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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 D1a ∂ [W ' ' ' ' 1W ' ²4 W ' W ' ' W ' ' ' W ' ' ³] h W ' ∫ Ẇ ' ²W ' Ẅ ' dS ∂t 0 L − h W ' ' ∫ S [∫ ] S 0 L (2) Ẇ ' ²W ' 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 13 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