## 4 Results and Discussion
### Discussion  
Figure 11a shows a double y plot for _NAC_ and _SNAC_ with the (\(VRR\)) in the \(x\)-axis. The figure shows the normalized average concentration (_NAC_) of aerosol droplets received by students' faces only and body only for the different ventilation rate cases.  
It is clear that, as ventilation increased, the average _NAC_ received by students generally decreased. On the other hand, as the ventilation rate increased, the number of students exposed to the aerosol droplets increased as well. This finding is based on the model results; however, it is not depicted in Figure 11.  
The _SNAC_ was calculated and is also presented in Figure 11a. We found that, as the ventilation rate increased, _SNAC_ decreased exponentially, and it tended to asymptotically reach zero _SNAC_ at the theoretically infinite value of the ventilation rate. The results  
Figure 11: Variation of (_NAC_) and (_SNAC_) with the ventilation rate and gate status. (**a**) Variation of (_NAC_) and (_SNAC_) with the ventilation rate. (**b**) Variation of the total (_SNAC_) (body+face) with door status (open/closed).  
indicate that increasing the ventilation rate ratio (\(VRR>3\)) is expected to have a marginal effect on reducing the _SNAC_.  
Figure 11b presents a comparison between the open and the closed-door cases, assuming a ventilation rate double the minimum value (\(VRR=2\)). The figure shows how _SNAC_ varies for the different exposed parts of the body. It can be concluded that opening the classroom door helped reduce the _SNAC_ and also reduce the risk of exposure to harmful aerosols by about 26 percent.  
Figure 12 shows a double y-plot for the variations of _NAC_ and _SNAC_ with the particle/droplet size in the _x_-axis. Both _NAC_ and _SNAC_ decreased as droplet size increased, and _SNAC_'s trendline appears to be quadratic with the droplet size. Based on the _SNAC_ values for the whole body, the 5 \(\upmu\)m size droplets appear to be less hazardous as they resulted in an 87% reduction in exposure when compared with the small 1 \(\upmu\)m size droplets.  
Figure 13 shows how the exceedance in exposure ratio (\(EER\)) index varied with the different ventilation rates after 180 s. The figure indicates that the highest exposure to droplets location was not in the front row but in the third row (for the scenario cases: R1 and R2). It can also be noted that the maximum scored values of \(EER\) were 3.5 and 2.15 for the no-ventilation (Figure 13a) and 50% ventilation (Figure 13b) cases, respectively. This means that, for the case of \(VRR=0\) (Figure 13a), the worst-case student had a risk of exposure to droplets that exceeded the reference average by 3.5 times, whereas the worst-case student for the case of \(VRR=1\) (Figure 13b) (run R2), had a corresponding risk that exceeded the reference average by 2.15 times. When the ventilation rate reached \(VRR\geq 2\) (Figure 13c,d), the location points of high exposure were not distinguishable, and almost all students had a negative \(EER\), which means the majority were exposed to risk less than the reference average.  
Figure 12: Variation of (_NAC_) and (_SNAC_) with particle/droplet size.