## 2 Models and Methods
### Numerical Setup
#### 2.2.2 CFD Simulation  
The mesh of the simulated TBR model is shown in Figure 2. The 6 mm \(\times\) 6 mm \(\times\) 9 mm TBR model was defined as the simulation region. Four different particle shapes were considered in this research, including sphere, cylinder, single-hole cylinder, and 4-hole cylinder. Table 2 shows the geometric size data of four kinds of particles.  
The diameter of the sphere was 2 mm. The surface area of the cylinder particle was the same as the sphere, and the ratio of diameter to height was 3/5. The diameters of the inner holes of the single-hole cylinder and 4-hole cylinder are half and a quarter of the cylinder diameter, respectively.  
About 56 random spheres and 77 cylindrical particles inside rectangular domains were generated through DEM method. The liquid was introduced into the TBR from the top through the four tubes with diameter D\({}_{\text{in}}\) = 0.5 mm and length L\({}_{\text{in}}\) = 1 mm, which were located on the top forming a 3 mm \(\times\) 3 mm square. Different numbers of inlets were tested, including 1, 4, and 9 inlets on the top. We found that there was no significant difference in simulation results between different inlet numbers. Therefore, the middle number of 4 inlets was selected. The residual area of the top was the gas inlet. The gas and liquid inlets were defined as velocity inlets and the region bottom was a pressure outlet. Four cross sections were set as symmetrical planes. The VOF model suffer from the generation of spurious currents near the interface. However, to get convergent simulation results, there is no treatment about spurious currents in this research. The time step was \(2\times 10^{-4}\) s and the mesh numbers were 269,516, 1,112,159, 1,395,718, and 1,604,862, respectively. Two high-performance compute cluster with 8 CPU-cores were used to perform the simulations. The calculation time of four different models are 9.0, 48.0, 57.3, and 65.9 h respectively.  
The independence of time step and mesh number was confirmed before the decisions were made. Except for the investigation of particle shape's influence, the investigations of the factors were implemented on a random 4-hole cylinder packing. All simulations were conducted in the theoretical trickle flow regime. The volume of liquid and the wetted area of each case are monitored. At first both two quantities increased fast, while after some time they stopped significant increase and began to fluctuate. After that the result data was calculated by time-averaging. In the following chapters, only  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Shape** & **Characteristic Size (mm)** & **Shape** & **Characteristic Size (mm)** \\ \hline Sphere & Diameter & 2 & \\ Height & 2.27 & Cylinder & Height & 2.27 \\
4-hole cylinder & Diameter & 1.36 & \\ Inner holes diameter & 0.34 & Single-hole & Height & 2.27 \\ Inner holes center distance & 0.68 & cylinder & Diameter & 1.36 \\ Inner hole diameter & 0.68 & Inner hole diameter & 0.68 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Geometric size of four kinds of particles.  
Figure 2: Illustration of four simulated packing meshes including sphere (**a**), cylinder (**b**), single-hole cylinder (**c**), and 4-hole cylinder (**d**).  
the investigated factors were changed, and the rest of fluid properties were kept constant as shown in Table 1.