Preliminary design of a windtunnelmodel of a tipvane windturbine

DELFT- UNIVERSITY OF TECHNOLOGy2, DEPT. OF AEROSPACE ENGINEERING

PRELIMINARY DESIGN OF A iiIINDMINELMODEL OF A .TIPVAN&IANDTUREINE.

Delft - The Netherlands

This report describes the

preliminary

design of a'"tipvane windmill"

test model.

The

experiments to be carried out withthis model, will take

place in the low-speed windtunnel of the department of Aeronautical Engineering as well as in the towing tank of the department of Shipbuil-ding, both of the Delft University of Technology (D.U.T.).

The dimensions and general layout of the model, and the measuring

Arrange-ments are described; .7

Stress analyses have been made, as far as they are relevant

from

the

Contents.

Contents

Notations

Introduction

General arraheement-of the model

1.1 Layout ofithe:windtunnel model 1 2 14.37014t of the towing tank model

3 Adjusting of the tipvanes 4-Overall dimensions.,

1.5 Choice of tipvane Sections

Measuring equipment

2.1 Total lift per tipvane

2.2

Drag

.3 Tipspeed

2.4 Time-averaged flow field 2.5 Qualitative flow inspection

Structural aspects

_

3.1 Bending moments in the extension rods

3.2 Production of the tipvanes 3.3 Magnitude of centrifugal forces

References

Appendix A: choice of main

B:T centrifugal forces

required motor performance

sizing of the extension rods Tables 1 to 3

Figutes 1 to 1/

parameters

Notations

factor used Tinppehd1x A

tipvane sPan

number of tipvaneg

chord of the tipvanes

two-dimensional drag coefficient, --two-dimensional lift coefficient

three-dimensional drag coefficient , three-dimensional lift coefficient

diameter of the extension rods drag

diameter of the mill

diameter of the slipstream diameter of the windtunnel

Youngs modulus centrifugal force

polar inertia moment

radial force per unit length

lift

moment

undisturbed pressure upstream pressure for downstream

power variable

R, R radius of the mill

Ut

Re Reynolds number

Rs radius of the slipstream RT radius of the vindtunnel

St surface of a tipvane

torque

velocity for downstream

-4-veicitity for :downstream

-.average velocity

iU'diaC:plaue,:40a.-tO

radial forces average axial velocity on 6Y1144er:d*e0t-bY,4Pt741,240, factot,Idefined in appendix. A

-factor, defined in appendix A

tilt

angle, deviatiou incidence

sweep

velocity ratio

nR/u

kinematic viscosity

density of the air

- .

solidity ratio referred

to the.tipvane_

area

angular -velocity

Introduction

By the Delft University of Technology a redearch program is being carried out to determine the feasibility of augmenting the power output of windturbines by the addition of socalled tipvanes. Tip-vanes are small auxiliary wings mounted on the blades of a wind

turbine in such a way that a diffuser effect is generated. A

brief description of the proposed research program is given in ref. I. A description of the physical principles involved will be found in ref. 2, as well as a theoretical analysis of the potential performance of the system. The theory developed in ref. 2 was based

on an analytical model of a tipvane turbine with an infinite number

of blades and consequently predicts only time-averaged flow

charac-'ieristics. A part of the future research will be devoted to the

development of a theory for the finite,bladed tipvane turbine.

T/ie theoretical redeareh will be accompanied by experimental work,

in order to verify theoretical predictions, and to obtain empirical corrections for effects not easily covered by the partially-linearized,

inviscid aerodynamic theory. The present report describes the preli-minary design of the first model that will be used for this purpose. The model will be tested La the lawspeed windtunnel and in the towing

tank of D.U.T.

This first model will consist of an array of tipvanes, mounted on aerodynamic inactive extension rods, in order to measure the following

flow characteristics and compare them with the theoretical predictions

derived in ref. 2:

the time-averaged flow field of tipvanes

the amount of mass-flow augdentation achieved as a function of the total

lift on the tipvanes

the power losses associated with the induced drag of the tipvanes.

In a later stage of the experimental work it is planned to add to the pure tipvane-model a second rotor, consisting of a model windturbine,

in order to measure the gross power augmentation (fig. 1)

The envisaged future extension of the model with a second rotor has influenced somewhat the layout of the presently described model.

-6-theory developed in ref. 2. The latter theory does not give guidance, however, as to the best vane-planform, twist, etc. Therefore, it was

decided to start the experiments using a model as simple as possible, i.e. having a rectangular planform without twist. The design,is such

that the vanes can easily be exchanged and replaced by other,

diffe-rently shaped vanes. The orientation of the vanes with reference: .to

the undisturbed flow can.be fully adjusted in all directions

(fig. 2).

This enables,an investigation to be made under widely different

J.,..conditions in order to get a first insight in the possible flow phenomena.

1 Reynolds-I-numbers the model tipvanes are inevitably relatively low, and'do,nor correspond to full-scale Reynolds-numbers. This is caused

on the one.hend by the small scale of the model necessary for-voiding

wall-interference, and on the other hand by the modest tipspeeds

chosen to avoid strength ,and stiffness problems caused either by

centrifugal forces,in the windtunnel or by large hydrodynamical forces

in the towing-tank. NOW one of the most important objectives of the experiments is, as stated, to verify the mass flow prediction as a

function of the radial forces. Therefore, the total liftforces on the modettipvanes should have a value corresponding in a non-dimensional

sens to the fullscale-values. To achieve this at the low

Reynolds-numbers test, it was decided to choose other vane-sections and-larger values of the chord-diameter ratio than would be _expected for full

. scale tipvanes. In this respect, therefore,

the.model is a typical research model.

. Due to the low Reynolds-numbers

involved the measurement of viscous

power losses on model scale does not yield any relevant information. ., However, a measurement of' drag will always contain both

viscous and induced, effects. It is intended to separate viscous drag

by using regression-analysts. This is a data-reduction technique based on the fact,thatvariation of certain model parametersimill

cause both types of drag to vary, but in different ratios. For this

reason the model has been designed such that the number of tipvanes can be varied between 2 and 8.

The range of tipspeed ratio's, for which the model is designed,. is

-

-from p = 5.up to 10. This 'yields a-constant

tunnelspeed1U.=

5 m/s and a

varyinvtipdpeed RR = 25 up to 50 m/s; .

4-In the towing tank -these values are U 6 m/s

R110F 3.

up.stoOm/ii,--,-The above isThfiefly the "design philosoPhy"-upon:which the . design has beetibased.--Details of the actual design are givenin the

folloWing

chaërS,

.

In fig. 10 an overall view of the

windtunnelmodel-is'given. Table 3

gives

,

-3-General arrangement of the model

1.1. Layout.of-thewindtunnelHmodel.

The central part of the first test model is an array of tipvanes mounted

on extension rods (see the right handside of fig. 1).

Each rod-with-tipvane is built as a unit: the tipvane is fixed to the

extension rod, but the unit itself is easily replaced by another. unit. The cross-sections of the extension, rods are circular, in order,to avoid

any lift force on the rods. The extension rod ends in a stremwise fin attached to the suction side of the tipvane, to minimize the disturbance of the flow (fig. 3). The hub must be capable of receiving sevpra17numhers of tipvane units, in such a way that exchanging of the units is easily

accomplished.

The shaft of the model, the motor and the measuring arrangement are all downstream. In the future, a separate windturbine and additional test equipment will be placed upstream. In the meantime, a spinner is fixed upstream. A streamline fairing is placed over the hub and shaft to

minimize aerodynamical interferences.

As the motor and measuring equipment are too big to be enclosed by the fairing it is necessary to make a long shaft (approximately 3 rotor diameters in length) to achieve a disturbance-free slipstream.

The first bearing is just downstream

of

the rotorhead, and

is

provided

with an accelerometer

which

activates the brake of the motor when the

model looses a tipvane.

The DC motor delivers 150 Watt at 2700 r.p.m., and is of the type

ZUrrer INT 65 with specially wound coils for our use.

No forced cooling of the motor is necessary, because of the air

flow of the windtunnel. The speed and power control is effected by the regulator: Hyper tacho 0.09 type 77-01. The accelerometer is not specified

yet. A sketch of the model is given in fig. 10.

1.2. Layout of the towing tank model

The principle of the towing-tank test arrangement is shown in fig. 4. The installation is mounted on a wagon, which pulls the model through the

-9-'

standard arrangement meet very well the requirements of the tipvane

conf4uration: the model is immersed deep enough to avoid free surface effepts,,the right motor is available (see appendix B) and a streamline

tube with the right diameter can be mounted over the hub, in order to

obtain similarity with the windtunnel configuration. The tipvane rod units for the windtunnelmodel can also be used in this configuration,

and even the hub may be the same. The motor delivers 15 Nm torque

at 3000 rpm.

1.3. Adjusting of the tipvanes.

The adjusting of the tipvanes is achieved by uSing a'setof replaceable units, each with another position of the tipvane with respect to the

extension rods.

The adjusting must be possible in 3 directions (fig. 2 and 10): the incidence 0, the tilt y and the sweep A. The incidence and tilt adjus-ting is effected by the replacing of the units, the sweep angle is varied by rotating the unit in its hub, like variable pitch propellers In_thisway_it is possible to keep the leading edge of the tipvane

perpendicular to the oncoming flow, which is a resultant of

tunnel-speed, tipspeed and induction velocities.

1.4. Overall dimensions

The diameter of the model is determined by the wall constraints in

the windtunnel test section (1,25 in x 1,80 m), and by the free-surface effects in the towing tank.

Figure 5 shows schematically the situation in the windtunnel. The pressure outside the slipstream p; differs less than 1% from the

upstream pressure p0, in the range of desired diffusion ratios.

The maximum diffusion ratio is a design parameter and is

chosen as DS /D = 3.

, I

determined by the requirement_{_} that even it the 'largest ratio s o a tipvortex interaction muse occur

(fig;

6), , net . upsfream"..

-..

tipvortex of a tipvade muse hit the 'downstream " tip of the folio.

wing tipvane, in order to S1313.*:oxilmately cancel thes-tipiroftex which_

springs from _there. In this way it ia,hoped_to minimize the induced power losses

.

is yields: b = B

OR

,

The axial velocity co

is

the sum, of the undisturbed velocity U and the.

self induced velocity at the tipvane (iipeddix A).-

-The required value of b is thus, as a function of the number of tipvades

-B.; given by: B = 3 B etc.

The-maximUm Value of the'.prodUCCC:.c pertaining to tipVide is

,cierived,- (appendix A) from the requirement

(D/Dq)max).,-....37;-. 'to' be

'- achieved at the optithithi.We'rking

tedditiOdS

of a- Complete:medelr'i.e:,

_ ... .

., --power extraction

by a

turhideTridcIdded.: In'atipendili.A.4tAashown .

. .

.,

that freth this requirement it follows.:

,

= 0,123

b 0,082,m b. 0,062, m

- 1,2 , which means

The choice of the tipspeed

and

the minirilign acceptable Reynolds

. .

number (see next section) 'determine_

the'chord:c:

c.= 0.06 m, independent Of the number of tipVades (appendix

A):-,

The required CL is: CL = 0,33. '

-The length of the shaft should be greater' than the distance needed

by-the - slipstream to develop fully It is expe'Cfe& that a shaftT [

lenith

of

3 times the rotor diameter will be sufficient, which is about 1 meter'.

which does not exceed 0.10 m.

1.5. Choice of tipvane section

The requirement for the sections is that they must operate satisfactorily

at low Reynolds numbers. For the purpose of the tipvane-model, an airfoil section was sought, capable of a relatively high Ct , and no separation

max

at moderate values of C at Re = 100.000.

A suitable airfoil appears to be the Eppler. 385, developed for model

air-planes,-the characteristics of which are known from windtunnel tests down

to very lot Re-numbers (lei = 60.000) (ref. )). It appears that Re=105

mn

is a. minimum, in order to prevent collapsing laminar separation bubbles

and a very wide wake. In fig. 9, the results for Re = 105 are.shOwn, and

table. 1 gives the coordinates of Eppler 385. The_airfoil itself is shown

in fig. 8. In ref. 4 it is shown that it is important to take the

thick-ness distribution and camber with respect to: the circular curved orbit

of the tipvane, instead of measuring it with respect to the usual straight

base-line.

This adjusting is shown in fig. 8 and the new shape is given there. Table 2 gives the new coordinatea.'

Looking at fig. 9 it seems reasonable to suppose that CL =' I. is attainable, so there is a margin in CL available.

Neasuring equipment

2.1. Total lift per tipvane

-12-It is shown in appendices A and B that during windtunneltests the lift forces are very much smaller than the centrifugal forces. So much so,

that it is not possible to measure the lift with any accuracy.

In water this ratio is much more favourable (see again appendices A and

s,

B) and it is therefore possible to calibrate the total lift per tipvane as a function of incidence in water. Towing-tank tests are performed at

exactly the same Re-numbers as occur during the windtunneltests, and

the shape 'of the watermode/ add the windtunnelmodel are identical, as far as possible.

The lift is measured by strain gauges on the rods. The signal is processed in the same way as the electrical signals associated

with the torque measurements in the windtunnel. The system is explained

in the following section.

1

The requirement that the Re-numbers must be the same in water and air

leads to very low tipspeeds in water (appendix A):

2 R varies from 3 up to 6 m/s. As a consequence, there is no danger

that cavitation occurs.

2.2. The Drag

The drag of the tipvanes is measured by a torque meter placed on the drive-shaft. This means that also the drag of the extension rods is

included. For this reason, one set of rods will be made without tipvanes, in order to make a calibration. The error which is still present then,

-13-is due to the fact that the interference drag of the extension rods,

indUeed 14' the presence of the tipvanes, is not taken into account, but

this hasito belaccepted. Another error is caused by the torque losses. , in the bearing behind the hub. As this is in the order of a PTomille, this is also accepted.

The torque meter makes use of contactless transmission of the.signal, (fig. 7). The signal which comes from a bridge of four straingauges, glued on the 'shaft is transformed by means of 'a frequency modulator, to

a 6,7, Hi signal. This modulator and a small batteiy are fixed on the

shaft. The signal is emitted by a rotating primary, coil and is received by the secondary coil, which is' stationary and is placed at a distance of a feii centitheter: The accuracy of the sOtemis 12:-. The type is:.

I'hirilisiFM-contatless signal minsmission/System PR 9913/14/16

The whole systemiS Placed just in front of dm. motor.

2.3. Tipspeed

The tipspeed is measured by means of a contactless revolution counter: a cogwheel is mounted on the shaft and a proximity detector gives an electric pulse every time a cog passes. By counting the pulses the

tipspeed is known.

The pulse-counter is standard equipment of the windtunnel; the detector

to be used is:

Llectro-Products Lab. Inc. type 3015-A.

This arrangement is also placed just in front of the motor.

In the towing tank the number of revolutions is measured by standard equipment built inside the torpedo-like streamline body on which the

-14-2.4. Averaged, flow field

1

The time-averaged flow fild downstream of the.rabdel.a4d:the undisturbed

flow velocity upstream are Meatured,byAmeans::Pf':A::hOt, wire anemometer

As

the velocities in question are very small,

it .ia2not_Tossible to measure

accurately with a pitot.

2.5. Qualitat-lve? flow

z

,

Smoke will be used for visualizing the general flow pattern,

and to have

a "quick look" system for measuring theLamounti-of diffusion. An oilfilra

method Will be used for qualitative inspection of the boundary layer on

the tipvanes; fOr_tracings4paration oriparso.

the vanes, etc.

.

In order tO:recOrethii.by:phOtographingorT,filMing-,-a stroboscope is

used

This stroboscope dan.besynchronized,automaticallyrby

coupling it

_

to the detector used

for"cOunting,themumber'of reVolutiohg-

-The: strôbaScopé is of the type:

'

Bruil Filqaer..

kotion Analyzer

. .

3. Structural aspects

3.1. Bending moments in the extension rods.

The tests in the towing tank cause the greatest. bending moments in the rods due to large hydrodynamic drag, so this situation is decisive for the diMensioning. The critical factor is the bending in the plane of the rotbr, because this means a change in incidence 8. If it is required that the makimum change of incidence is of the order of 1/1000 radian, it appears (appendiX-D) that the desired dimension becomes: from r/R=0 up to 2/3 the rod diameter d must decrease from 2 cm to 0,9 cm, and from

r1R2/3upto 1, &remains 0,9 cm.

Other important bending, moments: occur in the windtunnel, if the resultant of

the lift- and centrifugal forces-does not act precisely through the centre-line of the exfension

rod.

During the windtunnel tests, this resultant is almost equal to the centri-fugal force, so the rod has to be fixed at the centre of gravity of the tipvane. A similar situation may arise in the towing tank where, however, the lift force is even greater than the centrifugal force, so that the centre of pressure should be known in that case.

As the position, of the centre of pressure is not known beforehand, because

of the lack of theory developed so far, the amount of bending in the towing tank is to be measured using the same strain-gauge balance installed for measuring the total lift (section 2.1.).

3.2. Production of the tipvanes.

The tipvanes in this introductory experiment have a very simple plan form and each tipvane is exactly the same (only the angular position with

respect to the rod is variable). Furthermore, it is not necessary to make

very high demands on the quality of the surface, so it is possible to

make many tipvanes in a relatively simple manner: hollow tipvanes made of

fibre-reinforced plastic with a skin-thickness of 2 mm, filled with hardened

foam. As is calculated in appendix B, the mass of such a tipvane, including

the dorsal-fin, is approximately 0,15 kg.

-15-This:iteaSilyiCaried,bythe.rod,,

-16-If the model is made of solid alumininium the weight becomes slightly

higher, but still acceptable. The latter is still one of the alternatives

which is being studied.

3.3. Magnitude of_the

I

From appendix B it follows that in the,wiodtudnel the total centrifugal

force at the root of the extension rod of -a model with two tipvanes is

-F

= 3000 N. This is quite a lot, but when special

attention is paid

_t9Ie construction of the hub and the rod fixing arrangements, it

should not be too difficult to handle this load.

Decreasing the centrifugal force means also a diminishing of the Reynolds

number and as this isonot-allowable_ (chapter -1.5), the high centrifugal

iodds in the construction have to be accepted.

The experiments carried out in the water tank give a much better result:

-F

=%40,N 1(appendix B). Appendix A gives for the maximum lift Per

gmax

tipvane in this.case:

140_N -max

:4ii4hati.thete7.it'evenacompreion load in.the.rod of approximately 100

References: Th. van Molten Th. van Molten Th. Volkers G.J.W. van Bussel

-17-Onderzoek

aan

windturbines met zogenaamde "tipvanes". Enkele technische, organisato-rische en financale aspecten van de "tipvane"

project, Technioche Hogeschool Delft, Afd. der Luchtvaart- en Ruimtevaarttechniek, Memo-randum M-269, maart 1977.

Performance analysis of a windmill with increased power output due to tipvane induced diffusion

of the airstream. Delft University of

Techno-,

logy, Dept. of Aerospace Engineering, Memorandum M-224, November 1974.

Preliminary results of windtunnel measurements

on

some aerofoil sections at Reynolds numbers between Re = .6 x 10 and

5.0

x 1O5. Delft University of Technology, Dept.

of

Aerospace

Engineering. To be published as a Memorandum

M-276.

The formulation of the boundary value problem for an isolated rotating tipvane. Delft

University of Technology, Dept. of Aerospace

Engineering, Memorandum M-272, February 1977.

-18-Appendix A: Choice of main parameters.

The dimensions of the test-section of the LR-lowspeed windtunnel are 1.25 m (height) by 180 m (width), but for the purpose of some of the calculations presented here, a circular tunnelsection of 1.25 m diameter is assumed, whichfacilitates calculations of wall constraints, whereas

. .

the asumption is thought to be on the safe side. - .

The first design parameter to choose is the maximum diffusion ratio

D /D

(fig.

4). Here we take (Ds/Dm) = 3.

The tunnelwall influence is estimated far downstream. As a criterion is used

that the pressure pc', outside the slipstream must differ less than I% from the undisturbed pressure p for upstream of the mill.

The Bernoulli equation outside the slipstream yields

. . ,

po - po' = p (U'2 - U2)

Now suppose that the streamline tube upstream of the mill (fig. 4) is replaced by a straight streamline tube, with a diameter equal to

Dm.

This simplification is conservative, as far as the estimation of

wall-constraint is concerned.

The continuity equation applied to the flow outside the slipstream

gives:

Combining the Bernoulli and continuity laws, and using the largest

anticipated diffusion Rs = 3 Rm, we find:

AP = Po - P; = P U2 (a2-1) RT2 - Rm2

a

-RT2 - gRm2

1

For Rm = = 0,21 m it follows: Ap co.

For the choosen value of

Rm =0.18m it follows:

(DS/Dm)2 =

-19-Using p = 1,25 kg/m3 and Umax = 5 m/s, Ap(becomes:

Ap = 190 N/m2

which means: ti421 , 2 Zo

max

This is considered negligible, so we choose: Rm =0,18 m.

The solidity ratio at of the set of tipvanes:

When L is the total lift per tipvane, kr, the mean radial force per unit

length, is defined as:

B . L

k

-r 2 7r

Rm

For L we can write:

L =CL . p (PR2 + trx, + 2 Y) + 1+2 Y)2 + 1

A

_ u opt 3 U 9 U 3 (A-4) (A-5)

where w is the total axial velocity at the tipvanes.

Ref. 2 gives for w:

(13 (3 +

tr)

(A-2)

where a and 8 are given, for an assumed elliptic loading of the tipvane,

by (ref. 2): - 32R

f b 6 ,

3

4 4R

Lu (v)..

t

Furthermore, ref. 2 gives for DS/DM and (u0D/U)

opt

up, V

Now fig. 16, which has

with:

(aR)2 w2

Now A-1) becomes:

-k-AO 12102.

- -= -pu2R 0.12/1.2.a. b.c a. = B. 7R2 M 2 -(CL .0 _{;t max} = 4,8 following relation is satisfied:

-20-These last two equations ge: Yiv .= 0,9;

,

so with (A-3); it follows from (A-2):

T

27r12J w 1

B (-11). p

min

The maximum tipspeed ratio is choosen at p = 10, so:

V

been derived from ref. 2, gives for - = 0,9:. U

So that the paradeters C , tien .q -:-should be ChoSen Such that the

(A-9)

The span and choidnf-the

tipvAhe-The planform:of the.tipvanes-is chosen to be rectangular-. Ihe

span h.,

of the tipvanes is determined by the condition that the tipvortex:of,a

tipvane

is

convected such,, to coincide with its counterpart of the P#4,. 0.pvane (fig. 7).

From fig 7 it appears that

(A-10)

11co

= 0,164

= 409

(A-6)

LT-

-21-When

_(w/nR)

_{becomes smaller, the}

_{place where}

_{the tipvortex hits the}

next tipvane shifts towards the middle of the vane. (A-6) gives (w/u) = 1,09. With pmin = 5 (A-I0) yields:

b = 0,123 m for B = 2

0,032 m B = 3 _{1 (A-11)}

0,062 m B = 4

.

The chord c follows from the requirement: R = 105. With

en

(OR)

min = 25 m/s this gives:

mm Re . Q.R.c = 6,85 . 104. (OR) . . c min min C 0.06 m _{(A- 12)}

Now (A-9) combined with (A-I0) gives for at

1

= (11).

min

so

at is independent of the combination of b and B given in (A-II).

The lift and drag

With

u

= 10, at = 0,145, (A-8) gives:

max

CL = 0'33 (A-14)

Thus, the needed three-dimensional lift-coefficient _{of a tipvane must} be at least 1/3 to attain the diffusion ratio _{of 3 if the model works}

at its optimum working condition.

Looking at fig. 9, this _{seems quite possible even if the tipvane has}

an aspect ratio of 1 in the case of B = 4 (A-II), at least if _the

distribution of _{CR. along the vane span is not too irregular.}

It is assumed that the maximum attainable value of CL is CL = I, the maximum lift acting on _{a tipvane of a model with two vanes is:}

The drag

Otim/ted II

$14,Posidg- c

0,05, T

4 t40 4r40 a

tiovane of ,a two -vaudd -configutation becomes

LC

° C

As the solidity remains cOnstant when B increases

the viscous dra

remains constant too'. Sol:

so that

Y ;

-r-= 11,5 Li.

one

iipAran

one

tipva.ne

tlpvipe

'

L'* (RR)

2-- 0,575 N

= 1

15N

atray

When the same model is tested in the towing tank, at the sable Reynolds

. -

--numbers, the results of this appendix become:

6

= 006 .

10 (S1R)

(aRltain

4976 m/s = 3 m/s

=0,5m/s

one

tipvane

tiPvene

array

= 140 N

13,5 N

-Appendix B

The centrifugal-fdices

-23-This appendix deals only with a two b/aded 6:x1e/4-because in this case

the tipvanes are the largest ana titerefore also the centrifugal loads.

The projetted area of suth a tipvane is 75 cm2 (see A-11 and (A-12). With a skin thickness of 2 mm, a specific mass of fibre-reinforced-plastic of 2.10-3 kg/cm3 and with some allowance because the profile is not a flat plate, the mass becomes 0,075 kg.

To take care of the tipvane to rod connection and the foam filling of the profile, the total mass of one tipvane is estimated at1),15 kg., The maximum centrifugal force occurs in the windtunneltests, at (R) max:

Fg= m

(M2

_{= 2100 N} (B-1)

gtipvane

The centrifugal force, due to the extension rod, follows from:

grod

= Ed2.sm a2maxr dr = sm.d2(2R)2 (B-2)

4 6

with: s.m = specific mass = 7,8.10-3 kg/cm3 (steel)

d = diameter rod = 0,9 cm (straight part of the rod)

This gives

Fgrod

= 620 N (B-))

So the total centrifugal load in the root of the rod is F = 2700 N.

As will be seen in appendix C, the rod is not prismatic, but has a

foot diameter of 20 instead of 9 mm, in order to withstand bending. Therefore the F is factorized by I and the centrifugal load is

grod of the order of:

= 3000N (B-4)

gtotal

When the model is in the towing tank, the maximum total centrifugal

load is found in the same manner:

= 40 N (B-5)

A22endix C: Required motor performances

From (A-17) it appears that the viscous drag of the tipvanea-ls_

1,15 N in the windtunnell On top of this comes the induced drag,

and theilrat'.oUthettension'rods (ref. .2).'

TO take.adcduntatheseextra amounts ;of drag:the-total4Alrag is 'estimateiratH3I4- FOr,theAiurpose of sizing the model it is; assumed

to be actiligYis a 'singlelforde at the end of the rods. :-SO

IDtotal.

= 3 N C-1

The torque is thên

and the power needed is:

T = D x R = 0,54 Nm = T. 0 150 Watt Dtotal = 30 1.4 T = 5,4 Nm P = 180 Watt max. speed = 320 rpm (C-2) C-3)'

The motor has to reach these maximum values, at the maximum speed

of = 2652 r.p.M.

2n

In water these Values become, with the drag of the:tipVanes given,bY,

(A-18)1 D = 13,5 N tipvane array'

(C4)

(C-'5) (C-6) (C-8)

-25-Appendix D: The dimensioning of the extension rods

The experiments in the towing tank have the disadvantage of a large

bending moment in the rods', due to the high drag. As is shown by

(C-1) and (C-5), comparing the air- and water situation the drag differs

by a factor 10.

In order to keep similarity between the two series of experiments, the tipvanes must be kept at almost exactly the same incidence when turning in water or air. Therefore, one of the design objectives was, to keep the.angular deflection of the tipvanes less then 1/1000 radian in the

-w-ater.experimerits.

As indicated in appendix C, the load pattern is simplified as a single force acting at the end of the rod. (C-5) gives _{Dtotal = 30 N, or 15 N} on each rod individually, in the case of two rods. When more rods are used, the situation_becomes more favourable. With the help of simple

beam theory, a formula has been derived for the angular deflection

t.

1.44.4E

in terms of the parameters indicated

rv

in the accompanying figure.

Consider first the tapered part of the rod alone. We now apply the equation of deflection

dx2 EJ(x)

(D-1)

the rod has a circular cross-section, so for the inertia moment, e

substitute:

At the end of this tapered part, a moment m = + F. (R - 2.) and a force

F are present. Considering first the force F alone. Then with

M(x) = - x)

d2y-

x) 2 .E . rr :(d - d )) -64 1 ; 2

Substituting E = and

n=f

_(D-3)

becomes:

Now due to the ,moment

m =

F (R

-of; the rod is'os1O41sred

The equation of deflection ic now:

EJ(x)

again substituting: ,64 F(R 64. F(R g)t (dA

-d

2-7li

-(d1 ) d23 2

theend of the tapered part

-27-On top of this comes the angular deflection associated with the straight part of the rod, with the constant diameter d2. In this case, c is given by a

clisSical formula of beam theory:

2

E3

F(R

F(R - ft)

-

_{2 E J A 4}

''' 64 "2

The total angular deflection now follows from (D-5) (D-7) and (D-8):

C =

+ c di - d2 -01' - d2)2 64 E I2 e c ) + _{+ 3) +} 1 2 + = 3 Ti E- {--2----f

(I

di d2 3 d1 3(d,d )2 d1d2 I 2 ' 0)-9) (R -k)2 + 4) 2 d2 Forr!"FL= 15 N (O-5) 4 E = 20,5.10 N/2mm (steel rods) R = 180 mm D =120 tm' d = 26 lum d2 = 9 mm (D-9) gives: c = 0,001 radian (D-10)

Another critical stressing case can occur, when the resultant force on the tipvane, composed of the centrifugal force and lift, does not act

along 'the ' cintTeline of the rod.

When' thOnnection of rod to tipvane coincide with the position of the

centre of graility of the tipvane the bending moment due to excentricity

is the greatest during the water tests: here the lift is greater than in

air.

A formula like (D-9) can be derived for this case.

When the positive sign of M is as shown in the figure, the equation

This gives: 64. (d1

-d7)2

3

c

= ,2) 1 Tr E (d1 d2)3 (d1 d2'

For the straight part of the rod again a result of classical beam theory

is used:

. M (R-L) e2 - _{, n 4 /}

"

64.`j24

The total e is now:

-28-d2y M

dx2 EJ(x)

-This yields the same expression for

(27)

at the end of the tapered part, as is given in (D-7), when for F(R-L) is substituted M.

(D-11) (D-12) 2.,(d1-d2)2 3 ft

e=e1

+ e2-+

+ 3(R

-1

(D-12) 3 E-17 (d1d2)2 (d1 d2)3 d24,

(A-18) gives for the maximum lift of a tipvane in water L.,= 140 N. When

the excentricity is denoted by e, and the above mentioned values

of

the

rod dimensions are used, (D-12) gives:

e = 0,00019 e radian, e in mm

When this angular deflection must be in the same order of magnitude as (D-8), then emax = 5 mm. The maximum distance between the centre of pressure and the centre of gravity may be 5 mm. This can be achieved by shifting the centre of gravity of the tipvanes using small balancing

weithts; if necessary. Whether this provision is needed .cannot be predicted

at this Moment, but will be determined by measuring the bending moment

NO .X-PCT Y-PCT ,1 100..000 0.000 2 9..9.695 0.080 -..,3 4 97.3.84 -

0.716

5 95.4.80.. 1.231 t.

93..117! 1826

7- - 90.309,

2.482

. 8.- . 3,.194

--9

.81.4-89' 10. .79.569. 40745-H 11 ., 37-6 5.552 .12 ;

6358

-13 66.390- -.71.139.-.14 61.709' -7.873 15. . 56.981 8.529-16 52.250:.-. 9.070 17. 9-.467 18

42.898

.9705

.19

38.337

,9776--33.887 .21

29.571- 9412

22 2.5.420 -9.009 23

21.475

8.-483 24 17.776 '7.850 25 .-14.358

7.122

--26 -.11.253.; '60316 -.27 80490:

74447'

-28

6090 - 4.533

.4.0733.595'

30. 31.. .-1.233'. 1..750 32 - 0.626. 0.907 . -33.. 0.0025

0.187

-'34. . 0.306.°

0768

'36. - 1,996 0.790.--

.0.863

.30 6.131`.. -.0775a 9.:023 04603., -40

12.458: 0.350=

41: 16.339' 0.034. 42. 20.607 -1,0317 25.429. 0.688 -244 30..507 - 1.056 45

35.858

.

1405

46...41.414.. 1.717

47

47..100 1.980 .4-8 52.442:_

2.183

2.318 5a - 64.18,7

2.380

151; 65..656. 2.368 -52 74..457 2,281. 53_, .19.718: '2.126 . 210 1.907 .55.

633

-5.6 914,779 1.317 -..:'57 -964780 0.968

58

97.07.6 0..603

59

98.-722 0.281 :60.. . 685' 0.070 61 100.;000....0.000 trailing edge .-.'leading edge trailing edge

Table 2: Coordinates of the adjusted Eppler 385 profile.

NO

X-PCT

Y-PCT

Y-4M 1

99.9999

0.0 59.999c 0.0 _{trailing edge} 2

99.6950

0.020

59.3170

1.0174 3

98.8040

0.1210

59.2824

0.0726 4

97.3840

0.2560

55.4304

3.1715 . 5

95.4800

0.5020

57.2590

0.3012 6

93.1170

0.7450

55.P702

0:4470 7

90.3090

1.0060

54.1554

3.6036 8

87.0840

1.2990

52.2504

0.7794 9

83.4890

1.6320

50.0934

0.9792 10

79.5690

2.0100

47.7414

1.2060 11

78.3760

2.4310

45.2256

1.4556 12

70.9650

2.950

42.5790

1.7370 13

66.3900

3.3910

39.5340

2.0346 14

61.7090

3.9060

37.0254

2.3436 15

56.981C

4.414C

34.1886

2.6454

16

52.2500

4.1920

31.3500

2.9292 17

47.5450

5.2810

28.5270

3.1655 18 19

42.8980

38.3370

5.590

5.3070

25.738r,

23.n22

3.3558 3.4842 20

33.8870

5.9120

20.3322

3.5472 21

29.5710

5.9120

17.7426

3.5472 22

25.4200

5.8220 15.2520 3.4932 23

21.4750

5.6460

12.8850

3.3876 24. 17.7760 5.39G0

10.6656

3.2340

25

14.3580

5.0510 8.6143 3.0306 26

11.2530

4.6360

6.7518

2.7816 27

8.4900

4.1370

5.0940

2.4822 28

6.0900

3.5630 3.654C 2.1405 29

4.0730

2.9350 7.4431 1.7610 30 2.4500 2.2530 1.4700 1.3518 31 1.2330 1.5440 0.739;3 D.9264 32

0.4240

0.8360

0.2544

0.5016

33

0.0250

0.1830 0.0150 0.1098 _{leading edge} 34

0.1120

-0.3250

0.0672

0.1950 35 .0.7680

0.7360

0.4608

0.4416

36 1.9960 -.1.1200

1.1976

0.672C 37 3.7840

-1445d0

2.2704

-0.8748-38

6.1310

..1.7460

3.6786

-1.0476

39

9.0230

-1.9870

5.4135

-1.1922

40

12.4380

-Z.1850

7.4625

-1.3110

41

16.3390

2.3380

9.3034

-1.4028

42

20.6870

2.4430 12.4122

.1.4658

43

25.4290

-2.5000

_15.2574

-1.5000

44

30.5070

-2.5060

18.3C4.

45

35.8580

-2.4570

21.5143

1.4742

46

41.4140

'.'2.3560

24.5484

-1.4136 47

47.1000

-2.2023

28.2600' ..1.3212 48

52.8420

-2.C30D

31.7052

-1.200C

49 58.5640.

-1.7560

35.1384

-1.0536

50

_64.1870

_-1.4800

_38.5122

_.0.8880

51

_69.6360

.101850

41.7816

-0.7110

52

74.8370

-0.8850

_{44.9022 0.5310}

53

79.7180

..0.5940

47.530E

-3.354

54 84-.2100 C.3320

50.526:

.0.1992 55

88.2500

0.1150

52.9500

.0.0690 56

91.7790

0.0440

55.0674

0.0264 57

94.7430

0.1270

56.3458

0.0762 58

97.0760

0.1240

58.2456

0.0744 59

98.7220

0.06E0

59.2332

0.0408 60

99.6850

0.0170

59.8110

0.0102 61

99.9999

0.0

59.9999

0.6

trailing edge

1: Dimensions: span b = 0.123 m (for B=2) chord c = 0.06 m mill diameter D = 0.36 m 2 , r

rod diameter d

= 0.009mfor

increasing up to (at the axis)

r 2 0.020 m for 0

max. fairingfairing diam. = 0.10 in

shaft length = 1.00 in

Velocities

PR

Tipspeed ratio p= --u- varies from 5 up to 10

5.

so with R = 10 in both cases:

e.

min

U = 5 m/s

(R)max = 50 m/s } in the windtunnel

(i/R)min = 25 m/s

U = 0,6 m/s

(nR)max = 6 m/s

(OR).=3 m/s

_min

Required motor performance

max. rpm = 2650

max. power P = 150 Watt max. torque T = 0,54 Nm

Table 3; continuing on next page.

in the towing tank

in the windtunnel

max. rpm = 320

max. power P = 180 Watt in the towing tank

Occuring forces:

Centrifugal loads at the root of the rod of a configuration

with two tipvanes;

= 3000 N in the windtunnel

gma

= 40 N in the towing tank

ma.x

Maximum lift per tipvane, of the same configuration:

= 11,5 N in the windtunnel

t = 140 N in the towing tank.

max

propellor-like turbine

tipvane

Fig. 1:. Principle

of

test-configuration

extension rod

tipvane

Fig. 2 :

Adjusting

of

the tipvanes.

plate ,welded on rod end

plate is imbedded between sheets

of fibre reinforced

plastic .

Fig. 3 :

Fixing rod to tipvane

I.

h= 3. Dm

Fig. 4 : Principle of the test configuration in the water tank

.

___

---Po

_{1Drn ( ("}

_Si

--

...

..,-

.

---

....

_{-_}

/777/7/7/7/77z / /7/77/7/77/ Po 7//////7/7/7/

Fig. S :

Si tuation in

wind tunnel

motor

'gear

2,na

Fig. 6

:

Path of

tipvortex

water level

hub with

measuring streamline I

arrangements

bodies Uo, Ds

ot

b

_am

* w

B QR

mri

transmitting coil

receiving coil firm

of mill

_disc

original

amplifier

LF-FM oscillator

recorder

FIG. 7: PRINCIPLE OF THE TORQUE METER

adjusted with distance h

FIG.8 : THE EPPLER 385 PROFILE.

strain gage bridge

battery

111111

15,

10

05

0.5,

:.F10. 9 CHARACTERISTICS OF THE...;E:P.PLER.385 0.:ROFILE.,

AT Re

-.

0.02

1

16,"

0.18 ; ; '1,

4 oieep

tilt

1.7.

-pi to t tu be or anemometer.

- revolution

counter]

proximity detector!)

y MiifOr_(150V;,27.00'ItPr.P)

torque meter

,

bearing's

strearnline tube

_{-rod fixing and adjusting}

a r r:angement spinner

--Incidence