# Modelling Pollutant Dispersion in Urban Canyons to Enhance Air Quality and Urban Planning
## 3 Results
### Pollutant Dispersion  
Firstly, the renewal rate at the roof level is shown in Figure 8. The figure shows that all cases for each reference wind velocity have the same trend. In general terms, the air renewal rate descends as the AR increases. However, the slope of the curve does not  
Figure 7: Classification of the number of recirculations depending on the Reynolds number and the aspect ratio. remain constant. The maximum PFR value is found for the lowest AR value, which is when AR = 0.75. After this maximum, its value descends to approximately AR = 2. Within this range, the air renewal is reduced by more than half of its initial value. At this point, there is a change in the slope of the tendency line and the decline occurs more slowly. This might be explained because the street now exhibits two recirculations, which causes a reduction in ventilation effectiveness. Finally, for high AR values, approximately for AR = 3.5 and above, the reduction in the PFR value is very low. From this point, the difference in the PFR between different AR configurations is minimal, which is caused by the apparition of another vortex at the bottom of the street. This means that for very narrow streets or spaces, the purging flow rate remains practically constant with one order of magnitude less if compared with AR = 0.75, being approximately independent of the aspect ratio. This general behaviour can be verified for the reference case of \(\mathbf{u}\) = 1 m/s. The purging flow rate with the exterior for AR = 0.75 is approximately 0.25 kg/s. As stated above, this is the maximum value for this Reynolds number. Then, its value descends quickly until the AR = 2, where the PFR\(\sim\)0.1 kg/s, which is less than half of the initial case. As the AR continues to increase, this decrease slows down, so that for the last studied case of AR = 4.5, the value of the air pollution exchange is approximately 0.04 kg/s, which is an order of magnitude lower than the initial case. Regarding the effect of the Reynolds number regime, it is remarkable that the relationship between the purging flow rate and the Reynolds number is practically linear for a fixed aspect ratio since the effect of Re is to shift the curve by increasing or decreasing it proportionally to \(\mathbf{Re}\). With this finding, if some specific Reynolds number for a street configuration is needed, it can be obtained directly from Figure 8.  
Figure 8: Purging flow rate results for different ARs and Reynolds numbers. A deeper analysis can be conducted for street configurations in a multi-vortex regime, as the purging flow rate with the exterior does not define the real pollutant removal at the pedestrian level. The primary effect of vortices is the accumulation of pollutants in the bottom layer of the streets. For that purpose, a further analysis of the purging flow rate between lower recirculations within a street is needed. The purging flow rate between the internal vortices, when only two recirculations are found, is seen in Figure 9. In this case, there is no appreciable reduction when increasing the aspect ratio, partly because the multi-vortex street configurations are in the AR range where the decrease in the PFR is less appreciable. Furthermore, it can be seen that in this case, the relationship between the PFR and Reynolds number is also almost linear. It is worth noting that for all the cases studied the value of the PFR is approximately \(\sim\)0.02 kg/s, which means that the ventilation efficiency of the lower part of the street in the cases with two vortices is significantly worse than the case where only one vortex occurs. The PFR between the internal vortices, when three recirculations are found, is observed in Figure 10. The former discussion of the relation between the PFR and the aspect ratio and Reynolds number is valid in this three-vortex regime. However, the purging flow rate between the two lower vortices is very small, approximately \(\sim\)0.001 kg/s.