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COMPUTATIONAL ANALYSIS OF TIP-CLEARANCE-AFFECTED FLOW ON PERFORMANCE OF IMPULSE TURBINE FOR

WAVE ENERGY CONVERSION

A. Thakker* and T. S. Dhanasekaran†

Wave Energy Research Team, Department of Mechanical and Aeronautical Engineering University of Limerick, Limerick, Ireland

* Director, Wave Energy Research Team, University of Limerick, Limerick, Ireland † Research Engineer, Wave Energy Research Team, University of Limerick, Limerick, Ireland

ABSTRACT This paper depicts numerical analysis on impulse turbine with fixed guide vanes for wave energy conversion. From the previous investigations, it is found that one of the reasons for the mismatch between computed and experimental data is due to neglecting tip clearance effect. Hence, a 3-dimensional model with tip clearance has been generated to predict the internal flow and performance of the turbine. As a result, it is found that the comparison between computed and experimental data is good, quantitatively and qualitatively. Computation has been carried out for various tip clearances to understand the physics of tip leakage flow and effect of tip clearance on performance of such unconventional turbine. It is predicted that the turbine with 0.25% tip clearance performs almost similar to the case of without tip clearance for the entire flow coefficients. The designed value of 1% tip clearance has been validated numerically and computed that the efficiency of the turbine has been reduced around 4%, due to tip clearance flow at higher flow coefficients.

NOMENCLATURE lr chord length of rotor blade b height of blade rR mid span radius UR circumferential velocity at rR

va axial flow velocity z number of rotor blades φ flow coefficient ρ density of air

INTRODUCTION

For the last two decades, scientists have been investigating and defining different methods for power extraction from wave motion. These devices

utilize the principle of an Oscillating Water Column (OWC). OWC based wave energy power plants convert wave energy into low-pressure pneumatic power in the form of bi-directional airflow. Self-rectifying air turbines (which are capable of operating uni-directionally in bi-directional airflow) are used to extract mechanical shaft power, which is further converted into electrical power by a generator. There are two different kind of turbines are currently in use around the world for wave energy power generation, Wells turbine, introduced by Dr. A. A. Wells in 1976 and impulse turbine with self-pitch-control guide vanes by Setoguchi et al.1. This type of impulse turbine with self-pitch-control guide vanes has a disadvantage of maintenance of pivots on which the guide vanes are rotated automatically in a bi-directional air flow and therefore, the impulse turbine with fixed guide vanes has been investigated2. Both these turbines are currently in operation in different power plants in Europe, Canada, Australia and Asia on experimental as well as commercial basis. Currently, research around the world is focused on improving the performance of both these turbines under different operating conditions. There are few reports presented on the numerical analysis on impulse turbine with guide vanes. An optimal installation angle of the impulse turbine has been investigated by numerical and experimental analysis (Kim et al.1,2). The performance of the impulse turbine with unstructured grids and various turbulence models has been studied by Thakker et al.3. CFD analysis on CA9 Wells turbine has been made to validate the performance of the turbine and to analysis aerodynamics characteristics (Thakker et al.4). In all the earlier studies, tip clearance has not been incorporated in the numerical model. The tip leakage flow is one of the most prevalent and influential features of the flow through turbomachine rotors. In addition, the tip leakage flow is a phenomenon that is difficult to measure in most turbomachines. Computed effects of solidity on Wells turbine performance with tip clearance have been investigated (Watterson and

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Raghunathan5). The predicted effect of solidity on the turbine pressure drop, torque and efficiency are aftagreed qualitatively and quantitatively with the experimental data. Few authors (Raghunathan et al.6; Tagori et al.7; Raghunathan8) have been investigated the effect of tip clearance on the performance of Wells turbine experimentally and found that the turbine is very sensitive to tip clearance when compared to a conventional turbine. They have concluded that the decrease in tip clearance advances the stall but increases the cyclic efficiency as a result of reduced leakage losses. Also it has been proved that the turbine with a relatively large tip clearance could operate over a much wider range of flow rate range of flow rate without stalling. This paper describes the use of CFD method to investigate the performance of impulse turbine. The method employs structured grid, which allow inclusion of such features as the blade tip and casing treatments. The 3-D CFD model has been generated with tip clearance to validate the computed results with experimental data. The study has shown that the numerical method is able to predict with reasonable accuracy; the variations of pressure drop across the turbine rotor, torque and efficiency with flow coefficient, and the effect of tip clearance. An optimum tip clearance has been suggested where the effect of tip clearance is almost negligible. Furthermore, the design tip clearance (1mm) has been validated numerically.

REVIEW OF EXPERIMENTAL APPARATUS A schematic layout of the experimental rig of Wave Energy Research Team at University of Limerick is shown in Figure 1. It consists of a bell mouth entry, 0.6m test section with a hub-tip ratio of 0.6, drive and transmission section, a plenum chamber with honeycomb section, a calibrated nozzle and a centrifugal fan. Air is drawn into the bell mouth shaped open end; it passes through the turbine and then enters the plenum chamber. In the chamber, the flow is conditioned and all swirls/vortices are removed prior to passing through a calibrated nozzle and finally exhausting at the fan outlet. Using a valve at fan exit controls the flow rate. Details of the test rig calibration can be found from Thakker et al.3. The turbine was mounted on a shaft in a cylindrical annular duct, with a blade tip clearance of 1mm. The shaft is coupled to a motor/generator via a torque meter. The two guide vanes were mounted on the up-stream and down-stream hubs of the rig. The turbine was tested by keeping a constant axial velocity of 8.49 m/s. Data was collected by varying the rotational speed from 1250 rpm to 125 rpm, thus giving a flow coefficient range of 0.27 to 2.7 under uni-directional steady flow conditions. The Reynolds number based on the blade chord length was

0.74x105 at peak efficiency.

Figure 1. Schematic diagram of test rig. The overall performance of the turbine was evaluated by the turbine angular velocity ω, torque generated T, flow rate Q and total pressure drop δp across the rotor. The results are expressed in the form of torque coefficient CT, input power coefficient CA and efficiency η in terms of flow coefficient φ. The definitions are given below. CT = T/{ρ (va

2 + UR2)b lr z rR / 2} (1)

CA = δp Q/{ρ (Va2 + UR

2) b lr z va / 2} (2) φ = va/UR (3) η = T ω / (δp Q) = CT / (CA φ ) (4)

COMPUTATIONAL FLUID DYNAMICS

ANALYSIS Governing Equations GAMBIT 2.0 and FLUENT 6.0 were used for meshing and analyzing the problems respectively. The FLUENT solves the Navier-Stokes equations for conversion of mass and momentum (equations 5 to 8). Additional conservations of k and ε equations are solved for turbulence closure. Governing Navier-Stokes transport equations are:

( ) ( ) ( ))5(0=

∂∂+

∂∂+

∂∂

zw

yv

xu ρρρ

( ) ( ) ( ) ( ))6()( uudiv

zzx

yyx

xxx

xP ρτττ =

∂∂+

∂∂+

∂∂+

∂∂−

( ) ( ) ( ) ( ))7()( vudiv

zzy

yyy

xxy

yP ρτττ =

∂∂+

∂∂+

∂∂+

∂∂−

( ) ( ) ( ) ( ))8()( wudiv

zzz

yyz

xxz

zP ρτττ =

∂∂+

∂∂+

∂∂+

∂∂−

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Solver Parameter The solver treats each cell in the domain as a finite volume with a node at its center and the flow properties for the entire model are solved at each of these nodes. In order to predict the flow properties at the edge of control volume, the flow properties must be interpolated between two nodal points. The discretisation scheme governs the accuracy of its interpolation by controlling the number of terms in Taylor series used for the interpolation. The discretisation scheme found to be the most accurate for the second order scheme; this scheme was the highest order available in the code being used. The Mesh and Solver The computational grid is visualized in Figure 2, where only the grid lines attached to the surfaces are shown. Here, the resolution of all the boundary layers is visible. An enlarged view at tip clearance is shown in Figure 3. The complex 3-dimensional computational domain has been meshed with hexahedral elements. This has been achieved by partitioning the entire geometry into meshable pieces and meshed by mapping and submapping algorithms. The grids clustered near the hub, casing, and tip was close enough to give appropriate y+ values. The mesh was checked for low level of skewness and reasonable aspect ratio and volume change.

Figure 2. Computational grid

Figure 3. Grids at the turbine blade tip region. The grid independence test has been carried out on the computational domain with 350,000, 400,000, and 450,000 cells, Figure 4. The performance curves of turbine are seen almost similar for the cases with cells 400,000 and 450,000. Hence the grid cells 400,000 have been utilized for all the numerical studies in the present investigation. The

computational domain extended to 8.5 chord length upstream and down steam, it is restricted to one blade to blade and guide vane to guide vane passage with periodic boundaries. Computation has been carried out for various tip clearances; 0, 0.25, 1, 2, 4 and 6 percent of axial chord and for each case with various flow coefficients.

0

10

20

30

40

50

60

0 0.5 1 1.5 2

φ φ φ φ ηη ηη

Experimental

Computed(350000 cells)

Computed(400000 cells)

Computed(450000 cells)

Figure 4. Grid independence test. Boundary Conditions It was necessary to set up three fluid zones using mixing plane technique. Three zones are the upstream guide vane, the rotor and the downstream guide vane. Inflow is set as mass flow inlet, outflow is set as pressure outlet and periodic walls are set as transitional to allow cascade effect on blade and guide vane to be simulated. The fluid at rotor is defined as a moving reference frame with the angular speed equivalent to that of the blade. The flow is set as fully turbulent. Near-Wall Modeling Near-wall modeling has a great impact on quality of numerical solution as the variables mainly change near to the wall. The non-equilibrium wall functions were used, as they are capable of dealing with complex flows involving separations, reattachment or any other non-equilibrium effects and also severe pressure gradients. The near-wall cells were assumed to consist of a viscous sublayer and an inertia dominated layer.

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0

1

2

3

4

5

6

0 0.5 1 1.5 2

φφφφ

CA

Computed

Experimental

0

1

2

3

4

5

6

0 0.5 1 1.5 2

φ φ φ φ

CT

Computed

Experimental

0

10

20

30

40

50

60

0 0.5 1 1.5 2

φ φ φ φ

ηη ηη

Experimental

Computed

Figure 5. Comparison between computed and measured values: (a) Coefficient of input, (b) Coefficient of torque, (c) Efficiency.

RESULTS AND DISCUSSION Validation of Numerical Procedure The present numerical model has been validated with the experimental data with 1% tip clearance. Figure 5a through 5c show the comparison between computed and measured values for input coefficient, torque coefficient and efficiency against flow coefficient, respectively. From the Figure 5a, it can be observed that the computed values overpredict the measured values at high flow coefficients. But there is good agreement has been reached between computed and measured CT values, Figure 5b. Computed efficiency of turbine matches very well with experimental results, for the entire flow coefficient, except at very low coefficients (Figure 5c). This implies that the turbulence model k-ε produces good results in the lower rotational speed of turbine. Accuracy of the present computational model has been plotted as the percentage of error ε on the computed CT, CA and efficiency deviated from experimental values (Figure 6). From the figure, it can be observed that the accuracy of computed results were varying with flow coefficient. Particularly, the error of CT and CA fall approximately 10 percentage deviation from experimental value in the normal operating coefficients. At the two extreme flow coefficients, the percentage of error is seen considerably more due the nature of flow which seems highly unsteady and three-dimensional in the blade passages. As far as the computed efficiency of the turbine is concern, the error is almost zero. Especially, at the peak efficiency, where the flow through the blade passage much favorable in generating torque, the computed error is being close to zero (Figure 6).

-25

-20

-15

-10

-5

0

5

10

15

20

25

0 0.5 1 1.5 2

φφφφ

�� ��

C T

C Aη

Figure 6. Computational error on coefficient of torque, coefficient of input, and efficiency of the turbine.

(a)

(b)

(c)

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Effect of Tip Clearance on Performance of the Turbine Figures 7a through 7c show the variations of CA, CT and efficiency respectively for the cases of 0%, 0.25%, 1%, 2%, 4% and 6% tip clearances. Figure 7a shows that the input coefficient is almost same for the tip clearances 0% to 1%, up to the value of flow coefficient 1.0. The reason for this behavior is explained in the following section. Beyond this flow coefficient, the input coefficient is increasing as tip clearance increases. When the tip clearance increase from 1%, there is considerable effect due to tip clearance throughout the operating range of the turbine. It can be noted that the value of CA keeps almost similar for the cases of 0% and 0.25% tip clearance.

0

1

2

3

4

5

6

0 0.5 1 1.5 2φφφφ

CA

without tip clearance

0.25% tip clearance

1% tip clearance

2% tip clearance

4% tip clearance

6% tip clearance

0

0.5

1

1.5

2

2.5

3

3.5

0 0.5 1 1.5 2φ φ φ φ

CT

without tip clearance

0.25% tip clearance

1% tip clearance

2% tip clearance

4% tip clearance

6% tip clearance

0

10

20

30

40

50

60

0 0.5 1 1.5 2

φ φ φ φ

ηη ηη

without tip clearance

0.25% tip clearance

1% tip clearance

2% tip clearance

4% tip clearance

6% tip clearance

Figure 7. Effect of tip clearance: (a) Coefficient of input, (b) Coefficient of torque, (c) Efficiency.

It is evident that there is tremendous rise in pressure drop across the turbine due to tip leakage flow beyond 1% tip clearance. This effect has been reflected in terms of torque converted by the blades (Figure 7b). Hence the efficiency of the turbine is almost same for the cases of 0% and 0.25% tip clearance (Figure 7c). The efficiency with 1% tip clearance remains same as above cases up to the value of flow coefficient about 1.0 and reduces gradually beyond this value. Also it can be noted that the efficiency curve for the cases above 1% tip clearance is apparently sharp compare to the other cases. The peak efficiency of the turbine is being shifted towards left hand side as the tip clearance increases.

0

10

20

30

40

50

60

0 2 4 6 8

Percentage of tip clearance

ηη ηηm

ax

Impulse Turbine

Wells Turbine

Figure 8. Effect of tip clearance on max efficiency of various turbines.

(a)

(b)

(c)

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Figure 9. Velocity contours at various tip clearances: (a) 0% tip clearance, (b) 0.25% tip clearance, (c) 1% tip clearance, (d) 2% tip clearance, (e) 4% tip clearance, (f) 6% tip clearance. Figure 8 shows the distribution of maximum efficiency with tip clearance ratio. Here the effect of tip clearance of impulse turbine has been compared with the Wells turbine (Raghunathan6), as both the turbines operate in bi-directional flow applications. The maximum efficiency of the impulse turbine is almost constant up to 1% tip clearance, after this value; there is sudden decrease in efficiency. The reason for this behavior is explained with physics of flow in the following section. Beyond 4% tip clearance there is no noticeable decrease in efficiency. Hence it is validated that the design value of 1% tip clearance is an optimum value. Even though both the turbines are very sensitive to the tip clearance compared to conventional turbine, the impulse turbine is relatively less sensitive when compared to the Wells turbine (Figure 8). For example, the impulse turbine finds no effect due to tip clearance up to 1% tip clearance. But in case of Wells turbine, there is drop in efficiency which starts from 0.6% tip clearance itself. Generally, both the turbines seem sensitive in the range of tip clearance from 1% to 4%. Flow Physics and the Effect of Tip Clearance Height Figures 9a through 9f show the velocity contours at 96 percentages of blade height for the cases of 0%, 0.25%, 1%, 2%, 4% and 6% tip clearances respectively for the flow efficient of 1.68. Note that velocities are non-dimensionalized with the inlet

velocity to the inlet guide vane. From the figures, while considering the lead edge region of the blade, without tip clearance and 0.25% tip clearance show similar distribution and the forward portion of the blade passage, which are typical of a stagnating or low-velocity flow. This supports the contention that for the front part of the blade tip clearance gap could be blocked by the inlet boundary layer (‘aerodynamically closed’) and therefore could be sustaining a horseshoe vortex system. In the cases of relatively open 1% and above tip clearances size of the horseshoe vortex is seen reduced gradually (Figures 8c through 8f).

The size and location of vortex released from tip clearance can be clearly captured from the above figures. Even though there is no tip leakage vortex formed in case of without tip clearance, the flow separation from the suction surface can be seen from Figure 9a. In case of 0.25% tip clearance, the vortex takes place after approximately 50% of axial chord length (ACL) aside suction surface of the blade, Figure 9b. In case of low tip clearance, the trailing edge of the blade also closed aerodynamically. But the flow leaks through the clearance from 65% to 70% axial chord length. But in the cases of 1% and above tip clearances (Figures 9c through 9f) there is no aerodynamic lock seen in the trailing edge of the turbine, causing large mass flow of air leak through

(a) (b) (c)

(d) (e) (f)

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the tip clearance. Hence tip leakage vortex size is large when compare to the case of 0.25% tip clearance. From the figures, it can be observed that

Figure 10. Total pressure contours at 90 % ACL at φφφφ = 1.68 : (a) 0.25% tip clearance, (b) 1% tip clearance, (c) 4% tip clearance, (d) 6% tip clearance.

Figure 11. Total pressure contours at 90% ACL at φφφφ = 0.67: (a) 0.25% tip clearance, (b) 1% tip clearance, (c) 4% tip clearance, (d) 6% tip clearance. the vortex growing in size from the location of 60% axial chord to downstream of the blade trailing edge. As the strength of leakage vortex increases from 1% tip clearance, it enhances the flow separation at down stream guide vanes (Figures 9c through 9f). This may be the reason for sudden decrease in efficiency of the turbine beyond 1% tip clearance (Figure 8). The interpretation of this is that the pressure drop across the rotor plays an important role rather than torque in efficiency of turbine.

Figure 12. Static pressure contours on suction side of turbine blade at φφφφ = 1.68 : (a) 0.25% tip clearance, (b) 1% tip clearance, (c) 4% tip clearance. (d) 6% tip clearance. To picture the growth of the tip leakage flow vortex and its interaction with separated flow from suction side of blade, distribution of total pressure coefficient has been plotted at 90% of axial chord length for various tip clearances. These contours have been plotted for two flow coefficients of 0.67 and 1.68. These flow coefficients have been chosen, as the effect of tip clearance seems significantly different in the above flow coefficients (Figure 7c). Figures 10a through 10d show the total pressure contours for the cases of 0.25%, 1%, 4% and 6% tip clearances respectively for the flow coefficient of 1.68. From the Figure 10a, it can be noted that the tip leakage vortex is almost diffused for the case of 0.25% tip clearance. In case of 1% tip clearance, the vortex has been shed fully and the size of vortex keeps growing as tip clearance increases (Figures 10b through 10d). It can be seen very clearly that the vortex occupied nearly 10% of blade passage width for the case of 1% tip clearance and nearly 40% in case of 6% tip clearance. So, from the Figure 10 it can be interpreted that the tip leakage flow is inducing a significant area of low-momentum fluid. At the flow coefficient of 0.67 (Figure 11), there is no considerable effect due to tip clearance for the cases of 0.25% and 1% tip clearance. Also, there is no visible vortex seen due to tip clearance leakage flow in the above tip clearances. This may be due to high-pressure drop across the turbine, which occurs before 55 % of ACL. As the velocity of flow entering the tip clearance is low, it has less energy to create a vortex. Hence the efficiency of the turbine is

(a) (b)

(c) (d)

(a) (b)

(c) (d)

(a) (b)

(c) (d)

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same for the both tip clearances of 0.25% and 1%. But in case of higher tip clearances, as the mass flow through the tip gap increases, a vortex has been shed but in small scale. Hence there is reduction in efficiency of the turbine after 1% tip clearance in low flow coefficient also. This trend expounds that the lower tip clearances (below 1% tip clearance) affects the turbine performance in the higher flow coefficients only (after peak efficiency). As the tip clearance increases from 1%, it advances affecting the turbine performance in the lower flow coefficients itself.

Figure 13. Static pressure contours on pressure side of turbine blade at φφφφ = 1.68 : (a) 0.25% tip clearance, (b) 1% tip clearance, (c) 4% tip clearance, (d) 6% tip clearance.

Figure 14. Static pressure contours on tip surface of turbine blade at φφφφ = 1.68 : (a) 0.25% tip clearance, (b) 1% tip clearance, (c) 4% tip clearance, (d) 6% tip clearance. Static pressure distribution on suction and pressure side of the blade are shown in Figures 12 and 13 respectively for the flow coefficient 1.68. There is considerable effect due to tip clearance in the static

pressure distribution as seen throughout the blade length. However the effect is more predominant after 65% of ACL. The low-pressure region at mid portion of the suction side of the blade has been shifted towards hub of the blade due to tip leakage flow (Figures 12b through 12d). On the other hand static pressure distribution on the pressure side is seen shifted upward, as the blade passage flow diverted through the tip gap (Figures 13a through 13d). Static pressure distribution on the tip surface of the blade for various tip clearances at the flow coefficient 1.68 is shown in Figures 14a through d. The effective leakage area through the tip surface can be clearly captured from the above figures. At low tip clearance, the blade passage flow released through the suction surface effectively about 65-70 % due to aerodynamic lock in the blade leading and trailing edges. Hence vortex has been formed in negligible size and does not affect the main flow significantly (Figure 10a). But in case of 1% tip clearance, leakage takes place from 60% ACL to trailing edge of the blade and beyond 1% tip clearance, the leakage takes place through entire tip surface of the blade. It creates the relatively large vortex and makes the impact on efficiency of the turbine considerably.

CONCLUSIONS The present computational model has been validated with experimental results with reasonable accuracy and found well suitable for further design analysis. It is found that k-ε turbulence model can predict the performance of turbine well in the low rotational speed of turbine. The performance curves of the impulse turbine with various tip clearances have been arrived numerically. The flow physics of the blade passage flow interacting with tip leakage flow has been analyzed with computed results. It is investigated that the turbine is very sensitive to tip clearance when compared to a conventional turbine. It is predicted that the turbine with 0.25% tip clearance performs almost similar to the case of without tip clearance for the entire flow coefficients. The designed value of 1% tip clearance has been validated numerically.

ACKNOWLEDGEMENTS The authors would like to acknowledge the financial support given by ESBI, Ireland, Wave Energy Research Team and also Department of Mechanical and Aeronautical Engineering, University of Limerick.

(a) (b)

(c) (d)

(a) (b)

(c) (d)

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REFERENCES

[1] Setoguchi, T., Kaneko, K., Maeda, H., Kim, T. W., and Inoue, M., “Impulse Turbine with Self-Pitch-Controlled Guide Vanes for Wave Power Conversion: Performance of Mono-Vane Type”, International Journal of Offshore and Polar Engineering, vol. 3, No. 1, 1993, p.73-77.

[2] Kim, T.S., Lee, H. G.., lll-Kyoo Park., Lee, Y.W., Kinoue, Y., and Setoguchi, T., “Numerical Analysis of Impulse Turbine for Wave Energy Conversion”, Proceedings of the Tenth International Offshore and Polar Engineering Conference, Seattle, USA, May 28- June 2, 2000.

[3] Thakker, A., Frawley, P., Khaleeq, H. B., Abugihalia, Y., and Setoguchi, T., “Experimental and CFD Analysis of 0.6m Impulse Turbine with Fixed Guide Vanes”, Proceedings of the Eleventh International Offshore and Polar Engineering Conference, Stavanger, Norway, June 17-22, 2001.

[4] Thakker, A., Frawley, P., and Sheik Bajeet, E., “Numerical Analysis of Wells Turbine Performance Using a 3D Navier-Strokes Explicit Solver” Proceedings of the Eleventh International Offshore and Polar Engineering Conference, Stavanger, Norway, June 17-22, 2001.

[5] Watterson, J.K. and Raghunathan, S., “Computed Effects of Solidity on Wells Turbine Performance”. JSME International Journal, Series B, 41 (1), 1998, p.199-205.

[6] Raghunathan, S., Setoguchi, T., and Kaneko, K., “Aerodynamics of monoplane Wells turbine - A Review”, Proceedings Offshore and Mechanics and Polar Engineering Conference, Edinburgh, UK, 1991.

[7] Tagori, R., Arakawa, C., and Suzuki, M., “Estimation of Prototype Performance and Optimum Design of Wells Turbine”, Research in Natural Energy SPEY 20, 1987, p.127-132.

[8] Raghunathan, S., “The Wells Air Turbine for Wave Energy Conversion”, Prog. Aerospace Sci., 31, 1995, p.335-386.