Enhancement of the Piezoelectric Cantilever Beam Performance via Vortex-Induced Vibration to Harvest Ocean Wave Energy

Renewable and sustainable energies exhibit promising performance while serving as the power supply of a wireless sensor especially located in marine waters. Various microgenerators have been developed to harvest wave energy. However, the conversion ability from a dynamic oscillating source of wave is crucial to enhance their effectiveness in practical applications. In this paper, a new piezoelectric converter system is proposed to harvest the kinetic energy from ocean waves. -e vortex-induced effect in an air channel enhances the vibration performance, improving the energy harvesting efficiency. -e system comprises an oscillating water column (OWC) air chamber, a bluff body, and a piezoelectric piece for electromechanical transduction. -e fluid–solid–electric coupling finite element method was used to investigate the relation between the output voltage and geometrical parameters, including the size and position of the piezoelectric cantilever beam, which is based on the user-defined function of the ANSYS. It is found that the bluff body in the outlet channel above the air chamber induced high-frequency vortex shedding vibration. -e regular wave rushed into the air chamber with a frequency of 0.285Hz and extruded the air across the bluff body in the outlet channel. -is incurred the fluctuation of the air pressure and excited the piezoelectric cantilever beam vibration with a high frequency of 233Hz in the wake region. Furthermore, a continuous electrical output with a peak voltage of 6.11V is generated, which has potential applications for the wireless sensors on the marine buoy.


Introduction
Piezoelectric power generation driven by ocean waves is a promising alternative or self-contained power source for remote wireless sensor nodes [1,2]. Particularly, energy harvesting from flow-induced vibrations (FIVs) has become a hot topic [3,4]. Energy harvesting from FIVs includes generally vortex-induced vibration [5,6], galloping [7][8][9], and flutter and wake galloping [10,11]. Besides, energy harvesting from wave-induced vibration also calls a lot of attention; e.g., Nan Wu developed a piezoelectric coupled buoy energy harvester containing several piezoelectric coupled cantilevers attached to a floating buoy structure [12].
is energy harvester can be easily suspended in intermediate and deep ocean for energy harvesting by adjusting the sizes of the floater and sinker. However, it is considerably challenging to harvest this wave energy concentrated in a relatively narrow and lower frequency band. Recently, the piezoelectric generating patch operation frequency has been optimized to improve the energy harvesting efficiency; e.g., Zhao provided an optimized design of the piezoelectric cantilever beam at a low frequency based on theoretical analysis and simulation [13]. Zhang introduced a high-frequency generating piezoelectric beam with a lowfrequency drive beam from an impact rope as a tunable wideband frequency upconversion to harvest the vibration energy of low-frequency environments [14]. Fan proposed a nonlinear piezoelectric energy harvester containing stoppers and magnets, causing the operation frequency toward a lower frequency and monostability by modifying the gap between the tip mass and external magnets [15]. Moon expanded the bandwidth of the piezoelectric cantilever beam by tuning a proof mass that caused the difference between the consecutive flexural resonance frequencies of the beam [16]. erefore, the bandwidth increased by 426.6% at the same output level and the power improved by 508.5% when compared with the conventional device. Li M. exploited the nonlinearity and structural coupling effect in vibration energy harvesting to construct piezoelectric harvesters having X-structures characterized by two mounting configurations which meets with ultralow-frequency range of traditional cantilever-based harvesters [17]. e ocean wave frequency of 0.3-1 Hz is considerably low in comparison with a resonance frequency of several hundred hertz for the piezoelectric patch [18,19]. erefore, generation of high power cannot be achieved by simply synchronizing the movement of the piezoelectric patch with that of the ocean wave. e excitation frequency improves energy conversion efficiency because the piezoelectric generating power increases with an increase in the vibration frequency. Several studies have explored frequency adjustment techniques such as the addition of auxiliary massspring systems [20], the usage of generator arrays [21], and increasing the frequency fluctuation by the vortex shedding effect [22]. Nabavi studied a self-tuning beam-column piezoelectric-based energy harvesting system that can be optimally used as an ocean wave energy harvester when subjected to large wave height and a low frequency [23]. e bimorph piezoelectric generator described by Okada is excited by two pendulums that oscillate with a floating body motion at the ocean wave surface [24]. e pendulums hit the piezoelectric element six times within each wave cycle even though the wave period range is 0.5-1.5 s. e collision duration can be adjusted with the length of the fishing line used to suspend a ball. Viet proposed an innovative design containing a harvester comprising n blades and a stator attached to eight mass-spring-piston-cylinder-piezoelectricity devices [25]. e resonance and force magnification improved the power output of the harvester. Hwang introduced a piezoelectric energy harvesting system in which a magnet is the tip mass at the end of the piezoelectric cantilever structure and a rail with a metal ball is capable of harvesting energy from low-frequency vibrations induced by ocean waves [26]. Murray presented a two-stage piezoelectric energy generator with buoyant structures that interact with the ocean waves as a low-frequency source and excite an array of vibrating piezoelectric elements into higher-frequency resonance, similar to a musician strumming a guitar [27]. Zhang proposed a multi-impact piezoelectric harvester composed of a hung mass and two stiff piezoelectric cantilever beams to enhance the operation performance at a super-low frequency [28]. e harvester was triggered with high-frequency vibrations and the electric power converted from the series of sequential impacts is triple that of a single-impact device in one vibration cycle. Viet developed a variant of the harvester containing four magnetic bar-mass-spring-lever-piezoelectric systems that are symmetrically arranged to transform the low-frequency ocean wave energy into electricity, harnessing high power [29,30]. e natural fluid flows are flat, and a vortex can be generated by inserting a bluff body in the fluid to improve the harvesting efficiency [31][32][33][34]. Wang presented a flow-induced piezoelectric energy harvester comprising a diaphragm and a piezoelectric laminate subjected to a distributed and oscillating load in a flow channel with fluctuating pressure [35]. Petrini and Song presented piezoelectric energy harvesters involving vortex-induced vibrations based on air and water flows, respectively [36,37]. Akaydın used a thin flexible piezoelectric cantilever beam in case of a turbulent wake flow induced by the cylindrical bluff body at a high Reynolds number (Re > 10,000) to facilitate its utilization at high frequencies for energy harvesting [38]. Nguyen arranged tandem double bluff bodies to enhance the pressure fluctuation amplitude on the piezoelectric film denoting a vortex street [22]. Quan Wen simulated the vortex-induced pressure based on different bluff body shapes, including cuboid and cylinder shapes. e pressure of the former was approximately five times that of the latter. A comb-shaped bluff body in the wake can reduce secondary vortex shedding [39]. Yun studied vortex street vibration energy harvesting in airflow induced by running cars; meanwhile, Hu introduced a vortex-induced piezoelectric sensor to measure the low-speed wind flow [40,41]. e piezoelectric cantilever beam is easily broken by rigid mechanical shock. Harsh conditions are highly pursued to an ocean wave for obtaining reliable energy conversion technologies. We developed a piezoelectric harvester with an oscillating water column (OWC) in its air chamber. is device converts low-frequency ocean waves into higher frequencies of air pressure fluctuations, triggering the vibration of the piezoelectric cantilever beam, as depicted in Figure 1. e relation between the generating power and the geometrical parameters of the structure was investigated based on fluid-solid-electric coupling by the finite element method. e new energy harvesting system improves the fluctuating frequency and the output voltage amplitude of the piezoelectric cantilever beam induced by the ocean wave.

Structure and Operating Principle.
e wave energy harvesting device comprises a semiclosed air chamber and a piezoelectric patch. e air chamber is a semisubmerged vertical OWC converter on the water surface and it is attached to the seafloor with rope. e free surface oscillating motion in the chamber was induced by the incident waves, trapping the air above the free surface of the water to flow through a cylindrical bluff body fixed in the outlet channel and induce vortex shedding. e piezoelectric cantilever beam was positioned in the wake flow region to vibrate with swirling vortices, as presented in Figure 2. When the ocean wave flows into the air chamber, the ocean wave energy is transformed into oscillation kinetic energy at the free water surface of the internal chamber [42]. e air is compressed by the OWC and flows across the bluff body in the exhaust channel with a Reynolds number (40 < Re < 3.0 × 10 5 or Re > 3.5 × 10 6 ). A series of alternating vortices and unsteady pressure distribution of the vortex-induced vibration is generated thereafter in the wake flow region. Subsequently, the low-frequency ocean wave motion is converted to a higher-frequency airflow vortex-excited vibration. e operating frequency range can be adjusted through the gap between the bluff body and the piezoelectric cantilever beam to improve the energy harvesting efficiency.

Mathematical Expressions for the Vortex Shedding
Frequency.
e equations for the two-phase flow model of air and water were adopted by assuming potential flow and an incompressible fluid to analyze the hydrodynamic behavior of the OWC air chamber on the free ocean wave surface exhibiting a finite water depth in the time domain. According to energy balance and mass conservation in the water tank models of fluid flows, the water surface fluctuations with rising and falling movements compress the air flowing through the channel. Simultaneously, the airflow velocity can be calculated based on the change in the volume of the air chamber.
Further, the small amplitude wave theory was adopted to determine the incident wave energy. e wave oscillation amplitude of the free water surface ζ(t) can be expressed as where R is the horizontal distance of the source point from the field point and a is the wave amplitude. e source point is the point at which the water flows out from the left side of the sink, whereas the field point is the point at which there is no water. e parameters ω and φ denote the natural frequency of the wave and the initial vibration phase of the water surface in the air chamber. Subsequently, the oscillation velocity v(t) of the free water surface can be calculated as a derivative of (1) as follows: e ocean waves entering the air chamber result in a continuous OWC. e air above the water surface flows through the circular air outlet at the top of the chamber. Meanwhile, the air volume changes inside the chamber in a breath cycle of exhaust or suction was obtained as follows where S is the horizontal cross-sectional area of the air chamber in Figure 2, S = L C × W C , and T is the wave period. e airflow Q D in the air passage is equal to the air volume change in the chamber. e quantity of air flowing in the air passage can be calculated as Q D � V D × S 1 , where V D and S 1 denote the free water surface oscillation speed and the cross-sectional area of the air outlet in coping of the chamber wall, respectively.
Turbulence or vortex is formed when the exhaust or suction airflow passes the stationary cylindrical bluff body in the outlet channel, whether it is steady or unsteady. A stable periodic frequency of vortex shedding is related to the Reynolds number Re that can be described as follows [43]: where D is the diameter of the cylindrical bluff body and v is the dynamic viscosity coefficient of the air (1.789 × 10 −5 m 2 /s). When Re > 40, the sustaining pressure fluctuation produced in the area behind the bluff body is utilized to excite the piezoelectric cantilever beam. e fluctuation frequency related to vortex shedding is described using the diameter of the bluff body D, the flow velocity V D , and the Strouhal number S t as follows [44]: where S t is the nondimensional Strouhal number, which can be assumed to be 0.2 for the circular section, and f s is the fluctuation frequency in case of vortex shedding [36]. e generation efficiency is significantly improved when the piezoelectric cantilever beam vibration resonates with pressure fluctuation. Furthermore, the vortex-excited frequency and the eddy current velocity are optimized and adjusted based on the diameter of the bluff body and the spatial position of the piezoelectric cantilever beam based on the fluid-structure interaction (FSI) simulations using the finite element method.

Numerical Simulation Results and Discussion
A multiphysical field coupling model was introduced to simulate the performance of the new power generation system involving the fluid-solid coupling of the water and

e 3D CFD Numerical Wave Flume Simulation.
e 3D numerical wave flume with an oscillating air chamber model is presented in Figure 4. e CFD numerical model solves the Navier-Stokes equation instead of obtaining the potential flow based on the incompressible viscous fluid dynamics continuity hypothesis [45][46][47]. e specific wave and flume structural parameters are presented in Table 1. e volume of fluid (VOF) method was adopted to track the fluid interface of the air-liquid two-phase flow in the numerical wave flume and determine the volume fraction of fluids (air and water) in each control volume unit as shown in Figure 4(a) [42][43][44]. e compressed air resulted in continuous vortex shedding by flowing across the bluff body. Simultaneously, the positive and negative air pressures were alternated in the wake region, as depicted in Figure 4(b) with the wave period (T) of 0.4 s.
In the numerical analysis model of the generator, the ocean water depth was set to 4 m from the free surface of the wave to the bottom of the sea, as illustrated in Figure 2(a). e incident wave period (T) was 3.5 s, and the wave height (H) was 0.8 m. e OWC was placed at L d � 20 m from the wave inlet boundary.
e air velocity at the outlet was obtained after simulation. As the waves invaded the OWC air chamber in the numerical wave flume, the air velocity gradually increased and periodically stabilized and varied after 5.0 s. e time history of the velocity curve that approximately denotes a cosine wave is displayed in Figure 5. e maximum exhaust and suction velocities of the air are 46.78 and 57.01 m/s, respectively. e time history of air velocity includes the exhaust and inhalation states, with the oscillation of the OWC in the chamber. e fitting curve in a cycle of time history (T = 3.5 s) was extracted from Figure 5 to analyze the airflow process presented in Figure 6. e velocity values located above the zero line of the coordinates from 0 to 2 s represent the exhausted state, with a corresponding inhalation state being observed from 2 to 3.5 s. e piezoelectric cantilever beams were vibrated by the air pressure motions, as depicted in Figure 6. e variable velocity is the inlet parameter of the UDF numerical simulation obtained from the equation by curve fitting with the MATLAB software. is was simulated in a step-by-step manner for the flow solid coupling fields of the water and chamber, the high-pressure air, and the piezoelectric cantilever beam.

Piezoelectric Generation Simulation with Vortex
Shedding. Two bluff bodies were set up at the inlet and outlet air channel to harvest the exhaust and inhalation air kinetic energy, respectively, as shown in Figure 2(c). e finite volume method was adopted to model and solve the pressure-velocity coupling term and the large-scale turbulence structure to analyze the vortex aerodynamic characteristics [40,48]. Further, a sublattice model was constructed for the small-scale isotropic large-eddy simulation turbulence model to precisely distinguish the vortex-excited structure in the flow field.         e instantaneous velocity curve at point A in Figure 2(b) is displayed in Figure 8. Air velocity was induced by the cylinder bluff body with sizes of D � 40 mm, L1 � 140 mm, and L2 � 140 mm. e exhaust and inhalation velocities in the channel were significantly improved during two wave cycles in comparison to those without the bluff body.
e maximum suction and exhaust velocities increased from 46.78 and 57.01 m/s to 60.92 and 63.84 m/s, respectively. is resulted in high-frequency fluctuations in velocity for vibration energy harvesting. Accumulation of waves in the air chamber created an OWC with a wave frequency of 0.285 Hz, as shown in Figure 9(a). e first shedding pneumatic frequency of 233 Hz was extracted from the fluctuating airflow observed behind the bluff body by fast Fourier transform (FFT), as illustrated in Figure 9(b). e results denote that the vortex vibration with the bluff body in the outlet air channel transforms the low-frequency wave motion into a highfrequency air vortex vibration, improving the power     generation efficiency of the piezoelectric element based on the fluctuating air pressure.
As shown in Figure 2(c), a piezoelectric cantilever beam was set up in the outlet channel to harvest the air kinetic energy in the channel. e piezoelectric generator and material parameters are presented in Tables 2 and 3. e brass and PZT-4 materials were selected as the cantilever beam substrate and energy conversion element, respectively. e ANSYS simulation model sets the interface of air pressure and piezoelectric cantilever beam with solid elements. e symbols of A, B, and C in Figure 10 illustrate the airflow vortex formation and shedding processes. e piezoelectric cantilever beam vibrates in the wake flow region as shown in Figure 10 and the deformations are shown in Figure 11. e piezoelectric cantilever beam performs with the inherent frequency as shown in Figure 12 which is simulated with ANSYS. e piezoelectric cantilever beam synchronously varies with the aerodynamic force in the wake of the bluff body; the output voltages and free end displacements are presented in Figure 13. e output open-circuit voltages on the piezoelectric cantilever beams are presented in Figure 14.
e peak voltage is increased by a factor of 6000 compared to no bluff body in the outlet air channel with OWC wave energy harvest structure.

e Generation System Analysis.
In this study, the influence of the bluff body was examined, which related to the size of the circumfluence area and the output voltage distribution near the bluff body. e cylindrical bluff body was set in the outlet channel with serial diameters of 40 and 50 mm to create vortex-induced vibration. e dimensions of the piezoelectric cantilever beam are 50 mm × 30 mm × 1 mm. Further, the spatial position of the beam in the wake region was analyzed and compared with the CFD multiphasic fields. e simulation results exhibit variable vortex shedding flow speeds ranging from 0 to 57.01 m/s. e distance between the bluff body and the free end of the beam ranges from 80 to 240 mm. e responses of the output voltages with different locations (L 1 ) and diameters of the cylindrical bluff body during the exhaust process are depicted in Figure 15. e maximum voltage is approximately 6.8 V when L 1 = 200 mm and D = 50 mm. e plot denotes that the voltage decreases when the piezoelectric cantilever beam is located at a distance more than four times the diameter of the bluff body. Meanwhile, the voltage gradually decreases with reducing distance from the bluff body. e maximum peak voltage can be observed when L 1 = 160 mm for a bluff body diameter of 40 mm. e corresponding optimal energy acquisition spots exist in the bluff body wake regions for the exhausted state at approximately L 1 = 4D. e same spot also appeared in Figure 15 during the inhalation process. e peak voltage changes with the distance (L 1 or L 2 ) in case of similar bluff body diameters because the vortex excitation is intense at the optimal energy acquisition spot. It will disappear at a remote distance from the fluff body because the cantilever beam is in the vortex attenuation zone. On the contrary, if the cantilever beam locates at a smaller space near the bluff body, no airflow fluctuation in the region is experienced and the piezoelectric cantilever beam vibrates weakly. erefore, the piezoelectric cantilever requires stability in the optimal wake region with a strong vortex to generate electric power.

Conclusions
is study presented a new piezoelectric generation system with an OWC for ocean wave energy harvesting. Further, a simulation model was established to predict the dynamic response of the wave energy harvesting device. e power generation solution simulates with the air-liquid-electromechanical coupling model. In the air chamber, the velocity of the high-frequency airflow in the outlet channel significantly improved with the vortex vibration.
e maximum exhaust and suction air velocities increased from 57.01 to 63.84 m/s and from 46.78 to 60.92 m/s, respectively. And the vortex-induced vibration frequency is about 233 Hz in the air tunnel. e high-frequency vortex aerodynamics excite the piezoelectric cantilever beam to output the maximum opencircuit peak voltage of 6.11 V.
e results denoted that the bluff body at the air chamber outlet enhanced the vibration and improved the OWC wave energy harvesting system for the generated electric power. Further, an optimal energy-enhancing region related to the appearance of the vortex is evident in the wake region of the bluff body. e diameter of the bluff body and the spatial location of the piezoelectric cantilever beam will improve the wave energy harvesting.

Data Availability
e data used to support the findings of this study are available from the corresponding and first author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.