## 3 Results and Discussions
### Active Flow Control
#### 3.2.2 Influence of Jet Angle  
The second computational effort was carried out to investigate the evolution of the aerodynamic drag coefficient as a function of jet angle with different flow control techniques. The jet angles are changed as \(\beta=30^{\circ}\), \(45^{\circ}\), \(60^{\circ}\) and \(90^{\circ}\), respectively. The control frequency is kept at \(\mathrm{f_{c}}=34\) Hz for the synthetic and unsteady jets. The results obtained with jet angle of \(\beta=45^{\circ}\) have been presented in Section 3.2.1. The time-averaged drag coefficients at different jet angles are displayed in Table 2.  
The results in Table 2 show that, in all actuated flow, the drag coefficient reduction achieved with jet angle of \(\beta=90^{\circ}\) is the smallest. The optimal jet angle of \(\beta=45^{\circ}\) is determined when steady blowing and unsteady jets are applied. This is consistent with the numerical results obtained from the work of [PERSON] [12] and [PERSON] et al. [13]. In contrast, \(\beta=60^{\circ}\) is recognized as the optimal jet angle with a synthetic jet, and a drag reduction of \(2.81\%\) is achieved. The time-averaged normalized velocity contours and the streamlines at various jet angles with all actuated cases are shown in Figures 17-19. Figure 17a displays the presence of secondary small vortices located close to the rear surface of the model when a steady blowing jet with jet angle of \(\beta=30^{\circ}\) is applied, formed by the wall effect. The formation of these vortices seems to increase the drag coefficient obtained on the model. This phenomenon is not observed when using a synthetic jet (Figure 18a) and an unsteady jet (Figure 19a) at \(\beta=30^{\circ}\), because of the weak interaction between the control jet and the rear surface of the model. In the cases of steady blowing and unsteady jets at the angle of \(\beta\) = \(60^{\circ}\), the recirculation zones in the near-wake region are reduced (Figures 17b and 19b), but their size is still larger than the one in the cases with jet angle \(\beta=45^{\circ}\) (Figure 12a,c). Meanwhile, the application of a synthetic jet with a jet angle \(\beta=60^{\circ}\) contributed to a significant reduction in the size of the recirculation zones and displaced them away from \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Steady Blowing Jet** & \(\beta=30^{\circ}\) & \(\beta=45^{\circ}\) & \(\beta=60^{\circ}\) & \(\beta=90^{\circ}\) \\ \hline \(\mathrm{C_{D}}\) & 0.219 & 0.183 & 0.197 & 0.241 \\ \(\mathrm{\Delta C_{D}}\) (\%) & 12.05 & 26.51 & 20.88 & 3.21 \\ \hline
**Synthetic Jet** & \(\beta=30^{\circ}\) & \(\beta=45^{\circ}\) & \(\beta=60^{\circ}\) & \(\beta=90^{\circ}\) \\ \hline \(\mathrm{C_{D}}\) & 0.253 & 0.246 & 0.242 & 0.259 \\ \(\mathrm{\Delta C_{D}}\) (\%) & \(-1.61\) & 1.2 & 2.81 & \(-4.02\) \\ \hline
**Unsteady Jet** & \(\beta=30^{\circ}\) & \(\beta=45^{\circ}\) & \(\beta=60^{\circ}\) & \(\beta=90^{\circ}\) \\ \hline \(\mathrm{C_{D}}\) & 0.245 & 0.229 & 0.231 & 0.247 \\ \(\mathrm{\Delta C_{D}}\) (\%) & 1.61 & 8.03 & 7.23 & 0.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Drag coefficient reduction with different actuator types at various jet angles. Figure 16: The normalized streamwise contour at the iso-surface Q = 300,000 s\({}^{-2}\) with different actuator types. (**a**) A steady blowing jet; (**b**) a synthetic jet; (**c**) an unsteady jet. the rear surface of the model (Figure 18b), resulting in the largest drag reduction compared with the cases of the jet angle of 45\({}^{\circ}\) and 30\({}^{\circ}\). In addition, for all actuated cases, the control jet at an angle of \(\beta=90^{\circ}\) insignificantly deviated the streamlines, leading a wide transversal wake section. Hence, the aerodynamic drag reduction is minimum compared to the one with different jet angles of a control device (Figures 17c, 18c and 19c).