Download 1 A miniature pneumatic energy generator using Kármán vortex

A miniature pneumatic energy generator using Kármán vortex street
Hai-Dang Tam Nguyen1, Huy-Tuan Pham2 and Dung-An Wang1
1
Graduate Institute of Precision Engineering, National Chung Hsing University,
Taichung 40227, Taiwan, ROC
2
Faculty of Engineering and Technology, HCM city Nong Lam University, Linh Trung
ward, Thu Duc dist., HCM city, Vietnam
Abstract
A proof-of-concept of a miniature pneumatic energy generator for harnessing energy
from Kármán vortex street behind bluff bodies is presented. It converts flow energy into
electrical energy by piezoelectric conversion with oscillation of a piezoelectric film. The
tandem arrangement of the bluff bodies is designed to enhance the amplitude of the
pressure fluctuation in the vortex street, which vibrates the piezoelectric film. Prototypes
of the energy generator are fabricated and tested. Experimental results show that an open
circuit output voltage of 14 mVp and an average output power of 0.59 nW are generated
when the pressure oscillates with an amplitude of nearly 70 Pa and a frequency of about
872 Hz. This energy harvesting approach has the potential of converting the flow energy
of compressed air in a pipeline into electricity for powering wireless sensing devices.
Future design guidelines for increasing the electrical power output are suggested based on
analyses.
Keywords: Pneumatic energy generator; Kármán vortex street; Piezoelectric
____________
*
Corresponding author. Tel.:+886-4-22840531; fax:+886-4-22858362
E-mail address: [email protected] (D.-A. Wang).
1
1. Introduction
A considerable amount of energy can be generated by converting fluid kinetic
energy to electrical energy. Unsteady or turbulent flows provides a unique opportunity to
produce substantial pressure fluctuations which in turn may be utilized by energyconverting materials for generating electricity. Recently, development of wireless sensor
network (WSN) for industrial process monitoring and control, machine health monitoring
(Okamoto et al., 2009), environment and habitat monitoring, healthcare applications,
home automation, and traffic control demands an economical source of energy without
supply of fuel and replacement of finite power sources.
Combination of miniature
pneumatic power systems with WSN systems may provide a solution to this need,
because in some plants pneumatic power is available as long as air flows through the
pipelines.
Miniature pneumatic power systems using turbines can be used to convert
mechanical energy from air flow into electricity (Holmes et al., 2005; Herrault et al.,
2008; Krähenbühl et al., 2009; Lyshevski, 2011).
These devices require elaborate
techniques for fabrication of their stator-rotor subcomponents and high rotation speeds
for efficient energy harvesting. A device with simpler structure design and ease of
application is needed to extract energy from fluid motion. The installation of bluff bodies
in pipe-line systems may provide an alternative for harvesting small scale fluid flow
energy. Sanchez-Sanz et al. (2009) accessed the feasibility of using the unsteady forces
generated by the Kármán street around a micro-prism in the laminar flow regime for
energy harvesting. They presented design guidelines for their devices, but fabrication
2
and experiments of the proposed device are not shown in their work. Allen and Smits
(2001) used a piezoelectric membrane placed behind the Kármán vortex street formed
behind a bluff body to harvest energy from fluid motion (see Fig. 1(a)). They examined
the response of the membrane to vortex shedding. The power output of the membrane is
not presented. Taylor et al. (2001) developed an eel structure of piezoelectric polymer to
convert mechanical flow energy to electrical power (see Fig. 1(b)). They have focused
on characterization and optimization of the individual subsystems of the eel system with
a generation and storage units in a wave tank. Design and deployment of the eel system
need further investigation.
Tang et al. (2009) designed a flutter-mill to generate
electricity by extracting energy from fluid flow (see Fig. 1(c)). Their structure is similar
to the eel systems of Allen and Smits (2001) and Taylor et al. (2001). They investigate
the energy transfer between the structure and the fluid flow through an analytical
approach.
These authors utilized the flow-induced vibrations of fluid-structure
interaction system to extract energy from the surrounding fluid flow (Blevins, 1990).
The eel structures of Allen and Smits (2001), Taylor et al. (2001) and Tang et al. (2009)
have the potential to generate power from milli-watts to many watts depending on system
size and flow velocity.
Akaydin et al. (2010) investigated energy harvesting from unsteady air flows
using a piezoelectric cantilever beam in the wake of a circular cylinder (see Fig. 1(d)).
The beam is oriented parallel to the incoming flow and fixed at its downstream end.
They demonstrated that the distance of the beam from the vortices and their circulation
affect the output power. The maximum output power was about 4 μW with a value of
Reynolds number of 14800 at the resonance frequency of the beam structure. Zhu et al.
3
(2010) attached an aerofoil to a cantilever which is placed behind a bluff body in a wind
tunnel (see Fig. 1(e)). Their electromagnetic generator can operate at a wind speed of 2.5
m/sec with a corresponding electrical output power of 470 μW , and an initial
displacement of the aerofoil is required for its operation. One method of increasing
pressure fluctuation amplitudes in a vertex street is to use multiple bluff bodies in tandem
arrangement (see Fig. 1(f)). Fu and Yang (2001) and Peng et al. (2004) reported that dual
bluff body in tandem arrangement can enhance the hydrodynamic vibration generated by
the vortex shedding. Another advantage of the dual bluff body over single bluff body is
the regularity of the vortices (Venugopal et al., 2010).
In this paper, a device for pneumatic energy harvesting from pressure fluctuation
in Kármán vortex street is developed. As shown in Fig. 2(a), the device has a flexible
diaphragm installed on the wall of a flow channel.
Two bluff bodies in tandem
arrangement are placed in the flow channel. A piezoelectric film of a cantilever type is
glued to a bulge affixed to the top surface of the flexible diaphragm. The piezoelectric
film can oscillate with the flexible diaphragm due to the vortices shed from the bluff
bodies in an air flow. As illustrated in Fig. 2(b), the flow channel is connected to a flow
source. Pressure in the flow channel behind the bluff bodies may fluctuate with the same
frequency as the pressure variation caused by the Kármán vortex street. As shown in Fig.
2(b), the pressure in the channel causes the diaphragm and the piezoelectric film to
deflect in the upward direction.
As the pressure increases to the maximum, the
diaphragm reaches its highest position (Fig. 2(c)).
When the pressure drops, the
diaphragm and the piezoelectric film deflect downward (Fig. 2(d)). As the pressure
decreases to the minimum, the diaphragm reaches its lowest position (Fig. 2(e)). Thus,
4
by connecting the energy generator to a flow source, the oscillating movement of the
diaphragm with the cantilever piezoelectric film attached to it makes the energy
harvesting possible.
The proposed device is similar to a flowmeter used extensively in industries. The
focus is to explore the potential of pneumatic energy harvesting from pipeline systems
using a diaphragm installed on the pipe wall. In order to access the feasibility of the
proposed energy generator, numerical simulations are carried out to estimate the pressure
fluctuations behind the bluff bodies. The performances of single and dual bluff body
arrangement are compared in terms of the pressure amplitude. A prototype of a device
with dual bluff body in tandem arrangement is fabricated. Experimental setup used to
measure the pressure in the flow channel, the deflection and voltage output of the device
is reported. The experimental results are compared with the results of the simulations.
2. Design and Analysis
2.1 Design
Our design of the miniature pneumatic energy generator is based on the pressure
variation induced by the formation of the Kármán vortex street behind bluff bodies in an
air flow channel.
The variation of the air pressure in the channel drives a
polydimethylsiloxane (PDMS) diaphragm and a cantilever piezoelectric film into
vibration. The vibration energy is converted to electrical energy by the piezoelectric film
(Howells, 2009). A schematic of the piezoelectric energy generator is shown in Fig. 3(a).
Fig. 3(b) is an exploded view of the energy generator. It consists of a flow channel, two
triangular bluff bodies, a PDMS diaphragm bonded to the channel, and a piezoelectric
5
film attached to the PDMS diaphragm through a bulge made of acrylic blocks. The
triangular bluff body is selected due to its performance in terms of pressure fluctuation
amplitude. Venugopal et al. (2011) reported that triangular and trapezoidal bluff bodies
give higher wall pressure amplitudes than conical, ring-type and circular bluff bodies.
This harvesting of flow energy via the formation of Kármán vortex street behind
bluff bodies is related to the response of a flexible diaphragm to a periodical pressure
variation of air in a flow channel. Flow past a bluff body creates an unstable wake in the
form of alternating vortices and induces the periodic pressure variation (Violette et al.,
2007). An increase in the amplitude of pressure fluctuation can occur in the downstream
of the bluff bodies in tandem arrangement, as compared to that of a single bluff body (Fu
and Yang, 2001). The frequency at which the vortices are shed from the triangular bluff
body is given by the Strouhal number, St (Chung and Kang, 2000)
St fD / U 
(1)
where f is the frequency of oscillating flow, D is the characteristic length, and U  is
the free-stream velocity. The base length, D , of the isosceles triangular cylinder and the
height of the flow channel, H , are denoted in Fig. 3(a). The separation length of the
bluff bodies, L , is indicated in Fig. 3(b). The triangular cylinder is selected to ensure
that the flow is separated at its sharp edges irrespective of Reynolds numbers (Miau and
Liu, 1990).
The flow considered in this investigation is bounded by the flexible structure and
rigid walls. If the diaphragm has small inertia and is flexible enough to be able to
respond rapidly to the fluctuating pressure field set up by the vortex shedding, one may
expect that the diaphragm may oscillate with a frequency similar to the vortex shedding
6
frequency.
When the fluctuating pressure is applied on the bottom surface of the
diaphragm, the piezoelectric film with one end attached to the diaphragm and the other
end fixed to the upper wall of the flow channel strains laterally. The normal strain causes
electrical charge to accumulate on the piezoelectric electrode, resulting in a voltage in the
thickness direction of the piezoelectric film.
2.2 Model
In order to obtain the pressure fluctuation of the flow behind the bluff bodies,
two-dimensional flow analyses are carried out using a commercial software ANSYS
FLUENT. The dimensions of the device considered in this investigation are indicated in
Fig. 3(b). In the simplified simulations, it is assumed that the flow is bounded by fixed
walls. The effects of the fluid-structure interaction are ignored. Here, the simulations
serve the purposes of estimating the pressure amplitude applied on the flexible diaphragm
and testing the feasibility of the design.
Fig. 4(a) shows the computational domain for the model.
The distances of
upstream and downstream boundaries from the fore and aft bodies are 23.53 D and
44.59 D , respectively. The height of the domain and the distance between the fore and
aft bodies are 3.76 D and 2.47 D , respectively. Fig. 4(b) shows a close-up view of the
mesh near the bluff bodies. A mesh for the case of a single bluff body is also created for
comparison of the pressure fluctuation between the dual and single bluff body
arrangement. Fig. 4(c) is a close-up view of the mesh near the single bluff body. The
elements are about 0.25 mm in size near the bluff bodies. The numbers of triangular cells
for the single and dual bluff body cases are 9153 and 9028, respectively. The static
7
pressure at the center of the flexible diaphragm, indicated by the symbol S as shown in
Fig. 4(b) and (c), is monitored in the simulations. Point S is located 2 D downstream of
the aft bluff body. A grid size sensitivity analysis for the dual bluff body case reveals
that there is only 2% of relative error in the amplitude of the pressure fluctuation at point
S by doubling the number of cells near the bluff bodies.
In the investigation, a uniform velocity profile at the inlet along the direction of
the inlet flow is applied. No-slip (zero velocity) conditions all along the channel walls
and the perimeter of the bluff bodies are specified. The standard wall function is used for
the near-wall treatment. The fluid is considered incompressible. It is assumed that only
the relative value of pressure is important, and a zero pressure is applied at the outlet of
the channel. The Reynolds number is calculated in order to determine if the analysis is in
the turbulent region. The Reynolds number of the flow channel can be determined by
Re U D / 
(2)
where , 1.225 kg/m 3 , and , 1.789 105 Pa 
sec , are the density and dynamic
viscosity of the air, respectively. With an inlet velocity of 20.7 m/sec, the calculated Re
is 6024, which is turbulent. The size of time steps can affect the simulation results in a
flow field with high Reynolds numbers. In this investigation, the time step size is chosen
as about 1/100 of vortex shedding period. The chosen time step is nearly 0.05 Tc , where
Tc = D/U is the convective time.
2.3 Analyses
Using the k Realizable turbulent model of ANSYS FLUENT, the vorticity
contours and pressure fluctuations in the flow channel are obtained. Fig. 5(a) shows the
8
instantaneous vorticity contours behind the bluff bodies. A vortex street with alternating
vortices spaced at nearly equal distances extends downstream of the bluff bodies. The
alternative vortex shedding induces periodical pressure fluctuations in the flow channel.
Fig. 5(b) shows the time history of the pressure at the point S for the single and dual bluff
body cases. The pressure difference Pmax Pmin for the single and dual bluff body case
are 154 Pa and 214 Pa, respectively. The pressure fluctuation of the two bluff bodies in
tandem arrangement is nearly 1.5 times more than that of the single bluff body. The ratio
of the separation length, L 10.5 mm , to the characteristic length, D 4.25 mm , is 2.5,
which is comparable to the ratio, 3.9, obtained by Peng et al. (2004) with similar dual
bluff body arrangement for achieving maximum hydrodynamic vibrations.
The fundamental shedding frequency for both the single and dual bluff body cases
are 998 Hz based on the fast Fourier transform. Using Eq. (1), the calculated Strouhal
number is nearly 0.20. Venugopal et al. (2011) reported that the value of Strouhal
number varies with Reynolds number for different bluff body configurations. The flow
velocity, 20.7 m/sec, is comparable to the typical value of the speed of the compressed air
in a pipeline, which may be as high as 30 m/sec.
Depending on the operating
environment, a pneumatic energy generator can be designed for the suitable range of its
inlet air velocity.
The simulations are carried out in two dimensions. This may be adequate for the
purpose of testing the feasibility of the design, and the results of these simulations are
used to inform the experimental work.
The shortcomings of the two-dimensional
simulations should be expected due to the existence of three-dimensionality of flow in the
wake region at higher Reynolds numbers. The existence of spanwise structure in the
9
wake region of the flow in not captured by the two-dimensional simulations. Also, the
two-dimensional simulations fail to take into account of the end effects which have a
significant influence on the flow. For example, Sohankar et al. (1999) reported that flow
profiles around a square cylinder differ significantly between their two-dimensional and
three-dimensional simulations.
3. Fabrication, experiments and discussions
3.1 Fabrication
In order to verify the feasibility of the proposed energy harvesting device,
prototypes of the energy generator are fabricated. The PDMS diaphragm is fabricated by
a molding process in an acrylic mold. First, an acrylic mold is carved by a milling
machine (PNC-3100, Roland DGA Co., Japan). Next, the PDMS material is poured over
the mold. The PDMS material is composed of two parts, a curing agent and the polymer.
They are mixed with a volume ratio of 1:10. Before pouring into the mold, the mixture is
degassed under vacuum until no bubbles appear. The PDMS is cured at 80o C for 40
minutes. Then, the PDMS is peeled off from the mold.
Fig. 3(b) shows the components of the device. The walls, the top plate and the
bottom plate of the flow channel are manufactured by a milling machine. The top plate
of the flow channel with an embedded PDMS diaphragm is attached to the top surface of
the walls. The triangular bluff bodies are inserted through the opening on the side walls
and secured by an adhesive (3M Scotch). Subsequently, an acrylic bulge is glued to the
center of the PDMS diaphragm, and an acrylic anchor is glued to the top plate to provide
a support of a piezoelectric film. The piezoelectric film (LDT0-028K/L, Measurement
10
Specialties, Inc., US) is glued to the bulge and the acrylic anchor by applying an adhesive
(3M Scotch) to complete the assembly steps. The PDMS flexible diaphragm has a
thickness of 200 μm .
The piezoelectric film is a laminated film including a
polyvinylidene fluoride (PVDF) film, two silver electrode layers and a polyester (PE)
layer. The electrode layers with a thickness of 28 μm are attached to the top and bottom
surfaces of the PVDF film of 24 μm. A 125 μm PE layer is laminated to the top surface
of the top electrode layer. Fig. 6 is a photo of an assembled energy generator.
3.2 Experiments
Fig. 7 is a photo of the experimental apparatus for testing of the fabricated device.
The energy generator is fixed on a table. An inlet pipe, which is connected to the outlet
of a wind tunnel manufactured in England by Woods of Colchester Ltd., is run to the inlet
of the energy generator. Air from the wind tunnel is forced into the inlet of the energy
generator. The outlet of the flow channel is kept open to the atmosphere. Fig. 8 is a
schematic of the measurement apparatus. The oscillating deflection of the piezoelectric
film is measured by a laser displacement sensor (CD4, OPTEX FA Co., Ltd., Japan).
The generated voltage of the piezoelectric film is recorded and analyzed by a data
acquisition unit (USB-9234, National Instruments Co., US), which can retrieve data with
24 bit resolution at a sampling rate of 51200 samples/sec per-channel. The pressure in
the flow channel is measured with an acoustic pressure sensor (103B02, PCB
Piezotronics, Inc., US) embedded in the bottom plate of the flow channel, nearly 2 D
behind the aft bluff body and opposite to the flexible diaphragm. The pressure sensor has
a resonance frequency of more than 13 kHz and a resolution of 0.14 Pa.
11
The inlet velocity of the energy generator is set at 20.7 m/sec, measured using an
anemometer (SwemaAir 50, Sweden). The experimental results are shown in Fig. 9. Fig.
9(a) shows the pressure history at the bottom plate of the flow channel, where the
pressure oscillates with an averaged amplitude of nearly 70 Pa and a frequency of 872 Hz
during the recording period of 30 msec. The measured deflection history of the free end
of the piezoelectric film is shown in Fig. 9(b). The film oscillates with an average
amplitude of about 1 μm and a frequency of 889 Hz. The measured open circuit voltage
generated by the piezoelectric film is shown in Fig. 9(c). The average amplitude and
frequency of the output voltage is nearly 14 mVp and 876 Hz, respectively. Fig. 9(d-f)
are the power spectral density (PSD) corresponding to Fig. 9(a-c), respectively. Fast
Fourier transform is used to compute the power spectral density.
As seen in Fig. 9(d-f), the measured signals are close together in frequency. It is
evident that the flexible diaphragm and the piezoelectric film oscillate with the pressure
fluctuation. The experiments are carried out at an inlet velocity of 20.7 m/sec which
results in a value of Re = 6024. Akaydin et al. (2010) reported that at Re > 5000
turbulent structures are less organized and some minor fluctuations in forcing frequency
are expected. The frequency noise, below 700 Hz, observed in Fig. 9(e) can be attributed
to the fact that the experimental setup is always contaminated by ambient noise sources.
The frequency of the pressure fluctuation is nearly 872 Hz at which the vortices are shed
from the bluff body. Using Equation (1), the corresponding value of St is estimated as
0.18, which is close to the simulated value, 0.20. The average amplitude of the pressure
fluctuations, 70 Pa, is lower than that based on the simulation, 107 Pa.
Pressure
measurements are subjected to inevitable uncertainties. As shown in Fig. 9(a), the f
l
ui
d’
s
12
pressure can not be maintained for long period, unsimilar to the shedding frequency
which depends only on the shape and size of the bluff body (Venugopal et al., 2011).
Similar pressure fluctuations on the walls of the flow channel with single and dual bluff
body are observed by Miau and Liu (1990) and Peng et al. (2008), respectively.
In order to evaluate the harvesting system, experiments on the electrical power
output of the device are carried out by measuring the voltage drop across a load resistor.
A resistor sweep ranging from 250 kOhm to 350 kOhm is performed. The instantaneous
power can be calculated by
2
V
P p
R
(3)
where R is the resistance value of the load and V p is the peak value of the voltage drop
across the load. Fig. 10 shows the average power output as a function of the load
resistance. The maximum of the average power output is found to be 0.59 nW . The
output power of the device is extremely low, rendering the current design of the device
not practical. In order to obtain a higher output power of the miniature pneumatic energy
generator, the dimensions and structure of the device should be redesigned to optimize its
power output, and a piezoelectric material with higher piezoelectric constants can be
adopted. Based on the experiments of Ak
a
y
d
ı
ne
ta
l
.(
2
010
)
, the device could harvest
more energy if the flexible diaphragm were placed at specific positions relative to the
vortices shed from the bluff body upstream. The simulated wall pressure distribution
along the streamwise direction obtained for the dual bluff body case shown in Fig. 11
reveals that the maximum pressure fluctuation is located near where the minimum mean
pressure occurs. In the figure, the mean and amplitude of the static pressure fluctuations
are taken as the center value of the error bar and one-half of the length of the error bar,
13
respectively. Miau and Liu (1990) reported that maximum pressure fluctuation occurs
downstream of the location where the minimum mean pressure is measured for a circular
disk bluff body in a circular pipe. The flexible diaphragm of the device may be moved
upstream in order to increase its electrical power output.
From a geometric viewpoint, the base length, D , of the triangular bluff body
should be large enough in order that the unsteady pressure fluctuations in the wake can be
reflected from flow development near the wall. On the other hand, the base length can
not be too large to result in unnecessary momentum loss (Miau and Liu, 1990). Fig. 12
shows the simulated pressure fluctuations at the center of the flexible diaphragm versus
the blockage ratio, defined by the ratio of the base length of the triangular cylinder to the
height of the flow channel ( D / H ), for the dual bluff body case. In the figure, the center
value of the error bar and one-half of the length of the error bar represent the mean and
amplitude of the static pressure fluctuations, respectively.
The aspect ratio of the
triangular cylinder is kept as 1.95, the ratio of the base length (4.25 mm) to the altitude
(2.18 mm) of the triangular cylinder as shown in Fig. 3(b). The pressure fluctuation
increases with the blockage ratio initially, reaches its maximum at D / H =0.33, then
decreases gradually to nearly zero at D / H =0.42. The presence of the walls can inhibit
the vortex shedding completely for the blockage ratio above certain values (Miau and
Hus, 1992). Venugopal et al. (2010) found that a blockage ratio of 0.30 gives the highest
wall pressure amplitude among the three blockage ratios, namely 0.14, 0.24 and 0.30,
considered in their experiments with a trapezoidal bluff body. The blockage ratio of the
fabricated device, D / H =0.27, is not the optimum choice. The performance of the
miniature pneumatic energy generator can be improved using a blockage ratio of 0.33 and
14
moving the flexible diaphragm upstream based on the simulations. It is noted that
various shapes of bluff bodies and separation lengths between them can also be
considered in the future in order to stabilize and increase the strength of the growing
vortex and therefore to increase the power generation capacity of the proposed device.
If the flexible diaphragm is moved upstream 6 mm where the maximum pressure
fluctuation occurs (nearly 1.54 folds increase in pressure fluctuation compared to the
fabricated device based on the results in Fig. 11), and the blockage ratio of 0.33 is
selected (nearly 1.42 folds increase in pressure fluctuation compared to the fabricated
device based on the results in Fig. 12), the pressure fluctuation of the optimized device is
2.19 times larger than that of the fabricated device by assuming linear multiplication.
Based on the work of Wang et al. (2012) for a miniature hydraulic energy harvester with
a structure similar to the presented device, the instantaneous power P is proportional to
the square of the pressure fluctuation. Therefore, an estimated 4.80 times more power
could have been produced by the device if the set up had been optimized in terms of
device position and blockage ratio.
Energy harvesting wireless sensor networks should operate in one of the sleep
mode and the active mode. Because of the low power density of the energy harvesters,
the harvested energy needs to be stored in a capacitor during the sleep mode of the sensor
and dissipated during the active mode. Typically, the wireless sensor node requires tens
of mW to operate, which is much more than the power output of the presented device.
One to two orders of magnitude reduction in power dissipation of sensor networks are
required for the sensor networks to operate off of energy harvesters. Hempstead et al.
(2005) reported that with selection of process technology and novel circuit design, event-
15
driven sensor devices can be developed to provide a total active power of ~25 μW and
idle power of ~70 nW . With a duty cycle of 0.1 or less, the average power of their
device may drop to less than 2 μW . To account for the power requirement of the sensor
networks, an energy harvester with an array of structures with resonance frequencies
tuned to the pressure fluctuation frequency can be utilized. The other possible route is to
adopt a piezoelectric film with very high piezoelectric constants to increase power output
of the device. Kuwata et al. (1982) reported a piezoelectric constant of 1500 pC/N of the
0.91PZT-0.09PT material, which is two orders larger than that of the piezoelectric film,
23 pC/N, used in this investigation.
4. Conclusions
A miniature pneumatic energy generator based on pressure fluctuation in a vortex
sheet is developed. The energy is harvested from Kármán vortex street behind two bluff
bodies in tandem arrangement in an air flow. The pressure oscillation due to the Kármán
vortex street in the flow channel of the generator results in a periodical deflection of the
piezoelectric film and therefore the voltage generation. The dual bluff body in tandem
arrangement is found to have a higher pressure fluctuation behind the bluff bodies than
that of the single bluff body case, which is beneficial to the design of the energy
generator considered in this investigation. The open-loop output voltage and average
power of the fabricated device are approximately 14 mVp and 0.59 nW , respectively,
when the pressure oscillates with an amplitude of nearly 70 Pa and a frequency of about
872 Hz. The performance of the miniature pneumatic energy generator can be improved
by using a blockage ratio of 0.33 and placing the center of the flexible diaphragm at a
16
wall position just above the aft bluff body.
A piezoelectric material with higher
piezoelectric constants can be adopted for higher output power of the device. Sources of
pressure fluctuation of Kármán vortex street can be compressed air flow in pipelines, air
flow in tire cavities, or fluid flow in machinery.
Acknowledgement
This work is financially supported by a grant from National Science Council,
Taiwan (Grant Number: NSC 100-2221-E-005-078).
17
References
Aka
y
dı
n,H.D., Elvin, N., Andreopoulos, Y., 2010. Wake of a cylinder: a paradigm for
energy harvesting with piezoelectric materials. Experiments in Fluids 49, 291-304.
Allen, J.J., Smits, A.J., 2001. Energy harvesting eel. Journal of Fluids and Structures 15,
629-640.
Blevins, R.D., 1990. Flow-induced vibration 2nd edition. Van Nostrand Reinhold, New
York.
Chung, Y.J., Kang, S.H., 2000. Laminar vortex shedding from a trapezoidal cylinder with
different height ratios. Physics of Fluids 12, 1251-1254.
Fu, X., Yang, H., 2001. Study of hydrodynamic vibrations in dual bluff body vortex
flowmeter. Chinese Journal of Chemical Engineering 9, 123-128.
Hempstead, M., Tripathi, N., Mauro, P., Wei, G.-Y., Brooks, D., 2005. An ultra low
power system architecture for sensor networks applications, in Proceedings of the
32nd International Symposium on Computer Architecture, 4-8 June 2005, pp. 208219.
Herrault, F., Ji, C.H., Allen, M.G., 2008. Ultraminiaturized high-speed permanentmagnet
generators
for
milliwatt-level
power
generation.
Journal
of
Microelectromechanical Systems 17, 1376-1387.
Holmes, A.S., Hong, G., Pullen, K.P., 2005. Axial-flux permanent magnet machines for
micropower generation. Journal of Microelectromechanical Systems 14, 54-62.
Howells, C.A., 2009. Piezoelectric energy harvesting. Energy Conversion and
Management 50, 1847-1850.
Krähenbühl, D., Zwyssig, C., Weser, H., Kolar, J.W., 2009. Theoretical and experimental
results of a mesoscale electric power generation system from pressurized gas flow.
Journal of Micromechanics and Microengineering 19, 094009.
Kuwata, J., Uchino, K., Nomura, S, 1982. Dielectric and piezoelectric properties of
0.91Pb(Zn1/3 Nb 2/3 )O 3 0.09PbTiO 3 single crystals. Japanese Journal of Applied
Physics 21, 1298-1302.
Lyshevski, S.E., 2011. High-power density miniscale power generation and energy
harvesting systems. Energy Conversion and Management 52, 46-52.
Miau, J.J., Hus, M.T., 1992. Axisymmetric-type vortex shedders for vortex flowmeters.
18
Flow Measurement and Instrumentation 3, 73-79.
Miau, J.J., Liu, T.W., 1990. Vortex flowmeter designed with wall pressure measurement.
Review of Scientific Instruments 61, 2676-2681.
Okamoto, H., Suzuki, T., Mori, K., Cao, Z., Onuki, T., Kuwano, H., 2009. The
advantages and potential of electret-based vibration-driven micro energy harvesters.
International Journal of Energy Research 33, 1180-1190.
Peng, J., Fu, X., Chen, Y., 2004. Flow measurement by a new type vortex flowmeter of
dual triangulate bluff body. Sensors and Actuators A 115, 53-59.
Peng, J., Fu, X., Chen, Y., 2008. Experimental investigations of Strouhal number for
flows past dual triangulate bluff bodies. Flow Measurement and Instrumentation 19,
350-357.
Sanchez-Sanz,
M.,
Fernandez,
B.,
Velazquez,
A.,
2009.
Energy-harvesting
microresonator based on the forces generated by the Kammon street around a
rectangular prism. Journal of Microelectromechanical Systems 18, 449-457.
Sohankar, A., Norberg, C., Davidson, L., 1999. Simulation of three-dimensional flow
around a square cylinder at moderate Reynolds numbers. Physics of Fluids 11, 288306.
Taylor, G.W., Burns, J.R., Kammann, S.M., Powers, W.B., Welsh, T.R., 2001. The
energy harvesting eel: A small subsurface ocean/river power generator. IEEE
Journal of Oceanic Engineering 26, 539-547.
Tang, L., Païdoussis, M.P., Jiang, J., 2009. Cantilevered flexible plates in axial flow:
Energy transfer and the concept of flutter-mill. Journal of Sound and Vibration 326,
263-276.
Violette, R., de Langre, E., Szydlowski, J., 2007. Computation of vortex-induced
vibrations of long structures using a wake oscillator model: Comparison with DNS
and experiments. Computers & Structures 85, 1134-1141.
Venugopal, A., Agrawal, A., Prabhu, S.V., 2010. Influence of blockage and upstream
disturbances on the performance of a vortex flowmeter with a trapezoidal bluff body.
Measurement 43, 603-616.
Venugopal, A., Agrawal, A., Prabhu, S.V., 2011. Review on vortex meter –Designer
perspective. Sensors and Actuators A 170, 8-23.
19
Venugopal, A., Agrawal, A., Prabhu, S.V., 2011. Influence of blockage and shape of a
bluff body on the performance of vortex flowmeter with wall pressure measurement.
Measurement 44, 954-964.
Wang, D.-A., Chao, C.-W., Chen, J.-H., 2012. A miniature hydro energy harvester based
on pressure fluctuation in Kármán vortex street. Journal of Intelligent Material
Systems and Structures , DOI: 10.1177/1045389X12467517.
Zhu, D., Beeby, S., Tudor, J., White, N., Harris, N., 2010. A novel miniature wind
generator for wireless sensing applications, The 9th IEEE Conference on Sensors
2010, Waikoloa, Hawaii, USA, November 1-4, 2010.
20
Fig. 1. Schematic diagrams of the devices of (a) Allen and Smits (2001); (b) Taylor et al.
(2001); (c) Tang et al. (2009); (d) Akaydin et al. (2010); (e) Zhu et al. (2010); (f) Fu and
Yang (2001).
21
Fig. 2. Operation of a piezoelectric energy generator.
22
Fig. 3. (a) An assembled energy generator.
generator.
23
(b) An exploded view of the energy
Fig. 4. (a) Computational domain for flow over two bluff bodies in tandem arrangement.
(b) A close-up view of the mesh near the bodies. (c) A close-up view of the mesh for
flow over a single bluff body.
24
Fig. 5. (a) Instantaneous contours of vorticity magnitude for flow over two bluff bodies
in tandem arrangement. (b) Time histories of static pressure.
25
Fig. 6. Assembled energy generator.
26
Fig. 7. A photo of the experimental setup.
27
Fig. 8. A schematic of the measurement apparatus.
28
Fig. 9. Experimental results. (a) Pressure variation at the flexible diaphragm center. (b)
Deflection of the free end of the cantilever piezoelectric film. (c) Output voltage of the
piezoelectric film. (d-f) Power spectral density corresponding to (a-c).
29
Fig. 10. Experimental average power versus load resistance.
30
Fig. 11. Simulated wall static pressure distribution along the streamwise direction.
31
Fig. 12. Simulated static pressure fluctuations at the flexible diaphragm center versus
blockage ratios of the flow channel.
32