# Study of Airfoil Deflections for Unsteady Aerodynamics Optimization in Pitching Airfoils +
## 2 Materials and Methods
### Wind Tunnel and Particle Image Velocimetry System  
Experiments are carried out in a NDSU wind tunnel driven by an upstream blower with a variable frequency drive and designed to achieve speeds up to 60 m/s (Mach-0.17) with turbulence levels \(\sim\)0.5-1% and flow uniformity with minimal wall effects in the test section [21]. The design is modular, allowing for removal or insertion of flow conditioning devices such as screens and honeycombs for turbulence conditioning. It also has a section upstream of the contraction to allow for seeding of Di-Ethyl-Hexyl-Sebacate (DEHS) particles from spray nozzles into the test section for particle image velocimetry (PIV) [24]. The front and top test section walls are made of clear acrylic to allow for optical access for laser illumination and camera viewing. The rear and bottom walls are modular aluminum panels that allow for mounting of various models in the test section. Fundamentally, the two-dimensional (2D) PIV technique used here captures two sequential 2D particle image instances of the flow field, typically separated by a few microseconds. Cross-correlation can then be used to determine the displacement of particle ensembles in the flow. Once displacement and time separation are known for each particle ensemble, velocity can be determined. In this study, velocity fields are captured on the suction side with a global view, a leading edge view, and a trailing edge view to assess the dynamic stall features at several pitching angles and tandem configurations. It is important to note that although this is an oscillating system due to airfoil pitching, the point of interest is at specified angles of attack. The control system described in the pitching system design was incorporated to consistently capture data at a desired moment of actuation. This requires the relatively low repetition rate (compared to the flow and pitching frequencies) of the PIV system (laser/camera) to be synchronized in order to capture data at the desired point/phase (i.e., 'phase-locked'). When using phase-locked strategies to perform averages (e.g., 'phase-average'), it should be noted that repeatability of the flow during a particular phase is unknown, and it should be assessed, for example, using standard deviation analyses or reduced-order models, such as proper orthogonal decomposition (POD) [34], that can assess the phase-coherence levels within and between cycles. Nonetheless, for the current purpose of proof of concept, these analyses are not performed, and it will be shown that average data analysis suffices to assess the main differences of each deflected configuration. The fundamental setup of the PIV system can be seen in Figure 8a, and photography of an actual setup can be seen in Figure 8b, with three cameras here covering the tandem configuration field of views. The test section of the wind tunnel is illuminated by a double-pulsed Nd:YAG laser emitting two laser pulses of up to 100 mJ at a wavelength of 532 nm with a repetition rate of 15 Hz. The laser beam is directed to the test section using prismsand shaped to a laser sheet (thickness < 1 mm) by using spherical and cylindrical lenses that center it in the middle of the wind tunnel. The flow is seeded with atomized DiEthyl-Hexyl-Sebacate oil droplets to achieve particles with less than 1 \(\upmu\)m characteristic diameter. The flow is imaged by three LaVision IMAGER LX 2M cameras with a resolution of 1608 \(\times\) 1208 and interframe capability of 200 ns set up with their axis perpendicular to the laser sheet for image acquisition in various regions of interest, as shown in Figure 8b. For the desired flow speed and dynamic ranges expected, the time between images taken was set to \(\Delta\)t = 10 \(\upmu\)s. In this setting, one camera captures a global view of the full wing, while the others capture the LE and TE regions. The cameras and the Nd:YAG lasers are connected to a workstation and controlled with a LaVision Inc. (Ypsilanti, MI, USA).