## 2 Methodology
### Numerical Model Validation  
To validate the numerical model, on-site experiments were conducted in the subway carriage without passengers. Following the standard EN14750-1 [69], three repeatability tests were performed. The layout of 15 monitoring points inside the carriage is shown in Figure 3. The wire anemometer (CLIMOMATER6501, with probe 6543) used in the experiment can simultaneously measure the temperature and airflow velocity with a measurement error of 2%. Within each round of testing, the wire anemometer recorded 180 samples in 3 min, with a sampling frequency of 1 Hz. The probe's temperature \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Case** & **Initial Droplet** & **Initial Droplet** & **Release** & **Air RH** & **Passengers’** \\
**Number** & **Diameter (\(\upmu\)m)** & **Velocity (m/s)** & **Position** & **Density** \\ \hline
1 & 10 & 10 & D1 & 70\% & 2 p/m\({}^{2}\) \\
2 & 50 & 10 & D1 & 70\% & 2 p/m\({}^{2}\) \\
3 & 100 & 10 & D1 & 70\% & 2 p/m\({}^{2}\) \\
4 & 10 & 10 & D2 & 70\% & 2 p/m\({}^{2}\) \\
5 & 10 & 1 & D1 & 70\% & 2 p/m\({}^{2}\) \\
6 & 50 & 10 & D1 & 35\% & 2 p/m\({}^{2}\) \\
7 & 10 & 1 & D1 & 70\% & 4 p/m\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation case setting. Figure 2: The setup of simulations: (**a**) 2 p/m\({}^{2}\) scenario; (**b**) 4 passengers/m\({}^{2}\) scenario; (**c**) grid model. measurement range is \(-20\)\({}^{\circ}\)C to 70 \({}^{\circ}\)C (with a resolution of 0.1 \({}^{\circ}\)C), and the airflow velocity measurement range is 0.01 m/s to 5.0 m/s (with a resolution of 0.01 m/s). The experimental results are shown in Figure 4. The mean value and standard deviation for each monitoring point are calculated. The maximum ratio of the standard deviation to the mean temperature and air velocity value is 5.7% and 13.3%, respectively. The standard deviation to the mean value for airflow velocity is higher than that for temperature. The reason for this is that the air velocity is typically below 0.50 m/s in the subway carriage, and the randomness of the flow field easily influences the detected air velocity. Then, simulations with different grid scales (coarse, middle, and fine mesh) were conducted according to the on-site experiment conditions. The total grid number for three mesh sets are 35.8 million, 48.5 million, and 59.6 million, respectively. The predicted airflow velocities and temperature values are also compared to the experimental measurements at each monitoring point, as shown in Figure 4. Firstly, the discrepancy between the predicted results of the coarse and fine mesh is relatively large. In contrast, the predicted results of the middle and fine mesh are very close. The average relative error between the middle and fine mesh models is less than 1% in temperature and 6% in airflow velocity, respectively. This indicates that the middle mesh model is as adequate to produce a steady flow field as the fine mesh model. Therefore, the middle mesh scale is used for all the simulation cases in the present work. After the passenger models are added to the carriage, the number of grid models is approximately 53.2 million when the passenger density is 2 p/m\({}^{2}\) and 53.8 million when the passenger density is 4 p/m\({}^{2}\), respectively. Furthermore, the mean relative error of the airflow velocity (\(u_{m}\)) and temperature (\(t_{m}\)) between the simulation predictions and the experimental measurements is calculated. The values can be obtained using the following, Equations (12) and (13). The values \(t_{m}\) and \(u_{m}\) are 1.8% and 14.7% for the middle grid scale, respectively. For the fine mesh scale, the values \(t_{m}\) and \(u_{m}\) are 1.4% and 12.1%, respectively. Although the mean relative error of the airflow velocity is still relatively large, as mentioned earlier, the velocity at  
Figure 4: Simulation model validation: (**a**) airflow velocity; (**b**) temperature. Figure 3: Monitoring point layout: (**a**) top view; (**b**) front view; (**c**) on-site experiment.