## 3 Results  
### CFD Modeling Validation  
This study validated the CFD modeling with the experimental data and empirical model from previous study [29]. Figure 3 illustrates the investigated hotel building located in Toronto, Canada, which contained an elevator, a lobby, and a room, which was similar to the model in this study but with different dimensions. Table 3 provides the geometric parameters of the building. The pressure difference between the central lobby and the central room on the 15 th floor was measured. The elevator car was initially located on the 15 th floor, and the car was moved down to the 1 st floor at a speed of 1.73 m/s. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Item** & **Boundary Type** & **Boundary Values** \\ \hline Elevator car & Wall (dynamic mesh) & Moving at 1.5 m/s \\ Window & Pressure outlet & Zero \\ Vent hole & Pressure outlet & Zero \\ Interior openings & Interface & N/A \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Boundary conditions in CFD modeling. An empirical model [29] was derived for the pressure difference between the lobby and the room, in which the buoyancy, the wind, and the HVAC system were omitted. The pressure difference was calculated as [29]  
\[\Delta P_{li}=\frac{\rho}{2}\left[\frac{A_{s}V\left(\frac{A_{c}}{A_{li}}\right)} {N_{a}CA_{e}+C_{c}A_{f}\sqrt{1+\left(\frac{N_{b}}{N_{b}}\right)^{2}}}\right]^{2} \tag{1}\]  
where \(\rho\) is the density of the air inside the shaft; \(A_{s}\) is the cross-sectional area of the shaft; \(V\) is the speed of the elevator car; \(N_{a}\) and \(N_{b}\) are the floor numbers above and below the car, respectively; \(C\) is the flow coefficient related to the internal structure of the building; \(C_{c}\) is the flow coefficient in the annular space around the car, which is 0.83 for a single elevator shaft; \(A_{f}\) is the difference between the area of the shaft and the elevator car; \(A_{e}\) is the equivalent area composed of the leakage area between the shaft and the lobby; \(A_{sl}\) is the leakage area between the lobby and the internal structure of the building; and \(A_{li}\) is the leakage area between the internal and outside of the building. In this study, a geometric model was created in CFD. The generated grid cell number was 0.71 million. All of the settings were similar to those described in the previous section. Figure 4 compares the results provided by the measurement, the empirical model as Equation (1), and the CFD modeling. The position of the elevator car was also plotted on the upper boundary of this figure. As the elevator car started and left away from the 15 th floor, the pressure difference gradually decreased to zero. Both the empirical model  
Figure 3: Illustration of the building model used for model validation [29]: (**a**) planar view; (**b**) sectional view and the schematic of the elevator car from the 15 th floor to the 1 st floor. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Structure** & **Length (m)—X** & **Width (m)—Y** & **Height (m)—Z** \\ \hline Elevator shaft & 2.2 & 2.5 & 39 \\ Lobby & 2.0 & 4.0 & 2.6 \\ Room & 4.0 & 5.0 & 2.6 \\ Elevator car & 1.784 & 2.0 & 2.6 \\ Window & - & 0.6 & 0.75 \\ Opening between shaft & - & 0.4 & 0.3275 \\ and lobby & - & 0.3 & 0.3 \\ Opening between shaft & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \\ and room & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \\ \end{tabular}
\end{table} 
Table 3: Geometric parameters of the building for model validation [29]. and CFD underpredicted the pressure difference. There was no pressure fluctuation in the empirical model because the model could not consider the elevator car passing the clearance openings between the shaft and the lobbies on each floor. In general, both the empirical model and CFD provided pressures in agreement with each other. The measured maximum pressure difference was 16.1 Pa when the car started, while the empirical model calculated 13.5 Pa, and the CFD reported 15.25 Pa.