# Numerical Assessment of Side-Wind Effects on a Bus in Urban Conditions
## 3 Results
### Validation  
To compare the drag losses with other literature data, drag coefficient (\(C_{D}\)) is used, which is calculated by the following equation:  
\[C_{D}=2\cdot F_{X}\cdot\left(A\cdot\rho\cdot v_{c}^{2}\right)^{-1} \tag{2}\]  
where \(F_{X}\) is the sum of the force components, \(A\) is the projection area, \(v_{c}\) is the velocity of the bus in the cruising direction, and \(\rho\) is the density of air (1.225 kg/m\({}^{3}\)). The drag coefficient is only constant above a certain speed, around 100 km/h, and the \(C_{D}\) of a bus is relatively high 0.66 [25]. Based on the geometry of the bus at lower speeds, the \(C_{D}\) value could significantly decrease [26]. With the application of moving ground and wheels,  
Figure 10: Vertical velocity distributions at 20 km/h on the symmetry plane for (**a**) symmetrical flow and (**b**) 2 m/s side wind.  
[PERSON] et al. [27] attained \(C_{D}\) = 0.43 with numerical and experimental methods. \(C_{D}\) values, together with their standard deviations (due to its unsteady behaviour) from this study and other studies in the literature, are listed in Table 4.  
The abovementioned combined results of numerical and experimental measurements are in good agreement with the current numerical results, considering that experimental results are rare in this velocity regime due to the decreased confidence of the force measuring appliances. Nevertheless, experimental measurements show that by decreasing the speed, the \(C_{D}\) lowers [29].  
With particle image velocimetry (PIV), [PERSON] et al. [30] showed similar vertical flow patterns as that presented in Figure 10a, in which the lower recirculation bubble core is near the bottom edge of the bus, while the upper recirculation bubble has a longitudinal shape. However, the horizontal velocity distribution altered since, in this study, the rear wake region had unstable borders due to low speed.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Drag Coefficient** & **Comment** & **Source** \\ \hline
0.362 \(\pm\) 0.009 & 10 km/h & Current study \\
0.380 \(\pm\) 0.008 & 15 km/h & Current study \\
0.389 \(\pm\) 0.010 & 20 km/h & Current study \\
0.65 & 36 km/h & [PERSON] [26] \\
0.43 & 80 km/h & [PERSON] et al. [27] \\
0.66 & 100 km/h & [PERSON] et al. [25] \\
0.65 & 120 km/h & [PERSON] et al. [28] \\
0.41 & modified & [PERSON] et al. [28] \\ \hline \hline \end{tabular}
\end{table}
Table 4: Drag coefficients.  
Figure 11: Q-criterion distribution on (**a**) the bus and (**b**) near wheel; (**c**) symmetrical flow; (**d**) asymmetrical flow.  
In the work of [PERSON] et al. [16], where rotating wheels were assessed, it was shown that in tyres with simplified wheel geometry, the \(Q\)-criterion had a similar pattern. With more details on the tyre, the vorticity region would become larger.  
When velocity distribution of y-z vertical sections was assessed at x = 12.5 m, 13 m, and 14 m (see Figure 12), similar results were achieved as those reported in previous studies [15]. A comparison of the different sections indicates that, at the lower edge of the bus, longitudinal vortices were formatted. This similarity can be found in the work of [PERSON] et al. [15], though they showed higher velocities at the near ground level, while PIV measurement [30] indicates that similar longitudinal vortices occurred in this region (see Figure 12b). It is also notable that the mentioned lower vortices were moving upward, which corresponds to Figure 12c. These wake structures were also described in the work of [PERSON] et al. [31].