382 J. ENERGY VOL. 1,NO. 6

Selected Wind Tunnel Test Results forthe Darrieus Wind Turbine

B.F. Blackwell* and R.E. SheldahltSandia Laboratories, Albuquerque, N. Mex.

Five blade configurations of a 2-m-diam Darrieus wind turbine have been tested in the Vought Corporation4.6-x6.1-m (15-x20-ft) Low-Speed Wind Tunnel. Rotor solidity, Reynolds number, and freestream velocitiestested were in the following ranges: solidity, 13-30%; Reynolds number, 1-3 x l O 5 ; freestream velocity, 7-11m/s. The airfoil selection for all configurations was NACA 0012. The parameters measured were rotor torque,rotor rotational speed, and tunnel conditions. Data are presented in the form of power coefficient as a functionof tip-speed ratio along with comparative results from an analytical model.

NomenclatureAs — rotor swept areaC = blade chordCp = power coefficient,

/ = moment of inertiaN = number of bladesQ — torquer = radial coordinate of blade geometryR = rotor radius at equatorRj = constant, see Eq. (1)RJ = radial coordinate of junction between straight

line/circular arc segmentsRec = chord Reynolds number, Rtic/vt =timeV^ = freestream velocityX^ = tip speed ratio, RSl/V^z = vertical coordinate of blade geometryZ = constant, seeEqs. (1) and (2)Z,- = vertical coordinate of junction between straight

line/circular arc segmentsa. =angle of attackv — kinematic viscosityPoo = freestream densitycr = rotor solidity, ratio of blade area to turbine swept

areafi = turbine rotational speed

Introduction

THE previously published experimental performance datafor the Darrieus turbine are contained in a series of

National Aeronautical Establishment/National ResearchCouncil of Canada (NAE/NRC) reports1 '5 and a NASAreport.6 In order to verify some of the earlier findings, ex-pand the range of some of the pertinent parameters, andprovide a comprehensive data base for the development ofcomputer models for the prediction of aerodynamic per-formance and loads, an extensive wind tunnel test programwas undertaken. This paper summarizes the primary resultsfrom the test program conducted at the Vought Corporation,Vought Systems Division Low-Speed Wind Tunnel.

Received May 13, 1977; revision received Sept. 6, 1977.Index category: Wind Power.*Member of Technical Staff, Aerothermodynamics Division;

presently at Mechanical Engineering, Louisiana Tech University,Ruston, La.

tMember of Technical Staff, Aerothermodynamics Division.Associate Fellow A1AA.

Test Models, Instrumentation, and FacilityFigure 1 presents a typical 2-m-diam test model located in

the 4.6- x6.1-m (15- x20-ft) wind tunnel test section. Theturbine consists of the rotating components (tower andblades) held by bearings in the upper collar and in the lowersupport structure. The upper collar is restrained by steelcables with a predetermined tension; these cables are affixedto the walls of the test section. The blades were machinedfrom a high-strength aluminum alloy (7075-T6) to the NACA001 2 7 airfoil section specification as a flat ribbon and thenformed to the desired curved shape.

The curved blade shape was the straight line/circular arcapproximation to the troposkien8 shape and can be describedby the following equations:

(1)

where the constants are given by R/ = 0.3065025m,R = 0. 9798138m, Z=1.0m, Rj = 0.6721038m, andZ/=0.5654058m.

The rotating tower is attached to the power and in-strumentation train, which consists of a precision torque androtation transducer, a right-angle gear transmission with a 2:1gear ratio, and a speed-controlled 3.7 kW (5-hp) electricmotor/generator. The torque and rotation transducer was a

Fig. 1 Photograph of 2-m model in wind tunnel.

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NOV.-DEC. 1977 WIND TUNNEL TEST RESULTS FOR THE DARRIEUS WIND TURBINE 383

PowerFlow

5-kWLoad Bank

Fig. 2 Schematic of test setup.

200 i | i j r i .

= 35.0 FT/SEC

Q

0 o o o °0 100 2uO 300 40C ' 500 oOO 700

TURBINE SPEED, rpm

Fig. 3 Representative torque vs rpm curve.

commercially available Lebow Model 1404-200. The 2:1gearbox allowed a better match between the wind turbineand the motor/generator load characteristics. Themotor/generator speed was controlled by a Morse LTV-5 acadjustable speed controller. (The significance of maintaininga specified turbine rotational speed is discussed in a sub-sequent section.) Figure 2 is a schematic of the turbine, in-strumentation, and load system.

The Vought Systems Division Low-Speed Wind Tunnel9 isa horizontal single-return, tandem test section, closed-circuitfacility. The facility contains a rectangular 4.6-x6.1-m (15-x 20-ft) test section followed by a rectangular 2.1- x 3.0-m (7-x 10-ft) test section. The upstream test section has a wind-speed range of 3-23 m/s. Figure 1 shows the wind turbine inthe 4.6-x6.1-m section; the photograph was taken lookingdownstream into the contraction region of the 2:1-x 3.0-mtest section. Controls for both the wind turbine and the windtunnel are located behind the windows shown on the right sideof the photograph. The windows provided visual observationof the turbine and also allowed video and camera coverage.

Test Procedure and MatrixThe general character of the torque/speed curves for the

Darrieus turbine must be fully understood for proper design

of an experimental setup that will define the performance overthe tip-speed ratio range of interest. For example, consider theexperimental torque/speed curve shown in Fig. 3. If theturbine is started with no external load, it will simply ac-celerate to the runaway condition, which is in excess of 700rpm. Suppose an external load of 88 in-lbf is applied. Both365 and 540 rpm correspond to a load of 88 in-lbf. Fromelementary stability considerations, it can be shown that the365 rpm condition is unstable. In fact, all regions where theslope of the torque/speed curve is positive are unstable ifuncontrolled. To obtain performance data in the unstableregions, some type of control system had to be devised. Thesystem shown schematically in Fig. 2 accomplished thepurpose of maintaining a fixed rotational speed independentof tunnel conditions.

Since the Darrieus turbine is a lift device, one would expectthat the performance is a function of Reynolds number. Theobvious length scale for the Reynolds number is the bladechord; however, the velocity scale is not so obvious since thevelocity of the wind relative to the blade depends both onangular position of the blade and on location along the bladelength. If one observes the primary torque-producing portionof the blade (near equatorial plane) operating at high tip-speed ratios, it appears that the most appropriate velocityscale is the blade tip speed (/?Q). This suggests that con-figurational changes such as chord, number of blades, airfoilsection, etc., can be more readily compared at constantReynolds number, where the length and velocity scales areblade chord c and tip speed RSl.

(3)

Consequently, the tip-speed ratio for a given test con-figuration was varied as a result of tunnel speed changes whilea constant rotational speed (and hence Reynolds number) wasmaintained. The constant rotational speed method of testinghas the additional advantage of better simulating the syn-chronous grid application10 of the Darrieus turbine.

Although the primary test method employed involvedconstant turbine speed with variable tunnel speed, additionaldata were taken at constant tunnel speed with variable turbinespeed. The complete test matrix is presented in Table 1. Fivedifferent configurations consisting of three different chordsand two different numbers of blades were tested at a varietyof turbine and tunnel speeds.

Data Reduction and Test ResultsThe variables measured for each test configuration were

turbine torque, turbine rotational speed, and tunnel testconditions. A convenient means of characterizing theaerodynamic performance of a wind turbine is the plot ofpower coefficient Cp as a function of the tip-speed ratio X^.Before Cp and X^ can be calculated, the indicated torquemust be corrected for rotor bearing friction and thefreestream velocity corrected for wind tunnel blockage ef-fects. The bearing friction torque was determined bymeasuring the torque necessary to drive the rotor (minus theblades) without any tunnel flow. The freestream velocity wascorrected for both wake and solid body blockage, accordingto the relations suggested by Pope and Harper.11 Themaximum freestream velocity correction for blockage was2.6%. Additional details of the blockage correction can befound in Blackwell,Sheldahl, and Feltz.12

The blade geometry can be characterized by the solidity,which is the ratio of total blade planform areat to rotor sweptarea.§ Figure 4 shows the influence of Reynolds number on

JThe blade planform area for a constant chord blade is the productof number of blades, blade chord, and blade length.

§A rotating blade of the Darrieus turbine sweeps out a volume thatis symmetric about the axis of rotation; this is called the "swept"volume. The area common to the "swept" volume and to a planecontaining the axis of rotation is called the "swept"area.

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384 B.F. BLACKWELL AND R.E. SHELDAHL J. ENERGY

power coefficient for a solidity of 0.3. An increase inReynolds number by a factor of 3 produces a 30% increase inmaximum power coefficient. Increasing the Reynolds numberalso increases the tip-speed ratio range where useful power isproduced. The tip-speed ratio where the power coefficient is amaximum decreases with increasing Reynolds number and isbelieved to be due to the fact that the stall angle increases withincreasing Reynolds number. Once the blade Reynoldsnumber exceeds several million, significant increases in(Cp)max are unlikely.

Figure 5 presents power coefficient data for a solidity of20%. The trends with Reynolds number are similar to thosefor the 30% solidity data.

Figure 6 presents the effect of solidity on performance at anominal Reynolds number of 1.5x 105. The most noticeableinfluence of solidity is that the runaway-condition tip-speedratio increases with decreasing solidity; for a synchronousapplication where the tip-speed ratio varies over a wide range,power can be produced over a greater windspeed variation fora given turbine rotational speed. The tip-speed ratio at whichthe power coefficient is a maximum increases with decreasing

0.5

0.2

0.1

0.0

-0.1

0 D

a - 0.2 N - 3RUN RPM Re

O 13 270 101,000° 14 400 154,000

15 525 200.000

0o a $

Fig. 5 Influence of Reynolds number on power coefficient forsolidity of 0.2.

0.4

0.3

S0.2

0.1

0.0

-0.1

' ' ' ' ' ' ' ' ' ' . ' - a s ' N - J ' ' 'RUN RPM Rec

0 1 180 104,000a 2 267 150,000

AAA A 3 500 290,000A A closed symbol denotes

__ J a A A peak torque«D A

A I? 9° 0 A° ° A

A d? o

A O ° O D

A D ° 0 A

r A o D O o° AD O DA n O °

A C£> O

o o^SR)^ &° A0

aD

i i i I i 1 i I i 1 i i , I i I0 1 2 3 4 5 6 7 8

'

-

_

_

-_

_

i9

0.3

0.1

-0.1

%30vv

Re = 150,000 (nominal)

RUN N oO *•A 8D 140 19

3 0.33 0.253 0.202 0.202 0.13

Fig. 4 Influence of Reynolds number on power coefficient forsolidity of 0.3.

Fig. 6 Influence of solidity on power coefficient for nominalReynolds number of 150,000.

Table 1 Darrieus rotor tests in the Vought Systems Division Low- Speed Wind Tunnel

RunNo.

12356789

1011131U1516171819202122232k25262728

As =

ConfigurationNumber

1111122222

33333^u14khh55555

2.591*14. m2

No. ofBlades

33333333333333322222222222

Solidity(*)

303030303025252525252020202020

202020202020

1313131313

RotorSpeed(rpm)

180267500

VariableVariable

216320600

VariableVariable

270Uoo525

VariableVariable

180267350500

VariableVariableVariable

270UOO525

Variable

WindVelocity

(m/s)

VariableVariableVariable

119

VariableVariableVariable

119

VariableVariableVariable

97

VariableVariableVariableVariable

9117

VariableVariableVariable

9

Chord(cm)

8.8158.8158.8158.8158.8157.3^67.3^67.3^67.3^67.3^65.8775.8775.8775.8775.8778.8158.8158.8158.8158.8158.8155.8775.8775.8775.8775.877

ChordReynolds Number

10 ,̂000150,000290,000VariableVariable101,000151,000278,000VariableVariable101,00015^,000200,000VariableVariable106,000156,00020^,000290,000VariableVariableVariable10if,000155,000200,000Variable

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NOV.-DEC. 1977 WIND TUNNEL TEST RESULTS FOR THE DARRIEUS WIND TURBINE 385

o = 0. 2 Re = 155,000RUN N

O 14 3D 19 2

od?

i I

o l

OD

I I

Rec = 2 x 105

a = 0.13, N = 2

— THEORY

O DATA

Fig. 7 Influence of number of blades on power coefficient forsolidity of 0.2 and Reynolds number of 155,000.

Fig. 10 Comparison of theoretical model with data for solidity of0.13 and Reynolds number of 200,000.

| i I T T I 'Nc/R c(cm/in) source V^m's

a 0.265 8.82/3.47 Sandia 90 0.25 15.24/6.00 NRC 4.7-6 .1O 0.22 7.35/2.89 Sandia 9

n oDO O

D O

a o

Table 2 Aerodynamic section data for NACA 0012 airfoil

Fig. 8 Comparison of Sandia and NRC data.

Fig. 9 Comparison of theoretical model with data for solidity of 0.2and Reynolds number of 290,000.

solidity. To maximize the power coefficient, a solidity in therange 0.2-0.5 should be chosen.

Numerous theroetical models for Darrieus turbine per-formance have been proposed. In most of these models, theonly effect of the number of blades is through the solidityparameter. This implies that for a given swept area the per-formance of a two-bladed system is the same as that of athree-bladed system provided that the product (/Vc) remainsconstant. To verify this hypothesis, a two-bladed and a three-bladed configuration, both with a solidity of 20%, were testedat the same Reynolds number. The results are shown in Fig. 7.It appears that the three-bladed configuration is slightly betterthan the two-bladed one with the most pronounced difference

a, deg.

-23.5-21.5-19.5-17.5-15.5-14.5-13.5-12.5-11.5-10.5- 9.5- 7.5- 5.5- 3.5- 1.5

0.52.54.56.58.5

10.511.512.513.514.515.516.518.520.522.524.528.530.035.040.01*5.050.055.060.065.070.075.080.085.090.095.0

100.0105.0110.0115.0120.0125.0130.0135.0140.0145.0150.0155-0160.0165.0170.0175.0180.0

Re =

Ct

-0.745-0.676-0.648-0.623-0.632-0.674-0.718-0.792-0.967-0.926-0.868-0.737-0.606-0.428-0.143+0.055

0.3020.5380.6910.8190.9050.8650.7560.7090.6730.6370.6200.6320.6650.7010.7220.8750.9151.0201.0751.0851.0400.9650.8750.7650.6500.5150.3700.2200.070

-0.070-0.220-0.370-0.510-0.625-0.735-0.840-0.910-0.945-0.945-0.910-0.850-0.740-0.660-0.675-0.850-0^6900.0

3.6 x io5

cd.0.35380.30930.27120.23690.20300 . 18420.16580.12400.02930.02780.02560.02120.01740.01330.00920.00820.00880.01160.01460.01760.02010.05570.15440.1755o . 191*70.20910.22510.25830.30140.34430 . 38400.53980.5700.7450.9201.0751.2151.3451.4701.5751.6651.7351.7801.8001.8001.7801.7501.7001.6351.5551.4651.3501.2251.0850.9250.7550.5750.4200.3200.2300.1400.0550.025

Re =ci

-0.697-0.639-0.651-0.621-0.596-0.613-0.66?-0.761-1.005-0.958-0.89U-0.757-0.616-0.390-0.135+0.0580.2640.5380.7110.8340.9310.9630.7530.6570.6270.6070.6010.6590.6610.6980.7380.8750.9151.0201.0751.0851.0400.9650.8750.7650.6500.5150.3700.2200.070

-0.070-0.220-0.370-0.510-0.625-0.735-0.840-0.910-0.945-0.945-0.910-0.850-0.740-0.660-0.675-0.850-0.6900.0

5 x IO5

cd0.35560.30460.26860.23350.19830 . 1832o . 16920.13130.02760.02590.02380.01960.01600.01150.00840.00740.00770.01010.01290.01540.01780.01860 . 16120.1827o . 19290.20950.22820.27370.29750.34530.40640.53980.5700.7450.9201.0751.2151.3451.4701.5751.6651.7351.7801.8001.8001.7801.7501.7001.6351.5551.4651.3501.2251.0850.9250.7550.5750.4200.3200.2300.1400.0550.025

in the tip-speed ratio range 3-4. No satisfactory explanationfor this effect has been found.

The previous observed trends with increasing Reynoldsnumber suggest that for a given solidity and turbine rotational

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386 B.F. BLACKWELL AND R.E. SHELDAHL J. ENERGY

speed, the blade choru (Reynolds number) should be as largeas possible. This suggests that the number of blades should bekept as small as possible. While numerous two-bladed con-figurations have been tested, it is not yet known if a one-bladed configuration is practically feasible.

Figure 8 compares performance data for two of the Sandiaconfigurations tested at constant freestream velocity withNRC data presented by South and Rangi.5 The NRC testconditions were 50- to 250-rpm turbine speed and 3.05- to 6.1-m/s (10- to 20-ft/s) tunnel speed. The NRC data exhibit aslightly higher (Cp)max occurring at a higher tip-speed ratioand a lower tip-speed ratio for the runaway condition. Somediscrepancies obviously exist between the two data sets.

Figures 9 and 10 compare theoretical calculations withexperimental data for solidities of 0.2 and 0.13, respectively.The model, which is a multiple streamtube computer code,has been described by Strickland.13 The aerodynamic sectiondata utilized for the theoretical predictions are tabulated inTable 2. Logarithmic interpolation/extrapolation on chordReynolds number and linear interpolation on angle of attackwere utilized. Computational experiments have indicated thatthe performance results are very sensitive to Reynoldsnumber. The agreement between theory and data isreasonably good for the lefthand side of the power coefficientcurve. For the relatively low tip-speed ratio range, the bladesare "lightly loaded" and the theory has the most validity. Thepoor agreement between theory and data on the right-handside of the power coefficient curve can be attributed to thefact that the model assumes that the downwind portion of therotor sees the same induced velocity field as the upwindportion of the rotor, and that all streamlines behave in-dependently. Obviously, additional theoretical work remainsto be done for the high tip-speed ratio operation condition.

For those rotor configurations listed in Table 1 but notspecifically discussed here, the reader is referred to Black-well, Sheldahl, and Feltz.12

SummaryThe maximum power coefficient of all configurations

tested was found to be approximately 0.35. IncreasingReynolds number increases the power coefficient at all tip-speed ratios for all configurations. Decreasing rotor solidityincreases the tip-speed ratio range of operation for whichuseful power is produced. In order to maximize the peakpower coefficient for a given Reynolds number, a solidity inthe range of 0.2 to 0.25 should be chosen. The tip-speed ratio

for the runaway condition increases for decreasing solidityand/or increasing Reynolds number and windspeed. Two-arid three-bladed configurations were tested at the samesolidity and Reynolds number; from the standpoint ofaerodynamic performance, three blades are slightly betterthan two. However, this difference is within the experimentaluncertainty of the data.

AcknowledgmentThis work was supported by the United States Department

of Energy, formerly Energy Research and DevelopmentAdministration, Division of Solar Energy.

References1 South, P. and Rangi, R.S., "Preliminary Tests of a High Speed-

Vertical Axis Windmill Model," National Research Council ofCanada, LTR-LA-74, March 1971.

2South, P. and Rangi, R.S., "A Wind Tunnel Investigation of a14-ft Diameter Vertical-Axis Wind Turbine Developed at the NationalResearch Council, Ottawa, Canada," Agricultural Engineer, Feb.1974, pp. 14-16; (see also American Society of Agricultural Engineers,Paper No. PNW 73-303).

4Templin, R.J., "Aerodynamic Performance Theory for the NRCVertical-Axis Wind Turbine," National Research Council of Canada,LTR-LA-160, June 1974.

5South, P. and Rangi, R.S., "An Experimental Investigation of a12-ft Diameter High Speed Vertical-Axis Wind Turbine," NationalResearch Council of Canada, LTR-LA-166, April 1975.

6Muraca, R.J. and Guillotte, R.J., "Wind Tunnel Investigation ofa 14-ft Vertical Axis Windmill," NASA TM X-72663, March 1976.

7 Abbott, I .H. and Von Doenhoff, A.E., Theory of Wing Sections,McGraw Hill , New York, 1949.

8Reis, G.E. and Blackwell, B.F., "Practical Approximations to aTroposkien by Straight-Line and Circular-Arc Segments," SandiaLaboratories, SAND 74-0100, March 1975.

9Holbrook, J.W., "Low Speed Wind Tunnel Handbook," LTVAerospace, AER-EOR-12995-B, Feb. 1974.

10Banas, J.R., Kadlec, E.G., and Sullivan, W.N., "Application ofthe Darrieus Vertical-Axis Wind Turbine to Synchronous ElectricalPower Generation," Sandia Laboratories, SAND 75-0165, March1975.

"Pope, A. and Harper, J.J., Low Speed Wind Tunnel Testing,John Wiley&Sons, Inc., New York, 1966.

1 2Blackwell , B.F., Sheldahl, R.E., and Feltz, L.V., "Wind TunnelPerformance Data for the Darrieus Wind Turbine with NACA 0012Blades," Sandia Laboratories, SAND 76-0130, May 1976.

1 3Strickland, J.H., "The Darrieus Turbine: A PerformancePrediction Model Using Mult iple Streamtubes," Sandia Laboratories,SAND 75-0431, Oct. 1975.

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