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Visualization of Interactions Between Piezoelectric
Cantilevers using Soap Film Experiment
Layne M. Droppers1
, Veera Sajjanapu2
, and Akash Vidyadharan3
Iowa State University, Ames, IA,50011
The use of piezoelectric devices to generate electricity by harvesting wind has been an
area of increased interest in recent years. Here, we study piezoelectric films (cantilevers)
mounted in a low speed open circuit wind tunnel to investigate their wake interactions.
Under certain conditions, downstream distance and wind speed, we record a substantial
increase in the output voltage of the downstream piezoelectric film. The data is presented to
determine the most efficient method of low speed wind energy harvesting. In order to
understand these interactions, a soap-film experiment to understand the wake structure and
interactions was utilized. The soap film apparatus allows for the visualization of complex
two-dimensional vortex shedding and we use this to understand the interactions between
multiple cantilevers. With this study we hope to efficiently develop larger array for actual
power generation.
Nomenclature
Re = Reynolds number
t = time (s)
V = Voltage
I. Introduction
IEZOELECTRIC materials allow for the conversion of mechanical strain into electrical voltage. Utilizing
piezoelectric energy to power small, low-power electronic devices has emerged recently as an area of high
interest. Harnessing untapped energy from the environment - such as wind, solar, and tidal - has been proven
effective in recent years. Many approaches to harness piezoelectric energy have been studied, including placing
piezoceramic films in shoes and other various vibrational systems [1-7]. This project examines vortex interactions
between multiple flexible bluff bodies (piezoelectric films) so that more efficient piezoelectric energy harvesting
arrays can be determined.
To study the interactions between these piezoelectric beams, we visualize the wake patterns and the deformation
of these beams. To achieve these visuals, we use a soap film tunnel experiment. Soap film provides a unique way to
visualize two-dimensional downstream vortex interactions. Our soap film tunnel is based on the simple and effective
setup designed by Rutgers et al. (2001). This vertical soap film tunnel is able to produce a constant velocity soap
film that runs between two wires, driven by a pump. A film made of a soap solution is comprised of surfactant soap
molecules covering a sheet of water.
A soap film apparatus allows us to visualize the vortical flow and wake patterns with the help of Sodium
lamps. The Sodium lamps enable these interference fringes of the flow patterns present in the film to be visualized.
Because of the film’s thickness variation and the additional factor of air drag on the film, the question arises as to
whether or not a soap film is representative of an incompressible, two-dimensional flow. In general, if the film is
thin enough and the film velocity is slow enough, the effects of air drag become secondary, and the film may be
considered a two-dimensional liquid flow. Our investigation utilizes the assumption that the film is indeed two-
1
Undergraduate Student, Aerospace Engineering Department, 270 Barton Anders, Student Member.
2
Graduate Student, Aerospace Engineering Department, 1200 Howe Hall Ames, IA 50011-2271, Student Member.
3
Undergraduate Researcher, Aerospace Engineering Department, 2362 Howe Hall Ames, IA 50011-2271 , Student
Member.
P

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dimensional, making the process of studying flows much simpler, both computationally and experimentally. A more
in-depth explanation as to why the film can be considered as such is given in Rutgers.
II. Modeling
The piezoelectric beams used in the wind tunnel to get the power and voltage outputs were scaled down by a
factor of approximately 1:3 to fit in the soap film test region and to achieve geometric similarity between the test
pieces and the actual beams. The material of the laminated piezoelectric beams were simulated by using Practi-
Shim™ Color Coded Plastic Shims of thickness 0.0381 mm for the test sample beams. The floor used to mount
these beams on to were thicker 0.3048 mm Practi-Shim™ Color Coded Plastic Shims. The modulus of elasticity is
approximately equal for the piezoelectric beams and the soap film test pieces. Two different scenarios were tested in
the soap film tunnel to completely understand the dynamic interactions of the beams. The first model includes one
20mm beam attached to the floor to see the vortex sheddings and fluttering from a single beam. The second model
involves two beams of 20 mm placed at a distance of 8 mm apart from each other. The two models used in the soap
film experiment are shown in Figure.1 below. Table.1 below shows the geometric scaling used for making the soap
film models. A dynamic scaling was attempted to compare the Reynolds numbers of the soap film to the wind
conditions in the tunnel. The freestream velocity of the flow in the soap film experiment was controlled using a flow
meter which was connected to the pump.
Table. 1: Geometric Scaling between the Piezoelectric Films and the Soap Film Models
Length (mm) Distance (mm) Thickness (mm)
Piezoelectric Film 60 24 0.22
Soap Film Models 20 8 0.0381
Figure 1: Two different test case models used in the soap film tunnel
III. Setup
A. Wind Tunnel
In order to simulate a windy environment, a 12” x 12” x 24”
tunnel was made out of one-quarter inch thick acrylic. Round edges
were used at the entrance of the wind tunnel to smooth out the
airflow as it entered to minimize boundary effects. The entire wind
tunnel was held into place with bolts that were fastened into tapped
holes in the acrylic. At one end, a box fan was attached and sealed
using sealant. The fan was controlled using a variable
autotransformer, and pulled air from the opening at the opposite end
of the tunnel toward itself. Strips of piezoelectric film were
Figure 2: Wind tunnel setup with
piezoelectric films and oscilloscope

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mounted to a ¼’’ x ¼’’ x ¼’’ acrylic blocks via a small screw, and these blocks were mounted to the floor of the
wind tunnel with threaded bolts. The first piezoelectric film is mounted approximately 3 inches from the wind tunnel
entrance. Multiple holes were drilled into the bottom of the wind tunnel at spacings of one inch apart to allow for
multiple configurations of these piezoelectric films. These films had wires attached to them that were fed outside of
the tunnel. These were then connected to an oscilloscope, which was used to record the voltage over time created by
the vibrations of these films.
B. Soap Film
The soap film tunnel has four stages: the fluid injection section, the expansion or divergent
section, the test section, and the contraction or convergent section. These sections can be seen in Figure
3. The soap film tunnel used in this study consists of a metal frame, a flow frame, a recycle reservoir, a
pump, tubes, valves, and pull strings. Figure 4 below shows the schematic of the vertical soap film
tunnel, while Figure 5 shows the actual experimental setup.
Optimizing the apparatus was a multi-step process. Before alterations were made, the
design of the nearly vertical apparatus needed to be understood. An in-depth description can be found in Rutgers
paper. A low-pressure sodium lamp (SOX) light source is used to illuminate the film and a pump to recirculate the
soap solution. To gain more control over the flow rates, a flow meter was added in between the reservoir and the
nozzle.
The soap solution, 5%-Vol Dishwashing Liquid and 95%-Vol filtered cold water, is dispensed through the
reservoir and flows through tubing into a valve and then into the elliptical opening nozzle of 5.05mm major and
3.85mm minor length segments, from which two guide wires (of 0.7112mm diameter of Berkley Trilene Super
strong fishing line brand) come out. A connection piece is located between the valve and nozzle, enabling the tubing
to be separated and re-connected if there is a problem in the system. As our pump drives the film at very high
speeds, we had to use a bypass to reduce the driving pressure and hence gain better control over the flow. The soap
film is formed between the two guide wires.
The film can be thought of in three sections. The guide wires expand in the first section at a conical angle of 30°.
At the first set of adjustments, the angle of the guide wires is changed to 5° from the horizontal. The wires remain
parallel in the second section, at a separation width of 8.0 cm, until the second set of adjustments. At the second set
of adjustments, the angle of the guide wires changes to 30° down from the horizontal. The adjustments allow the
operator to move each guide wire horizontally by turning 2 screws. A wire (of 0.3mm diameter Berkley Trilene
Super strong fishing line brand) is tied around the guide wire, goes through a hole drilled into a nylon screw, and
then around the thread of the screw. Using a nut in the back of the screw and a conventional nut and washer enabled
the adjustment process to be easier. The solution collects in a lower reservoir, drains with a bulkhead connector, and
then is pumped (using a peristaltic pump) through more silicone tubing to nozzle.
Figure 4: Schematic of the soap film tunnel
Figure 3a: Divergent Section
Figure 3b: Test Section
Figure 3c: Convergent Section
Figure 5: Schematic of the soap film tunnel

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The apparatus is 2 m long from the main upstream support beam to the main downstream support beam. The
expanding section is 1 m, the parallel test section is 0.5 m, and the contracting section is 0.5 m. The angles and
lengths listed describe the settings used in this study, but the design of the apparatus allows these lengths and angles
to be adjusted.
A weight is attached to the guide wires to add tension. Depending on the angle of the test section, the weight
ranges from 5-10 kg. We use a 5kg dumbbell as a weight for all of our experiments.
A Hotshot high-speed camera is held above the film with a tripod and a clamp. The frame rate of the Camera
ranges from 500 – 100,000 fps, having one major drawback. At higher frame rates, the capturable region decreases.
Thus, for our experiments use a frame rate of 5000 fps, which still gives an optimum region of interest to study. The
light from the sodium lamp illuminates the film. The camera is connected to a Computer for collecting the Video
data.
IV. Procedure
A. Wind Tunnel
The goal of using the wind tunnel is to examine how the voltage, and thus displacement, of the
piezoelectric films changes with changes in air velocity. To test this, strips of piezoelectric film are placed in the
wind tunnel and their leads are connected to an oscilloscope. This oscilloscope records the changes in voltage over
time. Tests using a single piezoelectric film are used to obtain a baseline for comparison. The piezoelectric film is
oriented in the wind tunnel with its cross-sectional area facing the in incoming air flow. The air velocity is then
increased using the variable autotransformer, and voltages were obtained from the oscilloscope in one mile per hour
increments. Once a baseline was established, experiments were ran with multiple piezoelectric films. For the
purpose of this study, we will focus on the simplest interaction, which occurs between only two piezoelectric films.
Both films are aligned directly behind one another, with their cross-sectional areas facing the incoming air flow. The
same process used for the single film is then repeated.
B. Soap Film
The goals of operation are often to create a long lived film having constant thickness and flowing with a uniform
velocity. Once an apparatus has been built, the correct soap solution must be prepared, then injected from a nozzle
of the suitable shape into a properly shaped channel under the right ambient conditions to optimally achieve the
operational goals.
Once the setup of the apparatus is completed, 5% per volume liquid dishwash soap is added to the reservoir and
is stirred for 5 minutes till a decent amount of lather is formed over the soap water reservoir. The sodium lamps and
generator is turned on to illuminate the setup and to flow the soap water through the guide wires. In a few minutes,
the soap film will be formed within the boundaries of the strings. There are several ways of making a film. The
guide wires are pinched together at the nozzle with two pull strings. As the soap liquid flows downstream, the film is
made, the guide wires may be adjusted using the adjustment screw to fix the size of the test region and allow for a
stable and constant thickness soap film to be formed.
Once the soap film has been formed and stabilized, the
test piece may be mounted on the extendable arm and
gently inserted into the soap film. After the test piece
has been carefully inserted into the soap film, the flow
meter is used to set the velocity of the soap water
through the test region. Pictures and videos of the test
piece in the soap film may be recorded using the slow
motion camera to be further processed and refined.
The images that are captured are processed through
a code that we wrote in MATLAB which tracks these
Vortices and the pollutants in order to obtain their
respective Vortex rate and Free-stream Velocity. This
essential data helps us in relating the Strouhal number
and Reynolds number for the case of flutter in flexible
beams.
Figure 6: Voltage vs. Time at 8MPH Figure 7: Voltage vs. Re

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V. Results and Discussion
A. Wind Tunnel
A single piezoelectric film vibrates fairly uniformly. Figure 6 shows the alternating voltage that the films
produce when oscillating. Arranging the multiple films in such a way that they are in series with one another
significantly increases the amplitude of the voltage over time. The secondary film tends to oscillate less periodically,
often having large peaks caused by its interaction with the first film.
Figure 7 displays how the increased amplitude in voltage for the second film results in a significantly increased
voltage throughout the entire range of Reynolds numbers. The second film also produces a significant, measurable
voltage at a much lower Reynolds number than the first film. These increases in voltage can be attributed to the
wake created by the first film, which causes increased displacement by the second film.
B. Soap Film Experiment
Figure 8: Single Film Images Figure 9: Double Film Images
The above Figures 8 & 9 show the images obtained from the two different setups when soap film experiment
was performed. These experiments helped visualize the vortex sheddings and displacements on the beams.
Vibrations were observed on the beams during the experiment which helped to create a link between the soap film
experiments and the power generated by the piezoelectric beams in the wind tunnel. It was seen that when two
beams were placed together, the flow and vortices from the front beam significantly affected the displacements and
frequency of the rear beam. The displacement on the rear beam was found to be lesser than that of the front beam as
seen in Figure 9, but the frequency of the vibrations was larger on the rear beam than the front beam. This justified
the results obtained from the piezoelectric beams in the wind tunnel test, that the second beam generated more
voltage than the front beam. This is possibly due to the increased frequency of vibrations in the rear beam than the
front beam.

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Figure. 10-13: These plots give us an estimate about the velocity and the Reynolds number so as to show a dynamic
similarity between the Piezoelectric beams in the Wind tunnel.
Figure. 14: The plot shows the relation between the deformation of the beam’s free-end in the Single beam case and
Two beams case. As can be seen the second beam in the Two beam case is effected by the wake from the first beam
and this can also be visualized from the images we captured.
C. Relationship
Several relationships can be determined between the soap film visualization and the piezoelectric film
interaction. Using the geometric symmetry, we are able to determine that the vortices that are shed by the first film
did indeed induce additional vibrations in the second. The major role that the first film plays in this relationship is
transforming the flow from laminar to turbulent. Because of this, the subsequent films are displaced from the normal
mode at increasing distances.
Figure 10: Velocity vs. Flow Reading Figure 11: Velocity vs. Flow Reading Figure 12: Reynolds number vs.
Flow Reading
Figure 13: Reynolds number vs.
Flow Reading
Figure 14: Deformation vs. Flow
Reading

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VI. Conclusion
Interactions between multiple piezoelectric films in series produce a significant increase in generated voltage.
These interactions are in large part due to the vortices in the air flow created by the first film. By using the first film
as a bluff body, the flow can be changed from laminar to turbulent. This turbulence produces greater deflections in
the subsequent films, which in turn produces greater voltage which can be used for power generation. By continuing
to place piezoelectric films in series, one should be able to increase voltage output in each subsequent beam up until
a certain critical point which has yet to be decided. Regardless, this method can be used to more efficiently generate
power using piezoelectric film.
The interactions between flexible beams and fluids are studied using the flowing soap film. Soap film provides
an ideal two-dimensional flow field, in which a lot of two-dimensional experiments were carried out. Experimental
apparatuses’ designs and improvement.We improved the existing vertical soap film tunnel in our laboratory and
built a horizontal soap film tunnel. We also designed and built the illumination light for soap film and the tiny force
measurement system. For the Experimental data processing we designed the data process schemes and developed
corresponding programs. An image processing program was developed to extract rate of Vortices and the Pollutants
from the high speed camera images. In order to get a more intuitive understanding on the piezo beams, the vortex
street, another image processing program was developed to reassemble the high speed camera images to a streak
camera images. Through this scheme we could Visualize the wake patterns of these beams in order to estimate an
optimum position for the beams to make use of the fluttering to extract more energy.
Utilizing the information presented in this paper, the authors recommend future work to optimize the power
production of a large array of piezoelectric films. These arrays can be placed on the roofs of buildings, on top of
trains, or in open fields. The power produced by these arrays can be stored for future use, or used to power small
electronic devices. Understanding how these films interact with one another is imperative to reducing costs and
increasing practicality of energy harvesting using this method.
Acknowledgments
The authors would like to thank Dr. Thomas Ward III for his guidance throughout the entire research process and for
the use of his facilities.
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