Proceedings of the Propeller Symposium Lips, International Shipbuilding Progress, February and March 1971

ARCHIE

S H

SHIPBUILDI MARI ENGINEER!

MONTHLY

CONTENTS

PREFACE

by J. D. van Manen

INVESTIGATIONS ON DIFFERENT PROPELLER TYPES by M.W. C. Oosterveld

CAVITATION EROSION OF A SHIP MODEL PROPELLER by J.H. J. van der Meulen

THE MANUFACTURE OF BRONZE PROPELLERS FROM A METALLURGICAL POINT OF VIEW

by L. Bosman and J. Haanstra

PRINCIPLES OF MECHAN1SMSUSED IN CONTROLLABLE PITCH PROPELLERS

by J. Wind

PROPELLER PRODUCTION CONCEPTIONS by L. A. van Gunsteren and A. F. van Hall

PROFILE CHARACTERISTICS IN CAVITATING AND NON-CAVITATING FLOWS

by P. van Oossanen

SOME REMARKS ON LIFTING SURFACE THEORY by G. Kuiper

Formal contribution to the discussion by J. Forrest

PROPELLER SYMPOSIUM

at

_urni

P1971-1

t433221

OarReprinted from February and March 1971

PROPELLER SYMPOSIUM

Drunen - Holland

Published by

INTERNATIONAL PERIODICAL PRESS, Heemraadssingel 194, Rotterdam, Holland.

PAGE PREFACE

by J. D. van Manen 3

INVESTIGATIONS ON DIFFERENT PROPELLER TYPES

by M.W. C. Oosterveld 5

CAVITATION EROSION OF A SHIP MODEL PROPELLER

by J.H. J. van der Meulen 29

THE MANUFACTURE OF BRONZE PROPELLERS FROM A METALLURGICAL POINT OF VIEW

by L. Bosman and J. Haanstra 40

PRINCIPLES OF MECHANISMS USED IN CONTROLLABLE PITCH PROPELLERS

by J. Wind 53

PROPELLER PRODUCTION CONCEPTIONS

by L. A. van Gunsteren and A. F. van Hall 68

PROFILE CHARACTERLSTICS IN CAVITATING AND NON-CAVITATING FLOWS

by P. van Oossanen 86

SOME REMARKS ON LIFTING SURFACE THEORY

by G. Kuiper 102

For many years now Lips' Propeller Works

have been showing us how the right combination of design techniques and manufacturing methods can lead to a high quality product.

This attitude is in principle the basis on which the idea of organizing the first Lips' Propeller

Symposium came into being, leading to a programme such as that scheduled for the 20th and 21st May 1970.

A symposium programme that is well balanced

in its theoretical, physical, metallurgical and

production conceptions.

Moreover, the programme gives evidence of the fruitful cooperation between the Netherlands

Ship Model Basin as

an industrial service

laboratory, and Lips as a research-minded pro-peller manufacturer.

The rigorous changes in ship dimensions, speeds, requiredpower and special purpose ship types have also put pressure on the research at present being done in ship propulsion. In many cases quick and reliable answers must be given to complicated questions concerning our advanced designs.

Even small errors or simplifications can lead to serious economic penalties for large ships which represent enormous investments.

The specialist in ship propulsion is nowadays

confronted with the selection of a propeller

arrangement which must meet high demands with regard to efficiency, avoidance of cavitation and vibration, stopping ability, manoeuvring, all of

which form part of the total propulsion plant,

economics and reliability.

Seen against the background of these facts, the

fast growth in application of the

controllable-pitch propeller is not astonishing. Twin-screw and overlapping propeller arrangements are

competing against the conventional single-screw

propeller as never before in the field of

high-powered merchant ships. The time is coming when ducted and contra-rotating propellers will .) Managing director, Netherlands Ship Model Basin, Wageningen, The Netherlands.

PREFACE

by J. D. van Manen1

find application in large seagoing vessels. In

order to obtain better data on which to base the selection of the propeller type, the N. S. M. B. decided to build a large vacuum towing tank.

For special purpose, small, high-speed boats

the screw propeller, either supercavitating or

partially submerged, must defend its advantages against the special properties of water jets and air propulsion.

The rapidly increasing number of programmes for tackling propulsion problems on computers is very important for the rate of progress in our knowledge.

The systematic propeller design charts have recently been corrected for Reynolds' number effect.

The optimum diameter from the viewpoint of efficiency showed a noticeable increase. It becomes necessary to optimize the diameter not only on grounds of efficiency,

but also on

economic criteria.

The propeller designer is daily confronted with new developments such as these.

The need to obtain good solutions often calls for cooperation between various specialists: the ship and the propeller designer, the specialists in propulsion plants, in vibrations, in

manoeuvring, the hydrodynamicist and the experts in the propeller factory.

The aim of this symposium is to underline the importance of manufacturing the propeller within the tolerances required by our theoretical considerations and in harmony with our advanced production methods.

We in Holland are happy that in both fields, groups of specialists have grown up under the guidance of such well-known teachers as Troost and Van Lammeren.

May this symposium, with its introductions by

Dutch scientists and contributions to the

dis-cussion from our colleagues from abroad, be a

link in our attemps to build up a better

under-standing in the theoretical and technological field of ship propulsion.

INVESTIGATIONS ON DIFFERENT PROPELLER TYPES

lintroduction.

During recent years,

the formulation of

improved propeller design procedures have

become possible due to the availability of high-speed digital computers. Much more adequate

mathematical models to represent the

hydro-dynamic action of a marine propeller as well as

of the action of ducted propellers and

contra-rotating propellers can be used nowadays.

Recently, a discussion of the available screw

propeller theories and computional procedures was given by Cox and Morgan [1]. A general review of the r ecent theoretical studies on ducted

propellers has been given by Weissinger and

Maass [2]. A state of the art report with respect to propulsion by contra-rotating propellers was given by Hadler [3].

Although improved theoretical design pro-cedures have become available, for preliminary design studies the results of tests with systematic

series of screw propellers, with systematic

series of screw propellers in nozzles or with

systematic series of contra -rotating propellers .) Assistant managing director, Netherlands Ship Model Basin, Wa-geningen, The Netherlands.

by M.W.C. Ooster veld')

Summary.

This paper presents the results of open-water tests with different propeller types (the Wageningen B-screw series, ducted propeller series with nozzles of both the flow accelerating and decelerating type and contra-rotating propeller series). A discussion of the fairing of the results of such tests by means ola regression analysis is given. For systematic screw series, for instance, the thrust and torque will in future be given in the form of polynomials of the advance coefficient, pitch ratio, blade- area ratio and number of blades. The effect of the Reynolds number (scale effect) will also be taken into account in these polynomials. For the ducted propeller series andthe contra-rotating pro-peller series the thrust and torque will be given in the form of polynomials of the advance coefficient and pitch ratio.

The derived polynomials enable design calculations and analysis to be done with a computer in an easy way.

Finally some special applications of ducted propellers and contra-rotating propellers are discussed. In the case of ducted propellers attention is paid to nonaxisymmetrical nozzle shapes which may be attractive for minimizing problems relating to propeller induced vibrations and cavitation in single-screw ships (tankers) and twin-single-screw ships (fast naval ships). Finally, the specific field of application of contra-rotating propellers and of the overlapping twin-screw stern arrangement is discussed.

are very helpful. A systematic series of screws is formedby a number of screw models of which

only the pitch ratio P/D is varied. All other characteristic screw dimensions, such as

dia-meter D, number of blades Z, blade-area ratio AE/Ao' blade outline, shape of blade sections, blade thickness, and hub-diameter ratio d/D are the same. The drawback of the systematic screw

series is, of course, that the propeller must be

constrained to a specific geometry. This geometry may be unsatisfactory for reasons of

cavitation and propeller induced vibration,

particularly for propellers which operate in a

wake.

However, for preliminary design studies the

results of tests with systematic screw series,

ducted propeller series and contra-rotating pro-peller series are of importance. Furthermore it

is attractive to have the results of open-water

tests with systematic propeller series in such a way available that design calculations and analysis can be performed with a computer. In the following, the results of a fairing of

6

analysis will be discussed. The characteristics of the propeller series will be expressed in the form of polynomials which enable design calcula-tions and analysis in an easy way.

The polynomials and the values of the

cor-responding coefficients will be given of some

series of the Wageningen B-screw series, of

ducted propellers with both nozzles of the flow accelerating- and decelerating type anda contra-rotating propeller series.

A comparison between the different propeller types will be made and some special applications of marine propellers will be discussed.

2. Open-water tests.

2.1. Tests procedure.

The open-water tests with the B -screw series,

the ducted propellers and the contra-rotating

pr opellers were carried out with the apparatus as

shown in Figure 1. The immersionof the

pro-peller shaft was equal to the screw diameter. Before the tests were carried out, the system

friction and the dummy hub torque and thrust were determined so that the measured propeller thrust and torque could be corrected accordingly. The usual routine of open-water tests was followed; the rpm of the screw (or screws in the case of the contra-rotating propellers) was kept constantand by varying the speed of advance the desired value of the advance coefficient J was obtained. Usually the rpmwas chosen as high as possible toobtain

RPM

dynamometer

(impeller thrust and torque)

a high Reynolds number. The rpm was chosen in accordance with the maximum speed of the towing carriage and the capacity of the dynamometer(s)

used for the thrust and torque measurements.

Most of the open-water tests were made at 450 rpm.

2.2. Analysis of test results.

Usually the open-water test results of a series of screws are plotted in the conventional way with the coefficients;

KT =

pn2 D4

K

-pn2 D5

as functions of the advance coefficient J = VA/n D. Here T and Q denote the propeller thrust and torque. in the case of the ducted propeller T

denotes the total thrust of the system while the thrust of impeller and nozzle are denoted by Tn and Tp respectively. In the case of the contra-rotating propellers the thrust T and torque Q are based on the thrusts and torques respectively of

the forward and aft screw.

The diameter D

Dynamometer (nozzle thrust)

denotes the tip diameter of the screw (conven-tional screw), of the impeller (ducted propeller)

or of the forward screw of a set of contra-rotating propellers.

The fairing of the open-water test results is

performed with the aid of a CDC 3300 computer by means of regression analysis. The thrust and torque coefficients KT and K were expressed as polynomials of the advance coefficient J and the pitch ratio P/D: KT =Ao, o + Ao, 6 J6 + +

A(P/D)6

+ _{+A 6,6(P/D)6}J6 6,o K =B 0,0 + B (P/D)6 J6 6,6

In the case of the ducted propeller the thrust

coefficient KTn

was expressed as:

KTn =C0,0

+ C6, 6(P/D)6

6

J

With the aid of the regression analysis the

significant terms of the polynomials and the values of the corresponding coefficients were

determined.

2.3. Wageningen B-serew series.

At present, about 120 screw propeller models

of the B-series type have been tested at the

Netherlands Ship Model Basin. Screws of the

B-series type are usually applied behind normal

Table 1

Summary of the Wageningen B-screw series.

ships. (see Ref. [4], [5], and [6]). The B-series screws have relatively wide blade tips, circular

-back blade sections near the tip and airfoil

sections near the hub. Table 1 gives a summary of the tested series.

In general, the results of the tests were given in the form of K and K coefficients expressed

as a function of the advance coefficient J for analytical work, and in the form of B 6 and

Bu-6 diagrams for design purposes.

From a correlation between the available

dia-grams of the B-series

it appears that small

differences exist. However, during the last years the B -series have been extended considerably and a cross -fairing of the B-screw series diagrams for different blade-area ratios and for different numbers of blades must now be possible. Recently we have started the fairing of the B-screw series test results by means of the regression analysis as mentioned above. As a result of this analysis, the thrust and torque coefficients

KT and_KQ will

be expressed as polynomials of not only the

advance ratio J and the pitch ratio P/D but also of the blade-area ratio

AE/Aoand the number of blades Z.

In addition, the effect of the Reynolds number on the test results was taken into account by using

a method derived by Lerbs [7] from similar

methods used for the calculating of the perform-ance characteristics of airscrews from the characteristics of equivalent blade sections. This method has also been followed by Lindgren[8], Lindgren and Bjärme[9] and Newton and Rader [10]. The effect of the Reynolds number may be taken into account in the polynomials as well. Recently. the progress made in the cross-fairing of the diagrams of the B-screw series was given by Van Lammeren et al [6]. The results given

Blade number Z Blade area ratio A /A E o 2 0.30 3 0.35 0.50 0.65 0.80 4 0.40 0.55 0.70 0.85 1.00 5 0.45 0.60 0.75 1.05 6 0.50 0.65 0.80 7 0.55 0.70 0.85

8

MOM. ME=

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4-70 KT = Ax,y, z[AE/Ao]x[P/D]Y[J]z KQ = Bx,y, z[A E/Ao]x[P/D]Y[J]z

in that paper are preliminary becauseonly the

results of the cross-fairing of the 4 andthe 5 bladed-screw series to blade-area ratio are given. The blade number Z and the Reynolds number were at that moment not taken into account in the polynomials. This work is now at hand.

Some of the preliminary results are given here.

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Form of polynominal and coefficients of four -bladed B-screw series.

11 12

Figure 2. Open-water test results of B 4-70 screw series extra polated to Re075R =106.

The results of the 4-bladed B -screw series extra-polated and expressed in polynomial form are given in Table 2. In these polynomials, either KT or K was the dependent variable with the advance coefficient J, the pitch ratio P/D and the blade-area ratio AE/Ao as the independent

vari-ables. The form of these series together with

their coefficients are given in Table 2.

Also, the results of the analysis can be given in graphical form. With the aid of a tape controll -ed drawing machine the coefficients KT. KQ and nowere drawn in the conventional way as function

of J. The diagram of the B 4-70 screw series,

for a Reynolds number based on the chord length of the screw blades at O. 75 R of Re0.75R= 1. 0*106,

is given in Figure 2.

2.4. Ducted propellers.

A ducted propeller consists of acombination of

an annular airfoil and an impeller, acting as a propulsion unit. A schematic view of a ducted propeller is given in Figure 3.

The axial force acting on the impeller of a

Ax,y,z x Y z -.719975 = -2 0 0 0 -.790916 = - 1 1 o 0 -.179541= 0 0 o 1 -.625748 = - 1 1 o 1 -.311639= 0 0 0 2 +143160= 0 2 0 3 +.53l326= 0 0 1 0 -.114389= 0 1 1 1 +625376= -1 0 1 1 -+.125537 = 0 0 1 3 - .523821 = - 1 1 1 3 - .207108 = 0 0 2 0 - .270781 = 0 1 2 0 -.134182 = 0 o 2 1 -.121086= 0 1 2 1 -.189164= -1 3 2 1 -.439535 = - 1 3 2 2 -.624937 = - 1 0 2 3 -.496939 = -2 2 6 0 +115986= -1 2 6 1 Bx,y.z x Y z +.964375 = -2 0 0 0 -.104103 = -1 1 0 0 +.512431 = -2 / 0 0 +109936= -1 3 o o -.453419 = - 2 0 0 1 +216078= -1 1 0 1 -.507337 = - 1 0 0 2 +377970= -1 i 0 2 -.549486 = -1 3 0 3 -.507319 = -1 2 I 0 +368649= -1 0 1 1 -.106520 = -1 I 1 1 +.465315 = -1 3 1 2 +883010= -1 2 1 3 +.112619 = - 1 0 2 0 +.104825 = 0 1 2 o -.449154= -1 1 2 1 +378780= -1 2 2 1 +177304 = -I 0 2 / -.164687= -1 1 2 2 -.344328 = - 1 1_{- 2 2} - .249132 = - 1 3 2 2 -.233007 = - 1 1 2 3 -.120209 = -2 0 6 0 -.118997 = -2 3 6 0 + .458094 = -2 I 6 I CV el Do a. 07, DI a. 1I7

_.\7%,

,,,szsulea-

1,'\ 1

-Nat:

Figure 3. Ducted propeller.

ducted propeller usually differs from the net

thrust of the system. A positive or negative force may act on the nozzle depending on the nozzle

shape and the operation condition. Due to the

nozzle action the velocity at the impeller plane can be either less than or greater than the velocity at the propeller plane of a conventional screw with the same diameter and speed of advance.

The ducted propeller with the accelerating flow type nozzle is now used extensively in cases

where the ship screw is heavily loaded or where the screw is limited in diameter. The acceleratingnozzle offers a means of increasing the efficiency of heavily loaded propellers. The nozzle itself produces a positive thrust.

In the case of the decelerating flow type nozzle, the nozzle is used to increase the static pressure at the impeller. This ducted propeller system is the so called pumpjet. The duct will produce a negative thrust. This nozzle may be used if retardation of propeller cavitation is desired. For naval ships a reduction in noise level can be obtained which may be of importance for tactical reasons.

During the past 15 years extensive

investiga-VA

NOZZLE No19A

Figure 4. Particulars of nozzle no. 19A.

Figure 5. Particulars of Ka-screw series.

tions on ducted propellers were performed at the Netherlands Ship Model Basin. These investiga-tions dealed with both accelerating nozzles (Van Manen [11]), and decelerating nozzles (Oosterveld [12]).

The investigations on accelerating nozzles have

led to the development of a standard nozzle,

(nozzle no. 19A) applied by the NSMB in the case of heavy screw loads. For use in this nozzle, the Ka-screw series were specially designed. These screws have wide blade tips , uniform pitch and flat face sections. Experimental investigations show-ed that with regard to efficiency and cavitation this impeller type is just as good as those calculated according to vortex theory. Besides, they have reasonable stopping abilities.

The particulars of nozzle no. 19A and of the screw models of the Ka-screw series are given in Figure 4 and in Table 3 and Figure 5

respect-ively. The screws were located in the nozzle

with a uniform tip clearance of 1 mm (about 0.4 percent of the screw diameter D).

The fairing of the open-water test results of successively the Ka 3-65; Ka 4-70, Ka 5-75 and Ka 4-55 screw series with nozzle no. 19A was

Table 3

Particulars of KA-screw series.

Dimensions of the Ka-screw series

Table of the ordinates of the Ka-screw series,

Distance of the ordinates from the maximum thickness.

Note: The percentages of the ordinates relate to the maximum thickness of the corresponding section.

3

r/R 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Length of the blade sections in percentages

from centre line to trailing edge 30.21 36.17 41.45 45.99 49.87 52.93 55.04 56.33 56.44

Length of blade section of the maximum length

of the blade section at 0.6R

from centre line to leading edge 36.94 40.42 43.74 47.02 50.13 52.93 55.04 56.33 56.44 at 0.6R =

= 1.969.1/Z. A /A

E o

total length 67.15 76.59 85.19 93.01 100.00 105.86 110.08 112.66 112.88

_

Max. blade thickness in percentages of the diameter 4.00 3.52 3.00 2.45 1.90 1.38 0.92 0.61 0.50 Maximum t h i ckness at

centre of shaft = 0.049 D Distance of maximum thickness from leading

edge in percentages of the length of thesections 34.98 39.76 46.02 49.13 49.98

-

-

-From maximum thickness to trailing edge From maximum thickness to leading edge

OR 100% 80% 60% 40% 20% 20% 40% 60% 80% 90% 95% 100%

Ordinates for the back

0.2 38.23 63.65 82.40 95.00 07.92 90.83 77.19 55.00 38.75 27.40

-0.3 39.05 66.63 84.14 95.86 97.63 90.06 75.62 53.02 37.87 27.57 0.4 40.56 66.94 85.69 96.25 97.22 88.89 73.61 50.00 34.72 25.83 0.5 41.77 68.59 86.42 96.60 96.77 87.10 70.46 45.84 30.22 22.24

-0.6 43.58 68.26 85.89 96.47 96.47 85.89 68.26 43.58 28.59 20.44 0.7 45.31 69.24 86.33 96.58 96.58 86.33 69.24 45.31 30.79 22.88 0.8 48.16 70.84 87.04 96.76 96.76 87.04 70.84 48.16 34.39 26.90

-0.9 51.75 72.94 88.09 97.17 97.17 88.09 72.94 51.75 38.87 31.87

-1.0 52.00 73.00 88.00 97.00 97.00 88.00 73.00 52.00 39.25 32.31

Ordinates for the face

0.2 20.71 7.29 1.77 0.1

-

0.21 1.46 4.37 10.52 16.04 20.62 33.33 0.3 0.4 13.85 9.17 4.67 2.36 1.07 0.56 1 0.12 .-0.83 0.42 2.72 1.39 6.15 2.92 8.28 3.89 10.30 4.44 21.18 13.47 0.5 6.62 0.68 0.17

-

0.17 0.51 1.02 1.36 1.53 7.81

performed by means of the regression analysis. From this analysis it was found that most of the terms with high powers of J and P/D were insignificant.

The form of

the polynomials together with the coefficients are given in Table 4.

In addition, with the aid of a tape controlled

drawing machine the coefficients K , K , K

T _Tn Q

ando were

drawn in the conventional way as

function of J. The diagrams of the Ka 3-65,

Ka 4-70, Ka 5-75 and Ka 4-55 screw series in combinationwith nozzle no. 19A are given in the Figures 6 through 9.

The design of the decelerating nozzles with

which open-water tests were carried out was

based on the vortex theory. Ducted propellers with systematically varied negative loadings of the nozzle at the design condition were tested. The particulars of one of these nozzles (nozzle no. 33) and of the screw series specially

design-Table 4

Form of polynomial and coefficients of Ka 3-65; Ka 4-70; Ka 5-75 and Ka 4-55 screw series in nozzle no. 19 A.

Ka 3-65 Ka 4-55 Ka 4-70 Ka 5-75

y Axy Bxy (x!, Axy Bxy C., xy Axy 13, Cxy Axy rixy Cxy

0 0 +0.028100 +0.006260 +0.54000 - 0.375000 - 0.034700 -0.045100 +0.030550 +0.006735'+0.076594 +0.033000 .+0.007210 - 0.000813 0 1 -0.143910 +0.115560 -0.203050 +0.018568 _-0.148687 +0.075223 -0.153463 _+0.034885 0 2 -0.017942 -0.123761 +0.830306 -0.016306 -0.061881 -0.014670 0 3 -0.383783 -2.746930 -0.663741 -0.391137 -0.138094 -0.398491 -'0.276187 0 4 - 0.008089 -0.195582 -0.244626 - 0.1107244 -0.006398 0 5 -0.741240 +0.317452 -0.370620 0 6 +0.646894 +0.067548 - 0.093739 +0.323447 1 0 -0.542674 +2.030070 +0.158951 +0.244461 -0.271337 1 1 - 0.429709 - 0.749643 -0.392301 -0.048433 - 0.578464 - 0.432612 - 0.687921 - 0.435515 - 0.626198 2 -0.016644 -0.611743 +1.116820 -0.024012 +0.225189 -0.031380 +0.450379 1 3 +4.319840 +0.024157 +0.751953 1 4 -0.341290 1 5 -0.123376 1 6 -0.162202 -0.089165 -0.081101 0 +0.671268 +0.972388 -3.031670 - 0.212253 +0.667657 +0.666028 +0.664045 +0.359718 2 1 -0.146178 2 +0.286926 +1.468570 -0.917516 +0.005193 +0.734285 +0.283225 +0.010386 2 3 - 2.007860 2 4 2 5 2 6 3 0 - 0.182294 +0.040041 -0.317644 +2.836970 +0.156133 +0.068186 -0.172529 +0.046605 - 0.202467 -0,162764 +0.053169 - 0.087289 3 1 +0.17404! 3 2 -1.084980 +0.102331 -0.542490 3 3 +0.391304 3 4 3 5 3 6 - 0.032298 - 0.016149 4 0 -0.994962 -0.007366 -0.014731 4 1 +0.030740 4 2 +_0.073587 4 3 +0.199637 +0.099819 4 4 4 5 4 6 5 0 -0,031826 5 1 +0.060168 +0.015742 - 0.014568 +_0.030084 5 2 _-0.109363 5 3 5 4 +0.043862 5 5 5 6 6 (1 - (1.003460 +0.043782 +0.007947 - 0.008581 - 0.001730 6 1 -0.017378 - 0.000674 - 0.017293 - 0.000337 _{- 0.017208} 6 2 +0.001721 +0.038275 +0,000861 -0.001876 -0.00375! 6 3 6 4 -0.02197! 6 5 6 6 +0.000700 0 7 +0.022850 +0.088319

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Figure 6. Open-water test results of Ka 3-65 screw series in nozzle no. 19A.

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Figure 7. Open-water test results of Ka 4-70 screw series in nozzle no. 19A.

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Figure 9. Open-water test results of Ka 4-55 screw series in nozzle no. 19A.

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11111=1111111111111111111MINIMIMIIIIII

-,4 OS 07 OS as al -112 o al 2 03 OG 05 06 07 08 09 10

14

ed for use in this nozzle (the Kd 5-100 screw series) are given in Figure 10 and Figure 11

respectively. The fairing of the open-water test results was ag,ain performed by means of the

regression analysis. The coefficients of the

sig,nificant terms of the polynomials are given in

Table 5. The diagram of the Kd 5-100 screw

series in combinationwith nozzle no. 33 is given in Figure 12.

Table 5.

Form of polynomial and coefficients of Kd 5-100 screw series in nozzle no. 33.

Jr0010.41%27/JP41:1"

111

411111111111

-larie4or

Ar../

Figure 10. Particulars of nozzle no. 33.

Detail bladei Pitch di stri b _W. mins

wiNrow---mom nimr.i-

I- 1 IMINIIMIIIMIPM11111 IIIIIIIMIUMENIMIIIIM.1.1.1, Screw no3930 MIME WIPE PRIN PIMPS PIMPS

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.

11111111=111PWIIITIM It no.3932 ammoaituAwavo 11111=1111MVARRIMIIIMTM MIIIIMINIEROMMANW thickness prssure side 0° I back side .5°12' Particulars All screw: D -240 rnrn 7 -5 qb- al57 4%. 1.a

Screw no.3930 Ph0.10 let 07 R /

na393I -t2

no 3937 -16

no.3933 ..-16

no 3934 - -03

Kd 5-100 series in nozzle no. 33

Y Axy Bxy Cxy

0 0 0 -0.347562 -0.0077894 +0.083142 1 0 1 -0.321224 -0.0224240 -0.332286 2 0 2 +0.075277 +0.305926 3 0 3 -0.0090870 -0.1132106 4 0 4 -0.009560 5 0 5 6 0 6 -0.013948 7 1 0 +0.963261 8 1 1 -0.215803 9 1 2 -0.0104923 -0.349298 10 1 3 11 I 4 12 1 5 13 1 6 -0.000031 14 2 0 +0.0824632 15 2 I 16 2 2 +0.0261933 17 2 3 -0.0095845 +0.038469 18 2 4 19 2 5 +0.0010293 20 2 6 21 3 0 +0.119965 22 3 1 -0.0076923 23 3 2 +0.013401 24 3 3 25 3 4 26 3 5 27 3 6 -0.0000935 28 4 0 -0.016882 -0.0031955 -0.043816 29 4 1 30 4 2 31 4 3 32 4 4 -0.0001172 33 4 5 34 4 6 35 5 0 36 5 I +0.001752 37 5 2 38 5 3 39 5 4 40 5 5 41 5 6 42 6 0 43 6 1 44 6 _ ' 45 6 3 +0.0001523 46 6 4 47 6 5 48 6 6 -0,000028 49 0 - +0.003691 no3933 Noma N. worm-AN INI=11111 41 111111=1111011 . 11111EIMIZIIMINIS%1MW 1111111=11111WIMMINIEF MINIMA WNW . WIRY

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2.5. Contra-rotating propellers.

According to the lifting line theory, as described in[13], a systematic series of contra-rotating propellers, consisting of a four bladed forward propeller and a five bladed aft propeller, , was designed. A problem which may occur on contra-rotating propellers is that the cavitating tip vortices generated by the blades of the forward propeller may impinge on the blades of the aft propeller and cause damage there. This problem was avoided by reducing the diameter of the aft propeller. This reduction was based on the ex-pected slipstream contraction at design condition. The contra-rotating propeller sets were designed in such a way that one set is representative for tanker application (B 45) and another set for cargo liner application (B 15). Three additional sets complete the systematic series. The

particulars of the screw models of the

contra-rotating propeller series are given in Table 6 and Figure 13.

Tests were carried out in the towing tank to

determine the open-water characteristics of the

Figure 12. Open-water test results of Kd 5-100 screw series in nozzle no. 33.

series. The fairing of the open-water test results was performed with the regression analysis; the coefficients of the significant terms of the poly-nomials are given in Table 7. The diagram of the

contrarotating propeller series is given in Figure 14. In addition, the aft propeller

thrust-total thrust ratio Taft/T and the aft propeller torque-total torque ratio Qaft/Q are presented

in Figure 14.

3. General discussion of open-water test results.

The results of the open-water tests with the different propeller type series were expressed

in polynomials. In these polynomials, either K .

KTn

or K were the dependent variables with the advance coefficient J, the pitch ratio P/D (and

the blade-area ratio _{AE/Ao) as the independent}

variables. The form of these series together with their coefficients for the 4-bladed B-screw

series, the accelerating and decelerating ducted

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22 26 620 04

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1.0R Pitch distribution in percent 1

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Figure 13. Particulars of contra-rotating propellerseries.

AIIIIIMMINIi.

99.1

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ig

1 0.6R ..

r

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Table 6

Particulars of contra- rotating propeller series.

Figure 14. Open-water test results of contra-rotating propeller series.

propeller series and the contra-rotating

pro-peller series are given in the Tables 2, 4, 5 and 7 respectively. These results can be used direct-ly for solving problems which arise when design-ing and analyzdesign-ing screw propellers if a computer available.

The results of the analysis were also given in graphical form. With the aid of a tape-controlled drawing machine the coefficients K

T'. KQ and no

B = 33. 07 K /J2 = /V %

A

where,

N = number of revolutions per minute P = power in hp

VA = speed of advance in knots.

In the usual diagram, the design coefficient Bp is the base and a new speed ratio 5 is used. This speed ratio is defined as

= N D/VA = 101.27/J

SET 1 2 3 4 5

Forward Aft Forward Aft Forward Aft Forward Aft Forward Aft Diameter D (mm) 210. 179.34 208. 182.72 210. 191.01 217.50 203.33 210. 198.90

Number of blades 4 5 4 5 4 5 4 5 4 5

Pitch ratio at 0.7 R 0.627 0.957 0.779 1.034 0.931 1.110 1.083 1.196 1.235 1.306

Expanded blade area ratio 0.432 0.507 0.432 0.515 0.432 0.523 0.432 0.531 0.432 0.539

Daft/D forward 0.854 0.878 0.910 0.935 0.947 ,..

MI

MOM

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, 6 Q4

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-

J ThruStatt Thrust t to Torque aft torque10 05 di ,., f

are drawn as a function ofJ for the different

pro-peller types in Figures 2, 6 through 9, 12 and 14. By interpolating in the

KT-KQ-J diagram of

a propeller series most problems which arise

when designing or analyzing screw propellers can be solved. For design purpose various types of

1.5

more practical diagrams can be derived from the

KT -KQ-J diagram.

The most widely encountered design problem is that where the speed of advance of the screw VA' the power to be absorbed by the screw P,

o and the number of revolutions n are given. The

diameter D is to be chosen such that the greatest efficiency can be obtained. The problem of the optimum diameter can be solved in an easy way by plotting

no and J as a function of

1/2 %5,

-/2

K :

: nP

/v

A

The Taylor variable B is related to this

dimensionless variable by the equation:

0 02 04 06 08 ID

10Ka

18

in which

D = screw diameter in feet.

The B -5 diagrams of the different propeller types discussed before are given in the Figures

15 through 21.

Table 7.

Form of polynomial and coefficients of contra-rotating propeller series.

In cases where VA T andN or VA' T and D are given, the problem of determining the

optimum diameter or the optimum number of

revolutions can be solved by plotting

no and J as functions of

KT/J4 and KT/J2

As a comparison, the curves for optimum dia-meter (on a base of B and KT/J4) and optimum

rpm (on a base of KT/J4) of the B 4-70 screw

series, the Ka 4-70 screw series in nozzle no.

19A, the Kd 5-100 screw series in nozzle no. 33 and the contra-rotating propeller series are given

in Figures 22,

23 and 24 respectively. The

results with the different Ka-screw series in

combination with nozzle no. 19A are given in Figures 25, 26 and 27.

The lightly loaded screws of fast ships are on

the left side of the diagrams while the heavily

loaded propellers of towing vessels are on the right. Typical B , values for different ship types are indicated in Table 8.

If we consider Figure 22, it can be seen that at low B -values the open-water efficiency of both

the accelerating and the decelerating nozzle decrease with respect to the efficiency of the B 4 -7 0 screw series. This fact can be explained by the relative increase of the frictional andthe

induced drag of the nozzle. The curves of the diameter coefficient S of the accelerating and

the decelerating nozzle almost coincide; the B4-70 screw series has a larger optimum screw diameter. It is interesting to note that the curves of a diameter coefficient based on themaximum diameter of the system of both the accelerating andthe decelerating nozzle and the B 4-70 screw series almost coincide.

The accelerating nozzle (nozzle no. 19A), if

compared with a conventional screw propeller (B4-70 screw series) gives rise to an improve-ment in open-water efficiency n in the case of

o

heavy screw loads. The decelerating nozzle has a low open-water efficiency.

In the case of heavy screw loads (all types of towing vessels) the attractiveness with regard to propulsive efficiency of the accelerating nozzle CRP series x y Axy Bxy 0 0 0 -0.474334 +0.179448 1 0 1 +1.298290 2 0 2 -0.134774 +0.010267 3 0 3 -0.021349 4 0 4 5 0 5 6 0 6 7 1 0 +0.972350 -0.504458 8 1 I -3.721950 9 1 2 10 1 3 11 1 4 12 1 5 13 1 6 14 2 0 +0.153730 +0.426338 15 2 1 +2.010370 -0.069286 16 2 2 17 2 3 18 2 4 19 2 5 20 2 6 21 3 0 22 3 1 23 3 2 24 3 3 25 3 4 26 3 5 27 3 6 28 4 0 29 4 1 30 4 2 31 4 3 32 4 4 33 4 5 34 4 6 35 5 0 36 5 1 37 5 2 38 5 3 39 5 4 40 5 5 41 5 6 42 6 0 43 6 1 -0.122198 -0.013469 44 6 2 +0.019367 45 6 3 +0.002050 46 6 4 47 6 5 48 6 6 49 0 7

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Table 8

Typical Bp values for different ship types.

has been demonstrated in practise in the course

of the past thirty years. For middle and lower screw loads (tankers and single-screw cargo

ships) the increase in propulsive efficiency

through application of an accelerating nozzle

strongly depends on the stern-nozzle configura-tion.

In the case of lightly loaded screws the

applica-tion of

a decelerating nozzle may become

attractive when other requirements than the efficiency influence the choice. For naval ships it is of the utmost importance that the inception speed, or the speed at which cavitation phenomena occur at the screw will be as high as possible. For tactical reasons a minimum sound radiation of propeller noise due to cavitation is

necessary for these ships. Finally it must be

noted that the flow velocity at the impeller disk of

a ducted propeller is far less sensitive to the

variations in ship speed than the flow velocity at an ordinary propeller. Consequently the power absorption of a ducted propeller is relatively less

2 3 4 5 6 7 10 13

20 30 40 50 70 100 0

Figure 22. Curves for optimum diameter of different propeller types.

200 300 400

Figure 23. Curves for optimum diameter of different propeller types.

IN Mel

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CT Torpedos 10 0.5 Twin-screw ships 10 15 0.5 1 0 Fast warships (frigates, destroyers).

Single screw cargo ships 15 35 1.0 2.5

Coasters 35- 60 2.5 4.0

Tankers

35 70

2.5 5.0

Trawlers 60 100 4.0 8.0

Towing vessels (tugs, pushboats). 80 6.0

1 2

345

Is 20 25 30 40 50 ep 60 70 80 90 IDO 110 120 130 U0 150 160 170 180 190 200

Figure 21. Bp-6 diagram of contra-rotating propeller series.

13 D 06 11 07 6 09 5 05 4 1/ 3 0,4 2 03 o o 01 03 0405 0.6 07 2 3 4 567 10 20 30 571600, Q 061 500 05 40 .90 300 2 t21 100 01 0

2 2

sensitive to variations in the ship speed. This

feature has also been an important factor in the case of application of ducted propellers behind

tugs, pushboats and trawlers. All these ships

must operate satisfactory at different loadings (towing and free-running) of the screw.

If we compare the results of the contra-rotating propeller series withthe B 4-70 screw series, it can be concluded that the contra-rotating pro-pellers appear to give a higher efficiency than conventional screws, especially at lower screw loads. It must be noted, however, , that by applica-tion of a convenapplica-tional screw behind a ship, the

10 20 30 40 50 70 100

e, 200 300 400 500 700

Figure 25. Curves for optimum diameter of Ka-screw series in nozzle no. 19A.

rudder partly removes the rotational velocity

from the propeller jet and hence improves the efficiency of the propulsion device.

It is obvious that this improvement in efficiency will not be found by application of contra-rotating propellers behind a ship.

It can be seen from Figure 8 that the optimum diameter of the contra-rotating propeller series is considerably smaller than the optimum dia-meter of the conventional screw series.

In the following some special applications of ducted propellers, contra-rotating propellers

and the application of overlapping propellers will be discussed.

09

03 04 05 06 07 2

KT/02 3 4 5 6 7 10

20 30

Figure 27. Curves for optimum rpm of Ka-screw series in nozzle no. 19A.

111111=1111

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03 04 OS 06 07VKT/J, 2 3 4 5 6 7 10 20 30

Figure 26. Curves for optimum diameter of Ka-screw series in nozzle no. 19A.

Figure 24. Curves for optimum rpm of different pro-peller types. 07 6 o 05 0/. 3 03 2 02 1 0,1 0 1.3 P/13 1.1 0,8 0.9 07 06 Q 3 04 2 03 Q2 o 0.1 03 04 05 0607 KTA2 2 3 4 567 10 20 30 13 PA) 06 07 6 0g 5 0.6 00 ,/3 3 2 3 02 o 01 13 Pip 11 08 07 6 09 500 06 0540 30 04 200 03 100 02 01 0 13 P/D 08 II

4. Some special applications of the considered propeller types.

4.1. Application of ducted propellers on large tankers.

Based on results, as presented in Figure 22,

propulsion tests have been performed at the NSMB with a large number of tanker models

equipped with ducted propellers. Some results of

these tests were given in

[14, 15, 161. The

investigations by Lindgren et al [17], may also be mentioned in this respect. The results of these , tests generally confirm the conclusion that an increase in propulsive efficiency can be obtained by application of a ducted propeller for this ship type if compared with a conventional screw.

Some of the more extensive tests will be

discussed here. The total propulsive efficiency

of a self-propelled ship depends on the

open-water efficiency of the screw and on the mutual

interference of screw and hull. A screw fitted

behind a ship normally increases her

drag,

because of the decreasing pressure (suction field), which accompanies the acceleration of the flow

in front of the screw. This additional drag is

called thrust deduction. The open-water efficiency of a screw with an accelerating nozzle

is, for the range of screw loadings of tankers,

better than of an open screw, but the higher thrust deduction of the first system may reduce this gain.

Therefore, tests have been carried out with a

model of a 95000 TDW tanker with conventional stern andfitted with a conventional screw or one

of a series of ducted propeller systems. The nozzles were designed for different acceleration

ratios of the flow.

The profiles of the tested

nozzle shapes are given in Figure 28. The nozzle-area ratio Ao/AEX of the different nozzles are also indicated in the diagram since this ratio is the important characteristic for the acceleration ratio of the nozzle.

Analysis of the reduction in DHP due to the use of the different nozzles in comparison with the conventional screw propeller has been made for a ship speed of 16.5 knt and for the loaded and ballast condition of the vessel. The result is given

in Figure 28. This diagram clearly shows that

for the loaded as well as for the ballast condition the most accelerating nozzle (nozzle II) still gives the largest reduction in DHP.

Pi9/eEpe153 P,AEx.1042 AdA,,,a925 AphiE .960 bales! condition Snip spe a 165 kn."

J

09 e condition Ship Speed 16510.6 120 30 20

peP nor xie

OW, open screw

10D

90

130

Figure 28. Reduction in DHP due to the application of different axisymmetrical ducted propeller systems behind

tankers .

It is a well known fact that the propulsive

efficiency of a tanker can be further increased by application of a ducted propeller, in combination

with a cigar-shaped stern. The cigar-shaped

stern tends to make the flow more uniform and to bend the flow in horizontal direction. In this respect a non-axisymmetrical nozzle behind a conventional stern may also be attractive.

A propeller behind a ship operates in a

non-uniform flow. Measurements performed by

Wereldsma [18] show that for large tankers a

thrust eccentricity of 0.1 D is common practice. The inflow velocity of the propeller can be made more constant over the screw disk by surrounding

the propeller by a non-axisymmetrical nozzle

which is adapted to the wake distribution behind the ship. This nozzle accelerates the flow in the

upper part of the screw disk (by increasing the exit area of the nozzle) and decelerates the flow in the lower part (by decreasing the exit area of the nozzle). A view of a tanker with a

conven-tional stern and equipped with a

non-axisym-metrical ducted propeller is given in Figure 29. The non-axisymmetrical nozzle is still cylindrical at the inside from the leading edge of

the nozzle to the impeller; only the aft part is

non-axisymmetrical but still cylindrical.

Tests have been carried out with the model of

a 95000 TDW tanker fitted with successively

different non-axisymmetrical nozzles. The MCP open um* 500 13911 010 ',AI pi., ra 10 NyAExt1 12

-24

Figure 29. View of stern of tanker fitted with non-axi-symmetrical ducted propeller.

profiles of the tested nozzle shapes are given in Figure 29. It can be seen from this diagram that the maximum diffusor angles (in the upperpart of the screw disk) of the nozzles V, Va and VII are equal to the diffusor angle of nozzle II. Nozzle VI has a larger diffusor angle. Nozzles V, Va and VI are made nonaxisymmetrical in the same degree. Nozzle VII is less non-axisymmetrical.

An analysis of the reduction in DHP due to the use of the differentnozzles in comparison with the conventional screw propeller has been made

again for a ship speed of 16.5 knt. The result

is given in Figure 30. The curves obtained with

the axisymmetrical ducts are also indicated in

the diagram. From this diagram it can be seen

that nozzles V and Va give thelargest reduction in DHP. Nozzle VIwhich is the most accelerating nozzle type of the series probably suffers from

flow separation in the upper part of the screw

disk at the inside of the nozzle, as the diffusor

angle of the nozzle is too large. Nozzle Va is

slightly better than nozzle VII.

By comparing the resultspresented in Figures 28 and 30 it can be seen that the best non-axisym-metrical nozzle (nozzle Va or V) in comparison

with the best axisymmetrical nozzle gives a

reduction in DHP of about 2 percent.

In Table 9 the results are compared of a large number of model self -propulsiontests,

perform-ed with tankers with conventional and cigar-shaped stern arrangements and fitted with

o,./AE,0920 x 012 Acvaex .0935 A4AE x-09311 130 120 110 WO' 099 IDO 090 130 170 110 13911. nozzle 0 HP ape. xi... /00 090

Figure 30. Reduction in DHP due to the application of different non-axisymmetrical ducted propeller systems behind tankers.

conventional screws, ducted propellers (nozzles I and Ja) and non-axisymmetrical ducted pro-peller (nozzle Va). From this table it can be seen

that the conventional stern with

non-axisymmetrical ducted propeller gives a

reduc-tion in DHP which is still larger than can be obtained by application of a cigar-shaped stern with an axisymmetrical nozzle. In addition, it can be expected from the homogenizing effect of

the non-axisymmetrical nozzle on the inflow velocity of the impeller that the

non-axisym-metrical ducted propeller offers a means

of

minimizing propeller induced vibrationand cavi -tion problems.

Table 9

Reduction in DHP if compared with tanker with conventional stern and screw.

ballast condil.. Weed 16Sknots /Sl,i0 .0 99 7. Y Configuration Loaded condition Balast condition Ship with conventional stern and

axisymmetrical ducted propeller. 2 6%

Ship with conventional stern and reductions non-axisymmetrical ducted about 2-3%

propcIler 6 9%

Ship with cigar-shaped stern and

axisymmetrical ducted propeller 5 8% loaded condition 55.9 speed 165 knots Il a, 05 09 ID r

4.2. Application of non-axisymmetrical

nozzles on twin-screw ships.

For naval ships it is of importance that the inception speed, or the lowest speed at which

cavitation phenomena on the screw will occur,

should be as high as possible.

For tactical

reasons a minimum sound radiation of propeller

noise due to cavitation is necessary for these

ships. Usually, fast naval ships (frigates,

destroyers) are twin-screw vessels. The applica-tion of a decelerating ducted propeller may be attractive for fast naval ships, as this nozzle can attribute to a retardation of screw cavitation.

In the case of twin-screw ships, the propellers

operate in a varying inflow, due to the shaft

inclination. This inclination is a consequence of the fact that the propeller has a sizeable inclina-tion to both the horizon and the buttock lines in way of the propeller. Wake data indicate that the flow is probably following the buttock lines closely and should have a fairly uniform inclination over the disc. A view of the propeller and the hull in

way of the propeller is given in Figure 31. In

addition, the velocity diagrams of a screw

blade-element at a radius of 0.7 R are given in this

figure for different positions of the blade during a revolution.

From the viewpoint of retardation of screw

cavitation, the application of a

non-axisym-metrical nozzle may be attractive here. This

nozzle must be designed in such a way that the actual effective incidence changes of the blade sections of the impeller will be as low as possible during a revolution. Apart of the stern of a twin-screw ship fitted with non-axisymmetrical nozzles is shown in Figure 32. Particulars of the

starboard nozzle are given in Figure 33. This

nozzle accelerates the flow velocity with respect to the flow velocity at the starboard side(e 900)

by increasing the exit aera of the nozzle and

decelerates the flow at the port side (8 - 270°)

by decreasing the exit area of the nozzle. The nozzle is still cylindrical at the trailing edge.

The leading edge of the nozzle is adapted to the flow direction.

The velocity diagrams of a screw blade-element

at a radius of 0.7 R are given in Figure 32 for

the different angular positions of the blade. These diagrams show that the angle of incidence of the flow with respect to the blade element will be

looking nboard

Figure 31. View of propeller and hull of twin-screw ship.

0.180° 8.270°

Figure 32. HuIl of twin-screw ship fitted with non-axi-symmetrical nozzles.

constant during a revolution. However, the incidence velocity of the blade element will vary.

Preliminary results of tests performed with a

non-axisymmetrical nozzle at different shaft

inclinations in a cavitation tunnel of the NSMB have shown that an improvement in the cavitation characteristics of the impeller can be obtained.

Further investigations will be performed to

prove the reliability of this concept.

4.3. Applications of contra-rotating

propellers.

The most extensive investigations on the application of contra-rotating propellers on ships were performed by Hadler, Morgan and Meyers [191, Lindgren and Johnsson [17], Van Manen and

0.90°

26 270° 180°

v Ira

ft`VN

k

-40.= Net: 90°

Figure 33. Particulars of non-axisymmetrical nozzle.

Oosterveld [20] and Hecker and Mc Donald [21]. A review of this work was given by Hadler [3]. From these investigations the following conclusions can be drawn:

On full-formed ships such as tankers a reduc-tion of 6 to 7 percent in horsepower can be expected by application of contra-rotating propellers in comparison with a conventional screw propeller.

On fine-formed ships the gains made by the contra -rotating propellers are somewhat

crreater than for the tankers. Details of

aperture and rudder location can have a

market effect upon performance. The figures given here for the full- and fine formed ships

are for conventional apertures and rudder locations.

On high-powered fine -formed ships (container ships) the appended resistance of the twin-screw configuration is substantively greater

than that of the comparable single-screw

configuration. Here a reduction in DHP for contra-rotating propellers in comparison with the twin-screw arrangement of 20-25 percent can be found.

With respect to cavitation it was found that conventional screws and the forward propeller of the contra-rotating propellers are quite comparable as far as blade cavitation is concerned. The extend of sheet cavitation on

the blade of the aft propeller of the

contra-rotating propeller is relatively small. With

egardtothe propeller induced vibratory forces, it was concludedthat the thrust and torque varia-tions, as well as the thrust eccentricity of conventional screws and contra-rotating pro-pellers did not differ very much, although the

average thrust and torque of each of the

contra-rotating propellers are about half of that of a

comparable conventional screw. The application of contra-rotating propellers causes a consider-able reduction in transverse forces. These forces are practically constant both in magnitude and direction for the contra -rotating propellers. The stopping characteristics of contra-rotating

pro-pellers are at least equal to if not somewhat

better than a single-screw configuration of comparable power.

It is clear that the presence of two propellers

on the stern frame of a ship would impose

insignificantly greater structural problems. In

addition, the machinery for contra-rotating pro-pellers (high power gears, shafting system) may cause problems. Therefore the greatest potential for pay-off on the contra-rotating propeller

system is for the high-powe red fine -formed ships where the only current alternative is a twin-screw configuration. Reductions in DHP in the order of 20 - 25 percent are possible in such cases.

4.4. Application of stern arrangements with overlapping propellers.

Recently a new stern arrangement having a

twin-screw propulsion system with overlapping propeller fields was proposed by Pien and Ström-Tejsen [22]. The stern of a ship equipped with an overlapping twin-screw arrangement is shown in Figure 34.

From preliminary tests performed with ship

models with this new stern arrangement by Pien and Ström-Tejsen at the NSRDC and at the NSMB it can be concludedthat the reductions in DHP due to the overlapping twin-screw arrangement are

contra-Figure 34. View of stern of ship with overlapping twin-screw arrangement.

rotating propellers. Therefore, the best field of application for this new stern configuration will be high-powered fine formed ships were the only current alternative is a twin-screw arrangement.

5. Conclusions.

The derived polynomials of the thrust and

torque coefficients of the conventional screw series, the screw series in both accelerating (nozzle no. 19A) and decelerating nozzles (nozzle no. 33) and the contra-rotating pro-peller series enable design calculations and analysis with a computer.

The application of a wake adapted or non-axisymmetrical nozzle behind a full single screw ship (tanker,

bulkcarrier) offers a

means of making the inflow velocity of the

pro-peller more constant over the screw disc.

Consequently, this nozzle should minimize problems concerning propeller induced vibra-tions and cavitation. In addition, the applica-tions of such a nozzle leads to a reduction in

In the case of twin-screw ships, a non-axisym-metrical nozzle offers a means of minimizing

the actual effective incidence changes of a

blade section during a revolution. Con-sequently-, the non -axisymmetrical nozzle

improves the cavitation properties of the

screw. This is of particular importance for

fast naval ships.

The most important field of applications for

contra-rotating propellers and the stern arrangement with overlapping propellers will be the high-powered fine-formed ships (for instance container

ships) where the only

current alternative is a twin screw configura-tion.

References.

Cox, G.G., and Morgan, Wm.B., 'Application of theory to propeller design'. to be published. Weissinger, J., and Maass, D., 'Theory of ducted

propellers. A review'. 7th. Symp. on Naval Hydrodynamics, Rome, August 1968.

Hadler, J.B., 'Contra-rotating propeller propul-sion; A state-of-the-art report', New York Me-tropolitan Section of SNAME. December 1968

New York.

Troost, L., 'Open-water tests with modern pro-peller forms'. Trans. NECI. 1938, 1940 and

1951.

Principles of Naval Architecture, SNA ME, New York

1967.

Lammeren, W. P. A . van, Manen, J. D. van, and Oosterveld, M. W. C.; 'The Wageningen B-screw series'. Trans. SNAME. 1969.

Lerbs, H.W., 'On the effect of scale and roughness on free running propellers'. Journ. A SME . 1951.

Lindgren, H., 'Model tests with a family of three

and five bladed propelle rs Publ. no. 47, SSPA,

1961.

Lindgren, H., and Bjäme, E., 'The SSPA standard propeller family open-water characteristics', Publ. no. 60 SSPA 1967.

Newton, R.N., and Rader, H.P., 'Performance data of propellers for high-speed crafe.Tmns.

RINA, 1961.

Manen, J.D. van, and Oosterveld, M.W.C.,'Analysis of ducted propeller design'.Trans.SNAME 1966. Oosterveld, M.W.C., 'Model tests with decelerating nozzles'. ASME, Symp. on Pumping Machinery for Ship Propulsion, Philadelphia, May 1968. Manen, J.D. van, and Sentic, A., 'Contra-rotating

propellers'. Trans. INA 1956, I.S.P. 1956. Manen, J.D. van, and Kamps, J., 'The effect of the

shape of the afterbody on propulsion', Trans.

SNAME 1959.

Manen, J.D. van, Oosterveld, M.W. C., and Witte, J. H., 'Research on the manoeuvrability and pro-pulsion of very large tankers'. 6th Symp. on Naval Hydrodynamics, Washington 1966. Oosterveld, M. W. C., _{The application of}

non-cylindrical nozzles for large tankers and bulk carriers'. Shipb. and Shipping Record, November

1968.

28

of the application of ducted and contra-rotating propellers on merchant ships'. 7th Symp. on

Naval Hydrodynamics, Rome, August 1968. Wereldsma, R., 'Some aspects of the research into

propellers induced vibrations'. I.S.P., vol. 14, No. 154, June 1967.

Hadler, J.D., Morgan, Wm.B., and Meyers, K.A., 'Advanced propeller propulsion for high-powered single-screw ships'. Trans. SNAME 1964. Manen, J.D. van, and Oosterveld, M.W. C., 'Model

tests on contra-rotating propellers'. 7th Symp. on Naval Hydrodynamics, Rome, Aug. 1968.

Hecker, R., and Mc. Donald, N.A., 'The axial

spacing and optimum diameter of counterrotating propellers'. DTMB Report 1342. 1960.

Pien, Pao C., and Strom- Tejsen, J., 'A proposed new stern arrangement'. NSRDC Report 2410.

Nomenclature.

Ao = disk area of screw

AE = expanded blade area of screw

A = exit area of nozzle

EX

= loading coefficient, B = 33.07

= propeller hub diameter = propeller diameter

= advance coefficient, J = VA/n D = thrust coefficient. K = T/pn2 D4

= torque coefficient, K = Q/pn2 D5

= nozzle length

= number of revolutions per second and per minute

= power = torque = thrust

= undisturbed stream velocity = number of screw blades

A /A

= blade area ratio of screw

E o

A /A = ratio between impeller disk area and

o EX

exit area of nozzle P/D = pitch ratio of screw

8 = velocity coefficient. 8 = 101.27/J = specific mass of water

= open-water efficiency, o K KT KQ n, N VA