Wells Turbine for Wave Energy Conversion — Improvement of the Performance by Means of Impulse Turbine for Bi-Directional Flow

Wells turbine has inherent disadvantages in comparison with conventional turbines: relative low efficiency at high flow coefficient and poor starting characteristics. To solve these problems, the authors propose Wells turbine with booster turbine for wave energy conversion, in order to improve the performance in this study. This turbine consists of three parts: a large Wells turbine, a small impulse turbine with fixed guide vanes for oscillating airflow, and a generator. It was conjectured that, by coupling the two axial flow turbines together, pneumatic energy from oscillating airflow is captured by Wells turbine at low flow coefficient and that the impulse turbine gets the energy at high flow coefficient. As the first step of this study on the proposed turbine topology, the performance of turbines under steady flow conditions has been investigated experimentally by model testings. Furthermore, we estimate mean efficiency of the turbine by quasi-steady analysis.


Introduction
Several of the wave energy devices being studied under many wave energy programs in the United Kingdom, Japan, Portugal, India and other countries make use of the principle of an oscillating water column (OWC) [1].In such wave energy devices, a water column which oscillates due to wave motion is used to drive an oscillating air column which is converted into mechanical energy.The energy conversion from the oscillating air column can be achieved by using a self-rectifying air turbine such as Wells turbine which was introduced by Dr. A. A. Wells in 1976 [2][3][4][5][6].Figure 1 shows outline of Wells turbine.This turbine rotates in a single direction in oscillating airflow and therefore does not require a system of non-return valves.Furthermore, this turbine is one of the simplest and probably the most economical turbines for wave energy conversion.However, according to previous studies, Wells turbine has inherent disadvantages: low efficiency at high flow coefficient and poor starting characteristics in comparison with conventional turbines because of a severe stall [2][3][4][5][6].Therefore, although a number of OWC based wave energy plants using Wells turbine have been constructed and tested to date, the total conversion efficiencies of the plants were approximately 15% at the best [7][8][9].Moreover, Wells turbine has high noise level and maintenance problem because of high rotational speed.
Recently, in order to develop a high performance selfrectifying air turbine for wave energy conversion, an impulse turbine for bi-directional flow has been proposed by the authors [10][11][12].Figure 2 shows outline of the impulse turbine.There are many reports which describe the performance of the impulse turbine both at starting and running conditions.The experimental results of the model testing show that the efficiency of the impulse turbine is high in a wide range of flow coefficient, though its peak efficiency is almost the same as that of Wells turbine [10][11][12].
The authors propose Wells turbine with booster turbine in this study.An impulse turbine for bi-directional flow is used as the booster turbine in order to improve the efficiency of Wells turbine at high flow coefficient.This turbine consists of a large Wells turbine, a small impulse turbine and a generator, as shown in Figure 3.It was conjectured that by coupling the two turbines together, pneumatic energy from oscillating airflow is captured by Wells turbine at low flow coefficient and the impulse turbine gets the energy at high flow coefficient.As the first step of study on the proposed turbine topology, the performance of turbines under steady flow conditions have been investigated experimentally by model testing.
Further, mean efficiency of the proposed turbine for wave energy conversion has been estimated by quasisteady analysis in this study.

Experimental Apparatus and Procedure
A schematic view of the test rig is shown in Figure 4.
The test rig consists of a large piston-cylinder (diameter: 1.4 m, length: 1.7 m), one end of which is followed by a settling chamber.Turbine testing is done in 300 mm diameter test section with bell-mouthed entry/exit at both its ends.The piston can be driven back and forth inside the cylinder by means of three ball-screws through three nuts fixed to the piston.All three screws are driven in unison by a D.C. servo-motor through chain and sprockets.A computer controls the motor, and hence the piston velocity to produce any flow velocity.The test turbine is coupled to a servo-motor/generator through a torque transducer.The motor/generator is electrically controlled such that the turbine shaft angular velocity is held constant at any set value.The overall performance was evaluated by the turbine output torque T o , the flow rate Q, the total pressure drop across the turbine Δp, and the turbine angular velocity ω.The flow rate through the turbine Q, whether it is inhalation (i.e., flow from atmosphere into the settling chamber) or exhalation (i.e., flow from settling chamber to atmosphere), is calculated by measuring the motion of piston, where the value of Q agrees with that obtained by a Pitot tube survey.Tests were performed with the flow rates up to 0.320 m 3 /s and the turbine angular velocities up to 471 rad/s.The Reynolds number based on the blade chord was approximately equal to 2.5 × 10 5 for Wells turbine and 0.5 × 10 5 .The uncertainty of efficiency is about ±1%.This uncertainty has been obtained by taking into account the dispersions in the measurement of the physical parameters from which efficiency is obtained.

Tested Axial Turbines
Wells turbine adopted in the experiments is shown in Figure 5.The detail of tested Wells turbine in the case of casing diameter D W = 300 mm is as follows.The chord length, l = 90 mm; blade profile, NACA0020; number of blades, 6; solidity at mean radius, 0.67; hub-to-tip ratio, ν = 0.7; aspect ratio, 0.5; tip diameter, 299 mm; tip clearance, 0.5 mm; mean radius, r W = D W (1 + ν)/4 = 127.5 mm; width of flow passage, 45 mm.Note that the adopted turbine rotor is the most promising one in previous studies [3,5,6].As shown in Figure 6, the turbine configuration employed in the study is an impulse type having fixed guide vanes both upstream and downstream, and these geometries are symmetrical with respect to the rotor centerline.The specifications of the impulse turbine rotor in the case of casing diameter D i = 300 mm are as follows.The rotor blade profile consists of a circular arc on the pressure side and part of an ellipse on the suction side.A radius of the circular is 30.2 mm and the ellipse has semi-major axis of 125.8 mm and semi-minor axis of 41.4 mm.The chord length is 54 mm; solidity of 2.02 at mean radius; blade inlet (or outlet) angle of 60˚; thickness ratio of 0.298; tip diameter of 299 mm; hub-to-tip ratio of ν = 0.  downstream and upstream of the rotor (Figure 6).Detailed information about the guide vane is as follows: solidity of 2.27 at mean radius; thickness ratio of 0.0071; a guide vane setting angle of 30˚; camber angle of 60˚.The camber line of guide vane consists of a straight line with a length of 34.8 mm and a circular arc with a radius of 37.2 mm.The rotor blade and guide vane are also the most promising one [10][11][12].

Experimental Results
The turbine performance under steady flow conditions evaluated by turbine efficiency , torque coefficient C T and input coefficient C A against flow coefficient .The definitions of these parameters are as follows: where A, u, v and  denote the flow passage area , circumferential velocity at mean radius {= rω}, axial flow velocity {= Q/A} and density of air, respectively.
Figure 7 shows the experimental results of Wells turbine and the impulse turbine.The torque coefficients C T of both turbines increase with the flow coefficient  in the region of low flow coefficient (Figure 7(a)).However, C T in the case of Wells turbine drops rapidly at  = 0.34 because of stall and it increases with flow coefficient after the stall point again.C T of the impulse turbine slightly increases in the region of low flow coefficient.However, C T of the impulse turbine is considerably higher than that of Wells turbine after the stall point of Wells turbine.Similarly, the input coefficients C A of the turbines also increase  and C A of Wells turbine slightly decreases at the stall point (Figure 7(b)).C A of the impulse turbine increases with flow coefficient.But C A of the impulse turbine leveled off after the flow coefficient  = 1.3.As shown in Figure 7(c), the efficiency of Wells turbine is higher than that of the impulse turbine when  is less than the stall point.But after the stall point of Wells turbine, the efficiency of impulse turbine is considerably higher than that of Wells turbine and the efficiency of Wells turbine is less than 0.04.The peak efficiencies are almost the same and its value is approximately 0.48.

Estimation Method of Turbine Characteristics under Sinusoidal Airflow Conditions
Since the airflow into the turbine is generated by the OWC, it is very important to demonstrate the turbine characteristics under oscillating flow conditions.Here let us simulate the characteristics under sinusoidal flow conditions (Figure 8) in order to clarify the effect of booster turbine on the efficiency of Wells turbine.The steady flow characteristics of the turbine in Figures 7(a) and (b) are assumed to be valid for computing performance under unsteady flow conditions.Such a quasisteady analysis has been validated by previous studies [13,14].
In the calculation, flow rates through the two turbines are obtained by using the steady flow characteristics and solving these simultaneous equations.where q denote flow rate through the turbine and subscripts w and i mean Wells turbine T w and Impulse turbine T i , respectively (see Figure 3).Further, flow rate and rotor angular velocity in the calculations are assumed as follows: W i const.

  
   (10) Copyright © 2013 SciRes.OJFD where Q 0 , t and T are maximum flow rate, time and period of sinusoidal airflow.
When the turbine is in the running conditions, the parameters such as T o , , p and q vary periodically in a sinusoidal oscillating flow.In this case, the turbine performances should be represented by mean value such as mean efficiency.Assuming that only the turbine under forward flow condition operates, in the case of two generators, the running characteristics of the turbine under sinusoidal flow condition are evaluated by mean efficiency η m against the flow coefficient , which are defined as follows: The mean efficiency η m is defined as follows: In the study, turbine diameter ratio D W /D i changes from 1 to 5 in order to investigate the effect of turbine casing diameters D W and D i on mean efficiency.Here, we assumed that total flow passage area of the two turbines equal to area of cross section of the duct in the calculation (See Figure 3).That is, Figures 9 and 10 show the effect of turbine diameter ratio D W /D i on mean efficiency η m and its peak value η m,peak under sinusoidal airflow conditions.It is found from the figure that curves of the efficiency have two peaks.The one is at low flow coefficient which is near a flow coefficient of peak efficiency of Wells turbine.Another is at Φ = 1.2 which is near a flow coefficient of peak efficiency of the impulse turbine.The peak mean efficiency decreases with the increase of D W /D i when turbine diameter ratio D W /D i ≤ 1.2.The peak mean effi-D ciency increase with D W / i when turbine diameter ratio  D i single Wells turbine.However, mean efficiency at high flow coefficient in the case of Wells turbine with booster is higher than that of single Wells turbine.It is concluded from this fact that the mean efficiency at high flow coefficient is improved by mean of the impulse turbine as a booster turbine.
The authors propos in an OWC configuration in this study, in order to obtain much of wave energy.As the first step of this study, the performances of axial flow turbines under steady flow conditions have been investigated experimentally by model testing.Furthermore, we estimated mean efficiency of the turbine by quasi-steady analysis in this study.The conclusions obtained are summarized as follows. The on turbine diameter ratio.
igh flow coefficient is immean efficiency is lower than that of a sin-

Figure 4 .
Figure 4. Experimental apparatus and measuring system.

Figure 9 .
Figure 9.Effect of turbine diameter on mean efficiency under sinusoidal airflow conditions.

Figure 10 .
Figure 10.Effect of turbine diameter ratio on mean peak