Download Flutter-mills: from destructive phenomenon to the story of success

Flutter-mills: from destructive
phenomenon to the story of success
Author: Jure Ausec
Mentor: dr. Daniel Svenšek
Ljubljana, April 2012
Abstract
The flutter was considered as the unwanted, destructive phenomenon. But the modern
society with higher demands on electricity-production, forced scientists to develop new
energy harvesting devices, turning the devastating phenomenon into a new
environmentally friendly energy source. This paper presents some of the basic theoretical
background and the present state of the development. As it is shown, there are several
promising devices that are currently still under development, so their performance is
mainly predicted based on the small-scale devices.
Contents
Contents................................................................................................................................................2
1. Introduction......................................................................................................................................2
2. Theoretical background....................................................................................................................3
2.1. Flutter phenomenon..................................................................................................................3
2.1.1. Historical overview...........................................................................................................3
2.1.2. Limit cycle........................................................................................................................4
2.1.3. Hopf bifurcation................................................................................................................4
2.1.4. Basic assumptions and concepts.......................................................................................4
2.1.5. Final equation of motion...................................................................................................5
2.2. Induction and Faraday's law.....................................................................................................7
2.3. Transforming mechanical energy into electrical energy...........................................................7
3. Devices for harvesting electricity ....................................................................................................9
3.1. Flutter-mill................................................................................................................................9
3.2. Helmholtz-resonator-based scavenger....................................................................................11
4. Prototypes and commercially available products...........................................................................12
5. Conclusions....................................................................................................................................13
6. References......................................................................................................................................13
Figures and photos.........................................................................................................................14
1. Introduction
Scientists have been trying hard to invent new methods of producing electricity since the first
discovery of electric motor. Many ways have been introduced, but majority of them depended on
fossil fuels. That means they were environmentally unfriendly and will not last forever due to the
limited amount of fossil fuels. The production of electricity from renewable sources is a possible
answer to the higher energy consumption of modern society, with water, air and sun as possible
sources. In Slovenia, hydro power plants are important producers of electrical power and solar
power plants are getting more and more popular. Although Slovenia also has some regions with a
good potential for harvesting the kinetic energy of wind, such a power plant hasn't been built yet.
A classic horizontal axis wind turbine (HAWT, Fig. 1) is being built on
Volovja reber in Slovenia. This is a green way of producing electricity, but
many environmentalists aren't happy with this solution. They are afraid that
the big rotor could kill birds, some of them endangered species. Big
structures also destroy the scenic views and they can be quite noisy, which
can be very unpleasant for the local people. The new ways of harvesting wind
energy – invented in the past few years – promise a much better solution.
Wind belts, flutter-mills and similar devices transform kinetic energy of air
masses into vibrational energy of a strip of a very thin and strong material or
deformable plate. This energy can then be transformed into alternating
Fig. 1 - Classic
electrical current by induction or piezocrystals and with an appropriate
HAWT, build
electronic device into the desired electrical output (either direct current or
offshore.[1]
alternating current of right frequency).
Even though the main principle of such devices is fairly simple and understandable to a high school
2
student, it is only now that such devices are being invented. The main reason is probably the very
difficult theoretical description of the flutter phenomenon. The correct derivation of equations for
this fluid-structure system includes unsteady lumped vortex model coupled with nonlinear equation
of motion of a plate and a number of simplifications and assumptions. The whole derivation is
beyond the purpose of this paper, so only a short summary of the results necessary for the
understanding of this phenomenon will be presented.
2. Theoretical background
2.1. Flutter phenomenon
2.1.1. Historical overview
The most known example of flutter in everyday life is the
movement of a flag in the wind. Flutter is a self-exciting
oscillation, caused by aerodynamic forces coupled with the
object's natural mode of vibration. The amplitude of oscillation
can build up and cause even the destruction of the object if the
aerodynamic and mechanical damping is too small to efficiently
reduce the amplitude (see Fig. 2).
The phenomenon became scientifically interesting in the
beginning of the 20th century. Airplanes were improved and could
reach higher speeds and consequently their wings were subjected
to flutter. Many accidents of the early airplanes are thought to have been caused by this
phenomenon. There is a whole list of accidents caused by flutter: from chimneys to bridges being
completely destroyed. The most famous is the Tacoma Narrows Bridge in Washington, USA – the
bridge was badly constructed and it collapsed only four months after the opening (Fig. 2).
Fig. 2 – Tacoma Narrows Bridge
collapsing.[2]
The flutter phenomenon was first identified in
1918 on a bomber in England. The unsteady
aerodynamic theory was developed in the next
years and enabled scientists to calculate the
first solutions to simple, academic problems in
the 1940s and 1950s. In the next decades new
powerful
mathematical
methods
were
introduced, but the really useful solutions to
problems were calculated only in the recent
Fig. 3 – Model of wing for analyzing flutter motion,
allowing movement in vertical direction and rotation.[3]
years as computers' performance was
improved. Many real-world problems are
nowadays solved by numerical methods with powerful computer techniques. However, some
problems have remained too difficult for computation, so solutions to these are measured
empirically in wind tunnels with the use of specially designed models.
2.1.2. Limit cycle
A limit-cycle on a plane is a closed trajectory in phase space. Its property is that at least one other
trajectory spirals into it. If this happens as time approaches infinity, such a limit-cycle is called
3
stable or attractive, if this happens as time
approaches minus infinity, such a limit-cycle is
called unstable or unattractive, as all the trajectories
diverge from limit-cycle. Trajectories with such a
property are found in some non-linear systems,
such as Van der Pol oscillator, described by a
second-order
differential
equation
d²x
dx
−1−x²  x =0 , which has a non-linear
dt²
dt
damping  (Fig. 4). As it is seen in the figure,
perturbations from closed trajectories can disturb
the system only for a short period of time, as it
quickly returns to the limit-cycle. Stable limitcycles therefore imply self-sustained oscillations.
Fig. 4 - Phase diagram of the Van der Pol oscillator,
showing the slope field and the limit-cycle.[4]
2.1.3. Hopf bifurcation
A bifurcation occurs when a small smooth change in parameter values of the system causes a quick
qualitative change in system's behaviour. Local bifurcation can be analysed through a changes in
properties of the equilibrium of the system as parameters cross the critical point. In other words, a
parameter change causes the equilibrium to change. In continuous systems, described by a set of
differential equations, the bifurcation occurs at a certain point only if the Jacobian matrix of the
system at this point has an eigenvalue with zero real part. If the eigenvalue equals zero, the
bifurcation is called a steady state bifurcation, but if the eigenvalues are purely imaginary, it is
called a Hopf bifurcation. The later is especially interesting as it gives rise to a small-amplitude
limit-cycle branching from the fixed point. If the eigenvalues of the Jacobian matrix have a negative
real part and there is a pair of completely imaginary eigenvalues, a theorem 1 states that the Hopf
bifurcation occurs when the imaginary eigenvalues cross the imaginary axes. This happens because
of the variation of the system parameters.
We can conclude from the discussion above that if the parameters of the non-linear system are right,
the Hopf bifurcation occurs. It gives rise to a limit-cycle, which means that there is a self-sustained
oscillation, powered by the airflow – the amplitude of oscillations build up.
2.1.4. Basic assumptions and concepts
Following the derivation in [7], we will point out the main assumptions and steps in derivation of
equations of motion of the cantilevered pipe conveying a fluid (see Fig. 5). The final equation can
also be applied to a cantilevered plate in an axial flow. The description of such a system in its full
width is very complex, so there are seven assumptions made to make the description easier:
1. the fluid is incompressible – this holds well for liquid like water, but not for air;
2. the velocity profile is uniform – in other words, viscosity of the fluid is neglected, which is a
relatively bad approximation as the Reynolds number can be more than hundred thousand;
3. the diameter of the pipe is small in comparison to the length – a reasonable assumption that
can be satisfied with appropriate design of the pipe or plate in the experiment;
4. the motion of the pipe is planar – it seems hard to achieve a planar motion of a pipe, as it can
be quite chaotic, but the assumption can easily be satisfied when using a plate;
1 Hale, J.; Koçak, H. (1991). Dynamics and Bifurcations. Texts in Applied Mathematics. 3. New York: SpringerVerlag.
4
5. the deflections of the pipe can be large, but the strains are small – it simplifies the derivation
and can be practically achieved when plates bend easily;
6. rotatory inertia and shear deformation are neglected – if the thickness of the plate and its
mass are small, then these can be neglected in order to simplify the equations;
7. the pipe centreline is inextensible – it is a common assumption in continuum mechanics.
There are several different ways for deriving the equations of motion for such a system, but the two
of the most appropriate and easy ways are by the Hamilton's formalism (based on the energy of the
system) and by the force balance method.
Hamilton's principle is in its general form written as
t2
t2
∫ L dt∫  W dt=0 ,
t1
(1)
t1
where L=T −V is the Lagrangian of the system, T being the kinetic energy of the pipe and liquid
and V is the potential energy of both.  W in the second integral represents the virtual work due to
the non-conservative forces that are not included in the Lagrangian. Even though there are no
external forces on the pipe conveying fluid, this work doesn't equal zero if at least one end of the
pipe is free. Liquid transfers energy to the pipe due to the motion of the free end of the pipe. After
tedious derivation of the final equation, it can be solved with boundary conditions, namely:
y 0= y ' 0=0 (the pipe is fixed at one end and therefore cannot change the position or the
direction) and y ' '  L= y ' ' '  L=0 (there is no bending moment or shearing force at the free end
of the pipe).
The second way is based on the force balance method. Only a small length of the pipe is considered
and all the forces and moments have to be taken into account. The final equation can be produced
from the equations of force and momentum equilibrium with the use of inextensibility assumption.
The boundary conditions are the same as in the Lagrangian method.
2.1.5. Final equation of motion
Fig. 5 – Cantilevered plate in axial flow.[1]
A cantilevered plate in axial flow of air (or other fluid) is the most used kinetic-to-vibrational
energy converter in flutter-mills. Schematic of such a two-dimensional plate is shown in Fig. 5. L0
5
denotes the clamped rigid segment length, L is the length of the plate, h is thickness,  density,
D bending stiffness2, a viscoelastic damping and S is the distance measured along the centerline
of the plate. Fluid forces acting on the plate are marked as F D (in longitudinal direction) and F L
(in transverse direction). V  X , t marks longitudinal and W  X , t transverse displacement of the
plate from its original position. The main steps in derivation of the equation for transversal
displacement for such a system are in previous chapter, but the whole derivation is beyond the
purpose of this paper (it can be found in [7]), so only the final equation is presented just to illustrate
the complexity of the problem:
S
 h Ẅ  D1a
∂
[W ' ' ' ' 1W ' ²4 W ' W ' ' W ' ' ' W ' ' ³] h W ' ∫  Ẇ ' ²W ' Ẅ ' dS
∂t
0
L
− h W ' ' ∫
S
[∫
]
S
0
L
(2)
Ẇ ' ²W ' Ẅ ' dS dS =F t−W ' F l W ' ' ∫ F l dS
Here over-dot means temporal derivative
S
 ∂∂t  and prime represents spatial derivative  ∂∂S  , a
denotes the damping coefficient. In this derivation, only cubic non-linear terms are retained. It is
obvious that this equation is too demanding to be solved analytically. It can however be rewritten in
a dimensionless form and solved numerically if we apply the aforementioned boundary conditions.
Experiments showed that the theoretical
predictions made using this method are in
very good agreement with the actual
movement of the plate. It has been both
theoretically and experimentally confirmed
that the flutter occurs when flow velocity
exceeds a certain value, as it was suggested
in the discussion of Hopf bifurcation; this
critical flow velocity is determined by the
other parameters of the system, i.e. size and
shape of the plate. If the flow velocity is
just above the critical value, the oscillations
of the plate are almost harmonic, but they
become chaotic if flow velocity is too high.
Experiments also revealed that the
cantilevered plate already in flutter returned
Fig. 6 – Relationship between critical flow velocity and
[1]
to stability at a different critical flow
parameter H for plates with =1,215 .
velocity, which was lower than the former
one. That means that the hysteresis was formed. There is only one critical flow velocity (that means
no hysteresis) for plates with low aspect ratio3 (for H 0,8 ). For small lengths, the length
dependence on critical flow velocity is very strong, but there is almost no dependency for H 8
(Fig. 6).
2 Bending stiffness is calculated as
ratio.
D=Eh³ /12 1− ² , where E is Young's modulus and  is the Poisson
3 Aspect ratio is a ratio of width to length of the plate,
H=
6
width
.
length
2.2. Induction and Faraday's law
Electromagnetic induction is the production of electric current across a conductor moving in a
magnetic field. Michael Faraday is credited for the discovery of induction in 1831 although Joseph
Henry made a similar discovery at that time but published his findings much later. Faraday took a
step further by stating the Faraday's law of induction (although at first only in words), namely that
the voltage generated in the wire is proportional to the rate of change of the magnetic flux through
the area that such a wire encloses. This law was later formulated mathematically with the use of
Maxwell equations,
d m
(3)
−
=U i .
dt
Equation (3) is known as the Faraday's law of induction. The minus sign could be predicted by
Lenz's law which states that an induced current flows in such a direction that its magnetic field
opposes the change of the original flux.
The induction current is present only if the magnetic flux is changing and is proportional to the rate
of change. Constant magnetic flux (for example from a still permanent magnet) does not produce
induction current and is therefore useless in electricity production. But if the flux is changing (if the
permanent magnet is moving) then induction current is produced and could be used. Constant
movement of a permanent magnet can be provided for example by flutter.
2.3. Transforming mechanical energy into electrical energy
It was shown in previous chapters that flutter can occur in quasi-constant airflow meaning that a
mass plate (or strap) moves constantly, thus harvesting energy from the airflow. But the question of
transforming this mechanical (vibrational) energy into electric energy remains. Currently, there are
at least three more or less promising converters in use or under development (Fig. 7).
Capacitive or electrostatic converter is actually a capacitor where one of the plates can move and is
attached to mechanical resonator in flutter. As the distance between the plates of the capacitor
 S
changes, so does the capacity: C= 0
. The capacitor is initially charged by an external voltage
d
e
source so that the changing capacity causes also the change in voltage: U = . This type of
C
converter is very easy to produce and integrate with the existing technology, but has a major
disadvantage. It needs a constant
voltage source to maintain the charge
on the electrodes of the capacitor. This
source has to be replaced over time,
which means that such a device is not
appropriate for remote areas where
devices with zero maintenance are
required. What is more, this device has
to be placed in vacuum packaging in
Fig. 7 – Different types of energy converters (shematic).[2]
order to achieve higher efficiency.
The more promising converter is electromagnetic or inductive. It is made of a permanent magnet
and a multi-turn coil and makes use of the electromagnetic induction arising from the relative
motion of a conductor (coil) and the appropriately positioned magnetic flux (produced by a
7
permanent magnet). Such a device is very simple and easy to make (i.e. inexpensive). Several
different converters are already being produced commercially, as they exhibit high efficiency on a
macro-scale. They need no external voltage source and are almost maintenance-free, but they face a
rapid decline in induced voltage with reduced device size (the magnetic flux through a smaller coil
is smaller). This type of converter is therefore the best choice for large energy scavengers but is
inappropriate for small, hand held devices.
The third possibility of transforming energy from mechanical to electrical form is by piezoelectric
crystals. They can be integrated in small devices, as they produce high voltage difference between
the sides of the crystal. This voltage is the result of a broken symmetry in the distribution of dipoles
in such crystals. Practical use of this type of energy converter is limited for now as the integration
with standard technology is still under development.
It is now possible to estimate the energy transfer from the (air)flow to the cantilevered plate and the
power that such a device could produce. When transforming Eq. (2) to nondimensional form, the
nondimensional force ( f l ) and velocity ( v ) are introduced (refer to Fig. 5):
f l=
Fl
 f U²
and
v =UL

h
,
D
(4)
where U is the fluid velocity. To estimate the nondimensional power of the work done by the fluid
Fig. 8 – Different modes for (a) =0,01 , (b) =0,5 , (c) =2 and (d) =5 . P on the bottom of
each graph denotes regions of the plate where positive work is done to the plate and N denotes regions
where negative work is done (energy flows from plate back to the fluid). Variable s denotes the length
along the centreline of the plate and w denotes the deflections, as shown in Fig. 5.[5]
8
load on the plate (per unit length of the spanwise dimension), the plate is divided into N equally
wide panels, each of the length  s=1/ N . Power of the work done on one panel of the fluid is the
product of force and velocity:
P i ' =[ f l  s ] ẇ s i 
(5)
Here, subscript i indicates the panel under consideration. All such power factors for individual
panels have to be summed to get the power of the work done on the whole plate: P ' =∑ P i ' .
i
Power is changing as the speed of the panel changes (in size and direction), so it is reasonable to
talk about average power. It can also be calculated from (4) and (5) and is in its dimensional form:
 = f U²
P

D
P'
h
(6)
There is another parameter that influences the energy flow from the fluid to the plate, called the
 L
mass ratio = F . Here,  F is the density of the fluid,  the density of the plate, L the length
h
and h the thickness of the plate. This parameter crucially influences the modes of fluttering plate
(refer to Fig. 8). If the ratio is small, only lower modes are present, but if the ratio is large, let’s say
2 or 5, than higher modes also appear. Numerical calculations show that energy can be extracted
from the fluid (this energy is sustaining flutter) or can be transferred from the plate to the fluid. To
construct a useful device, there has to be more energy transferred from the fluid to the plate than in
the opposite direction. That means that the right mode of flutter has to occur and this can be
controlled by the mass ratio. What is more, the flutter mode is also influenced by the speed of the
surrounding fluid and that suggests that the dimensions of the plate in the working energy harvester
should be adjusted to the speed of the wind, reducing the general usefulness of such devices. In
order to improve the efficiency of energy harvesting devices, conductors (in case of the
electromagnetic converter) have to be arranged in
several sections, so that they are present only on
those places, where energy is transferred to the plate.
If there are to many sections, the supporting wiring
scheme gets very complicated. This can be omitted if
plates with 1 are used, as there are mainly second
mode vibrations present. When the mass ratio is
changed (but still 1 , refer to Fig. 8 (a) and (b)),
new unwanted sections emerge. But they occur in the
region near the fixed end of the plate, where
amplitudes of oscillation are small and therefore less
important (see Fig. 8 and 10).
3. Devices for harvesting
electricity
3.1. Flutter-mill
Tang et al. (Ref. [3]) have proposed a device, where a
conducting plate flutters between two magnetic
panels. The induction was used to produce an electric
9
Fig. 9 – Layout of the flutter-mill. An electric
potential difference is formed between its upstream
and downstream ends.[5]
current and the supporting wiring made DC current out of it. As seen in previous chapter, it was
more efficient when plates with small mass ratio were used, for example =0,5 and =0,2 . Such
plates oscillated in second mode which meant that energy transfer from the fluid to the plate was
greatest. The first device (with plate with the larger mass ratio) had dimensions of only 0.58 m
(length) x 0.2 m (width) x 0.58 m (height) and worked well in slower airflow. The critical flow
velocity to give rise to flutter in the experiment was 9 m/ s and the transferred average power to the
plate was more than 10 W /m . The dependence of the average power compared to the flow velocity
was measured and is shown in Fig. 10. It is evident that higher flow velocities mean more extracted
power. The second tested device, which was approximately half of the size of the first one, showed
an even better performance. The transferred power was of the order of kW/m at flow velocity
around 40 m/s. But this are already extreme winds that don’t occur everyday in our region. As seen
from the data, such devices should be designed specifically for the destination area, so that average
wind velocities could be taken into account when constructing the device.
Fig. 10 – The performance of two tested flutter-mills with =0,5 (left-hand side) and =0,2 (right-hand side).
Graphs (a) show amplitude of the free end of the plate, graphs (b) frequency dependence of airflow velocity and graphs
(c) average extracted power dependence of airflow velocity. Notice the difference in critical velocity for two different
mass ratios  and low dependence of frequency against flow velocity.[5]
The team compared their device with the usual horizontal axis wind turbine (HAWT). The
assumptions were made that the flutter-mill has the same area as the HAWT rotor (that means that
they get the same amount of wind) and that only 10 % of the energy transferred to the plate can be
transformed into electric energy, where the
rest of the energy is needed to sustain the
flutter of the plate under the action of the
induced electromagnetic forces (the usual
HAWT efficiency is 20 – 30 %). It was
shown (only theoretically as such a large
flutter-mill hasn’t been constructed yet) that
the flutter-mill with higher mass ratio worked
at lower wind velocities but produced less
energy than usual HAWT. Devices with
smaller mass ratio worked at higher wind
speeds, but on the other hand produced much
more electric energy that HAWT. It is
Fig. 11 – Comparison of electrical output of HAWT and two
flutter-mills with different mass ratio.[5]
10
expected that plates with mass ratios between the tested ones will work at similar wind velocities as
the usual HAWT, but producing more electricity. Such flutter-mills promise a new ecological way
of producing electricity, but some research and development still has to be done.
3.2. Helmholtz-resonator-based scavenger
The main difference between the Helmholtz and the wind belt-based scavengers (like flutter-mill) is
in the resonator. The usage of a resonator means a great advantage, as such a scavenger can be used
with lower flow velocities. The Helmholtz resonator is a simple gas-filled chamber with an open
neck, where – with the appropriate geometry of the resonator – the second mode oscillations can
occur (this is beneficial, refer to the discussion at the end of chapter 2.3.). When air moves across
the open neck, a high amplitude acoustic wave develops with resonant frequency defined solely by
the dimensions of the chamber (supposing that the velocity of sound is a given parameter, unable to
change):
c
A
,
(7)
=
2 V l

where A is the neck cross-section, V the rest volume of the chamber and l the length of the neck.
When the frequencies of the resonator and the mechanical device (foil and magnet) are equal, the
energy transformation has highest efficiency. This can be achieved by a proper design of the
resonator and device as mentioned before. Such scavengers (so called Helmholtz scavengers) have a
cross-section comparable to the cross-section of a usual coin and thickness of about two
centimetres.
Fig. 12 - Schematics of a Helmholtz-resonator and the
electromagnetic energy converter.[6]
Fig. 13 – Piezoelectric energy harvester packed in glass
packaging.[7]
It was reported (Ref. [2]) that a working Helmholtz scavenger was made and the peak-to-peak
voltage of 4 mV was measured. This was less than the output voltage of a windbelt-based
scavenger of the comparable size, but there was also a big advantage – this type of scavengers are
already working at wind velocity around 5 m/ s , which is less than the velocities at which the
flutter on a plate occurs. The output voltage seems too small to be practically applicable, but its
small size – the size of a coin – has to be taken into account. Large scavengers (or an array of such
small scavengers) with the surface area comparable to the circle area made by a HAWT rotor would
produce a lot more energy. But the actual performance of large scavengers is only predicted, as
none has been produced and tested yet.
Another way of transforming electricity is by piezoelectric crystals. Piezoelectric harvester is placed
in glass vacuum package in order to be shielded from unwanted viscous influence and to lower
parasitic dumping (refer to Fig. 13). Such converter has a footprint of less than 1 cm² and is
11
therefore appropriate for small devices. Due to its compact size, harvester can be placed on the
movable side of the resonator in order to adopt the resonator dimensions (and consequently
resonance) to the airflow velocity. Latest experiments on such devices (Ref. [4]) showed that the
output power was extremely sensible to the angle of incident airflow and the temperature of the air
(temperature changed the acoustic velocity and consequently the resonant frequency, refer to Eq. 7).
This two causes of lower power output could be partially eliminated: the angle can be actively
adjusted depending on airflow velocity and the temperature dependence can be lowered if a special
membrane is fixed on the bottom of the resonator. What is more, such a membrane increased the
harvester amplitude, resulting in even higher power output.
The first such harvester [Ref. 4] was capable of extracting power from the wind at speeds form
10 m/ s to 20 m/ s (this was actually the limiting speed of the experimental set-up) and producing
up to 45 W of electricity. The output power is small, but we have to bear in mind that this devices
are ultra-small (footprint of less than 1 cm² ). The experimentalists said that the size of the harvester
could be reduced even further. This is beneficial as smaller devices have higher resonant
frequencies and require lower airflow velocities for excitations.
4. Prototypes and
commercially available
products
Some flutter-mills or wind-belts are already
being produced, but none have been available to
the general public yet. The most serious attempt
has been made by Humdinger Wind Energy4, a
company established by the inventor of the
concept of a flutter-mill. The company is trying
to produce three types of energy harvesters,
differing in size. Micro harvester (Fig. 16) –
only 12 cm long – could replace batteries and is Fig. 14 – One of possible ways of integration of windcell
able to produce several mW of energy, enough panels with modern architecture. Medium-sized windcells
to power some sensors, for example. The could also be placed along the vertical edge of buildings.[8]
Windcell™ (Fig. 16) – medium size harvester –
is one meter long and capable of powering ten light-saving bulbs. This means it could make a real
difference in some remote areas and islands. It can be used almost anywhere as it can produce
electricity from wind speeds of 2 m/ s or more. The third device (large-scale) is in the form of a
1 m x 1 m steel frame that can be connected to form a longer fence-like structure (Fig. 14). One
such frame is capable to produce 7,2 kWh of electricity per month (at average wind speeds around
6 m/ s ). Such an energy output can compete with the output of photovoltaic power plants, but the
production of Windcell™ Panels is much cheaper. The inventor claims that these small-scale energy
scavengers are up to 20 times more efficient than small wind turbines.
It is not to demanding to make your own flutter-mill, if your demands regarding the output power,
frequency and signal shape are not too precise. For this reason, a lot of enthusiasts are attempting to
make a working flutter-mill in their free time. But such simple devices are build based on the
empiric trial-and-errory system to determine the best layout of the device and cannot compete with
professionally made flutter-mills. However, some designs are very interesting and could provide
some new ideas to the scientists working in this field.
4 http://www.humdingerwindenergy.com
12
Fig. 15 – Flutter-mill, made by an
amateur inventor.[9]
Fig. 16 – Medium (top) and micro (bottom)
Windcell™.[10]
5. Conclusions
As the amount of fossil fuels left on Earth decreases and the energy consumption increases, we will
be obliged to seek new methods of electric energy production. One of the more promising and
neglected ways (especially in Slovenia) is the transformation of kinetic energy of moving air masses
into electricity. But as shown in this seminar, flutter-mills can only provide electricity on a small
scale – currently, for example, to power lightning in houses in remote areas, such as islands,
mountainous regions and third world countries. However, they still need to be improved in order to
produce enough electricity to compete with the conventional ways of electricity production. But on
the other hand, these devices are already being produced, they are cheap and almost maintenancefree, and probably we will hear more about them in the future.
6. References
[1] W. Zhao et al., Theoretical and experimental investigations of the dynamics of cantilevered
flexible plates subjected to axial flow , Journal of Sound and Vibration (2012), 575-587
[2] S.H. Kim et al., An electromagnetic energy scavenger from direct airflow , Journal of
Micromechanics and Microengeenering (2009)
[3] L. Tang et al., Flutter-Mill: a New Energy-Harvesting Device , http://www.ontario-sea.org/
Storage/26/1817_Flutter-Mill-_a_New_Energy-Harvesting_Device.pdf
[4] S. P. Matova et al., Harvesting energy from airflow with a michromachined piezoelectric
harvester inside a Helmholtz resonator , Journal of Micromechanics and Microengeenering
(2011)
[5] V. C. Sousa, Enhanced aeroelastic energy harvesting by exploiting combined nonlinearities:
theory and experiment , Smart Material and Structures (2011)
[6]
C.
Hebert
et
al.,
Aerodynamic
Flutter
,
http://www.cs.wright.edu/~jslater/SDTCOutreachWebsite/
aerodynamic_flutter_banner.pdf
[7] C. Semler, G.X. Li, M.P. Paıdoussis, The non-linear equations of motion of pipes conveying
fluid, Journal of Sound and Vibration 169 (1994), 577–599
[8] http://en.wikipedia.org/wiki/Flutter (30. 3. 2012)
[9] http://en.wikipedia.org/wiki/Tacoma_Narrows_Bridge (30. 3. 2012)
[10] K. Seong-Hyok et. al., An electromagnetic energy scavenger from direct airflow , Journal of
Micromechanics and Microengineering, 2009
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Figures and photos
[1] http://upload.wikimedia.org/wikipedia/commons/b/ba/Windmills_D1-D4%28Thornton_
Bank%29.jpg (30. 3. 2012)
[2] http://en.wikipedia.org/wiki/File:Tacoma_Narrows_Bridge_Falling.png (30. 3. 2012)
[3] L. Tang et al., Flutter-Mill: a New Energy-Harvesting Device , http://www.ontario-sea.org/
Storage/26/1817_Flutter-Mill-_a_New_Energy-Harvesting_Device.pdf
[4] http://en.wikipedia.org/wiki/File:VanDerPolOscillator.png (14. 4. 2012)
[5] V. C. Sousa, Enhanced aeroelastic energy harvesting by exploiting combined nonlinearities:
theory and experiment , Smart Material and Structures (2011)
[6] K. Seong-Hyok et. al., An electromagnetic energy scavenger from direct airflow , Journal of
Micromechanics and Microengineering, 2009
[7] S. P. Matova et al., Harvesting energy from airflow with a michromachined piezoelectric
harvester inside a Helmholtz resonator , Journal of Micromechanics and Microengeenering
(2011)
[8] http://www.humdingerwindenergy.com/#/wi_large/ (30. 3. 2012)
[9] http://www.creative-science.org.uk/sharp_flutter.html (30. 3. 2012)
[10] http://www.humdingerwind.com/#/wi_large/ , http://www.humdingerwind.com/#/ wi_micro
(30. 3. 2012)
14