Proposed propeller diagrams for preliminary design

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ARCHIEF

HITACHI ZOSEN TECHNICAL REPORT

Proposed Propeller Diagrams

for Preliminary Design

By T. Tan imoto

August 1968

HITACHI ZOSEN

TECHNICAL RESEARCH LABORATORY: OSAKA, JAPAN.

HITACHI SHIPBUILDING & ENGINEERING CO., LTD.

y. ScJieepbou,nd,

Technische Hogeschool

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Summary

This paper deals with a new type of propeller diagrams by which much convenience will be expected in the

prelimi-nary stages of propeller design. These diagrams have been derived from the experimental results of AU - Series properers conducted by the Ship Research Institute, the Ministry of Transportation of Japan, and Dr. Nakajima's cavitation criterion.

In the early stages of ship design, the optimum pro-peller diameter or the rate of revolutions, pitch ratio and the corresponding propeller efficiency can be easily found

with these diagrams. In addition, it is also possible to

know whether or not a propeller designed by the use of the diagrams suffers from cavitation.

Introduction.

A lot of systematic propeller series have been tested for marine propeller design by various researchers and organizations: the results which are currently used in this country are those of the so - called AU - Series propeller

tested by the SRI*.

They have been published as design diagrams which are represented on the basis of the Bu-ô system like

Taylor's diagrams. It is needless to say that they are useful to practical design, but some complicated calcu-lations are required even when they are used in the early

stages of design. Additionally, the SRI diagrams do not

include those based on the

Bucl

system, and .are

unavailing when thrust or effective horse power is given

at first. There they have their disadvantages.

Furthermore, considerations for cavitation are

indis-pensable in propeller design at present the proper

particulars of a propeller are determined by using the SRI

diagrams together with other diagrams or formulae for

cavitation criteria. Under these circumstances, a great

deal of convenience will be expected if a diagram would simultaneously give the cavitation criterion as well as the optimum particulars regarding propeller efficiency in the preliminary design.

The author developed new simple diagrams, i which

the results of the SRI AU-Series propellers and a cavitation

criterion based on Dr. Nakajima's method are incorporated..

According to these diagrams, it will be possible in the

early stages of design to know whether or not a designed propeller, regarding the best efficiency under given con-ditions, will suffer from cavitation.

New Design Diagrams.

2.1 Symbols.

Symbols used in this paper are those generally used, and are as follows.

Symbols:

Shin speed in Knt.

V Advance speed of propeller in meters per second.

* The SRI is the abbreviation of the Ship Research, Institute, the Ministry of Transportation of Japan.

N Revolution per minute.

n Revolution per second.

D Propeller diameter in meter.

T Propeller thrust.

Q Propeller torque.

K1 _{Propeller thrust coefficient. =}

T/pn2 D4

Kq _{Propeller torque coefficient. =}

Q/pn2 t)

J

Speed coefficient of propeller. = V, mD

77 Propeller efficiency.

w _{Taylor wake fraction.}

Thrust deduction coefficient.

EHP Effective horsepower.

DHP Delivered horsepower.

Kid K1 / J2

Kqd

K1 K1 / j4

Kq/J5

2 .2

Description of New Diagrams.

In the Schoenherr-type diagrams, the line " '7max,

for K171 const. " or 17max,

for K, constant,

is

pre-sented. The SRI results were reproduced in the way of

Schoenherr's in the first place. Various values of Kid or

K1 in a reasonable range were given next, and the

parabolas K1 _- _Kid

x J? or K1 = K,0 x j

were

drawn on the diagram: Kid or K,5 being the given

values. Each point where the parabolas cross the " 7max.

lines was represented in a separate diagram with KId

or K,7 as the abscissa and J, pitch ratio and '7 as the

ordinate. A_,,, _{corresponding to J and} _, _{for given}

can be calculated in the same way. Kqd and Kqn are

also plotted on the basis of Kid and K,5 respectively

Kid can be easily calculated, and Kqn for given K,0

in the separate diagrams. These are very handy diagrams to find the optimum pitch ratio, propeller diameter or rate

of revolutions, and eventually the corresponding '7: they

are the diagrams for '7ma

2 .3

Introducing, a Cavitation Criterion

in the Diagrams.

A cavitation criterion curve based on NL. Sima ' s

method is incorporated in each of the diagrams for '7max..

and these are the proposed initial design diagrams. The

way how to relate the cavitation criterion to the diagrams

for '7max. iS as follows.

Dr. Nakajima's cavitation criterion is expiessed by the critical number of propeller revolutions, and it is as

follows.

*2 n

52D2(J2+8.0)iP/q (1)

It has been well known that cavities are formed on a pro-peller blade when the local pressure becomes equal to or numerically smaller than the vapor pressure of the water. The condition is expressed as follows:

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Dividing by the stagnation pressure q= -p V2.

P0 Pd JP

₍₂₎

PV2 q

where y is the intake velocity of the water to the propeller blade, and the term on the left side is usually defined as

the cavitation number, expressed by o-. In Eq. (2), the

critical condition of the formation of cavities is,

P0

Pd j

FP V2q

or

P0Pd

72

JP/q

2P .=-p Vi2+(2rrn)2 rLp V2(1+80/J2)

where V1 is the advance speed of the propeller. For

practical convenience, the cavitation number o- is modified

by adopting V1 instead of V : a new coefficient o- *

named here the cavitation criterion coefficient, is intro

-duced.

From Eqs. (3) and (4),

*_PoPd

_{iP/q1l+80/J2)}

- P V2

or

o- *J2= (J2- 8. 0)J P/q ₍₅₎

Putting Eq. (5) into Eq. (1), we get

*2 P0 - Pj (6)

52D2J2o- *

The critical number of propeller revolutions n* is found

at once on the basis of o- *

The values of o- * are calculated for a given pitch

ratio at various values of

j

within reasonable limits

the pitch ratio is taken from 0.55 to 1.0 at proper

inter-vals. The calculated result of the MAU4 -0.40 is shown

in Fig. 1 with o-' as the ordinate,

j

as the abscissa,

and the pitch ratio as a parameter. The others are shown

in Figs. 12-19 with J2o-* inplaceofo-*.

For an optimum pitch ratio and

j

obtained from the

diagram for '7max.. mentioned in 2.2, depending upon

given Ktd

or K,

, o-* can be found from Fig. I and

Figs. 12 l9.o-*thus obtained for various Ktd

or K10 are

plotted on the diagram for 1 and the new design

diagrams are completed. These design diagrams are

shown in Figs. 2 - 9. (3) o 0.9 08 Q7 06 05 o 2 d 08 05 Lo -Pitch Ratio 055 0.3 04 05 MAU 4-040 Fig. I U B 3 -G35,0.C(Constont Pitch) V

î

03 DHP Kd =0.8384 CI-w )3D2 VS3 l2_ _{2DzJ2c1 ,DO864}P=P4 Vs(L-w) NJ 0.5 06 Fig. 2 Foce Covitotion Bock 07 08 09 0.2 n b 17*_Po

'd

(4) I5 Io 0.4 03

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Io 09 08 07 o o

o-t

07 -06 -05 035 UB 3-Q35,Q50 (Constant Pitch) 3 ElPxN Ktn -4 0HPN2

I<t 8.80IxI0 _{(I-w ItV}

DJ 864 Mi-w)

5202J2OI N'S

Fig. 3

MAU 4-0.4O,O(Constant Pitch)

HP I(td = 5.268( -t >Ii _w)2v.3 0H P <qd0.83841_{I-w)3 02V53} LO 09 08 07 06 05 0.4 040 040 EHP Krd 52G8U:(I W)2V D2

Dz(c2

0H P Kgd =Q8384) _)3v93 2 D = 3Q4 Vs(I-w) 055

MAU '--0.4O,Q55(Ccnstant Pitch)

Kç, = 5.5Ox)O3_{Ii - t)II-w)4VX3}EHP X N

DHPX N2 Kqrt8.80IxI0(1)33

)08

2= Dr%'2 ,D30.864 Vs)I-w)_NJ 07 0.40 055 - .F 06 055 05 AU5-Q50,O.65(Ocnstant Pitch) 065 05 5 Q4 ilS Io 04 0 2 2 3 08 .2 r .0 07 05 05-o 02 03 05 06 07 08 I.I .2 1.3 1.4 .5 1.6 7 8 -Fig. 4 Fig. 6

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08 07 06 05 03 5

el

0. .0-04-09' 0.7 06-05

04-Ktn 530XIQ3 EHPX N2_{(i- t XI-w}

D t'4 po N2 Kqt8.801X10' (Iw)kxVO

¡-

_{- D2J252,}

_D-J864,

0.70 055 065 065 OSO 4 3 2 6 7 8 9 IO Fig. 7 0.56 0.70

AUw 6-0.55,070(Constant Pitch) <td5.268 (I-tIll D' DHP K0d0838411_-w)V,D° *2_ - DJO52 ,D-(.864 vHW) 070 055 Kqd tcn Rotio O") Sock) 055 Fig. 9 Kt, IO

3. .4 1)esign Example based on the New Diagrams.

Propeller design problems in the preliminary stages

generally belong to the following categories. The procedure of applying the new diagrams is illustrated on each category. ¡ (1) Given: The design speed of ship V , the

corre-06 sponding EHP and the rate of revolutions N . Required:

The optium propeller diameter D pitch ratio and the

corresponding propeller efficiency

K,5 _{is calculated on the basis of the given data,}

esti-mated value of wake fraction and that of thrust deduction

coefficient, pitch ratio,

J and

o' * _{is easily foundfrom}

the

' diagram for K5 '. The diameter is derived from

J , and N* from o' *

(2) Given: The delivered horse power DHP (in place of EHP ), and the others are the same as case (1). Required: The same as case (1).

A'q5 _{is calculated on the basis of the given data and}

estimated wake fraction, and the corresponding K,5 is

read in the diagram. Subsequently, the required values

are easily found on the basis of. K15

15 (3) Given: The design speed of ship V5 , the

corre-sponding EHP and the propeller diameter D

Required: The optimum pitch ratio and the rate of

revo-lutions , and the corresponding propeller efficiency.

K1d is calculated first, and the required are obtained

from the diagram for _Kid in the same way as case (1).

(4) Given: _{Delivered horse power DHP (in place of}

EHP ), and the others are the same as case (3).Required: The saine as case (3).

07

15

05-lo

AUw 6 -055,070 (Constant Pttoh)

U 5-0.50,O.65(Constant Pitch) 065 0.50 J L2 1.3 1.4 1.5 1.6 7 Fig. 8 IS 04 = 553JXIo'12).

Kqn =aaoixio,,

52J4', D3O.4 Vs(t-W) 6 8 9 IO II

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Kq(/ _{is calculated on the basis of the given data and}

estimated wake fraction, and the corresponding Kid is

read in the diagram. The required are obtained on the

basis of Ktd

For example, a preliminary design of a MAU4 - 0.40 propeller will be tried by the new diagrams under the

following conditions.

Given: V, = 18.8 kt., normal power of the main

engine 10,625 BHP x 109 RPM , wake fraction = 0.28.

In the first place, Kqn is calculated on the basis of the given conditions. The result is Kqp = 0.239, and K1

corresponding to the Kq is found 1.01 from Fig. 5.

The required pitch ratio, J 7) _and o * are read on the

basis of the K,

. D and N* are

deduced from J and

* respectively. The result is shown in Table 1. The

table also contains the results based on SRI 's original

Bu-ô diagram. Slight differences between the two

results are due to the difference of the fairing procedures, and have nothing to do with the correctness or any of these two diagrams. D N* (m) (RPM) 85 0.810 6.23 _{Backcavitation} 0.616 0.677 0.805 6,23 Preliminary Design Chart Chart 05-04Q Table 1

J

'7 0.616 0.674 UB 3-035,0 FROOST 3-035.050 .3 EI-4P,N Ktn _{555JXI0 (I-t)lI-w1V,5} Kqn B8DIx Fig.io Pitch Ratio

4. Comparison of Propeller Characteristics

between AU-Series and Troost-Series

Propellers

One of the advantages of the new diagrams is easy comparison of the characteristics of different propeller series. As the Troost propeller series are very popular, next to the SRI ones, among engineers in this country, the results of the Troost series are also arranged in the

same manner as the new diagrams. The SRI-Series and

Troost ones were compared in the form of the new diagrams based on K5, Fig. 10 shows the results of 3 - bladed propellers and Fig. 11 those of 4-bladed propellers.

According to these figures,

it is clear that the

Troost

series are inferior to the SRI AU-series both inefficiency

and in cavitation. However, there was one exception:

a 3-bladed propeller with 0.35 E.A.R. ,which was superior to SRI series with regard to cavitation. It is natural that the SRI AU - series have been found better, because the Troost series were used as a base for the development

of the SRI AU-series, which depended upon modern

knowledge of propellerhydrodynamics -TROOST 4-040.055 MAU 4-0.40.055 EHP N2 Ktr _{5530xI0'1Ì,)1I -wl'V,'} Kn .&80lXI005 2 P,-P fl _52D2.J2&* D -30864 .Jw1 Fig. II

-

K,, 1.2 io 09 08 Q? 06 05 04 03 o o 5 o 2 3 4

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8 o:Th b -) 8 03 04 05 06 0.7 J=_v.__ nD Fig. 12 MAU 4-0,40 MAU 4-055 2

-

8

Fece Ccvi tofion

..-Back o Foce Cavitation Back Foce Covitaton Back

//8/ /

03 04 05 06 07 08 09 LO _L, no Fig. 14 8 cf cf 2 8 6 AU 5-050 o 0.3 0.4 0.5 06 CL7 08 09 1.0 j=_L. nD Fig. 16 AU 5-0.65 03 0.3 04 05 06 07 08 09 10

- J=--.

_nD Fig. 17 AUw 6-055 05 io-06

_jiL.

07 nO Fig. 18 AUw 6-0.70 In

Foce Covitat ion Bock Foce Cavitation Back

/ /

09 .0 Foce Cavitation Bock io o 03 04 05 0.6 07 0 .0 03 04 05 06 07 08 09 1.0 Fig. 15 Fig. 19 03 04 05

-

06 0.7 08 09 I.0 no Fig. 13 09 1.0 8

/

f2

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5. Conclusion.

A new type of initial design diagrams for the marine

propeller have been proposed the diagrams are based on

the results of the SRI AU-series propellers. Moreover,

a cavitation criterion based on Dr. Nakajima's method is

incorporated in the same diagrams. In the preliminary

stages of design, the optimum propeller pitch ratio, and

diameter or the rate of revolutions, and the corresponding propeller efficiency under given conditions can be easily

determined by the new diagrams. It is confirmed by

comparison in the form of the new diagrams that the SRI

AU - series are better than the Troost ones both in

efficiency and cavitation characteristics.

Acknowledgement

This paper is published by permission of the Technical

Research Laboratory of Hitachi Shipbuilding &Engineering

Co., Ltd. The author wishes to express his thanks to Dr. Takagi of the Laboratory for the kind and useful advices.