# Study of Airfoil Deflections for Unsteady Aerodynamics Optimization in Pitching Airfoils +
## 2 Materials and Methods  
### Deflection Parameters  
Deflection of the leading and trailing edge regions of a standard Boeing VR-12 airfoil shape is investigated in order to improve the performance as angle of attack (\(\alpha\)) changes. The initial analysis is performed using potential flow solver XFLR5 [25] as a method of rapid testing of different shape alterations to the standard ('baseline') VR-12 airfoil, with a goal of finding optimal shapes as function of \(\alpha\). Ultimately, the deflections could improve performance in different flow conditions by transforming the airfoil into a new airfoil shape on demand by continuous or 'dynamic' morphing. In line with this goal, various LE and TE deflection angles and locations along the chord were tested to down select optimum deflections that provide improvements in lift and drag for the VR-12 airfoil. In order to manufacture the experimental model of the shape-morphing airfoil, it was decided to maintain the general shape of the VR-12 airfoil and limit deflections to LE and TE. The selected shapes are then investigated experimentally and with Reynolds-Averaged Navier-Stokes (RANS) numerical simulations using ANSYS CFX 18.2 [26]. The selection process was started by determining the optimal shapes for the deflected airfoils as a function of \(\alpha\). The shape change selection through these calculations for the airfoils is presented in this section. The TE and LE deflections introduced to the baseline airfoil are shown in Figure 1. Note that the profile coordinates for the airfoil ca n be readily found on various websites and in the literature, such as in Ref. [27]. Based on previous studies [5; 8; 15], a LE deflection at 25% chord and a TE deflection at 85% chord were selected as the initial deflection locations. The deflection angles are measured with respect to the chord line, in clockwise and counterclockwise directions for TE and LE deflections, respectively. The effects of these deflections on lift and drag coefficients were analyzed at Re = 250,000 using XFLR5 software v.6.4 corresponding to the nominal conditions of the experimental facility. The LE and TE deflection angles of 1 through 12 degrees with one-degree increments were computed for an angle of attack range of \(-10\) to 30 degrees based on previous research [2; 5; 15]. The design process starts by evaluating the effectiveness of various static deflections at different angles of attack by comparing their lift and drag coefficients. The performances of having'static' deflection for either the LE or the TE and for the combined LE/TE are compared. This procedure establishes the optimal camber shape at each angle of attack. The main findings regarding deflection optimization are described in the following and summarized in Figure 2, where various deflection configurations are shown for comparison. The computed variations of coefficients of lift, drag and their ratios, with \(\alpha\) for airfoils with select deflection angles, indicate that the LE deflection increases the maximum lift coefficient, C\({}_{\text{lmax}}\), and delays (increases) stall angle, with the most extreme deflections delaying stall until \(\sim\)20 degrees. The TE deflection also showed an increase in C\({}_{\text{lmax}}\) with increasing deflection angle; however, the stall angle of attack is reduced as the deflection angle is increased. These observed variations are due to the increased camber of the airfoil with increased deflection angles compared to the baseline airfoil [17; 28]. The variations of the drag coefficient, C\({}_{\text{d}}\), with \(\alpha\) indicate that the LE deflection lowers the drag coefficient at higher angles of attack and the TE deflection reduces drag at lower angles of attack. Unlike the lift coefficient, the TE deflection has less effect on the drag coefficient when compared to the LE deflection.