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Drag-type cross flow water turbine for capturing energy from the orbital fluid motion in ocean wave

Hiromichi Akimoto1, Kenji Tanaka2 and YongYook Kim3 1 Division of Ocean Systems Engineering, Korea Advanced Institute of Science and Technology 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, Republic of Korea

2 Department of Systems Innovation, Graduate School of Engineering, The University of Tokyo 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

3 KAIST Ocean Technology Center (KOTC), Korea Advanced Institute of Science and Technology 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, Republic of Korea

akimoto@kaist.ac.kr

Abstract. Since the energy of ocean wave exists mostly near the water surface and decreases exponentially with depth, the resource of wave energy is measured in the line density unit (kW/m). Therefore, in the scaling up of a wave energy converter, the captured wave energy increases slowly in proportion to the wave front width of the device while its cost tends to increase in a pace faster than the square of device size. To overcome the problem, the authors propose a drag type cross flow water turbine with its rotational axis lying horizontally and parallel to the wave front. Since the device will be light-weight and linearly extendable in the wave front direction, the larger (longer) converter can obtain the merits of scale for higher economic performance. The shape of proposed turbine is not axisymmetric for directly utilizing the orbital fluid particle motion in wave. The basic unit of the device is compact and the diameter of turbine is in the order of wave height. Two-dimensional flow simulation of the device in regular wave demonstrates the mechanism of the turbine and provides its preliminary performance prediction.

Keywords Rotational wave energy converter; cross flow turbine; single bucket wave turbine; orbital fluid particle motion; OpenFOAM; Savonius turbine

1. Introduction Wave energy is one of the most hopeful renewable energy resources available in the ocean. However, its commercial utilization has not been successful yet. At present, intensive sea-trials of full scale wave energy converts (WECs) are going on in Europe (EMEC [1] and Marinet [2]). Some of the concepts being tested may reveal their economic feasibility in the future applications.

The major concepts of WEC can be categorized into three types (Falcão [3]). They are (a) oscillating water column (OWC) with air turbine, (b) oscillating body utilizing heave, sway and/or pitch motions, and (c) wave overtopping type converter. All the three categories have both floating and bottom-fixed (or mounted on a quay) applications.

One of the difficulties of wave energy utilization comes from the characteristics of wave energy distribution. Unlike wind and water current, the wave energy flux is concentrated near the water surface

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and its density decreases exponentially with the depth from the water plane. Therefore, the wave energy resource is measured in the line density unit, i.e. kW/m. It indicates that the energy coming to a WEC is proportional to its wave front width. On the other hand, the output gain by increasing the water draft of converter is limited to a certain level because of the rapid decay of wave energy in the depth direction. The condition is quite different from that of wind and marine current energy utilization where the output is proportional to the square of device size (swept area of the device). The simple scaling-up of a WEC is beneficial when the larger device is installed in the severer (higher wave) site. However, the authors’ intention is to maximize the economy of wave energy conversion in the given sea state.

The OWC type converter and wave overtopping type converters require a water column chamber and water reservoir respectively. Their component costs are expected to increase with size in a pace faster than proportional to the size squared. The oscillating body type converters can utilize the high wave load on the floating/submerged bodies. However, one drawback of the idea is that at least one of the components must be massive or anchored to seabed to obtain the relative oscillatory motion between components for driving the connected generator. Reducing the cost of massive components is not an easy task.

The line density distribution of wave energy flux indicates the advantage of linearly extendable devices in wave front direction. An example is Salter’s Duck (Edinburgh Duck) invented by Salter [4]. In the concept, the output increases with the number of Duck units (pitching wave converter) connected to the spine shaft. In this linearly extendable design, the device cost will be linearly proportional to the wave front width. The total cost will be slightly less than proportional to the output by sharing the costs of anchor and transmission among the long multiple devices. The other approach is to add reflectors which increase the effective wave front width of the device and guide the collected wave power to a relatively small power take-off (PTO) unit. For example, WaveDragon receives wave power by wide reflectors which increase the wave height at the wave overtopping type PTO unit (Kofoed et al. [5]).

On the contrary, the reduction of wave front width can be an effective design if the survivability and long life of device in high wave sites are emphasized. Its example is the Pelamis concept which has snake like slender body stretched in the wave direction and has narrow wave front width (Handerson [6]).

With the above considerations take into account, the authors propose a new concept of rotational WEC. It is a drag-type cross flow turbine to be installed near the water plane supported by a float system. Its rotational axis is horizontal and parallel to the wave front so that the device is linearly extendable in the wave front direction. The rotational WEC can be compact and light-weight without massive components to achieve high economic performance. This paper describes the concept and the preliminary numerical flow simulation of the two-dimensional turbine in regular wave.

2. Single bucket turbine

2.1. Rotational wave energy converter Fluid particles in ocean wave show the orbital motion as shown in Fig. 1. The diameter of orbital path is in the order of wave height � near the water surface. The orbit decays in size and becomes elliptic with submergence. Direct utilization of the orbital motion reduces the cost of WEC because the reaction torque of generator can be easily absorbed by a small float system. In addition, the rotational motion simplifies the mechanism of converter.

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Figure 1. Orbital motion of water particles in wave

There are some researches of the cross flow turbine for wave energy conversion. Faizala et al. [7]

and Zullah et al. [8] tested the performance of a Savonius water turbine in wave and demonstrated the torque generation of their turbine in numerical simulations and experiments. Since their turbine is installed at the inlet of oscillating water column, it is the PTO system of the OWC type converter. Hindasageri et al. [9] tested the performance of Savonius rotor in shallow water wave condition. The rotational speed of their turbine is higher than that of orbital fluid particle motion. It indicates that the turbine is converting the kinetic energy of water flow in wave and not the orbital fluid particle motion.

Savonius turbine is categorized into the drag type vertical axis turbine because its rotational axis is in the vertical position in most of the wind turbine applications. However, the authors use the term “cross flow turbine” instead of vertical axis turbine for avoiding confusions because the rotational axis is horizontal in the wave energy applications in this study.

Siegel et al. [10, 11] proposed a lift-type cross flow turbine (cycloidal turbine) for wave energy conversion and demonstrated the cancellation of incident wave by the turbine. In their theory, the maximum efficiency of the turbine is more than 99% in inviscid flow condition. Jeans et al. [12] demonstrated the absorption of wave energy by the cycloidal turbine synchronized to the wave period in water tank experiments. They showed that the efficiency in irregular wave is 77%. One challenging feature of the concept may be its large diameter of turbine, which is λ/π in the optimized setting.

2.2. Single-bucket turbine The authors chose the drag-type cross flow turbine because its performance is not sensitive to the surface quality of turbine blade (or bucket). It is important in the warm water of East Asian seas because of the rapid accumulation of marine growth there. For example, Kyozuka et al. [13] reported that the uncoated blades of their model marine current turbine were fully covered by marine growth in two months of experiment in summer in Japan. The measured water temperature in the test was 22 ∼ 27°C. In such a condition, the lift-type cross flow turbines require frequent cleaning of blades to keep their performance.

Although fluid particles are in orbits in ocean wave, the flow field is irrotational as it is described in the wave velocity potential. The orbits do not have a single center of rotation as shown in Fig. 1. Therefore, if we install a Savonius turbine in the flow, the fluid particles around the two buckets have different centers of orbit as shown in Fig. 2 (left). Since the turbine diameter is practically small in comparison to the wave length, the two buckets are in almost the same phase of flow. In this case, the torque of turbine comes only from the small difference between the drags of two buckets.

Water depth

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Figure 2. Wave loads on a small Savonius turbine (left) and single-bucket turbine (right)

A simple method to increase the torque is to remove one of the two buckets and replace it by a

streamlined counter weight as shown in Fig. 2 (right). The hydrodynamic force on the counter weight is negligible in comparison to that on the bucket. With a torque control, the turbine rotation can be synchronized with the incident wave and provides torque in all the phase of rotation as shown in Fig. 3. In this concept, the turbine diameter is in the order of wave height.

Figure 3. Rotation sequence of the single bucket wave turbine

(Solid blue lines indicate the water surface)

The synchronization is by the load control of generator. If the power take-off is turned off, the turbine is in free rotation as shown in Fig. 4a. The bucket sways backward relative to the instantaneous flow direction and does not provide significant torque. By increasing the load on generator, the bucket rises against the flow direction to a certain angle as shown in Fig. 4b, where the turbine torque balances with the reaction torque of PTO system. The maximum output is available when the bucket keeps the right angle to the instantaneous flow direction by the proper control of generator load. In storm condition, the free rotating position will be used for reducing the wave load on the bucket. It is equivalent to the feathering position of wind turbine.

Figure 4. Schematic drawing of the load control of turbine; (a) free rotation without power take-off

and (b) assumed right angle position by load control

2.3. Analytical model of the turbine The authors provide a simplified model of the wave turbine for explaining the concept. The coordinate system of the model is shown in Fig. 5a. The wave elevation � and flow velocity � are given in the Airy wave theory as

A

B

A

(a) (b)

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�(�, �) = � cos��� − �, (1)

�(�, �, �) = ��, = �� ����������

� ���cos��� − � , � � ��������

� ���sin��� − ��. (2)

Here, �(= �/2) is the wave amplitude, the angular frequency of incident wave, � (= 2�/�) the

angular wave number, � the wave length, and ℎ the water depth. Velocity components � and are in the wave direction and in the vertical upward direction respectively.

(a) (b) Figure 5. Coordinate system; (a) turbine and wave; (b) shape of the present turbine (� = �/2)

The bucket rotates in synchronization with the incident wave. The position of bucket center is

�� = ���, �� = �� sin� , � cos� − �, � = � + �� . (3)

Here, � is the azimuth angle of the turbine from the top position and �� is the phase difference of turbine from that of incident wave at � = 0. The center of turbine �� is on the �-axis with submergence � from the still water plane.

For simplicity, we assume that the radius of turbine is small in comparison to the wave length �. It indicates that the difference of wave phase inside the turbine radius is negligible. The phase difference �� is zero in the present configuration. The orbits of fluid particles are approximately circular if sufficiently deep water is assumed. Then, the flow velocity around the bucket �� and the velocity of rotating bucket �� are

�� = �� cos� , −� sin� and �� = �� cos� , −� sin�, (4)

respectively. The bucket motion is similar to the orbital excursion of water particles. It provides torque when the relative tangential flow speed (� − �) is positive. The drag of bucket � and the torque of turbine � are

� = �� �

���� − ����, � = �� �

���� − ����� (� > �). (5)

Here, �� is the drag coefficient of the bucket, � the chord length of bucket, and � the density of water. When the wave amplitude is less than the rotational radius of the turbine, the assumed synchronization is not attainable because of the negative torque. In the condition, the turbine will be in slow unsynchronised rotation with intermittent torque or in an oscillatory motion like a pitching wave converter. The condition is not of interest in the present research.

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Since wave energy flux is the product of wave energy density � �=�

������ and the wave group

speed ��, the efficiency of the converter is written as

� =��

���=

���

�����⋅��

. (6)

The phase velocity �� and the group velocity �� in the Airy wave model are given as

= �� tanh �ℎ, �� = /�, �� = �� �

��1 + �ℎ

������� �

������. (7)

Therefore, the efficiency of converter becomes

� = 2�� �1 −

�� ���� ⋅ tanh �ℎ ⋅ �1 + �ℎ

������� �

����� ���

. (8)

In the present study, the authors use a bucket of the typical Savonius turbine as shown in Fig. 5b. In

this shape, the center of bucket rotates in the radius of � = �/2 and the diameter of turbine ! = 2�. The torque and the efficiency of the turbine are

� = �� �

!��� �� −

�

����, (9)

� = �� �1 −�

��� ���� ⋅ tanh �ℎ ⋅ �1 + �ℎ

������� �

����� ���

. (8’)

However, the simplified model above is valid only when the turbine size is small and the variation

of orbital flow speed in � direction is negligible. For capturing the considerable energy, the turbine cannot be small and the orbital flow speed around the bucket varies in a rotation according to its changing distance from the free surface.

In addition, the bucket is in a shear flow. The tangential flow speed decreases with radial distance from the rotational axis and the periodic flow acceleration provides inertia force. However, the hydrodynamic drag force of the bucket in such a complex condition has not been understood sufficiently yet. The complexity is shown in the numerical simulation in Section 3.

2.4. Limitations of the concept Since the rotational speed of turbine is adjusted to the incident wave, the device is applicable to wide range of wave period/length. However, the mechanism is based on the assumption that there is a dominant peak in the wave power spectrum for adjusting the rotation. In other words, it will not work in the fully irregular wave condition. This will restricts the installation sites of this concept. The degraded performance in the non-monotonic wave spectrum should be checked in the future study. Also, the device will not rotate when the wave amplitude is less than “cut-in wave height”. With this condition taken into account, the diameter of turbine should be optimized for maximizing its economy in the specific wave condition of the installation site.

3. Simulation of the flow around the turbine

3.1. Flow simulation method The authors conduct the two-dimensional (2D) computational fluid dynamics (CFD) simulation for checking the basic mechanism of the turbine. The simulation is based on OpenFOAM 2.2.0 [14]. The employed solver is waveDyMFoam which is the combination of pimpleDyMFoam (solver for unsteady multi-phase flow with dynamic mesh treatment) and waves2Foam (wave function and boundary

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treatment library [15]). The rotating turbine is modeled by the Arbitrary Mesh Interface (AMI) treatment (sliding mesh) of OpenFOAM.

(a)

(b)

(c)

Figure 6. Computational mesh; (a) overall computational domain (b) computational mesh and (c) close up view of the mesh around the turbine

Figure 6 shows the computational mesh of the simulation. The simulation condition is for the

laboratory scale experiment. The size of computational domain is �9m � � � 9m in the horizontal direction, water depth � is1.00m, and air draft is 0.6m. The wave length is 5.22m. The diameter of turbine � is 0.20m (the chord length of the bucket is0.10m) and the diameter of rotating domain containing the turbine is 1.4� which appears as a black circle in Fig. 6a. Relaxation zones of 5m length are in the inlet and outlet part of the domain for removing the wave reflection on the boundaries. The mesh generation is by the snappyHexMesh utility of OpenFOAM. It provides local refinement on the hexahedral mesh as shown in Fig. 6c and the insertion of prism mesh around the body surface for the high resolution inside boundary layer. The number of control volumes is 31,666.

Figure 7 shows the sample pressure and the velocity fields around the turbine in a rotation cycle. In this condition the wave amplitude is equal to the bucket size�� � � and the submergence of the turbine axis is� � . The figure shows that the rotating bucket keeps the right angle to the local flow. The wave induced velocity is higher when the bucket is around the top and bottom positions because of the elliptic orbital motion.

Although the bucket is always submerged, the wave breaking phenomena creates air cavities, which are trapped in the bucket from time to time. In the absence of a current, the vortices shed from the bucket are staying around the turbine and add complexity to the flow field.

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Figure 7. Flow visualization around the rotating bucket in the condition� � � � ; the sampling interval Δ� � 0.4sec is equivalent to the azimuth angle intervalΔ� � 0.4π

Figure 8. Time histories of the hydrodynamic force (left), and the torque (right) in 5 wave periods�� � � � �

Figure 8 shows the time histories of the thrust, lift and torque coefficients. They are non-

dimensionalized by division by �

������� for the hydrodynamic force and by

�

�������� for torque.

The thrust and lift forces are in almost the same amplitude and phase. It indicates that the hydrodynamic force is mainly in the directions of azimuth angle� � π/4and5π/4. The torque shows two peaks in a wave period in the same timing of the peaks of hydrodynamic force. The second harmonic is due to the elliptic shape of the orbital path, symmetry-breaking effect of the free surface and the non-linear characteristics of real waves. When the bucket is near the horizontal position (� � π/2, 3π/2�, the torque vanishes because the relative flow speed to the rotating bucket is low.

-6

-4

-2

0

2

4

6

30 32 34 36 38 40

C

T

, C

L

Time [sec]

Thrust CT

Lift CL

Wave elvation phase

-1

-0.5

0

0.5

1

1.5

2

30 32 34 36 38 40

C

Q

Time [sec]

Torque CQ

Wave elvation phase

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Figure 9. Instantaneous streamlines around the bucket at azimuth angle � � 0° Irregularities in the time history come from the vortices shed from the bucket as shown in the

snapshot of Fig. 9. The newly created vortex around the outer edge and convex side of the bucket contributes to the torque. However, the distribution of vortices is not periodically stable and changes the pressure distribution on the convex side of the bucket. The figure also shows the acceleration of the flow around the outer edge of the bucket. The blockage effect by the bucket and free surface leads to the contraction and acceleration of the flow between them.

Figure 10. Flow visualization around the rotating bucket with smaller submergence;� � , � � 0.5 ; sampling interval 0.4sec is equivalent to the azimuth angle interval0.4π

Figure 10 shows the case of � � 0.5 as an example of low submergence condition. Although the convex side of the bucket appears on the free surface, the concave side (pressure side) of the bucket still keeps its submerged condition. In this case, the larger deformation of free surface enhances the low pressure on the convex side of the bucket. The increased peak of hydrodynamic force appears in the time histories of Fig. 11. However, the peak values also show the irregularity caused by the shed vortices.

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Figure 11. Time history of the hydrodynamic force (left) and the torque (right) of small submergence in 5 wave periods, � = �,� = 0.5�

Figure 12. Averaged torque coefficients in the variations of wave amplitude � and submergence �

Figure 12 shows the time averaged torque coefficient in the variations of wave amplitude � =

0.50� ∼ 1.25� and submergence � = 0 ∼ 1.5�. Among the tested conditions, the torque coefficient is in the maximum value of �" = 0.528 at the condition of submergence � = 0.75� and the wave amplitude � = 1.00�. The small torque at low submergence conditions is because the bucket is exposed to the air at wave troughs.

The maximum torque coefficient gives the efficiency e=3.57% in the condition. Although this is not high, it should be noted that the diameter of turbine is in the order of wave height and the diameter is 0.038� in the present simulation. The small size will be an advantage in the consideration of economic performance. The steepness (2�/�) of natural ocean wave is less than 1/15 because of the instability of steep wave. Therefore, the diameter of turbine is less than 0.067� of the targeted wave component. Also, if there is still significant wave motion beneath the turbine, we can install additional turbines in as shown in the schematic drawing of Fig. 13. In this design, the interference between turbines must be considered.

-6

-4

-2

0

2

4

6

20 22 24 26 28 30

C

T

, C

L

Time [sec]

Thrust CT

Lift CL

Wave elvation phase

-1

-0.5

0

0.5

1

1.5

2

20 22 24 26 28 30

C

Q

Time [sec]

Torque CQ

Wave elvation phase

0

0.1

0.2

0.3

0.4

0.5

0.6

0.00 0.25 0.50 0.75 1.00 1.25 1.50

Torq

ue c

oeffi

cien

t

Depth of turbine axis

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Figure 13. Installation of multiple turbines

4. Floating wave turbine configuration Although the present WEC can be mounted on a bottom fixed structure or on a quay, the configuration of floating application will be an interesting start point. Figure 14 shows a sample configuration of floating wave turbine system. Circular disks are on both ends of each bucket to keep two-dimensionality of the flow and to provide the base of counter weight. An electric generator can be installed on the float above the water as shown in Fig. 14a for easy maintenance access and reducing the device cost. The rim of rotating disk provides the first stage speed-up gear before the inlet shaft of PTO. The PTO requires coverings (not shown in the picture) and water proof of a certain level for protecting

the device from wave. However, the cost of electro mechanics will be lower than that of submerged type PTO system. The bucket will be made from sheet metal and have hollows to obtain buoyancy.

Expected influence of floating configuration to turbine performance is mixed one. The heave and surge motion of the device will reduce the relative flow speed to the bucket. However, with an adequate heave oscillation, the bucket can keep closer position to the free surface and receives high speed flow there. Also, the heave motion prevents the bucket from being exposed to air. The condition should be checked in the extended simulation and water tank experiment.

The turbine is extendable in the wave front direction as shown in Fig. 14b. The costs of mooring and O&M decrease slowly with the scale of deployment because these costs can be shared by multiple converters.

The other opportunity of cost reduction is the combination with other floating type renewable energy converters. For example, the combination with floating offshore wind turbine (Fig. 14c) or marine current turbine [16, 17] reduces the motion of WEC and the costs of shared components including the support structure, transmission and O&M.

Electric generator

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(a)

(b) (c)

Figure 14 Sample configuration of floating wave turbine; (a) basic unit, (b) turbine design extended in the wave front direction and (c) the combination with floating wind turbine concept

5. Conclusion The new concept of a rotary wave energy converter was introduced. The drag-type single-bucket cross flow turbine captures energy from the orbital fluid particle motion in wave. The device is mechanically simple and the turbine diameter is in the order of wave height. The cost of converter will be proportional to the span length of the turbine. The two-dimensional computational fluid dynamics simulation demonstrated the basic mechanism of the turbine in regular wave and provided its torque coefficient. The resultant efficiency 3.57% is not high in comparison to other existing WECs. However, it should be noted that the size of WEC is small. The authors expect that the high power/weight ratio of the turbine covers the low efficiency and its economic performance will be in a satisfactory level.

The present numerical analysis is limited to a wave flume condition of finite water depth. The influence of water depth, performance in the deep water wave, and control of the rotation speed should be checked in numerical and experimental approaches. Also, the degraded performance in the conditions of irregular wave, multi-directional wave and existence of water current will be considered for the detailed discussion of the economic performance in the future work.

Acknowledgement This research was supported by WCU (World Class University) program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (R31-2008-000-10045-0).

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