Energy harvesting for actuators and sensors using free-floating flaps

Abstract

A novel configuration of an energy harvester for local actuation and sensing devices using limit cycle oscillations has been modeled, designed and tested. A wing section has been designed with two trailing-edge free-floating flaps. A free-floating flap is a flap that can freely rotate around a hinge axis and is driven by trailing edge tabs. In the rotational axis of each flap a generator is mounted that converts the vibrational energy into electricity. It has been demonstrated numerically how a simple electronic system can be used to keep such a system at stable limit cycle oscillations by varying the resistance in the electric circuit. Additionally, it was shown that the stability of the system is coupled to the charge level of the battery, with increasing charge level leading to a less stable system. The system has been manufactured and tested in the Open Jet Wind Tunnel Facility of the Technical University Delft. The numerical results could be validated successfully and voltage generation could be demonstrated at cost of a decrease in lift of 2%.

Keywords

Electromagnetic energy harvesting flutter limit cycle oscillations free-floating flap

Introduction

The structural design of aircraft wings and helicopter or wind turbine blades is strongly influenced by their response to gusts or turbulence. One way to address these gust-induced loads is to alleviate them by locally changing the aerodynamic properties using trailing edge flaps combined with a sensing system. One of the drawbacks of this approach is that the structural dynamics need to be monitored continuously to generate the input to control algorithms that move the aerodynamic devices. Therefore, a set of distributed sensors, processors and actuators is needed. Certainly, for large scale aeronautical applications, the power supply for these devices becomes a critical design aspect. A central power system has the disadvantage that electricity needs to be transferred to the sensors, resulting in complex cable systems. A promising alternative solution is to power the electric devices by means of local energy generation through energy harvesting.

One method that is particularly suitable for the alleviation of continuous gust loads uses free-floating flaps (FFF), which are controlled by trailing edge tabs. This concept was first introduced by Heinze and Karpel (2006), who use a single FFF for control applications on a highly flexible wing, and by Bernhammer et al. (2013), where an FFF was used as an aeroelastic control device for gust load alleviation. The studied control system is particularly effective when the flaps are underbalanced as they become highly responsive to any flap activity due to low aeroelastic damping. A disadvantage of this approach is that the damping might tend to become negative, which causes flutter in coupling with the first wing bending mode. Bernhammer et al. (2013) also showed that the FFF could suppress its own flutter by controlling the trailing edge tabs.

While those devices have so far been used to aerodynamically alleviate vibration loads, this article presents an approach to convert the energy associated with the flutter into electricity that can be locally used for sensors and actuators. This is done through electromagnetic conversion of vibrational energy into electrical energy. For this process it is desirable to maintain a certain vibration level, which is sufficient to charge the battery but must not exceed a maximum value to guarantee structural integrity. An option to achieve this goal has been evaluated by Pustilnik and Karpel (2013a,b), who investigated the behavior of the FFF in limit cycle oscillations (LCO), which is a type of nonlinear instability. A well-known control-surface LCO stems from free-play in the actuator connections. This free-play creates a zone in which the flaps can rotate freely around its hinge axis. These constraints are reached, when the flap deflection is large enough to be constrained by the presence of the actuator. The surface flutters within the free-play zone, but the stiffness outside the zone turns the flutter into LCO. Alternatively, the gain of the flutter-suppressing control system can be tuned such that the system is neutrally stable and the amplitude of the vibrations will not increase over time.

While energy harvesting from mechanical vibrations is a well-researched topic, generating energy by exploiting aeroelastic instabilities is a young field of research. The first work in this field was done by Bryant and Garcia (2011) and Bryant et al. (2010), who used a simple cantilever piezoelectric bender with a free-floating flap at the trailing edge to generate flutter that can be harvested. Bryant et al. (2011) have further expanded this conceptual work by studying the influence of the system parameters on the stability. It was found that, by changing component masses and stiffness, the system behavior could be significantly changed. Both models exploit a two degrees of freedom model, coupled with a two-dimensional unsteady, linear aerodynamic model. Park et al. (2012a) and Park et al. (2012b) use electromagnetic energy conversion instead of piezoelectric devices. Instead of exploiting a coupled flutter mechanism, a T-shaped cantilever beam is used. A magnet is attached at the end of the cantilever beam such that it sheds vortices that lead to flutter. Coils are mounted in the non-moving frame of reference. Also Bruni et al. (2014) have studied the effect of aeroelastic instabilities on energy harvesting by using embedded piezoelectric elements. Sirohi and Mahadik (2011) also use embedded piezoelectric patches to harvest electrical energy from mechanical vibrations of a galloping triangular bar attached to a cantilever beam.

The work presented in this article aims to provide an implementation of an energy harvester closer to actual aerospace applications. For this purpose, the concept of a free-floating flap (FFF) is used. The flaps’ hinge locations are designed such that they can easily be driven by the tabs and still produce flutter at low velocities. This ensures that, unless controlled otherwise, the flap responds to turbulence in the air flow and a significant amount of energy can be generated. A coil is mounted inside the flap, oscillating in a magnetic field generated by wing-mounted magnets. The relative motion between the magnet and coil due to the vibration generates electricity that can be either directly used for the actuators and sensors or be stored in a battery. Details of the aeroelastic design of the wing have been presented by Bernhammer et al. (2013). The dimensions of the model were not altered and are given in Table 1. The gap indicated in Table 1, was present in the physical model, but is neglected for the numerical simulations. Compared to the original model, two angular potentiometers were replaced by commercially available dynamos, as shown in Figure 1. To limit the cycle amplitude, two structural delimiters were installed for each flap, in order to keep the amplitude of the flap deflections between 10 and −10 degrees.

Table 1.

Wing model details.

Chord	Airfoil Thickness	Span	Flap chord	Flap span	Dynamo	Gap between flaps
400mm	11mm	1000mm	160mm	250mm	Basta Trio 3320	8mm

Figure 1.

Energy harvester concept.

Numerical model

The numerical model was created in MSC/Nastran, where a structural modal analysis was carried out as detailed by Bernhammer et al. (2013). In this study, a numerical and experimental investigation is performed of the wing-flap configuration without energy harvesting including different flutter prediction methods. The first 15 structural modes were passed to ZAERO, which was used to extract the aeroelastic state-space time domain model that is based on rational function approximation of the unsteady aerodynamic force coefficient matrices Zona Technology (2011). However, only the first three modes contribute to the unstable aeroelastic response. A modal damping coefficient of 0.03 has been applied to correct for structural damping. Finally, non-linear feedback loops were introduced in Simulink to model the effect of the structural free-play zone and the electromagnetic coupling with the system.

State-space aeroelastic model

The structural model was built in MSC/Nastran (Rodden and Johnson, 1994), consisting of 914 CQUAD 4 elements. Originally clamped at the root section, a spring was added to reflect the root extension of the model such that it could be connected to measurement equipment. The spring was tuned to match the first bending frequency measured in the wind tunnel experiment (Pustilnik and Karpel, 2013a). Two additional fictitious masses (Karpel and Presente, 1995) were added to facilitate an accurate inclusion of a structural free-play zone (Karpel et al., 2013). A modal analysis was carried out and the modal results were passed to ZAERO for constructing the frequency domain unsteady aerodynamic force coefficient matrices. The time-domain second-order equations of motion in generalized coordinates can be expressed as

M_{hh} \overset{\cdot\cdot}{ξ} + B_{hh} \overset{\cdot}{ξ} + K_{hh} ξ = F_{aero} (t)

(1)

where $M_{hh}$ , $B_{hh}$ and $K_{hh}$ are the generalized mass, damping and stiffness matrices, respectively. $ξ$ is a vector containing the generalized displacements. $F_{aero}$ is the generalized aerodynamic force vector due to structural vibrations, gust inputs and control surface motion. The aerodynamic model is divided into five zones, with individual paneling: namely, the root, two flaps, the section upstream of the flaps and the tip. The unsteady aero method of ZAERO, combined with natural modes from MSC/NASTRAN, was used for generating complex aerodynamic influence coefficient (AIC) matrices for harmonic oscillations at various frequencies. The minimum state method (Karpel, 1999) was then used to approximate the AIC matrices as rational functions of the iw. The replacement of iw by the Laplace variable s then lead to compact time domain state space matrices. A stability evaluation by root-loci analysis of the resulting system matrix has been carried out to find the open-loop flutter conditions. Figure 2 displays the resulting aeroelastic frequency and the damping of the main modes participating in the flutter mechanism versus the velocity. Modes 1 and 2 are heavily damped and omitted in the damping plot in Figure 2. Flutter occurs when the damping branch of the bending mode crosses the zero line, at 10.2 m/s with flutter frequency of 3.6 Hz. The flutter mechanism is an interaction of the first bending mode with the inboard and outboard flap deflection modes. Four snap shots of the flutter mode during one half of a cycle are shown in Figure 3. The control system will suppress this flutter most of the time, except for certain times when a controlled level of flutter is used to charge the batteries.

Figure 2.

Frequency relevant modes versus velocity, damping of flutter branch.

Figure 3.

Flutter mode shape at 10.2 m/s, snapshots along a halfcycle.

2.2 Electronic circuit

In this article, in addition to their basic purpose of dynamic load alleviation, the flaps function as a power supply for the actuators and sensors. The electronic circuit layout was kept as simple as possible. Figure 4 shows the schematic layout of a simple battery charging circuit. L1 represents the coil that is rotated in the magnetic field, DB1 is a rectifier and R1 is a variable resistor. For simplicity, a voltage drop over the rectifier has not been included in the model. This drop would depend on the actual circuit design and the selected low voltage rectifier. When undergoing motion, the change in the magnetic field as seen by the coil causes a current in the electric circuit. The associated open circuit voltage $U_{open}$ created is equal to

U_{open} = nl \frac{d ϕ}{dt}

(2)

where n is the number of coil turns, l the length of a coil loop and $ϕ$ the magnetic field strength. The latter has been experimentally determined for the dynamo used during the experiment. For that purpose an oscillation of 3.6 Hz, corresponding to the frequency of the unstable mode with an amplitude of five degrees was prescribed, thereby representing the test conditions. The magnetic flux was computed based on these measurements. As only low coupling between structural motion and electronics could be observed, the magnetic flux was increased by a factor of 10 for the numerical simulations, assuming that it could be practically obtained. For the experiment, the magnetic flux reported in Table 2 was used. The increase in magnetic flux causes an increase in voltage by a factor of 10 and an increase in power by 100 in the numerical simulations. This large increase was required to show coupling effects between electronic harvesting and vibrations.

Figure 4.

Schematic of modeled electronic circuit.

Table 2.

Properties of dynamo.

Number of coil turns	Length of coil loop	Magnetic flux coefficient
100	94mm	$9.6 e \cdot 10^{- 3} \frac{V s^{2}}{rad}$

The magnetic flux coefficient is the magnetic flux multiplied by the coil length, as given in equation 4. The generated voltage U has to overcome the voltage of the battery $U_{bat}$ . Assuming no power loss over the rectifier, this can be separated into two cases.

U = {\begin{matrix} n l \frac{d ϕ}{d t} - U_{bat} & U_{open} > U_{bat} \\ 0 & U_{open} \leq U_{bat} \end{matrix}

(3)

The voltage generated can be calculated based on the rotational velocity of both flaps. The effect of the battery voltage as shown in equation 3 is modeled as a free-play zone with the width of the battery voltage. Note that the maximum charging voltage is not limited in the simulation. In practice the limit would be around 5–10V, depending on the type of battery. As voltages above 2V do not occur in the simulation, probably a circuit to increase the voltage for the charging would be needed in the real application. Furthermore, the electrical power P that is harvested adds damping to the system. The generation of electrical power requires a mechanical power input of the same magnitude. Therefore, the equations of motion need to be expanded with a damping term that is quadratically proportional to the rotational speed of the flaps. The electromechanical power of the damping is given in equation 4.

P = \frac{{(nl \frac{d ϕ}{dt})}^{2}}{R_{coil} + R_{var} + j ω L} \approx \frac{{(nl ϕ_{k})}^{2}}{R_{coil} + R_{var}} {\overset{\cdot}{θ}}^{2}

(4)

$θ$ is the flap deflection angle. Note that equation 4 is approximated using a constant magnetic flux $ϕ_{k}$ multiplied by the square of the rotational velocity. Also, the impedance $j ω L$ is omitted as it is two orders of magnitude smaller than the resistance of coil ( $R_{coil}$ ) and the variable resistance ( $R_{var}$ ). The damping has been implemented in generalized coordinates into the state-space system together with a structural free-play zone as shown in Figure 5. The output of the state-space system is the tip acceleration of the wing and the rotation angles of both flaps. The rotational velocities are obtained as output of the aeroelastic state-space system and serve as input to equation 4. Based on this power a reaction torque was computed, which was fed back as input to the aeroelastic state-space system. The circuit resistance was varied to study the effect on the aeroelastic stability as shown in Figure 4. The coefficients K for the structural stiffness are −1900 N m/rad, while the coefficient k of the electromagnetic damping is −0.826 N m s/rad.

Figure 5.

Simulink scheme of an energy harvester model.

Figure 5 also indicates a gust input. The gust force history in generalized coordinates has been computed in ZAERO for a continuous gust signal with a von Kármán turbulence spectrum for an altitude of 250 m above ground level. Only the component of the gust velocity perpendicular to the wing was taken into account. The turbulence intensity, which is the ratio of the mean root square of the amplitude of the velocity fluctuation over the mean velocity, is 1.1%. For the gust load cases, the forces have been added to the equations of motion, as given in equation 1. When closing the control loop, the total state-space linear aeroservoelastic system, including the linear control system that relates the tab motion to the acceleration measurements, reads:

\begin{matrix} \overset{\cdot}{x} = [A] x + [B] (u + u_{gust}) \\ y = [C] x + [D] u \end{matrix}

(5)

where

\begin{matrix} A = [\begin{matrix} 0 & I \\ - M_{hh}^{- 1} K_{hh} & - M_{hh}^{- 1} B_{hh} \end{matrix}] \\ B = [\begin{matrix} 0 \\ M_{hh}^{- 1} \end{matrix}] \end{matrix}

(6)

A, B, C and D are the state, the input, the output and the feed-through matrices of the aeroelastic system. x is the state vector containing the modal displacements and velocities and aerodynamic lag states and u is the input vector containing the generalized force and moments due to the non-linear feedback loop. As shown in Figure 5, the outputs are the flap rotation angles and velocities, while the inputs are the generalized electromagnetic and mechanical moments related to the free-play zone.

Numerical results

The energy harvesting system using the free-floating system has been simulated in time domain with the state-space aeroelastic model and the non-linear structural free-play zone and electromagnetic feedback. As was outlined, the limit cycle behavior of such a system is of highest importance. Therefore the system has been simulated with an initial excitation and the structural response is analyzed. Special attention in this analysis is paid to the transition between diverging aeroelastic responses and limit cycle oscillation. A state-space system has been identified based on every voltage time history (van der Veen et al., 2010). Eigenfrequencies and damping coefficients presented in this section were retrieved from these state-space systems. System parameters such as the resistance in the circuit and the charge level of the battery have been varied during different simulations to study their impact on the system stability and the energy harvesting performance.

In total, four sets of aeroelastic simulations have been performed numerically:

time domain simulations of limit cycle oscillations;

stability evaluation with 0 V battery voltage and varying resistance in the circuit;

stability evaluation with 1.2 $Ω$ resistance and varying battery voltage;

gust response simulation with 0 V battery voltage and varying resistance in the circuit.

Time-domain simulation of limit cycle oscillation

The added damping due to the power harvester has significant impact on the stability of the system. Figure 6 displays the results of a time domain simulation at 11 m/s wind speed, which, in the very low harvesting case, is unstable (see Figure 7). The baseline operation without energy harvester is equivalent to the 1.2 $Ω$ case, as the power generated is not significantly contributing to damping. Both start to flutter at 10.2 m/s. This instability can be observed in the bottom plot of Figure 6, where only little power is generated, such that the system immediately shows an increasing oscillation. After four seconds a limit cycle state is reached and the voltage does not increase anymore. Decreasing the resistance leads to an increase in stability. The limit case here is a short circuit with only the resistance of the coil in the denominator of equation 4. The associated structural response is very stable and damps out quickly.

Figure 6.

Time domain simulation with varying resistance at 11 m/s wind speed.

Figure 7.

Frequency and damping of the flutter branch versus velocity depending on resistance.

A feature worth noting is that, in the case of limit cycle oscillations, as shown in Figure 6, the rectified voltage does not cross 0 V. Until limit cycle oscillations are reached, the voltage displays sinusoidal behavior. Figure 6 gives more insight into the growth of the oscillations and the transition to limit cycles. It should be noted that the reason for the limit cycle behavior is that the amplitude of the oscillations reaches the limits of the structural free-play zone. During the growth period, both flaps are oscillating in phase, as shown in Figure 8. When the transition to the limit cycle occurs, the smooth sinusoidal behavior disappears and higher order frequencies occur around the maximum velocity. It is assumed that this can be attributed to the interaction between the two flaps and the structural delimiters, and the phase shift that develops once a limit cycle is initialized. The phase shift in angular velocity between the flaps causes the voltage always to be non-zero.

Figure 8.

Transition to limit cycle oscillation.

Stability evaluation

As has already been noted, the stability of the system strongly depends on the resistance in the circuit. The free-floating flap concept benefits from this dependence as it is possible to regulate the stability of the system by using the variable resistance as a control parameter, thereby keeping the system close to neutrally stable. The power generated, and consequently the resistance moment on the rotational axis, decreases with increasing resistance. Figure 7 shows the damping coefficient and the frequency of oscillation of the flutter branch as a function of variable resistance. The baseline flutter speed was computed to be 10.2 m/s (Figure 2). Adding electromagnetic damping results in an increase of the flutter speed to 11.7 m/s. Controlling the resistance in the circuit can therefore be used to keep the system marginally stable for an operational velocity range of more than 10%. Increasing the magnetic flux in the dynamo will further increase this damping such that the desired wind speed region can be spanned. Furthermore, it can be seen that the change in damping coefficient between a short circuit and no electromagnetic feedback is 0.03, independent of the wind speed. While the damping is strongly influenced by the energy harvester, the frequencies stay almost unaltered. A small frequency drop can be observed around 12 m/s; however, this drop is only on the order of 3%. The monotonic relation between decreasing resistance and increasing damping can be attributed to the generator selection. The generator was not optimized for power harvesting at the very slow rotational velocities observed in this study. The operating point of the generator is off the ideal condition, such that the maximum power extraction is not limited by the impedance matching condition, but rather by the variable resistance in the circuit.

The same effect can be observed when changing the battery voltage. Adding a free-play zone for the battery voltage essentially decreases the added damping of the electromagnetic system. Figure 9 shows the frequency and damping versus velocity for various voltage levels with a constant resistance of 1.2 $Ω$ . The effect is not as pronounced as in Figure 7; still, a decrease in flutter speed by 4% can be seen. This is a rather undesirable effect, as the resistance needs to be adjusted constantly when harvesting energy to charge the battery to keep the system neutrally stable. The charging effect reduces with increasing wind speed. The energy harvesting system system can become unstable even when the battery is completely empty and no battery charging free-play is present. It is assumed that aerodynamic forces significantly overshadow the reduction of damping, such that the system oscillation will increase with the same speed. Similarly to the resistance variation, changing the battery voltage hardly causes a change in vibration frequency.

Figure 9.

Frequency and damping of the flutter branch versus velocity depending on battery voltage.

Power capture

The power capture simulation has been run for a constant inflow with an initial perturbation of the model for the first bending dominated mode as shown in Figure 3. The time history has been calculated for 30 seconds and the average power and voltage for four different wind speeds are plotted in Figures 10 and 11. When running the simulations for 9 m/s, the structure damps out quickly, regardless of the resistance applied. Consequently, hardly any voltage is created and the system is not suitable as an energy harvester. For 10 m/s the voltage is already significantly higher despite being damped, but the same trends in voltage and power still hold. Practically no power can be generated and the voltage is very low. For 9 and 10 m/s, increasing electrical resistance causes less damping, which means that the amplitude of the vibration due to an initial deflection decays slower, meaning that more energy can be extracted from the system.

Figure 10.

Power output versus resistance starting from initial deflection.

Figure 11.

Voltage output versus resistance starting from initial deflection.

Wind speeds of 11 m/s are the first unstable velocities evaluated. Two zones can be detected in the voltage and power curves. The first part of both curves is strongly increasing until a resistance of 0.3 $Ω$ . This is the point where the wing is neutrally stable. For lower resistances, the structure is damped and not much energy can be extracted. This changes as the oscillations decay slower and slower with increasing resistance up to a point where the system becomes unstable and amplifies until it reaches limit cycle oscillations which are limited by the structural free-play zone. In this region of resistances above 0.3 $Ω$ , the generated voltage is practically constant and the power is inversely proportional to the resistance. For 12 m/s, the region of increasing voltage and power disappears, as the system is unconditionally unstable regardless of the resistance as shown in Figure 7. Therefore, the voltage is constant throughout the resistance range. Only a discontinuity can be observed for low resistance values, where the system is marginally unstable. The first low point can be attributed to the slow increase of the amplitude, while the second point, which lies above the constant curve, can be associated with the transition to limit cycle oscillations. As shown in Figure 8, the transition mechanism produces higher angular velocities yielding a higher voltage output. In the case of 0.1–0.15 $Ω$ , this transition takes place over multiple cycles, which explains the local rise in voltage. In the power production case, the inverse proportionality with the resistance is too dominant to visualize this variation of the voltage for low resistances.

Gust response

The last simulation performed is the response of the system to a gust. The gust was modeled uniformly over the wing span. The simulation length was 15 seconds. A von Kármán wind spectrum was used with a turbulence intensity of 1.1%. Figures 12 –14 show the power production in response to the gust excitation. The low turbulence amplitude was chosen to demonstrate gradual transition to limit cycle oscillations. Overall, Figures 12 and 13 agree well with the simulations with an initial deflection (Figures 10 and 11). The higher the wind speed, the more energy can be harvested. The overall amplitude of voltages is lower, as the incremental phase before reaching limit cycle oscillations contributes more. Constant voltages in the case of 11 and 12 m/s wind speeds are only reached at resistances of 0.5 and 1.2 $Ω$ . A difference to the previous simulations can be found in the comparison of the amplitudes of Figures 11 and 12. While in the limited cycle oscillation case, the generated voltage is almost equal for 11 and 12 m/s, in the gust load case, the higher wind speed shows a much higher responsiveness to the input signal, thereby tripling the output voltage. When comparing the low and high wind speed results, a factor of three, from 10 to 11 m/s, and a factor of five between 11 and 12 m/s are visible. For the power production these factors increase to nine and 25, respectively. This clearly shows the advantage of aeroelastic instabilities in energy harvesting, as the output can be increased by a factor of 225 just by crossing the flutter margin and increasing the wind speed from 10 m/s to 12 m/s. An increase in power production in this order of magnitude strongly enhances the possibility of using energy harvesting, not only for sensing but as the power supply for active load alleviation.

Figure 12.

Voltage output versus resistance. (a) All wind speeds. (b) Zoom in on stable configurations.

Figure 13.

Power output versus resistance. (a) All wind speeds. (b) Zoom in on stable configurations.

Figure 14.

Voltage time history versus resistance due to gust.

In contrast to the previous simulations, a distinct peak can be observed for 0.07 $Ω$ . This peak is accompanied by a clear dip at 0.13 $Ω$ . The dip occurred for both 11 and 12 m/s air speeds and is particularly visible in the power production Figure 13. To explain the differences a closer look needs to be taken at the time history of the vibrations, which are plotted in Figure 14. The low gust amplitude causes a gentle increment in voltage. It is interesting to see that the response with varying resistance changes significantly. The first observation is that, with increasing resistance, less damping is in the system: once a significant growth of the vibrations is initialized, this increase rate climbs as well. This falls well with what has been predicted by the stability plots in Figures 7 and 8. Eventually, the time domain simulation in the subfigures for 0.13 $Ω$ , 0.2 $Ω$ and 1.2 $Ω$ create stable limit cycles. The more remarkable observation, however, is that the point of initialization of the vibrations varies, causing the aforementioned dip. While the short circuit simulation grows slowly but steadily from two seconds onwards, all cases with higher resistance postpone the initialization point of the vibrations. For 0.13 $Ω$ , the structure does not show any response until five seconds; increasing the resistance above this value also causes an increase in responsiveness.

This unexpected result can be attributed to the interaction of the two flaps. Figure 15 shows the limit cycle amplitude for both inner and outer flaps. Each flap behaves in a rather different fashion. While the outer flap has a constant limit cycle amplitude, the inner flap decreases with increasing resistance. For low resistance values, the inner flap becomes dominant. The electromagnetic damping has an equalizing effect on the two flaps. Most likely this is connected to the fact that the outboard flap mode is the mode that interacts more with the bending mode in the flutter mechanism. Adding damping to the outboard flaps therefore has a stronger impact as the flutter mechanism is responsible for the power generation.

Figure 15.

Power output versus resistance of different flaps.

Figure 16 confirms this hypothesis. Adding electromagnetic damping changes the flutter mechanism. For high resistances, the outboard flap is the driving mechanism behind the instabilities: the flaps show almost identical behavior for low resistance values. When observed closely, the inner flap shows even a slightly higher amplitude in these cases. It can be concluded that this flutter mode, with two equally participating flaps, is more responsive to excitation, while the negative damping is smaller, as it takes longer to increase in amplitude over time. The flutter mode that is dominated by the outboard flap is less responsive but the negative damping is higher, which causes the curves shown in Figure 15. Once an excitation is initialized, this flutter mode keeps increasing faster.

Figure 16.

Time history of angular flap velocities due to initial impulse of bending mode.

Wind tunnel experiments

The system presented in the previous section was manufactured according to the specifications given in Table 1. The two electromagnetic devices at the end of the flaps were connected, such that the stator is magnetic and fixed to the wing structure. The rotor is a coil that is co-located with the rotational axis of the flap. The wing-flap combination was tested in the Open Jet Facility (OJF) of Delft University of Technology. The root of the model was connected to a six-component balance. The properties of the wind tunnel and the balance are given in Table 3. The structure was passed through an aerodynamic fitting, shielding the balance from influences of the flow as shown in Figure 17. Two numerical results were reproduced: namely, the response of the structure and the associated harvested energy as a result of an initial deflection and a continuous excitation signal. For the initial disturbance, the wing tip was loaded by a force, which was released instantaneously. The constant excitation signal was created by a disturbance signal on the inner flap. The monitoring system needed to be outside of the wind tunnel. The dynamos were thus connected by cable to the data acquisition system. Unfortunately, the resistance in the cables was too high to demonstrate a significant mechanical power extraction, as has been shown numerically. Therefore, it was not possible to demonstrate stability variation by changing the resistance in the electric system (again, shown numerically).

Table 3.

Properties of the Open Jet Facility.

Max. wind speed	Test section	Max. load balance	Resolution balance	Resolution coefficients
35m/s	2.8 m by 2.8 m	250 N	0.1 N	0.004 at 10 m/s

Figure 17.

Test set-up of wind tunnel experiment.

The performance of the flap system was assessed before the wind tunnel tests were conducted. For this purpose, the flaps were connected to a shaker: this can cause flap rotations of up to four degrees to a maximum frequency of 10 Hz. Figure 18 shows the quadratic mean of the voltage output versus rotation angle and frequency. Equation 2 shows the relation between generated voltage and changing field strength. This linear relation can be observed for both flap deflection amplitude and flap deflection frequency, as shown in Figure 18. Only for high deflection frequencies above 6 Hz does the linear relation not hold true anymore and a reduction in voltage output can be observed.

Figure 18.

Quantification of power generation of flaps.

Low amplitude limit cycles

The first step during the wind tunnel tests was to assess the aeroelastic stability of the system. A closed-loop identification (van der Veen et al., 2010) has been carried out. The controller developed for the flutter suppression experiments by Bernhammer et al. (2013) was used to stabilize the system above the flutter speed. Figure 19 shows the comparison of the identified frequency and damping to the numerical values. The experimental damping has been found by system identification using a stochastic disturbance signal on the control tab. The damping values are obtained from the state matrix of the identified system. Increasing electrical resistance For both subfigures, the trends agree. A slight numerical underprediction of the eigenfrequency can be observed; however, the difference for the first bending dominated eigenfrequency is less than 5%. Even the small dip that is obtained numerically at 11 m/s is reproduced. While the numerical values show a more gradual decrease to this point, the experiment shows a sharper dip, a fact that could have been caused by the numerical fitting of the state-space system parameters to the measurement values. The damping plot performs excellently for the first two measurement points, which are practically identical with the numerical prediction. Around the flutter point, experimental and numerical predictions diverge such that at 11 m/s a difference in the damping coefficient of 0.01 can be seen. This difference increases with increasing wind speed to a value of 0.025 at 13 m/s. While the main part of the damping below rated wind speed is caused aerodynamically, it is believed that friction in the system adds damping, which, once the system becomes unstable, contributes visibly to the overall system damping. The flutter speed obtained in both cases is between 10.5 m/s and 11 m/s.

Figure 19.

Damping and frequency plot.

Periodic excitation

To further assess the responsiveness of the system to a disturbance input, a sinusoidal signal was sent on the trailing edge tabs on both flaps. Figure 20 shows the measurements of the voltage response for different frequencies. The background noise in the measurements, caused by turbulence in the flow, results in a base voltage of 0.005 V. An excitation signal at low frequencies of 1 or 2 Hz does not change the average voltage that is obtained, regardless of the wind speed. The same holds true for high frequencies of 4 Hz and above. Only for 3 and 3.5 Hz is a structural response visible. While the aerodynamic damping is still high, at wind speeds of 8 m/s, an increase to 9 m/s already shows an increase in achievable voltage output by a factor of three. When increasing the wind speed even further the maximum response is a factor of eight above the baseline value. Higher wind speeds in the experiment were not possible as for 11 m/s the system would be unstable and even a very small excitation would result in flutter. Consequently, any small excitation will limit cycle oscillations with a high voltage generation.

Figure 20.

Sinusoidal excitation of trim tab for different wind speeds.

Small initial displacement

In a third step, the system is given a small initial disturbance. For wind speeds below 10 m/s the initial disturbance is damped away relatively quickly: practically no energy is harvested, as displayed in Figure 21. At wind speeds of 10 m/s, the system is close to neutrally stable. Any disturbance, be it initial or through turbulence, provokes a slowly fading oscillation. Consequently, the achievable power output is higher than for lower wind speeds. For 11 m/s, the system is unstable and the vibrations increase in amplitude. In the current experiment, the controller designed by Bernhammer et al. (2013) was used to keep the system neutrally stable. For this purpose, the gain in the controller was altered manually, such that the peak accelerations would not exceed 2 g, where g is the gravity constant. One should notice that this is significantly below the physical delimiters of the system, which allow flap deflections of up to ten degrees. As expected, the voltage output increases yet another 40% compared to the 10 m/s case.

Figure 21.

Average voltage versus wind speed of inner and outer flap.

For wind speeds below the flutter speed, the energy production of both flaps is equally low. For aeroelastically triggered energy harvesting, the outer flap interacts more with the first bending dominated structural mode. The voltage generation is consequently twice that of the inner flap. Figure 22 shows the time history of the limit cycle oscillations for wind speeds of 11 m/s. The amplitude varies slightly over the cycles, which is a phenomenon that can be explained by turbulence in the inflow. The measurement data shows significant noise, which cannot be attributed to the aeroelastic response, but rather to the sensors and the acquisition system. It is interesting to see that, despite being a limit cycle, the oscillations of both flaps are in phase. The phase shift of 180 degrees shown in Figure 22 is caused by the installation of the electromagnetic devices (Figure 1): if the flaps oscillate in phase the voltage signal shows the opposite sign. As the devices installed on both flaps are identical, but mirrored in orientation, a synchronous flap deflection causes opposite voltage outputs. This is contrary to the numerical findings, which show a phase shift between the flaps when being in limit cycle oscillation.

Figure 22.

Limit cycle oscillations at 11 m/s.

One should, however, bear in mind that in the numerical case electromagnetic coupling and structural delimiters were used to create a limit cycle, while in the experimental case, the oscillation amplitude was limited by trailing edge tab control.

The same differences with the numerical simulations can be observed in Figure 23. While agreement is reached concerning the damping and decay of the oscillations for 8 to 10 m/s and the growing oscillation to limit cycle oscillations for 11 m/s, the synchronous nature of the vibrations of both flaps causes sinusoidal-like variations in the voltage that can be achieved. Notice that in Figure 23 the absolute values of the voltage generation are displayed. The voltage amplitude is a factor of ten lower than in the numerical results. This difference can be explained by the increased magnetic flux in the numerical simulations.

Figure 23.

Time history of voltage generation due to impulse, 8 m/s (top) to 11 m/s (bottom).

Fluctuation of the lift coefficient

Figure 24 shows the lift forces measured at the root of the wing when the model was put under an angle of 3.5 degrees. While the lift in the case of a fixed wing is practically constant in time – the variations are caused by low amplitude turbulence and the measurement signals – the force time history of the limit cycle oscillation shows oscillations around the value of the fixed flap case. The oscillation frequency coincides with the eigenfrequency of the first bending mode. The oscillations originate from variations of the aerodynamic forces over time and the structural dynamics associated with the flap motion. The difference in average value between the forces during the flap fixed case and the LCO case for wind speeds of 11 m/s is 2%, while the oscillation amplitude stays below 5% of the mean value. Unfortunately, a similar measurement for the drag could not be performed, as the differences found between the fixed flap and the LCO case fall into the measurement accuracy of the balance.

Figure 24.

Time history of lift forces.

High amplitude limit cycle

In a final step, the controller was switched off and experiments were performed at 11.5 m/s wind speed. The limit cycle amplitude was now not tuned manually as before, but only by the structural delimiters, which allow the flaps to rotate between 10 and −10 degrees. Figure 25 shows the tip accelerations of the wing as the system becomes unstable. Just after 17 s into the measurement the wing starts to oscillate. While these oscillations are at first small, they grow to tip accelerations of 6g at 22 s in the measurement, where the flaps touch the delimiters for the first time. From this point on time sharp peaks occur in the tip accelerations’ history, a result of the forces transfered between the flaps and the wing structure. These peaks in acceleration almost immediately reach amplitudes of over 20g. The aeroelastic system stabilizes in a limit cycle oscillation.

Figure 25.

Tip accelerations during limit cycle oscillation.

Figure 26 further elaborates on the structurally delimited oscillations as it shows the time history of the voltage generation. Up to 22 seconds the phase of the voltages of the inner and outer flap is perfectly aligned. The noise level is relatively low and the extrema of the voltages are smooth.

Figure 26.

Voltage generation of flaps during limit cycle.

Between 22 and 23.5 s, the peaks become sharper and increase rapidly. This corresponds very well with what has been presented in Figure 25. At 24 s, the system seems to have stabilized in the limit cycle configuration. The phase coupling between the two flaps is lost and the outer flap especially seems to suffer more from the delimiters, a fact that can be attributed to the higher interaction of the outer flap with the unstable bending mode compared to the inner flap. The deflection amplitudes are thus larger and the delimiters are reached earlier. While the frequency of the oscillation of the inner flap does not change, the frequency of the outer flap triples. One dominant oscillation peak in the outer flap voltage is observed which, after a transition period of 3 s, aligns with the oscillation of the inner flap. Two additional lower amplitude cycles occur, probably as a response to the impact the outer flaps and the delimiter. The experimental results only partially confirm the numerical simulations. While the loss of phase coupling during the transition period is present both in simulation and experiment, the permanent phase shift does not manifest itself in the experiment. The difference might be connected to the hard impact the flap sees every cycle, while the delimiter amplitude was significantly smaller during the numerical simulations and thus the maximum force is also smaller as the oscillation frequencies are identical. The additional peaks that occur in the experiment can consequently not be expected to be as large in the numerical simulations and might not be visible in the voltage history.

Conclusions

A novel energy harvester device has been designed, evaluated numerically, built and tested. The potential of exploiting aeroelastic instabilities has been demonstrated: the increment in power production can be more than a factor of 200, compared with turbulence harvesting. Furthermore, it was shown that changing the resistance is a suitable tool for controlling the stability of the system—it can overcome the destabilizing effect that battery charging can have on power production and the system’s stability. Furthermore, it can be concluded that including a structural free-play zone introduces limit cycle oscillations, which show a phase shift between the flap motion. The main results in terms of power production could be confirmed experimentally. The strong coupling between wind speeds and the potential energy generation has been underlined, as crossing the flutter speed yields a tenfold increase in voltage generation as predicted numerically. The complex nature of the limit cycle oscillations could only partially be confirmed. For a controller regulated low amplitude limit cycle oscillation, no phase shift between the flaps occurred. For a structurally limited oscillation, strong peak forces and voltages occur. However, the oscillation pattern converges to one dominant oscillation for the outer flap, in phase with the oscillation of the inner flap and two smaller oscillations that are out of phase. For the low amplitude oscillations, which are structurally preferred, the loss of lift of the structure is less than 2%.

To enhance comparability between experimental and numerical simulations, the experimental test set-up should be updated such that the electromechanical feedback that is observed in the numerical simulations can be reproduced experimentally.

While this article serves only as an analysis of the energy harvesting concept, for the next step a combined study of energy harvesting and load alleviation in an autonomous flap is recommended. This should include the energy balance between the actuation requirements and the power generated. Another point of attention is that the generator operated far from its most efficient operational point due to the low rotational speed. The challenge in follow-up research will be to increase the performance of the energy harvester: for example, by gearing up the rotational velocity. This can also overcome the problem of very low resistance requirements in the circuit to establish a coupling of energy harvesting and mechanical vibration.

A key challenge for the implementation of this concept to real applications remains the balance between increased loading due to oscillations and reduction of peak loads through active control. However, this is beyond the scope of this article and should be addressed in follow-up research.

Footnotes

Acknowledgements

The controller design was technically supported by dr. ir. Gijs van der Veen and ir. Edwin van Solingen of Delft University of Technology. Part of the measurement equipment was provided by the Delft Center for Systems and Control.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research has been funded by the Far and Large Offshore Wind (FLOW) project of the Dutch Ministry of Economic Affairs. P201102_006.

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