Forces and torques acting on a wind rotor that is propelled by an oblique air flow and rotates at a constant speed (cambered sheet, 8 rotor blades, tip speed ratio 2)

Forces and torques acting on a wind rotor that is propelled by

an oblique air flow and rotates at a constant speed (cambered

sheet, 8 rotor blades, tip speed ratio 2)

Citation for published version (APA):

Logtenberg, A. R. (1983). Forces and torques acting on a wind rotor that is propelled by an oblique air flow and rotates at a constant speed (cambered sheet, 8 rotor blades, tip speed ratio 2). (TU Eindhoven. Vakgr.

Transportfysica : rapport; Vol. R-590-S). Technische Hogeschool Eindhoven.

Document status and date: Published: 01/01/1983

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DOCUMENT ATIECENTRUM B.O.S. - T.H.E.

TECHNISCHE HOGESCHOOL EINDHOVEN

class.

/lit

1/-

8$f)V ..

Afdeling der Technische Natuurkunde

Vakg'roep TRANSPORTFYSICA

dv. datum·

Titel

Auteur

Vers

1 agno. :

Datum

Docent/contactpersoon:

Begeleider{s)

(chart abstrae:t) 20rcGs torques acting on a . 1.'1ind rotor t:1a t is propelled by

an oblique ~ir flow and rotates 2.t a C;)ustc.nt s~)e8d (cambered

sheet, 8 rotor blades, tip speed ratio 2)

A.It. LocteIlberg

. R-590-3

iIay 1983

i r . I . VU!1 der 3pel:/ir. P.T.3r':uldcrs

Korte samenvatting:

The present report is a sequel to that by ,J •..• U~):;r8an anti tIed: "forces and torques acting on a rot«1r prJpelled by an oblique air flow under no-load conditions

(1).

I t differs with this report in t:1a t here the rotor speed can be kept constant independent of the air flow angle, by means of a d. c. machine. ',Ie have calculated the lateral force, t axial force and the moment of t:le self-orientating torque as functions of the air flow anGle and tip speed ratio by the method of multiple linear regressio~.

8 307385

Contents, 1. 2.

3.

4.

4.1 4.1.2

4.2

4.3

4.4

4.?

4.6

5.

6. 7. (

..

) List of s:rmbJls '1'i1eory

Proce::;;;Jing of t1e measured vaJ.ues

Jpeed control L:oto r/ genera tor

.L'ransmisdion

~lectric installation liind veloci t~T

Determina tion 01" C_i'il

-;)etermination of t~e tip speed ratio

A

i:..djustment of t:le air-flow angle

b

JesuIts and discussion Conclusions

3uegestions for furtier investiGations

Ilage 1 2 5 7 8 8 8 9 9 12 14 1 A ~

...

14 16 18

23

24 Graphs 25

AplJendix A Processing of the measured data 36

Al)~)endix B Transmission specifications 37

-1-List of symbols B G l'vl_so e :t s

x

column vecto.r:, from. '>7a.ich \..11 •• so , L: ..c's and 01'"t can be calculated

/

t 2 2

coe:tr.icien~ or. axial iO.l..'ce C_F -:.=F t ;i::"VQlP1T'.H.

t 2 2

coer:i:icienl:; of lateral force (JpsF s/~-fV". Tfli

. f ~. .. I 1 w 2 -' t..i 3

coerl~cient 0 ::lament L:['r,i/";t, ,.'If Ll.

coef:ticien~

or. sel! -orienl;2ting moment (Jrvr :=Msal!

fV~

tr'.f:{3

so rotor excentricity

dis'cance bel;ween rotor plane and yawing axis

axial :torce

sel:t-orien~al;ing moment

rotor radius

scaGGer 01 ~. _!vi values wind velocit-y

mat..L:ix conl,aining (e,f) combinations column veCl;or of measured liM values air I low angle

tip speed ratio

inverse 01 rna ~rix

X'rx:

air dt:msi f,y

-.-.-.-.-.-.-.-.-.-.-.-Note: "lateral forcel! and IIside forcell _{are synonymous}

' )

-1. Introduction

The aicr of our and Up)ernant _{s re,seareh was to Gain an}

in-Si':lt into the ll.1'lstable behaviour of t 1_{le rotor/vane SYStSl:1}

, , ' ' I 'II . , .

t~13 w~nQ m~ ,wn1C~ has a rotor diacreter of ? 8, :las been desie;ned snecially lor use on 1,;:1e cape Verde Islands. _{* ,}

i'r; 1S provided rli 1,;;1 a so-called ecliptic safety device (7).

'.::l1.e unstable ;)e,laviour jUS"C l'SIeri ed -co occurs even undsL' mo.!. e or lesi3 ,steady wind condi "ions (3).

It seemed advisable -co look a1,; Ghe contribution to "he 1I0"al 1I0rque on the yawing axis of eaC~l individual emen'c

ot:

the l'01,;OI./vans s'ys~em, aSiJumine l.ha\" 1,,0 a good approxi-ma('ion, ill can be said t'~t -chess element,s are isolated.

In literature t:lere is little infor'"..2ation about the forces acting on a rotor driven

by

an oblique air flow.

J.r.

UpJer-man has determined t:le2e forces for an unloaded rotor. ".ie

have car::.ied out the Gubsequent i::lVestigation on a loacled rotor for tie following reasons:

1) In practice the rotor speed is substantially lower for a loaded tlan for an unloaded rotor.

2) ','[LIen a c:lange in t:1.e direction of the air flow causes the rotor head to rotate so as to tal~e up a different equili-brium position, then the rotor speed remains (approximately) con/stant during this rotation, because of its inertia. T:lis dynamic si tuation can be quantified from static mea-surements at a rotor speed that is held constant.

'i' .1is means that tle forces acting on the rotor durinG its rotation about the yawing: axis can be measured statical '.y

-3-as functions of t ~otor exce~tricity e

and ta~ce f bet~een t rotor ~lane and the yawin~

_.

-ciants c~

(',A),

c~ (~rA)

-t -s

ca= be calculated t various vc.lu'3s of

n

e, t a

and ~, t~lUS e11:1ina tine t:1e e;eomatry :-lapendence.

31nca man:r _{111e.3t1ons i~ our !:'BsearC'.1 have already been}

"'a' !:>v~'''' t (1)

.:.. .J..:... UJ...I...., : - _ .~=: excepti:m ~as been made for mattars

:lc:w'a to ba :'lentioncd to understand the conception of

eX}Je-ricants, the results and t~e conclusions of this report. ~e

used the i3e~me zyr1bols consistently. For clarity we &i ve t;'8 differences oetrleen our i::.1VGJtiCa tion and Upp erman t s C',s well

as t:le sisilari ties, botl expressed in keywords. T';" dif::e-rances g'lal1 be daalt "lit:1 in ,::;reater detail elsevr"lere in this reyort. For the si~ilarities the reader is re~erred

to (1).

3i:.i1_{arities: rotor (sc2"le Bodel of SWD 5000 R,:::7 r'jtor,}

~o

=

2; 8 blades made of cambered steel sheet; ra~ius 0,5 m) ; rotor head; tripod rotor support; lever; nosition of rotor, rotor head and tripod relative to t~e wind tunnel

(re~ard-less of slight differences in t~e po tion of the rotor rela-tive to tie rotor head); wind tun ~el (open, diameter 2,20 m, :10cesnelleic1s1aboratorium, afd. lUC:lt- en ruimteva<::rt T{ Delft) ; readinp.: of t'le a -ir--.. ~ .... i"'10"'.·,t --'-' ~n· -- ,_-- 0 <7:1 A (,0 :net'.'~1.'od of me~ c ... "'uri '1'" +'le ::> - ! b ,,(

rotor spe:;d, e- and f-value adjustment; absence of vanes; determination of the wind velocity by means of a Betz mano-meter, a barometer and thermometer; statistical processing

-4-of the measured. values tie method of multiDle linsar

re-Differences: T0tor S~~ control by means of a JC ~ac!ine

and,::ec:.:red-belt transmi:!--:;ion; st2elyard (:Jutch: vet;I'uf1,star)

claIJ.p~sd

_-

in a suu:)ort instead of held

. .

_~ by _~ 'land,' inter~_.J')lation

-\[ 'Lan a.n air flo'iT wit '1 veloci ty Vc» strikes a rotor of a.

wind i 1 . - m~'l u~a'Q~ t... ... __ .J.. . _ . . . . , . . an _ . . . ~n~'le (~O~ ~t ~i'l ~vnQrience no~ '_J .., OF , . . . L . " t - - """."'J,. - ... ... '..J onlv V an axial force

Ft

but also a lateral force ~ and a

se1f

-orientating torque with a moment Usa (fi;.l)

rotor axis

\

\

rotor plane

Fi "" .1 Sc hema tic top view of a rotor struck by an oblique air flmv.

...a.... ~

F t' F,s and Mso result in a torque 'a.D9ut axis ).',. wi t'l a total moment

It.

Axis A is at a distance e from the rotor axis and at a distance f from the rotor plane, so that we may YTrite:

in which e denotes the rotor excentricity. To render this equation independent of 1) rotor radiUS, 2) wind velocity

v:

_co

I'"

0

-at a 1ar00 stance (Le. jr,R) fron t'le !'otor and 3) t:te air d"m;si ty 'I ,,;,:'e divide it

by tpv2rrR

3 to obt2.in:

total moment, ("I

/':1

C J:>/') + v Ft • e n + F'"' .,!. ..,l ,:;, C_t' ,Cj1 .lSO J.: S

and refer respectivily to the -orientating mom~nt, lateral force and axial force. ~hey are d3fined

-7-'.rhe mea::;ured values have been processed using the ne-;;:10d of multiple linear recression (see

(1)

pp.9-13;

(4)

and

(5).

For a summary of tle results t reader is referred to ApP8n-dix. A of tl:,3 ent report.

per s9cond of th~ rotar) constant, it should be possible to bot 1 102.d drive on t rotor because:

1) t!1e rotor sh::)Uld be loeded anyviay wien t:1e air r~ow is normal 1;0 its plane, assuming t;la t the spef:?d requiTed it3 lovr;:;r

tha~ that under no-load conditions;

2) ti.le rotor s:L")uld at all times be driven when it h<.s been turned (almost) out of tOle wind direction. Under no-load conditions the speed then tends to zero;

For t:lis purpose use was made of a

DC

machine llhiC~l could operate ss a generator if the former, and as a motor if the

18. tter requirement h8,d to be satisfied. From the available mac lines vie :1ad to s e c t one t:lat on one hand was able to generate or consume a suffiCiently large quantity of mecha-nical or electrical ener:;y, respectively, and, on the otler

:1and had to be as s"Glar:.. as pos::;ible in view of aerodynamic e:t'!ects and tle thrust on the bearing of t:le yawing 2.xis. The specification of the

DC

machine we adopted is given Jl.ppendix B,10vr8ver its po\'!er features are lac1_{'ing here.}

For informa ti ve purposes, we could measure wi t"l a power sup-ply unit t18 power consumption of the

DC

machine under a maximum mec:1anical load as about 150 ~/att.

-9-4.1.2 Transmission

,Ie :l;;td to elJ1-yloy a transnis:::::ion wit;l a ratio 1:5 because of the ;liCh o.ac :line sp eed (3000 rpr:). 'I' 'lis ~]ig':l ratio as rIell as t:le required cinirnization of t:le transmis on-pulley dia-meter to ':eep aerodynamic ects as low as passable induced us to choo;:::e a geared-belt rather t~lan a V-vel t transmission becE.use t:le former is more flexible and 'lence permits snaller pulleys to be u3ed. ihe specification of this transnission is given

i'he assembly mac .ine/ transmission is shown in fir:'. 2.

Four bolts and 2i:;~lt nuts were used to fasten the DC machine to a 10 mm thick aluminium plate w'lic'1 in turn we.s fixed to tht.? :"otor :lead br oeans of four threaded rods. .j 1en t gea-red belt w~s tensioned, the stance between the

rotor-mac.line-s'laft centre-lines was 13,0 cm. 'Ehe four t'lreaded rods were used instead of the four bolts fixine the rotor-shaft bearing blocks to t)le rotJr head (fi::;. 3). T'lis construc-tion enabled the ge~red belt to be tensioned in a straight-fOl"",',ard fs.s lion. \Ie ha(~ to mount a red.ucer CD: verloopstuk) bet".'!een the nac;.1ine shaft and t:le smaller zeared-belt pulley because the machine shaft was too Ghort. T larGer pulley could be a ttac ied to t~le rotor snaft b:~ means of a socket-head screl': (D: inbusboutj e) •

To utilize 1 the pos3ibilities of control, we needed two controllable DC voltage sup~lies, i.e. one for the field

--

- - - ,

-

- - - - -

~

-In'

-

-

_rrn

/I

'--...-'

rl1

r

I

n

LgJ

I

]

'.

-

-,..

I i

r

I

\

0

-

-

I _I I I

--

I I I

-

9"::'-::1A I

.,

t I l - I I

C

I

-

-

I-" 10.-

-

rI

I

T

I

I

J

~ I I I io....- l"""- _I I

rr

I

II

n

I

1

JJ,..!.Jl

_u..:.J

I ~.-..

..-f'i ,- 2 "" view of :DC crachine,

..l.. 0- ""

transmission, rotor blc:des and :part of t!1e rotor head.

ef

fig.

3 in w:Jich tile transmission and the the machine are absent.

; .MoW """rMM : ... tlfft/l.

~~:::==~--

-- " ; ,-- '7 .:j e and t " - - ' , S - ' ; ' - ,,,op Vi3W 0:: C:18 3','lD 500r

2CV

rotor-head Bcale model (drawn by A. [racten, jul. 8t~, t81; ~artial repro-duction.. !"

•

t·r---1i---~-r-~-~----1'0-

-9'

. - - - - . _ : .!!'''''='' _ _ _ .... d I ~ ! I

,:, £=..::J:.' ---:--

-1

I • :I,~ £L_ ~.;...._..!,.'-"-_ _ - 1 I --~...,'

:"

k,j:1

t

I

2-volta::;e 2-11done for the rotor v()ltaDe (i.e. thG rotor

0:

the

DC vol t::::.ge Jup:c!l:~ our dis~)o3al; t~1e ro tor 'JC current ';;as tal:821 from a va~ciac ,;i"7;':: a recti er and a pole-revorsc:.l SYlitch. j lei1 t~le mac:1ine '.:2.::; used as a cen,grator (wind rotor

un(~ ,;r -; _{), it couJ.dsurr) 1.,,- electric energy to a}

d ecade-r:::3istance inc;trUTIe~lts. A circlli t (Lir,;-ram o,f t elec-trio i~3t~llation is ~iven in fi~.4

.,2'or model testa to be valid t:le J.eynolds numbers should be equal for this test and for the prototype used in practice. 1he rotor radius of the prototype is five times t'lat of t~a

t~e nodel at a ITind ve~ocity t)at is five times

t 'u:l.l1 -~ _{average ":-ind veloci ty in practice., 17'11ch was}

un-fe2.sible because t:le tun:1.el 'was only able to generate rrind. veloci ties Qelow 14

mia.

l\Ioreover, one had already experien-ced t'lat there is no oanse in carrying out measurements at '\';ind velocities :licl1er than 9

mis

on account of rotor and

tripod. vi bra tions w~ich renders a reJ.iable reading from the steelyard impossible. './1en tryinG out the set-up t ted wit '1

the apeed c::m trol ju;::;t described, t 'le resolved wind veJ.oci ty of 9

mis

Vias found to be unattainable. A,s a re-~ul t the motor became oV8r],oaded and was in a danger of gett ing overl1ea ted. 'rlerefore is was necessary to reduce the wind velocity to 7

nis,

at rr:ich the tip speed ratio ~ could be ke:c!t constant in the interval

1,8"A<2,8.

T'LUS we determined four values

-13-'"'~J.." - y * 4 ('! ; v __ -""''''''U; ~ _ t (~i'" ~-,...,. ~_~~_" rn of the

-2.4-of tJ.:? ro tor e9d, ':'liic~l lay in this interval and were used

t 11roW;10u t the r;: e8.suring yrO';rB::L1 e, m::.ne 1;; 4 4, 75 5,5 -6,2:> rps.

?he wind ,reGses to rotor Ho wiic~ is excentrically fastaned t) mounting yla

and 13v:r:r. The rotor - rlountine nle.te - she.ft - lav0:'~ assam-bly develoDs a tendency to rotr~ te about s:laft A. T ,is is pre-v·anted b:r _{t 1e clanp=d ,8::;:>rirlG steelyard U (t:le clamping place}

pensa. tio!': force. I ': all th e D'?a.:;:uremc;nts t'16 distance betrr::en the point of aIlfJlication of t~le com:p~msation force and :."avring axis was

55,0

cm.

4.4

JeterMination of the tip speed ratio

X

where Vtin is tie tip eed of the ro tor and VCQ represents the ,'lind veloci ty. Fig. Jb shons the di s:..o: 31 which has 20 notc'les. It is used, in conjunction wit'l a PlOto cell and a (ii2,'i tal pulse counter to determine t'1e r:tor apeed and t:1US v_tip accuratelJ. VOl was measured using a Pitot tube and a 3etz manometer w~1ic~1 were fJarts I')f the standard equi:rrmant of t;le vlind tunnel.

4.5

Adjustment of tie air-fcow ~ngle ~

steelyard in a stroboscope supfJort that happened t~ be available, instead Ofl01di it

..

_H

...

-H

A

IA

t I I I I I I

-15-),';:::;.4a Diagrammatic r2pre-sentation of the rotor head s'le"ft A and the compensa-tion of rnomen t !,I.

Fig.4b Fastening of the 1ev~r to the rotor-head si1aft. Definition of the symbols: A e f H L M U! P rotor-head shaft excentricity

distance between

A

and rotor plane

lever

adjustable rotor bearings mounting plate

one of the three poles suppor-tine A

aligning strips rotor

disk with 20 notches

disk with scale graduation pointer

-16-bYland, the measurint: E13thod could be iw.)roved. Thus virtu-ally vibration-free measurements could be undertaken to ob-tain a readin,; accurac~r in t 1e air flovl angle

&

better t:lan 0, ~o • . lis measuring met:lod inplied that it was impos.J i ble to perfor8. tlle measuremeilts exactly at

b=

100, 200, '30° •.• and so on (see 4.5). Por the method of statistic process of measured values ,,,dopted here it is horlever essential t:lat tIe values of the moments of torque are ;~nown for a fixed range of aneles

0,

so t'1at the;::;e values had to be found by interpolati::m aftervlards.

4

t::

. 0 Jegue:lce of the oeasurements

Just li1-:e the tests carried out under no-load conditions (1), tile f-value yras continuously variable by moving the ro-tor along the roro-tor shaft; to chanee the excentricity e, t:1e four nuts fastening the rotor shaft and t:1e DC mac'line to the rotor head had to be lo;sened, so that the whole could be moved to t'1e nearest ;101es of the mounting plate (rotor :lead); see fie.

2/3.

The ro tor shaft could be adjusted to ex-centricities of: 0; 1,5; 5; 10; 15 and 20 cm.

The measuring procedure was as fol2.ows (fie.5). we used a fixed (e,f) combination because changes in it were the most time-consuming operations. T next step was t:le adjustment of anGle~. In doine so, we uanipulated the SUPfort with the steelyard clanped in it until the direction of t'le cord con-necting the steelyard wi tl the lever was horizontal and at right angles to the lever. Th.is done, '."fe adjusted the rotor speed, eit~er by varying the field voltage and/or the load

-17-re.Jistance, or by vc:.r:'L1G t le field ~lol tags and/or t;le rotor

voltage. ]onoti2es the ::meed

scall distance in order to recovor t~e original, correct direction th e co I'd and t1G

ted frOB a sin.:::1e (8, f) co-:binc.tion, after whic'l a ::-al1,?;e of

~7as cOl!l2!leted • . /e at all times adju3ted speed to four values, c.entionod in 4.2, in succe.sion for a single

us of

&.

Prior to ~easurinc the cODyensation force asso-ciz,ted '\iit~ a Give:;. adjusted (e,f,b,s:peed) combination, \7e exC'.mined -fletter the riL1.e. '[eloci tYlad remained cona taut or not by chec~in~ the level of t water Cllumn o,r a 3etz

m8...."1.O-Vie have und2rtaten meazurenents for six (e,f) conbj~lGtions.

?or a 3unary of t :processing of the measured valu.·?s, se·:~

-18-,. 2esults snd discussion

prezents four cu:-veD cOrreZlymding Vii t:. four fixed val:l.es of ~ , i.e. 1,8 - 2,2 - 2,5 - 2,8 ••• 11e:-6 a:9pro':riate, we used the folloITing marks for the test points:

~= 1,8

<:>

~= 2,2 EI

).= 2,5

_A

A= 2,3

_V

Graphs I to VI

Here TIG have plotted tie Docent of tie torque about tie yawinC axis again3t t air-flow angle wit:1 X. as :pe.rameter

for six different positions of the rotor relative to tle

ya1'7in..:; a:;;:iS. Tle~-3e positions are always indicated in tle sra})~lS.

3et out along the vertical axis is the compensation force, measuren by the steelyard U, multiplied by tOle lenGth of lever :{ (O,50 m) and divided by

trfy

21J"R3 (see fie.5)

I t is inter!3,3tin,-~ to loo}e at grap"lS I-1fI in this order. Assuning C,~

=

-C'I·".~ + C1;'s' fiR + C-...

t • e/1, it will oe clear

n · ._so J,; J:

that in

II

_{the axial force Ft is insignificant because e=O.} The combined effect of Fs and mso causes

M

to increase with

&;

fu:-t'1erm02.~e t~lere is an obvious A-dependence: in the interval 1,8<.1\,(, 2,8, at a fixed

b,

rl can differ by a factor of 2 - 4.

Grap I referD to a situation in wiich the excentricity small (e

=

5,0 cm). II lis direct.ly resul ts in larGe c lanees in t trend of C,. The curves are rou£;'ll~r lorizontal. This

~ra taB t::.E.. t, -flow [.n~)_e, -.

~'O::'C? )Z'evai~_s over tle self -orien

t lG

is 2..130 saen

r;,

if and VI. In t '.1e l.:~.s

t-tlt::n:';i0-ance has pZ'actically rely vanis :ed..

and C .. as functions of t~e

ro •. )

t~ ~J~s

9ara8eter. ':';lese quanti ties ~ave

matiematical pr~cedure represented in appendix A (for a de-led d ari va tion of t:lis procedure, see (1), c :1Ctpter 5, Gec.1. Il1..:;rap:l VII the len.:;t'::. of the ordinates associcvtcd with the test PO:U.ltS is equal to twice t'le valuec 0::: the scr~-tter,

in appen-dix A. Grap 1 'lII S:lO'."fS that CT.! decreases wi t:l increasing ( •

.t4-"

values of t:le SCl? tter are low. There is a distinct, be it small, dep,endence on

X. •

The inset, top , is a

mag-ed representation of the variation of

_CF

for OOld~

30°.

t

~{oV'lever, t'le test points are not connected by a solid line, could not be determined by t'le met'lod described in ap-pendix A ::,ecause t'le nunber of values of _CM available for

b

l,"las insufficiently large (see graphs I - VI). By com-bining tvvo by ·~wo t 1e values from Graphs III, IV and VI Vie were able to find at all tim,ss t:1re? values of CFt for each

eO.

'r

.1is was possible because in III, IV <-nd VI the value of e was alwaJs t zaI:le (22,0 cm). As a result of t'lis

combination both

_CM

and C~ .e are eliminated from eg.

-20-C., := -Ci" + CF

s• f/j + C-_i<'t. e/3. 1.1 •. L

SO

scatter of the t:ree esti::J.: .. tes of C':l thuz obtained. 'rere t'le values of the

ccat-.l!t

tar ere liGLer, as \'lEvS to be ectad. (Uote: in the inset lengt:l of the ordine, tes drawn is equal to the scatter). Special attention deserv'3s t~le trend at &>600•

::;09S negative. TleY':. Fa and Eso were absent, t21is would imply tiat the rotor sets itself in the wind direction because for these angles

tie

rOl;or is driven .. At t1.e5e large air-flow angles the component or' tle wind-velocity vector perpendi-cular to the rotor plane is smaller t'lan is necessary t? mal:e tie rotor, under no-load conditions, rotate at a speed corres-pondinG' wit'l the interval 1,8L _{A{2,S. T'1is is sinilar to the}

5i tuation of a propeller in non-moving air. T'lis is why t'18 valUe of CFt for :1ig:ler air-flow angles is negative.

Graph VIII sho';'!s a plot of C_F as a function of

l; .

As s

tbe values of t'le scatter are substantially '1ig:ler t:lan those for CPt' we have given them at t21e bottom of the graph for ease of survey. 'i'he lengt:l of an ordinate drawn is equal to the scatter. Although here the picture is not so pronounced as t:lat of C·" , it is true to say t:lat CF roughly rises Wit'l _{~t s}

~

. All this also applies to graph IX, Wlere C_M is plotted so

against

b.

(]ere horrever t:le values of the scatter for

200 (;

&

~ 600 are given at tIe tJp of the grap 1)

Graphs X, XI

The values of the scatter in VIII and IX are fairly high and the dependence on ~ , particularly for C

F _s ' is not so obvious. It z;10uld be not that the contribution of F and

-21-il"SO to the total moment (except for lar,:;e air-floY; angles) is amall as compared to t lC'. t 0 f Ft. C4' and G,,! are as it

... s

i··

SO

were "dro':med" in t:le noise of C;..' , _J,;.J- at least in the metlod

U

of ~ultiple linear regres on used iere for t:w six different

Geometric configurationo. T~lero is an al ternative ill8t:10d of d sri vine: t :le varic, tion of C ~

-"e and C-r." '·so , i. e. from bra~") he I and

II

and

C .

=: -0, +

0

.. ; ISO •

a

(e

=

0).

T)e variation or

and C

l~lBO determined is represented in rraphs

X

e,ncl

, re3pecti vely. .L Ie met lad 0 f reliably estimating t::.e el"rOTS by :T.ulti:ple linear re.::::res_,ion T.';ever can~lot be used an:"rlore. I'he

h

-d e::? end el1C e of C·, _K mo:r.e distinct in grap'l X t

-s in .;-rap 1

VI

Graph ~II is ~irect1y obtained fron grap) VII. Dote: for ~ODe

points t:1e ordinates :,"epresent tle scatter-value, not tVlice this value; for instance CPt(

=

00 ; = 2,5)

=

0,82

Grap':l AIII is directly obtained from 3raph VIII. Note: the scatter-values are not indicated.

Graph VII. (extra remar::s)

1 VII four pOints indicating

Up.<ermc.l1' S re:.;u1t.3 (1), Le. tlOse mar:-ed

',A.B

CMCl.

G:I for

~= 33°, a

48°

a:ld --0 ?? , ::::'O.3~'l::,cti ve1~~ (and of course:

~=

2,3; 2,?; 2,2 ancl 1 Q _re ""cti _i!pl'~) ;,1

101.10'1 t , ...

-,'-'

""" ---. ""-.

.

J.. ' J

exa ctl:' lie on t 1e curves of associa ted ~ -paraneter, re::ml-tin; fr0~ our i2v9:tiGation, tley don't; ell four of t~eD

the air-flow fror1 t'lG 'trind tunnel is not only obztructed by

t is :'rind rotor, but also by t DC mac line and t :le pull sy s , 1'11ic1 are wounted be lind t:le rotor. T;ley form an addi tiona1 air-flow barrier and could t~erefore readil; lead to an in-crease in C~lt'

-23-tc:t'ctl :~orcG

and t 1e rJ.)ffi .11t of sclf -orientC'. tine; t0rque actinG o:n. a '.7in,:

rotor by means of tIe described eed control unit l~ads to

~cce~table rcsults.

of t'le axial force is t'18 _{most prono'J.l1c} •

.

t'lere i"'"-' ,~ Ol11~~ a ·t

A

-d.ey-:,ndence, .L"

vele c:.xial force decreases i)1 tl:" ",7i t '1

rising}. • for (yOt.J" <. :>00 , C?t

Cb)

follm7s the trend of ;~ (A) • co02

&

rat leI' exactly. For '>600 _{the pr~peller effect occurs.}

-'I'he valUes of t:le scatter are li:.{IGr for t'le lateral force. '[":e

A

-depend::::nce is considerably stronger than for the 2.xial force; the lateral force _{a rJ.3ll1e;} • • .t:' .I.' f \

..L unc ... lon 0 1\ •

-.2lW valUes of the ;Jca t'l;er in the self-orienta tine; moment

are i~htly smaller tlan those in the lateral force. 1)e

h

-del")811dcm.ce is obvious: the self-ori::mtating moment

increa-

-24-JU,-'estions for furt~.18T inv::;:Jti.':t.tiona

.. -.;:...~ - -~ ... ~ ... -. _ ....

_-

-:: f i t -:Jere c1e8ir8. e to :::;ai11 8, nora exact l·:nor,-lsdze of t'le

dable to

T

fiS t.le effect of t relatively l&rge axial force would used

Gr2.pn II t:easured values versus air-flow ~ and parameter page 18-19. of Cf~ angle ". See

-27-Gra.)h VI

1'.1easured ya1ues

versus air-flow

&

and parameter

J btevi:1.t3d tion from ver:T1l3 air- ~ •... ----- ~-.--, . . _D ---...p

-a~ld p8.rame -Ec-~:--:--:='~':':':';~':":';?""7T~~~+:;...:c~~-:-+~~t=-:::~:-cI

100 , , 1._.. , • . . ~J.~--:T~- :-~'~

--

~~=: -- --:---'~i -~:~---:! G ra T) ~ 71 I I

---'--'---:-'-!.' , Values o+' -'- (1., 'oJ J! S ' 0'0' , 1 , C v l l ' -'-~ • -1ed

'---:-:-~i:-=;::-:-:-i out 0 f info rma ti on fr;o

..::0-,~:---; :::;-raphs I-VI t versus air-, .- : " j flow an:';le (> and

narame-ter ~ Jee pa:;e

19

2.ncl. '20 ,~-. . . I - . . --- ' I '~--~~-:-.--T:-:--;-·"-:-r---- ~~-t '-=1 j - .

c:-t--'--,-- -: -'-,-

---~-­ _ _ _ _ _ ...l - -.:.. • ..: ~...:..t..:.... __ ~ .:...:._"

•

•

.._-_ _-... ~.---.---"~~----_, ._-- ._-- ._-- ._-- ._-- ._-- ._-- ._--.. ~.----.... _ .. _-...,..----_. __ .... --~ "' ".

0,011

graphs flo'.7

VJ!' :U.8

air-B..I:d. ~j[.rail1e· ..

ter A..i;3 Da':e l~ LnG

-32-... _ _ ..•. - - -32-... - .. - _ . ______ . ___ . ..;... ___ -i-____ , •. _ .. _.-'_ .• _ ... __ . _ . - -_. - ___ . . -Gra'oh .iU Values of~· , 0 out of infortlation ;;raphs I and I I air-fl·Jw anGle

t

--

..

---,~-­

_{"" ---"---" ---,--'}

_{'---~---- ~~"-}

"-

_{_}

_---.;;.;.;;~

_{__ "..:yYO}

.oO- _ _ _ _ .,.~ _ _ _ _ _ ~_. ,

---~~~"-""---~~---.~~t·"-R--~---3---·----;;-~~--~~--!-"

~---"--"

___ ._~,._ ... ___ ,,,~ .. _~i .. ___ :~~_. _______ ._. __ -:- -~-~:~. ___ "_. ___ ._ :1 '---_ ... -_ .• --+ - ... _--..;- ....:.-:...--. ~-. ...:.... ._---,_. _ ... _ - - - , - --_ •. -. + t ---,..~ • ~ --0--'-7----:-:-:-:-:=:.:--::---:_ '-_-"

_-'"-~~-~.:-:-_~-_-_,-_-_.-. "-"-"_-_-:_:-:7L-_~~_

-1 -"_

=J-J-,~_~_~:l_~t~~:c,~=_-~

t • , . - - I --, ___ ':--' __ "_-~-"-~:_-" ~__ - i : , _.' .--.t- .... :~:~~~ .... ~-__ .: .. -:~: 1 ': ~.=~ ::~'--'---:--:-~--:-:~~~----;:-:-"-,---" " " ; " "l~": "-" '" -1 --"" =-_1:'\ - . 1_" .. . -~-.-+---... .. .. , ~ "----~~--~---~t~:--1~"~ ~(--~-"-" -+1-' --"" ... ..::: ---r::---- ""--_-_ -+! -'--'--4-~'-_1-...;:~~,

-:-.

. . . ,. , --_ .. _---. , .... - ... , -. r"' __ .. _1 "---~ ---. ' .,. _. ---~.--

-_._---~~~:l""-L ~ ~_ _ __ .:..:... __ .:. ...: __ 1 ::=:c,-.~ -o,i,. "-:--- --,---. ---"-""'

..

-- . :

:

,._ ... - --:'': ~ -- ---;---:--::---r--- ... -- -.-.,.,._. - - - --:-, -=-::-~~~'-

.-11B

2.'1

X-_'1..:8.

--,... _h

, :

-0/1t· - -

.-0,10

°r:1-~t_}_L~~_-, -;~- -~-...::; -~

.:; ~:':" ... : :-. . -. 2). r ., .::..:= 3::::: 1 ~l e~ 1 I2 82 1 f e-· 1 1 1 ..., " -1- ~..:::' • . :: .', -c,::

,c '.,

"'SO - J := 1 O,lL~-~ 0 1 0,22

°

1 0,.14< 0,2 1 0,22 0,') 1 0, O,J_ 1 0,22 0,05 (I .. ,

V-'t

-37 ii-:' 't=:lcli~{ 3 -:OV-,.'n. 503 1'18 (100 teet'1 stand2:.rd) .1 eOC:le IV). 200 XL 037 i~cle

~e; code no. 72

XT

037 ,',=>r-' ,~''''d-'"' ,,," 1 t f'U1l e'T 7?

'...:....--'..., _J ... _ ' . .) ___ -i {. .. teeth; ~~," die.mete!' 116, mill; m8.ximu8 bore d.i8.E-::r

'1:-n; code no. 72

:rr

037

d ~)cun(:::::: tion C:2)11 tr;

Sn3cifica ti ::m of tle DC' mac ;line

£::1 DC m2.e;line from tlla stoel\: of t:1e r:roup of electro-Llee~lanics,

~4 eetro tee mical :'::n;ineerin; de:;8.rtnent 'i: T:':.

2 :-c 55 V

~:'otor voltaGe: 70 V

3000 rpm

-3':-t! • i- • •

,;'e21 GC :eef -:estr-'1-;'ricle

T8.ndleic1inz voor de wind tunnel en de l:oppelDef~t s-seJ.line voor ·,'Find rotoren van de T:! Delft, a:deling TJuc - en

I'r2.nspl)rtf~rsica va:1 de afd L'c':::; Tec :misc IT;:, tuurkund e , feoru2ri 1'1

( 3) ."i. I:ragten

.:Jescription at ';!inrl tun.'l81 m28.surements executed on a scale model of t head of the 3WD 5000

RCV

windmill,

~ap~ort rt 523 D, ~H loven, afdeline 'recmisci1e

tuur:<:unde, ~ial:3roep 'l'ran.sportfysica, februe.ri 182. (4) rlonte;omery D.C., ?ecl: ~.A.

Introduction to linear re{:;-res on 2,nalysis, 'Hle~r and

(5),/iskunde 49 CTansrekcniIL7, en statistiek), T:r Jind ;1oven, di: ~t. nr. 2.265

(6) R. Do jrnbos

3ta tistisc :le t>.eorie vall ::1ro2fo.9zett en,

-39-(7)

.::0 3.

,ns

J,

· YH

_j

sr«Gal

ihalAks

10

H.

14&1\

dex

Sr

ek,

-p./.

slMulders