# Numerical Investigation of Jet Angle Effect on Airfoil Stall Control
## 3 Results and Discussion
### Static Airfoil Simulations
#### 3.1.2 Flow Control  
The steady-blowing jet is applied to the OA209 airfoil to control the flow separation. The range of the angle of attack is \(0^{\circ}\leq\alpha\leq 20^{\circ}\). Two jet angles are applied to the OA209 airfoil: \(\theta_{jet}=80^{\circ}\) for the chord-normal jet and \(\theta_{jet}=22^{\circ}\) for the tangential jet. The jet momentum coefficient is \(c_{\mu}=0.06\) for both the jet actuations. The jet outlet is located at \(x_{jet}/c=0.1\) on the suction side. The aerodynamic lift, moment and drag coefficients are compared in Figure 7. Tangential jet enhances the lift and reduces the magnitude of the moment. However, the chord-normal jet reduces significantly the aerodynamic lift and the moment, undermining the performance of the baseline airfoil. Furthermore, the chord-normal jet causes a severe drag penalty, whereas the tangential jet is able to increase the lift without a significant increase in the drag. Flow fields of around the OA209 airfoil at \(\alpha=14^{\circ}\) and \(17^{\circ}\) are shown in Figures 8 and 9, respectively. The velocity in the chord-wise direction \(u_{x}\) and the spanwise vorticity \(\omega_{z}\) are used for the visualization. Please note that \(\alpha=14^{\circ}\) is close to the maximum lift angle in both the simulation and the test (see Figure 3). The overall baseline flow is attached on the airfoil at \(\alpha=14^{\circ}\) with a noticeable shallow separation near the trailing edge. The external flow is significantly deteriorated with the chord-normal jet which penetrates the boundary layer, forming a virtual wall. In contrast, the tangential jet remains successfully in the boundary layer. It can be expected that an additional momentum is provided directly into the boundary layer when the jet is ejected at an angle close to the direction of the flow. The vorticity field indicates that the tangential jet resides in the boundary layer with a minimum impact on the boundary layer thickness. Figure 6: Comparison between the clean and the tangentially slotted airfoils. Figure 8: Time-averaged flow field around the OA209 airfoil with and without steady-blowing jets. \(Ma=0.3\), \(Re=1.15\) M, \(c_{\mu}=0.06\) and \(\alpha=14^{\circ}\). Figure 7: Static OA209 airfoil with and without steady-blowing jets. \(Ma=0.3\), \(Re=1.15\) M, \(c_{\mu}=0.06\). The baseline stall is clearly visible at \(\alpha=17^{\circ}\) with the negative-velocity region and the large stall vortex on the aft airfoil (see Figure 9). The separated flow is well attached on the airfoil with the tangential jet even at this high angle of attack. The vorticity field with the tangential jet at \(\alpha=17^{\circ}\) is visually similar to the baseline and the tangential-jet case at \(\alpha=14^{\circ}\), yielding the similar lift \(C_{l}\simeq 1.2-1.4\). The gain in the flow momentum due to the jet can be diagnosed with the shape factor \(H\) of the suction-side boundary layer. The shape factor is the ratio between the displacement thickness \(\delta^{*}\) and the momentum thickness \(\theta\) in the boundary layer, i.e., \(H=\delta^{*}/\theta\). A small value of \(H\) indicates that the momentum of the boundary layer is high enough to withstand an adverse pressure gradient. As shown in Figure 10, the value of \(H\) for the chord-normal jet case is over 300 at \(\alpha=14^{\circ}\). In contrast, \(H\) for the tangential jet case is even lower than the baseline without flow control. Thus, the tangential jet can help to avoid the separation by providing additional momentum into the boundary layer directly. At \(\alpha=17^{\circ}\), the OA209 airfoil is completely stalled with the separation point at \(x/c=0.2\). The tangential jet delays the separation to the mid-chord point, significantly reducing the value of the shape factor, i.e., adding the momentum into the boundary layer without a significant increase in the thickness. The suction side is prone to separation when the shape factor is about 4 in the current simulation.