An experimental verification of a design method for ducted propellers

FRAN

STATENSSKEPPSPR:OVNI:NGS.ANSTALT

(PUBLICATIONS OF TEE SWEDISH STATE SHIPBUILDING EXPERIMENTAL TA?K)

Nr63 GUTEBORG 1968

AN EXPERThIENTAL VERIFICATION

OF A DESIGN METHOD FOR DUCTED

PROPELLERS

BY

GILBERT DYNE

Paper to be presented for the American Society of Mechanical Engineers PhiladeJphia May 1968. Symposium on

"Pumping Macbinery for Marine Propulsion".

SCANDINAVIAN UNIVERSITY BOOKS

Denmark: MUNXSQAABD, Copenhagen Norway: VlivEBsITETsFoBL&aET, Oslo, Bergen

Sweden: AZADEMU'ORLAGET-GVMPERTS, Oöteborg

SVENSK4t BOKPOBLAGET/NOrstedtsBOflmerS, Stockholm

PRINTED IN SWEDEN BY

A method for the design of ducted propellers has been developed at

the Swedish State Shipbuilding Experimental

T a n k (SSPA). Starting from known values of. total thrust, number of revolutions, duct vorticity etc. the method: determines ducted propeller efficiency, duct thrust, shape of the: duct and. the propeller etc. The distribution of, blade circulation is arbitrary and the number of propeller blades finite., To simplify the calculations a combination of the method of singularities and the momentum theorem is: used. In order to obtain an experimental verification a series of. open

water tests with four heavily loaded ducted propellers has been

ôarried out in the SSPA cavitation tunnel: At the advance ratio

J=0.412

the non dimensional total' thtust was. ' ' K.7.=0 278

The theoretical thrust of the duct KTD (ie. the duct vorticity) was varied systematically within the range,,

0.01 KTfl/KTT 0.4$.

The blade form and the distribution of blade circulation were the same as for a conventional propeller.' '.:

The thrust and torque measurements': indicated, a good general agreement between the experimental and theoretical values of total thrust, duct thrust and. propeller efficiency 'especially for. three of the four ducted propellers tested. The experimental duct thrust was, however, somewhat larger than' the theoretical, when the duct vorti-city was small and vice versa. " .' . . .,

,: ...

The most extreme .duoted propeller. which theoretically, should have, given' a duct thrust' of 'KTDtKTT=O.45 suffered from flow

separation'insid.e'the rear' part Of: the duct which, decreased KTD/KTT

to 0 29 The separation was detected m a series of flow visuahzation studies which were carried out using a quarzline lamp ffluminating

At the design total load K/J2= 1.63 the ducted propellers

tested1 had an efficiency of maximum 53%. The corresponding value for a conventional propeller was 46%, i.e. a power decrease of about To nvestigate the sensivity of the co-operation between duct and propeler, some of the ducts were also tested together with propellers origmlly designed for other ducts At the design KTT/J2 both the duct thrust1 and the propeller efficiency were decreased considerably if the pitch ratio of the propeller was lower and the camber of the blade sectioii higher than the design values In one case of two this was also true when the pitch ratio was higher and the camber lower than the

design) values. The flow visualization studies indicated that the

probable reason was a flow separation inside the rear part of the duct.

Plow separation outside the ducts was recorded orily at very low

values of

-Studies of cavitation inception showed that none of the ducted propellers tested suffered from suction side bubble cavitation at the design point In some cases, however, hunted cavitation was observed m the gap between the blade tips and the duct No significant differ-ences in the cavitation characteristics were found between the ducted propellers and a conventional propeller.

1. Introduction

A method for the design of ducted propellers has been developed at SSPA [1]') Startmg from known values of total thrust, number

of revolutions, propeller diameter, blade number and form, distribution

of blade circulation, duct vorticity, minimum cavitation margin, etc the method determines propeller efficiency, blade area, duct thrtist, shape of duct and pitch, camber and thickness of propeller

blade sectiOns. .:

H:.:..

To vrifr the design method a series of testsin homogeneous flow with four different heavily loaded propellers has been carried out. The experiments which comprised measurements of thrust and tor-que, determination Of incipient cavitation and flow visualization studies are described ui. the 'following. In the .beginnig of the paper a short describtion of the design method is given

2. List of SymbolS

A0 = - = propeller disk area

AD = developed blade area

coefficients for the distribution of blade circulation D = propeller diameter

/

= camber of blade sections

GL - _____ - non-dimensional blade circulation coefficient rDVA

V

J = advance ratio of ducted propeller nD

= = torque coeffióient T

= = duct thrust coefficient pD'n2

KTP

-

= propeller thrust coefficient T

KTT

= i--

total thrust coefficient

pD4n2

1 length of blade section

L = length of duct n = number of revolutions

PfD = propeller pitch ratio in ideal flow p = static pressure = vapour pressure Q =torque r = radius D 2 O.7 = Reynolds number. For propellers R5 =

-V

LV

For ductsR=-4

a = maximum thickness of blade section = duct thrust

= propeller thrust Tr = total thrust

V4 = advance velocity of ducted propeller r

r

= non-dimensional hub radius y = axial coordinate

r

V p a = blade circulation = duct vorticity

= duoted propeller efficiency

= kinematic viscosity = mass density of water

ppt,

-.

= _____ - test:cavitation number

p VA2

3. Design Method

In the main part of the calculations the propeller is replaced by an equivalent infinite-bladed propeller represented by continuous radial distributions of semi-infinite tubes of ringvortices and rectilinear vortices. The strength of the ringvortices is determined by the blade c]rdulatlon and the velocities m the ultimate wake The duct is repre-sented by systems of ringvortices and ringsources which simulate the flow acceleration (deceleration) and the thickness of the duct respec-tively. The hub is replaced by a source distribution along the axis. If the hub is cylindrical and the thickness distribution of the duct is prescribed, the strength of the source distributions of the duct and the hub is determined by the local axial velocities.

The definite strength of the different singularities is calculated in an iteration process described as

follows:--1 From the immediately preceding iteration approximate values of the following quantities are obtained

-blade area from which the -blade section length.is calculated (the blade form is given),

total axial velocity at the propeller disk and along the hub and

the. duct,

tangential velocity at the propeller disk, blade circulation.

The strength of the source distributions of the hub and the duct is calculated from the law of continuity.

The ideal total thrust determined by the momentum theorem is

compared with the total thrust desired increased by the axial

components of the drag caused by the propeller blades and the duct.

If the two values of ideal total thrust differ the blade circulation is corrected. Then the total axial velocities at the propeller disk and along the hub and the duct are determined. The velocities

induced by the propeller, duct and hub are thereby calculatediy

use of the law of BlOT-SAVAnT, see [1]. The calculations are repeated

from point 1 until convergence is obtained.

When this is true the thrust of the propeller is determined as the ideal thrust calculated by the law of BERNOULLI with the axial component of the drag of the propeller blades deducted.

A strength calculation according to the rules of D e t N o r $ k e V e r i t a s gives the thickness of the blade sections.

The local cavitation number is determined at various radii along the propeller blades. Thereby also the pressure change caused by the duct is considered. Comparing the local cavitation number with the critical cavitation number the cavitation margin is deter-mined. If the margin differs from the prescribed minimum value the blade area is corrected and the calculations are returned to point 1 above. The iterations are continued until convergence is obtained.

In order to determine the shape of the duct the axial velocities

induced by the singularities of the propeller, duct and hub are calculated by the law of BlOT-SAVAnT at different radii along the duct. The shape of the internal surface of the duct is then obtained applyiig. the law of continuity. From a practical point of view it is desirable that the duct is cylindrical at the propeller disk. To obtain this it is often necessary to complete the original duct vortex distribu-tion with an addidistribu-tional distribudistribu-tion. If the propeller is located at the midcord of the duct and an uxisymmetrical duct vortex distribution is introduced the velocities at the propeller disk and the thrust of the duct are only slightly influenced. The calculations, described above need therefore hardly be repeated. The duct vortices added can re-distribute the curvature of the duct profile and as a result an amount of duct thrust is shifted from the rear part of the duct to the fore part or vice versa.

In the propeller calculations the number of blades is assumed to be finite. Starting from the propeller thrust as obtained above the propeller induced velocities are determined by an ordinary lifting line method assuming the pitch of the helical vortices to be determined by the velocities in the ultimate wake 'Due to the relatively large blade widths generally used for ship propellers, the axial variation of the induced velocities make camber and pitch corrections necessary. Beyond the ordinary corrections calculated by some lifting surface

due to the vorticity of the duct. Pitch corrections due to viscosity and blade thickness are determined in the same way as for a con-ventional propeller.

In the actual investigation some deviations from the above men-tioned design method have been made. Thus,

the propeller efficiency is determined assuming the number of blades

to be infinite,

the source distribution of the duct is prescribed while the resulting thickness of the duct profile is calculated,

the influence of hub is not considered,

when the shape of the duct is determined, the velocities induced by the propeller are calculated using the blade circulation obtained from the infinite blade number calculations.

The influence of the deviations mentioned in point 1 and 2 above are

discussed in Sections 5 and 4. The deviations in point 3 and 4 are considered to be of less importance.

4. Ducted Propellers Investigated

Four different ducted propellers were calculated, manufactured and tested. The load was chosen to permit application to a 150000 TDW tanker with speed 16.6 knots, number of revolutions 105 r/m and propeller diameter 7.0 m.

Data for this case were as follows: -Total thrust KTT=O.278 Design advance ratio J_-0.412

Hub diameter XH=O.186

Number of blades z=5

Blade form and blade section thickness, see Fig. 1 Mean line of blade sections: NACA a=0.8

Thickness distribution of blade sections: NACA 16

Cavitation margin c=30%.

The distribution of blade circulation was normal with zero circula-tion at the hub and at the duct

GL= const(xxH)(1 x)(1 +bx) [a+(1 ±XH x)2]

where a and b are constants which determine the fullness and the position of the maximum of the distribution, see Fig. 2. In the actual investigation a=0.3 and b=1.0.

aoig

G/G

_{L max.} 1.0 0.8

06

04

0.2 0

Fig. 1; Outline of propeller P1315.

The efficiency of a ducted propeller is a function of the th±ust of

the duct.. In the present investigation therefore the duct thrust

KTD/KTT has been varied systematically, as shown in the table below.

The corresponding duct vortex distributions are shown in Fig. 3.

For the ducts D5D7 the original vortex distributions have been

modified to make the duCts cylindrical at the propeller, compare

Section 3.

0...Q2..

.0.4.

-06.

Fig. 2. Distribution of blade circulation.

0.8 x 0 rP I/O L'O I.0 9 0.8 0.7 05 0.502660.0.30 04 45 0.3 0.E3 035 -

.a

A

o:co;b:

a-co;b=1 a 03; 0

/

/

-

b =1 (actualdistributicn) I. .

LI

In a uniform flow with small induced velocities the source distribu-tion used for ducts D5D7 would have given a NACA 0015-profile while the thickness of duct D4 would have been one third of a NACA 0015-profile. Due to the large and varying induced velocities along the duct in the present cases, however, the maximum thickness of

the duct profile was decreased and moved aft.

3

A

IAIL.

-0.4 -02 Q2 0.4 Y/R

-1

Fig. 3. Duct vortex distributions.

Propeller Duct Calculated

KTD/KTT (VDIVA)p=o I AD/AO

P1313 D4 0.01 0 0.68

P1314 D5 0.15 0.43 0.65

P1315 D6 0.30 1.20 0.64

L=O5D.

The shapes of the ducts are given in Fig. 4. An increase in the thrust of the duct is obtained if the camber of the duct profile is m-creased and the geometriöal angle of incidence of the profile is dec-reased slightly.

The pitch ratio P/D and geometrical camber of the propeller blades f/i are shown in the diagrams in Figs. 5 and 6.

The propeller and duct models were manufactured in white metal (a special tin alloy) and in bronze respectively The propeller diameter was 181.5 mm and the radial clearence between propeller blade tips and duct was 0.3-0.5 mm.

All tests were carried out during 1967 in the SSPA cavitation

tunnel. The test section was 0.5.m X 0.5 m and the water velocity

Propel/er Na P1313 P1314 P13/5 P1316

0

02

0.4 0.6

08

,c 1.0

Fig 5. Geometric camber of the blade profiles.

004

003

002

Propeller No. P1313 P1314 P1315 P1316 0.2 04 06 0.8 x 1.0

Fig. 6. Pitch ratio curves..

generally 2.5-'3 rn/s. At the design advance ratio and VA= 3 rn/s Reynolds number was

R=76x 1O' for the propeller blade sections at x=O.7 and B=2.4x 1O for the duct.

5. Thrust and Torque Measurements Test Equipment. Accuracy of Measurements

The duct was mOunted on the propeller shaft via three arms, a hub and radial and thrust plain bearings as shown in Fig. 7. A strut

prevented the rotation of the duct. A conventional mechanical

balance described in [2] measured the total thrust and the torque.

The thrust of the duct was determined by the use of an annular

straingauge balance located between the duct hub and the propeller hub, seeFig. 7.

The water velocity in the tunnel was measured in accordance

with the venturuneter prmciple, i e the fall m pressure m the nozzle upstream of the test section was measured by a manometer. Wall effect corrections of velocity and static pressure were calculated according to equations given by GraurnT [3]..

£2 PID f.0 08 05 04 Q2 0 0

Strut Ball bearing Duct Propeller Arm Axial plain bearings Strain gouge balance Radial plain bearings

-..-i

Fig. 7. Test arrangement.

During a test series the uncorrected water velocity VA was main-tained constant while the number of revolutions, n, was varied in steps in the range

0.3 :J= -

O.8.

To decrease the errors in measurements several test series at

different speeds were carried out for every ducted propeller tested. The resulting curves were faired. The maximum errors at the design point were estimated as follows:

Total thrust AKTTIKTT= 0.01 Ducted thrust LIKTD/KTT== 0.01

Torque LKQ/KQ = 0.02

Results

The test results expressed in nondimensional form as K

_TTD4fl2

pD4n,2 Q KQ = pD5n2

J K7..

7o

-are presented in Fig. 8 as functions of the advance ratio

Dn

for the four ducted propellers P1313 D4, P1314 D5, P1315 D6 and P1316 D7 designed according to the method described in Section 3. The results of the conventional propeller P1313 are also given.

A comparison between theory and experiment is also given in Figs. 9-12 and following table valid for the design value of KTT/J2.

It is interesting to note that the experimental values of duct thrust are larger than the theoretical values when the theoretical strength of the duct vortices is small. When this strength is increased above a certain value the conditions are reversed. This effect can possibly

be explained as follows:

When calculating the ducted propeller the ringvortex tubes rep-resenting the duct and the slipstream of the propeller are assumed to be cylindrical with constant diameter. In reality the ringvortices

Propeller Duct KTDIKTT

theory exp. theory exp. theory exp.

P1313

-

-

-

0.416 45.9

P1313 D4 0.01 0.11 0.412 0.414 49.1 47.7

P1314 D5 0.15 0.20 0.412 0.406 52.0 49.9

P1315 D6 0.30 0.29 0.412 0.422 55.2 52.9

0.3 P1313 Conventional propeller P1313 04 )

---

P13/4 05 j Ducted -- P13/5 06 _[ propellers P13/6, 07 J 0.4

\

08

Fig. 8. Results from open water tests.

IOKQ 06 0.5 0.4 03 0.2 QI

/

---C-Duct D7 Duct D6 Duct 05 Duct D4

fr0 Duct and propeller designed together

x Duct and propeller not designed together

I

-i

P1313 P1314 P1315 P1316

Propeller No.

Fig. 9. Thrust of the duct for the different ducted propellers.

should be placed on the real streamtubes. If the duct vortex strength is small a contraction of these streamtubes not considered in the design method occurs behind the propeller For a certam value of the duct vorticity this contraction can be neutralized and a better agree-ment between the assumed and the real vortex systems is obtained.

In the actual case this should occur at KrD/KTT 0.25 where as shown in the table above a good agreement between the theoretical and experimental values of KTD/KTT can be expected,

If the theoretical duct vorticity is mcreased too much the thffusor

a4

A'TD

,rTT

03

0.2 0.1

0

0.45 .1 0.40 0.35 Duct D7 Duct 06 Duct 05 Duct 04

o Duct and propeller designed together

x

Duct and propeller not designed together

I I I I

P1313 P1314 P1315 P1316

Propeller No.

Fig. 10. Advance ratio at the design value of K./J2.

angle of the trailing edge of the duct is so large that flow separation occurs and the duct thrust is decreased. Thus the flow visualization

studies described in Section 6 indicate a flow separation inside the rear part of the duct of ducteci propeller P1316 D7. In the actual investigation the maximum duct thrust obtained at the design value

of KTT/J2=l.63 is KTD/KTT=O.29.

The agreement between the experimental and theoretical advance ratio J is extremely good in all cases except P1316 P7 where as

men-tioned separation occurs, see Fig. 10.

The experimental values of efficiency are all lower than the theoretical values. Since is a function of duct thrust the difference is best studied in a diagram where i is plotted against KTDIKTT, see Fig. 12. As shown _ezpis 3-6% lower than theory The main reason for this is that the number of propeller blades when

calcula-ting the efficiency was assumed to be infinite.

To investigate the sensivity of the co-operation between duct

,,

C

Duct 07

Duct D6 Duct 05 Duct 04

o Duct and propeller designed together

Duct and propeller not designed together

P1313 P 1314 P1315 P1316

Propeller No.

Fig. 11. Efficiency of the different ducted propellers at the design value of KTT/J2.

with propellers originally designed for other ducts. The results are shown in Figs. 9-11 where duct thrust KTD/KTT, propeller efficiency

and advance ratio J valid for the design value of KTTIJ2 have been plotted against the different propellers tested.

In five cases of six a considerable decrease both in propeller

ef-ficiency and in duct thrust was recorded if the pitch ratio of the

propeller and the camber of the blade sections deviated from the design values. In one case was decreased from 53% to 46% (P1315 D6P1313 D6). Only for P1315 D5, where the pitch ratio was higher and the camber of the blades lower than the design values, a slight

increase in 'lo was observed.

0.60

0.55

0.50

Conventional propeller

0 Duct and propeller designed together

x Duct and propeller not designed together

0

g. 12. Ef iciency versus duct thrust for the ducted propellers at the design va1ue of KTTIJ2.

6. Flow Visualization Studies Teét Equipment

The fkw vivaliation studies were carried Out to clarify some of the questions posed by the thrust and torque measurements.

During the tests small air bubbles were forced mto the main flow through an inlet in the diffusor of the tunnel The air bubbles were illuminatd by a special light source which produced a narrow beam of light 'ciith the cross section 300 x 5 mm2 The hght source which

wasdesignedandmanufacturedbySvenska Flygmotor AB,

Troliliattan [4], was made up of a quarzhne lamp, mirrors, two

adjustable slits and a cylindripal. lens. The streampaths of the air bubbks rere recorded photographically To get maximum reflection from the bubbles an angle of about 1100 between the optical axis of the camera and the incoming light was chosen.

I

..

02 Q3

"To

055 0.50 Q.45 r

-x 00 x

xx

xx

INo

separation at

jDesi9n

Duct

07-Duct D5

DuctD4

exterior surface of duct

I

.1

Separation at exterior surface of duct

o_

I I I

P13/3 P1314 P1315 P1316

Propel/er

No.

Fig. 14. Limits for. separtidn at the exterior surface of the duct.

Results

The visualization method used was particularly suitable to discover flow separation at the exterior surface of the duct. This kind of separation was however observed only at propeller loads less than the design value, see Fig 13 The critical values of K/J2 are shown in

Fig 14 for all ducted propellers tested If the propeller load was decreased below the critical value the region Of separatIon was gradually increased No sudden changes in the flow were recorded

Separation which occured inside the duct was difficult to detect mainly due to the fact that the duct was untransparent. Behind the duct, however, a region of unsteady flow was observed This flow was made up of the normal unsteady flow induced by the propeller the boundary layer of the duct and possible separation. The thickness of thö usteady flow region at the trailing edge of the duct was about the same for ducted propeller P1313 D4, P1314 D5 and P1315 D6

o Duct and propeller

designed together

x Duct and propel/er not designed together

3

Krr

2

If, however, duct D5 and P6 were tested together with propellers with a pitch ratio lower and a camber of blade sections higher than

the design values a considerable increase in the thickness was observed,

see Fig. 15. There is much to indicate that the thickening of the unsteady flow region as well as corresponding decrease in efficiency, see Fig. 11, were caused by a separation inside the rear part of the duct or at the tips of the propeller blades.

Also for duct P7 a rather thick region of unsteady flow was observed

behind the duct. To make a more detailed examination possible the

narrow beam of light was in some tests directed obliquely into theduct

from behind. The resulting flow pictures for ducted propeller P1315 P6 and P1316 P7 are reproduced in Fig. 16. The pictures indicate a flow separation or a tremendous increase in the thickness of the boundary layer at the rear part of duct P7.

7. Incipient Cavitation Test Procedure

During the cavitation tests the cavitation number

pPD

0 = PVA2

and the uncorrected velocity of the water V4 were maintained cons-tant while the number of revolutions was varied. The uncorrected water velocity was in all tests VA = 3 rn/s. The cavitation number

was varied in the region

4c22.

The limits for the different types of cavitation were determined by visual means. Partly due to the observing method used and partly due to unknown factors such as the amount of air bubbles in the water, the location of the cavitation limits was somewhat uncer-tain. Thus, when repeating the cavitation tests with one of the ducted propellers after hail a year differences in inception cavitation of about

EiK TT/J 0.2 at the same cavitation number were obtained. A certain caution is therefore recommended when examining the result.

Results

The results of the incipient cavitation tests with the conventional propeller P1313 and the ducted propellers P1313 P4, P1314 P5,

20 15 10 5 0 p0..) No cavitation 5JGtic?bbIe 51de

.to°

GII Design/point F ;4./' ,,/_

1/

.-;

/

__..'

/,,!

/

/

/

/

/

/

o'

'---:

,d

., p'.

F--F .1 F-4. P1313 Cony, propeller P1313 04 '1 P1314 D5 I Ducted P1315 06 (propellers P1316 07 J 0 Q5 1.0 1.5 2.0 2.5' _KTTIJ2

Fig. 17. Incipient cavitation curves.

P1315 D6 and. P1316 D7 are presented in Fig. 17 where the curves for incipient cavitation are plotted in a K/J2_a_diagram. The

incipient of tip vortex cavitation and suction side bubble cavitation can also be studied in Figs. 18 and 19 respectively. In these figures also the results for other combinations of ducts and propellers are

given.

The propellers were designed to have a margin of 30% to suction side bubble cavitation at the design point K/J2= 1.63. Since the

design cavitation number was a= 16 this implies that theoretically the propellers should cavitate when a was lower than 11.2. As shown in Fig. 19 almost all propellers tested had a cavitation margin larger than 30%.

In the case of the conventional propeller the tip vortex cavitation had a helical form and was visible all the way from the blade tips

Tip vortex. covitatios rct 124

Duct 05 Duct b6 Duct 07 I I P1313 P1313 Cony propeller

J

No tip vortex cavitation

Conventional prope!/er

o Duct and propeller designed together

x Duct and propeller not designed together

-I-

I - I

P1314 P1315 P1316

Duc ted propellers

Fig. 18. Limits for incipient tip vortex cavitation at the design cavitation number.

to the tiltimate wake. For the ducted propellers on the other hand the tip rortex cavitation appeared only in the gap between the blade tips an4 the duct In no case this cavitation was observed behind the

duct, pobably due to the flow equalizing effect of the duct Both for the conventional propeller and the ducted propellers the tip vortex cavitation continuously changed into suction side sheet cavitaton for mcreasing values of KTT/J2

Pressire side cavitation was observed only on the conventional

propeller.

At 1ow cavitation numbers and high load coefficients

KTT 2.5

cavitation occured on the fore, part of the interior surface of ductD4

tested together with propeller P13 13. In no other case duct cavitation

was observed. 0

KDesign

--3 2: 2 0

20 0

Design a-'.

15

No suction side bubble cavitation

,O I

.#-..x-,.--Duct D4 I DuctD5 I ® DuctD6

Duct D70

Suction side bubble cavitation

I I

I

I Conventional propeller

o Duct and propeller designed together

x Duct and propeller not designed together

I I I

o_

i I

I

I I

P13/3 P1313 P1314 P1315 P1316

Cony

propeller Ducted propellers

Fig. 19. Limits for incipient suction side bubble cavitation at the design value of Krr/J2.

8. Conclusions

The experiments described were Carried out to get a verification of a

design method for ducted propellers developed at SSPA. Four heavily loaded ducted propellers were designed to have the same total thrust while the thrust of the duct was varied systematically.

As long as no flow separation occured the agreement between the theoretical and experimental values of total thrust at the design advance ratio was extremely good. The duct thrust was found to be slightly too large for small duct vorticity while the opposite condition

-,-I1 0/₁₀

cavitation margin

was valid when the theoretical vorticity of the duct was large. The efficiency of the ducted propellers was somewhat lower than that predicted by the theory. Incipient cavitation tests showed that the cavitation qualities were comparable with those for a conventional

propeller.

Hence the design method seems to function satisfactorily under the conditions tested as long as no separation phenomena occur.

The efficiency of the ducted propeller is a function of the thrust of the duct. If the vorticity of the duct which determines this thrust is increased too much, however, the diffusor angle at the rear part of the duct internal surface becomes so large that the flow separates and the efficiency decreases. For a given total thrust, therefore, there exists a certain duct vorticity which gives maximum values of duct thrust and propeller efficiency. Factors which may influence the maximum duct thrust Obtainable are

the total load coefficient KTTIJ2,

the vortex distribution of the duct, the length of the duct and

the distribution of propeller blade circulation.

The results of the experiments also indicated that the co-operation between duct and propeller was critical. Hence, if a duct was tested together with prOpellers originally designed for other ducts, generally lower efficiencies were recorded probably due to flow separation inside the duct. To obtain a good result, therefore, the duct and the propeller must fit each other not only geometri6ally but also hydro-dynamically. The last requirement is probably the most important.

9. Acknowledgement

The author wishes to express his gratitude to the H u g o H a

m-mar Foundation for Maritime Research, the

Hugo Hammar Foundation for International

Maritime Research and the Martina Lundgren

Foundation for Maritime Research for sponsoring

the present investigation.

The author also wishes to thank Dr. HANS EDSTEAND, Director

General of the Swedish State Shipbuilding

Ex-e r i m Ex-e n t a 1

T a n k for the opportunity to carry out the

Dxcs, G.: 'A Method for the Design of Ducted Propellers in a Uniform Flow". Pubi. No. 62 of the Swedish State Shipb. Exp. Tank, Goteborg, 1967.

LnWGRESt, H.: "The Cavitation Laboratory of the Swedish State Shipbuilding Eperixnental Tank", Pubi. No. 43 of the Swedish State Shipb. Exp. Tank,

Goteborg, 1958.

Gitraar, H.: "Wind-Tunnel Interference on Wings, Bodies and Air Screws". A.B.C. R.M. 1566, 1933.

Lonnnoxie, 0., R&w, J.: "Vattentunnel for aerodynamsins forsOk". Teknik

Summary 3

1. Introduction . . . 4

2. List of Symbo1s .

...

5

3. Design Method 6

4. ,Ducted Propellers Investigated .

...

8

5. Thiiis1 and Torque Measurements 13

6. Flow Visualization Studies . .

...

20

7. Incipient Cavitation 22

8. ConcMsions 25

9. Acknowledgement 26