## 2 Materials and Methods
### Numerical Methods
#### 2.1.2. Modeling the Droplets  
The trajectories of particles were tracked using the Lagrangian method based on [PERSON]'s laws, and a discrete phase model (DPM) was used to discretize the effect of turbulent motion on particle transport, assuming that the particles did not interact with each other and that the forces were balanced on each particle. Droplets are subject to drag force, gravity force and additional forces after exhaling. The additional forces on the droplet include gravity, Saffman's force, drag force, thermophoretic force, additional mass force, air pressure gradient force, and Brownian force. Among them, the additional mass force and air pressure gradient force are two orders of magnitude smaller than the drag force and \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Equation** & **Continuity** & **Momentum** & **Energy** & **Turbulence**\(k\) & **Turbulence**\(\varepsilon\) \\ \hline \(\phi\) & 1 & \(\overline{u_{i}}\) & \(c_{p}\overline{T}\) & \(k\) & \(\varepsilon\) \\ \(\Gamma_{\phi,eff}\frac{\partial\phi}{\partial x_{j}}\) & 0 & \(\mu(\frac{\partial\overline{u_{i}}}{\partial x_{j}}+\frac{\partial\overline{u_ {j}}}{\partial x_{j}})\) & \((k_{f}+\frac{u_{i}}{\Gamma_{\phi}})\frac{\partial\overline{T}}{\partial x_{j}}\) & \((\mu+\frac{h_{i}}{\alpha_{i}})\frac{\partial\overline{u}}{\partial x_{j}}\) & \((\mu+\frac{h_{i}}{\alpha_{i}})\frac{\partial\overline{u}}{\partial x_{j}}\) \\ \(S_{\phi}\) & 0 & \(-\frac{\partial\overline{u_{i}}}{\partial x_{j}}\) & 0 & \(C_{k}-\rho e\) & \(\frac{\xi}{\xi}(C_{\xi 1}P_{k}-C_{\xi 2}\rho\xi)\) \\ \hline \hline \end{tabular} \(P\) is the pressure; \(\mu\) is the viscosity; \(\mu_{i}\) is the eddy viscosity; \(\
u_{k}\) and \(\sigma_{e}\) are the Prandtl numbers for kinetic energy and dissipation, respectively; \(G_{k}\) is the turbulent kinetic energy generation term; \(C_{\xi 1}\) and \(C_{\xi 2}\) are constants.  
\end{table} 
Table 1: Representation of the dependent variable in general conservation equation. Figure 1: Optimization process of hanging curtain design. can be ignored [31]. Meanwhile, in the cruise lounges, turbulent diffusion is dominant, and the diffusion effect of Brownian force is very small [32]. Therefore, only thermophoretic force and Saffman's force were considered for the additional forces in this study. Taking the Cartesian coordinate system in the x-direction as an example, the equation of particle motion is as follows:  
\[\frac{du_{p}}{dt}=F_{D}\big{(}u-u_{p}\big{)}+\frac{g_{x}\big{(}\rho_{p}-\rho \big{)}}{\rho_{p}}+F_{x} \tag{2}\]  
where \(u\) and \(u_{p}\) are the air velocity and droplet velocity, respectively; \(\rho\) and \(\rho_{p}\) are the air density and droplet density, respectively; \(F_{D}\) (\(u-u_{p}\)) is the drag force per unit droplet mass; \(\frac{g_{x}\big{(}\rho_{p}-\rho\big{)}}{\rho_{p}}\) is the gravity per unit droplet mass; \(F_{x}\) is the additional force per unit mass. The specific contents and expressions of \(F_{D}\) and \(F_{x}\) are shown in Table 2.  
Droplets evaporate when entering cruise cabins, using the discrete phase model as the mass transfer model [33]. The rate of droplet evaporation is governed by the concentration gradient between the droplet surface and the ambient air:  
\[\frac{dm_{p}}{dt}=k_{c}A_{p}M_{w,p}(C_{s}-C_{\infty}) \tag{3}\]  
\[k_{c}=\frac{D_{i,m}}{d_{p}}(2.0+0.6\text{Re}_{d}^{1/2}Sc^{1/3}) \tag{4}\]  
where \(k_{c}\) is the mass transfer coefficient; \(M_{w,p}\) is the molecular weight of the component; \(A_{p}\) is the droplet surface area; \(C_{s}\) and \(C_{\infty}\) are the water vapor mass concentrations at the droplet surface and in the air, respectively; \(D_{i,m}\) is the diffusion coefficient of water vapor in the air; \(Sc\) is the Schmidt number; and \(d_{p}\) is the droplet diameter. In this study, the convective heat transfer between droplets and air as well as the heat transfer that occurs during mass transfer were considered.