Experimental investigation on the performance of a

double-cylinder ow-induced vibration (FIV) energy converter

Hamid Arionfarda, Yoshiki Nishia,∗

aDepartment of Systems Design for Ocean-Space, Faculty of Engineering, Yokohama National University,

79-5 Tokiwadai, Hodogaya, Yokohama , Japan

Abstract

In this study, the performance of a double cylinder ow-induced vibration (FIV) energyconverter is experimentally investigated. The cylinders are free to rotate around a pivotand located in dierent congurations including both cylinders on the downstream, bothon the upstream, a cylinder on each side of the pivot point and one cylinder on the pivot.The dissipated power is calculated based on the measured displacement, angular velocityand damping. Each conguration is represented by the gap ratio between the two cylinder(G=gap/cylinder diameter) and center of gravity ratio (CG=gravity center/cylinder diame-ter). Locating the cylinders in dierent positions made it possible to activate a wide rangeof vibration mechanisms including: Vortex excitation (VE), wakeinduced vibration (WIV),galloping and gapswitchinginduced vibration (GSIV). The most ecient vibration mech-anisms are:(1) GSIV for CG = 0 and G = 0.9 (2) VE where CG = 0 and G ≥ 3.9 (3)dragassisted vibration where one cylinder is on the pivot point and another one on theupstream side, (4) WIV where one cylinder is on the pivot point and another one on thedownstream side,(4) both cylinder on the downstream side with no gap and (5) both cylinderon the upstream side with no gap.

Keywords: FIV, Gap ow, Current energy converter, Pivoted cylinder, FIV eciency

1. Introduction

The gradually depleting non-renewable energy resources have promoted the develop-ment of the renewable energy technologies. In recent years, the development of ow-inducedvibrations (FIV) energy harvesters has increased rapidly to improve the eciency of the en-ergy conversion process. There are two dierent categories related to the energy harvestingthrough FIV in the literature. Vortex excitation (VE) like vortex-induced vibrations (VIV)which is a uid induced vibration and uid-elastic vibrations like galloping and utter whichis a self exciting vibration where the negative dynamic damping leads to dynamic instability.Due to the large strains and geometric deformations, these types of induced vibrations have

∗Corresponding author. Tel.: +81 45 339 4087; fax: +81 45 339 4099.Email address: nishi-yoshiki-rg@ynu.ac.jp (Yoshiki Nishi)

Nomenclature

A Oscillation amplitude (Rad)

AR Aspect ratio (Lw/D)

CG Center of gravity ratio (cg/D)

CylA Upstream cylinder

CylB Downstream cylinder

D Cylinder outer diameter (mm)

G Gap ratio (gap/D)

I Total moment of inertia (kg.m2)

I0 Base moment of inertia (kg.m2)

K Equivalent torsional stiness(N.m.rad−1)

Lw Cylinder submerged length (mm)

P Dissipated power (W)

Pf Available power in the ow (W)

Q Quality factor

U Free-stream uid velocity (m.s−1)

Ur Reduced velocity (Ur =U

DfN)

θ Angular velocity (rad.s−1)

η Eciency (%)

ρ Water density (Kg.m−3)

fN Natural frequency (Hz)

fosc Oscillating frequency (Hz)

fv Vortex shedding frequency (Hz)

traditionally been classied as a destructive phenomena. One of the well-known examples ofow-induced destruction is the Tacoma Narrows bridge collapse in 1940, where torsional ut-ter at suciently large amplitudes caused catastrophic failure of the entire bridge. However,common and accessible FIV could be considered as a way to extract energy.

Dierent types of FIV have been investigated as an external source for energy generation.Among them, VIV-based energy harvesting has received more attention due to its uniquefeatures of self-excited and self-restricted oscillations in the lock-in (synchronization) regionwhen the vortex shedding frequency is close to one of the natural frequencies of the structure(Khalak and Williamson, 1999). A good example of harnessing VIV energy is the VIVACEconverter patented by Bernitsas et al. (2008), which consists of a cylinder submerged per-pendicularly to the water ow and a power-take-out (PTO) system to convert the kineticenergy to electricity.

In wind ow, Akaydin et al. (2012) investigated the performance of a piezoelectric energyharvester undergoes VIV oscillation in cross ow. Afterwards, Dai et al. (2014) developeda parametric model and studied the eects of dierent structural and electrical parameterson the output eciency and performance of the VIV-based energy harvester.

However, the main drawbacks in VIV energy harvesting are: (1) the narrow synchroniza-tion (lock-in) region and (2) sensitivity to structural characteristics. Hence, any uctuationin the ow velocity results in a drastic decrease of the harvested power (Mackowski andWilliamson, 2013). Although the synchronization region can be widened by reducing themass-damping ratio (Khalak and Williamson, 1999), it will reduce the extracted energy bythe generator as well. Therefore the eciency of energy harvesting from VIV is restricted

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to some extent.Contrary to the VIV phenomenon, where signicant oscillations develop in a small range

of ow velocities and with limited oscillation amplitudes, galloping, utter and buetingoccur for an innite range of ow velocities and without a self-limited response beyond thecritical ow velocity which makes these mechanisms more promising for generating energy.However, higher Reynolds number is usually needed to activate such vibrations comparingto VIV.

Barrero-Gil et al. (2010) reported an analytical study to prove the potential of transversegalloping in order to obtain energy from ocean currents. Even though the airfoil is notnecessarily the most unstable cross-section, most of the researches related to utter andgalloping has focused on the airfoil instabilities. Liu et al. (2001), Simpson et al. (2008) andKinsey et al. (2011) are some examples.

Recently, to improve the energy conversion eciency of FIV of a single cylinder in cross-ow, a "drag-assisted converter" is studied numerically by Sung et al. (2015) and testedexperimentally by Arionfard and Nishi (2017). The main idea is to take advantage of thedrag force by pivoting the cylinder eccentrically. While the lift force induced by the vortexshedding starts the vibration, the drag force assists the motion depending on the locationof the pivot point and the Reynolds number. Pivoting the cylinder makes it possible toexperience the galloping mechanism while the cylinder is close to the pivot and experienceVIV while the distance between the pivot and the cylinder is large enough.

Regardless of the vibration mechanism, investigating a group of energy converters ortaking advantage of wake induced vibration is one of the eective ways for improving theperformance. Nishi et al. (2015) examined the performance of an energy harvesting deviceusing wake-induced vibration and concluded that placing a xed cylinder near a moving oneexpands the range of synchronization and can increase the energy conversion eciency. Infact, the ow structure around a cylinder undergoes substantial changes when its a memberof a group of cylinders in close proximity.

An extensive review on interferenceinduced oscillations in ow past two circular cylin-ders in various congurations is provided by Zdravkovich (1988). The ow regime is classi-ed into three categories of ow interference: If the cylinders are far apart, the ow aroundthem is similar to an isolated cylinder. If the cylinders are close enough, the interferencebetween the two cylinders can be one of the three types: proximity interference, wake inter-ference, and proximity and wake interference. The origin of oscillations are also categorizedby Zdravkovich (1988) as jetswitching, gapowswitching, wakedisplacement and wakegalloping. It was reported that the hysteretic eect of the gapowswitching maintaineda large amplitude oscillation when the downstream cylinder was elastically mounted withonly a transverse degree of freedom which makes it an interesting mechanism for energygeneration from FIV.

Borazjani and Sotiropoulos (2009) studied the VIV of two cylinders in tandem arrange-ment and reported that a signicant portion of the incoming ow is able to pass through thegap between the two cylinders and the gapow mechanism starts to dominate the VIV dy-namics. The gap ow switching induces pressure gradients between the cylinders that resultsin a large oscillatory force in phase with the vortex shedding and lead to the experimentally

3

observed larger vibration amplitudes.In contrast to the gap ow force (that acts as a restoring mechanism), the drag force

(in a drag-assisted conguration) resist the restoring force in a single rotationally vibratingcylinder. As a follow up on our last research on a single cylinder system (Arionfard and Nishi,2017), our interest is to investigate the interaction of both gapowswitching-vibration(GSIV) and the dragassisted vibration in one system. In order to have a dragassistedvibration, it is necessary to have a rotationally oscillating cylinder. On the other hand, themost basic method of generating a GSIV is by having two circular cylinders in proximityrange. Therefore, by combining these two congurations we proposed a two mechanicallycoupled cylinders that are free to vibrate rotationally around a pivot point. By changingthe conguration of two coupled cylinder it is possible to investigate a range of vibrationmechanisms like VIV, WIV and galloping as well as GSIV and drag-assisted VIV. Therefore,it is of fundamental interest to understand how the energy conversion performance varies bychanging the conguration of the system.

1.1. A note on performance metrics

Regardless of the source of the energy and methods of conversion, the eciency is alwaysthe main concern. The total eciency is the ratio between the useful output of an energyconversion machine and the total input energy. This can be expressed as the resultingproduct of the hydrodynamic eciency and power-take-out (PTO) eciency in an FIVenergy converter. However, in the literature, several methods have been proposed to reportthe eciency. One approach is to use the time average of dissipated energy in one cycleof the vibration to calculate the performance. A key limitation of this method is that FIVis usually a non-linear phenomenon and cannot be described adequately by a sine wave,therefore averaging in one cycle doesn't give an accurate answer.

Another popular method is to consider the amplitude of vibration as the key parameterin performance. Unless the time period of the vibration is constant (or decreasing), anincrease in amplitude is not a sign of better performance. Clearly, there is a need for acommon benchmark for the power produced by a vibration energy harvester regardless ofthe source of the vibration. Since relative velocity in transitional motion or angular velocityin rotational motion is the critical factor in transducers to generate electrical energy (Zhu,2011), the eciency is calculated based on the angular velocity in this research. The equationof motion for a rotationally oscillating system is given by:

It θ +

√KI

Qθ +K θ =M (1)

Where It is the total moment of inertia of the rotating bodies, Q is the quality factor,K is the equivalent torsional spring stiness and M represent the total external momentaround the Z-axis. We use the power spectrum density (PSD) of the angular velocity (whichis widely being used for measuring the performance of random vibration converters) toanalyze the performance of the system. The cumulative spectral power (CSP) of the PSDis calculated by integrating over all frequencies base on the Parseval's theorem and used to

4

estimate the dissipated power:

CSP = P =ItQ

ˆ ∞0

(PSD)df (2)

Where the PSD is calculated by using the fast furrier transform of the angular velocity:

PSD = |FFT (θ(t))|2 (3)

Where θ(t) is the angular velocity of the vibration. The eciency is then dened as theratio of the maximum dissipated power, to the total power in the ow (Pf = 1

2ρLwDU

3)that is:

η (%) =P

Pf

(4)

2. Experimental setup and measurement methods

2.1. Water channel and test model

The experiments are conducted in a recirculating free surface water channel with thelength of 1 meter and a test section dimensions of 30 cm wide by 25 cm deep. The channeloor and the two side walls of the test section were made of transparent acrylic to enableoptical access. The ow rate was controlled by adjusting ow velocity in the test section toany value between 0.024 and 0.84 m s−1.

Two acrylic circular cylinders with a diameter of D=30 mm and length of 240 mm wereused in the experiments. To make it possible to test all the possible congurations, itwas decided not to install end plate, to have the gap between the cylinders as small aspossible if needed. The freestream turbulence level of the water channel on the centerline is measured between 4.3 and 10.2% based on the PIV analysis. The water depth ismeasured by an ultrasonic sensor and maintained around 230 mm to keep the wet lengthof the cylinders around Lwet = 180mm, resulting in an aspect ratio (AR) of around 6. Thetop end of both cylinders are xed on a connector arm by using three screws, allowing usto slide the cylinders along the connector arm and adjust the position of the cylinders andchange the center of gravity, gap between the two cylinders and the moment of inertia ofthe system.

The connector arm is pivoted outside of the water by using a rigid shaft and two ballbearings, enabling rotation around the Zaxis, where X is the streamwise coordinate, Y isthe crossstream coordinate and Z is the vertical coordinate. Dierent parts of the apparatusare shown in Fig.1. The conguration of the cylinders is dened by the gap ratio between thetwo cylinders (G=gap/D) and the center of gravity ratio (CG=cg/D) as shown in Fig.2(a).Based on the location of each cylinder relative to the pivot, three main congurations arepossible: (a) one cylinder on each side (b) both cylinder on one side, and (c) one cylinderon the pivot point as shown in Fig.2.

To provide the restoration moment for the system, two linear springs are connected to theshaft by using a spring connector arm. The total restoring spring stiness is calculated based

5

2

2

1

5

4

7

9

10

8

6

3

2

6

8

Lwet

xz

y

Figure 1: 3D view and front view of the experimental setup. (1) Camera, (2) Laser, (3) Fixing screws, (4)Cyl1, (5) Cyl2, (6) Forcemoment sensor, (7) Springs, (8) Bearings, (9) Spring connector arm, (10) Shaftencoder.

(a)

x

y

DU

D

cg

U U

(b) (c)

Figure 2: Three possible congurations basd on the location of each cylinder: (a)one cylinder on each side(b)both cylinder on one side (c) one cylinder on the pivot.(the small circle is the pivot point)

6

on the Zmoment determined by the forcemoment sensor during the rotation. The rotationof the system is limited to ±90 from the resting position due to the springs congurationand structural limits. The base moment of inertia (I0) of oscillating parts excluding thecylinders is determined by performing a series of free decay tests in air and checked with theCAD drawings of all parts. The total moment of inertia is then calculated by summing upthe moment of inertia of the cylinders around the shaft and I0 for each conguration. Twobearings are used on the shaft to reduce damping and to provide more rigidity in resistingdrag loads for higher Reynolds numbers.

Total of 65 congurations are studied by positioning the cylinders on dierent locationsalong the connector arm. In each test case the Reynolds number is increased with a minimumstep of 500 and the recording started from the onset of vibration and stopped if eithervibration is suppressed or a maximum of Re = 21509 is reached, to prevent structuraldamage.

2.2. Measurement methods

The forces on the shaft are measured by using a six degrees of freedom forcemoment sen-sor (BLAUTOTEC MICRO6/30) and used for calculating the equivalent torsional springstiness. The sensor measurement accuracy is rated ±2% for the forces and moments ac-cording to the manufacturer. The rotation of the shaft is measured by using a shaft encoder,which measures angular rotation by using two optical sensors and an encoder disk. There isno physical contact between the shaft and the encoder, hence there is no damping inducedby the encoder. Although the resolution of the encoder is 1320 lines/turn (≈ 0.3/line), theangle between two consecutive lines is also interpolated based on the phase dierence be-tween the signals from optical sensors resulting in an ultra precise position estimation (Kimet al., 2006). The signals from the shaft encoder and forcemoment sensor are recordedby using a Keyence data logger simultaneously to synchronize the data captured from bothsensors.

The dominant frequency of displacement (fosc) was evaluated by determining a frequencycorresponding to the largest FFT amplitude in the frequency domain. To accomplish this,the built-in discrete fast Fourier transform (FFT) function in MATLAB was used. Next,the single-sided amplitude spectrum was plotted, and the peak frequency was evaluated bydetermining the frequency corresponding to the largest FFT amplitude. The quality factor(Q) and the natural frequency of the system fN are measured by carrying out free decaytests in air and used for calculating the power and reduced velocity (U∗ = U/DfN); whereU is the free stream velocity.

3. Results and discussion

Fig.3 shows an overall view of all conducted tests in terms of displacement respondrelation with frequencies. Fig.3(a) clearly shows a resonance region in all cases since thefrequency of oscillation is close to the natural frequency for all cases. However, the vortexshedding frequency is not necessarily locked-in to the natural frequency for all cases accordingto the PIV analysis. The frequency of vortices shedding from the cylB (fcylB) is distributed

7

0 0.5 1 1.5 2 2.5 3fosc fN

0

10

20

30

40

50

A (

Deg

)

0 1 2 3fave

0 0.5 1 1.5 2 2.5 3fcylA

0 0.5 1 1.5 2 2.5 3fcylB/ fN// / fN/ / fN/

(a) (b) (c) (d)

Figure 3: An overall view of the displacement amplitude responses for all cunducted tests verses the frequecyratios. (a) The oscilation frequency ratio (b) The vortex shedding frequency ratio on the wake side of thedownstream cylinder (cylB). (c) The vortex shedding frequency ratio on the wake side of the upstreamcylinder (cylA). (d) The average of vortex shedding frequency ratio.

in a wider range of frequencies as shown in Fig.3(b). This range is even wider for thefrequency of vortices shedding from the cylA (fcylA)(Fig.3, c). Although the average vortexshedding frequency (fave) is also close to the fN , there are some cases with high amplitudeoutside of the resonance region. Two important conclusion are made based on Fig.3: (1) Inmost cases, the vortices shedding from cylA are responsible for the vibration because fcylAdistribution is more similar to fave than fcylB. (2) Two major mechanisms of vibration arerecognizable based on the displacement and frequency respond: vortex excitation (VE) anduid-elastic vibration (FE). VE happens in the resonance region where the vortex sheddingfrequency locks into the natural frequency of the system and FE happens outside of theresonance region where negative aerodynamic damping causes high displacement amplitude.A closer look on the displacement and frequency response for each case reveals that eachmajor mechanism of vibration may be a combination of galloping, wake-induced vibration(WIV), gap switching induced vibration (GSIV) and drag&lift assisted VIV.

An overall view of all vibration mechanisms are summarized in Fig.4. The main mech-anisms are simply determined based on the displacement and frequency respons: If thedisplacement amplitude starts to decrease after reaching a peak point by increasing U∗ andthe corresponding frequency response is following the St = 0.2 line, VEfSt mechanism isdominant. The similar displacement response that follows the f ∗ = fosc/fN line shows alock-in to the natural frequency and named VEfN . On the other hand, if the displacementresponse keeps increasing with U∗ and the frequencies are not close to the St = 0.2 line, FEmechanism is dominant. In addition to the main mechanisms, some sub-categories are alsodetermined based on the displacement response and wake patterns observed during the PIVanalysis. However, the details of vorticity dynamics for each case is out of the scope of thisstudy and will be reported in separate investigations. To keep our focus on the performanceof the system, we will discuss the conguration and Reynolds number eect on the perfor-mance by analyzing the dissipated power and the corresponding eciency in the followingsection.

8

2 4 6 8 10 12

U*

0

5

10

15

20

25

30

35

40

45

50

Am

ax (

deg)

0 2 4 6 8 10 12 14

U*

0

0.2

0.4

0.6

0.8

1

1.2

f *FE

-3 3X/D

G = 4.9, CG = 0(VEfSt)

VE

G = 0.9, CG = 0(GSIV)

G = 0, CG = 1.95

(VEfN)

G = 1.45, CG = 1.22(WIV)

G = 0, CG = -1.95 (Galloping)

G = 1.95, CG = -1.5(Drag&Lift-assisted VIV)

St=

0.2

Figure 4: Identied vibration mechanisms for dierent congurations. Left: Displacement amplituderesponse. Center: Vibration mechanisms and corresponding conguration. Right: Frequency response.

3.1. Dissipated power

The maximum power dissipated by friction damping in the system is illustrated in Fig.5 asan interpolated contour plot for ten Reynolds numbers. The center of gravity and gap ratiosfor each test case in each range of Reynolds is shown with a circle where the size of the circle isan indicator for P (larger circle shows larger P). It should be noted that the size of the circlesis normalized based on the maximum P only for the corresponding Reynolds number andsizes of circles belonging to dierent Reynolds numbers are not comparable. The best way tounderstand the eect of conguration and Re is to follow the white spot (maximum power)on each plot. As expected, the highest power in low Re range (Re ≈ 6585 to Re ≈ 8461),corresponds to the VE region where it starts from VEfN and continues to activate the VEfSt

and drag&lift assisted VIV in higher Reynolds. After reaching Re ≈ 14832, the white spotstarts to concentrate around CG = 0, G = 1 which corresponds to the GSIV region underFE category. Although the maximum P is located in this region, maximum P in otherregions under FE category also increases in higher Reynolds.

The corresponding contour plot for eciency is slightly dierent as shown in Fig.6. WhileP keeps increasing for higher Re, the eciency starts to decrease after Re ≈ 18188 becausethe rate of change of available power in the uid ow is higher than the imparted power to thedevice. A possible reason is turbulence: in higher Re, more energy wastes due to turbulencebefore being imparted to the device. Moreover, the frequency of (turbulent) vortex sheddingin higher Re is far above the synchronization range of the device and resonant is not observedas a result.

The displacement response, dissipated power and corresponding eciency for the top sixmost ecient congurations are shown in Fig.8 to Fig.10. Comparing the results shows that

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Figure 5: Interpolated contour plot of power for all congurations. Each circle represent a congurationwhere the size of the circle indicates the power, normalized for that particular Reynolds.

10

Figure 6: Interpolated contour plot of eciency for all congurations. Each circle represent a congurationwhere the size of the circle indicates the eciency, normalized for that particular Reynolds.

a higher displacement amplitude is not an indicator for having higher power or eciency,as mentioned before. The highest displacement amplitude achieved in our tests is for CG =−0.25, G = 0.4, while the highest power and eciency is observed for CG = 0, G = 0.9.Generally, all cases susceptible to drag-assisted vibration, experience larger displacementamplitude because the drag force reduces the restoring moment and delays the restorationconsequently, which is the main reason for having a larger displacement amplitude but lowerpower and eciency for CG ≤ 0 that is also observed for a single cylinder system (Arionfard2017).

According to Fig.9 and Fig.10, the best conguration (based on the maximum P and η) iswhen CG = 0 and G = 0.9. However, there is a sharp drop in all gures around Re = 2×104for this particular case. Although similar drop is recognizable in all displacement responses,the cases with larger gap ratio show a more signicant drop. Based on the PIV analysis,this drop is due to a transition between a split-glap ow and an entire-gap ow shown inFig.7.

In the "entire gap ow" ow regime, the frequency of the vortices passing by the down-stream cylinder and the vortices passing through the gap is close to the frequency of motion.

11

U

Entire gap flow

U

Split gap flow

Figure 7: Shear layer pattern notation for gap ow.

1.2 1.4 1.6 1.8 2 2.2

Re 104

0

5

10

15

20

25

30

35

40

45

50

A(Deg)

0X/D

1 2-1-2

CG=0, G=0.9, A = 48max

CG=-0.25, G=0.4, A = 48.9max

CG=-0.5, G=0.9, A = 47.4max

CG=0.5, G=0.9, A = 35max

CG=0.25, G=0.4, A = 42.8max

CG=-0.25, G=1.4, A = 40.2max

Figure 8: Top six most ecient cases: diplacement amplituse vs Reynolds number.

Therefore, the vortices passing through the gap redirect the shear layer and generate a stronggap ow. In the transition region, out of phase vortices split on the downstream cylinderand lose more energy before passing through the gap and cause decrease in displacementamplitude.

Generally, the drag-assisted conguration (CG < 0) is more ecient than gallopingor WIV (CG > 0) over a wide range of Reynolds even though the dissipated power maybe higher when Reynolds increases. Moreover, when the gap is small (G < 0.9), higherReynolds number is needed to start the vibration. Therefore, the best conguration shouldbe determined based on the range of available Reynolds number in the uid ow.

12

1.2 1.4 1.6 1.8 2 2.2

Re 104

0

50

100

150

200

250

P (

mW

)

0X/D

1 2-1-2

CG=0, G=0.9, P = 247 (mW)max

CG=-0.25, G=0.4, P = 225 (mW)max

CG=-0.5, G=0.9, P = 201(mW)max

CG=0.5, G=0.9, P = 141 (mW)max

CG=0.25, G=0.4, P = 217 (mW)max

CG=-0.25, G=1.4, P = 193 (mW)max

Figure 9: Top six most ecient cases: maximum imparted power vs Reynolds number.

0X/D

1 2-1-2

CG=0, G=0.9, h =44.4%max

CG=-0.25, G=0.4, h =42.7%max

CG=-0.5, G=0.9, h =39.8%max

CG=0.5, G=0.9, h =36.3%max

CG=0.25, G=0.4, h =36.2%max

CG=-0.25, G=1.4, h =33.5%max

Figure 10: Top six most ecient cases: maximum eciency vs Reynolds number.

13

23.7

42.3

19.1

12.4

0.5

6.2

0

10

20

30

40

50

VEfN GSIV Drag&Lift assist WIV Galloping VEfST

Eff

icie

ncy

(%)

Figure 11: The performance results for dierent congurations. The black lled circle shows the pivot point.

4. Conclusions

A novel device for generating clean and renewable energy from uid-induced vibrationhas been introduced. Two mechanically coupled cylinders are used as harvester that arefree to rotate around a pivot point. The conguration of the system is represented by thegap ratio (G) between the two cylinders and the center of gravity ratio (CG). Six majorvibration mechanisms are recognized by analyzing the displacement and frequency responsefor each conguration: vortex excitation (VE) with Strouhal synchronization (VEfSt) ornatural frequency synchronization (VEfN), dragassisted vibration, wakeinduced vibration(WIV), galloping and gapswitching induced vibration.

The highest displacement amplitude is observed for CG = −0.25, G = 0.4 where thedrag force assists the vibration. However, the highest power and eciency is achieved for"CG = 0, G = 0.9" in GSIV region where a strong gap ow improves the performanceby enhancing the restoring moment. The VEfN is the second ecient mechanism. Eventhough there is no gap ow in this region, the vortex shedding frequency lock-in to thenatural frequency of the structure and enhances the vibration (only in resonance range). Thethird most ecient mechanism is drag-assisted congurations (CG < 0). The displacementamplitude is dramatically higher in this region because the drag force reduces the restoringmoment. However, the drawback of this reduction is lower eciency. The fourth mostecient mechanism is WIV. Strong interference between the upstream cylinder's wake anddownstream cylinder improves the eciency in this region. The least ecient mechanismsare VEfStr and galloping with 6.2% and 0.5% eciency as shown in Fig.11. Although theimparted power keeps increasing by increasing Reynolds number for most cases, the eciencystarts to decrease after Re ≈ 18188 because more energy losses due to turbulence.

5. Acknowledgment

This study was nancially supported by the Grand-in-Aid for Scientic Research 15H04211.

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