## 3 Results and Discussion
### Computational Fluid Dynamics Simulations
#### 3.2.4. CFD Model Validation with Experiments  
CFD simulations were performed to investigate four distinct scenarios: N1H1, N1H2, N2H1, and N2H2. In all four scenarios, the simulations involved the injection of water droplets through nozzles situated at the shower head. These water droplets were treated  
Figure 8: (**a**) Computational parcel study. (**b**) Normal distribution fitting (Q\(-\)Q plot) with linear fit of \(R^{2}\) for N1H1. Figure 7: (**a**) Unsteady inner iteration independence study. (**b**) Normal distribution fitting (Q-Q plot) with linear fit of \(R^{2}\) for N1H1. as Lagrangian particles and introduced into the computational domain. The initiation of water droplet ejection from nozzles was facilitated by an initial injection velocity (\(\dot{q}_{l}\), flowrate/a, area) specified within the CFD simulation parameters. The downward motion of these droplets was primarily governed by the gravitational force acting in the negative y-direction. As the water droplets fell, they dynamically interacted with the initially stagnant air within the square tube. This interaction caused the stationary air to move, leading to the formation of air-velocity profiles in the CFD simulation domain. Figure 9 presents the air-velocity profiles generated in two CFD cases: N1H1 and N1H2. These profiles demonstrate the evolving airflow patterns resulting from the falling of the water droplets. As the water droplets descended from the shower head, their velocity increased due to gravitational effects, droplet collisions, and coalescence. Consequently, the air movement intensified around the droplets, as depicted in Figure 9. Notably, the air-velocity profile became more pronounced as the distance from the injection point (shower head) increased. The simulation results were compared to the experimental droplet size distribution and Sauter mean diameter (\(d_{32}\)) recorded at distances of 200 mm and 400 mm from the nozzle plate inlet for both the N1H1 and N1H2 cases, as outlined in Table 3. The results from both the experimental observations and simulations indicated that at the nozzle inlet, the droplet size distribution followed a log-normal pattern. However, at greater distances from the shower head, specifically at 200/400 mm, the droplet size distribution exhibited a reasonably good fit to a normal distribution. This trend is visualized in Figures 10-13. In the N1H1 CFD case, the total length between the shower head and the bottom of the square tube was 370 mm, whereas in the N1H2 case, it was 570 mm (Figure 3). Figure 9 illustrates that in the N1H1 CFD case, a moderate vortex of the air-velocity profile was formed. Conversely, in the N1H2 case, the intensity of the vortex, or the development of the air-velocity profile, was reduced. This disparity can be attributed to the greater length of the CFD domain in N1H2 compared to N1H1. Figure 11: (a) Experimental and CFD droplet size frequency distributions with fitted curves. (b) Normal distribution fitting (Q–Q plot) with linear fit of \(R^{2}\) for N1H2. Figure 12: (a) Experimental and CFD droplet size frequency distributions with fitted curves. (b) Normal distribution fitting (Q–Q plot) with linear fit of \(R^{2}\) for N2H1. Figure 13: (a) Experimental and CFD droplet size frequency distributions with fitted curves. (b) Normal distribution fitting (Q–Q plot) with linear fit of \(R^{2}\) for N2H2. Table 3 presents a comparative analysis of the average mean diameters, namely \(d_{10}\), \(d_{20}\), \(d_{30}\), and \(d_{32}\), for liquid droplets at two distinct heights--200 mm and 400 mm--across both nozzle plates. The difference between the experimental and CFD-derived arithmetic mean ranged from 10 to 13%, indicating a moderate level of confidence in the CFD model's ability to accurately predict the arithmetic mean diameter of water droplets at different elevations. Furthermore, for the surface area mean, the difference between the experimental data and CFD simulations ranged from 12 to 17%.