1

Energy Harvesting by Floating Flaps

Jose Pedro de Sousa Ferreirajosepedrof@tecnico.ulisboa.pt

Instituto Superior Tecnico, Universidade de Lisboa, Portugal

November 2017

Abstract

The increasing demand for energy efficiency have led to the development of an autonomous flap,which encompasses an energy harvesting system to power sensors and actuators that ultimately performactive gust alleviation. In this context, this research presents a novel mechanism for an electromagneticenergy harvesting concept which transforms self-induced aeroelastic oscillations into electricity. Thesystem exploits the benefits of a release mechanism to reduce the electromagnetic and inertial influenceon the flap motion, and its feasibility is evaluated using a numerical model, developing an experimentalapparatus, and performing an experimental study. As to the numerical model, the onset of flutterof the original system is calculated using the p-k method, and the energy harvesting potential isdetermined on a time-domain simulation that accounts for inertial and electromagnetic non-linearitiesin the aeroelastic response of the system. A 3D-printed aeroelastic model for wind tunnel testing isdeveloped to experimentally evaluate the energy harvesting mechanism. The test campaign is carriedout using vibration tests to structurally characterize the model and quantify the mechanism effectiveness,followed by wind tunnel testing. With a weight penalty of 0.6 % when compared to a standard energyharvesting mechanism with a reciprocating shaft, Free-Floating Flaps fitted with the novel mechanismshowed a 40 % decrease in structural damping and 45 % increase in power generation. It was alsoexperimentally demonstrated that the onset of flutter is controllable by adjusting the generator externalresistance. Future applications of such mechanism in wind turbine rotors are considered, and aircraftapplications are also investigated with promising results suggesting substantial fuel savings.Keywords: Aeroelasticity; Electromagnetic Energy Harvesting; Free-Floating Flaps; Wind Tunnel FlutterTesting; 3D Printing.

1. Introduction

With the ever-growing demand for energy efficientaeronautical systems, there has been an increasedresearch activity in the search for novel energy har-vesting solutions. This is motivated by the increas-ingly expensive fossil fuels and by the need to re-duce operational costs. The potential of renewableenergy power generators has seen a marked in-creased in proposed solutions in the aeronauticalindustry.

Amongst the wide range of possibilities for en-ergy harvesting, the one that mostly fits aeronauti-cal purposes is harnessing vibrations induced byfluid-structure interaction. This phenomenon isa common denominator in every dynamic fluid-immersed structure. Therefore, transducing kineticenergy into a usable resource, such as electricity,is the key for a smart structure application.

Researchers have been able to do so usingsmart materials in flexible high aspect ratio wings.The concept of a wing with one Free-Floating Flap

(FFF) [1] is introduced for gust alleviation withinflutter constraints. Later, a new aeroservoelasticapproach based on FFF actuated by piezoelectrictabs [2] is proposed, evidencing superior effective-ness in gust alleviation and flutter suppression.

The concept was took into another level whenan electromagnetic energy harvester was placedat the flap hinge to exploit flutter-induced Limit-Cycle Oscillations (LCO) [3], also numerically pre-dicting the flutter speed controllability by varyingthe generator external load. This leads to the pro-posal of an autonomous flap for offshore wind tur-bines [4], which envisages an energetically self-sustainable plug-in control surface that harvestsenergy to power an active gust alleviation sys-tem. However, such energy requirements demandfor large flap deflection and angular velocity. Toboost the energy harvested, a gearbox is intro-duced though the inertial effects deeply downgradethe overall performance of the system.

As such, the purpose of this research is to de-velop a harvester able to increase the produced

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energy by optimizing the rotational mechanism,proving it both numerically and experimentally.Moreover, the premise of flutter speed control isalso investigated experimentally. In the end, theenhanced mechanism is subjected to a preliminaryevaluation for future integration in airframes.

2. Methodology

The procedures presented hereafter aim to deter-mine the feasibility of an energy harvesting mecha-nism to exploit flutter-induced vibrations by meansof numerical and experimental simulations.

2.1. Numerical Methods

A numerical study is carried out to evaluate themechanism feasibility. The physical reality is nu-merically described and two methods are used tocalculate the instability boundary and time-domainresponse of the system. For the former, an eigen-value problem in the frequency domain is solvedbased on the p-k method to determine the flutteronset. Yet, and due to non-linear behavior of thenew mechanism that allows for shaft free-spinning,a time-domain simulation is also performed. After-wards, the code developed is benchmarked.

The numerical method is based on the theorypresented by Theodorsen [5] and follows the no-tation introduced in his report on aeroelastic flutteridealized for a classical 3DOF spring-damper air-foil. As such, the equations of motion are exposedaccording to the following equation.

[M]ξ+ [C]ξ+ [K]ξ = Q (1)

where [M] is the generalized inertia matrix, [C] thedamping matrix, [K] the stiffness matrix, Q thevector of generalized applied forces, and ξ thestate vector.

Introducing a generator at the flap hinge intro-duces a non-usual damping term into the system.Hence, the electromagnetic damping value estima-tor Cel is added to a standard viscous dampingmodel, considering it only affects the flap mode.

[C] = [Cvisc] +

0 0 00 0 00 0 Cel

(2)

Considering a brushed permanent magnet Di-rect Current (DC) motor retro-used as a generator,the circuit may be modeled as depicted in Figure1. Following such, the flap damping component isgiven by Equation 3 where GR is the gear ratio, φthe induction coefficient and Req the resistance asseen from the generator’s terminals.

Cel =(GR· < φ >)2

Req(3)

Figure 1: Electric circuit for energy harvesting

Flutter Model

For flutter calculation purposes, the only externalforce applied to the system is related with its aero-dynamics, modeled according to Theodorsen’stheory for unsteady aerodynamics [5] as depictedin Equation 4. This fully defines the 3DOF systempresented in Equation 1, using the p-k method [6]to compute the aerodynamic matrices.

Q = [Maero]ξ+ [Caero]ξ+ [Kaero]ξ (4)

The final set of equations of motion with bothstructural and aerodynamic properties poses aQuadratric Eigenvalue Problem (QEP). It is possi-ble to linearize the differential equation and reduceits order by introducing a new state variable λ,performing a First Companion Linearization (FCL).This origins a companion matrix [Z] that gathers allthe 3DOF system features. The eigenvalue prob-lem is then solved according to Equation 5. Modeswitching is avoided by using the Modal AssuranceCriterion (MAC) and the flutter onset interpolatedwhen one of the modes goes unstable.

([Z]− p[I])

ξλ

= 0 (5)

The algorithm is developed using Python R© pro-gramming language. Benchmarking is performedfor the 2DOF, 3DOF undamped and damped mod-els. The latter is presented in Figure 2, showingthat the output matches reference [7] and accu-rately predicts flutter for the heave mode.

Time-Domain Model

Frequency-domain flutter detection algorithms maysuccessfully detect the flutter boundary for com-plex systems but are unable to simulate the time re-sponse for underlying non-linear features as gear-boxes, release mechanisms and electromagneticdecay of a rotating shaft.

Firstly, one should note that inertia only plays arole in flap motion when the system accelerates.For geared systems, the input shaft inertia is givenby Equation 6, meaning that the larger the GearRatio, the larger the moment of inertia. Recentresearch has struggled in dealing with high gearratios coupled to FFF [4], as it increases the flap

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3

Damping Ratio [-]-2 -1.5 -1 -0.5 0

Fre

quen

cy [H

z]

0

2

4

6

8

10

12

14

16

18 HeavePitchFlapin Conner

Figure 2: 3DOF damped system root locus plotTime [s]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Fla

p A

ngul

ar V

eloc

ity [r

ad/s

]

-6

-4

-2

0

2

4

6

_-_- $

_- 0

Figure 3: One-Way Bearing mechanism time response

Algorithm 1 Release Mechanism

1: procedure INERTIA DECOUPLING2: if β(t) > β(t− 1) and β(t) > 0 then3: Iβ ← Iflap +GR2 · IGB

4: Cel ←(GR· < φ >)2

Req5: else6: Iβ ← Iflap7: Cel ← 0

Algorithm 2 Free-spinning shaft decay

1: procedure ELECTROMAGNETIC AND EFFICIENCYDECAY

2: κ← Cel2Iβωβ

+ 1− ηGB

3: if β∗(t) ≤ β∗(t− 1) and β′(t) > β∗(t) then4: β′(t)← β′(t0)e

−κ(t−t0)

5: else6: β′(t)← β∗(t)

shaft inertia. In order to avoid this feature, innova-tive mechanisms that reduce the influence of iner-tia and electromagnetic damping in the flap shaftshall be investigated.

Iβ = Iflap +GR2 · IGB (6)

One of the possible solutions is a mechanismthat somehow resembles the one of bicycles: aOne-Way Bearing mechanism. It is, in fact, a bear-ing that only transmits the stroke in one direction,consisting of a release mechanism; when the shaftrotates in the opposite direction, the input to thegenerator free-spins according to an exponentialdecay κ ruled by the gearbox efficiency ηGB andelectromagnetic damping. It can be modeled intime-domain according to Algorithms 1 and 2, andthe resultant plot is depicted in Figure 3.

A more complex version, the Two-Way Bearingmechanism, is also developed, though the muchsimpler counterpart has better trade-off and there-fore is chosen to pursue experimental validation.Likewise, a Standard version consisting of a recip-rocating shaft directly connected to the generatoris yet conceived.

As time marching is required to solve such prob-lem, a state space model is developed. However,incorporating the frequency-domain complex aero-dynamic matrices in that model lays out of thescope of this research. As such, a solution thatequally represents the physical reality of the aero-dynamic forces was applied - a harmonic function.In the end, the state space model based on thesystem of Equation 1 is presented as follows.

X = [A]X+ [B]uY = [C]X+ [D]u (7)

where [A] is the state matrix, [B] the input ma-trix, [C] the output matrix, and [D] the feedthroughone; X is the state vector, u the input vector,and Y the output one. The time-domain simula-tion for the One-Way Bearing and Standard mech-anisms is developed in Matlab/Simulink R© R2015aand presented in Figure 4.

Time-domain results are verified against the timeresponse based on the frequency-domain eigen-values calculated using the flutter model for zerovelocity. Figure 5 shows a snapshot of the timehistory for both methods with the same initial con-dition, which match.

2.2. Experimental Methods

An experimental setup to validate numerical pre-dictions is developed in accordance with their ge-ometric and structural inputs. Two test campaignsare planned: vibration and wind tunnel tests. Theformer aims to the structural characterization of themodel by defining its resonance modes, and thelatter focus on the flutter boundary and aeroelasticbehavior. Both are used to test the energy har-vesting performance by applying either forced har-monic vibrations in the vibration tests, or simplyby performing a wind tunnel flutter test where theaerodynamic force may be approximated as a har-monic function.

The structural properties of the experimentalmodel may be evaluated in Appendix A, Table A1.

3

4

States

u

Input Force

Derivatives

One-Way Bearing Mechanism

GR

Gearbox

Memory

f(u)

V^2/R

One-Way Bearing Mechanism old

-K-

Flux

<beta star dot>

<beta star dot old>

beta prime dot

Free-spinning shaft decay

ContinuousRMS

V_rmsContinuous

RMSP_rms

-C-

Generator Parameters

<u>

<C>

<beta dot old>

Xt

State Space Model for Release Mechanism

h/b

alpha

beta

alpha dot

h/b dot

beta dot

beta dot old

beta dot old

Powerbeta^prime dot w/ GBVoltage

beta^star dot

beta^star dot old

u

C

Figure 4: Matlab/Simulink R© model for the One-Way Bearing mechanism

Figure 5: Time marching code benchmark with the p-k method

Test bench

The experimental framework used to test the en-ergy harvesting mechanism is an acrylic wind tun-nel test section with dimensions of 0.35 × 0.4 ×1.0 m3. It holds a support system for a vertically-placed 2DOF rigid wing with integrated measuringsystems [8]. This is then upgraded to fit a 3DOFaeroelastic model as described in the next section.

Data is acquired using an automated acquisitionsystem consisting of a NI cDAQ-9172 chassis withtwo NI 9215 input modules and one NI 9263 outputmodule. The experimental procedure automationis achieved using LabVIEW R© 2017, as in Figure 6.

Wing Model

The experimental model consists in a NACA 0024profile with 240 mm chord and 360 mm diameter.The flap hinge is located at 72.5 % of the chord,with maximum thickness of 29 mm allowing to fit agenerator at the hinge line. It is designed to housethe whole energy harvesting setup, namely the re-

lease mechanisms which performance is to be as-sessed. Thereby, the assembly process is care-fully engineered such that it would be possible toswap between mechanisms while maintaining theremaining system untouched.

The full system CAD model developed inCATIA R© V5R21 may be evaluated in Figure 7.The generator may be seen in black, the One-WayBearing mechanism in a golden color, and a con-nector between them in red. Note that the flap tor-sional spring system allows for two flap configura-tions: Setup I with some flap torsional stiffness andSetup II with none (FFF). Moreover, the measur-ing system of flap deflection uses a potentiometerto measure the flap shaft angle with respect to themain wing. In summary, all the systems in this con-cept were custom developed for this application.

The model is then manufactured usingFormlabs R© Form2 3D printer. As such, itwas possible to engineer a lightweight skin-ribblended wing and completely model the concept tofit standard components as bearings, nuts, screws,and the generator itself.

Endplates with 1.2 times the chord length andalmost 4 times the maximum airfoil thickness aremanufactured using carbon-fiber reinforced poly-mer and attached during wind tunnel tests.

Calibration procedures are carried out to exper-imentally determine the model structural parame-ters, gathered in Table A1. In this procedure, bycomparing damping introduced by each mecha-nism in the flap mode, one concludes that the One-Way Bearing mechanism decreases in 40 % thedamping signature of the Standard solution.

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5

Figure 6: LabVIEW R© graphical interface for the automated flutter test

Figure 7: Wing assembly CAD model (flap uncovered)

Apparatus

The experimental test campaign starts with vibra-tions tests to structurally characterize the mecha-nisms by its resonance frequencies and assess theenergy harvested for different resistance values.

Modal analysis of complex systems outputsthe coupled natural frequencies for each vibra-tion mode after an hammer-like impulse excitation.These modes fully characterize the model and en-able the time-domain code validation by analyz-ing its time response. On the other hand, the en-ergy harvesting capabilities are tested with a forcedharmonic excitation emitted by an electromagneticshaker in which a fully-automated frequency sweepwill reveal the optimal condition for voltage produc-tion, as depicted in Figure 8. The mechanisms arethen compared at that point. The procedure is car-ried out solely for the Setup I flap configuration.

Afterwards, experimental flutter tests are per-formed to determine the flutter onset and assessthe energy harvesting mechanisms performance.

The test campaign is carried out in the low-speedW-Tunnel at Delft University of Technology, as seenin Figure 9. It is an open-jet wind tunnel facilitywith cross-section of 0.4 × 0.4 m2 and maximumvelocity of 35 m/s. The instability threshold is de-termined for different resistances as it influences

damping in the system, enhancing the flutter modelcode validation by estimating the damping associ-ated to the experimental response. At the flutterpoint, the energy harvesting capabilities are testedin the same way as done for the vibration tests.Note that the energy harvesting procedure is car-ried out for both flap configurations. The virtual in-strument developed to fully automate the data ac-quisition procedure is depicted in Figure 6.

3. Results & Discussion

This chapter focuses on the results obtained for thephysical model data without gearbox. Experimentsare planned in two different parts, both exciting thesame feature: the limit-cycle behavior of the sys-tem. In the end, an application of such mechanismwith a gearbox is studied with the validated time-simulation for an aeronautical case study. Discus-sion is structured around the main findings.

Data is acquired with a sampling frequency of1 kHz. Post-processing is performed by applyinga Lowpass Butterworth Filter with passband cor-ner frequency of 30 Hz, stopband of 50 Hz, pass-band ripple of 1 dB and stopband attenuation of25 dB to experimental data and using the FastFourier Transform (FFT) algorithm. The output isthen conducted into a Savitzky-Golay Filter to re-duce noise. The order and frame length of this filteris adjusted to achieve the smoothest output signal.The last step consists of calculating the FrequencyResponse Function (FRF) using the Hv estimator.

3.1. Vibration Tests

Results for these tests are obtained by analyz-ing the signal in frequency domain using FFT. Forinter-comparability purposes, the FRF is computedas an output-to-input ratio.

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6

Figure 8: Forced harmonic excitation test setup Figure 9: Wind Tunnel test section back view

Validation of the Time-Domain Model

Validation is performed to verify the match betweennumerical experimental results. The simulationis run with experimental data for the input force,namely the magnitude read by the load cell dur-ing the experimental tests and the frequency givenby the FFT applied to that signal. Time responseof heave, pitch, and flap modes, alongside withvoltage production are evaluated. Given the largecombination of modes, mechanisms such as theStandard and One-Way Bearing, and circuit condi-tions as Open-Circuit (OC) and Short-Circuit (SC),only one validation case is presented in Figure 10.

Note that experimental responses are phaseshifted with respect to the numerical output for eas-iness of interpretation. Apart from that, no furthermisalignment can be spotted, meaning that the nu-merical model accurately predicts the frequencyoutput. With respect to the magnitude, it quali-tatively estimates the experimental time response,despite over-predicting it by a range of 10 % to 15%. This is most likely due to physical features notpresent in the model such as friction. Nonetheless,numerical results show very good agreement withthe experimental ones, allowing for code validation.

Modal Analysis

The system is excited with an impulsive force, asharp peak that ideally excites all frequencies atwing’s mid-span and close to the leading edge.The force is applied by a hammer-like structurewith a rubbered tip and an incorporated load cell.Time history for left-to-right and right-to-left im-pulses is recorded to enrich the signal frequencyrange. 2DOF response is obtained for the flaplocked with null deflection. The 3DOF time historyis recorded for both mechanisms either OC or SC.

Figure 11 presents the experimental FRF for

Time [s]0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Fla

p D

efle

ctio

n [D

eg]

-40

-30

-20

-10

0

10

20

30

40

Numerical Standard SCExperimental Standard SC

Figure 10: Flap time response

both mechanisms under OC conditions in 2DOFand 3DOF systems, clearly showing the effect ofthe third degree of freedom in the system and howmechanisms influence the system response.

For the 2DOF system, two distinct peaks arespotted at 3 Hz and 5 Hz at 17.5 dB FRF mag-nitude, respectively corresponding to heave andpitch coupled natural frequencies. With the intro-duction of the third degree of freedom, the peakdrops below 15 dB and a slightly shifts to theleft. Most importantly, a third peak appears around7 Hz corresponding to the flap coupled naturalfrequency. Curiously, the pitch mode seems toalso increase its amplitude at this resonance pointwhereas the heave mode completely drops. Thissame coupling occurs for heave and pitch modesat lower frequencies. Comparing these resultswith the uncoupled natural frequencies in Table A1,both coupled and uncoupled natural frequenciesmatch for heave and pitch modes, whereas in theflap mode it is shifted to around 7 Hz.

It is worth noting that, with both mechanismsin OC conditions, the electromagnetic damping is

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7

Frequency [Hz]0 1 2 3 4 5 6 7 8 9 10

FR

F M

agni

tude

[dB

]

-10

-5

0

5

10

15

20

25

30

35

402DOF Heave2DOF PitchStandard HeaveStandard PitchStandard FlapOne-Way B. HeaveOne-Way B. PitchOne-Way B. Flap

Figure 11: FRF for impulse excitation applied to Setup I in OCconditions

Frequency [Hz]0 5 10 15 20 25 30

FR

F M

agni

tude

[dB

]

-60

-50

-40

-30

-20

-10

0

10

20

Load-to-HeaveLoad-to-PitchLoad-to-Flap

Figure 12: FRF for forced harmonic excitation applied to SetupI One-Way Bearing mechanism in OC conditions

minimal. Therefore, all measurements are strictlyrelated with viscous damping. As experimentallydetermined for the uncoupled system in Section2.2, the One-Way Bearing mechanism introducesless viscous damping than the Standard one. As aconsequence, the resonance peak in the flap modeis larger and thinner. The same behavior is gener-ally observed for the remaining modes.

Moreover, the same procedure is carried out inSC conditions. Results have shown the diminishingof resonance peaks, proving the increase of overalldamping when the resistance is decreased.

Energy Harvesting

The system is excited with a forced harmonic vibra-tion in several frequencies to determine the optimalpoint for energy harvesting. This is done for bothmechanisms, and corresponds to the frequencyat which flap deflection is largest. The frequencysweep is first performed for a range of 30 Hz as inFigure 12, and then shortened to converge for theoptimal values of 4.06 Hz for the Standard mecha-nism and 4.43 Hz for the One-Way Bearing.

At the optimal point, voltage is generated and theRMS of the signal positive stroke is performed ina 80-second time window to average the voltageinto a quasi-DC value. The results are depictedin Figure 13 and clearly quantify the advantagesof One-Way Bearing mechanism. In this Setup Iflap configuration, it produces 20.5 % more volt-age than the Standard one in OC conditions, and25.0 % more power at maximum power conditionaround 10 Ω.

3.2. Wind Tunnel Tests

Results for flutter plots are obtained by using theleast squares method to fit experimental time re-sponse with an exponentially damped harmoniccurve. Data for the energy harvesting assessmentis then gathered at the lowest velocity at which thesystem evidences LCO.

Resistance [+]0 10 20 30 40 50 60 70 80 90 100

Vol

tage

[V]

0

0.02

0.04

0.06

0.08

0.1

0.12

One-Way BearingInterpolatedStandardInterpolated

Figure 13: Voltage production for Setup I under forced har-monic excitation

Validation of the Flutter ModelValidation of flutter code aims to verify the matchbetween numerical and wind tunnel tests, with thesimulation running for the structural properties inTable A1. Time response is recorded and damp-ing ratio and frequency obtained after filtering thesignal and performing curve fitting for both mecha-nisms, circuit conditions and flap configurations.

A validation example may be evaluated in Fig-ure 14, where blue stands for heave and green forpitch. It evidences the electromagnetic dampingadded by increasing the damping ratio in SC con-ditions, though with a marginal decrease in flutterspeed. In the end, it is possible to state that exper-imental results corroborate the numerical predic-tions, counting with a difference of 10.1 % and 9.2% respectively for OC and SC conditions in flutterspeed, and 6.5 % and 7.0 % in frequency. Theseare acceptable values for numerical flutter modelvalidation which align with literature [7].

Flutter Speed ControlFlutter speed controllability by changing the resis-tance at the generator terminals is hereafter exper-imentally tested in order to prove previous numer-ical predictions [3]. To do so, both flap configura-

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8

Figure 14: Heave-pitch flutter mechanism for the Setup I Stan-dard mechanism

Resistance [+]5 10 15 20 25 30 35 40 45 50

Ope

n-C

ircui

t Flu

tter

Spe

ed In

crea

se [%

]

0

0.2

0.4

0.6

0.8

1

1.2

NumericalExperimentalInterpolated

Figure 15: Flutter speed controllability for Setup II One-WayBearing mechanism in OC conditions

tions and mechanisms are tested such that its flut-ter speed is compared with the numerical predic-tions for a wide range of resistances. Once more,only one case study is presented.

Experimental results in Figure 15 show amarginal but monotonic increase in flutter speedas damping increases, meaning that both numeri-cal and experimental results follow an exponentialrelation, though with a much lower decay rate forthe experimental case. Nonetheless, simulationshave shown a much more controllable range of re-sistances. This has to do with the generator in-ternal resistance of 8 Ω that limits the equivalentoutput resistance Req depicted in Figure 1.

Furthermore, and on the contrary of Setup II, ex-perimental data showed that flutter speed has notincreased for the same situation in Setup I, withthis being also predicted by the flutter code. Thismeans that only for the FFF configuration does theflutter velocity increases as initially thought. A thor-ough analysis to Setup II characteristics leads to apretty unusual damping characteristic: the flap crit-ical damping value is zero. Hence, by comparingtotal and critical damping values, one can concludethat Setup I is an underdamped system, whereasSetup II (FFF) is overdamped. This is a prominentfinding, confirming FFF as active flutter speed con-trollers by means of changing its external load.

Energy Harvesting

The system is forced into LCO at the flutter pointand the voltage generated is evaluated accordingto the same procedure of vibration tests. This isdone for both mechanisms and flap configurations,and over a wide range of external loads.

Experimental results show that Setup II One-Way Bearing mechanism produces 33.9 % morevoltage in OC conditions and around 45.0 % morepower than the Standard mechanism at the optimalresistance, as depicted in Figure 16. These resultsclearly outperform similar concepts using the same

energy harvesting technique [3]. Moreover, it wasevidenced that Setup II can generate almost twicethe power produced by Setup I, if compared the ab-solute maximum values. Furthermore, the powerpeaks obtained for both vibration and wind tunneltests are approximately located at 8 Ω, the exactsame value as the internal resistance for the gen-erator, confirming the maximum power theorem.

3.3. Concept Applicability

In this final section, and after being evaluated asa energy harvesting system for wind turbine rotors,the concept applicability to aeronautical industry isevaluated as an additional power source for low-power UAV in order to develop either hybrid or full-electrical power solutions.

To do so, the verified time-domain model em-ulates the experimental model and introduces agearbox with a ratio of 25:1. Simulations are runfor the same input harmonic force as in vibrationtests. It turned out that the mechanism is able togenerate 4.1 V and produce 2.1 W of energy at anexternal load of 8 Ω, as depicted on Figure 17.

To simulate an aircraft application, the mecha-nism is considered to engage in non-critical flightstages as loiter, lasting for 45 min. It may eitherbe placed in the ailerons, meaning that they wouldoperate either as control surface and energy har-vesting device; or slightly more inboard, such thatthe FFF may have no other function than harvest-ing energy. The energy produced by the generatorsums up to 1.58 Wh, stored in a compliant LiPobattery weighting 13.8 g and with specific energyof 114.5 Wh/kg. Together with the generator, itposes a 11.6 % mass increment in the wind tun-nel model when compared with one with no energyharvesting mechanism. In terms of aerodynamicefficiency, the FFF solution presents a CL loss inthe order of 2 % for low-amplitude LCO [3]. How-ever, no studies have been done so far concerningthe drag penalty of such mechanism. Nonetheless,

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9

Resistance [+]0 10 20 30 40 50 60 70 80 90 100

Pow

er [m

W]

0

0.05

0.1

0.15

0.2

0.25

0.3 One-Way BearingInterpolatedStandardInterpolated

Figure 16: Power Generation for Setup II configuration at theflutter point

Time [s]0 10 20 30 40 50 60 70 80 90 100

Vol

tage

[V]

0

1

2

3

4

Pow

er [W

]

0

0.5

1

1.5

2

2.5

Effective VoltageEffective Power

Figure 17: Numerical Simulation on Setup I One-Way Bearingmechanism with GR of 25

considering propeller-driven UAV powered by avia-tion gasoline, the mass of saved fuel is 0.115 g forthe experimental model.

Future applications in larger aircraft are also ofinterest, as the NOVEMOR project emerges as agood testbed. Results have shown that a generatorwith 21.5 cm diameter would fit in the wing breakpoint, leading to a 1.2 % penalty on the emptyweight of the airframe. However, the remainingstructural properties are not publicly available.

4. Conclusions

A disruptive energy harvesting system with a re-lease mechanism was numerically modeled, man-ufactured and experimentally tested during this re-search with the purpose of improving its perfor-mance, test the controllability of aeroelastic insta-bilities, and expand it to other areas of application.

This research has proved the usability of 3D-printed models in vibration and wind tunnel tests,in one of the first-ever flutter experiments usingsuch manufacturing technique. Also, the numeri-cal models developed were proved to be accuratein predicting the non-linear behavior of the system.

The accurate designing and manufacturing en-hanced a 40 % reduction in viscous damping whencompared to a standard reciprocating shaft. Thisposes a performance increase of 33.9 % in voltageand 45 % in power, for a mass penalty of 0.6 % ofthe wind tunnel model mass. Also, this researchachieved the first experimental proof of the flutterspeed controllability in overdamped systems.

Future applications in the aeronautical sector arenumerically predicted, with estimated mass penaltyof 11.6 % when compared with a model withoutenergy harvesting mechanism, and promising fuelsavings for increasingly larger gear ratios.

Acknowledgements

I would like to acknowledge Dr. J. Sodja and Prof.R. De Breuker from TU Delft, and Prof. A. Suleman

from IST for their thorough supervision and insight-ful guidance.

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[7] M. Conner, D. Tang, E. Dowell, and L. Vir-gin. Nonlinear behavior of a typical airfoil sec-tion with control surface freeplay: A numericaland experimental study. Journal of Fluids andStructures, 11(1):89 – 109, 1997.

[8] B. Gjerek, R. Drazumeric, and F. Kosel. A novelexperimental setup for multiparameter aeroe-lastic wind tunnel tests. Experimental Tech-niques, 38(6):30–43, 2014.

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Appendix A: Experimental System Properties

The system parameters presented hereafter are defined according Theodorsen aeroelastic 3DOF model [5].

Table A1: Wing Model Properties

ConstantVibration

TestsWind Tunnel

TestsStandard

MechanismOne-Way Bearing

MechanismGeometric Properties

Span [m] 0.36Chord [m] 0.24

Semi-chord, b [m] 0.12Elastic Axis, a (w.r.t. b) [-] -0.20Hinge Line, c (w.r.t. b) [-] 0.45

Stiffness PropertiesHeave Stiffness, Kh [N/m] 676.1

Pitch Stiffness, Kα [Nm/rad] 4.240

Flap Stiffness, Kβ [Nm/rad]Setup I: 0.178Setup II: 0.0

Damping PropertiesHeave Damping, Ch [Ns/m] 2.3547 1.7564

Pitch Damping, Cα [Nms/rad] 1.6360×10−2 1.3489×10−2

Flap viscous damping, Cβ [Nms/rad] 1.7457×10−3 1.0543×10−3

Generator Induction Coefficient, φ [Vs/rad] 1.8741×10−2

Inertia PropertiesWing Mass, m [kg] 1.2137 1.3777

Support Mass, ms [kg] 0.6293Pitch Static Moment, Sα [kgm] 2.9639×10−2 3.7793×10−2

Pitch Inertia Moment, Iα [kgm2] 4.8620×10−3 7.2199×10−3

Flap Static Moment, Sβ [kgm] 8.4823×10−3 9.6285×10−3

Flap Inertia Moment, Iβ [kgm2] 1.7481×10−4 1.5646×10−4

Wing CG distance from a, xα (w.r.t. b) [-] 0.2035 0.2286Flap CG distance from c,xβ (w.r.t. b) [-] 5.824×10−2

Heave Natural Frequency, ωh [Hz] 3.0486 2.9242Pitch Natural Frequency, ωα [Hz] 4.7000 3.8569Flap Natural Frequency, ωβ [Hz] 5.0786 5.3681