## 4 Designs of the Small-Scale Tower from Numerical Experiments
### Comparisons between Different Inlet Gas Flow Rates (Case E-Case G)  
From Case A to Case D, the inlet gas volume flow rates \(Q\) are all 24 m\({}^{3}\)/min, as shown in Table 6. Further increase in gas volume flow rates to 36 m\({}^{3}\)/min are applied at empty, one-tray, and four-tray tower as Case E, Case F, and Case G. The two-phase inertial loss  
Figure 16: This schematic shows the radius of liquid column of the small-scale tower for Case C and D.  
Figure 15: The figure displays (**a**) the liquid volume fraction, (**b**) streamlines of gas flow, and (**c**) the mass fraction of SO\({}_{2}\) from the top view at y = 0.615 m for Case C (empty tower) and Case D (one-tray tower).  
coefficients are set up as \(C_{g,y}=15.7\) (33% increase from Equation (16)) and \(C_{l,y}=10.31\) under the same treatments as described in Section 3.5.  
The stronger inertia of gas flow deflects the liquid flow into the right side of the tower for Case E (empty tower), as shown in Figure 17, and its streamlines of gas phase in Figure 17 indicate that the two-phase mixing is very weak in the left of the tower because of the deflection. Therefore, its SO2 removal efficiency is only 48% in Table 6. As for Case F in Figure 17, the sieve tray can enhance the uniformity of the gas flow [4] to avoid the deflection in the empty tower and exhibit a better two-phase mixing, as shown in Figure 17. As a result, the SO2 removal efficiency increases from 48% to 58.9%, as shown in Table 6.  
With a lower \(Q\) of 24 m\({}^{3}\)/min, the implementation of an additional three sieve trays reduces the SO2 removal efficiency from 61.6% (Case D) to 57.1% (Case A), as discussed in Section 4.2 and shown in Table 6. With all four sieve trays implemented, the gas and liquid flow structures of Case G in Figure 17 are very similar to those of Case A in Figure 12 under a lower value of \(Q\). However, the full implementation of sieve tray under a higher \(Q\) of 36 m\({}^{3}\)/min enhances the efficiency from 58.8% (Case F) to 63% (Case G) and even increases the efficiency by 15% from the empty tower (Case E).  
As the inertia of the uprising gas flow is stronger as \(Q\) increases, the acceleration of downward liquid flow as that discussed in Figure 8 for Case A becomes weaker. For Case A with \(Q=24\) m\({}^{3}\)/min, the downward liquid flow velocity can reach maximum velocity of 2.5 m/s between two trays, while it is only 1.9 m/s for Case G. This weaker acceleration leads to a gentler reduction of the size of liquid column. As a result, the radius of liquid column for four-trav Case G is only 26% smaller than that of one-trav Case F, as illustrated in Figure 18 (\(Q=36\) m\({}^{3}\)/min), while the additional three sieve trays incur a greater reduction of 48% (from Case A to Case D), as shown in Figures 14 and 16 (\(Q=24\) m\({}^{3}\)/min).  
Figure 17: The figure displays (**a**) the liquid volume fraction and (**b**) streamlines of gas flow for Case E–Case G.  
Correspondingly, in comparisons with Case F, the full implementation of sieve tray for Case G significantly enhances the two-phase mixing between neighboring trays in Figure 17b, and only reduces the size of liquid column by 26% in Figure 18. The former suppresses the latter and favors the SO\({}_{2}\) removal efficiency, as shown in Table 6 for \(Q\) = 36 m\({}^{3}\)/min.