Numerical investigation into the effects of arm motion and camber on a self-induced oscillating hydrofoil

Energy 115 (2016) 1010e1021

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Numerical investigation into the effects of arm motion and camber on a self-induced oscillating hydrofoil W. Jiang a, D. Zhang b, Y.H. Xie a, * a

School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi Province, 710049, China Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi Province, 710049, China

b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 25 May 2016 Received in revised form 5 September 2016 Accepted 7 September 2016

A new concept of power generator using self-induced oscillating hydrofoil with upwind arm and downwind arm configurations to extract energy from fluid is proposed and numerically tested in the present study. The pitching motion of the symmetrical hydrofoil with camber is induced by the shedding vortexes downward the hydrofoil, and a pitching damper with critical pitching angle is utilized to control the pitching amplitude. Two-dimensional Navier-Stokes simulation at Re ¼ 1100 are carried out to study the fluid-hydrofoil interaction as well as the performance of energy extraction. The effects of camber, critical pitching angle, arm length and swing direction are systematically studied. Numerical results demonstrate that camber and critical pitching angle have significant effects on the energy extraction performance of the power generator, and optimized camber and critical pitching angle configurations can increase the power coefficient and efficiency dramatically. With best structural parameters and hydrofoil shape, the power generator can reach maximum power coefficient of 0.8 and energy extraction efficiency of 0.285. Besides, the upwind arm configuration achieves better performance over the downwind arm configuration. The effect of arm length is not so profound as other parameters in our study. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Oscillating hydrofoil Energy extraction Vortex-induced vibration Renewable energy Camber effect

1. Introduction The continuous rise of world energy consumption and stricter carbon policy motivate the development of alternative energy extraction systems from renewable sources, such as wave, sunlight, tide and hydro. The traditional devices for wind or tidal energy extraction are turbines based on spinning blades [1,2]. However, many alternative concepts to extract energy from the flow was also proposed [2,3]. Two kinds of flow energy conversion technologies, namely oscillating hydrofoils or airfoils systems and vortexinduced-vibration systems, will be introduced in this paper. Based on these two concepts, a new power generator using selfinduced oscillating hydrofoil to extract energy from fluid is proposed. The concept of using oscillating foil to harvest energy from fluid was firstly tested by McKinney and DeLaurier [4]. The application of

* Corresponding author. E-mail addresses: [email protected] (W. Jiang), [email protected]. cn (D. Zhang), [email protected] (Y.H. Xie). http://dx.doi.org/10.1016/j.energy.2016.09.053 0360-5442/© 2016 Elsevier Ltd. All rights reserved.

oscillating wings for energy extraction is inspired by the biological ability of animals, such as aquatic animals and birds, who exhibit excellent hydrodynamic and aerodynamic performance by extracting flow energy through their wing and tail of fin's flapping motion [5]. The aerodynamics of oscillating hydrofoil with fully prescribed motion has been extensively investigated by many researchers [6e11]. According to these studies, the optimal reduced frequency corresponding to the peak efficiency was observed within the range from 0.10 to 0.15. The energy extraction efficiency increased significantly with the plunging amplitude at low plunging amplitudes, while the efficiency decreased once the plunging amplitude reached one chord length. Besides, it was found that the peak energy extraction occurred when the pitching and plunging motions was 90 out of phase and the maximum effective angle of attack was near 33 . Above all, these studies indicated that the power extraction systems based on oscillating hydrofoil can reach levels comparable to the best performances in terms of efficiency achieved with modern wind turbines based on spinning blades. Further, some new concepts and designs of oscillating foil generators with semi-passive or fully passive motion were proposed. In the semi-passive way, a motor was used to drive

W. Jiang et al. / Energy 115 (2016) 1010e1021

Nomenclature A c CP CPmean D f fd fl fNa fNq h hr Ia Iq ka kq l m md m* M(t)

plunging amplitude hydrofoil chord length power coefficient time-averaged power coefficient vertical extent of the hydrofoil motion plunging oscillation frequency streamwise fluid force (drag force) transverse fluid force (lift force) natural frequency for swing vibration natural frequency for pitching vibration camber height relative camber height swing moment of inertia pitching moment of inertia swing stiffness factor pitching stiffness factor mean camber line length hydrofoil mass displaced fluid mass mass ratio torque

the pitching motion, meanwhile the plunging motion was driven by the fluid and the power was extracted from the plunging motion [12,13]. In the fully passive way, all motions were driven directly by the fluid. The foil was either restrained to move with one single degree of freedom, where the pitching motion was linked to the plunging motion via the Geneva Wheel [14,15] or the crankshaft [16], or was allowed to move in pitch and plunge independently [17,18]. Following these ideas, some real energy extraction devices and prototypes have been proposed and tested. The first commercial prototype of an oscillating hydrofoil hydrokinetic turbine is the 150 kW “Stingray” developed by the Engineering Business Ltd [19]. The turbine consisted of a single hydrofoil pivoted on a swinging arm. It reported a maximal production of 85 kW and power extraction efficiency of 11.5%. Paish [20] described a 100 kW prototype named Pulse Stream designed by the UK company Pulse Tidal. Two foils are pivoted at mid-chord at the end of the swingarms. The foils are symmetric front-to-back so that the turbine can extract energy from both flow directions. Platzer [21] invented a fully passive device which requires no motor to drive the pitching motion. The foil plunges on a guide rail and pitches at the end of the rail so that the foil undergoes non-sinusoidal plunging and pitching motions. Kinsey [16] proposed a new concept of hydrokinetic turbine using oscillating hydrofoils to extract energy from water currents. The turbine includes two rectangular oscillating hydrofoils in tandem with pitching motion of each foil linked to the plunging motion. They demonstrated a hydrodynamic efficiency of 40% for the experimental prototype. According to the studies discussed above, the oscillating foil with fully prescribed motion or semi-passive motion has been widely investigated. However, research into fully passive oscillating foil is limited and far below adequate. There clearly appears to be a need for further improvement of fully passive oscillating foil as well as the fundamental physics involved with the mechanism of this device. The VIVACE (vortex induced vibration aquatic clean energy) converter developed by Bernitsas and Raghawan [22] may inspire the design of fully passive oscillating hydrofoil. Their design is based on the idea of maximizing rather than spoiling vortex

Mk(t) Mq(t) Ma(t) R Rc Re t T Ux Uy Ur U*a U*q U∞ a(t)

aeff h qc q(t) za zq u(t)

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spring torque pitching torque swing torque arm length radius of the base circle Reynolds number physical time swing motion period streamwise heaving velocity transverse heaving velocity relative velocity apparent to the hydrofoil reduced velocity based on fNa reduced velocity based on fNq free stream velocity swing motion effective AOA(angle of attack) energy extraction efficiency critical pitching angle pitching motion swing damping factor pitching damping factor angular velocity

shedding and exploiting rather than suppressing VIV. They found that the experimental models could maintain VIV over a broad range of vortex shedding synchronization and thus over very broad ranges of Reynolds number. Above VIVACE model was then tested in a Low Turbulence Free-Surface Water Channel [23]. The influence of some key parameters, like the mass ratio, the mechanical damping, the Reynolds number, and the aspect ratio were studied. The maximum peak efficiency achieved for the tested VIVACE model was 0.308, and the corresponding integrated power efficiency was 0.22. Barrero-Gil [24] built a theoretical model and established the relation between the mass and mechanical properties, cross-section geometry, flow velocity and energy efficiency. It was found that nonlinear springs might be used to improve an oscillating body's power generating performance by expanding the amplitude response. More recently, Narendran [25] experimentally investigated the efficiency of a vortex induced vibration hydrokinetic energy device, and reported peak mechanical efficiency value of around 90% with corresponding time average value of about 50% using linear generator at Re of the order (105). Following above-mentioned investigations, a new concept of power generator using self-induced oscillating hydrofoil to extract energy from fluid is proposed and numerically tested in our previous study. The pitching motion of the C-shape hydrofoil is induced by the shedding vortexes downward the hydrofoil just like the VIVACE device. As for the plunging motion, the conventional plunging motion or heaving motion is the pure translation one [26]. However, in most engineering applications, the heaving motion is rotation of a swing arm on which the foil is mounted. The 150 kW “Stingray” consisted of a single hydrofoil pivoted on a moveable arm [19]. The “BioSTREAM” [27,28] system tested by Australian company BioPower System also incorporates a single hydrofoil mounted on a swinging arm. The company Pulse Tidal in UK has developed “Pulse Stream” and also used swing motion of two arms in its design. We can see that the swing arm is more favorable in practice for the plunging motion. Additionally, the swing arm mode may increase the energy extraction performance of the power generator [29]. In this study, the self-induced oscillating hydrofoil

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will swing on an arm instead of translational plunging motion, and the plunging motion is equivalent to the swing motion. What's more, the camber and pitching damper with critical pitching angle are utilized to improve the performance of the fully passive generator. As shown in Fig. 2, the oscillating hydrofoil generator includes a C-shape hydrofoil pivoting about one end of the arm, a swing arm, a pitching spring connected to the hydrofoil, a swing spring connected to the base, a pitching damper (not shown) and a swing damper (not shown). We assume the hydrofoil has uniform density and can be treated as a rigid body. The main objective of this work is to systematically evaluate the effects of camber, critical pitching angle, arm length and swing direction on the energy extraction performance of the fully passive system. By modifying the shape of the hydrofoil and adding the pitching damper with critical pitching angle to our design, we expect that the pitching motion can be better controlled, and thus the new power generator can achieve better energy extraction performance over the old version. The rest of the paper is organized as follows. We first describe the numerical method and the mathematical formulation. Numerical simulations are carried out to evaluate and analyze the effect of camber, critical pitching angle and arm length for the upwind arm configuration. After that, same approaches are adopted to study the downwind arm configuration, and then the two configurations with different arm direction are compared. Finally, conclusions are drawn.

2. Numerical method 2.1. Solver The commercially available CFD package FLUENT 14.5 is used to simulate the unsteady incompressible and 2D flow field around the hydrofoil. Second-order-accurate schemes are chosen for pressure, momentum and turbulent viscosity resolutions. A second-orderaccurate backward implicit scheme is adopted for the temporal discretization. The SIMPLE algorithm is used for pressure-velocity coupling. All the cases of oscillating hydrofoil are investigated at Re ¼ 1100 and the flow field is assumed to be laminar as the studies by Kinsey and Young [9,14]. As shown in Fig. 1, the computational domain contains two subdomains connected by a sliding grid interface. Both of the two zones were meshed with a structured grid. The inner zone is a circle centered on the pitching motion's pivot point, with diameter of 16 chords. A no-slip boundary condition is applied along the hydrofoil surface. The farfield boundary is set to at least 30 chords away from the hydrofoil so that the boundary effect on the flow around the moving hydrofoil is negligible [30]. The interaction between fluid and the hydrofoil and the dynamic mesh motion are achieved by the FLUENT user defined functions (UDF) based on C programming

Fig. 2. Schematic of oscillating hydrofoil generator with (a) upwind arm, (b) downwind arm and (c) velocity triangular.

language. The inner zone employs a moving mesh for the pitching and swing motions, as employed by Ashraf et al. [31] and Lu et al. [5]. An O-topology mesh is adopted for the inner zone, and the height of the first row of cells near the wall is set as 105 chord [31] so that the Yþ is less than 1.

2.2. Kinematics The oscillating hydrofoil experiences simultaneous swing motion a(t) and pitching motion q(t). As shown in Fig. 2, q is defined as the angle between midchord and vertical line, and the initial equilibrium position of the hydrofoil is set at q ¼ 0 and a ¼ 0. As the hydrofoil is treated as a rigid body in presented study, the equation of the pitching motion for the hydrofoil can be written as:

Iq € qðtÞ þ zq q_ ðtÞ þ kq qðtÞ ¼ Mq ðtÞ

(1)

where Iq is the moment of inertia of the hydrofoil based on pitching center, zq is the pitching damping factor, kq is the pitching stiffness factor and Mq(t) is the torque applied by the fluid based on pitching center. A critical pitching angle is used to limit the pitching amplitude. When the actual pitching angle exceeds the critical pitching angle, the pitching angular velocity will decelerate to zero quickly due to a large pitching damping factor. So the pitching damping factor is defined as:

zq ¼




0; jqðtÞj  qc Inf ; jqðtÞj > qc

(2)

where qc is the critical pitching angle. The swing motion of the hydrofoil can be expressed as:

€ ðtÞ þ za a_ ðtÞ þ ka aðtÞ ¼ Ma ðtÞ Ia a

Fig. 1. Diagram of the model geometry and boundary conditions.

(3)

where Ia is the moment of inertia of the hydrofoil based on swing center (one end of the arm), za is the swing damping factor, ka is the swing stiffness factor and Ma(t) is the torque applied by the fluid based on swing center. The definitions of q, a and bhave been illustrated in Fig. 2. As

W. Jiang et al. / Energy 115 (2016) 1010e1021

shown in Fig. 2 (c), at the selected pitching angle, the hydrofoil is swinging clockwise, and thus both the streamwise heaving velocity Ux ¼ uRsina and transverse heaving velocity Uy ¼ uRcosa are positive. At the midpoint of the midchord, the velocity triangular indicates the relationship between the oncoming flow velocity U∞, the angular speed u and the relative velocity apparent to the hydrofoil Ur. Based on the induced swing motion, oncoming flow conditions and hydrofoil shape, the hydrofoil experiences an effective angle of attack aeff, expressed as follows:

 



U



 

y  ð90+  q  bÞ aeff ¼ arctan U∞  Ux       uðtÞR cosðaÞ ¼ arctan  ð90+  q  bÞ U∞  uðtÞR sinðaÞ

(4)

(5)

where u(t) is the instantaneous swing angular velocity. The instantaneous power extracted over one cycle can thus be computed in nondimensional form:

CP ¼ 1

P

(6)

3 2 rU∞ c

The time-averaged power coefficient CPmean is calculated by the integration of the instantaneous CP over one cycle:

CPmean ¼

1 T

ZT CP dt

(7)

0

The total energy extraction efficiency h is defined as the ratio of the mean total power extracted to the total power available in the oncoming flow passing through the swept area:

Pmean c ¼ CPmean 3d d r U ∞ 2

h¼1

sffiffiffiffiffi kq Iq

1 fNa ¼ 2p

sffiffiffiffiffi ka Ia

(12)

(13)

2.3. Validation studies

The instantaneous power extracted from the flow comes from swing motion, which can be expressed as:

PðtÞ ¼ Pa ðtÞ ¼ za uðtÞ2

1 fNq ¼ 2p

1013

(8)

where d is the overall vertical extent of the hydrofoil motion considering both the swing and pitching motions. The following nondimensional structural parameters are fixed in present study:

Uq* ¼

U∞ fNq l

(9)

Ua* ¼

U∞ fNa l

(10)

m* ¼

m md

(11)

Before conducting a detailed investigation, grid independence and temporal resolution validation were performed in order to establish a grid-independent and time-independent solution. In the first test, grid-independent computations have been performed for several sets of grid configurations with 3.6  104, 6.1  104, 9.5  104, 1.2  105 and 1.9  105 cells, corresponding to 150, 280, 400, 500 and 800 nodes along the hydrofoil surface respectively, for a Reynolds number Re ¼ 1100 at equilibrium. In the second test, for the temporal resolution analysis, the medium mesh (1.2  105) is examined for several time steps: 0.001, 0.002, 0.005, 0.008, 0.01 and 0.02 s, corresponding to about 7500, 3570, 1500, 938, 750 and 357 time steps per cycle. Fig. 3 presents the variations of the torque in one cycle for different grid and temporal resolutions. It is found that 1.2  105 cells and 1500 time steps per cycle are sufficient to yield a grid-independent and time-independent solution. Hence, all computational results in the present study are obtained on the 1.2  105 cells mesh with 1500 time steps per cycle. To further validate our numerical predictions, the flapping motions of a NACA0015 airfoil with nondimensional amplitude of 1, reduced frequency of 0.14 and pitching amplitude of 76.3 at Re ¼ 1100 are simulated with above-mentioned numerical method as well as the grid and time step configurations. The comparison of the power coefficient between our computational results and numerical results by Kinsey and Dumas [9] is shown in Fig. 4. As shown, our computational results agree well with the numerical results from other researchers. Unfortunately, there are yet no experimental data available for low Reynolds number (1100) oscillating hydrofoils in a power-extraction regime, so the authors chose an experiment at relative low Reynolds number (13800) to validate the numerical method. The oscillating motions of a NACA0012 airfoil with nondimensional amplitude of 0.75, reduced frequency of 0.1 and pitching amplitude of 71 at Re ¼ 13800 are simulated. The comparison of the lift coefficient between our computational results and experimental data by Simpson [32] is shown in Fig. 5. The computational results agree well with the experimental data. 3. Results and discussions 3.1. Camber effect

where U*q and U*a are the pitching reduced velocity and swing reduced velocity respectively, and m* is the mass ratio. U*q and U*a are fixed at 7, and m* is fixed at 10 throughout the paper. The l is the mean camber line length and U∞ is free stream velocity. The l is fixed at 1 m and U∞ is fixed at 1 m/s. The fNq and fNa are the pitching vibration natural frequency and swing vibration natural frequency, which are calculated as:

As mentioned before, the hydrofoil is perpendicular to flow direction at equilibrium, which means that the angle of attack fluctuates around 90 and thus the leading and trailing edges of the hydrofoil are alterable. In previous study, an elliptical hydrofoil was chosen to guarantee symmetric plunging motion. The effect of hydrofoil thickness on the torque variation was studied and it was found that the torque amplitude decreases with the increasing hydrofoil thickness, indicating that thinner hydrofoil may provide better energy extraction performance. As we did before [33], relative thickness of 0.1 is chosen for the present study. What's more, the hydrofoils have camber in the present study, and the effect of camber is studied in this section. Several typical hydrofoils are

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Fig. 3. Spatial grid and temporal independences.

Fig. 4. Time evolution of total power coefficient CP at A/c ¼ 1, fc/U∞ ¼ 0.14, q0 ¼ 76.3 and Re ¼ 1100 [9].

Fig. 6. Typical hydrofoils.

shown in Fig. 6. Different configurations for chord length, camber height, relative camber height, radius of the base circle and camber angle are listed in Table 1. The hr indicates relative camber height, which is defined as:

hr ¼

h c

(14)

The first elliptical hydrofoil is the base hydrofoil for the rest. The base hydrofoil is projected to a circle and forms the hydrofoils with camber. As the radius of the circle Rc decreases, hr increases. Table 1 Different hydrofoil configurations.

Fig. 5. Lift coefficient phasing for a plunging NACA0012 airfoil at A/c ¼ 0.75, Af/ U∞ ¼ 0.1, q0 ¼ 71 and Re ¼ 13800 [32].

h/m

c/m

hr

Rc/m

b/

0 0.04 0.08 0.15 0.23 0.27

1 0.99 0.98 0.94 0.84 0.76

0 0.04 0.08 0.16 0.27 0.36

∞ 3 1.5 0.8 0.5 0.4

0 9.5 19.1 35.8 57.3 71.6

W. Jiang et al. / Energy 115 (2016) 1010e1021

As shown in Fig. 2, we define the camber with positive hr as downwind camber and the camber with negative hr as upwind camber. Fig. 7 shows the variations of energy extraction efficiency and power coefficient with relative camber height at R ¼ 6, qc ¼ 132 and za ¼ 30. It has to be pointed out that the generator cannot obtain stable power output as hr is greater than 0.04, thus Fig. 7 does not show data relative to hr greater than 0.04. From Fig. 7, we can find that the efficiencies and power coefficients for upwind camber are much higher than that for downwind camber. The CP and h increase with hr at first and further increasing hr leads to decreasing CP and h. The maximum CP and h are observed at hr ¼ 0.27. In order to explain how the camber affects the energy extraction performance, we explore and compare the motion trajectories and the fluid forces for the hydrofoils with upwind camber (hr ¼ 0.04) and downwind camber (hr ¼ 0.04) in Fig. 8. The black lines in Fig. 8 indicate the midchord of the hydrofoil, the red vectors on the hydrofoil indicate the instantaneous fluid forces, and the black vectors beside the hydrofoil indicate the moving directions of the hydrofoil. The two motion trajectories share some similar features. The instantaneous fluid forces are roughly normal to the hydrofoils surface all the time, suggesting that the pressure forces dominate the shear viscous forces at this Reynolds number. Besides, there exist two distinct phases in half swing cycle. In first phase, the hydrofoils rotate rapidly. The variations of drag force and lift force are very large and the drag force reaches its maximum value in this phase. In second phase, the pitching angle changes slowly and the angle of attack almost remains unchanged. Apart from these same patterns, these also exist some obvious differences. It is noted that the swing amplitude for upwind camber is much larger than that for downwind camber which means that the hydrofoil with upwind camber can capture more fluid and energy. What's more, the angle of attack is positive in the second phase for the upwind configuration, while the angle of attack is negative for the downwind configuration. We know that the lift force largely depends upon the angle of attack, and so does the energy extraction performance. How the camber direction affects the pitching motion and the corresponding angle of attack will be discussed below. To gain more insight into the effect of camber direction, we explore the variations of the effective AOA and lift force in one swing cycle for two hydrofoils with different camber in Fig. 9. The hydrofoils undergo upstroke in the first half cycle and downstroke in the second half cycle. We can find two drastic jumps in the effective AOA, which is caused by the shift of leading edge and trailing edge when the hydrofoil passes the equilibrium position. The change of the lift force is complicated and irregular. There exist three ups and downs in one cycle for the lift force. A drastic

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Fig. 8. Diagram of the hydrofoil motion indicating the magnitude and orientation of the force vectors throughout the stroke; R ¼ 6, qc ¼ 132 and za ¼ 30.

Fig. 9. Variations of the effective AOA and lift force in one swing cycle.

Fig. 7. Variations of energy extraction efficiency and power coefficient with relative camber height at R ¼ 6, qc ¼ 132 and za ¼ 30.

fluctuation of lift force appears in first phase of upstroke and downstroke (0e0.25, 0.5e0.75), which arises from rapid hydrofoil rotation, and the variation of lift force is relatively smooth in second phase (0.25e0.5). What's more, the effect AOA for downwind camber is negative in second phase of the first half cycle. It is interesting to note that although the angle of attack is negative, the lift force is positive all the way in second phase. But for the upwind camber, the angle of attack is positive during most time of second

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phase, which is conducive to produce larger lift force (see Fig. 9). According to the definition of effective AOA, the difference in effective AOA for downwind camber and upwind camber is due to different camber angle b as defined in Fig. 2. Larger lift force helps the hydrofoil with upwind camber to sweep a larger area and to extract more energy per swing cycle. Above analysis illustrates the direct reason for the better energy extraction performance of the upwind camber. In a word, the pitching amplitude has significant effect on the energy extraction performance, and the hydrofoil with upwind camber can help to produce larger effective AOA and thus better energy extraction performance. To further understand the camber effect, we need to explore the torque development in a swing cycle. Fig. 10 presents the variations of the effective AOA and torque in one swing cycle. As shown, the angular velocities reach maximum value near L1, meanwhile the aerodynamic torques Mq also reach the local extremum. The aerodynamic torque and spring torque will suppress the pitching motion so that the hydrofoils begin to decelerate after L1. As the absolute value of effective AOA decreases, the aerodynamic torques change direction in a short time, and the aerodynamic torque will offset some spring torque then. Although the hydrofoils are decelerating, the deceleration is slowing down due to increasing aerodynamic torque. During second phase, the aerodynamic torque for the upwind camber is much larger than that for the downwind camber most time, while their spring torques almost equal to each other. Larger aerodynamic torque in second phase helps to produce positive effective AOA. As shown in Fig. 10, after the effective AOA for upwind camber reaches 0 , the aerodynamic torque is still strong to offset the spring torque so that the hydrofoils with upwind camber can obtain a positive effective AOA during second phase (see Fig. 8). In conclusion, the hydrofoil with upwind camber has larger aerodynamic torque to produce positive effective AOA and thus achieves higher energy extraction performance. In Fig. 11, we qualitatively analyze how upwind camber produce beneficial aerodynamic torque. The dash lines indicate the initial state of the hydrofoils, the solid lines indicate the present state of the hydrofoils, and the red vectors indicate the simplified aerodynamic forces. As shown, the hydrofoil with upwind camber undergoes clockwise rotation from the equilibrium position to present state, while the hydrofoil with downwind camber undergoes anticlockwise rotation from the equilibrium position to present state. The aerodynamic forces in present state generate clockwise torque on both hydrofoils, which will promote the clockwise rotation of the hydrofoil with upwind camber but suppress the anticlockwise rotation of the hydrofoil with downwind camber. Above explanation agrees well with our finding. It is

Fig. 10. Variations of the effective AOA and torque in one swing cycle.

very hard for the hydrofoil with downwind camber to generate positive effective AOA in second phase or to reach a maximum pitching angle of 90 . In contrast, it is easy for the hydrofoil with upwind camber to generate a very large pitching amplitude. Besides, the pitching amplitude increases with the upwind camber height, and the pitching amplitude can even exceed 180 with a large camber height. If we do not limit the pitching amplitude for upwind camber, the overlarge pitching amplitude may become a detrimental factor for energy extraction performance. We will use a pitching damper with critical pitching angle to further control the pitching motion in the next section. 3.2. Effect of pitching damper It is found that the hydrofoil with upwind camber can produce larger pitching amplitude, but overlarge pitching amplitude may bring adverse effect on the energy extraction performance. We explore the effect of critical pitching angle on the energy extraction performance in this section. The definition of critical pitching angle is in Formula (2). A very large damper is placed in the pitching direction. The damping factor is so large that the angular velocity decelerates to zero immediately when the pitching angle exceeds the critical pitching angle. Fig. 12 presents the variations of energy extraction efficiency and power coefficient with critical pitching angle at R ¼ 6, hr ¼ 0.27 and za ¼ 30. The maximum efficiency (0.24) and the maximum power coefficient (0.77) are both observed at qc ¼ 143 . Note that the pitching amplitude will exceed 180 without the pitching damper and the critical pitching angle greater than 180 is not taken into consideration in this work. From Fig. 12, we conclude that limiting the pitching amplitude has significant effect on the energy extraction performance, and the use of pitching damper can control the pitching motion and thus affect the energy extraction process. The motion trajectories and the fluid forces for the hydrofoils with qc ¼ 143 and qc ¼ 172 are presented in Fig. 13. The motion pattern for qc ¼ 143 is similar with that in Fig. 8(b), but the swept area and the lift force in second phase are much larger in Fig. 13(a). The motion patterns are completely different between Figs. 13(a) and 12(b). In Fig. 13(a), the hydrofoil rapidly rotates in first phase and undergoes approximate translational motion in second phase. The maximum drag force appears at the end of the motion trajectory. In Fig. 13(b), we cannot find two distinct phases as we did in Figs. 8 and 13(a). The hydrofoil rotates throughout the swing cycle so that the second phase where the hydrofoil keeps a constant angle of attack disappears. The maximum drag force is observed at the middle of the motion trajectory, and the motion trajectory is much more symmetric which leads to a more symmetric lift force distribution in one stroke. Fig. 14 presents the variations of the effective AOA and lift force in one swing cycle for qc ¼ 143 and qc ¼ 172 at R ¼ 6, hr ¼ 0.27 and za ¼ 30. The hydrofoils undergo upstroke in the first half cycle and downstroke in the second half cycle. We can find that the effective AOA for qc ¼ 172 changes with time in a sinusoidal form, while the effective AOA for qc ¼ 143 has a flat top and a flat bottom as indicated by the gray areas. Besides, the phases for these two critical pitching angle are also different. Obviously, the flat top and bottom are caused by the pitching damper, leading to totally different lift force variations as shown in Fig. 14. In the gray area, the effective AOA for qc ¼ 143 almost keeps constant and the actual pitching angle is locked near the critical pitching angle. In the first gray area, the lift force keeps relatively high and positive value, and the direction of the lift force is consistent with the motion direction of the hydrofoil, which guarantees strong and stable power output. As mentioned before, the hydrofoil mainly extracts energy in

W. Jiang et al. / Energy 115 (2016) 1010e1021

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Fig. 11. Schematic of hydrofoil motion and aerodynamic force for different camber direction.

Fig. 12. Variations of energy extraction efficiency and power coefficient with critical pitching angle.

AOA for a long time. Judging from Fig. 14, this optimum effective AOA is near 70 in our study. When the critical pitching angle is too large, the actual AOA can only stay near the optimum AOA for a short time as shown in Figs. 13(b) and 14, so the second phase becomes very short. All above explain why overlarge pitching amplitude is detrimental and why the pitching damper can help to improve the energy extraction performance. In a word, the best pitching damper forces the actual AOA stay near the optimum AOA for a long time. The high and stable lift force during this time maximizes the power output, resulting in high efficiency and power coefficient. We analyzed the effect of the camber and critical pitching angle on energy extraction performance in Section 3.1 and 3.2. From our analysis, we can note that both the camber and critical pitching angle affect the energy extraction performance by controlling the pitching motion. The camber can help to produce larger pitching

Fig. 13. Diagram of the hydrofoil motion indicating the magnitude and orientation of the force vectors throughout the stroke; R ¼ 6, hr ¼ 0.27 and za ¼ 30.

second phase. The critical pitching angle of 143 helps to extend the second phase in time and space. As for the critical pitching angle of 172 , we can hardly find a distinct second phase from the lift force variation. We infer that there exists an optimum angle of attack to produce largest lift force and best energy extraction performance, and the pitching damper can lock the actual AOA to this optimum

angle, while the critical pitching angle limits and locks the pitching angle. The variation of the pitching angle is the key factor in energy extraction. Our fully passive power generator uses the shedding vortex to drive the pitching motion of the hydrofoil and utilizes the camber and pitching damper to control the pitching motion passively.

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Fig. 14. Variations of the effective AOA and lift force in one swing cycle.

3.3. Effect of arm length Arm length will affect the cost of the actual energy extraction device. In the actual design, we prefer using shorter arm length to save material and to increase the structural strength. Longer arm length means smaller swing angle and thus stronger magnetic field to offer enough damping factor. Besides, in the dual configuration, the arm length can affect the energy extraction performance of the hydrofoil downstream. So it is very necessary to study the effect of arm length in consideration of engineering practice. We obtain a rough optimal camber (0.27) and an optimal critical pitching angle (143 ) in last two sections. We consider the effect of arm length with these two optimal parameters in this section. Fig. 15 presents the variations of h and CP with arm length and swing damping factor at qc ¼ 143 and hr ¼ 0.27. The trends of h and CP for different arm length are similar and obvious. For each R there exists different optimal za for the maximum h and CP and the increasing R induces an increase in the optimal za. It is easy to understand the variation of the optimal za. With the increase of R, the swing amplitude and swing angular velocity decrease, hence a larger za is needed to guarantee same power output. What's more, the maximum h and CP for different R do not vary much. The maximum h decreases slightly with R, while the maximum CP increases slightly with R. From the data in Fig. 15, the maximum h is

0.285 and is observed at R ¼ 3 and za ¼ 15 and the maximum CP is 0.8 and is observed at R ¼ 8 and za ¼ 45. It is also found that the increasing za has different effect on h and CP, and the optimal za for h is larger than the optimal za for CP. According to the expressions of h and CP, we know that these differences are due to the variation of the swept area d. Considering the actual engineering applications, we may prefer the energy extraction device to extract more energy from the flow but not to achieve the best efficiency. The effect of camber, critical pitching angle and arm length have been investigated for upwind arm configuration so far. Detailed examination of the evolving flow structure around the hydrofoil can help to understand the energy extraction mechanism of our fully passive power generator. Fig. 16 presents six images of the vortices fields and velocity vectors in the upstroke at qc ¼ 143 , hr ¼ 0.27, R ¼ 8 and za ¼ 45. The arrow directions indicate the orientation of local fluid velocity. It is observed that several vortexes occur in first phase. These vortexes are caused by the rapid rotation of the hydrofoil. A vortex is about to detach from the trailing edge at t ¼ 0T. This vortex reaches its highest strength and detaches from the trailing edge between t ¼ 0T0.1T. Two new vortexes of different direction generate near the leading edge and one new vortex appears near the trailing edge at t ¼ 0.1T. All three vortexes detach from the hydrofoil between t ¼ 0.1Te0.2T. Four vortexes form and detach in the first stage of the upstroke. After that is the second phase. The hydrofoil moves upward in a stable way at t ¼ 0.3T, and a vortex forms near the leading edge on the suction surface. This vortex produces a low pressure area above the suction surface, leading to a large lift force. Afterward, several vortexes detach from the suction surface successively. Compared with the hydrofoil without camber, the hydrofoil with camber produces more complicated vortexes. We infer that the camber is beneficial to the formation and detachment of vortex, and the reason is the camber changes the angle of attack dramatically. As shown in Fig. 16(d), the angle of attack is very close to 90 , and the angle of attack is so large that the leading edge vortex is very easy to generate and detach. Leading edge vortex generation and shedding are believed to play a significant role in power generation flapping hydrofoil generator [34]. This conclusion can be also reached in our work. 3.4. Downwind arm configuration Fig. 2 presents the diagram of the upwind arm configuration and downwind arm configuration. The upwind arm configuration has

Fig. 15. Variations of energy extraction efficiency and power coefficient with arm length and swing damping factor at qc ¼ 143 and hr ¼ 0.27.

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Fig. 16. The evolution of vorticity fields and velocity vectors in the upstroke at qc ¼ 143 , hr ¼ 0.27, R ¼ 8 and za ¼ 45.

been studied in previous three sections. Same approaches are adopted to study the downwind arm configuration. Fig. 17 shows the variations of energy extraction efficiency and power coefficient with relative camber height for downwind arm at R ¼ 6, qc ¼ 143 and za ¼ 25. Similar phenomenon is found in the downwind arm configuration. The efficiencies and power coefficients for upwind cambers are much higher than that for downwind camber. Moreover, even slight downwind camber cannot obtain stable power output, so only the h and CP for upwind camber are shown in Fig. 17. Comparing Fig. 7 with Fig. 17, we can find that the h and CP for upwind arm are obviously higher than the downwind arm, and the variations of h and CP for downwind arm are more complicated. As we did before, the hr corresponding to the highest CP (0.08) is used to study the effect of critical pitching angle. Fig. 18 presents the variations of h and CP with qc for downwind arm at R ¼ 6, hr ¼ 0.08 and za ¼ 25. As shown, the h and CP increase with qc less than 2.4, and do not change much with qc greater than 2.4. It is hard to find a predominant qc for the downwind arm configuration to obtain the maximum h and CP. The variations of h and CP with arm length and swing damping factor for downwind arm at qc ¼ 138 and hr ¼ 0.08 are presented in Fig. 19. The trends of h and CP for downwind arm configuration

Fig. 17. Variations of energy extraction efficiency and power coefficient with relative camber height for downwind arm at R ¼ 6, qc ¼ 143 and za ¼ 25.

are different from those for upwind arm configuration (see Fig. 15). The h suddenly decreases to a low value after h reaches its maximum value and CP also suddenly jumps to a very low value. For

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Fig. 18. Variations of energy extraction efficiency and power coefficient with critical pitching angle for downwind arm at R ¼ 6, hr ¼ 0.08 and za ¼ 25.

each R there exists different optimal za for the maximum h and CP, and the increasing R induces increasing optimal za. The maximum h for different arm length are close. As for CP, the maximum CP increases with R when the arm length is too short, while the maximum CP stops increasing with arm length long enough. From the data in Fig. 19, the maximum h is 0.226 and is observed at R ¼ 8 and za ¼ 95 and the maximum CP is 0.655 and is observed at R ¼ 10 and za ¼ 90. In conclusion, the effects of the camber, critical pitching angle on the energy extraction performance are much more complicated in the downwind arm configuration. What's more, the h and CP for the downwind arm are significantly less than those for the upwind arm, which can be qualitatively explained in Fig. 20. As shown, the drag force on the hydrofoil with upwind arm always pushes the hydrofoil away from the middle position, while the drag force on the hydrofoil with downwind arm always pulls the hydrofoil back to the middle position. Therefore, the drag force on the hydrofoil with upwind arm can promote the oscillation of the hydrofoil, while the drag force on hydrofoil with downwind arm will suppress the oscillation. In this way, the upwind arm configuration achieves better energy extraction performance. The results and findings in this paper can provide some guidance for the design of further fully passive energy extraction device. Without any motor or actuator, the promising power generator can

Fig. 20. Schematic of the drag force on hydrofoils with upwind arm and downwind arm.

achieve satisfactory energy extraction performance. However, there still are some limitations in this new concept. The power generator can only achieve the best performance at optimal swing damping factor, so an adjustable swing damper is suggested to adopt in engineering application. Besides, the output power is not constant in one cycle, so special regulator is needed to transfer the fluctuant power to constant power.

4. Conclusions A fully passive oscillating hydrofoil for energy extraction has been proposed and numerically tested in present study. The pitching motion of the hydrofoil is driven by the shedding vortexes downward the hydrofoil, meanwhile the hydrofoil is swinging on an arm. The effects of camber, critical pitching angle, arm length and swing direction on the energy extraction performance are investigated at a chord Reynolds number of 1100. The study of camber effect reveals that the hydrofoils with upwind camber obtain better energy extraction performance over the hydrofoils without camber or with downwind camber, and there exists an optimal camber height for energy extraction. The best relative camber height is 0.27 for upwind arm configuration. The

Fig. 19. Variations of energy extraction efficiency and power coefficient with arm length and swing damping factor for downwind arm at qc ¼ 138 and hr ¼ 0.08.

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upwind camber can help the hydrofoil to produce higher pitching amplitude, and thus higher lift force and energy extraction efficiency. The upwind camber can generate beneficial torque on the hydrofoil to promote the pitching motion, which explains how the upwind camber affect the energy extraction process in a positive way. Overlarge pitching amplitude is found to be unfavorable to the energy extraction performance. So a pitching damper with critical pitching angle is utilized to further control the pitching motion. The study on the effect of critical pitching angle shows that the optimal pitching damper forces the actual angle of attack stay near the optimum angle of attack for a long time, during which the large and stable lift force maximizes the power output, resulting in higher efficiency and power coefficient. The best critical pitching angle is 143 for upwind arm configuration in our study. With the optimal camber height and critical pitching angle, we then study the effect of arm length for the upwind arm configuration. The results indicate that the effect of arm length on the maximum energy extraction efficiency and power coefficient is not so profound as other parameters in our study. But the arm length has significant effect on optimal swing damping factor, and longer arm length always leads to a larger optimal swing damping factor. Above all, the power generator can reach maximum power coefficient of 0.8 and energy extraction efficiency of 0.285 with the best configuration. At last, the effect of arm direction is studied. The energy extraction performance for the downwind arm is significantly worse than that for the upwind arm. The reason is that the drag force on the hydrofoil with upwind arm can promote the oscillation of the hydrofoil, while the drag force on the hydrofoil with downwind arm will suppress the oscillation. The power generator based on semi-active flapping hydrofoil can achieve a relatively high power coefficient and efficiency, but it has relatively high maintenance demand, less robustness and high life cycle cost. The vortex induced vibration aquatic clean energy (VIVACE) converter has low maintenance demand, being robust and less costly, but the energy extraction efficiency is relatively low. The present study provides a new method to drive the pitching motion of oscillating hydrofoil just lie the VIVACE devices using VIV to drive the plunging motion, and proposes a fully passive power generator based on oscillating hydrofoil. This work merges the developing routes of these two concepts to some extent, and absorbs the advantages from both sides. References [1] Bryden I, Grinsted T, Melville G. Assessing the potential of a simple tidal channel to deliver useful energy. Appl Ocean Res 2004;26(5):198e204. [2] Laws ND, Epps BP. Hydrokinetic energy conversion: technology, research, and outlook. Renew Sustain Energy Rev 2016;57:1245e59. [3] Lago L, Ponta F, Chen L. Advances and trends in hydrokinetic turbine systems. Energy Sustain Dev 2010;14(4):287e96. [4] McKinney W, DeLaurier J. Wingmill: an oscillating-wing windmill. J Energy 1981;5(2):109e15. [5] Lu K, Xie Y, Zhang D. Nonsinusoidal motion effects on energy extraction performance of a flapping foil. Renew Energy 2014;64:283e93.

1021

[6] Jones K, Platzer M. Numerical computation of flapping-wing propulsion and power extraction. AIAA Pap 1997;97:08e26. [7] Davids ST. A computational and experimental investigation of a flutter generator. Monterey, California: Naval Postgraduate School; 1999. [8] Dumas G, Kinsey T. Eulerian simulations of oscillating airfoils in power extraction regime. Advances in fluid mechanics VI. 2006. p. 245. [9] Kinsey T, Dumas G. Parametric study of an oscillating airfoil in a powerextraction regime. AIAA J 2008;46(6):1318e30. [10] Xiao Q, Liao W, Yang S, Peng Y. How motion trajectory affects energy extraction performance of a biomimic energy generator with an oscillating foil? Renew Energy 2012;37(1):61e75. [11] Kinsey T, Dumas G. Optimal operating parameters for an oscillating foil turbine at Reynolds number 500,000. AIAA J 2014;52(9):1885e95. [12] Zhu Q, Peng Z. Mode coupling and flow energy harvesting by a flapping foil. Phys Fluids 2009;21(3):033601. [13] Huxham G, Cochard S, Patterson J. Experimental parametric investigation of an oscillating hydrofoil tidal stream energy converter. Conference Experimental parametric investigation of an oscillating hydrofoil tidal stream energy converter. [14] Young J, Ashraf M, Lai J, Platzer M. Numerical simulation of flow-driven flapping-wing turbines for wind and water power generation. Conference Numerical simulation of flow-driven flapping-wing turbines for wind and water power generation. p. 5e9. [15] Young J, Ashraf MA, Lai JC, Platzer MF. Numerical simulation of fully passive flapping foil power generation. AIAA J 2013;51(11):2727e39. hut A, Viarouge P, et al. Prototype [16] Kinsey T, Dumas G, Lalande G, Ruel J, Me testing of a hydrokinetic turbine based on oscillating hydrofoils. Renew Energy 2011;36(6):1710e8. [17] Peng Z, Zhu Q. Energy harvesting through flow-induced oscillations of a foil. Phys Fluids (1994-present) 2009;21(12):123602. [18] Zhu Q. Energy harvesting by a purely passive flapping foil from shear flows. J Fluids Struct 2012;34:157e69. [19] Limited TEB. Research and development of a 150 kW tidal stream generator. Crown Copyright2002. [20] Paish M, Giles J, Panahandeh B. The pulse stream concept, and the development of the pulse stream demonstrator. Conference The pulse stream concept, and the development of the pulse stream demonstrator. [21] Platzer M, Sarigul-Klijn N, Young J, Ashraf M, Lai J. Renewable hydrogen generation using sailing ships. Conference Renewable hydrogen generation using sailing ships, vol. 4. p. 1119e25. [22] Bernitsas MM, Raghavan K, Ben-Simon Y, Garcia EMH. VIVACE (vortex induced vibration aquatic clean energy): a new concept in generation of clean and renewable energy from fluid flow. J Offshore Mech Arct Eng 2008;130(4): 041101. [23] Bernitsas MM, Ben-Simon Y, Raghavan K, Garcia E. The VIVACE converter: model tests at high damping and Reynolds number around 105. J offshore Mech Arct Eng 2009;131(1):011102. [24] Barrero-Gil A, Alonso G, Sanz-Andres A. Energy harvesting from transverse galloping. J Sound Vib 2010;329(14):2873e83. [25] Narendran K, Murali K, Sundar V. Investigations into efficiency of vortex induced vibration hydro-kinetic energy device. Energy 2016;109:224e35. [26] Young J, Lai JC, Platzer MF. A review of progress and challenges in flapping foil power generation. Prog Aerosp Sci 2014;67:2e28. [27] Kloos G, Benitez Z, Gonzalez CA. The BioWAVE and BioSTREAM test unit. Conference The BioWAVE and BioSTREAM test unit. [28] Kloos G, Gonzalez C, Finnigan T. The bioSTREAM tidal current energy converter. Conference The bioSTREAM tidal current energy converter. p. 426e33. [29] Karbasian HR, Esfahani JA, Barati E. The power extraction by flapping foil hydrokinetic turbine in swing arm mode. Renew Energy 2016;88:130e42. [30] Bos FM, Lentink D, Van Oudheusden B, Bijl H. Influence of wing kinematics on aerodynamic performance in hovering insect flight. J fluid Mech 2008;594: 341e68. [31] Ashraf MA, Young JS, Lai JC, Platzer MF. Numerical analysis of an oscillatingwing wind and hydropower generator. AIAA J 2011;49(7):1374e86. [32] Simpson BJ. Experimental studies of flapping foils for energy extraction. Massachusetts Institute of Technology; 2009. [33] Xie Y, Lu K, Zhang D. Investigation on energy extraction performance of an oscillating foil with modified flapping motion. Renew Energy 2014;63:550e7. [34] Xiao Q, Zhu Q. A review on flow energy harvesters based on flapping foils. J Fluids Struct 2014;46:174e91.