Optimum diameter 3- 4- and 5-blade screws for large tankers

(1)

ARC,.

See note inside cover

L:2 V. ; E

Deitt

NATIONAL PHYSICAL

LABORATORY

SHIP DIVISION

OPTIMUM DIAMETER 3- 4- AND 5-BLADE

SCREWS FOR LARGE TANKERS

by

T. P. O'Brien

(Reprint from Shipbuilding and Shipping Record,

17th November 1966)

A Station of the

Ministry of Technology

SHIP REP. 95

(2)

Extracts from this report may be reproduced

provided the source is acknowledged.

Approved on behalf of Director, NPL by

Mr. A. Silverleaf, Superintendent of Ship Division

(3)

Reprinted from Shipbuilding and Shipping Record, November 17, 1966

Propellers

Optimum diameter 3- 4- and 5-blade screws

for large tankers

THIS ARTICLE discusses the effects of varying the number of blades of marine screws and refers to recent published work concerning the comparative performance of 3-, 4-, 5- and 6-blade screws of the same diameter when operating under both non-cavitating and cavitating conditions. It describes optimum diameter and blade area charts and it derives correction factors which enable the data previously given to be extended and the effects of variation in screw dia-meter to be studied. The results are given in the form of corrections which enable 3- and 5-blade screws of optimum diameter to be designed and comparative performance estimates to be made using data for 4-blade screws as

1 Introduction

Work previously published based on

research at NPL into the effects of

variation in number of blades on model screw performance has been limited in

application to screws of the same

diameter. The basic experiment results are given in the paper (Reference 1) and practical applications to screws for tugs, passenger vessels and tankers are given in the articles (References 2, 3 and 4). The work previously published gave design data and correction factors enabling 3-, 5- and 6-blade screws to be designed and comparative estimates of their performance to be made using 4-blade standard series data as the bases. The correction factors were derived on the basis of constant diameter.

The object of the present article is to combine the results previously given and to extend the data to enable additional effects of varying diameter to be studied and give the results in a form enabling

screws of optimum diameter to be

designed and to apply the results in

designing additional

3- and 5-blade

screws for a tanker for which the design

calculations for 4-blade screws have

already been made.

2 Correction factors

In designing screws of unrestricted diameter to absorb a stipulated delivered horsepower DHP (or to apply a

stipu-lated thrust horsepower THP) when

running at given rate of rotation N with the screw advancing a speed of advance VA in propelling a hull at a correspond-ing speed V, the diameter can be selected using either the B,,-8 or B u-8 charts (Reference 5) and procedures for doing this are discussed in the book (Reference

8). Alternatively,

the optimum

dia-meter and Blade Area Charts given in this book can be applied. In applying

B,,-8 charts the design conditions are linked to a delivered horsepower co-efficient B,, and a speed coco-efficient 8 defined by B A2

N jeRDHP

,, sVA

8 =

ND VA

where N is the rate of rotation in revolutions per minute D is the screw diameter in feet

is the relative flow factor as defined by equation 6 DHP is the delivered horsepower

in British units

s is the specific gravity of the

fluid

in which the screw

operates (average value for sea water s = 1.206)

V4 is the speed of advance of

the screw in knots which can be linked to the speed Of the

hull

V, using

the :wake

fraction WT defined by V4 = (1-w )V,

In using either the Be-8 charts or the

Optimum Diameter and Blade Area

Charts the thrust horsepower coefficient B u replaces the delivered horsepower coefficient 13. It is defined by

B u =

V A2 s V A

N /THP

and it can be derived from the delivered horsepower coefficient using the relation

B u

=

vn,

where THP is the thrust horsepower in British units

is the screw efficiency in uniform flow in open water which is linked to the screw efficiency in non-uniform flow behind the hull 71B by the relative flow factor e defined by

71B= Rn0

T. P. O'Brien, C.G.I.A., M.R.I.N.A. Ship Division, National Physical Laboratory the bases. It gives worked examples on designing additional 3-blade and 5-blade screws for a large tanker for which the design data for a basic 4-blade screw are available. For the basic 'i4-blade screw the screw efficiency and propulsive efficiency, were 71 = 0.485 and n = 0.703, respectively.

For the 3-blade screw the relevantl performance values were 7),9 = '0-500 and 7), 0-725 while for the 5-blade screw they were 720 = 0485 and )70 = 0.703, respectively. Thus, if the vessel were fitted with a replacement screw having three instead of four blades this would result in an increase in efficiency of 3 per cent.

Some of the optimum diameter and blade area charts originally given in the books are reproduced in Figures 1, 2 and 3. Procedures for using these charts are described and worked examples are

given in the article2.

Each chart

comprises two parts: a contour chart which enables the blade area ratio aE to be assessed; and a graph from which the

screw diameter D pitch ratio p and

screw efficiency no can be obtained. The contour chart comprises contours of cavitation number c r ," on co-ordinates

of square root of thrust horsepower

coefficient B u and expanded blade area

ratio aE. The cavitation number is

defined by

2(p.8-e) cr.8

Pv 2

where (p.8-e) is the static pressure

measured at the x = 0.8 radius fraction of the screw when at minimum immer-sion.

v is the speed of advance in feet/ second

p is the mass density of the fluid in which the screw operates (for fresh

water p = F938, for sea water

p = 1.988).

The optimum diameter and blade area charts can be applied in deriving correc-tion factors which would enable the geometric features (diameter D, pitch ratio p and expanded blade area ratio aE) and screw efficiency no of either 3- or 5-blade screws to be derived from those of basic 4-blade screws and a procedure for doing this is as follows:

First, a series of values of speed

coefficient 8 pitch ratio p1 and screw efficiency 71013 all related to a constant blade area ratio aE (a convenient value is aE = 0-55), are obtained from the optimum diameter and blade area chart

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for the basic 4-blade screw (Fig. 2).

Next, corresponding values of these parameters for the non basic screw are obtained (3-blade, Fig. 1 or 5-blade, Fig. 3). This enables the following correction factors for departure from four blades to be evaluated.

The screw diameter for the non-basic screw D is derived from that of the basic

(4-blade)

screw Di by applying

a

diameter ratio ki defined by

D 8

(8)

=

where 8i is the speed coefficient for the basic 4-blade screw (Fig. 2) 8 is the speed coefficient for the

non-basic screw (Figs. 1 or 3)

The blade

area ratio and screw

efficiency are derived in a similar way using ratios k, and k3 defined by

k, =

aEi

k,

7/01

where aE, and7101are the blade area ratio

and efficiency

for the basic

four-blade screw (Fig. 2) aE and no are the blade area ratio

and efficiency for the non-basic screw (Fig. 1 or 3)

The blade area ratio correction is derived on a basis of constant

cavitation number a4.8.

In deriving the pitch corrections a procedure similar to those discussed above is followed, but here an additional correction needs to be made. The data on which the optimum diameter and blade area charts are based are those of the Troost B standard series'. For this series both the 3- and 5-blade screw had uniform pitch, but the 4-blade screws had non-uniform pitch (constant over outer region of the blades with reduced

values near the boss and relation

between maximum pitch pT and mean

pitch p given by pT= 1-016 p.).

Con-sequently, the pitch correction is defined by

k4 = = 1016

-Pi

Pr

where PTis the pitch ratio for the basic

4-blade screw

Pi is the mean pitch ratio for the basic 4-blade screw (Fig. 2) p is the mean pitch ratio for the

non-basic screw (Fig. 1 or 3)

A procedure for deriving

blade-thickness correction factors based on the Taylor strength criterion (Reference 7) is as follows:

An approximate equation for the

compressive stress Sc at the blade

sectional element at the x = 0-2 radius fraction is given by

S ,DHP

S2

-BND372

C.2--D

where S2 is a coefficient the value of

Table 2-Screws 6 and 7-Design Calculations

Hence, equation 12 can be re-stated in the form

S2DHP

S, =

KND'aE1-2

Applying the condition of constant stress to two screws of different diameters and different blade area ratios, absorbing the same delivered horsepower at the same rate of rotation, the blade-thickness correction is given by

k6 = 17i

=

-35D 1)3/2 CEIS 2) which reduces to

1

k 6 = = k13 12 (k5k2)

where ki and k, are the ratios defined by equations 8 and 9

and k

is the ratio of the strength

coefficient S, for the non-basic

aES 21

Table 1-Correction Factors For 3- and 5-Blade Screws-Optimum Diameter

co a, 'a u, it .... 0 ci 2

Power coeff. Corrections to basic (4-blade) screw values

Bu

Diameter Blade area Efficiency Pitch ratio Thickness ratio D

tir

as n01no P PL T .r, as, ki k,

i

.t.° 10 20 30 1055 1.045 1.035 0.825 0.815 0.825 1.015 1.020 1.030 0-915 0.925 0.925 1.06 1.08 1.07 ao 40 1.035 0.825 1.030 0.935 1.08 F..' .o 1.... 50 60 1.035 1.025 0.830 0.835 1.030 1.030 0.950 0.985 1.07 1.06 10 0.970 1.090 0.960 1.080 0.97 0 ₂₀ _0.975 1.095 0.985 1.030 0.98 -ig .3 30 0.975 1.105 0.995 1.020 0.98 .ca 40 0.970 1.100 1.000 1.030 0.99 2 50 0.965 1.100 1.000 1.045 0.99 gl.: 60 0-955 1.105 0.990 1.085 0.98

Basic screw (screw 1) D=23.25,1, four blades as=0.625,n, -0.485,p -0.77, T=0.000, Power coefficient Bu=38.0

t

2 m 43 0 ci 2

Corrections to basic (4 blade) screw

Pitch ratio

values

Diameter Blade area Efficiency Thicknessratio

Remarks D as no P PI k, T Di as,. NI T, k, 1 6 7 3 4 3 5 1.000 1.035 0.970 1.000 1.000 0.825 1.030 1.100 1.000 1.000 0.935 1.030 1.000 1.0801 0.9901 Basic screw Values from Tab/el t a

a

4... o d Z Screw particulars Diameter (feet) Blade area

ratio Efficiency Pitch ratio

Thickness ratio Remarks D as no pr T (1) (2) (3) (4) (5) 1 6 7 4 3 5 23.25 24.0 22.50 0.625 0.515 0.690 0.485 0.500 0485 0.770 0.720 0790 0-0550 0.0595 0.0545 Basic screw (1) (equation 8) D =kJ), (2) (equation 9) as=k.asi (3) (equation 10) n,, =ko,, (4) (equation 11) p =k,p, (5) (equation 16) 7= her,

which can be obtained from Fig. 4

DHP is the delivered horsepower in British units

B is the number of blades N is

the rate of rotation

in

revolutions per minute D is the screw diameter in feet C.2 is the chord-diameter ratio

at the x = 0-2 radius frac-tion is the blade thickness-diameter ratio (equivalent value at screw axis).

For two screws of the same basic

blade outline the product B C.2 can be expressed in the form

(13) B

_-D

C.2 = KaE where K is a constant

(6)

screw to that S21 for the, basic screw.

The graph of the strength coefficient S2 on a base of pitch ratio p (Fig. 4) is of hyperbolic form: consequently, a

graph of the reciprocal of S2 would be of linear form; thus, the strength coefficients would be inversely proportional to the pitch ratios and the ratio of the strength coefficients could be re-stated in the form

S PI 1

S21 p k4

and this would enable equation 15 to be re-stated in the form

1 1

(16) k6

=

-T1 k,312( k2k),

The corrections are listed in Table 1 where two sets of correction factors are given, enabling the geometric features of either 3- or 5-blade screws to be derived from data for basic 4-blade screws.

Worked examples illustrating the

application of the correction chart are given in the following Section.

3 Worked examples

It is required to prepare design calculations and to make propulsion estimates for two additional screws for a

large tanker. It is proposed that one of

these screws will be a replacement screw

for the vessel for which the design

calculations for four, five and six blade screws, all of the same diameter(Screws 1 to 4) are given in an article recently

published4. The additional screws

(Screws 6 and 7) are to have three and five blades, respectively, and are to be designed applying the procedure de-scribed in Section 2 above, and using the corrections given in Table 1 and Screw 1 as the basic four blade screw.

Design data

Hull-Single-screw tanker; length 830ft, breadth 125ft, draught (level) 45ft (252.98 x 38-10 x 13.72m) block coefficient 0.8

Estimated trial speed-17 knots. Engine-Diesel; delivered horsepower

22,000 DBP, rate of rotation basic

value NF 110 revolutions per

minute.

Stern details-Streamline rudder. Shaft immersion I = 30ft (914m).

Stipulations-Screw

diameter D =

24.25ft (7-38m). rate of rotation

(Screws

1, 2 and 3) NF = 110

revolutions per minute (Screw 4), value to be chosen to give optimum

performance. Screw material,

nickel aluminium bronze.

Design condition-22,000 DHP. Basic

rate of rotation N = 0-98

NF

--108 (2 per cent make scale effect

see Reference 10 Section 4.9).

Trial speed 17 knots.

Propulsion factors-Wake fraction

WT = 0-43, relative flow factor

eR = 1-02, hull factor ell = 1-42.

Screws 6 and

7-design calculations

In making the

design calculations

given in Table 2:

first, the value of the thrust horsepower

coefficient Bu is

derived from the

value of the delivered

horsepower

coeffi-cient B,, for the basic 4-blade screw (Ref-erence 4, Table 4). Next, values of

cor-rection factors for

diameter D, blade

area ratio aE, pitch

ratio p, thickness

ratio -1- and screw

efficiency (kI3 k23

kb k6 and k3,

respectively) for 3- and 5-blade screws are read from Table 1. Finally, each

correction factor is applied to the

respective parameter of the basic four blade screw (Screw 1) to give correspond-ing values of diameter, blade area ratio, pitch ratio, thickness ratio and screw efficiency for the 3-blade screw (Screw 6) and for the 5-blade screw (Screw 7).

4. Comparison of results

The geometric features and perform-ance data for Screws 6 and 7 are sum-marised in Table 3 together with those of Screws 1 to 4 (Ref. 3) and Screw 5 (Ref. 5) where performance comparisons are also made using data for the 4-blade screw (Screw 1) as the bases. These comparisons show that reducing the number of blades from four to three results in improved performance; but increasing the number of blades from four to five results in no appreciable change in performance, as summarised below.

For the basic 4-blade screw (Screw 1) the diameter was 23.25ft (7-09m), the blade area ratio 0.625, the pitch ratio 0.77, the thickness ratio was 0-055, the screw efficiency 0-485 and the propulsive efficiency 0-703.

For the 3-blade screw (Screw 6) the diameter would be 24ft (7.32m), the blade area ratio 0.515, the pitch ratio 0-72, the thickness ratio 0.0595; the screw efficiency 0-500, and the propulsive

TABLE 3.-SCREW 1 to 7-GEOMETRIC FEATURES AND PERFORMANCE DATA

Delivered Horsepower 22,000 DHP

efficiency 0-725; thus the gain in

efficiency would be 3 per cent.

For the 5-blade screw (Screw 7) the diameter would be 22.5ft (6.86m), the blade area ratio 0-69, the pitch ratio 0-79, the thickness ratio 0-0575, the screw efficiency

0.485, and the

propulsive efficiency 0-703; thus there would be no appreciable change in pertormance

It is significant that if a replacement screw having three blades were fitted this would result in an increase in efficiency of 3 per cent.

References

O'BRIEN, T.P. Some effects of variation in number of blades on model screw performance.

Trans. N.E. Coast Instn. Engrs. Shipb. 1965 81, 233.

O'BRIElg, T.P. Designoftug propellers-part 2-performance ofthree, four and five blade screws.

London, Ship and Boat Builder International, 1965, 18.

O'BRIEN, T. P. The performance of three- four-and five-blade screws. Effects of variation in diameter and rate ofrotation in passenger liner applications. London, Shipbuilding and Shipping Record, October, 1965, 106,481.

O'BRIEN, T.P. Comparative performance of 4-5- and 6-blade propellers for large tankers. London, Shipbuilding and Shipping Record, International Marine Design and Equipment

Number, 1966, 24.

TROOST, L. Open-water tests with modern propeller forms, Trans. N.E. Coast Instn. F.ngrs. Shipb., 1951, 67.

O'BRIEN, T. P. Optimum performance screws for large tankers, London, Shipbnfirling and Shipping

Record, May, 1966.

O'BRIEN, T. P. Designof tug propellers, London,

Ship and Boat Builder International, April, 1965

18,22,.

O'BRIEN, T. P. Designofmarine screw propellers, London, Hutchinson Scientific and Technical Press, 1962.

Ps-listed in Great Britain by Cornwall Press, Paris Garden, London, S.E.1. 1038-P2460

Hull Screw No.

of Blades Rate of Rota-Trial Speed GEOMETRIC FEATURES T

tion Diam Blade

Area PitchRatio

Thick-ness B Np Vs D Ratio Ratio (r.p.m) (knots) (feet) az Pr T 1 1 4 110 17 23.25 0.625 0.770 0.0550 (7.09m) 1 2 5 110 17 23-25 0-700 0-750 0.0520 (7.09m) 1 3 6 110 17 23.25 0.780 0.740 0-0500 (7.09m) 1 4 6 100 17 23.25 0.800 0.840 0.0470 (7.09m) 2 5 4 75 174 29.50 0.530 0.820 0-0490 (8.99m) 1 6 3 110 17 24.00 0.515 0.720 0.0595 (7.32m) 1 7 5 110 17 22-50 0.690 0.790 0-0545 (6.86m) PERFORMANCE DATA

Screw Pro- %increase Effici-ency pulsive Effici-ency above in ,lo Screw 1 in np no np 1 1 4 110 17 0-485 0-703

-

-1 2 5 110 17 0-485 0-703 o 0 1 3 6 110 17 0.475 0.689 -14 -14 1 4 6 100 17 0.490 0.710 4 4 2 5 4 75 174 0-575 0.770 18 10 1 6 3 110 17 0-500 0-725 3 3 1 7 5 110 17 0.485 0-703 0 0