# The PIV Measurements of Time-Averaged Parameters of the Synthetic Jet for Different Orifice Shapes
## 2 Methods  
The circle, slot, and square orifices printed with PETG (polyethylene terephthalate glycol-modified) were fastened in the PMMA actuator body (Figure 1). The thickness of the orifice wall was 2 mm. The characteristic parameters of the SJ orifices are presented in Table 1. The diameter of the actuator cavity was 150 mm, and the height was 20 mm. The STX M.18.200.8.MCX loudspeaker with a nominal impedance equal to 8 \(\Omega\), sensitivity (2.83 V/1 m) equal to 89 dB, and a nominal resonance frequency equal to 37 Hz was used as an actuator in the SJA. The same actuator body, loudspeaker, and orifices were used in [26], where the characteristic frequency of the SJA was designated as \(f=44\) Hz in the case of the circle and the square orifice and \(f=54\) Hz in the case of the slot orifice. The ratio \(d/D=0.17\) (where \(d\) is the equivalent diameter of the actuator orifice (mm), and \(D=130\) is the diameter of the effective area of the loudspeaker (mm)) was used to calculate the diameter of the circle orifice. The value \(d/D=0.17\) is in the range for which [PERSON] and [PERSON] [28] found the optimal diameter for the SJ actuator. The actuator was supplied with a sinusoidal signal from the signal generator GWIN-STEK AFG-2225 and amplified by an EMOTIVA A2 amplifier. The true-RMS current and voltage were measured with GWINSTEK GDM-8351. Instantaneous SJ velocity fields were measured by using PIV from Dantec Dynamics. The laser sheet was generated with the Litron Bernoulli series laser system with two pulsed and Q-switched Nd: YAG laser resonators, producing visible green 532 nm laser light. The laser had a maximum output energy equal to 200 mJ per pulse and a repetition rate equal to 15 Hz. The thickness of the laser sheet was approximately 1 mm. The laser sheet covers the camera field of view and passes through the orifice radial coordinate presented \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Office** & **Dimension (mm)** & \(A\) (mm\({}^{2}\)) & \(d\) (mm) & \(U_{e}\) (m/s) & \(f\) (Hz) & \(Re\) & \(L_{0}\) & \(St\) \\ \hline Circle & \(d=22.4\) & 394 & 22.4 & 3.37 & 75 & 5000 & 2 & 0.5 \\  & & & & 3.37 & 15 & 5000 & 10 & 0.1 \\ Square & \(a=b=20\) & 400 & 22.57 & 3.35 & 74 & 5000 & 2 & 0.5 \\ Slot & \(a=10\), \(b=40\) & 400 & 22.57 & 3.35 & 14.8 & 5000 & 10 & 0.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Geometric and operation parameters of SJA. Figure 1: Synthetic jet actuator with various orifice shapes: circle, square, and slot. in Figure 2; the axial coordinate, \(x\), passes through the orifice centerline and starts at the orifice exit plane. The images were acquired with an Imperx B3440 CCD camera with a sensor resolution of 3388 \(\times\) 2712 pixels at 17 fps, and each pixel depth equals 12 bits. The camera used a lens with a 50 mm focal length, and the aperture was set to 1.8. The field of view is equal to 256 mm \(\times\) 205 mm; thus, the resulting resolution for the digital image is 13.2 pixels/mm. A component of the PIV system was synchronized with the use of the Dantec Dynamics High-Performance Synchronizer with 32 independent outputs. The air was seeded with DEHS oil droplets with a nominal diameter of approximately 2 \(\upmu\)m. The SJA was closed in a 1000 \(\times\) 500 \(\times\) 500 mm transparent box to prevent the spread of DEHS and to ensure adequate seeding concentration in the measuring area. Measurements were performed on the STANDA optical table equipped with vibration dampers. The entire test stand and its components are shown in Figure 3.  
The adaptive PIV algorithm was used to calculate velocity vectors, and the interrogation area was automatically chosen between the 32 \(\times\) 32 and 64 \(\times\) 64 pixel range. The final vector map has 210 \(\times\) 168 vectors, which correspond to the spatial resolution of a single vector equal to 1.22 \(\times\) 1.22 mm. A validation algorithm was applied for the rejection of the outlier vector, and the relative value of the rejected vector was less than 3%.