# Numerical Investigation of Jet Angle Effect on Airfoil Stall Control
## 3 Results and Discussion
### Pitching Airfoil Simulations
#### 3.2.2 Flow Control  
The steady-blowing jet is applied to the OA209 airfoil under the deep dynamic stall. The two jet angles, \(\theta_{jet}=80^{\circ}\) and \(\theta_{jet}=22^{\circ}\), are used, same to the static case. As shown in Figure 15, the lift is significantly enhanced both in the upstroke and the downstroke by the tangential jet. Entire lift coefficients are improved, compared to the baseline during the upstroke. Additionally, the lift recovers at higher angles around \(\alpha=14^{\circ}\), compared to the recovery angle \(\alpha\approx 10^{\circ}\) in the baseline. The lift and moment loops in the baseline include one major stall, whereas these loops in the tangential-jet case include two major stalls, showing two distinct peaks in each loop. Although the significant rise in the  
Figure 14: A supersonic pocket near the leading edge in the upstroke. Figure 13: Pitching OA209 airfoil in the test [38] and current simulations. \(Ma=0.3\), \(Re=1.15\) M, \(k=0.05\) and \(\alpha=13^{\circ}\pm 7^{\circ}\). lift is worthwhile, additional event of the dynamic stall due to the tangential jet is not desirable in the control aspect. The amplitude of the negative moment peak is not reduced with the tangential jet. As the lift stall is delayed with a higher lift peak with the tangential jet, the drag divergence is also delayed in the upstroke, which is expected as a common feature of dynamic stall [4]. The chord-normal jet reduces the lift significantly. The degrade in the lift is similar to the static case. The moment coefficient around \(c_{m}\simeq-0.1\) in the pitch cycle without a distinct peak, which is preferable in rotor blade control. The low oscillatory moment, however, comes with a detrimental lift reduction--the hysteresis lift is even lower than the downstroke lift of the baseline. The evolution of the vorticity \(\omega_{z}\) around the pitching OA209 airfoil is compared, as shown in Figure 16. The zero phase \(\phi=0\) corresponds to the mid-upstroke angle \(\alpha=13^{\circ}\). The onset of DSV due to the leading edge separation is visible at \(\alpha=15.4^{\circ}\) in the upstroke of the baseline. The tangential jet delays the DSV onset which occurs around \(\alpha=17^{\circ}\) when the DSV in the baseline is being detached from the airfoil. The DSV in the case of the tangential jet separates from the airfoil after \(\alpha=18^{\circ}\) in the upstroke. Around the peak angle \(\alpha=20^{\circ}\), the tangential jet is dynamically interacted with stall vortices. For example, at \(\alpha=20^{\circ}\), the tangential jet penetrates deeply the re-circulation region. It is interesting to notice the similar presence of the jet in the massively separated region at both the peak and the downstroke angle \(\alpha=17.5^{\circ}\). The interaction between the tangential jet and the separating flow may induce the formation of the secondary DSV at \(\alpha=19.8^{\circ}\) in the downstroke. The maximum size and the strength of the secondary DSV are anticipated to be similar to those of the initial DSV, based on the secondary moment and lift stalls in the case of the tangential jet (see Figure 15). The tangential jet helps the external flow to reattach on the airfoil around \(\alpha=15.4^{\circ}\) in the downstroke, which is even before the mean pitch angle (also the static stall angle without flow control). The suction-side  
Figure 15: Pitching OA209 airfoil with and without steady-blowing jets. \(Ma=0.3\), \(Re=1.15\) M, \(c_{\mu}=0.06\), \(k=0.05\) and \(\alpha=13^{\circ}\pm 7^{\circ}\). boundary layer without the flow control is still in the re-attachment process at the mean pitch angle \(\alpha=13^{\circ}\). Figure 16: Vorticity \(\omega_{z}\) field for the pitching OA209 airfoil with and without steady-blowing jets. \(Ma=0.3\), \(Re=1.15\) M, \(c_{\mu}=0.06\), \(k=0.05\) and \(\alpha=13^{\circ}\pm 7^{\circ}\). The chord-normal jet causes a massive flow separation near the jet location during the overall pitch cycle.