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Journal of Fluids and Structures

Journal of Fluids and Structures 57 (2015) 1–14

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n CorrE-m

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Energy harvesting of a heaving and forward pitching wingwith a passively actuated trailing edge

Firas Siala, James A. Liburdy n

School of Mechanical, Industrial & Manufacturing Engineering, Oregon State University, Corvallis, OR 97330, USA

a r t i c l e i n f o

Article history:Received 7 January 2015Accepted 17 May 2015

Keywords:Energy harvestingFlexible trailing edgeForward pitching

x.doi.org/10.1016/j.jfluidstructs.2015.05.00746/& 2015 Elsevier Ltd. All rights reserved.

espondence to: 204 Rogers Hall, Oregon Staail address: james.liburdy@oregonstate.edu (

a b s t r a c t

This study experimentally investigates the energy harvesting capabilities of an oscillatingwing with a passively actuated trailing edge. The oscillation kinematics are composed of acombined heaving and forward pitching motions, where the pitching axis is well behindthe wing center of mass. Passive actuation is attained by connecting the trailing edge withthe wing body using a torsion rod. The degree of flexibility of the trailing edge isrepresented by the Strouhal number based on the trailing edge natural frequency. Thetrailing edge passive response is studied for oscillation Strouhal numbers of 0.017, 0.025and 0.033. Instantaneous aerodynamic forces are measured in a closed loop wind tunnelat a Reynolds number of 40 000, based on the free stream velocity and the wing chordlength. Measured results include the effective angle of attack induced by the trailing edgeactuation as well as the lift and moment during the oscillation cycle. For the imposedkinematics in this study, the pitching motion has a positive contribution to the meanpower output whereas the heaving motion has a relatively small but negative contribu-tion. Additionally, by decreasing the natural frequency of the trailing edge closer to that ofthe imposed oscillation frequency, the magnitude of the lift and moment forces and hencethe mean power output, increases. It is found that there exists a strong correlationbetween mean power output and the effective angle of attack, shown through the passivetrailing edge response, resulting in an increase in energy harvesting potential.

& 2015 Elsevier Ltd. All rights reserved.

1. Introduction

The energy of fluid flow in tidal currents, rivers and the wind is an attractive alternative renewable energy resource.Harvesting this kinetic energy is usually accomplished through the use of rotating turbine based devices. However, theseconventional devices possess many undesired economical and environmental impacts (Saidur et al., 2011). This has led to theinvestigation of alternative mechanisms to exploit the kinetic energy of both steady and transient fluid flows. An increasinglypromising concept relies on the use of oscillating energy harvesting devices. The main advantage of oscillation based energyharvesters compared to conventional rotating turbines is the alleviated impact upon the environment and wildlife as well asreduced high noise output due to their relatively low blade tip speed (Zhu, 2011). Initially, this concept was studied byWu (1971),who showed through experimental and theoretical analysis that a foil submerged in a fluid had the ability to extract energy fromincoming waves to propel itself. This concept was further investigated and developed by McKinney and DeLaurier (1981). They

te University, OR 97331, USA. Tel.: þ1 541 737 7017; fax: þ1 541 737 2700.J.A. Liburdy).

F. Siala, J.A. Liburdy / Journal of Fluids and Structures 57 (2015) 1–142

performed experiments to examine the energy extraction of an oscillating windmill and they showed that it was capable ofefficiencies comparable to conventional rotary designs. Furthermore, Lindsey (2002) suggested that the concept of energyharvesting using oscillating wings could be understood through the flutter theory. Flutter is essentially a dynamic instability of awing in a fluid flow and it is caused by the interactions of the wing's elastic and aerodynamic forces. During this interaction,energy is transferred from the surrounding fluid to the wing. While this fluid structure interaction can be a destructivephenomenon in airplanes, the vibrations it provides offer opportunities for innovative energy harvesting techniques.

Substantial research has been done in the past years using mostly numerical and some experimental methods to betterunderstand the fluid device interactions responsible for efficiency energy harvesting. For example, Kinsey and Dumas (2012)recently studied oscillating hydrofoils using Unsteady Reynolds Averaged Navier Stokes (URANS) simulations. They modeled ahydrofoil to undergo sinusoidal heaving and pitching motions with a phase shift of 401 at a Reynolds number of 1100. They foundthat the energy harvesting efficiencies were as high as 34%. Their results were in good agreement with their prototype field tests,Kinsey et al. (2011). Kinsey and Dumas (2008) previously discussed the boundary between energy harvesting and thrust productionregimes of an oscillating foil. They suggested that the boundary between prolusion and energy extraction relies heavily on theoscillation Strouhal number, which is defined as St ¼ 2f A=U where f is the oscillation frequency, 2A is the peak to peak heavingamplitude and U is the free streamvelocity. At very high Strouhal numbers, the shed vortices in thewake of an oscillating wing takethe form of a reverse Karman street. In this condition, the vortices induce a jet like pattern near the center of the oscillating wing,thus providing a momentum surplus, and hence thrust is generated. On the other hand at lower Strouhal numbers, the wake takesthe form of the standard Karman street, where momentum deficit exists near the center of the wing. This momentum deficit isbelieved to be related to the amount of energy extraction, however the exact relationship is yet to be determined.

Extensive research has been carried out to investigate the mechanisms that improved the aerodynamic forces ofoscillating wings (Ellington et al., 1996; Van den Berg and Ellington, 1997; Birch and Dickinson, 2001, 2004; Shyy and Liu,2007; Lu and Shen, 2008; Muijres et al., 2008). These studies concluded that the strength and the evolution of the leadingedge vortex was the most important factor in enhancing the aerodynamic performance. When a wing oscillates at certaincombinations of frequency, heaving amplitude and pitching angles, the timing of leading edge vortex shedding issynchronized such that flow separation and dynamic stall become beneficial to the unsteady aerodynamic loadings. Theshed vortices have a low pressure core, which creates a suction effect that increases the pressure difference between the topand the bottom surfaces, thus enhancing aerodynamic forces.

Recent studies have focused on alternative mechanisms to further enhance the aerodynamic performance of oscillating foils.One such mechanism that is still under investigation is the effect of complex motion trajectory of an oscillating wing on forcegeneration. Xiao et al. (2012) studied the influence of a non-sinusoidal pitching trajectory profile with a sinusoidal heaving onenergy harvesting. A trapezoid like pitching profile was investigated, with the portion of flat pitching angle within eachoscillation cycle being adjustable to alter the form from a trapezoid to a square wave to a sinusoidal profile. Their numericalsolutions showed that the benefits to energy harvesting enhancement relied on this waveform. For a given nominal angle ofattack and heaving amplitude, there is an optimal waveform at which power output significantly increases. In another study, Xieet al. (2014) modified the pitching motion by setting an initial pitching angle equal to π/2. Numerical simulations were performedfor a range of reduced frequencies and pitching amplitudes. They found that energy extractionwas mainly caused by the heavingmotion and the average energy harvested from pitching motion was approximately zero. It was also shown that for the modifiedpitching motion, changing the pitching angle resulted in a change of timing of leading edge vortex formation and shedding.

An alternative mechanism that may have potential for energy harvesting is wing surface flexibility. Studies on insect wingsand fish fins suggested that flexibility may lead to the generation of higher lift and thrust (Katz and Weihs, 1978; Heathcote etal., 2004; Miao and Ho, 2006; Heathcote and Gursul, 2007; Zhu, 2007; Yin and Luo, 2010; Eldredge et al., 2010; Rushen et al.,2014). Some degree of flexibility can increase the effective camber of the wing, thus enhancing the strength of the leading edgevortex. Additionally, wing deformation can re-align the forces such that thrust is produced. On the contrary, the effect of wingflexibility on energy harvesting is not well understood. Liu et al. (2013) showed, using 2D computational modeling, that adeforming trailing edge of a wing is beneficial to energy extraction by increasing the instantaneous lift force. On the otherhand, a flexible leading edge has the ability to manipulate the phase shift between the instantaneous forces and the wingmotion. It was emphasized that to increase the energy harvesting, the leading edge vortex should be formed on the bottomsurface while the wing is heaving downward, such that the product of lift force and heaving velocity is positive. Nevertheless,it is left to quantify wing flexibility and understand how it actually affects the instantaneous forces and the resultant flow field.

In the present work, the energy harvesting capabilities of an oscillating airfoil with heaving coupled with a relatively largepitching axis is investigated. Unlike previous studies, this motion accentuates the role of pitching on energy harvesting. Themotion consists of pitching about an axis that is located behind the trailing edge of the wing. This configuration is given thedescriptive name of “forward pitching”. The pitching and heaving occur with the same frequency, however a phase shift isimposed, as described later. In addition, enhancement caused by a flexible trailing edge is demonstrated. Due to the highcomplexity of continuous flexibility, this study focused on the use of a two component wing model. The wing model consistsof a trailing edge connected to the wing by a torsion rod. The torsion rod provides passive rotational flexibility as the wingundergoes oscillation kinematics. The aerodynamic forces acting on the wing are measured to quantify the power-output.Furthermore, the induced effective angle of attack is evaluated and related to the power output.

This paper is organized as follows. Section 2 describes the experimental method including the wing design and the motionkinematics. Section 3 describes the data analysis techniques. Section 4 presents the results and discussions for a rigid and flexiblewing. Finally, conclusions relative to this imposed heaving and pitching motion and the flexible trailing edge are provided.

F. Siala, J.A. Liburdy / Journal of Fluids and Structures 57 (2015) 1–14 3

2. Experimental method

2.1. Apparatus

The experiments were conducted in a low-speed recirculating wind tunnel located at Oregon State University. The test sectionhas internal dimensions of 1.37 m�1.52 m. The maximum wind velocity is approximately 20 m/s and the turbulence intensitylevel is less than 1%. It is featured with plexiglass side walls for convenient optical access. The test device, shown in Fig. 1, wasbuilt to provide the oscillation motion and measure the forces acting on the wing. Fig. 1(a) shows a drawing of the device withthe wing attached, Fig. 1(b) is a photograph of the device showing the pitching and heaving motions and associated motor drivesand Fig. 1(c) shows the load cells used to measure normal and axial forces. The heaving and pitching motions were controlled bytwo servo motors which were operated through a LabVIEW interface program. A data acquisition system that also employed aLabVIEW programwas used to record the output of the load cells that measured the normal and axial forces acting on the wing.The load cell analog signal was filtered in a signal conditioner and then converted to a digital signal using a 10 bit analog-to-digital converter. The maximum load that can be measured is 22.2 N with a resolution of 0.002 N.

A sketch of the wing, shown in Fig. 2, was fabricated from PC-ABS using fused deposition modeling. It has a chord andlengths of 20 cm and a thickness of 4 mm (2% of the chord length). The leading and trailing edges are elliptical with a 5:1major to minor axis ratio. Additionally, a trailing edge is hinged with a torsion rod that can be changed to provide differentdegrees of rotational flexibility. This trailing edge flap spans the entire wing and is one third of the chord length.

The wing was supported from the underside using a mounting plate that was 3 mm thick by 20.5 mmwide and 200 mmlong. The mounting plate was attached to the test device as shown in Fig. 1. At the maximum deflection of the trailing edgeduring the flapping motion, the wing was a minimum of 13 cm away from any obstruction from the device or the windtunnel walls.

Fig. 1. Drawings of the test device (a) three dimensional view of support mechanism and wing, (b) heaving and pitching mechanism, and (c) location of theload cells.

Fig. 2. Illustration of the wing cross-section, the pitching angle, θP and the trailing edge actuation angle, θTE.

F. Siala, J.A. Liburdy / Journal of Fluids and Structures 57 (2015) 1–144

2.2. Motion dynamics

The oscillatory motion of the wing used in this study consists of heaving and pitching motions that were prescribed,respectively, according to the following equations:

h tð Þ ¼ h0 sin ð2πf tþψÞ ð1Þ

θP tð Þ ¼ ϕ0þθ0 sin 2πf tð Þ ð2Þwhere h0 is the nondimensionalized heaving amplitude (normalized by chord length c) ϕ0 is the initial pitching angle, θ0 is thepitching amplitude, ψ is the phase shift between pitching and heaving motions and t is time. The pitching axis is located at adistance rp behind the center of mass of the pitching components (wing, device, load cells etc.), as shown in Fig. 3. The centerof mass of the combined pitching components of the wing was determined using the methods described by Rushen (2014).

The combination of the location of the pitching axis behind the wing and a pitching motion used in this study rangingfrom 01 to 401 results in a forward pitching-like motion. This is in contrast to a root fixed pitching motion, which waspreviously studied by Hu et al. (2011). Furthermore, the imposed motion consists of simultaneous vertical heaving coupledwith the phase shifted forward pitching. The latter results in a significant moment generated about the pitching axis, as

Fig. 3. Illustration of pitching axis located behind the wing center of mass at distance rP .

Table 1Experimental conditions.

Parameter Value

C 20 cmh0 0.25I 8.7�10�5 kg m2

rP 20 cmRe 40 000St 0.0166; 0.0249; 0.0331StN 1; 0.1735; 0.1338ϕ0 201θ0 201Ψ 901

Fig. 4. Angle of attack induced by the trailing edge.

F. Siala, J.A. Liburdy / Journal of Fluids and Structures 57 (2015) 1–14 5

discussed later. To measure heaving and pitching positions as a function of time, fiducial marks were placed on the sideedges of the wing and a digital camera with 1280�1080 pixel resolution at a framing rate of 120 Hz was used inconjunction with an image processing software to track the wing position.

The passive actuation of the trailing edge was established by inserting a torsion rod into slots along both the wing bodyand trailing edge, forming a hinge. The rod was secured at one end to the wing body and the other end to the trailing edge,providing a means to allow rotation of the trailing edge controlled by the torsion characteristics of the rod material. Theneutral position of the trailing edge was controlled by pre tensioning the torsion rod to account for the weight of the trailingedge. When the wing is set into motion, the trailing edge passively actuates which provides dynamic changes of the effectivecamber during the heaving and pitching cycle. The trailing edge actuation motion was also recorded during the heaving andpitching cycle to determine the angle of the trailing edge, θTE.

The degree of flexibility of the torsion rod was measured by attaching a known mass to the trailing edge while the wingwas static. Images of the downward deflection were captured and used to obtain the angle of deflection. The rod torsionconstant, κ is expressed as

k¼ FTθTE

ð3Þ

where FT is the torque due to the attached mass,m and defined as FT ¼mglTE cos ðθTEÞ, where g is gravity and lTE is the lengthof the trailing edge. A Strouhal number based on the natural frequency of the rod is used to describe the wing flexibilitysuch as

StN ¼ f NlTEU

ð4Þ

where the natural frequency is defined as f N ¼ 1=2πffiffiffiffiffiffiffiκ=I

pand I is the trailing edge moment of inertia about the hinge.

Physically, this Strouhal number represents the ratio of convective time scale along the trailing edge to the natural time scaleof the spring response. A synchronization between force measurements and the corresponding oscillatory motion andtrailing edge actuation was accomplished by setting the camera to be activated with an external trigger from the LabVIEWprogram when the load cells begin being recorded.

The instantaneous forces were measured for a range of oscillation frequencies and torsion rod flexibilities at a constantflow Reynolds number, defined as Re¼ Uc=ν, where c is the kinematic viscosity of air at room temperature. Table 1summarizes the parameters that were investigated in this study.

3. Data analysis

3.1. Effective angle of attack

To gain useful insight about the behavior of the unsteady aerodynamic forces, it is important to synchronize them withthe motion dynamics of the flapping wing. This is usually done by combining heaving and pitching motions into a singleparameter known as the effective angle of attack, αeff, which for a rigid body, expressed as

αeff ¼ αP;hþθP ð5Þwhere αP;h is the angle of attack induced by the heaving and pitching motions which is expressed as

αP;h ¼ arctanVh�rtipω cos ðθP

U

� �ð6Þ

where Vh is the heaving the heaving velocity and rtipω cos ðθPÞ is the vertical component of the pitching velocity. Thevariable rtip represents the distance from pitching axis to the tip of the leading edge and ω is the pitching angular velocity. Inorder to include the effect of the induced trailing edge motion on the effective angle of attack the angle, β is introduced, asshown in Fig. 4.

The variable β is defined as the angle between the chord line and the free stream velocity, which is essentially the angleof attack induced by the trialing edge actuation. From the geometry shown in Fig. 4, the flexible trailing edge allows the

Table 2Uncertainty estimates.

Error St¼0.017 (%) St¼0.025 (%) St¼0.033 (%)

ϵh 1.76 2.65 3.43ϵθP 1.69 2.66 3.47ϵθTE;StN ¼ 0:17 15.1 13.1 12.5

ϵθTE;StN ¼ 0:14 11.2 10.5 10.3

ϵFL 8.34 11.8 14.3ϵFD 8.93 11.2 14.0ϵM 9.54 12.3 15.1

F. Siala, J.A. Liburdy / Journal of Fluids and Structures 57 (2015) 1–146

angle of attack to increase to values greater than θP. So, the effective angle of attack is obtained by replacing c in Eq. (5) withβ, such that

αeff ¼ αP;hþβ ð7Þ

3.2. Force calculations

The response of the load cells designated as the normal and axial components, FN and FA, respectively, were converted tolift, FL and drag, FD accounting for wing orientation during the cycle based on the effective angle of attack. The effectiveangle of attack was chosen here and not the pitching angle, since it represents the instantaneous angle between theoncoming flow and the wing's effective reference line that's induced by the oscillatory motion and the trailing edgeactuation. Note that the effect of tip downwash velocity on the angle of attack was not included. Furthermore, the momentabout the pitching axis was obtained based on these lift and drag forces and their respective moment arms.

In addition to aerodynamic forces, the load cells also measure the forces due to gravity and the inertia of the flappingwing and its support. The contribution due to the gravitational force on the wing and the support was removed during thestatic calibration procedure of the load cells. The contribution of the inertial forces is divided into three parts; inertia due toheaving, due to pitching and due to trailing edge actuation. The heaving inertia is defined as

FI;h ¼mhαh ð8Þwhere mh and ah represent the mass of the heaving components (wing, load cells and wing support) and heavingacceleration, respectively. The pitching inertia consists of two accelerations; tangential and normal to the pitching arcmotion. The tangential acceleration is defined as the rate of change of the pitching velocity. The tangential force is expressed

Fig. 5. (a) Transient heaving and pitching motion over two cycles where T is the period of one cycle; angle of attack due to heaving, αh, and pitching, αP, for(b) St¼0.017 and (c) St¼0.033.

F. Siala, J.A. Liburdy / Journal of Fluids and Structures 57 (2015) 1–14 7

as

FI;t ¼mPd2θPdt2

ð9Þ

wheremp is the mass of the pitching components. The force due to normal acceleration is pointing outward from the centerof pitching rotation, which is

FI;N ¼mPrPd2θPdt2

!2

ð10Þ

The inertia due to the trailing edge actuation was obtained using a similar method. The change of angle of actuation iscaused by tangential and normal accelerations of the trailing edge, which are expressed as

FI;t;TE ¼mTEd2θTEdt2

ð11Þ

FI;N;TE ¼mTElcm;TEd2θTEdt2

!2

ð12Þ

where lcm,TE is the distance from the actuation hinge to the trailing edge center of mass. All these inertias were decomposedinto two components; one parallel to lift force and the other parallel to drag. Finally, the aerodynamic lift, FL, drag, FD andhence the moment M, were calculated by subtracting the decomposed Eqs. (8)–(12) from the measured forces by the loadcells. The following form of the nondimensional aerodynamic forces is used to present the results:

CL ¼2FL

ρU2Scð13Þ

CD ¼ 2FDρU2Sc

ð14Þ

CM ¼ 2FLρU2Sc2

ð15Þ

where ρ is the air density and S is the wing span. The instantaneous power extracted from the flow is determined bysumming the power generated by the heaving, Ph(t) and the pitching Pθ(t) motions

P tð Þ ¼ Ph tð ÞVh tð ÞþPθ tð Þω tð Þ ¼ CLVh tð ÞU

þCMω tð Þrtip

U16Þ

3.3. Uncertainty

The uncertainty in aerodynamic forces and associated power was calculated based on the errors of the measured lift, ϵFL,drag, ϵFD, moment, ϵM , the wing heaving and pitching positions, ϵh and ϵθP , respectively, and the trailing edge actuation angle,ϵθTE . These errors consist of camera resolution uncertainty based on pixel size of the images (0.195 mm/pixel), as well as therandom errors in experiment repeatability. For adequate statistical analysis, each experiment was performed seven times, andall the errors are reported for 95% confidence level. The aerodynamic force measurements contain the additional uncertaintydue to the load-cells resolution (0.002 N). Furthermore, the uncertainty in power generation is calculated using the methoddescribed by Kline and McClintock (1953). Table 2 lists all of the components of the uncertainties and how they vary with St.

4. Results

To better illustrate the performance of the imposed unique motion in this study, the results are presented for the rigidwing case first. Then the results of the flexible wing will be presented to investigate the effect of trailing edge flexibility onenergy harvesting.

The heaving and pitching configuration used in this study is very different fromwhat is found in the literature, where thetypical pitching axis occurs somewhere along the chord line. However, to help evaluate the performance for the rigid wingto the more standard pitching the following comparisons can be made. At a similar Strouhal number, 0.033 in this studyversus 0.050 by Wu et al. (2015), the mean value of the power coefficient, Cp, is 0.144 in this study versus 0.032 for Wu et al.This indicates the advantage of the added component due to angular motion induced by the present study. Similarly, at areduced frequency of 0.048 in the present study versus 0.05 used by Liu et al. (2013), the mean value of the powercoefficient in the present study is 0.12, compared with that of Liu et al. of 0.0625. So in both of these cases, a significantincrease in the mean power coefficient is obtained for equivalent measures of Strouhal number and reduced frequency for a

F. Siala, J.A. Liburdy / Journal of Fluids and Structures 57 (2015) 1–148

rigid wing undergoing the off-chord pitching motion. Below detailed results are presented for first the rigid and then theflexible wing cases.

4.1. Rigid wing

Fig. 5 shows the transient relationship between the effective angle of attack, αeff prescribed pitching angle, θP, pitchinginduced angle, αP and heaving induced angle, αh over two oscillation cycles, where T is the period of one cycle. Data wascollected for three values of St, 0.017, 0.025 and 0.033, with results for the smallest and largest values displayed in this figure.The heaving and pitching motions are shown in Fig. 5(a). As can be seen in Fig. 5(b) and (c), the prescribed pitching motion, θP,

Fig. 6. CL and normalized heaving velocity for (a) St¼0.017 and (b) St¼0.033; CM and normalized pitching velocity for (c) St¼0.017 and (d) St¼0.033.

Fig. 7. Coefficient of power generated by heaving and pitching for (a) St¼0.017 and (b) St¼0.033.

F. Siala, J.A. Liburdy / Journal of Fluids and Structures 57 (2015) 1–14 9

slightly leads αeff by approximately 51. The effect of increasing the heaving Strouhal number is an increase in peak values of theeffective angle of attack, with corresponding larger negative values. It should be noted that here the effective angle of attack isonly slightly negative for a short time of the cycle when the pitching angle is close to zero. To achieve a larger contributionfrom a negative angle of attack the pitching angle would need to extend to further negative values as well.

The transient coefficients of lift, CL, and moment, CM, are shown in Fig. 6 for the lowest and highest values of St. Also shownin the figure are the normalized values of the relative wing velocity components due to heaving and pitching, Vh=U andωrtip=U, respectively, during the cycle. The peak values of CL and CM are shown to increase with increasing St due to theincrease in the effective angle of attack. Additionally, it can also be seen that there exists a phase shift between CL, CM as well astheir associated relative velocities. In Fig. 6(a) and (b), it is seen that the phase shift between the heaving velocity and CL ismuch greater than the phase shift between the pitching velocity and CM, which is shown in Fig. 6(c) and (d). The heavingvelocity is leading CL with an angle of approximately 1351 whereas the pitching velocity is leading CM with an angle ofapproximately 601. Both of these phase shifts are essentially independent of the values of Strouhal numbers studied. For powerto be extracted, the orientation of the force and velocity vectors should be aligned in a positive sense (that is both vectorspointing in the same direction). This indicates that for CL there is only a short amount of time where the sign of the lift forcecorresponds to that of the heaving velocity. However, for CM, the reduced phase shift results in allowing the moment and thepitching velocity to have the same sign for most of the cycle, providing a net resultant positive work component.

The power coefficients, CP,θ and CP,h associated with the pitching and heaving motions respectively, are shown in Fig. 7.The power generated by the pitching is significantly larger than that of the heaving for both Strouhal numbers. Furthermore,there are distinct differences, represented by small and large peaks in pitching generated power, CP,θ, during the upwardheaving motion (from t/T¼0 to 0.5) compared with the downward heaving motion (from t/T¼0.5 to 1), respectively. This isparticularly apparent at the lower St case. This is due to the phase difference shown in Fig. 6(c) and (d), where the momentleads the pitching velocity, as previously stated. At higher Strouhal numbers, the ratio of pitching velocity to the moment isless than for the lower oscillation frequencies, resulting in a reduction in the difference of the power generation between theearly and late portions of the cycle. The minor peaks occur when the pitching angle is decreasing and as the upstroke inheaving just begins. At this point in the cycle, it is speculated that a leading edge vortex (LEV) forms on the bottom surface ofthe wing due to the heaving motion reversal, as described by Apte et al. (2012). The LEV creates a negative lift by decreasingthe pressure at the bottom surface relative to that of the upper surface. As a result, CP,θ is positive since the wing is rotatingdownward, in the same direction as the lift (and hence the moment). On the other hand, the heaving generated power, CP,h,is negative because the wing is heaving upward, in the opposite direction of the lift force. Moreover, the larger peaks of CP,θoccur when the wing is at the beginning of downward heaving, while the pitching angle is increasing. Due to the heavingmotion reversal from upstroke to downstroke, the LEV forms on the top surface of the wing, thus creating a positive lift. Inthis case, the lift and hence the moment, are in the same direction as the pitching motion, and therefore CP,θ is positive.

Fig. 8 gives the instantaneous transient power coefficient, CP, and the corresponding mean power output as a function of St.In general, Fig. 8(a) shows that peak negative power output occurs when the wing heaves upward and pitching motion goesthrough a reversal from down to up, as well as when the wing heaves downward and pitching motion reverses from up todown (t/TE0.3 and 0.8, respectively). In contrast, peak positive power is generated during the beginning of the cycle when theheaving upstroke begins and pitching angle decreases (t/TE0.05). This is due to the moment being aligned with the pitchingvelocity, both being negative. Another peak positive power is generated slightly before the pitching angle reaches itsmaximumwhile the pitching velocity is aligned with the moment and is still sufficiently large (t/TE0.55). Fig. 8(b) shows howcycle mean power output varies with St by varying the oscillation frequency. It can be seen that as St increases, the meanpower output increases. This is a consequence of greater moments and velocities associated with the high frequencies.

Fig. 8. (a) Transient power coefficient for the lowest and highest St values and (b) mean power coefficient as a function of St.

F. Siala, J.A. Liburdy / Journal of Fluids and Structures 57 (2015) 1–1410

4.2. Effect of trailing edge passive actuation

To help improve the total power output generated by this prescribed motion, the use of a passively actuated trailingedge is investigated. By influencing the effective camber and angle of attack, it may be possible to enhance the overallpower output using a totally passive response of the trailing edge. The key parameters include the length of the flap(held constant in this study) and the torsion spring constant used to attach the flap to the wing. The latter is expressedin terms of the natural frequency, fN, which is nondimensionalized as StN. Two values of StN were studied; 0.14 and 0.170which correspond to fN¼6.5 Hz and 8.1 Hz, respectively, where the smaller value represents the more flexibletrailing edge.

The trailing edge response for the two spring natural frequencies to the heaving and pitching motion is shown in Fig. 9for two different heaving frequencies St¼0.017 and St¼0.033. Note that a positive value is a downward deflection since itresults in an increased effective camber that increases the effective angle of attack. The complex flapping motion induced bythe heaving and pitching motion of the wing is apparent. The lower St case invokes a higher relative frequency (higherfrequency contents per oscillation cycle). It is also possible to see a relative phase shift between the two spring constants,with a shift of the peak deflection angle to later times during the cycle for the lower value of StN (more flexible case). Thehigher St case shows a less definitive lower frequency content. That is, the higher frequency content of the motion reducesthe apparent peaks and troughs of the lower frequency component of the signal.

These results were analyzed for their frequency content using a Fast Fourier Transform (FFT) decomposition of the time-series data over ten cycles. Results for the two heaving frequencies and are shown in Fig. 10. The large peaks at the lowerfrequencies correspond to the heaving and pitching frequencies imposed for both St cases. In other words, the dominantfrequency of flapping is coincident with the heaving and pitching frequency. However, the trailing edge flap also oscillates ata secondary peak shown for each spring that is close to their natural frequency, as indicated on the figure. For instance, forSt¼0.017 and StN¼0.14, the value of f lTE=U at the second peak is approximately 0.13, which is equivalent to a frequency of6.1 Hz. Furthermore, the higher natural frequency spring oscillates faster than the lower natural frequency spring, as wouldbe expected. These two dominate motions (the heaving and pitching oscillations and the natural spring oscillations)combine to yield the net trailing edge motion.

The trailing edge actuation angle was cross correlated with the pitching motion to identify the phase relationshipbetween them. The phase shift was identified based on the phase-lag at which there is a peak correlation between thetrailing edge flapping and pitching motion, as shown in Fig. 11(a). Fig. 11(b) shows the phase shift between the trailing edgeangle and pitching angle, ΔΦ, as a function of St for the two values of StN. A negative phase shift implies that the trailingedge angle is leading the pitching motion. These results show that for low values of St, both trailing edges lead the pitchingmotion. As St increases, the trailing edge become more in phase with the pitching motion and at the highest value of St, themore flexible trailing edge (StN¼0.14) starts to lag behind the pitching motion.

The effect of the trailing edge passive response on the mean power output is shown in Fig. 12 for varying values of St. Forreference, the mean power output of the rigid surface, denoted by StN¼ inf., is also plotted, which means that the naturalfrequency is essentially infinitely large. As shown, the mean power increases rather sharply as the oscillation Strouhalnumber increases. The consequence of the passively oscillating trailing edge is seen to be an enhancement of the overallpower output at higher heaving frequencies. In particular, the most flexible trailing edge results in the greatest mean poweroutput. To explore the relationship between flexibility and power output, the effective angle of attack for both StN is plottedand compared with the rigid wing effective angle of attack and the pitching angle, θP in Fig. 13. As can be seen, the greaterthe flexibility, the higher the induced effective angle of attack. The difference between the effective angle of attack between

Fig. 9. Transient trailing edge actuation angle for (a) St¼0.017 and (b) St¼0.033 for both spring natural frequencies.

Fig. 10. Frequency spectra of the trailing edge actuation motion for (a) St¼0.017 and (b) St¼0.033 for both spring natural frequencies.

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the flexible and rigid wing increases with increasing St. This is because the amplitude of the trialing edge actuation increaseswith increasing St, as is shown in Fig. 9.

Fig. 14 shows the percentage increase of power relative to the rigid trailing edge for the two flexible trailing edges as afunction of oscillation Strouhal number. Also displayed in the figure is the percentage increase of the effective angle ofattack, αeff, relative to the rigid surface with increasing St. The resultant increase of effective angle of attack caused by theflapping motion of the trailing edge correlates well with the increase in power for both of the flexible trailing edges at thesame heaving and pitching conditions. The more flexible case has a higher effective angle of attack and a correspondingincrease in power output.

Based on the current results, there is potential for increased mean power output for this heaving and pitching device thatextracts most of its power from pitching due to the extended pitching armwhen applying a passive oscillating trailing edge.The proper trailing edge flexibility is yet to be determined, although the results presented here do indicate that greaterflexibility yields more power output. Fig. 15 shows the mean power input with oscillating frequency normalized by thetrailing edge natural frequency, f =f N . It is seen that as f =f N increases, the mean power output substantially increases.Furthermore, as the ratio approaches unity, the trailing edge motion will follow the prescribed heaving/pitching motionmore closely. This is illustrated in the FFT analysis plots of the trailing edge motion shown in Fig. 10. That is to say, as thetrailing edge natural frequency gets closer to the heaving and pitching frequency, the extra induced motion at the naturalfrequency will be superimpose on the prescribed motion. This superposition allows the trailing edge actuation angle toincrease, which results in a higher net power output. The results of Fig. 15 are encouraging for increasing the mean poweroutput of the device with increasing flexibility. Unfortunately the current device cannot operate accurately at higherfrequencies, and so the rising trend of oCp4 cannot be confirmed beyond f =f N ¼ 0:15.

5. Conclusions

Experiments were performed to investigate the energy harvesting capabilities of a heaving and forward pitching wingwith a flexible trailing edge. Aerodynamic forces and power output were measured in a recirculating wind tunnel at aReynolds number of 40 000. The tests were performed at a fixed normalized heaving amplitude of 0.25 and a pitching rangeof 01 to 401. The trailing edge flexibility was characterized using a Strouhal number based on the natural frequency of thetrailing edge. Three trailing edges were tested that correspond to Strouhal numbers of 0.14, 0.17 and 1, where the latterrepresents a rigid trailing edge.

The results suggest that the heaving and forward pitching wing extracts the flow energy by mainly the pitching motiondue to large aerodynamic moments generated by the long moment arm. Conversely, the contribution of heaving motion toenergy harvesting is mostly small or even negative. Additionally, increasing the oscillation Strouhal is found to affect themagnitude of the lift and moment and hence the mean power output, without altering the phase shift between lift andheaving velocity and moment and pitching velocity. Furthermore, it is found that there exists a strong correlation betweenthe effective angle of attack and mean power output. Consequently, the use of a flexible trailing edge, which is shown hereto increase the effective angle of attack, results in greater power output. The mean power output significantly increases asthe trailing edge natural frequency is closer to the oscillation frequency. In other words, as flexibility of the trailing edgeincreases, the effective angle of attack and hence the mean power out increase. Since in oscillating energy harvestingdevices the strength of the leading edge vortex is strongly linked to the power output, it is surmised that the trailing edgeflexibility may enhance the strength of the leading edge vortex.

Fig. 11. (a) Cross correlation of the trailing edge actuation angle with the pitching angle as a function of phase lag for St¼0.017 and (b) phase shift betweentrailing edge actuation and pitching as a function of St.

Fig. 12. Mean coefficient of power as a function of St for two values of trialing edge flexibilities and the rigid case, StN¼ inf.

Fig. 13. Transient response of the angle of attack for different values of StN and the pitching angle for (a) St¼0.017 and (b) St¼0.033.

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This study was primarily aimed at the development of an energy harvesting device, as such a number of design andaerodynamic aspects suggest further investigation. A parametric study of operational parameters such as the location of theforward pitching axis, the range of pitching motion and oscillation amplitudes and frequencies are needed in order tooptimize the energy harvesting efficiency. Also, detailed, high resolution, flow field measurements are required to evaluatethe transient flow field and to identify critical flow features that are responsible for efficient energy harvesting.

Fig. 14. Percentage increase in the coefficient of power and effective angle of attack versus St.

Fig. 15. Mean coefficient of power as a function of f =f N for both torsion spring flexibilities.

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Acknowledgements

The authors would like to acknowledge Jesse Rushen, Alexander Totpal and Cameron Planck for their assistance in datacollection and analysis.

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