Low speed water-pumping wind-mills : rotor tests and overall performance

performance

Citation for published version (APA):

Beurskens, H. J. M., Hageman, A., Hospers, G. D., Kragten, A., & Lysen, E. H. (1980). Low speed water-pumping wind-mills : rotor tests and overall performance. (TU Eindhoven. Vakgr. Transportfysica : rapport; Vol. R-427-D). Technische Hogeschool Eindhoven.

Document status and date: Published: 01/01/1980

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LOW SPEED WATER PUMPING WINDMILLS : ROTOR TESTS AND OVERALL PERFORMANCE

H. Beurskens A. Hageman G. Hospers A. Kragten E. Lysen March 1980 R 427 D

UNIVERSITY OF TECHNOLOGY EINDHOVEN WIND ENERGY GROUP

This paper has been submitted to the 3rd International Symposium on Wind Energy Systems (BHRA) , Copenhagen, August 26-29, 1980.

LOW SPEED WATER PUMPING WINDMILLS : ROTOR TESTS AND OVERALL PERFORMANCE

H.J.M. Beurskens

A.J.F.K. Hageman

G.D. Hospers A. Kragten E.H. Lysen

Wind Energy Group, Laboratory of Fluid Dynamics and Heat Transfer, Department of Physics, University of Technology, Eindhoven, the Netherlands.

SUMMARY

In the process of developing low speed water pumping windmills the aerodynamic properties of four different rotors of 1.5 m diameter were tested in an open wind-tunnel.

The influence of a number of design parameters on the power output has been studied. These include linearization of the blade setting angle and blade chord, blade tip geometry, the effect of guy rods and other structural elements tb strengthen the blades, and the effects of obstacles in the rotor wake.

Other experiments include the effect of changing the geometry of the leading edge

to increase the starting torque of the rotor. The results of these experiments are

reported and compared with theoretical predictions.

The field performance of a water pumping windmill has been measured at a test field. The theoretical performance of the windmill could be predicted by measuring the characteristics of the pump and coupling this to the measured performance of the

rotor. The discrepancies between field data and theoretical predictions will be

NOMENCLATURE B CD C L Cp C P max C Q C

Q

st c D H P Q _st R Re r V x

₌

r R a B 0 A A 0 A-max A

= -

r

.

A-r R 0 1>

=

a + S Bc (J '" -2\'l'R P -2-number of blades drag coefficient lift coefficient power coefficient

maximum power coefficient torque coefficient

starting torque coefficient chord diameter of rotor head of well power output starting torque radius of -rotor Reynolds number

distance to rotor ax~s wind speed

relative distance to rotor axis angle of attack

blade setting angle angle of yaw

tipspeed ratio

design tipspeed ratio maximum tipspeed ratio

relative design tipspeed ratio angle of relative wind

solidity

a compromise and ease of

Basically, curved added to sustain a tipspeed ratio The Steering Committee Wind Energy Developing Countries (SWD) was established in 1975 by the Netherlands' Minister for Development Co-operation. The aim of the SWD is to help governments, institutions and private parties in the Third World with their efforts to utilize wind energy. The Swn-prograrnme comprises three aspects : 1. Assistance to wind energy projects in developing countries

2. Wind energy research, mainly undertaken in the Netherlands 3. Transfer of knowledge on wind energy technology

The swn programme is being carried out by the Eindhoven University of Technology, the Twente University of Technology, DHV Consulting Engineers and until June 1980,

Organisation for Applied Scientific Research, TNO. In this paper some results of the research programme of the Eindhoven University are presented.

Until now the swn programme has mainly concentrated on the development of water pumping wind energy systems, that are operating in pilot projects in, for example, Sri Lanka, Tunisia and Pakistan.

In designing these windmills, great attention was paid to finding between maximum power output and starting torque on the one hand, manufacture and use of commonly available materials on the other. plates are used as airfoil sections; supporting rods however, are the blades. The diameter of the rotors of these windmills, having of about 2, vary from 2.7 m to 5 m.

The main reasons for choosing such rotors are

These rotors are considerably lighter than the classic American rotors, driving piston pumps. This results in decrease of costs.

The r.p.m, of these rotors are such that reciprocating pumps can be driven without a step-down gearing, although some modifications on the pumps are necessary.

In the process of developing the water were made. The aerodynamic properties tunnel on 1.5 m diameter models (Fig.

pumping wind energy systems, a number of tests of the rotors were tested in an open wind-1 - 5). The purpose of these tests are a. _{to measure the Cp -}

A

curve because this is not exactly known ~m theory.

b. to check the validity of a number of simple design rules, that have been derived from blade element theory, as a useful tool for field workers (Ref. I).

c. to study the influence on rotor performance of linearization of blade setting angles and chord length.

d. to gain information on the influence of various kinds of structural elements sue as guy strip, tiprounding and supporting rods.

Chapter 2 deals with the design and testing of the rotors. In chapter 3, field test are reported with a water pumping windmill equipped with one of these rotors (Fig. 1 The field data will be compared with the data obtained under laboratory conditions. 2. ROTOR DESIGN AND WINDTUNNEL TESTS

Starting points in designing a windrotor are A_{o ' diameter and the choice of a blade} profile. In the design procedure a compromise between power output, starting torque and ease of manufacture will lead to a choice of the number of blades, blade twist and chord.

-,.-~/: ~:;::...~l ·.'_ii":~i:- ~:··",,'::-'di~cussion to a:. '-' i: :'(~:-{.!!':. F:'-'- :-:)tor diameters up to _:r.

~..:·"':c.l ~:;;_Yl1·jl,j5 nLi.illbe"rs are small- ;u~ .._ 2. ,;C''5-,!

Th'~ aerady!lami:.: properties of a ".1 O~ .cur'~Jed pl:lte are taken from Buehringt VolkerE

d~J ~c~e~~ly from Bruining (Ref. 2~ 3, 4), se~ Fig. 6 and 7. The influence of a

pipe (as a constructive element) on the high p~essure side of the profile is alse "";;~",n. I t can be seen that minimum CD/CL values lie between 0.04 and 0.1.

::: designing the blade geometry, the equations of Glauert (Ref. 5) have been used 2,

starting points :

A

r = sin ~ (2 cos ~ - 1)

(I - cos q,)(2 cos ~ + I) = COCan .12 ..+.~

(2. 1 • I )

= 4 (1 - cos ~) (2.1.2)

from which the blade setting angle

~

=

~

- a and the chord c =

Z-B

2~r ~~n

be

calculated. The maximum obtainable power coefficient, taking account ct tiplosses. blade drag and wake rotation losses, has been calculated according to the method given in (Ref. _{1) and is shown in Fig. 8, with CO/CL and B as parameters.} From thi graph it fol:cws that a design value of Cp would be around 0.40. Too many blades should be avoided as in that case the Reynolds number becomes too low and profile drag increases. A choice of from 4 to 12 blades seems acceptable.

For ease of manufacture

a

is linearized. We can further simplify the design by choosing a linearly tapered blade or one with constant chord. Fig. 9 shows blade angle settings

e

of'the rotors in comparison with theoretical values for

m

and 8. The starting torque is calculated as follows

= R } pV2 . B

J

c(r) C_L(90 - B(r»r dr q '-'- 15 linear between 50° < a < 90 0 ~see Fig. 7)

lhe d~~ensi~nl~ss startlng torques C have been calculated for the i~fferent

~.)tcr

types and "re given in table I? stThe local contribution to this torque is depi<~red in fig. 10.

',:'",~dring a blade with a constant chord to the ideal blade shap ... j>oth having the ,ame area (Fig.]l), it shows that the former has a higher starting torque. The .·",Cer part of the blade having a longer chord must be set at a larger blade angle B

for maximum power output, at the same time increasing starting torque. In

consequence the CL and CD/CL values vary along the blade (commonly C.9 < _CL < 1.25) and a small decrease in maximum obtainable power must be accepted.

-;h~ '~'reviously desc·ribed design considerations have .been_llsed ..in :.the··,desig~.

'?~:;,""Jurc<of theHEU-I-2, WEU-II-I, THE-I-2 and for the'THr--I-J "rotor, Fig.

·-l~ ~E~-I-2, developed by the Wind Energy Unit, Sri La~ka in co-operation wier.

,:,:e.

6) has been designed with a relatively high lift coefficient (about' .Z5)

which leads to relatively small cr values. The number of blades has been chaser

.~ :he best compromise between maximum obtainable power output and manufacturing

costs. The rotor diameter is 3.05 m, blade camber is 10%. The rotor drives a

piston wate-r pump. ,

The wr.U-II-I, developed for India (Ghazipur) by the Working Group on Development Technology WOT (volunteer student organisation at the Twente University of

Technology) has been taken over by S\.Jl) for the Sri lanka project. Optimum power

output has been the demand for the rotor because of the low average windspeed

(2 - 3 m/s) tn the region of set-up. The rotor diameter is 5 ffi, the lift coefficient

is 0.9 ~nd blade camber is 6.7%.

The TH£-[-I developed by SUD at the Eindhoven University of Technology (THE) 10

simple and of light construction and standard le.ngths of materials have been used;

the aluminium blades are folded around a U-shaped tube (fig. 3). The design tip-speed ratio for this rotor is 2.5. At the time of design, no aerodynamic properti.es

were available of such a profile, therefore blade geometry has been calLulated as if

it were a curved plate with sharp edges. The r'otor diarnecer is 2.7 m, lift co-efficient is 0.9 and blade camber is 8%. The rotor drives a membrane pump, equipped with an air-snifter that practically reduces the starting torque to zeru.

The THE-1-2 has also been developed at THE. and designed for driving a piston pump, has The lift coefficient varies from 0.9 at the

The rotor with a diameter of 2.74 m a higher starting torque than the '1'11£-1-1 tip to 1.25 at the base of th. blade. The blade geometry and other details of the scale model rotors are present~d in

table I.

Rotors have been tested in an open windtunnel, described in Ref. 7, 8, at ttle Institute for Mechanical Constructions of the Organisation for Applied Scientific Research (TNO-1WECO). The tunnel generates a free airstream of 2.20 m. The velocitj range is from 0 to 15 mIs, enabling simulation of the effects of Reynolds numbers to

be expected in ~ield conditions on full sca~e rotors. The windrotor ~s placed do\vu-stream at 2 m d~stance from the tunnel open~ng. Tests have shown (Rer.··~) that at this distance from the opening the free boundary layer between moving and stagnant air is only a few centimetres thick and that the velocity of the flow that passes the location of the rotor is still the same as in the tunnel opening. Other measure-ments have shown that, when the windrotor is operating, the velocity distribution at the tunnel opening is not affected by the presence of the windrotor. It is therefore assumed that the flow is sufficiently similar to the wind in open air. To study blockage effects due to the finite· diameter of the open jet, a test has been carried out with a relatively small rotor (0 rotor/D windtunnel = 0.34). The C - , charact-eristic has been measured in the full airstream- of the windtunnel. A£t~rwards the outside part of the airstream was deflected in such a manner that tH€ effective tunnel opening was reduced to 1.1 m. Within the accuracy of measurement no changes have been found in the C - A chacteristic compared with the former one. A theoreti( study is underway to exp£ain the very small blockage effects caused by a windrotor ~r an open air jet. The air velocity is measured with the help of a Prandel tube,

connected to a Betz-roanometer. The rotor to be tested is coupled to a d.c. generator The field voltage and a resistive load can be adjusted. In this way it is possible to choose any number of revolutions between zero and maximum and the complete C -

x.

characteristic can be found. The generator housing is set in bearings in such

R

way that it is free to rotate aro.und its axis except for.._the fact-·that a support arm ' :. prevents rotation ... The torque· that is generated by--the windrotor is found_ by - .

measuring the force that this arm exerts on a force tTansducer. This transducer is of the strain gauge type. The voltage of the transducer is amplified and converted to a frequency. This signal is averaged by counting the pulses during 10 sec. The read out of the counter is proportional to the exerte~ torque.

In Fig. 12 the performance of the model rotors, designed to the specifications of table 1, are compared. It can be seen that the C value of the WEU-r-2 rotor compares well with theoretical predictions (see t~bT~xl). These measurements were performed twice with an interlude of several months arid rendering the sanle results. All rotors designed for Ao = 2 do indeed show a maximum C at this value. The THE-I-! _{rotor however, has a lower value at which Cp max ii attained: Xo} = 2.2 experimentally versus Ao = 2.5 as designed. This decrease in ti~s~eed ratio is

pr~.~ably,due to the folded edges of the blades whicn somewhat spoil :-l1e G.e.~GGynamic

----_

..

--

.-

---

-6-properties of the curved plates. This also influences C measured equal to 0.362. This indicates values of cD/CL just below O. I, wRic~a~eems reasonable

(1"ig. 8).

The THE-r-2 rotur, designed with CL and CD values for Re

=

2.10 5 , shows a lower C !:lax than predicted by theory. By changing the blade setting angle, however, oBer _30, C max became 0.40. After Bruining's publication (Ref 4) it was realised that the characteristic properties of the curved plates are rather sensitive to the Re - values and that the design blade setting angles were a few degrees too high. The Cp max values of the WEU-II-] rotor are lower than predicted. It seems

reasonable to expect some power loss due to all the supporting structural elements (Fig. 2), not accounted for in the design procedure.

The influence of linearization has been investigated with the WEU-I-2 rotor. Fig. J3 Shows the performance of the rotor with linearized blade angle set tings and with angle settings conforming with theory. Differences in blade angles are

particularly noticeable near the base of the blade. This explains that only a small increase in power output and torque is observed.

The geometry of the tip, whether rectangular or rounded off, plays no significant part in power output. Measurements have been carried out on the WEU-I-2 and the WEU-II-] rotor, both with analogous results. Only the WEU-I-2 results are presented in Fig. 14.

The IlliU-II-] rotor has been designed for low windspeed regions. However, the rotor has to withstand stormy weather conditions. Guy strips are a simple method of strengthening the blades but will augment drag losses. To investigate this effect guy strips have been added to the WEU-II-I model rotor in a way similar to the full scale rotor. In Fig. 2 it is seen that these flat strips are connected from the rotor axis to the outer ring. Fig. 15 shows that an 8% reduction in power output is caused by these guy strips.

The I~EU-II-l has an onloff safety mechanism that is operated by a vane, placed

perpendicular to the rotor axis in the rotor wake. The influence of this vane on the power output of the rotor was studied on the model rotor: the model vane had dimensions 0.295 x 0.195 m, situated at 0.205 m behind the rotor plane, with the near edge at 0.095 m from the rotor axis. The surface ratio of the vane and the rotor is 3.2%. Fig. 15 shows a rather large decrease (8.2%) in power output due to the vane.

Fig. 16 shows the results of experiments to check the sensitivity of variations ~n blade setting angles on power output. The influence of the Reynolds number on design blade setting angles has already been discussed at the beginning of this

section. When this remark is taken into account it can be concluded that optimum rotor performance is obtained at blade setting angles confirming design theory. When Fig. 6 is observed it is seen that C1 depends linearly on a when a is in the region between 500 _{and 900 • Special attention is paid to the C}

1 -a characteristic that belongs to the profile with a tube at the leading edge. It is seen that C1 values are higher in the mentioned a region than those of the other profiie

configurations. This phenomenon can be used to increase starting torque of a wind-rotor. To check this thesis, preliminary experiments have been carried out with the THE-r-2 rotor with additional tubes attached to the leading edges of the blades. Fig. 17 presents results of these experiments. It shows that an increase of starting torque is obtained but that C max decreases with 7.5%. It is stated that more

experiments have to be

carrie~

out on other profile configurations and blade setting angles to overcome power loss.

The effect of yaw on power output has been measured with the THE-I-} rotor. The results are shown in Fig. 20. _{It can be seen that Cp max is approximately} proport-ional to the third power of the angle of yaw. This compares well with theoretical predictions. In the next chapter, use is made of these results in the calculation of the output performance of a membrane pump, coupled to the THE-I-I windmill

at the test sice at THE (Fig. 19) .

j . F LEW TESTS \, lTH A \,ATER PUHPDiG \n1lU~IILL

The THE-I '..Jindmill (Fig. 19), developed at the l::.indhove.n Unive.r::;ity at Technology,

is designed to irrigate about 0.5 hectare in wind regimes witll Vmean ~ 3 m/s fr0ffi

shallow wells (H = 4 m). With an estimated daily water requirem~nt of 50 mJ , this

leads to a rotor diameter of about 3 ffi. For reasons of construction <l rotor dLJl1l("[t:[

of 2.7 m was chosen. The characteristics of tIle four-bladed rotor are glven ln

Fig. 18.

Via a crank (with adjustable strok~) a membrane pump is driven, with two air chambers and an air-snifter to lower the starting torque.

The safety system of the rotor consists of a hinged tail vane, counteracted by a small auxiliary vane attached to the rotor head. The safety system is designed in such a way that the rotor is perpendicular to the wind at about 3.5 m/s. Both at lower and higher wind speeds the rotor is in a yawed position (Fig. 20).

~~~_~~~E_£h~E~£!~Ei§£b£§

In the laboratory the membrane pump was tested under conditions similar to that ~n

the field: suction head 3.5 ID, pressure head zero, stroke 3 and 4 cm.

Output was measured by weighing the amount of water pumped in

25

strokes at various speeds. The time interval was measured by a stopwatch.

Torque was measured as the reaction torque on a gearbox in the main shaft. This

shaft, equipped with an adjustable crank, turned two bearings similar to the situation on the windmill. A~ a result the losses in the bearings and the crank are included

in the pump torque and the windrotor data can be directly applied to the pump data.

The greatly varying torque was

R x C

=

I MQ x 20 ~F

=

20 sec.

d stable value was reached.

averaged by means of a single step R-C filter with

The readings on a digital voltmeter were taken when

The resulting torque-speed curve (Fig. 21) shows two clear resonance peaks, one of the suction air chamber (~ 5 rad/sec) and the other of the pressure air chamber

(~ 10 rad/sec). The overall efficiency decreases from 70% at low speeds to less

than 50% at high speeds, the losses of bearings and crank included.

1~1_~i~1~_~~~~~E~~~!_EE2£~~~E~

field data were taken at a small test field at Eindhoven University of Technology. The local annual average windspeed is about 4 m/s. Two and four storey buildings at a distance of approximately 100 m and a 12 storey building at about 200 m influence ·the turbulence pattern in the (prevailing:) South-West wind direction. With. preference

measurements were carried out with Easterly winds.

The measurement procedure consisted of taking 3 to 5 minute averages of wind~peed,

rotorspeed and water quantity. Some hourly averages and averages over a number of hours were also taken for comparison purposes. The anemometer was mounted on a mast at the height of the rotor shaft, about 5 m upstream of the rotor.

Windspeed was measured by counting the pulses from a laboratory made cup counter anemometer, that had been calibrated in the 2.2

m0

open ended windtunnel. For long

term ~easurements a Casella cup counter anemometer was used.

Rotor speed was measured by counting the number of strokes with a mechanical counter.

Water was pumped into an open rectangular tank. For short time measurements the water level was measured both by hand and with the aid of a commercial Woltmann watermeter (¢ 5 cm) behind the tank. As a watermeter requires a certain minimum

-8-tank output ,,,h,,n the head above the watermeter dropped below 0.4 metres. Tank

measurements and watermeter readings correlated within 5%. For long term measure-ments, only the watermeter was used.

3.4 Results

---\.[hen the wind tunnel data of the rotor are coupled to the laboratory data of the pump the ideal net output characteristic P(V) of the water pumping ",indmill "an be

found. This output curve will be <..:ompared with the field performance curve, taking

all data per m2 of swept rotor area.

The coupling of windrotor and pump is sho~n in Fig. 22. For a series of wind speeds ,

powerspeed curves of the rotor are drawn. These curves are corrected tor the yawed

position of the rotor, given by Fig. 20. The intersections with the curve of the mechanical power required for the pump are the operating points of the windmill. Descending to the curVe P water (W) gives the corresponding net output of the windmill. Plotting these net outputs as a function of windspeed, after dividing by the swept area of the rotor, gives the curve in Fig. 23.

In this figure the field data are also given. As we expected the windmill produces. less than in the ideal situation and this will be discussed in the next section.

The performance in the field is on laboratory data of the components. of the windspeed, particularly its

the whole somewhat lower This is probably due to direction.

than predicted from the the strong variability

Variations in magnitude around

V

have relatively little effect, as the power output curve of a windrotor/displacement pump combination is approximately linear over the ma1n range of windspeeds. This also explains that measuring the output by averaging over 3 minute periods renders approximately the same results as averaging over one hour periods.

The effect of variations in the direction of the windspeed are more difficult to understand, as they are influenced not only by the inertia around the yawing axis, but also by the inertia of the rotor itself. Van Meel and Van der ~inderen, Ref. 9, have sho'vn for the same location, that the fluctuations in wind direction can be

approximated by a first order stochastic signal with a typical time constant of 5 to 15 seconds and a standard deviation of 200 or more.

The time constant of the rotor itself and that of the yaw1ng system are of the same order. Let us then consider the effect of variations in the wind direction by assuming that the position and r:p.m. of the rotor are temporarily frozen. At low windspeeds, where" ~

"max'

the power coefficient may then be assumed to be prop-ortional to cos36. For 0

=

200 this leads to a reduction of 18% in power output.

At ~igher wind speeds the tipspeed ratio rises and Fig. 18 shows that variations in 0

have a non-linear effect upon Cpo At_·" =_.2.5-for·-example C = 0.25 for 6 = 20 0 ;

if 6 decreases to 00

the Cp becomes 0.34, but if 0 increaseE to 400 the Cp becomes

O. I

~ The C_{p - " curve of slow running rotors can be approximated fairly "'ell by the}

following expression :

C

P Cp max

C p max

This expression is valid for" > 0.8 .

A

It is reasonable to expect that the above mentioned effects, although not exactly qualified, lead to the measured reduction in power output of about 157..

4. CONCLU SiONS

From tite results it can be seen that the rotors yield good performance under

laboratory conditions: the maximum power coeffici.ents are about 0.40, \Jhich value

is just below theoretical predictions for these types of ~otors.

Care should be taken with regard to the location of additional constructional elements, especially at the low pressure side of the rotor blade or in the rotor wake; even small elements can severely affect output performance.

Field tests of one of these rotors, coupled to a reciprocating membrane pump, inuic~

that laboratory data of the components give a reasonable prediction of the field performance. The local variability of the wind leads to a reduction in power outpul

This reduction merits a further qualitative investigation of the dynamic behaviour

of water pumping windmills.

Note: Additional data of field tests with the THE-I-2 rotor, coupled to a high. efficiency piston pump, will be presented at the conference.

5. REFERENCES

I. Janssen, ~.A.M., Smulders, P.T. SWD 77 I (May 1977).

"Rotor design for horizontal axis windmillsl 2. Buehring,

I-Co11ege, London

"Performance characteristics of simple airfoils".

(1977)

Imperial

3. Volkers, D.

sections at

I1Prelirninary results of wind tunnel measurements on some airfoil

Reynolds numbers between 0.6 x 10 5 and 5.0 x 105 ". T.H. Delft (1977·

4. B.ruining, A. "Aerodynamic characteristics of a curved plate airfoil section

at Reynolds numbers 60.000 and 100.000 and angles of attack from -10 to

+90 degrees". LR.281 T. H. Delft (May J979). 5. Clauert

(1963) .

"Aerodynamic Theory" edited Durand, W.F. Vol IV. Dover Publication'

6. Janssen, J,.,'.A.M. "Wind Energy Utilisation Proj eet Sri Lanka".

Progress Report : Evaluations of Phases 1 and 2. Period: April 1978. SWD (January 1979). Report VI 1977 - Septemb, 7. Geirnaert, P. laboratory for (In Dutch).

"Description of the windgenerator with appurtenances at the

fluid engineering at Waddinxveen" TNO-UiECO 76120 (April 1977)

8. Janssen, 1,.,'.A.M. countries!'. SWD

"Horizontal -axis fast runr~lng wind turbines for developing

76-3 (June 1976).

9. Kinderen, h.J.G.J. der, Heel, J.J.E.A. van, SDulders, P.T. Fluct.uations on Windmill Behaviourll

• Wind Engineering, 1,

"Effects of Wind 2, pp.126-140 (1977)

Theoretical Experimental

"-MODC~J ~~.r_

D CAMBER C L c f3 CP max .CQ st Cp max C

Q

st f.--- 1 -1

I

I

-26.47 x + 40.24 0.45 0.123 0.434 0.097 "'EU-I-2

_I

_{I: 2} I.52 10% )-I .5 0.108 -I 0.377 , WEU-n-I ) : 3.33 I . SIS 6.

n.

0.9 -0.0635_ x + 0.1455 I -29.60 x + 42.10 0.43 0.194 0.150 (0.39~ x ~I) I 0.362 t THE-I-) ) : ) •8 1.50

i

8% 0.9 -0.29 x + 0.54 -28.72 x + 36.72 0.42 no

I

0.069 ! data I

I

I

THE-I-2 ) : 1.83 1.50 10% 0.9-1.25 0.324 -15.22 x + 32.56 0.44 0.152

i

_0.385 0.1 )0 TABLE 1 • .

,

I ..-o I

..

N I

Fig. 2 Model of the WEU-II-) rotor

..

-14-"

•

Re=

2.10

5

I

~I

~ lit.

I

₅

I

~

0

I

eLi

,

_I

_I

... Re= 10

I

I

5

_I~

I

1.5~--l

-"-'-' Re=10

----I

5

I

'",J'

-- --- Re= 10

I

-0\ , I

Re=105

I

~I

.

.

,

0.0

0'

25

50

75

()(.

Fig. 6 CL-a characteristics of 10% curved plates with several spar locations (Ref. 4)

I

-... I

... Re=

105

I---

0

I

-.-._. R

e

=

1

0

5

[0

:::::::: ]

. -

~

--- R

e

=

10

5

I

~

I

~

Re

=

10

5

[

---

l

Co

ell

[--I

1.

51

~

I

~

>4 ,

-+

! I

1 0

.

lIt I I I '- .•\: qi. \l'I I

O.5L1

I I I ,'.:",,,1 !

· 0.0"

0:5

1:0

1:52'.0

I Fig. 7 CL-C

D characteristics of 10% curved plates with several spat locations (Ref. 4)

-18-o

O. 5

I---+---~.~~~:-::--

""'"="--:"";-

-::::=:,

002

_0_0"'" '

.--0

- - -

-'---0--4

0.05

0.4

I

-...

_0

/ '

0.3

0.1

•

B=12

1

-+--

B

=

8

Co

-0-8= 6

-C

_L

0.2

-·...·-8

=

4

0.1

1 - - - + - - - - , - - - ---.--- ....-- ._. .----.- .---

---a

1

2

3

_A

o

4

Fig, 8 Theoretical obtainable power coefficient as function of design tipspeed ratio

Ol---I----+---+--..:~~~~----j

)0

1 \ 4 + -! I .1

I

~-~~---+----+-!---+---~.

~O

!

I

o

l - - - t -I

- - - - + - - - + - - - t - - - j

Fig. 9 Blade setting angles as a function of x

o.a

I

~

I

~

~----I N o I

0.11

I / ' I

_~

I

I

'

1

ICQS~

Ix

1

O

21

+

/

1-' , ,- -

-~

I

"

!

.

r

~

I

'I

'\

o

0.2

0.4

0.6

0.8

_---.

x

1.0

Fig. ]0 Local contribution to the starting torque coefficient

Fig. II Comparison of blade profile with constant C

L with blade profile with constant chord

Areas are the same

I N

....

I N N I

4

A

3

2

1

Fig. 12 Performance of

model~otors

under design conditions

o

I

'\.

'" \.

I

0.1

I

/7~

I

I

"

,

o

C

p

I

• : T HE-1-1

0.4

I

0:

THE-1-

2l

G:

WEU-I-21---"/

I

~

I I

0.31

+:

WEU-II-1

1 / '

r

I

~

~ ~

"!

I

0.2

I

Ii'

/

I

I"'''

, 4 1 :

'\

~

I

,

A

3

2

1

Fig. 13 Performances of

WEU-r-2

rotor with linearized blade setting angles (e)

and with blade setting angles resulting from theory (_)

''''''- L I I I ' I

0

4

I

:A'""

I

I

I

I

\.\

I

0.0 4

o

o

0.1

C

_p

I

I'

.lm~.~

I-

I

em

10.16

0.41

IT

kfC

~

_I

\0.14

0.3

r:~

0.2

0.12

I N W I

0.08

~ I tv .f:-I "

4

~

3

2

\

1

o

0.21

I

J'

0 :

IfC/\

»

I

l~\ ~I

0.1

o

0.3

C

PI

'

I

I

I

o:[@]

--~

I

I

0.41

I

~

- -

.

A:

~

Fig. 14 Performance of WEU-I-2 rotor with the different tiproundings

,

C

_p

0.4

0.3

0.2

0.1

o

o

1

2

_A

4

I N VI I

Fig. 15 Performance of WEU-II~~ rotor 1) according to design

2) with additional guy strips 3) with a vane in the rotor wake

4

A

3

2

1

o

o

C

PI

_I

I

I

0

0·

0

• 0

I

d~A

I

E1:

+3

0.4 I

0

x

·+6

• 0

~·-3

I--~

..

I~" ~I

• 0

0.31

'\l -... "\..

_.:-5

_I

I

I

.

'\

~ ~~

_I

N

0.21

U

'"

I

0.1

Fig. 16 Performance of the THE-I-2 rotor with several blade setting angles. The deviation from the design angles is given.

\

I N -...J I

4

A

.:~,- ~

.:~

3

2

1

Fig, 17 Performance of the T~E-I-2 rotor under 1) design conditions ~nd

2) design conditions plus an extra tube at the leading edge.

o

o

0.3

0.1

I tv 00 I

4

A

.

_..

3

Ci)"

.

'> 0

\

..

_...

....

_.

.

_.

_..

.

_..

...

· 0

0

•

•

0.4

J

I

,

~G

:

10°

&:

20°

0.31

1 . / """"'-l

--m_

"

In.... :

3

OlaPProx)

7rrt?:

A

~

" " 0

0:40

0.2

,

~G-

@

0.1

I

.~

~~

~

·2

o

1--.1.0-4

1

0

C

_p

Fig. 18 Performance of the THE-I-I rotor for different angles of yaw

.,

It

I

I I

. /

4

v:.

V

. /

~

V

..

~

••

l

-~

'~

_t3

_~

₅

₆

r

₈

₉

₁

.

•

\

o

60

&

40°

o

20

o

o

o

-20

Fig. 20 Angle of yaw as a function of windspeed

the THE-I windmill, resulting from the hinged tail vane

of

V

(m/s)

I

w o

I W

-

I

6

4

10

~

• I

I

I

l-~

! I

Q

(~)8

2

Torque-speed curve of membrane pump with a stroke of 3 cm at a head of 3.5 m.

The two peaks indicate the resonances in the two airchambers

o

o

Fig. 21

2

4

6

1

8

10

12

W

14

16

(rad/s)

18

·20

-

,

"-32-..

16

1

P.

~nd

~n I i i

12

14

w

(rad/s)

10

with me hanical i put

6

4

2

I

I

I t + + + + H k t -I I

I

1 i r 1 : = F

-o

o

I

- - i

I I

I

200

1---te-'I~ffi:2_±_e_e~--+--

++---+---+---T---

---~~

corre ponding w th these

I

winds eeds

I

I

-- --i-

I

1- '

:

I

I

-

---"--1

I

I

P'

4

I

P

(W)

I w w I

8

7

6

V

(m/s)

~ ~

4

3

2"

1

----T~--r-0

'

j

---I __ _ . _ - - f

a

--

-

--•

-•• •

0

••••

•

•

•

•

+

e

•

e -

-e.

.'

00

2

4,

10

Field measurements of the effective power output (per m2 swept rotor area) of the THE-I water pumping windmill, with a stroke of 3 cm at a head of 3.5 m. The three field data indicated with U+",are long term measurements of several hours. The curve represents the

theoretical output determined with fig. 22.

PlrrR2. 8

Fig. 23