1. Introduction
Thermal management has become one of the important design considerations for electronics as devices keep reducing in size [
1]. Due to the limited space, the natural convection is ineffective for heat dissipation, and this makes an extra cooling device crucial in this scenario [
2]. Comparing to conventional rotatory fans in the field of electronic cooling, piezoelectric (PZT) fans have received more attention in recent years because of the advantages of low power consumption, high reliability and the small geometric deformation to generate a significant airflow [
3,
4]. A typical PZT fan consists of a blade and a PZT actuator. The PZT actuator is clamped to a stationary base at one end, whereas the fan blade is installed on the other free end. When an alternating high voltage is applied to the PZT actuator, the free end vibrates with the same frequency as the input signal. When the input signal frequency is tuned to the resonance frequency of the fan blade, the oscillating amplitude is significantly amplified, resulting in a useable airflow speed [
5].
Previous studies have focused on the lift, thrust, mass flow and other characteristics that PZT fans can provide in relation to thermal and mechanical applications. Eastman et al. [
6] tested the thrust of a piezoelectrically actuated oscillating cantilever in different Reynolds numbers and correlated it with the vibration amplitude. Stafford and Jeffers [
7] discussed the bulk pressure-flow rate performance and efficiency characteristics of confined PZT fans. A recommended operating range was given between the points of maximum efficiency and maximum flow rate from the experiment results. Prince et al. [
8] discussed the ionic polymer metal composite (IPMC) cantilever vibrating hydrodynamics in water.
More detailed studies on the characteristics of the flow field induced by PZT fans and the underlying mechanism have been performed both theoretically and experimentally. Kim et al. [
9] investigated the velocity field of a vibrating cantilever plate using PIV. A Y-shape pseudo-jet flow dominated by vorticial structures was found beyond the plate tip. They obtained individual vortex information such as the size, strength, distribution and position by wavelet analysis for single phase data. Meanwhile, they applied the proper orthogonal decomposition (POD) technique to deduce the transient evolution process of the regional vortex. Hu et al. [
10] conducted a phase-locking PIV experiment on a root-fixed piezoelectric flapping wing in a wind tunnel. Different vortex behaviors are found at different wingspans. The inner half close to the wing root produces drag, whereas the outer half was found to produce thrust. Besides, the flapping wing was also found to lift producing when it was mounted with a positive static angle of attack. Conway et al. [
11] applied PIV technique and numerical method to study the effect of the thickness of a cantilever plate on the flow structure. They concluded that as the beam became thicker, the wake was dominated by the lateral jet region and the propagation of vortices was prevented. Moreover, they suggested vorticial structures were consistent with bluff body aerodynamic theory.
Multi-angle PIV measurements are also adopted to show the flow field details. Bidakhvidi et al. [
12] investigated the flow field in both longitudinal and transverse planes of the fan blade using PIV measurement. Vortices and jet-like flow generated at the PZT fan tip were presented under different plane positions correlated with the Keulegan–Carpenter (KC) numbers. Eastman and Kimber [
13] pointed out that the flow in the region near the corner of the oscillating cantilever beam would become extremely three-dimensional, i.e., two-dimensional measurements can hardly reflect the real flow structure around these regions. They made PIV measurements in both longitudinal and transverse planes at multiple locations to obverse the two-dimensional flow affected by the sharp edges.
The three-dimensional flow field induced by PZT fans is studied recently. Oh et al. [
14] developed a three-dimensional simulation model for the confined vibrating flat plate. They claimed that the interaction of side vortices and tip vortices produced by confined piezoelectric fans lead to the velocity defect near the end wall, which agreed with the experimental data. Agarwal et al. [
15] performed 3D phase-locked PIV measurements for the flow structure of an unconfined piezoelectric fan working at its first vibration mode. The structures of the vortex generated by the oscillation were constructed by interpolated PIV data, which initially appears as a horseshoe; the vortices generated by side edges form the two legs of the horseshoe vortex, then the tip-induced vortex separate from the trailing edge and formed into a hairpin shape with two legs still connect the blade tip. Numerical simulations were also performed to confirm the PIV result. Ebrahimi et al. [
16] conducted 2D and 3D PIV measurements and numerical simulations to obtain detailed jet flow and vortex structures generated by the oscillation of a PZT fan with different oscillating frequency, amplitude and geometric parameter. They found that the breakdown of the shed vortex from the cantilever tip and the reorientation of the substructures are the primary factors that affect the shape of the induced jet.
From the literature mentioned above, effects of the thickness, frequency and amplitude of a PIZ fan blade on the flow field have been investigated in two-dimensional cases. Most 3D flow field measurements mainly focus on the evolution of the flow structures within one oscillating period for the same parameter. Few three-dimensional measurements have been conducted to investigate effects of fan blade geometry and oscillating frequency and amplitude. With the increase in the oscillating Reynolds number, the flow produced by the oscillating blade becomes more unsteady. In the current study, three-dimensional flow fields induced by a PZT fan blade in an unconfined quiescent air environment are measured at Reynolds numbers up to 550. The higher Reynolds number investigated in this study is more consistent with the piezoelectric fan operating condition in real applications.
The level of turbulence in the flow field induced by a piezoelectric fan is closely related to the performance of the piezoelectric fan. A high level of turbulence indicates a large kinetic energy loss, resulting in a less efficient fan to drive the fluid. However, a high level of turbulence can also increase the heat transfer coefficient. The overall role of turbulence generated by the piezoelectric fan blade on the heat dissipation is very complicated and still not clear. So far, there have been few studies focused on the turbulence characteristics generated by a piezoelectric fan blade. In the current study, the turbulence intensity levels at different Reynolds number conditions are evaluated, the maximum turbulence intensity at high Reynolds numbers up to 14.
The paper is organized as below.
Section 2 introduces the PIV experiment setup and the measurement procedures.
Section 3 presents the experiment results and discussion of the flow characteristics induced by the oscillating PZT fan blade.
Section 4 concludes this study.
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 × 300 mm × 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
fr = 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 ±0.09 mm, corresponding to 1 pixel in the image. The characteristic tip velocity of the PZT fan is defined as:
which is the average velocity of the trailing edge in a cycle. The geometrical parameters of the PZT fan blade include the length
lb, the width
wb and the thickness,
tb. The geometrical parameters of the PZT fan blade are fixed in this study with
lb = 65 mm,
wb = 15 mm and
tb = 0.1 mm (See
Figure 2), resulting in an aspect ratio (
AR =
wb/
lb) around 0.23. We adopted the definition of oscillatory Reynolds number
Re [
16] as:
where
ν = 14.8 × 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 200KS-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 Δt between two laser pulses is set at 60 μs, i.e., the interval time between two PIV images in a pair is 60 μs. 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 × 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.
The image pre-processing and post-processing are performed using the commercial software TSI Insight 4G. A subtraction operation is performed by subtracting a minimum image to remove the background. The minimum image is generated by the minimum intensity method. Then, the multiplication operation is performed to every pixel in order to improve the image luminance; the operation does not eliminate image noise but makes the image clearer. The pre-processed images are then loaded to the PIV algorithm using a recursive Nyquist grid with an overlap gird spacing of 50%. The interrogation window size refines from 64 × 64 pixels to 32 × 32 pixels, ensuring at least 15 particles exist in the interrogation area. An FFT correlator is chosen as the correlation engine, and a Gaussian Peak with the signal to noise ratio of 1.5 is used for the peak engine. The calculated velocity is first validated globally by a standard deviation velocity range filter at a standard deviation factor of 7. It is subsequently validated locally using a median test method with a 5 × 5 pixels neighborhood size. The holes in the data were filled recursively using a local mean method with a 5 × 5 pixels neighborhood size. Finally, smoothing is performed after all the post-processing procedures, with a filter size of 5 × 5 pixels and sigma value of 0.8.
The 3D vortex structure was constructed by combining a group of 2D transverse plane along the
y axis, 1 mm apart (see
Figure 3). The transverse measurement plane was first placed at the midspan. After each PIV measurement, the plane translated along the positive direction of the
y axis for
dshify,y = 1 mm. Due to the symmetric nature of the PZT fan blade, 16 planes are extracted from the midspan of the blade to the plane 15 mm away from the midspan in +
y direction. To better visualize the 3D vortex structure, the measured data is mirrored at the mid-span to construct the other half. The 3D vortex structure at each phase is (defined in the next section) constructed by 32 2D ensemble-averaged flow field image. This procedure is also used in other studies [
15,
16,
17].