## 3 Results and Discussion
### Factors Investigation  
#### 3.2.1 Catalyst Particle Shape  
In TBRs, the voids formed between particles affect the fluid flow structure significantly hence affect the liquid holdup and wetting efficiency. The scope is limited when altering the local characteristics of packing/voids, but the manipulation of particle size and shape may allow some degree of control [1]. Packings formed by particles of different shape have different porosities and specific surface areas, and the different flow channels of various complexity have a great influence on the distribution of the flow field. Here four particle shapes (sphere, cylinder, single-hole cylinder, and 4-hole cylinder) were investigated for their characteristics of liquid holdup and wetting efficiency. Characteristic data of three kinds of random packings was given in Table 4, and the liquid distributions inside four packings are shown in Figure 4. It can be clearly seen that the liquid inside four packings tended to accumulate in the inner holes and voids between particles. The cylinder packing had the lowest porosity liquid holdup among all. The difference in liquid holdup between spheres and cylinders was not significant since the contact form between cylinder particles was more complex than spheres, including point contact, line contact, and surface contact. This caused a higher number and more complex shapes of voids between particles, from which the cylinder packing got a stronger ability of keeping liquid by capillary effect. However, cylinders got higher liquid saturation than spheres due to their lower porosity. Single-hole cylinders showed much higher liquid holdup and saturation than both spheres and cylinders. In addition, 4-hole cylinders had both the highest liquid holdup and saturation. It can be found that the inner holes in the 4-hole cylinder packing were easier to be filled with liquid than those in a single-hole cylinder packing, due to the smaller inner hole diameter. The larger number of holes made the 4-hole cylinder packing gain the highest porosity and improved the ability of trapping liquid significantly. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Shape**} & \multirow{2}{*}{**Porosity**} & **Liquid** & **Liquid** & **Surface** & **Wetting** & **Pressure** \\  & & **Holdup** & **Saturation** & **Area (m2)** & **Efficiency** & **Drop (Pa)** \\ \hline Sphere & 0.55 & 0.1784 & 0.3246 & \(4.49\times 10^{-4}\) & 0.5883 & 236.50 \\ Cylinder & 0.51 & 0.1711 & 0.3329 & \(6.20\times 10^{-4}\) & 0.6322 & 401.60 \\ Single-hole cylinder & 0.63 & 0.2272 & 0.3600 & \(8.29\times 10^{-4}\) & 0.6289 & 344.19 \\
4-hole cylinder & 0.66 & 0.2633 & 0.3955 & \(1.02\times 10^{-3}\) & 0.6566 & 351.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Characteristic data of four kinds of random packing structures. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**t (ms)**} & \multicolumn{6}{c}{**Liquid Film Thickness (mm)**} \\ \cline{2-7}  & **0\({}^{\circ}\)** & **20\({}^{\circ}\)** & **40\({}^{\circ}\)** & **60\({}^{\circ}\)** & **80\({}^{\circ}\)** & **100\({}^{\circ}\)** \\ \hline \multirow{2}{*}{10} & Exp. & 1.30 & 3.79 & 1.82 & 1.33 & & \\  & Sim. & 0.23 & 3.35 & 2.87 & & & \\ \hline \multirow{2}{*}{15} & Exp. & 1.25 & 0.85 & 1.22 & 1.56 & 2.05 & \\  & Sim. & 0.49 & 2.94 & 2.14 & 0.95 & & \\ \hline \multirow{2}{*}{20} & Exp. & 0.09 & & & 0.90 & 1.58 & 1.89 \\  & Sim. & 0.62 & 0.47 & 0.78 & 0.85 & 1.11 & \\ \hline \multirow{2}{*}{25} & Exp. & & & & 1.21 & 2.44 & 2.56 \\  & Sim. & 0.81 & & & & 0.52 & 1.22 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Thickness of liquid film on particle surface of different positions. The particle surface area showed a remarkable difference between four kinds of particles. Sphere packing had the lowest surface area and wetting efficiency. For cylinders, single-hole cylinders, and 4-hole cylinders, the surface area increased with the rise of the inner hole number.