## 5 Conclusions  
This study applied an Eulerian-Eulerian two-phase model with Navier-Stokes equations, porous media model, standard \(k\)-\(\epsilon\) turbulence closure, and species equations to investigate the fluid mechanics and desulfurization process within the FGD tower of sieve trays. Important findings and contributions can be highlighted as follows:  
1. The complex structures of sieve trays are replaced by the porous media model, which significantly saves the computational time with consistent results with those simulated by detailed perforated structures and measured data in a small-scale FGD tower. As for the full-scale tower, the computational cost with detailed structure is too expansive considering the enormous scale ratio between the perforated hole at the sieve tray and radius of tower. The porous media model makes the simulations of full-scale tower more practical and was validated in the experiments, which further proves the feasibility of using a porous media model. 2. The liquid column from the nozzle experiences deceleration near the top surface of sieve tray and acceleration within it. As the liquid flow has not reached its terminal velocity, the acceleration remains even the liquid passes the tray region. The deceleration leads to the accumulation of liquid volume fraction near the sieve tray, while the acceleration reduces the size of liquid column because of continuity. These mechanisms result in the reduction of liquid column between two neighboring sieve trays and affect the two-phase mixing within the FGD tower. 3. The empty, one-tray, and four-tray towers were simulated at different flow conditions. The size of liquid column with better two-phase mixing in the center and the area of uprising gas near the wall play the most important roles to determine the desulfurization performance. At different flow conditions, such as the variation of inlet gas flow rate, these two competing effects end up with different results, which also affects the selections of tray setups. 4. The four-tray tower has the best two-phase mixing. However, its liquid column is the smallest, which also ensues the largest area of uprising gas near the wall with higher SO\({}_{2}\) concentration. As a result, the four-tray tower at a lower gas flow rate fails to improve the SO\({}_{2}\) removal efficiency from the other two tray setups at a lower gas flow rate. 5. For a higher inlet gas volume flow rate, the stronger inertial of uprising gas flow leads to a weaker acceleration of the liquid column, and hence, the reduction in size of the liquid column is gentler. Correspondingly, implementing four sieve trays is more  
Figure 18: This schematic shows the radius of liquid column of the small-scale tower for Cases F and G.  
efficient under a higher gas volume flow rate. It enhances the performance by 15% from empty tower and 5% from one-tray tower. 6. Sections 4.2 and 4.3 indicate that the sieve tray can enhance two-phase mixing within the liquid column, but it also increases the region of uprising gas where the SO\({}_{2}\) mass fraction is higher. Depending on different values of the gas volume flow rate \(Q\), these two competing effects end up with different trends for SO\({}_{2}\) removal efficiency. Conceptualization, C.-C.T. ; methodology, C.-C.T. ; software, C.-J.L. ; validation, C.-C.T. and C.-J.L. ; formal analysis, C.-C.T. ; investigation, C.-C.T. and C.-J.L. ; resources, C.-C.T. ; data curation, C.-C.T. ; writing--original draft preparation, C.-C.T. ; writing--review and editing, C.-C.T. ; visualization, C.-J.L. ; supervision, C.-C.T. ; project administration, C.-C.T. ; funding acquisition, C.-C.T. All authors have read and agreed to the published version of the manuscript. This research was funded by MOST under Grant No. MOST 110-2628-E-006-002-and China Steel Cooperation under Grant No. 03A210393. Not applicable. The data presented in this study are available upon request from the corresponding author.