the design of vortex induced vibration fluid kinetic energy harvesters

THE DESIGN OF VORTEX INDUCED VIBRATION FLUID KINETIC ENERGY
HARVESTERS
Q. Wen1,2, R. Schulze1, P. Streit1, D. Billep2, T. Otto2, and T. Gessner1,2
1
Technische Universität Chemnitz, Center for Microtechnologies (ZfM)
2
Fraunhofer Institute for Electronic Nano Systems (ENAS)
Abstract: Due to the rapid development in the field of microsystem technology during the last decade, micro
energy sources become the bottleneck in most of the applications. In order to extend the usable range of
environment energy sources, a fluid kinetic energy harvester is proposed. Compared to a hydro-turbine structure it
is more robust and has a better performance at smaller scale. The related theoretical background is introduced as
well as different simulations in order to optimize the performance are carried out. The demonstrator design based
on those simulation results is tested and evaluated. First experimental results are presented and compared with
simulation results.
Keywords: Energy harvesting, Fluid kinetic energy, Vortex Street, Piezoelectricity
a series of alternating vortices at each side of the bluff
body in downstream is generated, which show
opposite rotating directions. Therefore an unsteady
pressure distribution is formed, which leads to a
vibration of the piezoelectric transducer placed in the
downstream (Fig.1).
INTRODUCTION
Due to the rapid development in micro- and
nanotechnology within last decade, both size and
power consumption of microsystems has been
reduced [1]. For example, applications like wireless
body sensor networks or wireless pulse oximeters
even require less than 100µW during a measurement
and signal transmission period [2]. Hence, using
micro energy harvesters as power supply become
feasible in wireless sensor networks.
On the other hand, many different micro energy
harvesters have been investigated in the recent years
mainly utilizing solar, thermal and vibration. Both of
those harvester demonstrators show impressive
performance, but in order to improve the
environmental adaptability of a final system, the range
of usable energy sources also need to be extended.
According to [3], fluid kinetic energy can also provide
very reasonable amounts of energy compared to other
environmental energy sources. Unfortunately, with
device miniaturization, the efficiency of traditional
hydro-turbines is reduced, which is caused by the
proportional increased frictional forces. Hence the
vortex induced vibration approach was first
introduced for micro fluid energy harvesting by
Taylor [4] in order to avoid frictional forces during
energy conversion.
Figure 1: Scheme of the basic working principle
Due to the piezoelectric effect, the fluid kinetic
energy is finally converted to electrical energy.
Compared to the traditional hydro turbine, this energy
conversion approach promises a better performance
when the system size is reduced. Furthermore, its
rotation free structure avoids wear damage during
long term operation.
To achieve a Karman vortex street, the Reynolds
number must in the range between 47 and 10 000 (for
cylinders shaped bluff bodies) [5][6]
THEORETICAL BACKGROUND
ܴ݁ ൌ
In this contribution a fluid kinetic energy
conversion structure is proposed. It consists of a bluff
body and a piezoelectric transducer within a tunnel
test bench. The fluid flows across the bluff body
which is located inside a tunnel at a certain Reynolds
number. According to the Karman vortex street effect,
978-0-9743611-9-2/PMEMS2012/$20©2012TRF
஽ή௩
ఔ
(1)
which is determined by the fluid’s kinematic viscosity
ȣ, its velocity v and the diameter D of the bluff body.
The turbulent flow located behind the bluff body is
hard to describe with Navier-Stokes equations [4], but
it can be simplified as a sum of two velocity
243
PowerMEMS 2012, Atlanta, GA, USA, December 2-5, 2012
components, which are the flow along the
downstream with a velocity vlam and rotational flow
with a velocity vrot. It is assumed that the vortices
follow the Rankine vortex model and the distance
between two vortices at both sides of the bluff body is
above two times the cylinder vortex core radius [7-9].
According to the Bernoulli equation, the pressure p at
the surface of the cantilever, which is generated by the
Karman vortex street effect, can be written as
ఘ
ఘ
ଶ
‫ ݌‬ൌ ‫ݒ‬௟௔௠
െ ሺ‫ݒ‬௟௔௠ േ ‫ݒ‬௥௢௧ ሻଶ
ଶ
ଶ
Furthermore, the vortex induced pressure
distribution is calculated as basis of a subsequent
optimization.
Several simulations with the same inlet velocity
and same vortex shedding frequency but different
bluff body shapes are done to maximize the pressure
difference behind the bluff body.
By additionally using a specific sized tunnel with
cylinder-shaped bluff body, the pressure difference
can increasing from 10% up to 13% under the same
inlet velocity. This can be explained with the fact, that
the additionally channel increased the Reynolds
number in the sub domain.
(2)
The frequency of the pressure change is equal to
the vortices shedding frequency. It can be described
with the diameter of the bluff body D, the flow
velocity v and the Strouhal number Sr
݂௙௟௨௜ௗ௦ ൌ
ௌ௥ή௩
஽
(3)
MODELING AND SIMULATION
In order to analyze the interaction between the
structural and the fluidic domain and to optimize the
performance of the energy harvester, a two-way Fluid
Structure Interaction (FSI) model is set up. It is based
on a structural finite element and fluidic finite volume
analysis.
To explain the generation of vortices, a
Computational Fluid Dynamics (CFD) simulation is
used (Fig. 2). As initial condition, an inlet velocity of
2 m/s is stated and a cylinder-shaped bluff body is
used, that is comparable to the classical Karman
vortex street demonstrator [5].
For determining the size of the applied
piezoelectric cantilever and to avoid multiple bending,
the dimensions of the vortices are predicted. Bending
in multiple modes leads to a reduction of the electrical
energy conversion due to opposite occurring
mechanical strain within the piezoelectric transducer
caused by the pressure load.
Figure 3: CFD simulation - calculated pressure
difference across a cuboid-shaped bluff body (left);
pressure distribution of the arrangement (right)
By changing the bluff body shape to a sharper
geometry like a cuboid (Fig. 3), the pressure
difference can be increased four times compared to
the cylinder-shaped bluff body.
However, a secondary vortex is observed, which is
shed and moves following the main vortex. Those
vortices will lead to a small peak or delay on the
pressure difference curve (show as Fig 2) near the
zero crossing section.
It is constituted that this has a negative influence on
the energy conversion performance of the harvester
because the emerging pressure peaks damp the
vibration of the piezoelectric cantilever.
Figure 4: CFD simulation - calculated pressure
difference across a comb-shaped bluff body (left);
pressure distribution of the arrangement (right)
Figure 2: CFD simulation - calculated pressure
difference across a cylinder-shaped bluff body (left);
pressure distribution of the arrangement (right)
Therefore,
244
the
comb-shaped
bluff
body
is
an air flow inlet velocity ramped from 0 to 2 m/s is
presented in Fig. 6. An inlet velocity of 2 m/s leads to
cantilever vibration with frequency of 137 Hz and a
maximum deformation at the cantilever tip of 2.8 mm.
The total pressure and the cantilever deformation
over time can be seen in Fig. 7. Using the cuboidshaped bluff body, the secondary vortex is minimized.
introduced to reduce or entirely avoid pressure peaks
caused by secondary vortex. The results of this
improvement are shown in Fig. 4 and Fig. 7.
To describe the interaction between the structural
and the fluidic domain, a two-way Fluid Structure
Interaction (FSI) model is shown in Fig. 5. A
cantilever structure is placed in the downstream
behind the bluff body. For each time step in the
simulation, the vortex induced pressure at the
cantilever surface is calculated and used as input for
the cantilever deformation calculation. The resulting
mesh deformation in the structural simulation is
transferred back to the fluid simulation because the
cantilever deformation influences the pressure
distribution in the following step of the fluidic
simulation.
Figure 7. Total pressure on the cantilever and mesh
deformation due to the cantilever deformation over
time
EXPERIMENT
According to the simulation results, a demonstrator
including
a
piezoelectric
cantilever
(33mm x 12mm x 30mm) is assembled. It consists of
a cuboid-shaped aluminum bluff body and a
piezoelectric polymer (PVDF) transducer. This
demonstrator was tested in a self-assembled test bench,
which shown in Fig. 8.
Figure 5: Pressure distribution in the fluid of a Twoway Fluid-Structure Interaction simulation.
The pressure distribution in the fluid calculated in a
FSI simulation is shown in Fig. 5. As a reference,
structure‘s displacement profile is also depicted. It can
be seen that the length of cantilever is two times
shorter than the vortex diameter, therefore a onedirection bending bow is observed. Thus, additional
damping due to multiple bending is avoided.
Figure 8: Image of self-assembled demonstrator
setup
The air flow is generated by a fan and regulated, so
that a low turbulence level at the test section is
constituted. The air flows across the bluff body and
excites a series of vortices at the harvesting section
where the piezoelectric cantilever is located. As a
result, a cantilever vibration is induced because of the
vortices. Due to the piezoelectric effect charges are
Figure 6: Maximum deformation of the cantilever
(left); Cantilever deformation versus time for ramped
inlet velocity (0 up to 2 m/s) (right)
The corresponding deformation of the cantilever at
245
[2]
generated as a consequence of the occurring
mechanical strain and can be measured by an
oscilloscope. An air flow velocity of 2 m/s was
measured within the test section. The size of the bluff
body (33 mm x 12 mm x 1 mm) was chosen as a
result of the simulation to excite a specifically vortex
shedding frequency corresponding to the previous
measured natural frequency of the one-side clamped
piezoelectric cantilever.
0,2
[3]
[4]
Voltage
[5]
Peak of secondary vortex
Voltage (V)
0,1
[6]
0,0
[7]
-0,1
-0,2
-0,33
0,00
0,33
[8]
Time (s)
Figure 9: Voltage output at 2 m/s air flow over a
100 kŸ resistor
[9]
The output voltage over a 100 kŸ resistor load is
shown in Fig. 9. It can be seen, that the demonstrator
generates a peak to peak voltage of about 0.25 V. As
previously predicted in the simulation, a secondary
vortex can be observed in the output signal, which is a
small voltage peak behind the main peak.
CONCLUSION
In this paper, a fluid kinetic energy harvester based
on vortices induced vibration has been proposed. The
related theoretical background has been introduced as
well. Several simulations are presented for the
optimization of the final harvester’s performance. The
first experimental result shows, that a demonstrator
(33mm x 12mm x 30mm) is able to produce 0.25V
peak to peak output within an air flow with a velocity
of 2 m/s. Also the secondary vortex, which was
predicted in previous simulations, could be confirmed
by the experimental results. Based on CFD
simulations, a comb-shaped bluff body has been
recommended to minimize that secondary vortex.
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