# Experimental Study on Piezoelectric Energy Harvesting from Vortex-Induced Vibrations and Wake-Induced Vibrations

Authors: Min Zhang; Junlei Wang
Journal: Journal of Sensors
 (2016)

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## Abstract

A rigid circular cylinder with two piezoelectric beams attached on has been tested through vortex-induced vibrations (VIV) and wake-induced vibrations (WIV) by installing a big cylinder fixed upstream, in order to study the influence of the different flow-induced vibrations (FIV) types. The VIV test shows that the output voltage increases with the increases of load resistance; an optimal load resistance exists for the maximum output power. The WIV test shows that the vibration of the small cylinder is controlled by the vortex frequency of the large one. There is an optimal gap of the cylinders that can obtain the maximum output voltage and power. For a same energy harvesting device, WIV has higher power generation capacity; then the piezoelectric output characteristics can be effectively improved.


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## Body

## 1. Introduction

In recent years, many researchers have started the study of various replaceable and environment-friendly energy harvesting ways due to the traditional global energy and environment-protection issues. Utilizing the energy harvested from atmosphere or aeroelastic vibration to supply power for electronic devices becomes a hot-topic. Most researches have given attention to the power-supply of the lower power-consumption devices including MEMS, actuator [1, 2], wireless sensor networks, and health monitoring device [3, 4], or seeking replacements for the batteries used on the devices which are expensive and hard to maintain [5]. The issue of harvesting aeroelastic energy from airfoils has been widely studied [6–12]. In addition, some other researches are focused on the energy conversion generated by the vortex-induced vibrations of flags or microbimorph structures [13–15].Vortex-induced vibrations (VIV) and wake-induced vibrations (WIV) are two main types of flow-induced vibrations (FIV). VIV is a self-excited vibration; when the vortex shedding frequency is near to the natural frequency of the bluff body, “lock-in” or synchronization phenomena will happen [16], and the amplitude is decided by the mass-damping ratio. When an elastically mounted cylinder is immersed in the wake of another bluff body, WIV occurs, which is usually completely different from the VIV of a single cylinder in free stream. Researches on two cylinders of same diameter [17–20] show that proper spaces between cylinders can make downstream cylinders obtain higher amplitudes and larger vibration intervals. In addition, according to the researching results on the vibration of smaller cylinders in the wake of bigger cylinders [21, 22], when cylinders are arranged in sequence, the vibration frequency of the smaller downstream cylinder is dependent on the vortex shedding frequency of the bigger upstream cylinder, and if the range of speed is bigger, then the higher amplitude can be obtained.In order to research the harvesting of piezoelectric energy generated from VIV, Akaydin et al. [23] carried out a tunnel test on a single piezoelectric transducer equipment with the diameter of 26.7 mm and got the max power of 0.1 mW. Molino-Minero-Re et al. [24] tested the VIV energy harvesting on a series of single cantilever cylindrical piezoelectric devices; these tests were made in water channel. The max power of 0.31 μW was obtained at the diameter of 8 mm. Mehmood et al. [25] calculated the energy harvested from the VIV with low Reynolds number and high mass ratio and obtained the maximum power of 10 μW. Zhang et al. [26] carried out a numerical study of the similar structure, which shows that the harvested level in SS and SP&PS modes is the same with different values of load resistance.On the basis of relevant researching results on VIV and WIV, this paper’s research involved three aspects: (1) the energy harvesting of a cylinder installed with two piezoelectric cantilevers; (2) the voltage outputs of VIV under different load resistance; (3) the impacts of the space between the two circular cylinders on the voltage output under WIV of the big cylinder.


## 2. The Piezoelectric Energy Harvesting Model

As shown in Figure1, two bimorph piezoelectric cantilevers are attached to the cylinder as elastic support; when the cylinder is suffering VIV or WIV in the transverse direction, the deformations of the cantilevers produce stress in the piezo layers. Based on the piezoelectric effect, there will be voltage produced between the piezo layers and current produced in the circuit as well. Thus the piezoelectric energy harvester can output power if there is a load in the circuit. The control equation of the system can be represented with the coupled equations of the spring supported rigid cylinder and the Gauss law [6, 9]:(1)
M
Y
¨
+
2
M
ξ
ω
n
Y
˙
+
M
ω
n
2
Y
-
θ
V
=
F
t
,
C
e
V
˙
+
V
R
+
θ
Y
˙
=
0
,where M is the mass, ξ is the damping ratio, ω
n is the natural frequency of the structure, F
(
t
) is the lateral fluid force, θ is the electromechanical coupling coefficient, V is the voltage on the load, R is the load resistance, and C
e is the piezoelectric equivalent capacitance.Figure 1
Schematic of a piezoelectric energy harvester.Figure2 displays the structure, circuits, and equivalent circuits for the system. The piezoelectric layers of one cantilever and the two cantilevers are connected to R in parallel and serial way, respectively.Figure 2
(a) Energy harvesting circuit connection, (b) equivalent circuit, and (c) cross-sectional view of a bimorph cantilever.
(a)
(b)
(c)C
e, the piezoelectric equivalent capacitance, and θ, the electromechanical coupling coefficient, can be expressed by the following equation [27]:(2)
C
e
=
C
p
=
ε
0
ε
r
b
L
p
h
p
θ
=
e
31
h
p
+
h
s
b
,where C
p is the capacitance of a single piezoelectric layer, e
31 is the piezoelectric coefficient, ε
0 is the permittivity of vacuum, ε
r is the relative dielectric constant, L
p, b,  and h
p are length, width, and height of the piezoelectric layer, and h
s is height of the base layer.


## 3. Experimental Study

In this paper, the diameter of the small cylinder (d) is 10 mm, the diameter of the big cylinder (D) is 40 mm, the piezoelectric material is PZT-5H, and the material of the sublayer is copper. Parameters of the piezoelectric device are shown as in Table 1. The experiment is carried out in a subsonic open circuit wind tunnel, where air is driven by a centrifugal fan powered by a 1.5 kW motor. The section of the testing piece is 300
∗
300 mm2, and its length is 2000 mm. Two piezoelectric cantilevers of the experimental facility clamp vertically the middle location of the testing piece for doing the VIV experiment. There is no change for the location of the piezoelectric device. A circular cylinder of 40 mm diameter is put upstream for making the WIV experiment, and space S between two cylinders is adjusted by moving the bigger cylinder’s position.Table 1
Parameters of the four considered configurations.
Symbol
Parameter
Value
M
Mass (g)
5.8
D
Diameter of big cylinder (mm)
40
d
Diameter of small cylinder (mm)
10
L
c
Length of cylinder (mm)
25
L
Length of cantilever (mm)
45
b
Thickness of cantilever (mm)
15
L
p
Length of piezoelectric layer (mm)
30
h
s
Thickness of coppery base layer (mm)
0.2
h
p
Thickness of piezoelectric layer (mm)
0.2
ω
n
Natural frequency (rad/s)
164.5
θ
Electromechanical coupling efficient
1.976
e
-
4
C
e
Equivalent capacitance (F)
7.969
e
-
8The voltage output from the load resistance is recorded with the oscilloscope of TEK2002B, and the main experimental device and its installation are shown as in Figure3.Figure 3
Experiment setup of piezoelectric energy harvesting.
(a)
VIV
(b)
WIV
(c)
Oscilloscope


### 3.1. VIV Energy Harvesting Experiment

Four different load resistance values, 104 Ω, 105 Ω, 106 Ω, and 107 Ω, are selected for the VIV experiment. The experiment at a certain load resistance is done by gradually increasing the wind speed, and total four groups of experiments are done and corresponding voltage outputs are recorded, respectively. The range of wind speeds is 0.82
≤
U
∗
≤
7
.
03, where U
∗
=
U
/
f
n
D, with  U being the freestream velocity in m/s and f
n being the natural frequency in Hz. Figure 4(a) shows that the voltage output reaches the maximum value when U
∗
=
5; this indicates that the system is in lock-in status and the largest amplitude is obtained. Thus, the voltage increases with the load resistance. When the load resistance varies in the range of 104~105 Ω, the absolute voltage is lower and the amplification is small. But when the load resistance is up to 106 Ω, there is a clear increase in the voltage output. Similarly, when R is in the range of 106~107 Ω, the voltage output still increases, but the amplification narrows. Figure 4(b) shows that the maximum power of each load resistance happens near U
∗
=
5, and when R is 106 Ω, the system’s power reaches its maximum value.Figure 4
VIV response curves of the voltage and power at different load resistances.
(a)
(b)


### 3.2. WIV Energy Harvesting Experiment

The results of VIV experiments show that the power output atR
=
10
6 Ω is the largest. So, the load resistance in the WIV experiments is fixed at 106 Ω. By adjusting the location of the bigger cylinder, the value of S changes between 1
D and 5
D. For each S, experiments are done in the range of 2.3
≤
U
∗
≤
31.8, and the corresponding voltage outputs are recorded. Figure 5(a) shows that each S reaches its maximum value when U
∗
≈
19, which indicates that the wake shedding frequency of the bigger cylinder upstream is close to the natural frequency of the system at this time and the system is locked and the amplification is larger, so larger voltage output is obtained. With the increase ofS, the voltage output of the system is up at first and then down. This is because the space flow does not develop fully at smaller S, so there is no strong vortex existing in the space. However, when S continues to increase, the wake vortex also cannot play obvious coupling effect due to the decrease of the dissipating intensity. The voltage output reaches the maximum value at S
=
3
D, which indicates that the wake produced by the bigger cylinder upstream has the strongest coupling effect with the smaller cylinder at this time, and the large amplification is attained. Because the load resistance is fixed, so the power output curve is similar to the voltage output and also reaches the maximum value at S
=
3
D, just as shown in Figure 5(b).Figure 5
WIV response curves of the (a) voltage and (b) power at different load resistances.
(a)
(b)


### 3.3. Discussions

Figure6(a) shows the time history curve of voltage outputs recorded by oscilloscope in the WIV experimental at U
∗
=
18.984. Figure 6(b) is the spectrogram plot attained by carrying out FFT operation over the time history curve; the vibrational dominant frequency is 26.37 Hz which is very close to f
n
=
26.18 Hz. The vortex shedding frequency of the bigger cylinder upstream can be represented by f
=
S
t
U
/
D
. Because of D
=
4
d, if we assume that the Strouhal number S
t is unchanged, then the vortex shedding frequency of VIV is four times as much as that of WIV under the same wind speed. Therefore, in order to make the vortex shedding frequency match with the natural frequency, the wind speed at WIV is needed to be higher.Figure 6
(a) WIV time traces of the voltage and (b) power spectra of voltage whenU
∗
=
18.984.
(a)
(b)Figure7(a) shows that the lock-in region moves backward obviously, and the locked interval enlarges. The maximum value occurs at U
∗
=
18.984 when S
=
3
D. For a single cylinder, the maximum value occurs at U
∗
=
4.913. The ratio of the above two velocities is 3.86, which indicates that the vibration of the smaller cylinder is controlled by the wake vortex shedding frequency of the bigger cylinder upstream at WIV. For the WIV case with fixed larger cylinder upstream and smaller cylinder downstream, there is a best gap which can make the effect of fluid-structure interaction be enhanced and obtain a larger amplification. For the piezoelectric energy harvesting, this feature of WIV is helpful for obtaining the higher voltage and power output.Figure 7
Comparison of (a) voltage output and (b) power output for WIV and VIV.
(a)
(b)


## 3.1. VIV Energy Harvesting Experiment

Four different load resistance values, 104 Ω, 105 Ω, 106 Ω, and 107 Ω, are selected for the VIV experiment. The experiment at a certain load resistance is done by gradually increasing the wind speed, and total four groups of experiments are done and corresponding voltage outputs are recorded, respectively. The range of wind speeds is 0.82
≤
U
∗
≤
7
.
03, where U
∗
=
U
/
f
n
D, with  U being the freestream velocity in m/s and f
n being the natural frequency in Hz. Figure 4(a) shows that the voltage output reaches the maximum value when U
∗
=
5; this indicates that the system is in lock-in status and the largest amplitude is obtained. Thus, the voltage increases with the load resistance. When the load resistance varies in the range of 104~105 Ω, the absolute voltage is lower and the amplification is small. But when the load resistance is up to 106 Ω, there is a clear increase in the voltage output. Similarly, when R is in the range of 106~107 Ω, the voltage output still increases, but the amplification narrows. Figure 4(b) shows that the maximum power of each load resistance happens near U
∗
=
5, and when R is 106 Ω, the system’s power reaches its maximum value.Figure 4
VIV response curves of the voltage and power at different load resistances.
(a)
(b)


## 3.2. WIV Energy Harvesting Experiment

The results of VIV experiments show that the power output atR
=
10
6 Ω is the largest. So, the load resistance in the WIV experiments is fixed at 106 Ω. By adjusting the location of the bigger cylinder, the value of S changes between 1
D and 5
D. For each S, experiments are done in the range of 2.3
≤
U
∗
≤
31.8, and the corresponding voltage outputs are recorded. Figure 5(a) shows that each S reaches its maximum value when U
∗
≈
19, which indicates that the wake shedding frequency of the bigger cylinder upstream is close to the natural frequency of the system at this time and the system is locked and the amplification is larger, so larger voltage output is obtained. With the increase ofS, the voltage output of the system is up at first and then down. This is because the space flow does not develop fully at smaller S, so there is no strong vortex existing in the space. However, when S continues to increase, the wake vortex also cannot play obvious coupling effect due to the decrease of the dissipating intensity. The voltage output reaches the maximum value at S
=
3
D, which indicates that the wake produced by the bigger cylinder upstream has the strongest coupling effect with the smaller cylinder at this time, and the large amplification is attained. Because the load resistance is fixed, so the power output curve is similar to the voltage output and also reaches the maximum value at S
=
3
D, just as shown in Figure 5(b).Figure 5
WIV response curves of the (a) voltage and (b) power at different load resistances.
(a)
(b)


## 3.3. Discussions

Figure6(a) shows the time history curve of voltage outputs recorded by oscilloscope in the WIV experimental at U
∗
=
18.984. Figure 6(b) is the spectrogram plot attained by carrying out FFT operation over the time history curve; the vibrational dominant frequency is 26.37 Hz which is very close to f
n
=
26.18 Hz. The vortex shedding frequency of the bigger cylinder upstream can be represented by f
=
S
t
U
/
D
. Because of D
=
4
d, if we assume that the Strouhal number S
t is unchanged, then the vortex shedding frequency of VIV is four times as much as that of WIV under the same wind speed. Therefore, in order to make the vortex shedding frequency match with the natural frequency, the wind speed at WIV is needed to be higher.Figure 6
(a) WIV time traces of the voltage and (b) power spectra of voltage whenU
∗
=
18.984.
(a)
(b)Figure7(a) shows that the lock-in region moves backward obviously, and the locked interval enlarges. The maximum value occurs at U
∗
=
18.984 when S
=
3
D. For a single cylinder, the maximum value occurs at U
∗
=
4.913. The ratio of the above two velocities is 3.86, which indicates that the vibration of the smaller cylinder is controlled by the wake vortex shedding frequency of the bigger cylinder upstream at WIV. For the WIV case with fixed larger cylinder upstream and smaller cylinder downstream, there is a best gap which can make the effect of fluid-structure interaction be enhanced and obtain a larger amplification. For the piezoelectric energy harvesting, this feature of WIV is helpful for obtaining the higher voltage and power output.Figure 7
Comparison of (a) voltage output and (b) power output for WIV and VIV.
(a)
(b)


## 4. Conclusions

This paper does the VIV experiment on the energy harvesting device with a circular cylinder and two piezoelectric beams, and the WIV experiment is done by putting a fixed bigger cylinder upstream to study the impacts on the piezoelectric energy harvesting by two types of flow-induced vibrations. The results of the VIV experiment show that the voltage output increases with the increase of the load resistance; there is a best load resistance for the power output. The results of the WIV experiment indicate that the vibration frequency of the smaller cylinder is controlled by the vortex shedding frequency of the bigger cylinder upstream, and there is a best gap between two cylinders for obtaining the maximum voltage and power output. Compared with VIV, the lock-in region of WIV wholly moves backward due to the bigger diameter of the cylinder upstream, which means slightly higher wind speed is needed to obtain the maximum power output. It is also found that the maximum power output of WIV is larger than that of VIV, so for the same energy harvesting device; WIV has much higher power generation capacity and can improve the piezoelectric output properties effectively.



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*Source: 2673292-2016-04-27.xml*