Recent developments in marine propeller hydrodynamics

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Recent develoPments in marine propeller hydrodynamics

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Introduction

On looking back on a 40 year period of work in the

field of ship hydrodynamics at the Netherlands Ship odcl Basin (NSMB) a number of memorable highlichts

çn he discerned. A number of these highflghls are noted c!cwhere in this book. Most of these memorable

jtivities vere the result of seif-sponsoced research with

the aim to promote the efficient designing of ships.

:riicuiarly intensive research has constantly been devot-cd to the various aspects of ship prcpulsion, the results

of which were nearly always published in well-known maeaziiies and periodicals.

li , not the intention of this paper to review past activities in the field of ship propulsion, but rather to

rc.nsider more recent work in this field, carried out or Fing carried out, in particular at the NSMB.

' his paper is divided into the following four main topics: I. Theoretical propeiJer theory.

2. Experimental (conventioria i) p opcller characteristics. .3. Characteristics of non-conventional propulsion

ices.

4. Propdlcr testing techniques and facilities.

i he state-of-the-art of sub-cavitating optimum propeller theory has progressed to a stage ensuring the highest possible efficiency in both the free-running and wake-ndaptcd cases. A short review of past developments in theoretical propeller theory particularly concerned with

ub-cavitating optimum propellers is included in this

p.per. With the unmistakable trend towards higher ship

sreeds and larger displacements, howcver. non-optimum

propl1er design in connection with securing the best

psib1e cavitation properties is becoming relativelymore

important. As a consequence, many research institutes have recently intensified work on this aspect of propeller

theory. At the Netherlands Ship Model Basin a method

h.t _{been developed to determine overall and local}

PrOpeller geometry in accordance with obtaining

maxi-mum latitude to the angle of attack. In this method

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complete integration of the design willi the wake at the propeller position is obtained. A short exposition of the

principles of this method is given.

Experimental projlIer characteristics such as

open-water test results are increasingly used in preliminary

propeller design and parameter studies by means of high speed computers. For this purpose it is

veryad-vantageous to have these experimental propeller

charac-teristics in the forni of polynomials or formulas. Among

the well-known screw series developed by Schaifran, Gawn artd ailiers, the Wageningen B-screw series of the

Netherlands Ship Model Basin are perhaps the most

used. This screw series has through the years been ex-tended and now comprises some 120 models with blade

numbers ranging from 2 to 7 and binde ai-ca ratios from 0.3 to 1.05. The cross-fairing of the open-water test data by means of the computer for a Reynolds number of

2 x lO& has now been completed, and it was considered

appropriate that these results should be pubhshed for the first time in this paper. The thrust and torque polyrio-mials given incorporate the results of some 40 years of

open-water testing at the NSMB.

In the chapter on non-conventional propulsion devices, particular attention is given to the characteristics of the

various propulsion devices. The application of

non-con-ventional propulsion devices is increasing due to the fact

that modern ships sometimes demand specific propulsion

requirements which can not be obtained with the

ventional screw propeller. The propulsion devices con-sidered are the following:

- ducted propellers,

- contra-rotating propellers, - overlapping propellers, - controllable pitch propellers, - vertical axis propellers.

c-:the above mentioned. ducted propellers are being

increasingly applied behind large tankers. Ducted

propellers are therefore considered in more detail.

Accelerating, decelerating and non-axisymetrieal nozzles are regarded.

Lastly, this paper deals with some recent developments

in the cavitation testing of propellers, both from the

viewpoints of techniques and facilities.

Model tests are often employed to determine the best propeller-afterbody configuration. The main reason for

this is the difficulty involved in the theoretical

determina-tion of unsteady propeller acdetermina-tion, cavitadetermina-tion, and

propel-ler-afterbody interaction effects when the propeller opera-tes in a wake.

With modern propeller theory the determination of unsteady propeller forces in the non-uniform velocity

field can, to a certain extent, be realized. Theoretical assessment of the cavitation properties and, in turn, the influence of propeller cavitation on propeller action and interaction effects, has not progressed that far. In conse-quence, model testing is particularly employed to deter-mine propeller cavitation properties, induced vibrations

and other adverse effects of cavitating ship screws. The tests to determine propeller-induced vibratory forces

acting on the afterbody of a ship vere up till now performed in conventional towing tanks. In this ship

model testing facility the effect of propeller cavitation is

not taken into account. It has recently been established, that the effect of cavitation on the vibratory forces on the ship's afterbody and appendages and on the

propeller itself is considerable [1, 2]. Complementary

tests with model propellers in cavitation tunnels in

wake-simulated flows are therefore often necessary to

obtain an impression of the cavitation properties of the

propeller. Actual interaction effects between propeller

and afterbody are, however, not taken into account in

this way, while it is found extremely difficult to simulate

the required distribution of the axial and tangential

wake components. These and other difficulties have led

the Netherlands Ship Model Basin to construct a depres-surizcd towing tank, in which the air pressure can be lowered to such an extent that ship model testing can be

performed a the correct cavitation index. The

climens-ions of this towing basin are such that ship and propel-ler models are of a size with which it is possible to

avoid unpredictable scale effects.

Besides a short description of this facility, this part of the paper includes a review of the many problems

as-sociated with ship model testing including such subjects as scale effects and cavitation scaling.

Propeller Theory

Rev/en' of past developments

Before considering some recent progress made in

propeller theory, a survey of past developments is appropriate. In 1865, Rankine [3] developed the fore-runner of momentum theory as it is known today. This theory is based on the change of momentum and the related axial motion of the fluid passing through an actuator or propeller disk. [n 1889, R.E. Froude [1] considerably extended this theory and it has

subsequent-ly become known as the Rankine - Fronde axial

mornen-turn theory. The effects of the rotational motion of the

slipstream were included by Betz [5] in 1920. This

theory is today used in various propeller problems. The fact that it gives no indications of the geometry of the propeller causing the changes in the flow is a large drawback, and in fact the reason for it not being used in

general design problems.

The first to attempt to formulate the relation between propeller geometry and the associated propeller thrust and torque was W. Froude [6] in 1878. His crude blade element theory was the forerunner of all theories relating the lift and drag of an clement of a blade to its

geome-try. Later, Drzewiecki [7] considerably extended this

theory and suggested performing tests to determine the

lift and drag forces experienced by blade section forms

at various angles of attack when he found that he could not calculate them. The uncertainty as to the

character-istics which must be assumed for such sections was, and

to a certain extent still is, an unsatisfactory feature of such theories. Furthermore, early workers in this field

failed to recognise finite aspect ratio effects, causing the

arithmetical results obtained with this theory to be

far from satisfactory.

In consequence of the large discrepancies between the

momentum theory and the blade element theory, at-tempts were made to combine the two, and to use

the induced velocities as determined by the momentum

theory to reduce the angle of attack in the blade element

theory. In this way large differences between experiment

and theory were avoided but duc to the still

unaccount-ed finite aspect ratio and chordwise effects, and the still

unknown variation of blade section characteristics with

Reynolds number, these differences remained

unaccep-table, in particular for broad bladed marine propellers. In 1907, Lanchester [8] put forward a new theory which accounted the lift of an aeroplane wing duc to the

development of circulation around each section in the span direction. He postulated that the vortex movement around such an aeroloil is continued in the fluid in the forni of vortices trailing from the ends, and in the case of propeller blades, passing downstrean in approxinia-tely helical paths from the tips. This concept of the shedding of vortices from the tips of propeller blades was shown to be true by Flamm [9] in 1909 by means of photographs of the wake of a propeller. Many scientists

subsequently endeavoured to calculate the induced velocity associated with this system of trailing vortices,

and in this regard the work of Joukowski [10] in 1912, Grammel [11] in 1917 and Wood and Glauert,[12] in

1918 should be noted. In 1918, Prandtl [13] succeeded,

and the concept of trailing vortices became fully accept-ed. Prandtl concluded to state that the behaviour of an element of an aerofoil of finite span can only be consid-ered the same as in two-dimensional flow when proper

allowance is made for the induced velocities caused by the shedding of vortices from such ari aerofoil. This first

vortex theory is often referred to as a lifting line theory due to the fact that a wing of finite span is replaced by a vortex line. In this way it was possible to account for spanwise variations in the circulation distribution, the circulation of the vortex line at each section being put equal to the chordwise integrated circulation at that section. This theory is therefore not able to calculate subsequent effects of the fact that the circulation around a section of a propeller blade or a wing is not concen-trated at the position of the line vortex, but distributed along the chord. For moderate aspect ratios it was found that the Prandtl lifting line theory was very satisfactory, and this very soon led to the standard procedure in airscrew design to use two-dimensional lift and drag

characteristics (so-called profile characteristics) at an angle of incidence corrected for the induced velocities.

For the broad bladed propeller this theory was still not

satisfactory, however.

On assuming that the trailing vortices behind a

propel-ler blade follow helical paths with a constant angle of advance (implying a uniform propeller inflow and that the induced velocities are small, i.e. that the propeller is lightly loaded), and on neglecting the profile drag of

the blade sections, Betz [14] in 1919 succeeded in

esta-blishing the best load or thrust distribution along the blades for minimum induced drag. Due to the involved

mathematical difficulties, Betz had to assume that the

propeller had an infinite number of blades. In an appen-dix to Betz's paper, Prandtl established an approximate correction to account for a finite number of blades. The

difficulty inherent to the finite blade nunìbcrcase lies

in the complexity of calculating the induced velocities

caused by the system of trailing vortices constituting a finite number of vortex sheets. Particular credit must be paid to J3etz's paper, not only for determining the op-timum radial load distribution from the viewpoint of

efficiency, but also for being the first to successfully

apply the Prandil vortex theory to propellers and to

define the mathematical model concerned.

With these new vortex conceptions, which in fact con-stituted an important break-through in propeller theory,

various importanit propeller theories were developed in

the years that followed. Amongst the most important is

tIte work of Glauert [15] in 1926, Pistolesi [16] in 1922

and particularly, the work of Kawada in 1933, 1936 and

1939 [17, 18, 19]. Bienen and Von Karman [20] in 1924

extended Betz's 1919 paper and performed the addit-ional calculations for the case that the effects of profile

drag arc included. In 1927 Betz [21] extended his work

to the heavily loaded, free-running case. In the case of a

heavily loadòd propeller the influence of the induced

velocities on the shape of the helical vortex sheets is taken into account as well as the effects of centrifugal forces and of the contraction of the induced velocity components. Only in the case of the lightly loaded

propeller are the vortex sheets true helical surfaces. In 1929, Goldstein [22] successfully considered the flo\v

past a finite number of true helical vortex sheets and obtained an expression for the ratio between the mean circulation taken around an annulas and the circulation at the helical surfaces for a 2 and a 4 bladed propeller. From these values the ratio between the mean inflow velocity taken around any annulas and the

corres-ponding larger inflow velocity in way of the helical

vortex sheets at the position of the propeller blades was derived. The values of this ratio for various values of the propeller radius, the hydrodynaniic pitch angle and the number of blades have since been designated as Gold-stein factors. A large number of these values ware

calculated by Lock and Yeatman [23] in 1935, in 1941 by Kramer [24], and very accurately in 1950 by

Tach-mindji and Milam [25]. The TachTach-mindji and Milarn values arc valid for the case of zero circulation at the

hub, which case is now considered as correct.

Today these Goldstein factors are extensively used, and often in cases where they are not applicable. They are

strictly only valid for uniform propeller-inflow (so-called

free running propellers), having a constant radial virtual pitch, i.e. the Betz optimum radial circulation

distribu-tion. Furthermore, none of the devised marine propeller design methods based on the Goldstein factors are

sui-table for heavy screw loading. Very few recognize

slip-stream contraction and the influence of the radial pressure gradient. The most used marine propeller design methods based on the lifting line procedure incorporating Goldstein factors are those due to Burrill

[26, 27] in 1943 and 1955, Lerbs [28] in 1945, Hill [29] in 1949, Van Manen [30] in 1952 and Eckhardt and Morgan [31] in 1955.

When Lerbs [32] in 1952 published his lifting line

method bascd on induction factors as defined by Kawa-da in 1933, it was a timely introduction of a method suitable for a radially varying wake and a non-optimum circulation distribution. In 1958, Van Manen [33] show-ed that important differences occur between the results of the induction factor method and the Goldstein factor

method when applied to so-called wake adapted

propel-lers.

As mentioned above, lifting line procedures were found to be very suitable for the design of propellers and wings of moderate aspect ratios as low as 3. This was contrary to the case with wide bladed propellers having lower aspect ratios. Soon after lifting line procedures were introduced it was found necessary to supplement design procedures based on the lifting line concepts for

wide bladed marine propellers with emporical or

theore-tical correction factors. lt is now known that this is due to the fact that in the case of wide propeller blades it is rio longer correct to calculate the induced velocity at the position of the vortex line representing the blade and to neglect the variation of the induced velocity along the

chord. A distribution in the induced velocity or

down-wash along the chord results in a specific curvature of

the flow over the blade which, amongst other effects,

changes the effective camber of the blade setons. Such

effects remain unaccounted fer in lilting line procedures.

In the case of moderate aspect ratios it is more or less

correct to consider the induced velocity at the lifting line as a correction to be applied to the geometric

angle of incidence in determining an effective angle of

incidence to which the corresponding blade section reacts as if it were in a two-dimensional flow. In the case of low aspect ratios, however, the decrease in effective camber and, in general, the way in which the blade sections react to the curved flow, must also be accounted for. Changes in the ideal angle of attack and, in the case of non-symmetric chordwise loading of the meanline about the midchord position, in the

hydro-54

dynamic pitch angle are a result.

Ludwieg and Ginzel [34] in 1944 were the first to recognize this influence and they actually calculated

some correction factors with which the amount of blade section camber could be corrected for the induced curvature of the flow. These camber corrections were given in the form of a ratio between the effective camber and the geometric camber of the blade sections as a function of propeller radius, blade area, blade number and hydrodynarnic pitch. These particular correction

factors were, however, only strictly valid for the

opti-mum radial circulation distribution, uniform chordwise

loading (circular arc rncanhines) and a uniform propeller

inflow. Due to the large amount of work involved in calculating such correction factors, the Ludwieg and Ginzel camber factors were used for a large number of

years following 1945. Very often they were applied in cases where they were unsuitable, resulting in fact in

larger errors than caused by the correction factors based

on experiments with profiles in cascades which they replaced.

Prior to the work performed by Ludwieg and Ginzel, all lifting line procedures for the design or analysis of marine propellers incorporated correction factors based

on previous experience or theoretical or experimental vork on cascade effects. The opinion, that the differen-ces occurring between theory and the results of experi-ments with marine propellers are due to so-called casca-de effects, was then a general one, and many efforts

were made at developing reliable theories and at

ob-taining relative experimental information in the 50-year period following the first suggestion to rio so by Drze-wiecki in 1892. DrzeDrze-wiecki first found that the lift and

drag forces appeared to depend considerably on the ratio of length to breadth of the propeller blades. The

experimenta! investigatious eventually culminated in the work of Gutsche in 1933 [35] and 1938 [36] who

tested a series of cascades of aerofoils and propeller

blade sections at different pitch angles and variousgap

ratios.

Particularly good theoretical work on cascades _was

performed by Weinig in 1932 [37].

After the J.udwieg and Ginzel paper, the application

of cascade corrections in marine propeller problems

continued. The reason for this is best reproduced by

Burrill in the discussion of his 1955 paper on the

op-timum diameter of marine propellers [27]. To quote

For myself, I am noiconvinced that (the

Ludwieg-Ginzel theory is the right one for correcting the vortex

line into a vortex sheet theory) this is corrcct, despite

the correction factors and other devices which have been

introduced recently to enable the correct pitches to be

obtained, as the centrelinc camber corrections suggested

by this method lead to very high cambers indeed at the tip of the blades and much lower canibers at the root.

One of the deficiencies of the Ludwieg-Ginzel

corree-lions is that they have been worked out for wide-tipped outlines arid another is that the basic aerofoil section characteristics obtained from wind tunnel work must be

corrected by similar lifting surface curvature effects

in order that they may be applied to propeller design work.

The use of the Gutsche cascade corrections may seem

to he out-of-date, but they have the merit of simplicity and they do seem to be of the right order and to give satisfactory integrated values of thrust, torque and effi-ciency.'

With the advent of high speed computers, gradually proper and more accurate lifting surface calculations

were made, and now most propeller design procedures incorporate lilting surface correction factors, in 1961

Cox [38] derived a set of camber corrections valid for 4 different types of blade shapes, with 3, 4 and 5 blades, applicable to the case of constant chordwise loading at shock-free entry of the flow. In the last 10 years, lifting

surface corrections have been derived for various types

of propeller designs. Of these, the correction factors of Morgan, Silovic and Denny [39] for a family of

non-skewed and non-skewed propellers, should be mentioned. These correction factors were derived from the lifting surface programs developed by Cheng [40] for blade

loading and Kerwin [41] for blade thickness. They are valid for the NACA a = 0.8 meanline and the NACA 66 thickness distribution. The number of blades for which (liese corrections are given are 4,5 and 6. For the

res-pective 3-bladed propellers of this series, the correc-tion factors were derived by Minsaas and Slattelid [42] by means of the sanie programs.

Lilting surface theory for marine propellers has develop-ed basically along two different paths. 'The first calcula-lions and theories were really extended lifting-line methods. These evcitually developed into so-called vor-tex lattice methods, in which the lifting surface is

re-presented by a descrete lattice of vortices. After the Ludwieg and Ginzel theory, the work done by

Guillo-ton in 1949 [43] and 1955 [44, 45] by Strecheletzky in

1950 [46] an.d 1955 [47], by Kerwin in 1961 [48]. 1963 [49] and 1964 [50], and by English in 1962 [Sl]

was based on the vortex-lattice representation of a

propeller blade. Then in 1959 Sparenberg [52] derived the three-dimensional integral lifting surface equation for a screw propeller in a steady flow. This theory

in-corporated a continuous vortex sheet representation of the lifting surface, i.e. without physical or mathema-tical assumptions and models for the arrangement of the lattice. Such a formulation for a lifting surface (a wing)

was first given by Garner in 1948 [53] and 1949 [54] and by Multhopp [55] in 1955. In 1962 Hanaoka [56]

extend-ed Sparenherg's work to the case of unsteady flow. This

theory was then further developed by Pien [57],

Nishiya-nia and Nakajima [58], Yamazaki [59] and others. In obtaining numerical results with this theory, various

different numerical procedures have evolved to solve

the integral equation. In this connection the work done

by Cheng [40], Tsakonas et al. [60, 61, 62, 631, Brown [64, 65], Greenberg [66] and Verhrugh [67] should be

particularly mentioned. The necessary approximations and linearizations necessary for the solution must be carefully chosen in order not to cause appreciable errors

in the numerical results.

In 1965, Harley [68] carried out a comparison between

the results of Kerwin's vortex lattice program and Cheng's program for the continuous voi-tex theory of

Pien. He found that the differences were small. It should

be mentioned, however, that Cheng's numerical

proce-dure is essentially a vortex lattice representation of Pi.ens theory.

Recen! developments

Application of lifting surface theory to propeller design has as yet not been carried out to a large extent. Fur-ther refinements to the numerical procedures are yet to be iiiade in order to perform the necessary calculations faster and more efficient. For the analysis of propeller

performance, however, lifting surface theory has already proven invaluable. In 1967 and 196S Tsakonas etui

[69, 70] performed a comparison of vibratory thrust and torque calculations with experimental values obtained

at the isssn by Wereldsmna [71] in 1966. The results

showed the same agreement in trends of vibratory thrust and torque bui relative large discrepancies in magnitude. This has been ascribed to the insufficient number of

readings in the wake survey.

56

been the development of propellers having large skew.

'With lifting surface theory it is possible to determine the desired radial load distribution and the associated

necessary ideal angle correction to the hydrodynarnic pitch angle. Lifting surface calculations and

measure-ments show that propellers with a large skew experience

substantial reductions in propeller force and moment fluctuations [72, 73]. Recent work by Boswel and others

at the NSRDC [74] has also shown that the cavitation

performance of skewed propellers can be superior to the cavitation performance of the comparative propellers

without skew.

Due to the importance of designing propellers with

acceptabl cavitation properties, research into non-optimum propeller design has recently received a great

deal of attention. At the NSMB, a method has been

developed to account for the peripheral inequality of

the wake in the design process [75]. The necessary

cal-culations and iterations, performed on an electronic computer, have been found to give good results, Pro-peller pitch, blade thickness and camber are calculated in accordance with obtaining maximum latitude to variations in the angle of attack. From 5-hole pitot-tube measurements, an accurate survey of the axial, tangen-tial and radial wake components is made. These

components determine the geometric inflow conditions. By assuming a specific blade section geometry, the effective propeller inflow at a large number of' points in the screw disk is calculated. Together with the

calcula-tion of the cavitacalcula-tion index over the screw disk, it

becomes possible to select a new blade section geometry

at each radius having the necessary cavitation-free angle of attack range and the required average lift. With this

second geometric configuration, the associated induced velocities are again calculated, the blade section

geome-try determined, etc. initiating an iteration procedure

which is continued until the effective propeller ipflow

at the various points in the screw disk no longer

chang-es.

Calling the total variation in the effective inflow at a

certain screw radius and ship speed it is possible

to construct a diagram showing the variation

with ship speed and screw radius on a base of cavitation number. in Fig. i these results arc given for a

twin-screw destroyer type vessel. A figure of this nature

illustrates th necessary cavitation-free angle of attack or lift coefficient range the blade sections must have to be free of cavitation at a specific ship speed.

This procedure for the determination of blade section geometry very often leads to higher blade thicknesses

0,6 03

V1

4 116

Fig. I Angular variations in effective propeller inilow at

various propeller radii and ship speeds for a destroyer type

vessel.

than the blade thicknesses resulting from current

stan-dard design practices. This is particularly the case for the outer propeller radii. It is therefore often necessary

to specify a maximum blade section thickness to avoid bubble cavitation and unacceptable high drag coefficients. \Vhen relative high values occur at low values for the cavitation number, it is impossible to design prop-eller blades free of sheet cavitation. In that case this design process can be applied, e.g., to avoid cavitation

on the face.

Besides the aspects of propeller pitch, blade thickness

and camber, recent studies have also shown that a

carefull selection of propeller diameter, rotative speed,

direction of rotation and the number of blades should be made.Unloading of the blade at the tip and at the hub by means of a carefully selected radial load distribu-tion should be seriously considered and more often applied, particularly in view of the fact that the

prop-eller efficiency is not seriously cifected. When in

particul-ar hub vortex cavitation is a problem, use of a

diver-gent fairwater has been found to be very successful [761. Experimental propeller characteristics:

tile Wageningen B-screw series

An important method of screw design is that based on

the results4 of open-water tests with systematically varied series of screw models. Among the well-known screw

series developed by Schaifran, Taylor Gawn and others,

the B-screw series of the Netherlands Ship Model Basin, often designated as the 'Wageningen B-Screw Series', take an importuni place. The B-series screw type is

o

t

0

frequentlY used due to its satisfactory efficiency and Table 2a Dimensions of four five, six and seven bladed

adequate cavitation properties. Wagcningcn B-screw series.

The first tests with systematic series of screw propellers

at the Netherlands Ship Modcl Basin were performed

¡ 1936. From model experiments carried out by Baker

and Riddle [77] and Baker [78] it had become evident

that screws with circular-back blade sections and

ellipti-cal blade outline such as the Taylor and Schaifran series

were inferior as regards efficiency to propellers with

aero-foil sections. At the Netherlands Ship Model Basin these

conclusions were verified. These results led to the

devel-opment of a series of model propellers having acrofoil

sections. This series was called the A4-.40 series as it vas

a series having 4 blades and a blade area ratio of 0.40.

The results of the open-water tests with this series were given by Troost [79].

Later, it was found that the A4-40 screw series were only suitable for use in cases where no cavitation danger

was prcsnt. This was found to be due to the fact that the narrow blade tips and the aerofoil shaped blade

sections gave rise to very unfavourable pressure

distribu-lions on the blades. In addition, the A4-40 screw series

possessed unfavourable hacking characteristics. It was therefore decided to design a new screw series having

wider blade tips, circular blade sections near the tips and aerofoil blade sections ilear the hub. This new

prop-eller series was designated as the series. The first B-screw series to be designed was the B4-40 series and due to great popularity this screw series was gradually

ex-tended to other blade numbers and blade area ratios. The

results of the first open-water tests were given by Troost [80] and others [81, 82]. Table I lists the available B-screw series. The geometry of the B-B-screw series is given in Table 2.

At present, about 120 model propellers of the B-series

have been manufactured and tested at the NSMB. The

results of the open-water tests are given in the form

Table I Table of existing Wagcningcn B-screw series.

Table 2b Dimensions of three bladed \Vageningen B-screw

series. nR

--.---

Cr. Z D. A1;/A0 ar/Cr br/Cr Sr/D = ArBrZ Ar Br 0.2 1.662 0.617 0.350 0.0526 0.0040 0.3 1.882 0.613 0.350 0.0464 0.0035 0.4 2.050 0.601 0.350 0.0402 0.0030 0.5 2.152 0.586 0.350 0.0340 0.0025 0.6 2.187 0.561 0.389 0.027$ 0.0020 0.7 2.144 0.524 0.443 0.0216 0.0015 0.8 1.970 0.463 0.479 0.0154 0.0010 0.9 1.582 0.351 0.500 0.0092 0.0005 1.0

-

O

-

0.0030 0 r/R C, z at/Cr br/Cr Sr/Dr ArBrZ D.AE/AO Ar 1r3r 0.2 1.633 0.616 0.350 0.0526 0.0040 0.3 1.832 0.611 0.350 0.0464 0.0035 0.4 2.000 0.599 0.350 0.0402 0.0030 0.5 2.120 0.583 0.355 0.0340 0.0025 0.6 2.186 0.558 0.389 0.0278 0.0020 0.7 2.168 0.526 0.442 0.0216 0.0015 0.8 2.127 0.481 0.478 0.0154 0.0010 0.9 1.657 0.400 0.500 0.0092 0.0005 1.0

-

-

-

0.0030 0

l3tade number z Blade al-ea ratio AL/Ao

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}

of the thrust and torque coefficients KT and KQ

express-ed as a function of the advance coefficient J and the pitch ratio P/D, where:

K T pn2D4 K and

J=

(3) nD in which

T = propeller thrust,

p = fluid density,

n = revolutions of propeller per second,

D = propeller diameter,

VA velocity of advance.

Some years ago it was decided to cross-fair the B-screw series open-water test results by means of a regression

analysis. in this way the existing small errors in the diagrams would be eliminated and the resulting analyti-cal expressions for the thrust and torque would be very

welcome for use in preliminary design calculations by

means of high speed computers. One reason for the small errors in the diagrams was the inconsistancy of the Reynolds number during open-water tests. The early open-water tests were carried out at a lower rotational propeller speed than the more recent tests. For the correction of the test results for Reynolds number

effects the method developed by Lerbs [83] was applied.

This method is a so-called 'equivalent profile method', consisting of replacing the propeller by one of its profiles, the equivalent profile, and deducing the prop-erties of the propeller at other scale and roughness values from the known properties of this profile Titis idea was first considered by Lock [84] and Von Doepp

[85] and was previously apphed by Driggs [86] and Kramer [87].

Tite cross-fairing of the B-series was first attempted

for each blade number separately. The results of the

investigations for the four and five bladed 13-series were given by Van Lammeren etal [88] in 1969. It was

later decided to include the blade number as an inde-pendent variable in the cross-fairing and also to include the Reynolds number as an independent variable in the polynomials for K and KQ.

In the Lerbs equivalent profile method it is shown that

58

the blade section at 0.75 R is equivalent for the whole blade. At a specific value of the advance coefficient

the lift and drag coefficients and the corresponding

profile angle of attack is deduced from the KT- and KQ

values from the open-water test. In this way the polar curves for C0 and CL on a basis of a is calculated from

the known propeller characteristics KT and KQ on a

basis off. Reynolds number effects are only considered

to influence the drag coefficient of the equivalent profile.

It is furthermore assumed that the influence of Reynolds number on the drag coefficient is n accordance with a vertical shift of the C0 curve equal to the change in

the minimum value of the drag coefficient. This

mini-mum value is for thin profiles composed of mainly

frictional resistance, the effect of the pressure gradient being small.

According to Hoerner [89] the minimum drag coefficient of the profile is:

CDni n = 2Cf

(i

+ 2()O75R) in which

Cf =

[043429ln(R0_75R _2]2 0.075 where

Cf is the drag coefficient of a flat plate in a turbulent

flow and the term (I + 2(O.75R) represents the effect

of the pressure gradient.

On setting out the minimum value of the drag coefficient as obtained from the polar curve for each propeller on

a base of Reynolds number, large scatter was

appas-ant as shown in Fig. 2. \Vhen this mimimum value of

the drag coefficient ¡s set out against for each

pitch-diameter ratio, it is seen that below a specific value of the blade area-blade number ratio an increase in the

CD,fl;fl value occurs. For a pitch-diameter ratio equal

to 1.0, this i's shown in Fig. 3. The existance of such a

correlation of the CD,,jn value with propeller geometry

points to the fact that the scatter in Fig. 2 is not

entirely due to Reynolds number effects and experimen-tal errors. It is obvious that the drag coefficient is influen-ced by a three-dimensional effect. it is necessary,

there-R,,

-

CO7SR /v4 2 + (0.75 rnD)

2

O.75R

TOREE - 1010005101ML

.0008AGE PELArION

FOR P/O lO

AR/AO

Fig. 3 Three-dimensional effect on minimum drag coefficient

of equivalent profile of B-series propellers.

TlO

Fig. 2 Uncorrected value of the minimum drag coefficient

of equivalent proflle of B-series propellers.

¿D n O FOR ALL POINTS

04-RO - 00.80

04.100 07-30 07-85

fore, before correcting for Reynolds number according to equations 4, 5 and 6to subtract this three-dimensional

effect from the CD20I,2-value. An estimation of this effect

was obtained by applying regression analysis.

The lift and drag coefficients oblained in this way were

each expressed as a function of blade number, blade area ratio, pitch-diameter ratio and angle of attack by

means of a multiple regression analysis method. By

applying this process in reverse, thrust and torque

coefficient values were next calculated. The basis for this reverse process was formed by calculating CL and

D coefficients from the CL and C, olynomials for

specific combinalions of z, AE/Ao, P/ e' and R3. The resulting values formed the input for the

devel-opment ola th-ust coefficient and a torque coefficient polynomial. Foc R8 = 2 x 106 the polynomials obtained in this way are given in Table 3. The choice of choosing a Reynolds number value of 2 x 106 for the characteris-tics on the model scale followed from the fact that the

corresponding 1D;njo value is an average of all model

values.

With the aid of a tape-controlled drawing machine a new set of open water diagrams has been prepared. Figs. 4, 5, 6, 7 and 8 show the results for the B3.65,

B4-70, B5-75, B6-80 and B7-85 propellers for the

Reynolds number value of 2 x 106. in formulating the minimum value of the drag coefficient as a function of the Reynolds number, it is possible to cale ilate thrust and torque values valid for the full-scale by correcting

the CD-values as described above. lt is therefore possibl to calculate a nev set of coefficients in the KT and KQ

polynomials alie-ady obtained foi R0 = 2 X l0'. The

necessary calculations can be performed by a least

squares method. By correlating the values of the

respect-ive coefficicnts with the value of the Reynolds number, a final KT and a final KQ polynomial is to be developed

having as independent variables the number of blades, the blade area ratio, the pitch-diameter ratio, the

advan-ce coefficient and the Reynolds number.

A program ha also been started to include the thick-ness of the propeller blades at a characteristic radius in

these polynomials. The ultimate aim is to determine the

following relations: KT = f1 (J, P/D, AE!AO,; R,,, and (7) KQ = f2 (J, P/D, AE/Ao, , "721 C

With these relations it will be possible to perform preliminary design calculations to determine the op-timum propeller geometry parameters in connection

with obtaining a specific ship speed, the required strength o 0:4

O 020

colo

O 003

.1

Table 3 Coefficients and terms of the KT and KQ polynomials for the Wagen_{ingen B-screw series for R = 2 X 106}

KT = .Z - (J)S(p/D)t(A/A)U(zV) K0 = L (J).(P/D)t.(AE/AO)u.(zv) KT: C. S t u _y K0: _Cs.1. uV s t u y (J) (P/D) (AE/Ao) (z) _{(J) (P/D) (AE/Ao) (z)} ±0.00880496 0 0 0 0 -rO.00379368 O O O O -0.204554 1 0 _{0 0 +0.00886523 2 0 0} 0 +0.166351 0 1 0 0 -0.032241 1 1 0 0 ±0.158114 0 2 0 0 +0.00344778 0 2 0 0 -0.147581 2 0 1 0 -0.0408811 _{0 1} 1 0 -0.4S1497 I i 1 0 -0.108009 ₁ 1 i O ±0.415437 0 2 1 0 -0.0885381 _{2 J I} O ± 0.0144043 0 0 0 1 + 0.188561 0 ₂ 1 0 -0.0530054 2 0 0 1 -0.00370871 1 0 0 1 +0.0143481 0 1 0 1 +0.00513696 0 1 0 ± 0.0606826 1 1 0 1 -F 0.0209449 1 1 0 1 -0.0125894 0 0 1 1 ±0.00474319 2 1 0 1 +0.0109689 0 1 1 -0.00723408 2 ₀ 1 I -0.133698 0 3 0 0 ±0.00438388 i i 1 1 +0.00638407 0 6 0 0 -0.0269403 0 2 I -0.00132718 2 6 0 0 _+0.0558082 3 0 1 0 ±0.168496 3 0 1 0 ±0.0161886 _{0 3 i} O -0.0507214 0 0 2 0 +0.00318086 1 3 1 0 ±0.0854559 2 0 2 0 _{±0.015896 0 0 2 0} -0.0504475 3 0 2 0 ±0.0471729 I 0 2 0 ±0.010465 I 6 2 0 ±0.0196283 _{3 0} 2 0 -0.00648272 2 6 2 0 _{--0.0502782 0 I 2 0} -0.00841728 0 3 0 1 -0.030055 _{3 1 2 0} +0.0168424 1 3 0 1 ±0.0417122 _{2 2 2 0} -0.00102296 3 3 0 1 -0.0397722 _{0 3} 2 0 -0.0317791 0 3 1 1 -0.00350024 0 6 2 0 ±0.018604 1 0 ₂ 1 -0.0106854 _{3 0 0 i} -0.00410798 0 2 2 i +0.00110903 3 3 0 1 -0.000606848 0 0 0 2 -0.000313912 0 6 0 1 -0.0049819 1 0 _{0 2 +0.0035985} 3 0 1 1 -F00025983 2 0 0 2 -0.00142121 0 6 I -0.000560528 3 0 0 2 --0.00383637 1 0 2 1 -0.00163652 I 2 0 2 +0.0126803 0 2 2 -0.000328787 I 6 0 2 -0.00318278 2 3 2 1 +0.000116502 2 6 0 2 _{+0.00334268 0 6 2 i} ±0.000690904 0 0 1 2 --0.00183491 ₁ 1 0 2 +0.00421749 0 3 1 2 _{±0.000112451 3 2} 0 2 + 0.0000565229 3 6 1 2 -0.0000297228 _{3 6 0} 2 -0.00146564 0 3 2 2 _{±0.000269551} 1 0 1 2 -j- 0.00083265 2 0 1 2 +0.00155334 0 2 1 2 +0.00030283 0 6 1 2 -0.0001843 0 0 2 2 -0.000425399 0 3 2 2 R,, = 2 x 106 _{+0.0000869243 3} 3 2 2 -0.0004659 0 6 2 2 +0.0000554194 1 6 2 2 60

10K

Ko

01

K,

o

Fig. 4 Cross-fai red open-water

test results for B3-65 propellers

for R,, = 2 x 10e.

Fig. 5 Cross-faired open-water

test results for 134-70 propellers

for R = 2 x 1O.

8365

.1

i

liii

i:i

!I:

,!

ii

ua

14

Ii!!'

uI

misi

4.

LN

Ii IiL!I

qo

/4

-. LL

.

-UUNNR

IP,

ì.i!iiUIi

:i :

..::::::::.a

:::u::::IE

F1It1

I!1hìp!PiirIi

R

I1i

09 io i-' 12 13 06 o, ii i) i' ¶3 16

13 ti io cg 10k0 08 07 0. 0. 00 i. 09 IO k ti o, 400 62

Fig. 6 Cross-faircd open-water test results for135.75 propellers

for R9 = 2 x

Fig. 7 Cross-faired open-water

test results for 136-80propellers

for R9 = 2X 106.

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02 03 00 05 06 07 08 09 12 i' 15 02 03 09 07 06 09 15

'3

and acceptable cavitation properties.

For design purposes, the B,, diagrams at the Reynolds number of 2 x 106 for the propellers for which the

open-water diagrams are given are shown in Figs. 9, ifi, II, 12 and 13. The Taylor variable B,, is related to the various dimensionless variables by the equation:

B = 33.07

KQ'1/f512 = NP'1/V512 (8) 'hcre

N = number of revolutions per minute,

P = power in hp,

VA speed of advance in knots.

The speed ratio is defined as:

= 101.27/f = ND/VA

Curves, showing the efficiency ,defined as

KTJ

11e

2IrKQ'

the speed ratio , and the pitch ratio P/D corresponding to the optimum diameter, are given in Figs. 14, 15, 16,

17, and 18. Each figure is for one blade number.

Fig. 8 Cross-faired open-water

test results for B7-85 propellers for J,, = 2 x 106.

1:111

!:I.'i1l'

_N

_P

:

F: Ji:

II

'. .111:

IlL:1!

.iiIuÏ..

N

-r

uiVIvri4ii

j---t'áVIiÁL!

p

i

ìu

aun.

'-

I

I i

rnu

:i

N

r

-03 00 05 06 07 08 09 lo Is li 10 09 oe o, 06 C' o' 03 K, OC 0' (9) (IO)

Fig. 13 Bp-ó diagrams of B7-85 propellers based on cross-faired open-water test results for _{R0 = 2 x 106.}

33o

i/

/P

I!:

_{'4 t%ÒS$}

S

$$4Yv44'444A,

20 25 90 ¿D so 60 70 BD 90 lOO lID 120 I lOO ISO 167 170 180 199 200

Fig. 12 Bp-ö diagram of B6-80 propellers based on cross-faired open-water lest results foi R = 2X 1O.

'10 07 0,6 05 0.4 0.3 66 S' 14 1.2 to P/D 0.8 06 83 - 35 8 3 - 50 B 3 - 65 8 3 - 80 83 - 95 - 400 04 r i i i i i o 4 6 8 10 20 30 4050 100 200 300 B

33.08 f7jc

Fig. 14 Curves for optimum diameter of thrcc-bladcd

300 200 100 05 14 1.2 5 1.0 04-03 PIO 08 06 04 4 84 - 40 84 - 55 84-70 84-85 84 - 100 i i i I i___.J_._....__. ii I 6 8 10 20 30 40 50 100 200 300 B

Fig. 15 Curves for optimum diameter of four-bladed

B-B-series propellers at R = 2 x 106. , series propellers at R = 2 z 106.

500 400 300 200 100 5 0.7 500 06

06 05 0.3 14 1.2 10 P/S 08 0.6 04

ii

r _O 4 6 8 10 20 30 4050 100 200 300

/k/j

Fig. 16 Curves for optimum diameter of five-bladed

B-series propellers at R = 2X 106. 400 300 200 roo o 10 06 05 04 03 14 - 1.2 1.0 08 0.6 136 - 35 8 6 - 50 136 - 65 13G - 80 f36 - 95 (36 -110 04 i r r r

ir

o 4 6 6 10 20 30 40 50 100 200 300 33,0g

Fig. 17 Curves for optimum diamcter of six-bladed B-series

propellers al R,, = 2 x 106. 07 85 - 30 500 07 135 - 45 65 - 60 85 - 75 135 - 90 55 - 105 50G 400 300 o 200 100

68 6 7 - 40 87 - 55 87 - 70 67 - 85 67 - 100 0.11 1 I t I 4 6 8 lO 20 30 40 50 100

Characteristics of non-conventional propulsion devices

Gai¡eral considerations

The mair. requirerrens for a ship propeller aie, as

summarized by Van Manen [90]: - high efficiency,

- no adverse effects of cavitation, viz, erosion, - minimum vibration-exciting load fluctuations, - good stopping abilities,

- favourable interaction with the rudder to improve manoe uvrabi li ty,

- reliability and invulnerability, low initial and maintenance costs.

Due to its advantageous properties with respect to these requirements, the conventional ship propeller has dominated for more than a century among Ihe modes

of ship propulsion.

200 300

Fig. 18 Curves for optimum diameter of seven-bladed

B-series propellers at R = 2 x 1O.

In the designof recent-day ships such as high speed cargo ships and very large tankers with full hull forms, special attention has lo be given to the growing danger

°° _{of vibrations generated by the ship propeller. Recently,}

it was found that cavitation has a substantial effect on the vibratory forces acting at the stern of the ship and on the bending moments acting on the propeller shaft

400 [91, 2]. There is also a growing demand for thruster

systems which are able to improve the manoeuvrability and position-keeping ability of vessels, especially those vessels used for ocean exploration. These new trends in ship design demand a well balanced compromise

be-300

tween the main requirements for a ship propeller as already mentioned. Non-conventional propulsion devices

5 which may have advantageous properties over the

conventional ship propeller due to these new trends in

200 ship design are:

- ducted propellers, - overlapping propellers, - controllable pitch propellers, - contra-rotating propellers,

100

- vertical axis propellers.

-0f these propulsion devices the ducted propeller is by far the most important and therefore discussed in more detail in the section on ducted propellers. In the case

of heavy screw loads (all types of towing vessels) the attractiveness, with regard to propulsion efficiency, of the application of accelerating nozzles has been

demonstrated in practice in the course of the past thirty years. Recently, the field of application of ducted

propellers was extended tQ large tankers.

Other propulsion devices, which may be of use for high

speed craft, are the fully-cavitating or super-cavitating propeller [92, 93, 94], the waterjet propulsion system with internal pumps [95], the water-air ramjet [96, 97],

and the airscrew and ducted airscrew. For high speed craft the selection of the propeller type has a

dominat-ing effect on the whole design configuration. Controllable pitch propellers

Overlapping and controllable pitch propellers are two

special configurations of the conventional screw propel-ler. The controllable pitch propeller can be used succes-fully when good accelerating, stopping and

manoeuvr-ing qualities are desired or when in the operation of the

ship widely diverging speeds or widely varying degrees of loading occur [98, 99]. The attractiveness of applying

controllable pitch propellers lias already been

demon-strated in practice for tugs, fishing vessels, incebreakers,

07 06 14 05-12 10 04 e/O 08 0.3 0.5

ferry boats etc. The sblution of various mechanical and

cchnological difficulties and the development of

suita-ble control systems has recently led to the application to frigates and oilier warships and to various types of

merchant ships. Shaft horsepowers of up to 30000 are

flow being installed. The supreme stopping and

accelerat-ing properties of controllable pitch propellers promise continuing application of this propeller type.

Overlajpiitg prope/Icis

The overlapping twin screw propeller arrangement, see

Fig. 19, may soon find application in cases of high powered ships where the single screw soluiio«has to ha left out of consideration. From the results of various

model tests [100, 101] it cati be concluded that the reductions in DHP which cati be obtained with this

propeller configuration are of the order of 5 to 8 percent compared to the conventional single screw propeller and 20 to 25 percent compared to the

con-ventional twin screw arrangement. The hull excitation

ievel appears lo be somewhat higher than that of the conventional twin screw arrangement, but comparable

lo that of the regular single screw configuration. The cavitation properties of each of the propellers also appear to be comparable to those of the respective

conventional single screw configurations. Unfavourable

interaction of cavitating tip vortices, as shown in Fig.

20, can occur however.

Fig. 19 Drawing of overlapping twin-screw arrangement.

Fig. 20 Sketch of observed interference of tip vortices of

Vertical axis propellers

The group of propulsion devices in which a number of perpendicular mounted blades rotate around a vertic-cal axis are specified as Cycloidal Propellers', see Fig. 21. By means ola special mounting mechanism, each

blade is given a movemeCt whereby a thrust is created.

The vertical axis propeller is a propeller type with out-standing manoeuvring capabilities. Ferries, tugs and

supply vessles are examples of ship types where

succes-full application of the vertical axis propeller is

frequent-ly realized. Recent applications include ships and float-ing structures in the field of ocean engineerfloat-ing, where

dynamic positioning capabilities must be high. Future

prospects may be hidden in developing the vertical axis

propeller for very high speeds, in which case the blade motion ressembles the motion of a fish. Very high

efficiencies are then possible. Due to the peripheral

Fig. 21 Photo of model ship fitted with vertical-axis

pro-pellers. 70

variations in the effective angle of attack, however,

cavitation may set a bound to such high speeds [102,

103].

Contra-rotating propellers

The contra-rotating propeller arrangement may form a serious competitor of the conventional ship screw on fast and large container ships where the required power cannot be installed on one screw. However, applications

have not been realized up to date due to problems

involv-ed with the shafting system. Contra-rotating propellers

consist of two co-axial screw propellers situated a

short distance apart having opposite directions of rota-tions, see Fig. 22. The aim of such a propeller con-figuration is to reduce the rotational losses in the screw race. Results of open-water tests with this propeller type

show that in the case of light loads higher efficiencies

can indeed be obtained. Fig. 23 shows curves for the efficiency .,, the pitch-diameter ratio P/D and the speed

ratio for the optimum diameter of a conventional

screw propeller series (B4-70 series), an accelerating d acted-propeller and a decelerating-ducted propeller series (Ka 4-70 in NSMB nozzle no. 19A and Kd 5-100

inNSMB nozzle no. 33 respectively) and a

ing propeller series, on a base of B. This contra-rotat-ing propeller series has a 4-blade forward screw and a 5-bladed screw aft having a smaller diameter so as to avoid that the tip vortices of the forward screw interfere with the blades of the aft screw [104]. With such a

contra-rotating propeller series, low propeller induced

vibratory forces can be obtained. With respect to

Fig. 22 Photo of contra-rotating propeller arrangement

08 07 00 05 04 03 02 600 500 400 s 300 200 100 0.) 0 1.3 P/c 1.1 09 B L-70 serien Ka 4-70 in 19A -- Kd5-lOOïn 33 CRP series

Fig. 23 Curves for optimum diameter of different types of

propellers.

and

cavitation and stopping abilities, no marked advantages or disadvantages with respect to the conventional screw

propeller appear to exist [99, 105).

Ductc'd piopellers

Insight into the working principle of a ducted propeller

can be gained by the application of fundamental mo-mentum relationships. Fig. 24 shows the simplified

system by which the ducted propeller can be replaced. Here the screw propeller is represented by an actuator disk rotating at infinite angular velocity. The tangential

induced velocities and consequently, the losses due to 20 Olp 30 40 50 fo 200 300 LOO L/2 VA VP/VA

(loe rotation of the fluid are then zero. The influence of friction is neglected. With momentum ihcory the

follow-¡ng expressions for the ideal efficiency ij and the ratio between the velocity V, at the impeller llane and the

undisturbed stream velocity VA can be derived:

2 24 1.6 Os CT

V/I'4 =

0.90 070 ,tI 050 O - 030

Fig. 24 Control for volume momentum considerations of Fig. 25 Efficiency and mean axial velocity of a ducted

dueled propeller. propeller.

2

E- i +

_/'i

₊

(12)

t=Tp

₍₁₄₎

T

T and T denote the total thrust and the impeller thrust respectively; D is the propeller diameter. These formulas are graphically represented in Fig. 25. From this dia-gram it can be seen that due to the nozzle action the inflow velocity of the impeller can b either less or greater than the inflow velocity of an open propeller under equal condii ions. For a thrust ratio -r cua1 to 1.0, no force acts on the nozzle and the flow pattern is comparable with that of an open screw. With decreasing

valves of -r, the nozzle produces a positive thrust, the inflow velocity of the impeller is increased, and an

where T (13) PVA2 D2 70 100 0.25 0.5 2 _c1 ' 6 Pl VP

improvement in ¡deal efficiency ¡s found. For thrust

ratios greater than 1.0, a negative thrust or drag force acts on the nozzle, the inflow velocity of the impeller

decreases and the ideal efficiency ¡s lower.

Insight into the shape of the nozzle profile of a ducted propeller can be gained by means of Fig. 26. Here the

flow through different types of ducted propellers is

superimposed on the flow through an open propeller. Both the open- and the ducted propellers are designed for the same mass flow rate and velocity in the ultimate wake. Consequently the thrust and ideal efficiency of

these systems are equal.

DECELERATING

NOZZLE

t

ELE PATIN G

NOZZLE

Fig. 26 Streamline forms induced by diffircnt nozzle types.

The ducted propeller with the accelerating flow type of

nozzle is now used extensively in cases where the ship screw is heavely loaded or where the screw is limited in

diameter. The accelerating nozzle offers a means of

increasing tl:e efficiency of heavely loaded propellers.

The nozzle itself produces a positive thrust. In the case

of the decelerating flow type of 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 cari be ob-tained, which may be of importance for tactical reasons.

72

Although the idea of surrounding a propeller by a nozzle is very old, it was not until the early 1930's before the ductcd propeller came into praëtical use. Luisa Stipa and later Kort [106] experimentally proved the advantages which can be obtained by application of

the accelerating nozzle. These investigations clearly showed that an increase in efficiency can be obtained with this nozzle when applied in the case of heavy screw

loads. Primarily due to the work done by Kort, the application of ducted propellers behind certain ship

types (tugs, pushboats, supply vessels, trawlers) has

become common practice. This may be the reason that

the accelerating ducted propeller is frequently referred

to as the Kort' nozzle.

Many studies on ducted propellers have been made dur-ing the last 40 years. An extensive sum mary of this work was made by Sacks and Burnell [107] in 1960. A

general review of the more recent theoretical studies on

ducted propellers has been given by Weissinger and Maass [108]. Among the theoretical studies on ducted propellers the investigations of Horn and Amtsbcrg [109], Kücheman and Weber [I IO], and Dickman and Weissinger [1111

may be mentioned in particular. Especially, the work of Dickmann and Weissinger was a first step to develope a more refined theory for ductcd propellers. This paper was the basis for the work which has been performed

at Karlsruhe by Dickmann, Weissinger, Wiedemcr,

Boliheimer, Brakhage, Maass and Rautmann. Some of the basic ideas used at Karlsruhe were also used by other investigators such as Ordwy, Ritter, Greenberg, Rough, Kaskel, !.o. Sluytcr, Sonnerup,

Morgan, Caster, Chaplin, Voight, Nielsen, Krievel, Mendenhall, Sacks, Spangler etc.

Most of the theoretical investigations on ducted propel-lers were concentrated to a large extent on the lineariz-ed theory and on axisymmetrical nozzles in a uniform flow. These theories do not give data about the danger of

flow separation on the nozzle. 1f flow separation occurs, which may happen if the nozzle is very heavily loaded, the drag of the nozzle will increase sharply. The efficien-cy of the system will decrease and the propeller will

operate in a highly irregular flow. Flow separation on the nozzle surface should be avoided. For the design of a ducted propeller it is therefore necessary to have available a sound theoretical method supported by the

results of carefully seiected systematic experiments.

A comparison of theory and experiments on ducted propellers has been made by Morgan and Caster [112]. Tests on ducted propellers are scarce, however, and

-most of these tests arc restricted to isolatcd applica-lions. By far the most extensive systematic experiments

on dueled propellers for application on ships have been

performed at the NSMB over the last 20 years. These investigations included nozzles of bolli the accelerating [113, 114, 115, 116, 1 7] and decelerating [118, 119] flow type.

Accelerating nozzles

The investigations on accelerating nozzles have led to

the development of a standard nozzle (nozzle no. l9A) for application in the case of heavy screw Iqads. This nozzle has, from the structural point of view, a simple shape. The inner side of the nozzle at the location of the screw lias an axial cylindrical form. The outside of the nozzle profile is straight and the trailing edge of the

nozzle is relatively thick. The profile of nozzle no. I 9A is shown in Fig. 27.

Fig. 27 Profile of nozzle no. l9A of the NSMR.

For use in nozzle no. I 9A, special screw series (the so-called Ka-screw series) were designed. Screws of these series have relatively wide blade tips which niake theni less susceptable to blade tip cavitation Extensive investigations performed at the NSNI}3 have led to the

design of these series having uniform pitch and fiat face

sections. The results of the experiments mentioned show

that this type of screw has no drawbacks with respect

to efficiency and cavitation. The particulars of these screw models are given in Table 4 and Fig. 28.

Nozzle No. 19A has a length-diameter ratio LID equal to 0.5 For application on pushboats and tugs, nozzles with larger length-diameter ratios may he attractive.

Therefore two other nozzles were designed of which the

basic form is equal to the shape of nozzle no. l9A,

possessing length-diameter ratios LID of 0.8 and 1.0. These nozzles were designated as No. 22 and 24. The backing characteristics of these nozzle types are

¡111.:

-1

Ka h S S

Fig. 28 Blade planlorm of the Ka-series propellers.

rather puer. For towing vessels (espeia1ly pushboats).

the thrust which can be developed at bollard pii11

condition either with the propeller running ahead or astern is of the utmost importance. In such cases it is attractive to tise a nozzle with a relative thick trailing

edge. Therefore, a new type of nozzle, especially suited for astern operation was developed. The profile of this. nozzle is given in Fig. 29. In comparison with nozzle no. 19A, this nozzle (designated as nozzle no. 37) lias a well-rounded and relatively thick trailing-edge. This prevents flow separation in reversed condition.

Open-water tests were performed with all these nozzles in combination with the Ka 4-70 screw series. The fair-ing of the open-water test results was performed by

.1-w)

Table 4 Dimensions of the Ka-screw series.

Distance of the ordinates from the maximum thickness

From maximum thickness to trailing edge

R

56.44 Length of blade

section at 0.6 R =

total length 67.15 76.59 122.88

100% 80% 60% 40%

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

means of regression analysis and the polynomials together with the coefficients are given in Tables Sa and

Sb. The open-water diagrams are given in Figs. 30, 31,

32 and 33. 74 1.0 56.44 = 1.969

±

AE/Ao Maximum thickness 0.50 at centre of shaft = 0.049 D

From maximum thickness to leading edge

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

rl

Ordinates for the back

0.2

-

38.23 63.65 82.40 95.00 97.92 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 37.37 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 7;.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 20.21 7.29 1.77 0.1

-

0.21 1.46 4.37 10.52 16.04 20.62 33.33 0.3 13.85 4.62 1.07

-

-

0.12 0.83 2.72 6.15 8.28 10.30 21.18 0.4

9.7

2.36 0.56

-

-

-

0.4.1 1.39 2.92 3.89 4.44 13.47 0.5 6.62 0.68 0.17

-

-

-

0.17 0.51 1.02 1.36 1.53 7.81 0.4 0.5 0.6 0.7 0.8 0.9 41.45 45.99 49.87 52.93 55.04 56.33 43.74 47.02 50.13 52.93 55.04 56.33 85.19 93.01 100.00 105.86 110.08112.66 3.00 2.45 1.90 1.38 0.92 0.61 46.02 49.13 49.98 nR 0.2 0.3

from centre line 30.21 36.17

to trailing edge

36.94 40.42

froni centre line to leading edge Length of the blade

sections in percentages of the maximum length of the blade section

at 0.6 R

4.00 3.52

34.98 39.76

Max. blade thickness in percentages of the diameter

Distance of maximum thickness from leading edge in percentage of the length of

Table Sa Cocílìcienis and terms of the K.,-, K.,- and K0 polynomials of the Ka 4-70 screw series in nozzles nos. 19A and 22.

x y

Nozzle no. 19A Nozzle no. 22

Ax)' Bxy Ccy Axy Ax)' Cx)'

o o o 0.030550 +0.076594 ±0.006735 +0.008043 +0.001317 ±0.032079 1 1 -0.148687 ± 0.075223 2 2 -0.061881 -0.016306 -0.208843 -0.020219 3 3 -0.391137 -0.138094 -0.902650 -0.021294 4 4 -0.007244 -0.937036 5 5 -0.370620 -0.369317 6 6 +0.323447 -30.682898 7 1 0 -0.271337 -0.102805 8 1 -0.432612 -0.687921 -0.661804 0.559885 9 2 -1-0.225189 -0.024012 +0.752246 10 3 _+0.951865 11 4 -0.376616 12 5 _-0.159272 13 6 -0.081101 14 2 0 +0.667657 +0.666028 -3-0.720632 +0.371000 ±0.140281 15 1 16 _{2 ±0.285100 H-0.734285 +0.005193} 17 3 18 4 19 5 20 6 21 3 0 -0.172529 -0.202467 ±0.046605 -0.202075 -0.096038 -0.026416 22 1 +0.011043 23 2 -0.542490 24 3 25 4 26 5 27 6 -0.016149 28 4 0 -0.007366 29 1 30 2 31 3 +0.099819 32 - 4 33 5 34 6 35 5 0 36 1 +0.030084 -0.008516 37 2 38 3 _-0.093449 39 4 40 5 41 6 42 6 0 -0.001730 43 1 -0.017283 -0.000337 _{+ 0.005229} 44 2 -0.001876 +0.000861 45 3 _{+ 0.045373} 46 4 _{-0.000 195} 47 5 48 6

Table 5b Coefficients and ternis of the KT, KTN and KQ polynomials of the Ka 4-70 screw series in nozzles nos. 24 and 37.

X y

Nozzle no. 24 Nozzle no. 37

Axy Bxy Cxy Axy Bxy Cxy

0 0 0 -0.068666 -0.026195 +0.023557 --0.162557 -0.0l6S06 0.016729 i i ± 0.098268 2 2 -0.483300 -0.016989 3 3 _{-1.190490 -0.838832} 4 4 -0.077387

55

6 _{6 + 1.005980} ±0.555129 0.082386 -0.099544 ±0.030559 7 1 0 +0.242630 ±0.109624 +0.072021 -0.598107 0.048424 8 1 -0.781923 -0.681638 -1.009030 -0.548253 -0.011118 9 2 ± 1.136930 ---0.773230 ±0.230675 -0.056199 10 3 _-0.037596 11 4 -0.034871 12 5 13 6 14 2 0 ±470803 ±0.259217 +0.103364 +0.085087 +0.460206 ±0.083476 15 1 +0.425585 16 2 _+0.045637 17 3 _-0.042003 iS 4 -0.131615 19 5 -0.276362 20 6 21 3 0 --0.121062 -0.058287 -0.013447 .-0.216246 -0.008652 22 1 23 2 24 3 25 4 26 5 -0.021044 27 6 ±0.013180 28 4 0 _-f-0042997 29 1 30 2 _-0.012173 31 3 +0.046464 32 4 -0.035041 33 5 34 6 35 5 0 36 1 --0.038383 37 2 38 3 -0.044629 39 4 40 41 6 42 6 0 43 1 -0.001176 44 2 -0.014992 ± 0.002441 45 3 + 0.026228 46 4 47 5 48 6 ±0.009323 49 0 7 -0.239044 -0.049039 +0.036998 +0.051753 - 0.012160

O 7 03 O' O' 00 06

Fig. 30 Open-water test results of Ka 4-70

screw series in nozzle no. 19A.

Fig. 31 Open-water test results of Ka 4-70 sciew series in nozzle no. 22.

K LQ SCREW NOZZLE SERIES N2.IRA --uIN

!UI

Ju

u

O

iiI

ui

u

i!

4iui

u..

_u

L

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02 K.'.,

u....

-

IIIii

K 0.10 SCEW SERIES

IN NOZZLE 10022 I

. uuuuiuiu

uuuuu uu u

-u

u.. u

u

:riL

1Ui1ii:

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ifrÀI&

u um s

uuuuu

R

uuuu

Ql 08 00 QQ 12 O' 02 O) Oh w 02 03 0L 02 06 J w OB 09 BO ti 12

ti a o 0 78 J

Fig. 32 Open-water test results of Ka 4-70

screw series in nozzle no. 24.

Fig. 33 Open-water test results of Ka 4-70

screw series in nozzle no. 37.

- -

u

L-76 SCREW SOPlES IN N0ZZE NOiE

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'iIì0

1'

U

j k

I11!!iuIiIiIi!

,fr

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ft0.

fl

Ijil

IIIIIIIIIIIII

1;!JHIIHIIHHIII

lin

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I

UUUUUUUUUUUUUUUUUUUU

1I1IIIHIIIHIHHIII

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03 GO as 06 j 07 03

Important factors i the selection ol' a propulsion device

for tugs, pushboats etc. are: - the forward static bollard pull, - the astern static bollard pull, - the free-running speed.

A comparison between the forward static bollard pull of nozzles nos. 24, 22, 19A and 37 and a conventional

screw series (the B4-70 series) can be made with the aid of Fig. 34. In this diagram the thrust coefficient KT, the torque coefficient KQ, the impeller thrust-total thrust ratio T and the efficiency coefficient of the different

propulsion devices are given on a base of the pitch

ratio F/D. The efficiency coefficient 11d is defined as:

This efficiency can he used as a direct measure for the effectiveness of different propulsion devices at the static

condition, if systems with the same diameter and power

are considered. However, this coefficient must not be used if there are restrictions in choosing the RPM of the

different prol)UISiOfl devices.

o

06 1.0 1.2

P/

Fig. 34 Characteristics of different propulsion devices at

forward static bollard condition.

(15)

14 16 19

From Fig. 34 it can be seen that for ducted propellers

the efficiency coefficient qj is much higher than for

conventional screws. Further, it can he seen that the

effect of nozzle leiìgtli on 17d is small. With increasing

length-diameter ratio of the system a slight increase in

the efficiency factor ?/j has been found.

A comparison between the astern static bollard pull of

nozzles nos. I 9A and 37 and the 134-70 screw series

can be made with the aid of Fig. 35. From this diagram

it can be scen that the efficiency factor tid for nozzle no.

37 is much higher than for nozzle no. 19A. This can be explained by the fact that nozzle no. 19A suffers from

flow separation when operating astern. The efficiency

factor Jd of nozzle no. I 9A is still higher than the value

of this factor for the B4-70 screw series.

1,8 17 1.5 1.5 13 1.2 10 K1 10K0 0.5

Fig. 35 Characteristics of different propulsion devices at

astern static bollard condition.

For the method of selecting the propulsion device based

on the free-running speed of the vessel, more practical information can be derived from the KTKQ--.J diagram.

The most widely encountered design problem for the screws of cargo ships is that where the speed of advance

(Kr/2t)3"2

'/a=

KQ

o