Design of tug propellers. Part 3: Effects of optimum diameter and rate of rotation

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January 1967.

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NATIONAL PHYSICAL

LABORATORY

SHIP DIVISION

DESIGN OF TUG PROPELLERS

PART 3

EFFECTS OF OPTIMUM DIAMETER AND RATE OF ROTATION

by

T. P. O'Brien

(Reprint of an article in

Ship and Boat Builder International, September 1966)

A Station of the

Ministry of Technology

,

-.Extracts from this report may be reproduced

provided the source is acknowledged

,

Approved on be:half:Of DirectOr,NPL

1...c. Am, IP 4 I 404 .44 -ID

(I)

Introduction

TN designing a series of screws of different diameters to operate at varying rates of rotation, complete calculations

could be made, if desired, by repeating the same design

procedure for each -screw. However, this work can be

Amplified by introducing correction factors which can be applied to the geometric features and to the performance values of a basic screw to enable the corresponding para-meters of the series of screws to be derived.

A change from the basic screw diameter or design rate of

rotation results in variations in thrust-loading coefficient and cavitation number; consequently, blade-area ratio corrections

are needed to obtain equivalent cavitating performance.

Similarly, departures from the basic design features result in variations in the stresses applied to the blades; consequently,

blade-thickness corrections are needed to obtain conditions

of equivalent strength.

Before deriving the various correction factors for departure

from standard it is desirable to discuss variations inscrew

diameter and rate of rotation and their resulting effects on screw performance.

(2)

Variation in diameter

A screw can be designed to absorb a given delivered

horse-power DHP at a given speed of advance V, to run at a

stipulated rate of rotation N, or at a rate of rotation selected from a stipulated range of values. If the rate of rotation is

specified, as it is if the propeller shaft is either directly coupled

to the engine or driven via a single-speed gearbox, its value

J

fa

w

44

vitaisfAL.ta: by T. P. O'BRIEN, C.G.I.A., M.R.I.N.A.,

Ship Division, National Physical

Laboratory

PART 3

OPTIMUM DIA-.

AND

RATE OF ROTATION

can be chosen to correspond to the advance coefficient at which the screw efficiency is a maximum, i.e. the optimum

diameter can be chosen.

A convenient method of selecting the diameter is by the

use of the B-8 charts and a procedure for doing this was

described in a previous series of articles'. If it is required to restrict the screw diameter from practical considerations it

might be necessary to choose a diameter lower than the

optimum value and this generally results in a loss in efficiency.

Practical considerations affecting screw diameter include adequate tip clearances, maximum size of screw that can be handled by the propeller manufacturers, and polar moment of inertia (for some screws it may be necessary to select a small diameter in order that the screw may have a low polar

moment of inertia).

For some tug screws designed for free-running conditions it may be advantageous to adopt a diameter larger than the optimum value derived from the B-8 charts. This results

in a small loss in efficiency at free-running conditions, but it

also results in greater thrust and pull at towing condition. However, if the diameter is increased too much the loss in

efficiency becomes large and the blade sections operate under adverse conditions at negative incidence; this can result in the occurrence of face cavitation.

In designing screws the choice of diameter, though generally

determined by other considerations, affects cavitating per-formance. The optimum non-cavitating performance gen-really occurs at conditions corresponding to low section drag

and small angles of incidence. Since low incidence is

associated with favourable pressure distribution, an

diameter" screw in non-cavitating conditions is equivalent to an "optimum-incidence" screw in _cavitating conditions.

A reduction in diameter below the optimum value would

result in an increase in section incidence and a local reduction in pressure on the back of the blades, and the screw would be

susceptible to back cavitation. Conversely, an increase in

diameter above the optimum value would result in a reduction

in section incidence and a local reduction in pressure on the

face of the blades, and the screw would be susceptible to face cavitation.

This is illustrated by the model screw photographs shown

in Figs. 1, 2 and 3 reproduced from my book2. In Fig. 1 the

operating conditions correspond to a screw of diameter

about 10 per cent below the optimum value and there is back cavitation.

In Fig. 2 they correspond to an

optimum-diameter screw and, apart from slight tip vortices, there is no cavitation. In Fig. 3 they correspond to a screw of diameter

about 10 per cent above the optimum value and there is face

cavitation.

(3)

Variation in rate of rotation

Some of the effects of variation in rate of rotation at both

towing and free-r6nning conditions were shown in Fig. 2 of a previous article3. The towing performance data show that optimum towing performance is associated with high rate of rotation and low pitch ratio. The free-running performance

50

4

30

Fig. 4

data show that there is an optimum rate of rotation the value

of which corresponds to maximum propulsive efficiency and

is determined by the co-ordinate of N corresponding to

maximum -alp.

For tug and trawler screws where design calculations and performance estimates are required for towing or trawling

conditions as well as for free-running conditions it is desirable

to use the [4a charts, following the procedure described in

the previous article3. However, should the design calculations

be restricted to free-running conditions, it is convenient to apply a procedure using the Bpa charts as discussed below. If the rate of rotation N is fixed, the Bp and a coefficients can be computed using equations 13 and 15 defined in the

series of articles' and repeated below:

ND

8

N 4/E,,DHP Bp

where N is the rate of rotation in revolutions per minute' D is the screw diameter in feet, VA is the speed of

advance in knots, DHP is the delivered horsepower,

eR is the relative flow factor (Ref. 1, equation 9), and

s is the specific gravity of the fluid in which the screw operates (1.026 for sea water).

If D is fixed and N can be selected, values of Bp, and

T . THRUST IN LBS

-

Alia EXP. AREA X (1.067-0 2290

. pELATNE VELOCITY

.7)

AT Q. TIP RADIUS.

a . FACE PITCH RATIO.

/

/

,

,

e

0.

r

IP 1,1,

4*

.4

4. '1' 4 _# .. ,)Y-"-..bti5 4. 4-c.v. 4.... ,e. .. + :. v . ..s. s. ..., . ..

-LIMIT OF FACE CAW!.

4-111B11 .... II ItSff- ' MAITOF FACE BO? A. R

.

0.665CAVITAT1011

MT OF FACE CAVITATION EXPA.R -0

li

UMITOF FACE CAVITATION EXP A.R..1.00

010 015 0-20 0 3 O4 05 0.6 0.7 0-8 0.9 1-0

LOCAL CAVITATION NUMBER AT 0-70 RADIUS = _{R (0.7)}

.0 0

STRENGTH OF SCREWS (TAYLOR)

Sc _{BALDS Cf,,er}S 2 x b.m.p D.H.P. :- DELIVERED HORSE POWER OF BLADES S, (..p. _9 N REvOLuTIONS PER MINUTE

:- DIAMETER IN FEET

- 50464+u:tat) 02,6:- CHORD RA/10 xr X 0-2

:- THICKNESS RATIO ('D) AT AXIS

s'(1234 _C.*tlyt TNCKNESS RATIO AT X 0-2

CHORD RATtO AT mAximum CHORD DENSITY oF MATERIAL ttv LEAuPT

s,

COMPRESSIVE srmEss 5 + 3,c (1_55/94.1N)

TENSILE STRESS ST TSIT (LES/SQ IN)

00 1.0

MEAN FADE PITCH RATIO

Fig. 5

Si can be computed using the basic value of rate of rotation NI, and this enables corresponding values of Bp and 8 to be

derived by applying a factor k defined by

N = kNi

8 = /c81

Bp = kBp,

In applying this procedure, a range of values of rate of

rotation is chosen, a set of values of 8 and Bp are derived. This enables corresponding pairs of values of pitch ratio p

and screw efficiency 10 to be read from the Bp-8 chart.

Values of propulsive efficiency lp are derived from 710 and the results are plotted on a base of rate of rotation N as shown in Fig. 7 (to be published in the second half of this article).

(4)

Blade-area corrections

In designing a series of screws of varying diameter to operate at varying rates of rotation, blade-area estimates

could be made by repeating the same cavitation calculation's

for each screw. However, this work can be simplified by

using correction factors which are applied to the value of the

blade-area ratio of the basic screw to derive corresponding values for each of the non-basic screws. A cavitation chart

giving some of the data upon which the correction factors are based is shown in Fig. 4. This chart, which gives the

results of cavitation experiments obtained at King's College, Newcastle, is described in Section 6.7 of my book2.

The K.C. area chart comprises a series of contours of

limiting lines on coordinates of cavitation number a, and thrust coefficient Tc. A contour convenient for basing

blade-area estimates upon is that corresponding to point of

thrust breakdown (line F). The equation of this line is given by

(6) Tc = 0.69aR,

which can be restated in the alternative form

3.46 ku

(7) aE =

(1 0.215p)a'

where aE is the expanded blade-area ratio, ku is the thrust 0-80 _{loading coefficient, ai, is the cavitation number, and}

pis the pitch ratio.

The thrust loading coefficient and cavitation number are

defined by 20 (8) (11) 0 1 1 0.3 0.4 0-5 0.6 013 .1 Fig. 6 Traand p

542(po e)

(9) crA pv,2

where T is the thrust applied by the screw, D is the screw

diameter, vA is the speed of advance, (poe) is the static pressure measured at the screw axis, and p is the mass

density of the fluid in which the screw operates (for

fresh water 1.938, for sea water 1.988).

If desired, equation 7 can be restated in the form

1.73T (10) aF

D2 (p0 e) (1 0.215p).

In designing screws equations 7 and 10 can be applied in estimating the minimum value of blade-area ratio to avoid thrust breakdown. In practice the blade-area ratio is

generally increased by applying an arbitrary factor FT to

provide a margin against thrust breakdown (an average value is FT = 1.3).

Equation 10 can also be applied in deriving blade-area

correction factors, and the procedure for doing this is as

follows:

Should it be desired to compare the performance of two screws of different diameter and different pitch ratio on the basis of constant thrust, constant speed of advance, constant

static pressure and constant margin against thrust breakdown,

the ratio of their blade area ratios is given by

)

(D1)1

0.215p2

(1 0.215p1

aEi _D

I I I _{I I}

_THICKNESS CORRECTIONS FOR SCREWS DESIGNED FROM TROOST B4-55 13p-6 CHART.

% REDUCTION IN O AND -,1 FOR 100% INCREASE IN BLADE THICKNESS RATIO --(STANDARD TYPE MODERATE DUTY SECTIONS)----OPTIMUM_{DIAMETER (DO}

-REDUCED DIAMETER (0-95D0

_ ...,... ----REDUCED DIAMETER (0.90 DO PITCH RATIO (0)

10

.---_,1

which can be restated in the alternative form

kip

k 2 =Cie k22

where an is the blade-area ratio of the basic screw, aE is the

blade-area ratio of the non-basic screw, Di is the

diameter of the basic screw, D is the diameter of the

non-basic screw, pi is the pitch ratio of the basic screw,

p is the pitch ratio of the non-basic screw, and k and ki, are the diameter ratio and pitch-correction factor

defined by

k =

132 1 0.215 pi K1

0

-1 0.215 p 5) Blade-thickness corrections

A procedure for deriving blade-thickness correction factors, rased on the Taylor strength criterion discussed in Section 6 if the series of articles', is as follows:

An approximate equation for the compressive stress S, at he blade sectional element at the x = 0.2 radius fraction is

given by

S2DHP

S,

C.2

BND3

where S2 is a coefficient the value of which is obtained from

Fig. 5, DHP is the delivered horsepower, B is the

number of blades, N is the rate of rotation in revo-lutions per minute, D is the screw diameter in feet,

C.2.

is the chord-diameter ratio at the x = 0.2 radius fraction, and 7 is the blade thickness-diameter ratio

(equivalent value at screw axis).

For two screws of the same basic blade outline shape the

C.2

produce B can be expressed in the form

C.2

B = KaE,

where K is a constant.

Hence, equation 15 can be restated in the form

S2 DHP

,

(17) S

KND3a2-r2'

Applying the condition of constant stress to two screws of different diameter and different blade-area ratio operating at different rates of rotation but absorbing the same delivered

horsepower, the blade-thickness correction is given by

k.= T

(Dly1/2 (N1aElS2 )119

D

N S2/ which can be restated in the alternative form

=L=

1 1 ics )112

VCT1

k/3/2 k 2

where k, Ic2 and k2 are the ratios defined by equations 3, 13 and 12; k5 is the ratio of the strength coefficient for the

non-basic screw S2 to that for the non-basic screw S21, i.e. S

k5 = 2

If the variation in blade-thickness ratio is appreciable

further correction factors are needed to make allowance for

the change in blade-section shape. Blade-thickness correction

factors derived using the data given in the papers are shown

in Fig. 6.

REFERENC'ES

O'Brien, T. P., Design of Tug Propellers, SHIP AND BOAT

BUILDER INTERNATIONAL, April 1965.

O'Brien, T. P., The Design of Marine Screw Propellers,

Hutchinsons Scientific and Technical Press, 1962.

O'Brien, T. P., Propeller Design and Two-speed Gearboxes

with Particular Reference to Tugs and Trawlers, SHIP AND

BOAT BUILDER INTERNATIONAL, November 1964.

Gawn, R. W. L., and Burrill, L. C., Effect of Cavitation on the

Performance of a Series of 16-in. Model Propellers, Trans.

R.I.N.A., Vol. 99, 1957.

O'Brien, T. P., Some Effects of Blade Thickness Variation on Model Screw Performance, Trans. N.E.C. Inst. Engrs. Shipb.,

1957, 73, 405.

O'Brien, T. P., Design of Tug PropellersPerformance of Three- Four- and Five-Blade Screws, SHIP AND BOAT BUILDER

INTERNATIONAL, November 1965.

(6) Worked examples

IT

_{groups of screws each of constant diameter for a range of}is required to prepare propulsion estimates for two

rate of rotation. The results of these estimates are to be applied in deriving the geometric features and performance values for two screwsScrew 7 of the same diameter as the

basic screw, and Screw 8 of a larger diameter consistent with

aperture size, each operating at its respective optimum rate of rotation.

The design calculations and performance estimates for the basic screw (Screw 1) were given in Section 8 of the previous

07 I 4 I 2 04 120 140 180 180 200 220 RATE OF ROTATION F.

SCREWS 1,7 AND 8 PROPULSION ESTIMATES

FREE - RUNNING CONDITIONS

Fig. 7

article', where calculations and estimates were also given for another screw (Screw 2) similar to Screw 1 but designed for

towing conditions. In a subsequent article° calculations and

estimates were given for two pairs of additional screws (Screws 3 to 6) comprising three- and five-bladed screws designed for free-running and towing conditions.

The propulsion estimates for Screw 7 are to be derived

from the data given in Table 1 of the previous article;

those for Screw 8 are to be made using the Bp 8 charts and

applying the procedure described in Section 3 of the first part

of this article published in last month's issue. The design

calculations for Screws 7 and 8 are to be made using these

propulsion estimates and applying the correction factors

derived in Sections 4 and 5. Design calculations are also to be made for two screws (Screws 9 and

10), similar to Screws 7 and 8 but designed for towing

con-ditions, using the V. a charts and following the procedure

given in the previous article'.

Towing performance estimates are to be made for Screws

7 and 8 and free-running propulsion estimates are to be

Table 1. Propulsion EstimatesVarying Rate of Rotation

(Ref. 2, Section 4.9) N = 0.98

(Equation 5) Bp = k Bp,

(Equation 4) 8 = k8,

Values from Bp chart (Ref. 1, Fig. 1) (Ref. 1, Equation 12) 71P = eP = 1.027.0

Bp, = 22

Basic design values 81 = 207 D = 10.25 ft. N Bp 8 P 710 119 k (1) (2) (3) (4) (4) (5) 0.6 120 118 13.2 124 1.34 0.635 0.648 0.7 140 137 15.4 145 1.05 0.647 0.660 0.8 160 157 17.6 166 0.86 0.635 0.648 0.9 180 176 19.8 186 0.735 0.605 0.617 1.0 200 196 22.0 207 0.63 0.565 0.576 260 280 240

made for Screws 9 and 10, the former estimates using the u- a charts and the latter estimates using the Bp- 8 charts,

applying the procedure described in the previous article'. Screws 7 and 8-Propulsion Estimates

The propulsion estimates for Screw 7 were derived from the data given in Table 1 of the previous article3, and the results were plotted in the form Shown in Fig. 7

In making the propulsion estimates for Screw 8 given in Table 1, first the basic value of power coefficient Bp, is obtained from

the table of the previous article' and the basic value of the speed coefficient 8, is derived from that for Screw 1 also

given in that table.

Table 2. Screws 7 and 8-Design Calculations

Next a series of values of power coefficient Bp and speed coefficient 8 are derived covering a range of rate of rotation. This enables a series of corresponding values of pitch ratio

p and screw efficiency 12 to be obtained from the Bp- 8 chart

shown in Fig. 1 of a previous article'.

Finally a set of values of propulsive efficiency lp are

derived from lc, and the results plotted on a base of rate of

rotation N, together with the values of pitch ratio p, as shown in Fig. 7.

Screws 7 and 8-Design Calculations and Towing Performance Estimates

In making the design calculations given in Table 2, first BASIC SCREW-SCREW 1 (Ref. 1, Table 2)

BASIC DATA

Screw Diameter D (ft.) Rate of Rotation N Bp 8

1 9.00 200 22 182 7 9.00 160 17.6 145.5 8 10.25 140 , 15.4 145 CORRECTION FACTORS N D P k k, kJ.° k2 S2 k5 k, Screw (I) (1) (1) (2) (3) (4) (5) (6) (7) (8) 1 200 9.0 0.82 1.0 1.000 1.00 1.00 1,260 1.00 1.00 7 160 9.0 1.14 0.8 1.000 1.09 1.09 925 0.734 0.92 8 140 10.25 1.05 0.7 1.139 1.065 0.821 990 0.785 0.96

(1) Values from Fig. 7 (5)

(Equation 12) k, =

-ki2 N

(2) (Equation 3) k =

-N, (6) Value from chart (Fig. 5)

D S2

(3) (Equation 13) k, = (7) (Equation 20) k, = c,

Di

an

(4) (Equation 14) klo -

1 - .215pi

0 (8) (Equation 19)

k, =

1 (____5_k

2)1'I 2 k k 1 - 0.215p ki3/2 SCREW PARTICULARS Screw Dia-meter D N (r.p.m ) aE T Chart p 7]. Ai,

-

P An

-1 P ' 710 113 (9) (10) (11) (12) (12) (13) (13) (14) (14) (15) (ft.) 1 9.0 200 0.5 0.047 0.833 0.618 0 0 0.833 0.618 0.629 7 9.0 160 0.55 0.043 B-4-55 1.14 0.625 1.01 1.005 1.150 0.627 0.640 8 10.25 140 0.41 0.045 B-4-40 1.05 0.665 0 0 1.050 0.665 0.678

(9) (Equation 12) a,- k2 aEl (13) Thickness correction (Fig. 6)

(10) (Equation 19) T = kg T1 (14) Corrected values

(11) Bp - 8 charts (Ref. 2) (15) (Ref. 1, Equation 12) lp = fp 7h, = 1.02710 (12) Values from charts

Table 3. Screws 1 to 10-Geometric Features

the optimum values of rate of rotation and corresponding

values of pitch ratio are obtained from Fig. 7. Next the blade-area corrections and blade-thickness corrections are derived following the procedure given in Sections 4 and 5

and applied to the respective geometric

parameters of the basic screw to obtain corresponding values

of blade-area ratio and blade-thickness ratio for the

non-basic screws.

Then values of pitch ratio p and screw efficiency 7)0 are

obtained (by interpolating between standard blade-area ratio where necessary) from the Bp- 8 charts (Reference 2, Section 3.4). Finally pitch ratio and efficiency corrections are obtained

from Fig. 6 to make allowance for

de-parture from standard blade-thickness ratio. The

geo-metric features of Screws 7 and 8 are summarised in Table 3

together with those of Screw I. The screw performance

data and comparisons are given in Table 4.

The towing performance estimates were made using the

[2.-a charts and following the procedure for Screw 1 as given

in Table 4 of the previous article.' The geometric features

of Screws 7 and 8 are summarised in Table 3 together with

those of Screws 1 to 6 and 9 and 10. The screw performance data and comparisons are given in Table 4.

Screws 9 and 10-Design Calculations and Free-Running

Propulsion Estimates

The design calculations were made using the 4- is charts

and following the procedure for Screw 2 as given in Table 3

of the previous article.' The free-running propulsion esti-mates were made using the Bp- 8 charts and following the procedure for Screw 2 as given in Table 5 of the previous article.'

The geometric features of Screws 9 and 10 are summarised

in Table 3 together with those of Screws 1 to 8. The screw performance data and comparisons are given in Table 4.

(7) Comparison of results

The screw performance dafa for Screws 1 to 10 are given in Table 4, where screw performance comparisons are also made using data for Screws 1 and 2 as the bases. These

comparisons show that significant improvements in

per-Table 4. Screws 1, 2 and 7 to 10-Performance Data and Comparisons Screw. No. Design Condition Delivered H.P. Rate of Rotation Diameter (ft.) No. of Blades Blade-Area Ratio Pitch Ratio Thickness Ratio DHP R.p.m. D B aE PT T 1 Free-running 1,100 200 9.00 4 0.50 0.833 0.047 2 Towing. 1,100 200 9.00 4 0.60 0.580 0.052 3 Free-running 1,100 200 9.45 3 0.44 0.798 0.049 4 Free-running 1,100 200 8.70 5 0.59 1.012 0.045 5 Towing 1,100 200 9.45 3 0.53 0.560 0.054 6 Towing 1,100 200 8.70 5 0.71 0.620 0.049 7 Free-running 1,100 160 9.00 4 0.55 1.150 0.043 8 Free-running 1,100 140 10.25 4 0.41 1.050 0.045 9 Towing 1,100 160 9.00 4 0.66 0.825 0.048 10 Towing 1,100 140 10.25 4 0.49 0.760 0.050 ' Screw No. Diameter (ft.) R .p.m. ConditionDesign Operating Conditions

Free-running ! Towing (at Vs= 0)

Propulsive

Efficiency Speed Pull

Vs _PU 711. knots tons 1 9.00 200 Free-running _{0.629 12.50 11.47} 2 9.00 200 Towing

-

10.60 14.60 7 9.00 160 Free-running 0.640 12.50 11.00 8 10.25 140 Free-running 0.678 12.50 12.20 9 9.00 160 _Towing

-

_{11.00 14.20} 10 10.25 140 Towing

-

10.90 15.60

7 _{Per cent increase in efficiency and 2.0}

-

_-4.0

8

-

-

_{pull 8.0}

-

_6.5

9

-

-

Per cent increase in pull and speed

-

4.0

-2.5

formance can be achieved if either the design rate of rotation can be selected or if the screw diameter can be increased within

practical limits of aperture size for single screwsor tip

clearance for twin screwsas summarised below.

For Screw 7, designed for free-running conditions and of the same diameter as the basic screw (D = 9.0 ft.), the opti-mum rate of rcitation would be 160 r.p.m. (compared with

200 r.p.m. for the basic screw) and the corresponding increase

in efficiency would be 2 per cent. However, at towing conditions there would be a reduction in pull of 4 per cent. For Screw 8, designed for free-running conditions and of

maximum diameter consistent with aperture size (D = 10.25

ft.), the optimum rate of rotation. would be 140 r.p.m. and

the corresponding increase in efficiency would be 8 per cent. At towing conditions the increase in pull would be 64 per cent.

For Screw 9, similar to Screw 7 but designed for towing

conditions, there would be a reduction in pull of 24 per cent.

However, at free-running conditions there would be an

increase in speed of 4 per cent.

For Screw 10, similar to Screw 8 but designed for towing conditions, there would be an increase in pull of 7 per cent. At free-running conditions there would be an increase in

speed of 3 per cent.

REFERENCES

O'Brien, T. P., Design of Tug Propellers, SIC? AND

BOAT-BUILDER INTERNATIONAL, April 1965.

O'Brien, T. P., The Design of Marine Screw Propellers,

Hutchinsons Scientific and Technical Press, 1962.

O'Brien, T. p., Propeller Design and Two-speed Gearboxes

with Particular Reference to Tugs and Trawlers, SHIP AND

BOATBUILDER INTERNATIONAL, November 1964.

(lawn, R. W. L., and Burrill, L. C., Effect of Cavitation on the

Performance of a Series of 16-in. Model Propellers, Trans.

R.I.N.A., Vol. 99, 1957.

O'Brien, T. P., Some Effects of Blade Thickness Variation on Model Screw Performance, Trans. N.E.C. Inst. Engrs. Shipb., 1957, 73, 405..

O'Brien, T. P., Design of Tug PropellersPerformance of Three-, Four- and Five-Blade Screws, SHIP AND BOATBUILDER

INTERNATIONAL, November 1965.