# Modelling Pollutant Dispersion in Urban Canyons to Enhance Air Quality and Urban Planning
## 2 Materials and Methods
### Case Studies  
The main parameters affecting the results of street ventilation are the aspect ratio of the street and the Reynolds number [49; 50]. The aspect ratio (AR) measures the ratio between the height of the street (H) and its width (W), expressed as AR \(=H/W\). This indicates the street's narrowness. On the other hand, the Reynolds number (\(Re\)) represents the turbulent behaviour of the flow and is defined as \(Re=uH/\
u\)[25; 51]. This parameter can be affected by factors such as the reference wind speed (\(u\)), building height, and kinematic viscosity (\(\
u\)) of the fluid. The characterisation of street ventilation around these two parameters is crucial because they directly influence the flow characteristics within the street and its ventilation efficiency.  
For a full characterisation of this phenomenon, different street configurations will be tested. Street canyons of with an AR ranging from 0.75 to 4.5 are chosen since this value range represents the most common city street configurations, as evidenced by previous research works in this field [19; 52]. Lower AR streets are not considered as their high ventilation helps dissipate pollution.  
Nevertheless, the number and position of vortices are highly influenced by the Reynolds number, which depends on both the external airspeed and the building height. For this reason, a deeper study is necessary where this parameter is varied in a realistic range to recreate typical city configurations. For this reason, the Reynolds number varies from 3.4 \(\times\) 10\({}^{5}\) to 2.8 \(\times\) 10\({}^{6}\) for each AR tested, which is achieved by varying the wind velocity from 0.75 to 4 m/s. Traditionally, the Reynolds number values used were low (approximately 12,000) as they were experiments conducted in wind tunnels. However, some authors [25; 33] spotted the influence of the Reynolds number in streets with an AR > 1.5, as  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Zone** & **Boundary Condition** \\ \hline Inlet & Velocity Inlet : x-Velocity \(u=u_{\text{ref}}\big{(}\frac{\
u}{H}\big{)}^{0.18}\) \\ Outlet & Pressure Outlet \\ Far-field & Symmetry \\ Upstream & Wall. Roughness : \(z_{0}=0.1\) m \\ Downstream & Wall, no slip condition \\ Street & Wall, no slip condition \\ \hline \hline \end{tabular}
\end{table}
Table 1: Boundary conditions of the model.  
Figure 3: The meshing of the numerical domain.  
the ventilation was highly influenced by it. Therefore, to obtain practical results for real-life applications, the Reynolds number range must be appropriately chosen. Consequently, a highly valuable graph will be provided, which illustrates the number of vortices formed within a street canyon as a function of the aspect ratio (AR) and the Reynolds (\(Re\)) number. These data are crucial for the assessment of ventilation performance, which is vital for the development of effective strategies for pollution dispersion and heat dissipation in urban environments. Then, a total number of 45 cases are studied in this work, obtaining the previous indicators for each one.