One-dimensional Analysis of Impulse Turbine Self …downloads.hindawi.com/journals/ijrm/2000/287275.pdfof this turbine in a sinusoidally oscillating flow, higher turbine efficiency

International Journal of Rotating Machinery2000, Vol. 6, No. 2, pp. 151-157

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One-dimensional Analysis of Impulse Turbine withSelf-pitch-controlled Guide Vanes for Wave

Power Conversion*

M. INIOUE a, K. KANEKO b’t and T. SETOGUCHI b

Department of Energy and Mechanical Engineering, Kyushu University, Fukuoka, Japan,"Department of Mechanical Engineering, Saga University, 1, Honjo-machi, Saga-shi, Saga, 840-8502, Japan

(Received 11 August 1997; In finalform 28 July 1998)

A classical one-dimensional analysis in turbomachinery was presented to estimateaerodynamic characteristics of an impulse turbine with self-pitch-controlled guide vaneswhich is proposed by the authors for ocean wave power conversion. With some simplifiedassumptions, the efficiency vs/flow-rate coefficient curves were calculated and comparedwith the experimental results both in a unidirectional steady flow condition and a sinusoidallyoscillating flow condition. The estimated results reveal a behavior of the actual char-acteristics curve of the turbine. Possibility of further improvement in efficiency was discussedfrom a viewpoint of specific speed and specific diameter.

Keywords: Fluid machinery, Ocean wave energy, Self-rectifying-turbine, Impulse turbine,Guide vane, Wave energy conversion

INTRODUCTION

In order to overcome the global environmentalproblem, it is important to develop an effectivetechnique of utilization of natural energy which isinherently low density but has no harmful effects onthe earth. Various investigations have been carriedout on wave energy conversion in the past. Amongthem Wells turbine combined with oscillating watercolumn (OWC) is assumed to be a most promisingdevice (Inoue et al., 1986; 1988). Wells turbine is a

self-rectifying-turbine and it needs no rectifyingvalve system. The most favorable character of theWells turbine is relatively higher tangential bladevelocity compared with axial air velocity, resultingin a compact generator size. However for higherturbine loading, for example when input of Wellsturbine increases by a energy enhancing techniquesuch as wave focusing submerged plate, the abovementioned merit becomes weak point from theviewpoints of blade stress, maintenance ofmechan-ical parts and noise generation. Furthermore,

* This paper was originally presented at ISROMAC-7.Corresponding author. Fax: +81-952-28-8587. E-mail: [email protected].

151

152 M. INIOUE et al.

efficiency of the Wells turbine is relatively lowerthan the ordinary turbines.For higher wave energy density, the use ofimpulse

turbine is more reasonable because it operates withhigher pressure drop at high efficiency. The authorshad proposed an impulse turbine with self-pitch-controlled guide vanes, which were set at both sidesof the rotor blade. The guide vanes were forced tooscillate automatically by the reciprocating air flowto operate as nozzle and diffuser. The model tests ofthe impulse turbine have been carried out to developan efficient low speed air turbine for wave powergenerator (Kim et al., 1988; Setoguchi et al., 1993;1994; Maeda et al., 1995). In this paper a simple one-dimensional theory is proposed to estimate theperformance of the impulse turbine, and possibilityof an improvement of the turbine performance isdiscussed.

BACKGROUND

In the first proposed air turbine with self-pitch-controlled guide vane (Kim et al., 1988), it wasfound by the model test that the diffuser efficiencywas low due to improper movement of the down-stream guide vanes (Setoguchi et al., 1993). Accord-ingly improved version was proposed introducingsplitter vanes into the guide vanes as shown in Fig. 1.

In this case only the splitter vanes make an

oscillating motion, upstream splitter vanes play-ing as nozzle and downstream ones as diffuser(Setoguchi et al., 1994). As a result of the model testof this turbine in a sinusoidally oscillating flow,higher turbine efficiency was obtained than themost efficient Wells turbine (Wells turbine withguide vanes) tested in the same test rig with thesame size of rotor as the impulse turbine. At thesame time, it was pointed out that maximum effi-ciency was obtained at a higher flow coefficient

(the ratio of axial flow velocity to tangential velo-city of rotor blade at mid span). It means that theturbine operates at about a half-rotation speedcompared with the Wells turbine. This is advanta-geous from the viewpoint of mechanical stress andnoise generation. Therefore this turbine seemedto be worth while for practical use although ithad moving parts in the guide vane system. Thensystematic experimental investigations had beencarried out to improve the performance, in whichrotor geometry, number of blades, setting angle ofthe splitter vane were varied (Maeda et al., 1995).As a result, turbine efficiency was not so improvedas expected from ordinary impulse turbine. In orderto investigate the reason for this and to discuss thepossibility ofimprovement ofturbine efficiency, theturbine performance is analyzed theoretically inthe following section.

FIGURE Blade geometry and velocity diagram.

ONE-DIMENSIONAL ANALYSIS

Performance under Unidirectional Steady Flow

Although the upstream and downstream guidevanes of the present turbine make an oscillatingpitching motion to operate as nozzle and diffuser,the motion occurs very quickly when flow directionchanges, then the pitch angle is fixed to a certainsetting angle for the most part of the period.Therefore, similar to a simple theory for ordinaryturbomachine, the following assumptions can begiven to analyze the turbine performance.

(1) Turbine performance is estimated from thecondition at mean radius.

ONE-DIMENSIONAL ANALYSIS 153

(2) Absolute nozzle exit flow angle c1 is constant.

(3) Relative rotor exit flow angle/2 is constant.

Following these assumptions and velocity diagramshown in Fig. 1, theoretical enthalpy drop of theturbine Ith is written as:

where UR is the tangential blade velocity at meanradius, Vol the swirl component of inlet absolutevelocity, Vo2 the swirl component of exit absolutevelocity, Va the axial velocity, K- cot c1 + cot/32and O--va/UR. Loss coefficient is defined as

-AI/(vZa/2) for enthalpy loss AI through wholeturbine including rotor, upstream and downstreamguide vanes. Actual enthalpy drop through theturbine I is written as:

I- Ith + All U2(Kc- + 1/2@52) (2)

and turbine efficiency r/is written as follows:

r/-- T Kq5 q- @52/2 (3)

The values of K and introduced above areestimated from torque coefficient Gr and inputcoefficient CA obtained by performance test understeady flow condition. CT and CA are defined as

follows, respectively:

2CT T/(p(vaq-- uZp,)blzr/2); (4)

CA pQ/ (p(V2a q- U2R)blzva/2), (5)

where T is the turbine shaft torque, p the density ofair, b the span length of rotor blade, the chordlength of rotor blade, z the number of rotor blade,rr the mean radius, p the total pressure dropthrough turbine and Q the flow rate. Output andinput powers are given as follows, respectively:

pvaAlth T( UR/rR); (6)

pvaAI=pQ, (7)

where A is the cross sectional area of flow passageand pvaA the mass flow rate. From Eqs. (1), (2),(4)-(7) and defining solidity as cr=blz/A-1/(2rcr/z), the equations for K and { are obtained:

- r(CA + (9)

With Eqs. (8) and (9) into Eq. (3), turbine efficiencyis obtained as follows:

--CA0which is the same as the ratio of Eq. (6) to Eq. (7).

According to our experiments, there was consider-ably a wide range of 05 where K and were nearlyconstant as will be shown in the next section.Therefore, for simplicity, K and are assumed tobe constant to estimate an approximate character-istics of this turbine. In this case, the maximumefficiency T]max is obtained at q5 =2/K:

rlmax + (2/K2) (l l)

Performance under Reciprocating Flow

In this section the turbine performance underreciprocating flow is estimated by quasi-steadyanalysis with K and obtained in steady flowexperiment.When axial velocity va changes sinusoidally with

amplitude Va and period Tw, is written as

05 sin , (12)

where Va/UI, 2rct/Tw. Then mean turbineefficiency is calculated from

IthlVal d, Jo Ilval dg. (3)


Introducing Eqs. (1), (2) and (12), and executing theintegration assuming K and to be constant again,

(Tr/4)K,I)-- (Tr/4)K- 1+ 2/3 (14)

The maximum efficiency is obtained at - 8/(rrK):

rnaxif- 64ff/(3rrZK2) (15)

COMPARISON WITH EXPERIMENTALRESULTS

Table I shows the geometrical parameters ofthe testturbines investigated in the past (Setoguchi et al.,1994). Among them relatively higher efficiency wasobtained by the turbine with the following combi-nation of parameter: #= 30, 01 15, 02= 50,Zg=20. On the other hand, efficiency wasmoderate with: #=200,30 0=15 02=50Zg= 18. These two types were selected to discussthe validity of the present one-dimensional theory.

Figure 2(a) and (b) show plots ofKand againstb, respectively, where the values of K and are

TABLE Geometrical parameters of test turbine

Rotor blade (Impulse blade)Suction side Elliptic-arcPressure side Circular-arcChord length 52 mmSolidity cr 2.0Blade angle # 20, 30, 40 (see Fig. 1)Guide vane (with splitter blade)

Fixed vane:Blade section Circular-arcCamber angle 70Chord length 36.7 mmBlade thickness 1.5 mm

Movable vane:Blade section Circular-arc (camber angle

of 45 and straightChord length 50mmBlade thickness 1.5 mmNumber of blade zg 15 30Setting angle of nozzle 01 10 20Setting angle of diffuser 0 15 70

Tip dia. 298 mmHub-to-tip ratio 0.7

calculated from torque coefficient CT and inputcoefficient CA obtained under steady flow turbinetest. The points indicated by circle in the figure arethe operating point for maximum efficiency. It isobserved that the value of K is almost constantexcept for very low b, and this means the validity ofassumption of the present one-dimensional theory.On the other hand, the value of is roughlyconstant at high flow-rate coefficients, but increasesremarkably with b decreasing at low flow rangeincluding maximum efficiency point. In order todiscuss the reason for this unexpected high in lowflow range, inlet and exit velocity diagram of therotor was investigated from experimental data atmean radius. As a result, it was found that exit

(a)

3.0

2.00.0 0.5 1.0 1.5 2.5

(b)

I0.0

FIGURE 2 (a) K- b characteristics for steady flow. (b) if- bcharacteristics for steady flow.


absolute flow angle Ct2 was higher than 90 near

maximum efficiency point. This led to ill matchingcondition with the downstream guide vane, anddiffuser efficiency decreased. The lower the flowcoefficient is, the higher OZ2 becomes, and the lowerefficiency becomes.

According to the assumption of the presenttheory, turbine efficiency can be estimated by Eq. (3)if the values of K and ff were given. Figure 3 showsthe theoretical efficiency comparing with experi-ment. In this case the values of K and ff were keptconstant to the values at the maximum efficiencypoints (dot dashed line in Fig. 2), respectively. It isobserved from this figure that the present simpli-fied theory can predict the behavior of efficiency-flow rate characteristics quite well. Discrepancybetween theory and experiment becomes noticeablein low flow range due to higher loss coefficient inthat region.From the velocity diagram discussed above, it is

expected that exit absolute flow angle O2 may fitwith the downstream diffuser angle 02 for muchhigher flow coefficient than that for maximumefficiency point. But experimental and theoreticalvalues of efficiency at such a high flow coefficientare low. The reason for this is concerned with thevalues of specific speed ns and specific diameter dsfor axial impulse turbine. According to Balje(1962), high efficiency can be realized only within

0.8

0.6

0.4

0.2

0.00.0

Simple Theory -Experiment .q

0.5 1.0 1.5 2.0 2.5

FIGURE 3 Efficiency characteristics for steady flow.

a very limited area on ns-ds diagram for axial

impulse turbine. Figure 4 shows the ns- ds diagramby Balje. The relation between the flow coefficientdefined in the present theory and the values of nsand ds by Balje is written as follows:

q5- 16/(7v(1 + u)2(1 u)nsd), (16)

where u is hub ratio. The dot dashed line in thefigure indicates the relation for u-0.7, that is thevalue for the test turbine. From Eq. (16) it is

observed that high efficiency can be obtained forq5-0.20.8 and efficiency drops noticeably forq > 1.5. Therefore it is important to select optimumvalues of ns and ds for the design of the presentimpulse turbine, and it is also noted that one cannotdiscuss performance of the present turbine onlyfrom a compatibility of the velocity diagram.

In Fig. 5, the mean turbine efficiency from Eq.(14) for oscillating flow is compared with experi-ment. It is shown that the efficiency characteristicscan be well estimated qualitatively. Drop in turbine

efficiency for oscillating flow is only about 2%compared with steady flow. This is a preferablecharacter of the present impulse turbine.

Finally a possibility of improving efficiency ofthe present turbine is discussed. In Fig. 6 the valueof maximum efficiency is plotted from Eq. (11). Toget higher efficiency higher value of K and lowervalue of are desirable. The value ofK depends onnozzle exit angle 01 and rotor angle #. Experiment-ally the highest value of K(= 4.1) was obtained at

0- 15, #- 30. It may be possible to increase Kto some degree if exit deviation angle could bereduced by optimum rotor design. On the otherhand it is most important to reduce loss coefficientat maximum efficiency point, qS-2/K. Howeverthe relations 1/q5 cot a cot/3 cot/32 cot

K- cot al + cot/32 must hold, and then cot a2-cot/31 must be satisfied near maximum efficiencypoint. This means that it is necessary to design a

diffuser with angle 02 which fits for absolute flowangle a2 > 90. This may be difficult from structuralstandpoint for the present turbine in which guidevanes make a pitching motion automatically.


40.0 i"

/v=0 4

20.0V 0.5

I0 0

s

4 0

2 0

r/=0 3/

1 0

O. O1 0. 02 0. 04 O. 1 "’0. 2 0. 4 1. 0 2. 0

=0. 1

O. 20. 4O. 6O. 8

05

2. 02. 5

FIGURE 4 ns- ds diagram for impulse turbine.

0.8 ii11] 1.0/

l- Simple Theory "-]0.6 ----o---- Experiment -] 0.8

0.4 0.65.04.54.0

0.2 0.4 3.53.0

o.o 0.20.0 0.5 1.0 1.5 2.0 2.5 0.0 2.0 4.0 6.0 8.0 10.0

FIGURE 5 Efficiency characteristics for oscillating flow. FIGURE 6 Relation between maximum efficiency and losscoefficient.

SUMMARY

In this paper a simplified one-dimensional theorywas proposed to estimate the performance of theimpulse turbine for wave energy generator based on

a classical turbine theory. The present theory can

explain the efficiency characteristics quite well. Thetheoretical value was compared with experimentalvalue and some measures for improving the turbine

efficiency were discussed. Main points mentioned


are optimum selection of specific speed and specificdiameter, rotor design with lower deviation angleand improvement of inlet condition to downstreamguide vane.

Acknowledgements

This investigation is supported by Grant-in-Aid forScientific Research from The Ministry of Educa-tion, Science and Culture, Japan and IwayaFoundation for Science and Technology. Theauthors would like to thank for these financialsupports.

References

Balje, O.E. (1962) Study on design criteria and matching ofturbomachines: Part A similarity relations and designcriteria of turbines, Trans. of ASME, Journal of Eng. forPower, 84(1), 83-102.

Inoue, M., Kaneko, K., Setoguchi, T. and Raghunathan, S.(1986) Simulation of starting characteristics of the wellsturbine, AIAA/ASME 4th Fluid Mech. Plasma DynamicsLasers Conf AIAA-86-1122.

Inoue, M., Kaneko, K., Setoguchi, T. and Saruwatari, T. (1988)Studies on the wells turbine for wave power generator:Turbine characteristics and design parameter for irregularwave, JSME Int. Journal, Ser. II, 31(4), 676-682.

Kim, T.W., Kaneko, K., Setoguchi, T. and Inoue, M. (1988)Aerodynamic performance of an impulse turbine withself-pitch-controlled guide vanes for wave power generator,Proc. of 1st KSME/JSME Thermal and Fluid Eng. Conf, 2,pp. 133-137.

Maeda, H., Setoguchi, T., Kaneko, K., Kim, T.W. and Inoue, M.(1995) Effect of turbine geometry on the performance ofimpulse turbine with self-pitch-controlled guide vanes forwave power conversion, Int. Journal of Offshore and PolarEng., ISOPE, 5(1), 72-74.

Setoguchi, T., Kaneko, K., Maeda, H., Kim, T.W. and Inoue, M.(1993) Impulse turbine with self-pitch-controlled guide vanesfor wave power conversion: Performance of mono-vane type,Int. Journal of Offshore and Polar Eng., ISOPE, 3(1), 73-78.

Setoguchi, T., Kaneko, K., Maeda, H., Kim, T.W. and Inoue, M.(1994) Impulse turbine with self-pitch-controlled tandemguide vanes for wave power conversion, Int. Journal ofOffshore and Polar Eng., ISOPE, 4(1), 76-80.

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One-dimensional Analysis of Impulse Turbine Self …downloads.hindawi.com/journals/ijrm/2000/287275.pdfof this turbine in a sinusoidally oscillating flow, higher turbine efficiency