4000_A Review of Impulse Turbine for Wave Energy Conversion

8/2/2019 4000_A Review of Impulse Turbine for Wave Energy Conversion

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Renewable Energy 23 (2001) 261292

www.elsevier.nl/locate/renene

A review of impulse turbines for wave energyconversion

T. Setoguchi a,* , S. Santhakumar b, H. Maeda c, M. Takao a ,

K. Kanekoa

a Department of Mechanical Engineering, Saga University, Saga, Japanb Department of Aerospace Engineering, I.I.T., Madras, India

c Torishima Pump Manufacturing Company Limited, Saga, Japan

Received 25 May 1999; accepted 24 August 2000

Abstract

Oscillating Water Column based wave energy plants convert wave energy into low pressurepnuematic power in the form of bi-directional air ows. Air turbines which are capable of rotating uni-directionally in bi-directional air ow, otherwise also known as self-rectifyingturbines, are used to extract mechanical shaft power which is further converted into electricalpower by a generator. This paper reviews the state of the art in self-rectifying impulse airturbines. New results on optimum parameters for the xed-guide-vane impulse turbine are alsopresented. Starting characteristics and conversion efciencies of two types of impulse turbinesare compared with the well known Wells turbine. 2001 Elsevier Science Ltd. All rightsreserved.

Keywords: Fluid machinery; Impulse turbine; Wells turbine; Guide vane; Ocean energy; Wave energy

conversion

1. Introduction

One of the methods for wave energy conversion utilises an Oscillating WaterColumn (OWC) which in turn converts wave energy into low pressure pneumaticenergy in the form of bi-directional air ow. An air turbine which rotates in a singledirection and extracts mechanical shaft power from such bi-directional air ow is

* Corresponding author. E-mail address: [email protected] (T. Setoguchi).

0960-1481/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved.PII: S 0960-1 481(00 )00175 -0


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262 T. Setoguchi et al. / Renewable Energy 23 (2001) 261292

Nomenclature

a semi-major axis of ellipse Ac air chamber cross-sectional area At turbine ow passage areab blade heightC A input coefcient {Eq. (1)}C T torque coefcnet {Eq. (2)}d slot width {see Fig. 3(b)}e semi-minor axis of ellipse f frequency of wave motion f mean frequency of wave motion = 1/ T f * nondimensional frequency = f / f h wave height in air chamberh* nondimensional wave height in air chamber = h / H 1/3 H incident wave height H 1/3 signicant wave height H * nondimensional incident wave = H / H 1/3 I moment of inertia of rotorlr chord length of rotor bladelg chord length of guide vane

N number of wavesm At / AcK nondimensional period = r Rm / H 1/3Q ow rater R mean radiusr r radius of circular arc of pressure side of elliptic prole {see Fig.

4(b) and Fig. 21} R1 radius of circular arc of pressure side of simple prole {see Fig.

4(a)} R2 radius of circular arc of suction side of simple prole {see Fig.

4(a)}Sg guide vane pitchSr rotor blade pitchS* nondimensional spectrum of wave motiont timet * nondimensional time in sinusoidal ow = t / T t nondimensional time in irregular ow = t / T t a width of ow path (see Fig. 4)T period of wave motionT o turbine output torqueT L loading torqueT mean period in irregular ow 1/ f U R circumferential velocity at r R a mean axial ow velocity


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263T. Setoguchi et al. / Renewable Energy 23 (2001) 261292

a * nondimensional axial ow velocity = a / V V reference velocity = H 1/3 /(mT )V a peak value of a in sinusoidal owW i incident wave power {Eq. (10)}W 0 OWC output power {Eq. (11)} X I nondimensional moment of inertia = I /(pr a r 5 R) X L nondimensional loading torque =T L /(pr a V 2a r 3 R), T L /(pr a V 2r 3 R) z number of rotor blades incident angle of guide vane (see Fig. 2) rotor blade inlet angle (Fig. 4) rotor blade sweep angle (Fig. 10) camber angle of guide vane

p total pressure drop between settling chamber and atmosphere turbine efciency under steady ow condition {Eq. (3)}m maximum value of h mean turbine efciency under sinusoidal ow condition {Eq. (5)}h m maximum value of h h conversion efciency under irregular ow condition {Eq. (18)}h c efciency of air chamber {Eq. (12)}h t mean turbine efciency under irregular ow condition {Eq. (17)} setting angle of xed guide vane

p pitch angle of guide vane1 setting angle of upstream guide vane2 setting angle of downstream guide vane hub-to-tip ratioa density of air s density of seawater solidity of rotor at r R ow coefcient {Eq. (4)}

ow coefcient {Eq. (6)} angular velocity of turbine rotor

*

nondimensional angular velocity in sinusoidal ow = T w nondimensional angular velocity in irregular ow w T

required to drive a generator to produce electricity. Such a turbine is also called aself-rectifying turbine. Different types of impulse turbines have been proposed overthe years [1] but generally their performance has not been investigated except maybe in the case of McCormick turbine whose efciency is found to be rather low.

The Wells turbine was the rst choice for all the OWC based wave energy plants

which were built in Norway, Japan, Scotland, India and China.There are many reports which describe the performance of the Wells turbine both

at starting and running conditions [24]. According to these results, the Wells turbine


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has inherent disadvantages: narrow range of ow rates at which it operates at usefulefciencies, poor starting characteristics, high speed operation and consequent noiseand high axial thrust.

Setoguchi et al. [512] developed an impulse turbine with self-pitch controlledguide vanes and subsequently with linked guide vanes to overcome the drawbacksof the Wells turbine.

This design delivers useful efciencies over a wide range of ow rates, has verygood starting characteristics and low operating speeds. These characteristics havebeen borne out by eld trials conducted by the National Institute of Ocean Tech-nology, India, on a 1-meter-diameter turbine at Vizhinjam on the west coast of India.

Notwithstanding the superior characteristics of the impulse turbine with self-pitch-controlled guide vanes, certain disadvantages are imposed by such variable-geometrydesign. The guide vanes pitch at the wave frequency calling for a robust mechanicaldesign to withstand a large number of oscillation cycles per day. Presence of manymoving parts lead to maintenance and operating life problems and more cost. If xedguide vanes are provided instead, it was felt that these problems will be mitigatedeven though the performance may be poorer. With this in view, model tests wereconducted to determine the characteristics of xed-guide-vane impulse turbine. Theresults were encouraging and more tests were conducted to optimise various para-meters of the turbine. Site trial also shows the validity of this concept.

The objective of this paper is to show the present state of the art of the impulseturbine with self-pitch-controlled guide vane and of the xed-guide-vane impulse

turbine. In addition, new results on the effect of hub-to-tip diameter ratio and rotor-stator gap on the performance of xed-guide-vane impulse turbine are also presented.

2. Description of the oscillatory ow test rig

The test rig used for testing turbines consists of a large piston-cylinder, a settlingchamber and 300 mm diameter test section with entry/exit at its two ends which are

bell-mouthed (Fig. 1). The test-turbine is placed at the centre of the test section. Itis coupled through a torque transducer to an electrical generator/motor which iselectronically controlled to maintain the rpm constant at any set value. The pistonis translated by means of three ball-screws which are driven by a d.c. servo-motorby chain and sprockets. A computer controls this motor to produce sinusoidal ow,any random/irregular ow or steady ow (for a short period) through the turbine.Average ow rate is measured by pitot-tube survey. Settling chamber pressure ismeasured by a pressure transducer. Turbine performance is evaluated from turbinerpm, turbine output torque, ow rate and total pressure drop between settlingchamber and atmosphere. Tests were performed for total pressure drops in the range

of 200 to 800 N/m2

, turbine angular velocity up to 370 rad/s and ow rates upto0.63 m 3 /s. The measurement uncertainty in turbine efciency is about 2%. Formeasuring guide vane angle p, a potentiometer was used.


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Fig. 1. Test rig.

3. Experimental results and discussion

3.1. Impulse turbine with self-pitching guide vanes

A number of studies were conducted on impulse turbine with self-pitch-controlledguide vanes (Fig. 2) over a period of time. The turbine has a rotor with impulseblading. There are two sets of guide vanes on either side of the rotor. These guidevanes are pivoted and are free to rotate between two preset angles determined bymechanical stops. Whenever airow changes direction, the guide vanes ip underthe action of aerodynamic moments acting on them and take up the right orientations(that is, upstream guide vanes acting as nozzle cascade and downstream guide vanesacting as diffuser cascade) for efcient operation. Different types of guide vanes anddifferent rotor blade geometries were studied. The guide vanes were set on a spherical

hub so as to keep hub clearance (0.5 mm) constant while the vane rotates. However,the outer casing is cylindrical and mean tip clearance varies from 0.5 mm to 3 mmas changes from 50 to 15.

3.1.1. Effects of guide vane and rotor geometries on performanceFigs. 3(a) and (b) show two of the guide vane arrangements [5,7,8,11] studied.

One is called the mono-vane type and the other is called the splitter type inwhich a part of the guide vane is xed.

The mono-vane type consists of a straight line for half the chord length and circu-lar-arc with camber angle of 70 for the rest. The so-called splitter type has a movable

guide vane consisting of a straight portion and a circular arc with camber angle of 45. There are xed circular-arc vanes of camber angle of 70 in between. Thegeometry of two rotor blade proles are shown in Fig. 4 [6,9]. The blade shown in


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Fig. 2. Impulse turbine with self-pitch-controlled guide vanes.

Fig. 4(a) is designated simple prole. This is constructed by two circular arcs atmid-chord portion and four straight lines near leading and trailing edges. The passagewidth between neighbouring blades is constant. On the other hand, Fig. 4(b) showselliptic prole. This prole is elliptic shaped on the suction side and circular arcshaped on the pressure side. The ow passage is designed to be slightly wider at

mid-chord to avoid unnecessarily high ow speeds there.

3.1.2. Typical characteristicsTypical characteristics of the impulse turbine in steady uni-directional ow was

obtained by suitably xing the orientations/angles of the guide vanes [5]. The per-formance is presented in terms of input coefcient C A, torque coefcient C T , turbineefciency and ow coefcient. Their denitions are as follows:

C A pQ /{ r a (n2a U 2 R)bl r zna /2}

C T T 0 /{ r a (n2a U 2 R)bl r zr R /2}

h T 0w /( pQ) C T /(C Af ) (3)

f va / U R (4)


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Fig. 3. Guide vane geometry. (a) Mono vane type. (b) Splitter type.

The turbine characteristics are presented in Fig. 5 [5] for simple prole rotorand mono-vane. The Reynolds number based on the rotor blade, chord is approxi-mately 0.4 105.

Input coefcient, C A increases continuously with ow coefcient f . On the otherhand, torque coefcient C T increases from negative values at small ow coefcientsand increases gradually for large f . As a result, turbine efciency increases fromzero at f = 0.15 to reach a maximum value at f = 0.4 and thereafter falls graduallyand smoothly with increasing f . This is different from the behaviour of Wells turbine

[3,4] whose efciency drops abruptly due to stall beyond a certain f . There is nosuch stall region for the impulse turbine.A prototype of the McCormick turbine was constructed and tested [13], and aver-

age efciencies near 0.3 appear to have been attained. This shows that the presentimpulse turbine is also superior to the McCormick turbine.

3.1.3. Effect of rotor geometryMean efciency in sinusoidal ow h (that is, va varying sinusoidally with time

V a being the peak value) is given by

h f

1/ f

0

T 0w dt | f 1/ f

0

pQdt (5)


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Fig. 4. Rotor blade prole. (a) Simple prole. (b) Elliptic prole.

The peak ow coefcient is dened by

V a / U R (6)

Fig. 6 shows the comparison of maximum mean efciency h m between ellipticand simple rotor prole [6]. The elliptic prole is superior to simple prole forlarger 1. This is because the elliptic one can be designed optimizing the boundarylayer development.

The effect of blade inlet angle on efciency is shown in Fig. 7 [9]. The maximumefciency is obtained for g = 60. Here note that the case of g = 60 corresponds toa/e = 3. So, the optimum value of a/e has been found to be 3 [9].


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Fig. 5. Turbine characteristics in steady ow.

Fig. 6. Effect of rotor blade prole on maximum mean efciency.

Fig. 8 represents the effect of pitch/chord ratio of rotor, Sr /1r [5]. The efciencyis the highest at Sr /1r = 0.5, that coincides with the result of the conventional subsonicimpulse turbine [14]. The efciency of this turbine system is higher and keeps highvalues in a wider range of V a / U R in comparison with the Wells turbine [3,4]. Thismeans that the operational speed of the impulse turbine is lower, and it has a meritin noise reduction.

The effect of the ratio of ow path width to space of rotor blades is shown inFig. 9 [5]. The efciency is the highest at t a / Sr = 0.4.

In order to investigate the effect of sweep angle on the turbine performance, three

kinds of rotor were provided as shown in Fig. 10. Here, sweep angle is dened asangle l for convenience. Fig. 11 shows the maximum mean efciency against l [6].Highest efciency is obtained by the rotor with l = 7.5 for both rotor proles.


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Fig. 7. Effect of rotor blade inlet angle on efciency.

Fig. 8. Effect of rotor space/chord ratio on mean efciency.

For the rotor with l = 7.5, the positive lean at the tip region leads to higher bladeloading and it is a possible cause of high efciency. The value l = to 7, 5, by itself,is not important. What is signicant is that highest efciency is obtained when thepeak points on the suction side of blade lie along a radial line of rotor.

3.1.4. Effect of guide vane geometryFig. 12 shows the effect of guide vane type on maximum efciency [9]. It is clear

from the gure that the mono-vane type is superior to the splitter type ( d/l g = 0.1:optimum slot width [8]). This is due to the fact that the diffuser angle q2 for mono-vane type can be set larger than that for the splitter type. Note here that the perform-


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Fig. 9. Effect of width of ow path on mean efciency.

Fig. 10. Sweep angle of rotor blade. (a) = -7.5, (b) = 0, (c) = 7.5.

Fig. 11. Effect of sweep angle on maximum mean efciency.


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Fig. 12. Effect of guide vane space/chord ratio and guide vane prole on maximum efciency.

ance for mono-vane type was not so superior to the splitter type in a reciprocatingow. This will be shown in Section 3.1.5.

Fig. 12 also shows the effect of space/chord ratio of guide vane Sg / lg . on maximumefciency [9]. The optimum values of Sg / lg are Sg /lg 0.65 for mono-vane type andSg / lg = 0.8 for splitter type, respectively.

The effect of diffuser angle q2 on maximum efciency h m is shown in Fig. 13[5,9]. In general, h m increases with q2 . However, there exists an optimum one ( q2= 50) for the splitter type. In this case of q2 = 55 for the splitter type, the splitterblade touches the xed one in working as a diffuser. So this discrepancy betweenthe two cases arises from interference between the splitter and the xed part.

Fig. 13. Effect of diffuser setting angle on maximum efciency.


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Fig. 14 shows the effect of nozzle angle q1 on the maximum efciency [5,9]. Theoptimal setting angle of upstream guide vane is q1 = 15.

3.1.5. Behaviour of guide vaneFig. 15(a) shows the variation of axial ow velocity va with time [8]. Under this

ow condition, the time variation of q p for va / U R = 1.332 is shown for two types of guide vanes in Fig. 15(b). When the guide vanes work as nozzle ( va 0), the pitchangle is kept at the setting angle of q1 for both types of guide vanes. On the otherhand, for va 0, the pitch angle is unchanged until va becomes a certain value(point ). Then, it turns rapidly to the diffuser setting angle of q2 = 50 and itremains at that angle for the splitter type. In the case of the mono-vane type, however,q p changes with time in the process of increase and decrease in va as shown by adotted line. It is clear that the mono-vane does not take up diffuser orientation asexpected. Finally the condition of q p=q2 is kept unchanged until va becomes positive(point ) for both types. This means that the efciency for the mono-vane type inreciprocating ow becomes smaller than that shown in Fig. 12, and the behaviourof guide vane in the process of diffuser action is improved by the use of splittertype guide vane.

3.2. Impulse turbine with self-pitching linked guide vanes

It was seen in the last section that the guide vanes on the downstream side did

not rotate as expected to assume q2 position. A new type of impulse turbine withself-pitching linked guide vanes was proposed [12] to overcome this difculty. Fig.16 shows the meridinal section of this turbine. The guide vanes are set on a sphericalhub so as to keep hub clearance (0.5 mm) constant while the vane rotates. The outercasing is cylindrical and the mean value of vane tip clearance is about 2 mm. Thebearings of the vane are set in the outer casing. Every vane on one side of the rotoris connected by a link outside the casing to a vane on the other side of the rotor.That is, any pair of vanes on either side of the rotor is constrained to rotate together.In particular, when one vane is at an angle of q1 , the other vane will be at q2. There

Fig. 14. Effect of nozzle setting angle on maximum efciency.


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Fig. 15. Variation of pitch angle of guide vane showing comparision between splitter vane and monovane. (a) Axial velocity. (b) Pitch angle.

are mechanical stops which limit the rotation between q1 and q2. The aerodynamicmoment acting on the upstream guide vane (acting as nozzle) is utilised to rotatethe downstream guide vane to diffuser setting ( q2) through the connecting link.

3.2.1. Effects of rotor and guide vane geometries on performanceThe results and discussion given under Section 3.1.1 for mono-vane type are appli-

cable here also. From Fig. 6 [6], the elliptic prole Fig. 4(b) is superior to simpleprole Fig. 4(a) for rotor blades. The optimum value of a/e is about 3. Maximumefciency is obtained for rotor inlet angle g = 600 as seen from Fig. 7[9]. Fig. 8 showsthat efciency is highest for rotor pitch/chord ratio Sr / lr = 0.5 [6]. The efciency is

highest for rotor ow path width to pitch ratio t a / Sr = 0.4 from Fig. 9 [5]. Highestefciency is obtained for l = 7.5 [6].The guide vane geometry is the same as in Fig. 3(a). The optimum value of guide


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Fig. 16. Meridinal section of impulse turbine.

vane pitch/chord ratio is Sg / lg 0.65 from Fig. 12 [10]. h m increases with diffusersetting angle q2 for mono-vane angle seems to be q2 50 [5,10] because the smaller

the value of q2 is, the larger does the aerodynamic moment become. The optimumnozzle setting angle q1 is around 15 from Fig. 14 [5,10].

3.2.2. Behaviour of guide vanesThe variation of axial ow velocity va with time is shown in Fig. 17(a) [12]. Under

this ow condition, in Fig. 17(b), the time variation of q p at V a / U R = 0.666 is shownfor two types of guide vanes, that is, the cases with and without links. It is clearlyseen that the use of links brings the vane to diffuser setting angle and keeps it thereand so improving diffuser action compared to vanes without links. Mean efciencyh is plotted against ow coefcient for three types of turbines in Fig. 18. It is evident

that linking the guide vanes has improved the efciency and that it is superior toWells turbine in efciency. The Reynolds number based on lr is approximately0.5105 . It seems possible to realise higher efciencies by making the outer casingalso spherical so that the large clearance between vane and a cylindrical outer casingcan be reduced.

3.3. Fixed guide vane impulse turbine

There are two rows of symmetrically placed xed guide vanes on both sides of the rotor and two types of guide vanes are tested, that is, plate and airfoil type of

guide vanes. Fig. 19 shows the outline of the impulse turbine using plate type guidevanes. Each row contains 26 vanes. The camber line of plate type guide vane consistsof a straight line and a circular arc. The chord length of that guide vane is 70 mm,


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Fig. 17. Behaviour of guide vane showing comparision between with and without links. (a) Axial velo-city. (b) Pitch angle.

Fig. 18. Comparison of mean efciency.


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Fig. 19. Fixed guide vane impulse turbine.

and the spacing and thickness are 30.8 mm and 0.5 mm, respectively. Five sets of such guide vanes were tested. Their geometries are given in Table 1. The settingangle q and the camber angle d are varied such that the guide vanes always havean axial outlet angle.

Table 1Specications of plate guide vane

Ra mm

15 32 7522.5 34.6 67.530 37.2 6037.5 41.7 52.545 47.5 45


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An airfoil type guide vane has also been tested in order to clarify the effect of vane prole on turbine characteristics. Fig. 20 shows the outline of the airfoil typeguide vanes tested. The chord length of guide vane is 70 mm, and the pitch is 30.8mm. The leading edge has a circular-arc with 9 mm radius, and the setting angleis 30.

The geometry of rotor blade prole tested is illustrated in Fig. 21. The bladeprole consists of a circular arc on the pressure side and part of an ellipse on thesuction side. It has the chord length of lr = 54 mm, and the leading and trailingedges have a radius of 0.5 mm. The tip clearance is 1 mm. The number of bladesis 30. The rotor has a tip radius of 298 mm and a hub radius of 210 mm. Concerningthe blade inlet (or outlet) angle g , it was shown in a previous study that the favourable

Fig. 20. Airfoil guide vane.


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Fig. 21. Rotor blade geometry.

angle is 60 if the setting angle of upstream guide vane is 15 [9]. However, therelative inlet angle to the rotor in the case of q 15 is larger than that of q = 15because the impulse turbine is tested for q 15 in this experiment. Therefore, inconsideration of adaptability between the rotor geometry and the inlet ow velocity,the rotor blade with g = 50 is also tested in this study. The detailed informationfor the rotors is shown in Table 2.

The effect of gap between the xed guide vanes and the rotor blades, G, on theperformance was tested for G / lr ratios 0.09, 0.19, 0.37, 0.56 and 0.74.

Finally, keeping the hub diameter constant 210 mm, tests were carried out alsofor hub-to-tip diameter ratios of 0.70, 0.75 and 0.85.

Model testing of the Wells turbine with guide vanes was also made to comparethe turbine characteristics of the present impulse turbine. The specications of theWells turbine rotor adopted in the experiments are as follows. The rotor blade proleis NACA0020 with chord length of lr = 90 mm; solidity of rotor at mean radius of 0.67; aspect ratio of 0.5; tip diameter of 298 mm; tip clearance of 1 mm; hub-to-tip ratio of 0.7. Guide vanes with a chord length of 91 mm are symmetrically installed

Table 2Specications of rotor

r r mm e mm

50 34.6 43.160 30.2 41.4


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at a distance of 39 mm downstream and upstream of the rotor. Detailed informationabout the guide vane is as follows: circular are prole with constant thickness ratioof 0.011; solidity at mean radius of 1.25; camber angle of 60 0; aspect ratio of 0.5;gap to chord ratio of 0.43; stagger angle of 16.3 0; and leading and trailing edgesrounded to a semicircle with a radius of 0.5 mm. Note here that this turbine isconsidered the most promising one in the previous studies [1517].

The characteristics of the impulse turbine with xed guide vanes are shown inFig. 22, together with that of the Wells turbine. Fig. 22(a) shows the relationshipbetween h and , where plate guide vanes are used for the rotor with g = 60. Asfor this impulse turbine, the peak efciency h m increases with the increase of q atrst, and the maximum is obtained for q = 30. For q 30, h m decreases with theincrease of q. It is clear that the peak efciency of Wells turbine is higher by about8 percent compared with that of the impulse turbine in the case of q = 30. However,

Fig. 22. Turbine characteristics under sinusoidally oscillating ow. (a) Mean efciency against owcoefcient. (b) Peak mean efciency against guide vane setting angle.


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the efciency of the impulse turbine is higher over a wider range of peak owcoefcient in comparison with the Wells turbine.

Fig. 22(b) shows the effect of setting angle q on the peak mean efciency h m fortwo inlet angles of rotor blade. h m for g = 60 is higher than that for 50 for the allsetting angles. Therefore, it is clear that the favourable inlet (or outlet) angle of rotorblade is 60 , which is similar to the previous result [9].

Now, let us consider the causes of the above mentioned characteristics on thebasis of experimental results obtained under steady ow conditions.

Fig. 23 shows the effect of setting angle q on turbine characteristics under steadyow conditions. It can be said from Fig. 23(a) that the value of C T is the largest inthe case of q = 15 and decreases gradually with increasing q. This is because thewhirl velocity of ow from the upstream guide vane decreases with increasing q.From Fig. 23(b), it is clear that the value of C A is also the largest in the case of q= 15 and decreases with increasing q. This is because the diffuser effect of down-stream guide vane deteriorates for decreasing q. But it becomes almost the same forq 30.

Fig. 23. Turbine characteristics under steady ow condition. (a) Torque coefcient. (b) Input coefcient.


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The difference in the running characteristics between the impulse turbine and theWells turbine can be explained as follows. From Fig. 23(a), at small ow coefcient,high output torque T 0 is obtained in the case of Wells turbine, and then the efciencywould become higher. However, for f 0.36 (this corresponds to a stall point), T 0for the case of Wells turbine is very small, and the value of C A increases with theincrease of f as shown in Fig. 6(b). Therefore, the turbine efciency of Wells turbinewould become quite low for f 0.36. This means that the performance of Wellsturbine might deteriorate in irregular oscillating ow since it will experience highow coefcients often.

Fig. 24 shows the mean efciency of impulse turbine using the airfoil guide vanesunder sinusoidally ow condition. The case of impulse turbine using the plate guidevanes with q = 30 is denoted by the solid line for comparison. As is evident fromthe gure, h in the case of airfoil guide vane is almost the same as that of impulse turbine.

The performance characteristics for different hub-to-tip diameter ratios are shownin Fig. 25(a), (b) and (c). In the range of values tested, a hub-to-tip diameter ratioof 0.7 is the best.

The effect of inter rotor-guide vane gap on performance is shown in Fig. 26. Thevariation of h m with guide vane angle is plotted in Fig. 26(a) for different G / lr ratios.The optimum value of G / lr is seen to be 0.37 giving the highest value of h as wellas showing low sensitivity to q. However, Fig. 26(b) shows h m is almost invariantwith G / lr in the range considered.

3.4. Starting characteristics in sinusoidal ow

The ability of a turbine to start from rest and accelerate under the action of owis termed its starting characteristics. It is obtained by measuring the variation of angular velocity of rotor with tune as it starts from rest under no load conditions.The results are presented in the form of dimensionless angular velocity w * versusdimensionless time t *. S, X I and X L denote dimensionless frequency of ow, dimen-

Fig. 24. Comparison of mean efciency for plate and airfoil guide vanes


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Fig. 25. Effect of hub-to-tip diameter ratio on performance. (a) Efciency. (b) Torque coefcient. (c)Input coefcient.


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Fig. 26. Effect of gap/chord ratio on maximum mean efciency. (a) Variation with guide vane settingangle. (b) Variation with gap/chord ratio.

sionless mass moment of inertia of rotor and dimensionless loading torque respect-

ively.The starting characteristics of impulse turbine with self-pitching guide vane andWells turbine are given in Fig. 27(a) [7].

Impulse turbine with self-pitching linked guide vane is compared with a Wellsturbine in Fig. 27(b) [12].

Starting characteristics of xed guide vane impulse vane are compared with aWells turbine with guide vanes in Fig. 27(c) for different vane setting angles q. Itis seen that acceleration is faster for smaller q which is consistent with the torquecharacteristics seen in Fig. 23(a).

All three types of impulse turbine accelerate faster than the Wells turbine.

It can be seen from Fig. 28 that there is practically no difference in starting charac-teristics between a xed vane impulse turbine with plate type guide vanes and theone with airfoil shaped guide vanes.


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Fig. 27. Comparison of starting characteristics in sinusoidal ow. (a) For impulse turbine with self-pitching guide vane and Wells turbine. (b) For impulse turbne with self-pitching linked guide vanes andWells turbine. (c) For impulse turbne with xed guide vane and Wells turbine


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Fig. 28. Comparison of starting characteristics for plate and airfoil guide vanes.

4. Simulation of turbine characteristics under irregular ow conditions

Since waves in the sea are irregular, and the air ow generated by the oscillatingwater column is also irregular, it is very important to clarify the turbine character-istics under irregular ow conditions. Here let us simulate the characteristics in orderto clarify the usefulness of the impulse turbine with xed guide vanes and the impulseturbine with self-pitching linked guide vanes.

The test irregular wave used in this study is based on ISSC (International ShipStructure Congress) spectrum which is typical in the eld of ocean engineering [18].The spectrum is given as:

S ( f ) 0.11 f 5exp( 0.44 f 4) (7)

The incident wave height H is given as a function of time by such a spectrum. Atypical example of wave height in dimensionless form H *= H / H 1/3 is shown in Fig.29, where the signicant wave height H 1/3 , the wave mean frequency f and the arearatio m are 1.0 m, 0.167 Hz and 0.0234, respectively.

Fig. 29. Test irregular wave.


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On the other hand, for a wave energy device as shown in Fig. 30, the relationshipbetween the incident wave height and the wave height within air chamber is given as:

d dt

r shAcdhdt { r sg( H h) p} Ac (8)

where r s: density of seawater, Ac: air chamber cross-sectional area, g: gravity. Since

na =1m

dhdt

, p is a function of dhdt

if the rotational speed U R is given. As the relationship

between p anddhdt

is obtained from C A f characteristics, here let it be put as

p

r sF

dh

dt ,

Eq. (8) is rewritten as follows:

hd 2hdt 2

dhdt

2

F dhdt

g( H h) 0. (9)

The above equation can be solved by using Runge-Kutta-Gill method, and thenthe wave height within air chamber is obtained. The incident wave power W i andOWC output power W 0 are dened as follows:

W i N

i 1

132p

r sg2 H 2i T 2i / N

i 1

T i (10)

W 0 N

i 1

132p

r sg2h2i T 2i / N

i 1

T i (11)

Then, the efciency of air chamber is

h c W 0 / W i (12)

Fig. 30. Schematic layout of OWC-air turbine type wave generator system.


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Assuming incompressible ow, the axial ow velocity is directly proportional toa variation of the wave height. The nondimensional axial ow velocity through theturbine na is written as:

nad (h / H 1/3 )

d (t / T )dh

dt (13)

The running and starting characteristics of the turbine in irregular ow were calcu-lated by numerical simulation. The steady ow characteristics of the turbines areassumed to be valid for computing performance under unsteady ow conditions.Such a quasi-steady analysis has been validated by previous studies for both Wells

turbine [19] and the impulse turbine [7].The equation of motion for a rotating system of the turbine in irregular ow canbe described in dimensionless form as:

K 2 X 1d w

dt X L C T (f )

(K w )2+n 2a2

s 4(1n)

1+n(14)

where, f =na /(K w ), K w =w mr RT / H 1/3 and n

a =mT na / H 1/3 . The rst and second termson the left side of Eq. (14) are inertia and loading torques respectively, and the righthand side represents the torque generated by a turbine. It is clear from Eq. (14) thatthe behaviour of the turbine (starting characteristics) can be calculated as a function

of K w

and n

a , when loading characteristics X L(w

), torque coefcient C r (f ) rotorparameters such as X I , s and n are specied.Similarly, the running characteristics are obtained by keeping rotational speed con-

stant. In this case, the mean output C 0 and input coefcient C i from t *=0 to t *=10(see Fig. 10) are given respectively as:

C 01t

t

0

C T (f )(K w )2+n 2a

2s

4(1n)1+n w

dt (15)

C i1t

t

0

C A(f )(K w )2+n 2a

2K s

4(1n)1+n

na dt (16)

Then, mean turbine efciency is

h t C 0 / C i (17)

Therefore, the conversion efciency of the wave energy device is

h h c.h t (18)

In the calculations, the ow condition is assumed to be quasi-steady, therefore,the values of C T and C A in steady ow can be used here.


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Fig. 31. Comparison of wave energy conversion efciency under irregular ow condition.

The conversion efciencies of three types of turbines under such irregular owconditions are shown in Fig. 31. The efciency of both the impulse turbines is higherover a wider range of 1/( K w ) in comparison with the Wells turbine, and their peak efciencies are also higher. This is because there is no stall for the impulse turbines,and the turbine efciency of the impulse turbines is higher over a wider range of ow coefcient f in comparison with Wells turbine.

Fig. 32 shows the comparison of wave height in air chamber at the conditionsshowing the peak efciencies for the xed guide vane impulse turbine and the Wellsturbine under irregular ow condition. As is evident from the gure, the wave heightin the case of Wells turbine is rather restrained by higher pressure in air chamber.This fact means that the efciency of air chamber for the Wells turbine becomessmall. On the other hand, the height for the case of impulse turbine is similar to theincident wave as shown in Fig. 29. This is because the maximum efciency isobtained at low ow coefcient for the impulse turbine as shown in Fig. 22(a). Thismeans that the overall conversion efciency of impulse turbine could be better thanthat of the wells turbine because of lower rotational speed for the impulse turbine.

Fig. 32. Wave height in air chamber corresponding to maximum efciency condition.


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The starting characteristics for the turbines are shown in Fig. 33. The impulseturbines can start in a very short time. Furthermore, the rotational speed at operationis much smaller than that of Wells turbine. This is because the torque coefcient C r of the impulse turbines is higher than that of Wells turbine, and the ow coefcientat loading-free condition for the impulse turbines is larger than that of the Wellsturbine. Therefore, it is possible to design an excellent impulse turbine with lowoperational speed, which is desirable from the viewpoints of noise reduction andmechanical design.

5. Conclusions

The performance of the impulse turbine with self-pitch-controlled guide vanes andthat of the xed guide vane impulse turbine have been investigated by model testingand numerical simulation. The results have been compared with those of Wells tur-bine. It is concluded that, under irregular ow conditions, the impulse turbine withself-pitch-controlled linked guide vanes is superior to the xed guide vane impulseturbine which by itself is superior to the Wells turbine.

The optimum parameters for an impulse turbine with self-pitch-controlled linkedguide vanes are as follows.

Rotor elliptic prole blade with

Sr / lr 0.5, t a / Sr 0.4, g 60a / e 3 and l = 7.5,Guide Vane linked mono-vane type withSg / lg 0.65, q1 15 to 17.5, q2 55 to 72.5.

The optimum parameters for a xed guide vane impulse turbine area as follows:

Rotor elliptic prole blade withSr / lr 0.5, a / e 3, t a / Sr 0.4, g 60 and l 7.5

Fig. 33. Starting characteristics under irregular ow conditions.


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Guide Vane The turbine characteristics are not different for airfoil shapedguide vanes and plate-type guide vanes. The optimum guidevane angle is 30 .

References

[1] Kaneko K, Setoguchi T, Raghunathan S. Self-rectifying turbines for wave energy conversion. Proc1st Int Offshore and Polar Engg Conf 1991;1:38592.

[2] Gato L, Wareld V. Performance of a high-solidity wells turbine for an OWC wave power plant.Proc 1993 Euro Wave Energy Symp 1994;NEL:18190.

[3] Inoue M, Kaneko K, Setoguchi T, Saruwatari T. Studies on the Wells Turbine for wave power

generator (turbine characteristics and design parameters for irregular waves). JSME Int J Ser 21988;31(4):67682.[4] Raghuanathan S, Tan CP. Performance of the Wells Turbine at starting. J Energy 1982;6(6):4301.[5] Kim TW, Kaneko K, Setoguchi T, Inoue M. Aerodynamic performance of an impulse turbine with

self-pitch-controlled guide vanes for wave power generator. Proc 1st KSME-JSME Thermal andFluid Engg Conf 1988;2:1337.

[6] Kim TW, Kaneko K, Setoguchi T, Matsuki E, Inoue M. Impulse turbine with self-pitch-controlledguide vanes for wave power generator (effects of rotor blade prole and sweep angle). Proc 2ndKSME-JSME Thermal and Fluid Engg Conf 1990;1:27781.

[7] Setoguchi T, Kaneko K, Maeda H, Kim TW, Inouse M. Impulse turbine with self-pitch-controlledguide vanes for wave power conversion: performance of mono-vane type. Int J Offshore and PolarEngg 1993;3(1):738.

[8] Setoguchi T, Kaneko K, Maeda H, Kim TW, Inoue M. Impulse turbine with self-pitch-controlledtandem guide vanes for wave power conversion. Proc 3rd Int Offshore and Polar Engg Conf 1993;1:1616.

[9] Maeda H, Setoguchi T, Kaneko K, Kim TW, Inoue M. The effect of turbine geometry on theperformance of impulse turbine with self-pitch-controlled guide vanes for wave power conversion.Proc 4th Int Offshore and Polar Engg Conf 1994;1:37882.

[10] Setoguchi T, Kaneko K, Maeda H, Kim TW, Inouse M. Impulse turbine with self-pitch-controlledtandem guide vanes for wave power conversion. Int J Offshore and Polar Engg 1994;4(1):7680.

[11] Maeda H, Setoguchi T, Kaneko K, Kim TW, Inoue M. Effect of turbine geometry on the performanceof impulse turbine with self-pitch-controlled guide vanes for wave power conversion. Int J Offshoreand Polar Engg 1995;5(1):724.

[12] Setoguchi T, Kaneko K, Taniyama H, Maeda H, Inoue M. Impulse turbine with self-pitch-controlledguide vanes for wave power conversion: guide vanes connected by links. Int J Offshore and PolarEngg 1996;6(1):7680.

[13] Richards D, Weishopf FB Jr, Studies with, and testing of the McCormick Pneumatic Wave EnergyTurbine with some comments on PWECS systems, Proc Int Symp on Utilisation of Ocean Waves Wave to Energy Conversion, ASE, ASCE;1986:80102

[14] Tanaka M, Kawashima T, Isozaki T, Takehira A. Investigation of the two-dimensional performanceof supersonic impulse turbine blade cascades (1st report, general characteristics of blade cascade).Trans of the JSME (in Japanese) 1981;47(421):16819.

[15] Kaneko K, Setoguchi T, Inoue M. Performance of Wells Turbine in sscillating ow. Proc CurrentPractices and New Tech in Ocean Engg ASME 1986;2:44752.

[16] Setoguchi T, Kaneko K, Inoue M, Determination of optimum geometry of Wells Turbine rotor forwave power generator (Part I), Proc 3rd Symp on Ocean Wave Utilisation (in Japanese), JAMSTEC,1986:141149.

[17] Setoguchi T, Takao M, Kaneko K, Inoue M. Effect of guide vanes on the performance of a WellsTurbine for wave energy conversion. Int J Offshore and Polar Engg, ISOPE 1998;8(2):15560.


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[18] Hineno M, Yamauchi Y, Spectrum of sea wave, J Soc Nav Arch Japan, (in Japanese),1980;609:160180.

[19] Inoue M, Kaneko K, Setoguchi T, Raghunathan S. Simulation of starting characteristics of the Wells

Turbine. Bull JSME 1986;29(250):117782.

Documents

4000_A Review of Impulse Turbine for Wave Energy Conversion