## 3 Results  
### Model Validation Results  
Figure 5a compares the simulated and measured steady-state airflow distribution in the section across the fourth row. The experimental test data can also be found in one of our previous publications [20]. The downward jet flow in the aisle was relatively strong, which separated the two large vortexes on both sides of the cabin. The major flow pattern and the velocity magnitudes were in good agreement between the CFD and the measurement. However, there were some deviations in the downward jet directions in the aisle. This was ascribed to the unstable swinging flow in the aisle, which was beyond the capability of the steady-state modeling.  
Figure 4: The geometry of the cabin mock-up.  
Figure 5: _Cont._  
Figure 5b,c compare the CFD modeled and measured steady-state dimensionless concentration fields of particles in the cross-section across the fourth row and the longitudinal section across the C\({}^{\text{th}}\) column. The simulated particle concentration fields were generally similar to the measurement results. In the cross-section, the high particle concentration was concentrated in the region near the ceiling above seats 4B and 4C, and the particle was transmitted to the left half cabin, which was captured well by CFD. In the longitudinal section, the particles were spread further forward in the measurement than in the CFD, which may be caused by both the longitudinal airflow and the turbulence. It should also be noted that during measurements, the movement of the three-dimensional guide rails mounting the measuring instruments could induce certain disturbances to the flow field and promote particle dispersion.  
To further evaluate the CFD results, the normalized root-mean-square error (RMSE) was used to describe the discrepancy with the measurement data [13,32] as:  
\[RMSE\big{(}C_{pi},C_{mi}\big{)}=\sqrt{\frac{\sum_{i=1}^{n}\big{(}C_{pi}-C_{mi} \big{)}^{2}}{\sum_{i=1}^{n}C_{mi}{}^{2}}} \tag{4}\]  
where \(C_{pi}\) and \(C_{mi}\) represent the predicted results and measured data, respectively, such as air velocity and particle concentration at certain locations. Dimensionless velocity and concentration were defined as:  
\[V^{*}=\frac{V_{local}}{\overline{V}},C^{*}=\frac{C_{local}-C_{in}}{C_{out}-C_{ in}},\text{ and}C_{in}=0 \tag{5}\]  
where \(\overline{V}\) is the average velocity at all of the measured locations, and \(V_{local}\) and \(C_{local}\) are the air velocity and particle concentration, respectively, at a given location [13,32].  
Figure 5: Validation of CFD model: (**a**) comparison of airflow field in a cross-section across the fourth row, (**b**) the steady-state concentration fields of dimensionless particle concentrations by measurement, (**c**) the steady-state concentration fields of dimensionless particle concentrations by CFD simulation.  
The factor of two observations (FAC2) [33] is another metric used to evaluate the discrepancy between the measurement and the modeling as:  
\[FAC2=\frac{1}{n}{\sum_{i=1}^{n}{N_{i}}}\text{ with }N_{i}=\left\{\begin{array}{ll}1&for \text{ }0.5\leq\frac{C_{pi}}{C_{mi}}\leq 2.0\\ 1&for\text{ }C_{mi}\leq W\text{ and }C_{pi}\leq W\\ 0&else\end{array}\right\} \tag{6}\]  
where \(W\) is the absolute difference. \(W\) was 0.003 [33] for the normalized contaminant concentration.  
As shown in Table 6, the RMSEs in this study were smaller than those reported in [13]. The FAC2 for particle concentrations was 0.67, which was greater than 0.5. In summary, the CFD simulation provided the airflow field and particle concentrations in generally good agreement with the experimental measurements.