1. Introduction
It is true that energy harvesting technology based on vibration to drive various miniaturized and low-power sensors has attracted a lot of attention for many years. Especially among the different types of energy sources available in water, vibrational energy is known to be the most attractive because it is a kinetic energy that is abundant, readily accessible, and can be easily converted into electrical energy using piezoelectric, electromagnetic or electrostatic principles [
1,
2]. There are several piezoelectric materials that can convert this vibrational energy in water into electrical energy and are used in a variety of sensing and actuation applications. In energy harvesting, technologies using piezoelectricity, thermoelectricity, and triboelectricity are being actively studied. Among them, piezoelectric energy harvesting (PEH) is widely used by many researchers [
3,
4,
5,
6,
7,
8] because it has advantages of high power density and various application fields compared to other technologies.
PEH is based on the phenomenon of generating a current flow by creating a potential difference through mechanical energy and vibrational displacement using an element with a piezoelectric effect. The most used piezoelectric material for PEH is PZT, which has excellent cost-effectiveness and mass productivity, but is very weak to impact due to the characteristic of ceramics. In terms of durability of materials, polyvinylidene fluoride (PVDF), fiber-type macro fiber composite (MFC), PMN-PT, PMN-PZT, etc. are being actively studied [
9]. In underwater energy harvesting using piezoelectric materials, important power generating devices can be classified into two main categories. As in the study of Erturk et al. [
8] and Shan et al. [
10], those using cantilevers and those using flow around circular rods or cables [
11].
Erturk et al. [
8] manufactured a cantilever type underwater energy harvesting device in the form of a caudal fin using MFC of the concept of piezohydroelasticity, which is capable of underwater propulsion and energy harvesting, and verified the energy harvesting performance through experiments. It was predicted that 2.5 mAh of power could be charged through about 20 h of charging for vibration with a 0.5 g acceleration of 56 Hz. Recently, Shan et al. [
10] verified the performance of an MFC-based energy harvesting device using an underwater vortex environment. They built a mathematical model for an energy harvesting device using a piezoelectric material in a vortex environment and predicted the energy generation performance. The performance of the energy harvesting device according to the flow rate were also conducted. It was stated that a maximum of 1.32 μW of energy could be generated when a vortex was generated with a 30 mm diameter cylinder at a flow rate of 0.5 m/s.
Bezanson et al. [
12] reported that supply utilizing vortex induced vibration energy (SURVIVE) is a structure in which a thin cantilever is attached to the surface of a cymbal-type piezoelectric transducer and these are installed on the electronics housing so that the vortex flow generated by the fluid flow vibrates the cantilever. The design targets ocean current of 0.25 m/s and each generator was found to generate a minimum of 6 mW based on the experimental result.
Taylor et al. [
13] developed a flag device composed of two embedded PVDF layers by applying the body and movement of an eel. The vortex alternates, which causes the flag to flutter and consequently generates electricity from the piezoelectric material due to charge separation [
14].
As a study using a piezoelectric cantilever beam, Akaydin et al. [
7] measured the energy harvesting ability of PVDF beams in unstable turbulence (Reynolds number > 10,000). In the wake of the turbulent flow of a circular cylinder, the fluid passes along the surface of the beam placed at an optimized position, and the beam is placed on a vibrating turbulent boundary layer to generate power.
Power generated by using PEH basically is alternating current (AC) because it is based on deformation caused by vibration. Since AC current cannot be used directly in batteries and direct current (DC) power applications, DC conversion through a rectifier circuit is required. The basic rectifier circuit used in PEH is full bridge rectifier (FBR) [
2,
15,
16]. When the FBR composed of 4 diodes is used, forward voltage drop of diode in a low voltage circuit is a loss that cannot be ignored. To overcome this shortcoming, a circuit adopting a voltage doubler rectifier (VDR) has been proposed [
17]. The VDR has two advantages over the FBR; (1) because of half usage of diodes, voltage drop is small.; and (2), the voltage output of PEH can be increased up to 2 times [
18].
As a method for generating flow induced vibration in underwater, there can be a method using a vortex flow generated on the rear surface of an object with a circular cross section, and a method using a vortex flow generated on the surface of an object having a cantilever shape. However, the cantilever type, which has a relatively wider surface area than a circular cross-section and vibrates sensitively to small changes in external force, was selected in this paper as a structure that can self-excited the residual vibration in water for a long time.
In this study, a cantilever type funnel type energy harvester (FTEH) using PVDF, a piezoelectric material, was fabricated. PVDF is considered as a material that can vibrate freely according to the fluid flow and can obtain a large amount of vibration displacement rather than other rigid PZT material. PVDF film is relatively a simple monomer structure. It is made of organic polymer and is resistant to corrosion in underwater. FTEH has a spiral screw shape mounted on the support and the inlet is wide and the outlet is narrow. Vibration displacement generation according to the design parameters of FTEH was analyzed through numerical simulation. The effectiveness of the FTEH was verified by manufacturing an experimental device and installing VDR and FBR at the output terminal of the FTEH to measure the amount of power generated according to the flow rate through the experiment.
2. Numerical Simulations and Results
In the energy harvester, the piezoelectric energy is generated from the displacement of the PVDF piezoelectric body installed in the funnel-shaped outlet part.
is the vibration response, i.e., transverse displacement at position
x and time
t,
is the voltage response across the external resistive load
. Based on the standard modal analysis procedure the vibration response is expressed in terms of the modal mechanical coordinate that gives the transverse vibration displacement
and the mode shapes
as [
1]
The electromechanically coupled ordinary differential equations in modal coordinates are [
1]
where
is the undamped natural frequency in constant electric field conditions,
is the modal mechanical damping ratio,
is a modal forcing function,
is the modal electromechanical coupling, and
is a permittivity component of the piezo-ceramic layers. Hence, these Equations (1)−(3) can predict the coupled system dynamics and one obtains voltage response which depends on the vibration displacement [
1].
Numerical analysis and optimization studies of energy harvester devices using flow-induced vibrations around FTEH generated by the fluid flow in water were conducted. A displacement occurred in the PVDF piezoelectric film due to the pressure change due to the flow of the fluid, and a bidirectional coupling analysis was performed in which this displacement again affects the flow field. The material properties of the PVDF were 1780 kg/m3 in density, 2500 MPa in Young’s modulus, and 0.35 of Poisson’s ratio. For the fluid 11,952 of Reynolds number was applied to the depth of 10 m.
2.1. Energy Harvester Model with FTEH
As for the model used for the analysis, an energy harvester device with a funnel-type inlet shape was devised as shown in
Figure 1. The flow of the fluid runs from the left with a wide inlet to the right with a narrow inlet. At the end of the outlet, a PVDF piezoelectric body for harvesting energy using vortex vibration caused by the flow of fluid is assembled.
In the funnel-type structure shown in
Figure 1, the cross-sectional area at the end of the energy harvester is smaller than the inlet, so an increase in flow rate can be expected according to Bernoulli’s theorem. In general, it would be a good approach to perform the optimal design of the energy harvester according to the shape of the FTEH. However, in this study, the shape and size (cross-sectional area of inlet and outlet) of the FTEH had to be analyzed in a condition where it was specially limited for the purpose of use. Therefore, in this study, due to the limited purpose of use in the marine environment, the amount of vibration displacement was observed with respect to changes in the length and thickness of PVDF and the rate of inflow of ocean currents.
Assuming that only a piezoelectric body without a fluid collecting device is independently placed in water and an energy harvester model with a funnel-type inlet, set to case (a) and case (b), respectively, and calculate the velocity distribution, pressure distribution, and vibration displacement as shown in
Figure 2 and
Figure 3.
Figure 2a and
Figure 3a show the velocity distribution and pressure distribution in the shape without a funnel, respectively.
Figure 2b and
Figure 3b respectively show the velocity distribution and pressure distribution in the FTEH shape. In this case the input flow velocity was set to 0.24 m/s, which is the average current velocity. As a result, the maximum speed at the outlet of case (b), where the funnel type fluid collector exists, increased about 1.9 times from 0.24 m/s to 0.45 m/s. Accordingly, the pressure difference was also relatively large. As shown in
Figure 2, it can be seen that FTEH generates a lot of vortex flow in the velocity distribution, which increases the amount of vibration in PVDF.
Figure 4 shows the vibrational displacement at the tip of the PVDF piezoelectric body. Unlike case (a), which is a simple piezoelectric model with little vibration displacement, in case (b), a funnel-type energy harvester model, the maximum displacement is 0.01 mm, which can be seen to generate a much larger vibration displacement compared to case (a).
Figure 4c shows the structure in which the shape of the funnel is symmetrical on the inlet side and the outlet side, and the vibrational displacement is shown in (d) when the fluid flows under the same conditions. As can be seen from
Figure 4a,b,d, it can be found that the shape as shown in
Figure 1b had a lot of vibrational displacement.
2.2. Optimal Design of FTEH
In the FTEH model, which has a larger vibration displacement than the simple piezoelectric model without an fluid collecting device, the vibration displacement according to the thickness, length, and input flow rate of the piezoelectric element was measured to determine the trend. A PVDF piezoelectric film was used as the piezoelectric material, and the thickness (t) of the film-shaped piezoelectric material was decreased from 1.0 mm to 0.75 mm at 0.125 mm decrements, and analysis was performed in three cases, respectively. The film length (L) was increased from 50 mm to 100 mm in 25 mm increments, and the inlet velocity (V∞) was increased or decreased based on the average seawater velocity of 0.10 m/s, 0.24 m/s, and 0.50 m/s. A total of three cases were determined and analysis was performed. The design variables are summarized in
Figure 5 and
Table 1. The analysis results are graphically shown in
Figure 6,
Figure 7,
Figure 8 and
Figure 9. When comparing the vibration displacement according to the thickness and length of the piezoelectric body, the inlet speed was fixed at 0.24 m/s, which is the average seawater speed.
Figure 6 and
Figure 7 show the vibration displacement and frequency spectrum for each inlet velocity of the funnel-type energy harvester device, respectively. As the inlet speed increased from 0.1 m/s to 0.5 m/s, the vibration displacement increased. As the speed increased, the high frequency vibration displacement was measured on the PVDF piezoelectric film. In
Figure 8, the vibration displacement according to the length of the PVDF piezoelectric body is compared when the average current velocity V∞ = 0.24 m/s. As the length of the piezoelectric body increased from 50 to 100 mm, the vibration displacement increased. As shown in
Table 2, in the case of the PVDF piezoelectric film, as the length increased by 50%, the vibration displacement increased by 2.3 times and 100% was increased by 8.6 times based on the maximum displacement difference.
In
Figure 9, the vibration displacement according to the thickness of the PVDF piezoelectric body is compared when the average current velocity V∞ = 0.24 m/s. As the thickness of the piezoelectric material decreased from 1.0 mm to 0.75 mm, the vibrational displacement increased. As shown in
Table 3, in the case of PVDF piezoelectric film, as the thickness was decreased by 12.5%, the vibrational displacement increased by 4.2 times and 25% was increased by 5.7 times.
The predicted electric energy harvesting value of the FTEH device derived from the optimal design analysis is 2.299~43.17 μW as shown in
Figure 10. When PVDF with a length of 100 mm and a thickness of 1 mm was used, it was found that power of 39 μW was generated at a flow velocity of 0.25 m/s. Therefore, as shown in
Figure 10, as the vibration displacement of PVDF increases, the generated power is proportionally higher, indicating that the vibration displacement and the generated voltage have a proportional relationship.
3. Power and Energy Generated by FTEH
The proposed PVDF harvester generates an irregular low voltage signal according to the underwater flow and the signal cannot be used for battery charging and DC power application. Therefore, a full-wave rectification circuit capable of voltage boosting is required. In this paper, we use a VDR as a rectifier circuit and present its improved performance over typical FBR.
The VDR and FBR connected to the PVDF element are shown in
Figure 11. In
Figure 11.
is the input voltage,
is the output voltage,
is rectifying diodes, and
is rectifying capacitor. The PVDF harvester is represented as an equivalent model composed of internal capacitance
and source voltage
[
19].
Suppose that voltage source
a sinusoidal wave having different frequency at every half cycle and
is the angular frequency at nth cycle as shown in
Figure 12.
Then the maximum average output power of the VDR
and FBR
during half cycle [
] are as follows [
18]
where
is the voltage drop due to diode
,
is the peak voltage of the
th half cycle. Note that the only one
occurs in the VDR whereas the FBR has two
in the path of the current. The accumulated energy via N frequency signals of VDR
and FBR
can be written as
Since direct measurement of the source voltage of the actual harvester is not possible, it is necessary to estimate the source voltage from the output observed by the measuring equipment.
To estimate the source voltage
, the open circuit voltage of the harvester was measured using an oscilloscope as shown in
Figure 13. In
Figure 13a,
is the resistor 10 MΩ of the oscilloscope,
is open-circuit voltage of harvester measured by oscilloscope,
is internal capacitance 10.26 nF of the PVDF.
Figure 13b shows the
of the harvester actually measured in water. The circuit in
Figure 13a can be interpreted as a first-order analog high-pass filter with one resistance and capacitance so that reverse transfer function of the circuit
can be obtained as follows:
where
is the time constant. Finally, source voltage of the harvester
can be obtained as follows:
Figure 14a shows source voltage
of the harvester estimated using Equation (6) from the measured open-circuit voltage
in
Figure 13b.
To evaluate the performance of the VDR, we estimate voltage source by approximating as a sinusoidal signal having different angular frequencies in five time intervals as shown in red dotted line in
Figure 14a.
When the approximated sinusoidal signal is used and
= 0.09, the output energy of each rectifier calculated using Equations (3) and (4) for 100 s are shown in
Figure 14b. As shown in
Figure 14, the VDR generates 17% more energy than the FBR because of smaller voltage drops.
By using the estimated harvester source voltage in
Figure 14a, we made a SPICE model via the same configuration shown in
Figure 11, such as
= 10.26 nF,
= 22 μF and BAT43 as diode model
.
Figure 15 shows the simulation results of the output voltage and charging energy of each rectifier for 100 s.
As shown in
Figure 15, the VDR shows 2.12 times higher voltage and 13% more charged energy than those of the FBR at 100 s when the voltage converges. These results confirm that the VDR is advantageous for a low-voltage voltage source compared to the FBR.
5. Conclusions
A method of supplying power by applying energy harvesting technology to a wireless sensor used underwater is a very useful technology. A method of obtaining voltage by generating vibration displacement in a piezoelectric material using flow induced vibration generated by the flow of an underwater ocean current is a technology that can stably supply power to a wireless sensor.
In this study, FTEH using flow-induced vibration in underwater was devised and its usefulness was verified through numerical analysis and experiments. FTEH is a funnel type in which the fluid inlet has a larger cross-sectional area than the outlet, and PVDF is installed at the outlet to generate voltage. At the inlet side, a spiral structure was mounted on the FTEH’s support to generate a vortex flow of the fluid. As a result of the numerical analysis, it was found that the structure with the funnel generated more vibration displacement than the structure without the funnel, and it was confirmed that as the flow rate increased, the thickness of the PVDF decreased, and the length of the PVDF increased. When PVDF with a length of 100 mm and a thickness of 1 mm was used, it was found that power of 39 μW was generated at a flow velocity of 0.25 m/s. In the energy storage circuit development, it was confirmed that the VDR stores 13% more energy than the FBR.
An experimental device equipped with FTEH was manufactured, and the electric power generated by FTEH was stored in the rectify circuit while the flow velocity was changed from 0.25 m/s to 1.0 m/s. As a result of the experiment, it was confirmed that the average RMS voltage of FTEH increased by 0.0209 V when the flow rate increased by 1 m/s. In order to see the performance of the electric circuit, the voltage charged in the rectifying capacitor of each rectifier was measured and the power and energy were compared. When measured for 25 s at a flow rate of 0.25 m/s, it was confirmed that VDR has a voltage 2.25 times greater than FBR. The energy charged in the capacitor was measured, and it was confirmed that the VDR was charged as much as 44.3 nJ, which is 14% higher than the FBR. In the future, if the effective voltage generation in the water of FTEH is stored using the VDR electric circuit, it is judged that it will greatly contribute to the stable power supply of the wireless sensor.