
* Section I: DEM simulation was used to model the pebble packing process and to obtain the pebble bed model of the specific packing structures. To start DEM modeling, firstly, the parameters of bed dimension, pebble material properties, pebble size, pebble distribution, etc., should be determined. Then, gradually insert pebbles into the bed container by the gravity falling rain method. The pebbles fall down and become packed in the container. When a specific bed height is reached or a specific number of pebbles are inserted, the pebble inserting process is stopped. The pebbles gradually reach a stable state through energy dissipation. Finally, the pebble bed model with a specific packing structure is obtained. Then, the pebble bed model data are passed to the CFD software (ANSYS CFX 2019R2) through a coupling interface program.
* Section II: CFD simulation was adopted to model the purge gas flow behaviors of helium in the void structure of the pebble beds. At first, the pebble bed model is regenerated and established after obtaining the pebble bed data, which were transferred from the VB interface program. The point of contact between the pebbles makes it difficult to mesh; therefore, a handling of contact point is necessary. Then, the fluid domain is meshed. After setting the boundary conditions for fluid computation, the numerical solution can be performed. Finally, the pebble bed flow field data are obtained and post-processing of the simulation results can be performed to obtain detailed flow characteristics of helium in pebble beds.