## 4 Conclusions  
This study presents comprehensive simulations of droplet transmission in a typical subway carriage. Initially, a full-scale numerical model of the subway carriage, incorporating the complete ventilation duct system, is developed based on its actual geometry. Subsequently, the numerical and droplet evaporation models are validated using measurement data and the existing literature. Finally, the effects of some primary parameters (including initial droplet size, initial velocity, release position, \(RH\), and passenger density) on the droplet dispersion and passengers' infection risk are investigated.  
(1) Regarding the spread of droplets within the carriage, large droplets (100 \(\upmu\)m) are deposited on the carriage floor before completely evaporating, while tiny droplets (10 \(\upmu\)m) undergo rapid evaporation, leading to a larger spread within the carriage and a longer suspension time in the air.  
(2) The release location of the droplets from the source within the carriage significantly affects the efficiency of the ventilation system in removing the droplets. When the infected individual is at position D2, the ventilation system can remove 60% of droplets within 20 s. In contrast, the same proportion takes three times longer when the infected individual is at position D1.  
(3) The relationship between humidity, passenger density, and the proportion of droplets captured by passengers is closely linked. At 35% relative humidity, the number of droplets captured by passengers is approximately twice that at 70% relative humidity. Similarly, increasing the passenger density from 2 persons per square meter to 4 persons results in a higher proportion of captured droplets, increasing from less than 20% to over 50%.  
(4) The exposure and infection probability of passengers traveling together in the carriage depends on the droplet size and quantity captured by the passengers. The exposure and infection probability of passengers is generally higher in scenarios with an initial droplet size of 50 \(\upmu\)m (cases 2 and 6) compared to scenarios with an initial droplet size  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Infection Risk (\(P\))** & **Case 1** & **Case 2** & **Case 3** & **Case 4** & **Case 5** & **Case 6** & **Case 7** \\ \hline \(\geq\)0.01 & 3 & 15 & 3 & 0 & 2 & 16 & 4 \\ \(\geq\)0.05 & 0 & 13 & 3 & 0 & 0 & 14  
of 10 \(\upmu\)m (cases 1, 3, 4, and 7). In cases 2 and 6, the maximum exposure and infection probability for passengers exceeds 0.5, while in cases 1, 3, 4, and 7, the maximum exposure and infection probability for passengers does not exceed 0.1.  
In this study, in order to simplify the modeling process and reduce the computational costs, there are inevitable limitations in some of the assumptions. For example, we only considered two standing positions for infected passengers (D1 and D2), and there needs to be a more in-depth investigation into the distribution of the standing positions among the co-passengers. The distribution of passengers' standing positions within the carriage is highly random, and the impact of how passengers are distributed on the spread of respiratory droplets needs more attention in future research.  
F.W.: conceptualization, supervision; C.Y.: writing--original draft; R.X.: methodology, validation; H.L.: validation, visualization. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Science Foundation of China [Project name: on the transmission mechanism and control of respiratory droplets in the passenger compartment of high-speed trains; Grant number 52072413].  
Not applicable.  
The data that support the findings of this study are available from the corresponding author upon reasonable request.  
The authors are grateful for resources from the High-Performance Computing Center of Central South University.  
The author(s) declare no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.