# Study of Airfoil Deflections for Unsteady Aerodynamics Optimization in Pitching Airfoils +
## 3 Results and Discussion
### Demonstration of Tandem System
We also note that the broad effect of having an airfoil in front of another is threefold (front wake flow, actual \(\alpha\), and blockage), which is affected by their distancing. While the velocity field generated from the pitching wing ahead is associated with the much more chaotic separation and wake flow than a free stream flow, the velocity magnitude is much lower and the effective Reynolds number and angle of attack diminished. At the distancing studied, the effect of blockage is similar in all cases in the higher back-wing \(\alpha\) cases and much less pronounced at lower \(\alpha\) values, as expected. The data illustrate how these factors influence the in-phase scenarios, preventing stall even with baseline at the maximum phase (Figure 13a), but still more so with LE deflection (Figure 13b), with the out-of-phase scenario showing full dynamic stall (Figure 15) regardless of the wing deflection. The TE and LE/TE deflections showed less benefits, and are omitted from the cases presented (fully reported in ref. [21]). The effect of the various deflections during tandem is shown for the in-phase case in Figure 13 during the maximum phase of the downstream airfoil (22\({}^{\circ}\)), with the LE deflected airfoil appearing to have the best performance. As can be clearly seen, the stall wake is the smallest with the least amount of recirculation for this LE deflection case (Figure 13b). Both the LE and TE deflected combination and the TE deflected airfoil performed similarly to each other, with what appears to be attached flow up until about the 25% chord length (Figure 13c,d). At this point, the flow separates quickly, follows an upward motion clearly marked by 70% of the maximum velocity ('yellow' velocity contour region) and the upward direction of the vectors, and forms larger wakes with downward motions and recirculation (blue contoured regions). These motions are opposite to the baseline and LE deflected airfoil flows. It is worth noting that when compared to the single airfoil, the overall performance is improved for the aforementioned 'tandem-effect' reasons. Figure 13: Velocity fields for linear tandem airfoils pitching in phase at 22\({}^{\circ}\) max-\(\alpha\): baseline **(a)**, LE deflected **(b)**, TE deflected **(c)**, and LE/TE deflected **(d)**. Center of pressure and pitching is at x/c = y/c = 0.2 for the upstream wing and at x/c = 3.2 and y/c = 0.2 for the downstream wing. Figure 14: Velocity fields for linear tandem airfoil pitching in phase at 16\({}^{\circ}\)\(\alpha\) (\(\downarrow\)): baseline (**a**), LE deflected (**b**). Center of pressure and pitching is at x/c = y/c = 0.2 for the upstream wing and at x/c = 3.2 and y/c = 0.2 for the downstream wing. Figure 15: Velocity fields for linear tandem airfoil pitching out of phase \(-10^{\circ}\) (front wing) and 22\({}^{\circ}\) max (back wing) \(\alpha\): baseline (**a**), LE deflected (**b**). Center of pressure and pitching is at x/c = y/c = 0.2 for the upstream wing and at x/c = 3.2 and y/c = 0.2 for the downstream wing. Note that the phase-averaged flow between the two wings is repeatable in all these cases, ensuring that comparisons between the four cases have matched upstream conditions. The other phase shown for the in-phase arrangement is the \(16^{\circ}\) pitching down (Figure 15) and reveals a different pattern near the LE deflected airfoil, delaying the onset of low speed and separation point along the suction surface. In the case of the out-of-phase pitching, more unsteady interactions are observed for the \(22^{\circ}\) case shown in Figure 15, where the flow can be seen to have a large separation/recirculation across the suction side of the airfoil, reflecting that dynamic stall is occurring (the region just after the first wing TE is  
Figure 16: Velocity fields for linear tandem airfoil pitching out of phase \(-4^{\circ}\)\(\alpha\) (\(\uparrow\)) (front wing) and \(16^{\circ}\)\(\alpha\) (\(\downarrow\)) (back wing) \(\alpha\): baseline (**a**), LE deflected (**b**).