# Unsteady Flow Characteristics of an Oscillating Piezoelectric Fan Blade at High Reynolds Numbers
## 2 Experiment Methodology  
The experiment system for the flow field visualization is shown in Figure 1. The PZT fan (Sinocera Piezotronics, Yangzhou, China) is mounted at the bottom of a container box in the central position. The container box is made of transparent acrylic glass for observation and illumination. The space inside the container is large enough (300 mm \(\times\) 300 mm \(\times\) 300 mm) to avoid the sidewall effect. The container box is sealed so the outside environment can not interfere with the flow field inside this box. The container box is fixed on an \(x\)-\(y\) translation stage driven by two stepper motors (GCD-202002M, Daheng Optics, Beijing, China) with a resolution of 0.001 mm. The translation stage is used to adjust the position of the PZT fan blade relative to the laser sheet. The performance of the PZT fan blade can be correlated to the vibrating frequency \(f\) and tip-to-tip amplitude \(A\). In order to achieve the maximum amplitude, the vibrating frequency is fixed at the resonance frequency \(f_{\mathrm{r}}\) = 58 Hz. The tip-to-tip vibration amplitude can be adjusted by changing the AC voltage applied to the PZT actuator. In this study, we select a series of different voltages to reach different vibration amplitudes in the range of 4.77 mm \(<A<\) 18.72 mm. The vibrating tip-to-tip amplitude \(A\) is measured optically by a pixel-analysis method, the tip position is determined by marking the pixels where the blade tip is at its maximum amplitude. The uncertainly of the pixel-analysis method is \(\pm\)0.09 mm, corresponding to 1 pixel in the image. The characteristic tip velocity of the PZT fan is defined as:  
\[U_{\mathrm{t}}\ =\ 2 fA \tag{1}\]  
which is the average velocity of the trailing edge in a cycle. The geometrical parameters of the PZT fan blade include the length \(l_{\mathrm{b}}\), the width \(w_{\mathrm{b}}\) and the thickness, \(l_{\mathrm{b}}\). The geometrical parameters of the PZT fan blade are fixed in this study with \(l_{\mathrm{b}}\) = 65 mm, \(w_{\mathrm{b}}\) = 15 mm and \(l_{\mathrm{b}}\) = 0.1 mm (See Figure 2), resulting in an aspect ratio (\(AR\) = \(w_{\mathrm{b}}/l_{\mathrm{b}}\)) around 0.23. We adopted the definition of oscillatory Reynolds number \(Re\)[16] as:  
\[Re\ =\ \frac{U_{\mathrm{t}}w_{\mathrm{b}}}{4v}\ =\ \frac{fAw_{\mathrm{b}}}{2v} \tag{2}\]  
Figure 1: Schematic of PIV experiment setup. where \(\
u\) = 14.8 \(\times\) 10\({}^{-6}\) m\({}^{2}\)/s is the kinematic viscosity of the air. The oscillatory Reynolds number in this study is in the range of 140 \(<Re<\) 550. The sinusoidal voltage for actuating the PZT fan blade is generated by a function generator (SDG 1062X, SIGLENT, Shenzhen, China) and an amplifier (ATA-2042, Aigtek, Xi'an, China). A 527-nm double-pulse Nd:YLF laser (Vlite-Hi-527-40, Beam Tech, New Taipei, China) is used to illuminate the measurement region. The laser beam is expanded into a one-millimeter-thick laser sheet in the focused area. A high-speed camera (FASTCAM Nova S12 type 200 KS-M-32G, Photron, Tokyo, Japan) is used to record the images. A laser pulse synchronizer (TSI Model 6130036 LASERPULSE) is used to control the pulsed laser and the high-speed camera. The interval time \(\Delta t\) between two laser pulses is set at 60 \(\upmu\)s, i.e., the interval time between two PIV images in a pair is 60 \(\upmu\)s. In this study, the maximum induced air velocity is less than 2 m/s, corresponding to 0.12 mm of particle displacement, so the time is short enough to enable the velocity calculation. The capture rate is set to 5800 Hz, which is 100 times of the oscillating PZT fan's frequency \(f\). In this way, 100 pairs of PIV images can be acquired within a single period of oscillation, equivalent to 5800 pairs of PIV images per second. The image resolution was set to 1024 \(\times\) 1024 pixels with 12 bits per pixel. Seeding particles were generated by a Laskin nozzle oil droplet generator using olive oil. The air-oil droplet mixture is settled for 5 min before the PZT fan is actuated.