# Study of Airfoil Deflections for Unsteady Aerodynamics Optimization in Pitching Airfoils +
## 2 Materials and Methods
### Pitching Parameters
The computational domain was meshed using ANSYS-ICEM-CFD using a y+ = 1 near the airfoil surface to provide the required mesh resolution for the turbulence and transition models employed in the computations. Starting from an initial mesh consisting of 558,880 nodes and 1,016,440 elements, a grid independence study based on the surface pressure distribution was performed. The final mesh with 1,157,640 nodes and 1,279,760 hexahedral elements yielded grid-independent results and was used for all computations. The first set of airfoil performance for the pitching VR-12 airfoil includes data of the baseline VR-12 shape, the trailing edge deflection of 2.5\({}^{\circ}\), the leading edge deflection of 6\({}^{\circ}\), and a  
Figure 3: Pitching airfoil terminology. combination of the leading edge deflection of 6\({}^{\circ}\) and the trailing edge deflection of 2.5\({}^{\circ}\). These tests were performed to see how these different static airfoil deflections perform over an entire pitching regime. The first set of tests were performed by pitching the airfoils from \(-2^{\circ}\) up to 14\({}^{\circ}\), with a frequency of 4.8 Hz based on the reduced frequency 0.04. These conditions were chosen based on nominal operation conditions for a rotorcraft at a cruise with an average load. The unsteady Reynolds-Averaged Navier-Stokes computations for these cases were performed using ANSYS CFX, employing the SST k-\(\omega\) two-equation turbulence model coupled with \(\gamma-Re_{\theta}\) transition model. Figure 4 shows the computed C\({}_{\rm J}\), C\({}_{\rm d}\), and C\({}_{\rm I}\)/C\({}_{\rm d}\) time-averaged results over 12 pitching cycles along with their time series to illustrate the cycle-to-cycle variations with time. It is noted that these results represent the mean value over several cycles and show their repeatability from cycle to cycle. These data were used as the initial setting as to what deflection of the leading and trailing edges is going to be needed at what angles of attack in order to eventually optimize the airfoil shape dynamically to control the C\({}_{\rm I}\)/C\({}_{\rm d}\) performance (although the dynamic morphing flow effects are not considered in this investigation). These data show that on the upstroke from \(\alpha=-2\) to 4\({}^{\circ}\), the trailing edge deflection of 2.5\({}^{\circ}\) is the most optimal, from 4 to 5.5\({}^{\circ}\), the combination of leading edge deflection 6\({}^{\circ}\) and trailing edge deflection of 2.5\({}^{\circ}\) is the most optimal, and from 5.5 to 14\({}^{\circ}\)\(\omega\), the leading edge deflection performed the best. Then, on the downstroke from \(\alpha=-14\) to 11\({}^{\circ}\), the leading edge deflection of 6\({}^{\circ}\) is the most optimal, from \(\alpha=11\) to 7\({}^{\circ}\), the combination of leading edge deflection of 6\({}^{\circ}\) and trailing edge deflection of 2.5\({}^{\circ}\) is most optimal, and from \(\alpha=7\) to \(-2^{\circ}\), the trailing edge deflection of 2.5\({}^{\circ}\) is most optimal. The improvements from each case can be calculated from the percentage difference of C\({}_{\rm I}\)/C\({}_{\rm d}\) between configurations at a given angle. As such, the overall improvement of the LE deflection (blue lines) configuration provides about 10% improvement with respect to the baseline (red lines) at the higher angles of attack, followed by the combined LE&TE deflection configuration, which provides 8%. These data are summarized in Table 1 below. Figure 4: Computed coefficients of lift, drag, and lift over drag vs. \(\alpha\) and time at Re = 250,000: C\({}_{\rm I}\) (**a**), C\({}_{\rm d}\) (**b**), C\({}_{\rm I}\)/C\({}_{\rm d}\) (**c**) for deflected airfoils during pitching (\(k=0.04\)). Again, the results of these tests do not consider the dynamic morphing of the airfoil surfaces, which will inevitably have an effect on the performance of the airfoil. The statically morphed pitching airfoil tests show that a regime can be developed where a vast improvement is seen over the entire regime when compared to the baseline airfoil.