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Power extraction using flow-induced vibration of a circular cylinder placed near another fixed cylinder Yoshiki Nishi a,n, Yuta Ueno a, Masachika Nishio a, Luis Antonio Rodrigues Quadrante a, Kentaroh Kokubun b a Department of Systems Design for Ocean-Space, Faculty of Engineering, Yokohama National University, 79-5 Tokiwadai, Hodogaya, Yokohama 2408501, Japan b National Maritime Research Institute, 6-38-1 Shinkawa, Mitaka 1810004, Japan

a r t i c l e i n f o

abstract

Article history: Received 23 April 2013 Received in revised form 11 December 2013 Accepted 8 January 2014 Handling Editor: L.G. Tham Available online 6 February 2014

We conducted an experiment in a towing tank to investigate the performance of an energy extraction system using the flow-induced vibration of a circular cylinder. This experiment tested three different cases involving the following arrangements of cylinder(s) of identical diameter: the upstream fixed–downstream movable arrangement (case F); the upstream movable–downstream fixed arrangement (case R); and a movable isolated cylinder (case I). In cases F and R, the separation distance (ratio of the distance between the centers of the two cylinders to their diameters) is fixed at 1.30. Measurement results show that while cases F and I generate vortex-induced vibration (VIV) resonance responses, case R yields wake-induced vibration (WIV) at reduced velocity over 9.0, which is significantly larger than that of the VIV response, leading to the induction of higher electronic power in a generator. Accordingly, primary energy conversion efficiency is higher in the case involving WIV. & 2014 Elsevier Ltd. All rights reserved.

1. Introduction Arrangements of multiple slender and long structures close to each other are used in many engineering applications such as pipe work in an energy plant, chimney stacks, and bridges. In a few of these structures, many of the cylinders used are directly exposed to fluid flows. It has been found that these cylinders vibrate considerably when the fluid flow velocity is within a certain range. Prolonged vibration can cause serious damage to structures or result in the development of fatigue in structural materials. Therefore, mechanical engineers and fluid–structure interaction researchers have expended considerable efforts on suppressing such vibration. In a slender, long body subject to fluid flow, vibrations are caused by oscillatory fluid forces acting on the body. Placing the body in a fluid flow produces complex flow patterns downstream of the body. Such patterns comprise thin layers containing large velocity shear, deflected streams, wake regions, and vortices formed behind the body and then consecutively shed from the body, thereby exerting fluid force on the body. VIV ascribed to the fluid phenomenon has been studied extensively because it is a crucial design factor in terms of structural safety apart from being of much scientific interest.

n

Corresponding author. Tel.: þ81 45 339 4087; fax: þ81 45 339 4099. E-mail address: [email protected] (Y. Nishi).

0022-460X/$ - see front matter & 2014 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jsv.2014.01.007

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The fluid dynamic mechanism of the vibration of multiple slender and long bodies in proximity is to some extent similar to the mechanism of the VIV of a single body; however, these two types of vibration are generally regarded as different phenomena because the response of a body varies largely depending on its proximity to other bodies. Several previous works on the response of two adjacent cylinders have clarified that the response has very large amplitudes for a wide range of flow velocities with a certain distances between two cylinders (separation distance), both in-line and transverse to the flow direction [1–10]. Vibration amplitude monotonically increases with flow velocity; this is in contrast to the amplitude of the VIV of a single cylinder, which is large within a limited range of flow velocities. Fluid dynamic explanations for very large amplitudes, which are unique to two cylinders, have been provided in previous works, a few of which note that if a vortex generated behind a body interferes with an adjacent body or with other vortices generated behind another body, vibratory responses of these bodies are more intense than the VIV response of an isolated body. In particular, a strong flow formed at the gap between the two cylinders, i.e. the gap flow plays an important role in enhancing the amplitude. On the basis of their understanding of such a response as a type of fluid dynamic instability, Bokaian and Geoola [3] refer to it as wake-induced galloping. Assi et al. [10] refer to it as WIV: we use this term in this paper to refer to the response of two cylinders, as presented below. Our study attempts to develop a WIV-based renewable energy technology. The concept of extracting available energy through flow-induced vibration has been considered previously. Bernitsas et al. [11,12], Raghavan and Bernitsas [13], and Lee et al. [14,15] developed the VIV aquatic clean energy (VIVACE) converter, which consists of a spring, a generator, and a submerged cylinder. They experimentally investigated the influence of a few design parameters such as damping, mass ratio, and Reynolds number on the magnitude of generated electronic energy. Barrero-Gil et al. [16,17] theoretically addressed the properties of energy conversion through the galloping and VIV of a moving body by analyzing the equations of motion describing the galloping and VIV of a bluff body. Zhu et al. [18] developed a theoretical model for harvesting energy using oscillating flapping foils and identified parameter areas of large energy and high conversion efficiency. We experimentally examined the output performance of the energy harvested from the vibratory motion of a circular cylinder mounted elastically close to a fixed cylinder, with the aim of extracting a greater amount of available power from WIV. To this end, the experimental apparatus used in our previous study [19] on energy conversion using VIV was recreated and installed in a towing tank in which we conducted power extraction measurements. The remainder of this paper is organized as follows. Section 2 describes the method of measurement and data processing. Section 3 details a method for estimating a power output, and Section 4 presents the obtained results. These results and a few proposed improvements are discussed in Section 5, and the conclusions of this study are presented in Section 6. 2. Experiment 2.1. Experimental equipment and data analysis The experiment was conducted in a (100 8 3.5) m3 (length breadth depth) towing tank at Yokohama National University. We used two aluminum cylinders of identical diameter and span length (Table 1). These cylinders were towed with a carriage running along the length of the tank to reproduce a situation in which the cylinders are exposed to fluid flow (Figs. 1 and 2a). The first cylinder is movable, horizontally submerged, and supported elastically by coil springs, while the second is fixed adjacent to the first cylinder such that the two cylinders are in a tandem arrangement and the centerlines of the two cylinders are at the same height. The separation distance was fixed at 1.30D m (X/D¼ 1.30). Square acrylic plates were attached at both ends of the cylinders to avoid the influence of disturbances at cylinder ends on the measurements. The motion of the movable cylinder includes horizontal excursions because the motion is rotational. However, the horizontal excursion length is on the order of 1.0 10 5 m, which is considerably lower than the vertical excursion length; thus, the motion can be approximated as translational motion in the vertical direction. The cylinder motion is transmitted to a generator via the motion of rigid frames. The generator contains a ring-shaped coil made of an enameled wire, the oscillatory motion of which is driven by the cylinder motion and is accompanied by the insertion of a bar magnet into the coil, inducing an electric current in the enameled wire (Fig. 2b). Towing velocity was measured using a rotary encoder. The displacement of the vibratory cylinder was measured using a laser displacement sensor (LM500, Keyence). Forces acting on the vibratory cylinder in the in-line and transverse directions were measured using strain gauges. Using strain amplifiers (AM10, Unipulse), bridge voltages were applied to the strain gauges for signal amplification. All digital signals generated by the abovementioned measurement equipment were recorded using a data logger (NR2000, Keyence). Before measurements in the towing tank, the strain gauges were loaded with standard weights for calibrating force–voltage conversion. Hydrodynamic forces were extracted by subtracting inertial forces from the measured forces because the strain gauges moving with the cylinder detect the inertial as well as the hydrodynamic forces. 2.2. Measurement conditions The towing carriage was driven forward and backward to investigate the two following tandem arrangements: (1) the vibratory cylinder was at the rear and the fixed one was in the front (hereinafter, this case is referred to as case F, with the first letter of the term “front” identifying the position of the fixed cylinder), and (2) the vibratory cylinder was at the front

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Table 1 List of experimental parameters and dimensionless numbers. Notation

Definition

Value or unit

CD

Drag force coefficient defined as

FD 0:5ρDLV 2

CL

Lift force coefficient defined as

D f

Diameter of movable and fixed cylinders Vibration frequency Steady drag

FD

FL 0:5ρDLV 2

– – 0.025 m Hz N

Amplitude of fluctuating lift

N

L m mn

Natural frequency in water with spring 1 Natural frequency in water with spring 2 Span length of movable and fixed cylinders Mass of movable cylinder m Mass ratio defined as πρ ð0:5DÞ 2 L

1.229 Hz 1.859 Hz 0.474 m 0.263 kg 1.14

St

Strouhal number

t TE TS V Vr

Time End time of an interval for FFT analysis Start time of an interval for FFT analysis Towing velocity Reduced velocity defined as f VD

0.20 (cases R and I) 0.21 (case F) S s s m s1 –

X Y Y_

Separation distance Transverse displacement Transverse velocity

0.0325 m (X/D ¼ 1.30) m m s1

ζ

Damping ratio in water with spring 1 Damping ratio in water with spring 2 Water density Phase of force relative to phase of displacement

0.079 0.064 998 kg m 3 Deg.

FL fn

ρ φ

n

Fig. 1. Schematic side view of experimental apparatus placed in a towing tank. The two arrows in a dashed box indicate towing directions.

and the fixed one was at the rear (this case is referred to as case R, the first letter of the term “rear” identifying the position of the fixed cylinder). In addition, measurements were performed for an isolated movable cylinder (referred to as case I, the first letter of the term “isolated”) for comparing the response of the vibratory cylinder both with and without the fixed cylinder in proximity. The measurement conditions are summarized in Table 2. In the following description, the notation “case F” (“case R”) without subscripts 1 and 2 denotes both cases F1 and F2 (R1 and R2). We used two coil springs with different stiffness to support the movable cylinder. The spring 1 was used to compare the tandem arrangements, cases F1 and R1 with the isolated cylinder, case I. Using the spring 2, we examined the effect of damping ratio on the response of the tandem arrangements (Table 2). Before the cylinders were towed, free damping tests were conducted with the towing carriage at rest for estimating the damping ratio and natural frequency of the system comprising the cylinder, frames, and spring. The movable cylinder was manually imparted an initial displacement and then released to oscillate freely. Time histories of the movable cylinder's position in the free damping test are shown in Fig. 3. Damping ratios were calculated by fitting an exponential decay function to the time history envelope. The damping ratios and natural frequencies are listed in Table 1. The towing carriage was operated with the movable cylinder clamped also to

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Fig. 2. Photographs of (a) experimental apparatus and (b) generator.

estimate the Strouhal number St for the three arrangements, cases F, R, and I, which was measured to be 0.20 for cases R and I, and 0.21 for case F. The speed of towing the cylinders was set such that the reduced velocities tested covered the range 5oVr o9, within which VIV of cylinders generally occurs, and the range 9 oVr, within which WIV is expected to develop. In the latter case, an upper limit was set for the towing velocity to avoid the contact of the coil with surrounding parts and damages to them since a towing velocity beyond the limit was expected to produce a considerably large amplitude of vibration.

2.3. Data processing Temporal records of the vibratory cylinder's position and forces were processed through fast Fourier transform (FFT) to obtain the frequency spectra of the position and forces, from which the amplitude and phase of the most predominant frequency component were extracted. Prior to the FFT, the temporal records of the data were shifted only if measurement device outputs non-zero values under a rest condition to adjust zero responses to the value of zero. Temporal series of drag and lift forces were normalized for defining the drag and lift coefficients, respectively, as follows: CD

FD 0:5 ρ V 2 D L

; and C L

FL 0:5 ρ V 2 D L

(1)

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Table 2 Measurement conditions. Case

F1 F2 R1 R2 I

Spring

Cylinder arrangement

1 2 1 2 1

Movable

Fixed

Downstream Downstream Upstream Upstream Isolated

Upstream Upstream Downstream Downstream –

Fig. 3. Solid lines represent time series of displacements in free damping tests with springs (a) 1 and (b) 2. Closed circles are the maximum displacements, and dashed lines are the exponential functions fitted to the maximum displacements.

where CD and CL are functions of time. We defined steady drag and fluctuating lift coefficients denoted by C D and C L (Table 1), and determined the maximum amplitude of the lift from a spectrum of the lift. We defined the phase difference as φ φf φd , i.e. the phase of the lift force φf relative to the phase of the displacement φd , which is computed by FFT analyses on the lift force and displacement. To quantify the energy converted from fluid flow to cylinder vibration, the primary conversion efficiency is defined as follows: η1 ¼

ð1=ðT E T S ÞÞ

R TE TS

3

F L y_ dt

0:5 ρ V D L

;

(2)

and the energy converted from cylinder vibration to electric power is given by the secondary conversion efficiency, which is defined as follows: η2 ¼

R TE

ðE2 =Rst Þdt : R TE ð1=ðT E T S ÞÞ T S F L y_ dt

ð1=ðT E T S ÞÞ

TS

(3)

An attention was paid to choosing the times TS and TE such that an oscillatory displacement of the cylinder is located at crest at TS and TE to incorporate full cycles into the FFT analysis, thereby suppressing the end effect caused by cutting a time record out.

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Table 3 List of experimental parameters and variables used in the model for power output estimation. Symbol

Definition

Value or Unit

C

Damping coefficient

E FL Fm Fr I k

Voltage induced in coil Lift force acting on cylinder Electromagnetic force in coil Restoring force of spring Moment of inertia of bar Stiffness of coil spring 1 Stiffness of coil spring 2 Length of coil Magnetic charge of bar magnet Number of turns in coil Resistance of load in electric circuit Distance between an acting point of lift force and pivot Distance between coil and pivot Distance between spring and pivot Empirical coefficient in Eq. (7) Rotation angle of bar from horizontal Circular frequency of lift force Natural circular frequency

l M N Rst rL rm rr α θ ωL ωn

pﬃﬃﬃﬃ 2ζ Ik

kg m2 s 1

2πf n

V N N N 0.560 N m2 136 N m 1 300 N m 1 0.043 m 6.38 10 4 W b 2.0 103 42.0 Ω 0.50 m 0.45 m 0.50 m 29.76 V s m 1 rad rad s 1 rad s 1

Fig. 4. Schematic illustration of the model of a rigid bar rotating influenced by hydrodynamic force, restoring force exerted by a spring, and reaction force generated from electromagnetic induction.

3. Estimation of power output We have built a model that estimates a power output by receiving the measured magnitude of a fluctuating lift as an input. The model represents the dynamics and electromagnetics of the experimental apparatus [19]. Notations of the model are listed in Table 3. This model simplifies the rotational motion of the frames connecting the submerged cylinder and generator into the rotation of a single rigid bar around a pivot (Fig. 4). The rotation equation is expressed as follows: I θ€ þ C θ_ þkr r 2 sin θ cos θ ¼ F L r L cos θ F m r m cos θ

(4)

A magnetic field formed by a magnet bar interferes with that induced by an electric current in the coil, exerting the reaction force according to Coulomb's law as follows: F m ¼ mH;

(5)

where the magnetic field H is related to the electric current i induced in the coil in the following manner (Ampere's law): H¼

N i: l

(6)

Applying Faraday's law stating that a voltage induced in the coil is proportional to the rate of temporal change in a magnetic flux passing through a closed plane surrounded by a conductor (coil), we write the induced voltage as: E ¼ α r m θ_ cos θ:

(7)

The electromagnetic laws above and Ohm's law (E ¼ Rst i) give the electromagnetic force as follows: Fm ¼

αmN r m θ_ cos θ; Rst l

_ the force Fm produces the damping moment. which includes the angular velocity θ;

(8)

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Fig. 5. Time series of displacements at V r ¼ 6:0 for cases (a) F1, (b) F2, (c) R1, (d) R2, and (e) I.

In the following description, the notation of over bar such as E denotes the amplitude of induced voltage. Assuming that the lift force FL varies trigonometrically as F L ¼ F L cos ωL t and that the rotation angle θ is very small, i.e., cos θ ﬃ1 and sin θ ﬃθ, and substituting the expression of the forces above into Eq. (4), we can express the voltage induced in the generator as follows: E¼α

ωL r L r m F L ½ðω2L ω2n Þ2 þ ω2c ω2L 1=2 ; I ω2n

k rr 2 I

;

1 αmN 2 Cþ rm ; I Rst l

ωc

(9)

(10)

where ωc represents the magnitude of resistance arising from the mechanical energy loss and electromagnetic induction. Eq. (9) proves that the electric power is maximized if ωL ¼ ωn holds, corresponding to the locking of the vortex shedding frequency into the natural frequency. The output voltage E were calculated by substituting F L obtained through FFT into Eq. (9) and by applying the relation ωL ¼ ωn . The output voltage can be optimized further by regulating the position of the generator relative to the pivot. Regarding Eq. (9) as a function of r m , we can show that output voltage is maximized if rm equals r m_opt , which is defined as follows: rm ¼

C Rst l αmN

1=2 r m_opt

(7)

In every measurement case, the generator was positioned at r m_opt , the value of which was computed using the parameters listed in Table 3. The optimum position r m_opt depends on the resistance Rst ; we thus used a single value of resistance to stay the coil at r m_opt .

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Fig. 6. Time series of displacements at V r ¼ 11:0 for cases (a) F1, (b) F2, (c) R1, (d) R2, and (e) I.

4. Results 4.1. Cylinder vibration Fig. 5 shows temporal variations in the positions of the two cylinders at a reduced velocity of 6.0. The amplitudes for case F are larger than those for case R. The effects of stiffness of the springs 1 (Fig. 5a and c) and 2 (Fig. 5b and d) were compared, and it was found that spring 2 yields higher amplitudes because of its lower damping ratio. Temporal variations in the isolated cylinder (Fig. 5e) supported by spring 1 are comparable in amplitude to those in case F with spring 1. At a reduced velocity of 11.0 (Fig. 6), displacement amplitudes for case R are considerably large. In contrast, case F has very small amplitudes. The time series for case I has very small amplitudes, similar to that of case F. To capture more clearly the variations in response at various reduced velocities, we show the results obtained from the FFT in Fig. 7. At a reduced velocity of 5.0, the frequencies for cases F and R are slightly smaller than the natural frequency. The frequency for case R has wider lock-in range. The difference in the response curves of cases F and R is also apparent from the amplitude response curve. The amplitude for case F has a maximum at a reduced velocity of 6.5, whereas, in case R, the amplitude monotonically increases as the reduced velocity increases up to 8.0 (case R2) and 9.0 (case R1). It is notable that the amplitude increases drastically when the reduced velocities exceed these values.

4.2. Hydrodynamic force acting on moving cylinder Fig. 8 shows the time series of drag and lift forces at a reduced velocity of 6.0. Comparing the drag forces between cases F and R, we note that the fluctuating component (deviations from temporal average) of the drag force has a larger amplitude in case F than in case R. The temporal average of the drag force for case F is negative, while that for case R is positive. The amplitude of the fluctuating lift force is larger for case F than that for case R. The larger amplitude for case F stays mostly constant, whereas the time histories in case R have smaller and irregular amplitudes.

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Fig. 7. Frequencies and amplitudes of vibration against reduced velocities for cases (a) F1 (open circle) and R1 (closed circle), (b) F2 (open circle) and R2 (closed circle), and (c) I (opened circle: towing in the direction for case F; closed circle: towing in the direction for case R). The inclined lines in the panels of frequency are the relation of the Strouhal number of 0.20 (cases R and I) and 0.21 (case F) measured in this study.

When the reduced velocity is 11.0, case R has higher amplitude than case F (Fig. 9), in contrast to the above results (Fig. 8) at a reduced velocity of 6.0. Looking at the relationships of the forces with the reduced velocity (Fig. 10), we observe that the drag coefficients for case F are negative for reduced velocities of 5.0–9.0, as shown in Fig. 8. For case R (Fig. 10b), the drag coefficients are positive, the absolute values of which are a few times greater than those for case F. Within the reduced velocity range of 5.0–9.0 (case R1) and 5.0–8.0 (case R2), the drag coefficient has values of 0.7–0.9, whereas the drag coefficients increase abruptly if the reduced velocity exceeds 9.0 (case R1) and 8.0 (case R2) in a manner similar to the amplitude (Fig. 7). Response curves of the lift coefficient have a pattern similar to that of the amplitude: there is a maximum at a reduced velocity of 6.5 for case F; the lift coefficients for case R tend to increase with an increase in the reduced velocity up to 9.0 (case R1) and 8.0 (case R2). We can clearly see an abrupt increase in the lift coefficient at reduced velocities beyond the abovementioned values. Case F2 yields the phase difference (Fig. 11) that increases from 101 to 451 as the reduced velocity increases from 5.0 to 11.0. In case R, the phase difference tends to increase as well, although the rate of increase against reduced velocity is modest compared with that for case F2, the phase difference staying mostly constant around 241 when the reduced velocity is greater than 8.0. With reduced velocities over 7–8, peaks and scattering of the phase are observed for cases F and I (Fig. 11a and c), resulting from an inaccuracy in the phase estimation using the FFT, which is ascribed to the quite small amplitudes of the vibration (Fig. 6) and lift force (Fig. 9).

4.3. Power generation and energy conversion efficiency Fig. 12 shows the magnitude of the voltage induced in the generator. For cases F (Fig. 12a and c) and I (Fig. 12e), the voltage reaches its maximum at a reduced velocity of 6.5. Conversely, in case R, the voltage has no distinct maximum

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Fig. 8. Time series of drag and lift forces at V r ¼ 6:0 for cases (a) F2, (b) R2, and (c) I.

(Fig. 12b and d). These voltage patterns in response to the reduced velocity are similar to those of the amplitude and hydrodynamic forces, as shown above. For case F, the experimental voltage values agree reasonably with the values calculated by the model, while for case R, the experimental values are smaller than the estimated values for reduced velocities greater than those at which the displacement (Fig. 7) and force (Fig. 10) amplitudes increase abruptly. Cases F and R are different in the primary conversion efficiency η1 (Fig. 13). Case R offers a very high efficiency of more than 10 percent within a wide range of reduced velocities greater than the values at which the discontinuous changes occur in the amplitude and voltage. The maximum primary conversion efficiency for cases F and I is about 1.0 percent. In Fig. 14, we show a plot of the secondary conversion efficiency η2 against reduced velocity. For case F, the efficiencies tend to increase as the reduced velocity increases, averaging 30.6 percent (case F1) and 27.8 percent (case F2) for reduced velocities of 5.0–9.0. The efficiency distribution for case R, which seems to be scattered, has a peak around the reduced velocity range of 5.0–10.0, the averages of which are 22.3 percent (case R1) and 26.6 percent (case R2).

5. Discussion 5.1. Hydrodynamic interpretation of measured vibrations Tandem arrangements composed of a fixed upstream and an elastically mounted downstream cylinder have been examined in a few previous studies. Brika and Laneville [6] performed an experiment using a wind tunnel for separation distances greater than 7, reporting that smaller separation distances result in larger amplitudes at the downstream cylinder. Hover and Triantafyllou [7] investigated a similar two-cylinder arrangement with a separation distance of 4.75 and observed the downstream cylinder to exhibit a galloping motion, which starts to occur at a reduced velocity of 2 and has the maximum amplitude of 1.9 at a reduced velocity of 17. Assi et al. [10] conducted an experiment using a water channel and separation distances greater than 4.0, and discussed the mechanism of WIV for a downstream cylinder. Smaller separation

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Fig. 9. Time series of drag and lift forces at V r ¼ 11:0 for cases (a) F2, (b) R2, and (c) I.

distances (1.09 rX/Dr5.00) were employed in the experiment using a water channel conducted by Bokaian and Geoola [3], who reported wake-induced galloping of the downstream cylinder. Compared to the vibrations of cylinders in tandem arrangement shown in these previous works, cases R1 and R2 in this study has a couple of features of WIV: the responses exhibit remarkable growths in amplitude as the reduced velocity increases from 5 to 19 (closed circles in Fig. 7) and the vibration has a more resonant property: the frequencies for cases R1 and R2 are closer to the natural frequency throughout the reduced velocities tested (closed circle Fig. 7); meanwhile the amplitude of the isolated cylinder (case I, opened circles in Fig. 7) has a maximum around V r ¼ 6:5, and vanishes if the reduced velocity is over 9, a typical response of VIV. The very large amplitudes observed for case R can be attributed to flow interference between the two cylinders. Many previous studies have explained the fluid mechanics of such interference; however, few studies have done so for the same arrangement as case R, i.e., an elastically mounted upstream cylinder and a fixed downstream cylinder. To the best of our knowledge, the study of Zdravkovich [1] is the only one that addressed the same arrangement, but detailed results were not presented. Our experiment alone cannot fully clarify the flow interference occurring in case R because pressure fields around the cylinders were not measured in this study unlike in [8]; we thus interpret the outcome of case R by referring to the discussion of Borazjani and Sotiropoulos [9], in which the vortex dynamics around two cylinders mounted elastically in tandem with X/D¼1.5 were analyzed by numerically simulating the flows around the cylinder pair. They noted that the passage of shear layers separated from the upstream cylinder into the gap region plays an important role in flow interference. In our experiment, the vortex formed behind the upstream cylinder interferes with the gap flow as follows. While the upstream cylinder is displaced above the initial position and moving downward (Fig. 15), a lower shear layer is separated from the upstream cylinder; concurrently, the vertical separation between the two cylinders is so wide for fluid to form a strong gap flow. This brings about upward transportation of the lowpressure region behind the upstream cylinder and a further pressure decrease in the region owing to the large velocity of the gap flow. The front side of the upstream cylinder is always exposed to the free stream, which stagnates in front of the upstream cylinder, resulting in the formation of a high-pressure region on the front side of the upstream cylinder. The resulting formation of a pressure contrast (high- and low-pressure regions mentioned above) leads to highmagnitude downward lift forces acting on the upstream cylinder. A schematic of the above interpretation of flow

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Fig. 10. Drag and lift force coefficients against reduced velocities for cases (a) F1 (open circle) and R1 (closed circle), (b) F2 (open circle) and R2 (closed circle), and (c) I.

interference is drawn in Fig. 15. While the upstream cylinder is located below the initial position and moves upward, an upper shear layer interferes with the gap flow in a manner similar to the one described above, forcing the low-pressure regions to move downward, and producing high-magnitude upward lift forces. This mechanism explains the great lift force observed in case R (closed circle in Fig. 10). For case R, the phase of lift force precedes the phase of displacement by 20–251 (Fig. 11), which is favorable to exciting the vibration. The flow interference mechanism through which the lift force is built up excites the WIV, and its large magnitude offers a quite large power extraction. The experimental condition of [3] is much the same as case F in this study. However, our study observed vortex resonance response (VIV) within a limited reduced velocity range (Fig. 7), differently from [3]. We infer that the difference in responses can be attributed to (a) the small difference in separation distances, (b) the effect of the electromagnetic damping moment, or (c) the high mass ratio in our setup. We explain (a) in terms of flow interference. According to the classification of flow interference around two adjacent fixed cylinders in tandem arrangement [4,20], if the separation distance is very small (X/Dr 1.1), the two cylinders behave as if they were one slender body; if the distance is 1.1 oX/D r1.6, shear layers separated from the upstream cylinder alternately reattach onto the front side of the downstream cylinder; and if the distance is 1.6oX/D r2.4, the separated shear layers quasi-steadily reattach onto the front side of the downstream cylinder. Applying this classification to the experiments in our study and those in [3], we can see that our experiments correspond to the alternate reattachment category, while the experiments in [3] correspond to the single slender body and quasi-steady reattachment category. This difference in flow patterns may result in a difference in the downstream cylinder's response. Further measurements with a greater number of separation distances will be carried out to validate (a). The experimental data pertaining to the relationship between the response and the structural damping reported in [3] can support (b): a downstream cylinder with very high structural damping exhibits vortex resonance, whereas as structural

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Fig. 11. Phase of lift forces relative to phase of displacements against reduced velocities for cases (a) F1 (open circle) and R1 (closed circle), (b) F2 (open circle) and R2 (closed circle), and (c) I.

damping decreases, the galloping response becomes predominant. This suggests the presence of a large damping factor in our experiment, which can probably be ascribed to the electromagnetic induction in the generator. The movable parts above the water surface (Fig. 1) explain the point (c). The magnitude of flow-induced vibration generally depends on mass ratio as well as damping. If we consider only the mass ratio of the submerged cylinder, our experimental setup would have low mass-damping parameter, the mostly same as that in [3]. In reality, our setup includes the translating bars, rotating levers, and moving coils other than the movable cylinder submerged, and their effective masses make the mass-damping parameter higher than that in [3], vanishing the VIV response in case R.

5.2. Power harvesting using WIV The very high primary conversion efficiency obtained in case R indicates that power harvesting using WIV is promising to generate available energy from fluid flows. The highest achieved primary conversion efficiency was about 15 percent, and

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Fig. 12. Amplitudes of voltages induced against reduced velocities for (a) F1, (b) R1, (c) F2, (d) R2, and (e) I. Closed circles are the measured voltage and solid lines are the voltage estimated using Eq. (9). Small dashed boxes in (a) and (e) enlarge the response curves.

the efficiency is more than 10 percent in the reduced velocity range of 9–14. Hence, the power harvesting can be optimized by installing this system in a flow circumstance that covers a reduced velocity range within which WIV is pronounced. In the event of WIV occurrence, measured output voltages were lower than the estimated ones (Fig. 12). This was caused by periodic contact of the moving coil with an L-shaped bracket (Fig. 2b) fixed for supporting the magnet, which interrupted the coil's oscillatory motion. The amplitudes of the vibration for case R with reduced velocity greater than 9 were so large that they unexpectedly exceeded its design upper-limit. This aspect has to be improved for better performance.

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Fig. 13. Primary energy conversion efficiency measured against reduced velocities for cases (a) F1 (open circle) and R1 (closed circle), (b) F2 (open circle) and R2 (closed circle), and (c) I. A small dashed box in (c) enlarges the response curve.

The VIV resonance observed in cases F and I yielded conversion efficiencies lower than that in case R. Notably, this does not mean that the upstream movable–downstream fixed cylinder arrangement (case R) is always the best for harvesting energy from WIV. Previous studies e.g. [3,6] reported very large WIV responses for other cylinder arrangements, such as upstream fixed–downstream movable (the same as case F) and dual movable. Hence, further examination with a variety of two-cylinder arrangements is required for identifying the arrangement that offers the best performance. To improve the conversion efficiency, Reynolds number should be considered. The measurements in this study covered Reynolds numbers from 2.48 103 to 1.50 104, which are perhaps smaller than the Reynolds numbers providing the optimized performance. A couple of experimental studies on harnessing energy from VIV [13,14] showed that the Reynolds number regime involving fully turbulent shear layers (2 104 4 104 o Re o 1 105 2 105 ) gives the highest VIV responses, resulting in the most effective energy harvesting. Barrero-Gil et al. [17] achieved higher conversion efficiency at a Reynolds number of 1.0 104 than that at a Reynolds number of 3.8 103 through a parametric study using their theoretical model. These suggest that a movable cylinder with a larger diameter than that in this study can provide greater power output. It follows that a Reynolds number of order of 104–105 is the optimal for a full scale power extraction system using

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Fig. 14. Secondary energy conversion efficiency against reduced velocities for cases (a) F1 (open circle) and R1 (closed circle), (b) F2 (open circle) and R2 (closed circle), and (c) I.

the WIV. We need to monitor the flow velocity at a site where the system is installed to evaluate the Reynolds number there, and then by regulating the mass and damping ratios we can produce the WIV optimized under the circumstance at the site.

6. Conclusion In this study, we carried out an experiment on renewable energy extraction through WIV of two cylinders in tandem arrangement. We fabricated an apparatus for obtaining measurements in a towing tank containing an elastically mounted submerged cylinder placed close to another fixed cylinder. Three cylinder arrangements were tested: the upstream fixed– downstream movable arrangement (case F); the upstream movable–downstream fixed arrangement (case R); and an isolated moving cylinder (case I). The separation distance, defined as the length between the centers of the two circular cylinders divided by the cylinder diameter, was fixed at 1.30. We discovered that the case R yields very large vibration amplitudes at reduced velocities greater than 9.0, providing higher electronic power output and energy conversion efficiency. This vibration is interpreted as WIV, resulting from the

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Fig. 15. Schematic drawing of flow interference around upstream moving cylinder and downstream fixed cylinder. The dashed line represents the moving cylinder's initial position. The opened block arrow behind the upstream cylinder indicates the transportation of the low-pressure region due to the gap flow.

interference of vortices shed from the upward moving cylinder with strong gap flow. Measurements for cases F and I yielded normal VIV resonance responses with vibration amplitudes and output voltages lower than those for case R.

Acknowledgments This work was financially supported by the River Fund 25-1221-001, River Foundation, Japan. We are indebted to Prof. Y. Hirakawa and Mr. T. Takayama for their technical supports in the measurement, and to the anonymous reviewers who provided us with insightful comments which helped us improve the quality of our manuscript. References [1] M.M. Zdravkovich, Flow-induced vibration of two cylinders in tandem, and their suppression, Proceedings of IUTAM-IAHR Symposium Karlsruhe “FlowInduced Structural Vibrations,” August 14–16, 1972, Springer-Verlag, Berlin, 1974, pp. 631–639. [2] R. King, D.J. Johns, Wake interaction experiments with two flexible circular cylinders in flowing water, Journal of Sound and Vibration 45 (2) (1976) 259–283. [3] A. Bokaian, F. Geoola, Wake-induced galloping of two interfering circular cylinders, Journal of Fluid Mechanics 146 (1984) 383–415. [4] M.M. Zdravkovich, Flow induced oscillations of two interfering circular cylinders, Journal of Sound and Vibration 101 (4) (1985) 511–521. [5] M.M. Zdravkovich, Review of interference-induced oscillations in flow past two parallel circular cylinders in various arrangements, Journal of Wind Engineering and Industrial Aerodynamics 28 (1988) 183–200. [6] D. Brika, A. Laneville, The flow interaction between a stationary cylinder and downstream flexible cylinder, Journal of Fluids and Structures 13 (1999) 579–606. [7] F.S. Hover, M.S. Triantafyllou, Galloping response of a cylinder with upstream wake interference, Journal of Fluids and Structures 15 (2001) 503–512. [8] N. Fujisawa, Wake galloping of circular tandem cylinder and surface pressure distribution on them, Journal of Japan Society of Civil Engineers Series A 65 (4) (2009) 966–979. [9] I. Borazjani, F. Sotiropoulos, Vortex-induced vibrations of two cylinders in tandem arrangement in the proximity-wake interference region, Journal of Fluid Mechanics 621 (2009) 321–364. [10] G.R.S. Assi, P.W. Bearman, J.R. Meneghini, On the wake-induced vibration of tandem circular cylinders: the vortex interaction excitation mechanism, Journal of Fluid Mechanics 661 (2010) 365–401. [11] M.M. Bernitsas, K. Roghavan, Y. Ben-Simon, E.M.H. Garcia, VIVACE (Vortex Induced Vibration for Aquatic Clean Energy): a new concept in generation of clean and renewable energy from fluid flow, Journal of Offshore Mechanics and Arctic Engineering 130 (4) (2008) 041101, http://dx.doi.org/10.1115/ 1.2957913. [12] M.M. Bernitsas, K. Raghavan, Y. Ben-Simon, E.M.H. Garcia, The VIVACE converter: model tests at high damping and Reynolds number around 105, Journal of Offshore Mechanics and Arctic Engineering 131 (1) (2009) 011102, http://dx.doi.org/10.1115/1.2979796. [13] K. Raghavan, M.M. Bernitsas, Experimental investigation of Reynolds number effect on vortex induced vibration of rigid circular cylinder on elastic supports, Ocean Engineering 38 (2011) 719–731. [14] J.H. Lee, M.M. Bernitsas, High-damping, high-Reynolds VIV tests for energy harnessing using VIVACE converter, Ocean Engineering 38 (2011) 1697–1712. [15] J.H. Lee, N. Xiros, M.M. Bernitsas, Virtual damper-spring system for VIV experiments and hydrokinetic energy conversion, Ocean Engineering 38 (2011) 732–747. [16] A. Barrero-Gil, G. Alonso, A. Sanz-Andres, Energy harvesting from transverse galloping, Journal of Sound and Vibration 329 (2010) 2873–2883. [17] A. Barrero-Gil, S. Pindado, S. Avila, Extracting energy from vortex-induced vibrations: a parametric study, Applied Mathematical Modelling 36 (7) (2012) 3153–3160.

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[18] Q. Zhu, M. Haase, C.H. Wu, Modeling the capacity of a novel flow-energy harvester, Applied Mathematical Modelling 33 (2009) 2207–2217. [19] Y. Nishi, K. Ono, K. Kokubun, Development of a renewable energy system utilizing vortex induced vibration of a cylinder and principle of leverage aiming for application in deep sea, Journal of Marine Science and Technology 17 (3) (2012) 382–389, http://dx.doi.org/10.1007/s00773-012-0174-1. [20] T. Igarashi, Characteristics of the flow around two circular cylinders arranged in tandem (1st report), Bulletin of the Japan Society of Mechanical Engineers 24 (188) (1981) 323–331.

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