Marine propellers for large power and high speed

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Technische HogçiçhI

Marine popeIiers for large poweM

.

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¿TtL

and hi h

Ir. L. A. Van Gunsteren, C.Eng. A.M.I.Mar.E.*

An analysis is made of the limits imposed by cavitation to the

power and the speed of propellers for fast container ships. For

controllable pitch propellers blade root cavitation is

deter-minant, for fixed pitch propellers and counter-rotating propellers back cavitation at 07 radius is the restricting factor. Limits due to cavitation to the power per shaft line and the speed of ships equipped with controllable pitch, fixed pitch or counter-rotating propellers are predicted in the order of respectively 70 000 hp at 35 knots. 100 000 hp at 39 knots and 150 000 hp at 45 knots. Introduction

During the past decennia the horsepower per shaft installed on

fast merchant ships has shown a steady increase.t1 In Fig. 1, the world records of installed horsepower per shaft of both solid and controllable pitch propellers are indicated. From the spectacular

growth over the past years in horsepower per shaft the question arises as to what extent this development may be expected to

continue. The purpo of this paper is to pay attention to this

question from a hydrolynamic point of view.

Sea-land

10

000hp-ARCHEF

Lips NV, Drunen

JANUARY MARINE ENGINS REVIEW

i I I United Staten Quei, Elizabeth Z ganen ELizabeth

-Queen Mary C. ¡r,rand,n PROPELLERS

-SOUD PROPELLERS _Aniatiner Euratinir -Tiiskeri Satanas Unni ja Anda, ra Silver tali Los Angelot 1800 1850 1900 1950 ZCO0 Fig 1Power increase per propeller for solid and controllable

pitch propellers of merchant and passenger ships

Obviously, the speed and the power of ships depend on many factors, of which economical considerations and prestige

are generally the most important. To make predictions on future

trends inevitably is a kind of crystal looking. We therefore

confine ourselves to indicate the limits which are imposed by hydrodynamical factors, and in particular cavitation. Whether these limits will become reality remains an open question. For

instance, it is quite possible that ship vibrations will impose more

severe restraints, so that the limits due to cavitation on the

propellers will not be reached.

Restraints regarding the design ranges of propulsors (and

ships) can be divided into: physical, technological and economical.

A physical restraint to the size of a ship is that the draught should always be some feet less than the lowest depth in the anticipated route. An example of a technological restraint is the limit to the finishing precision of propellers imposed by the accuracy of the method of measuring the propeller geometry.

Economical restraints preclude certain alternatives that are

simply too expensive.

Technical and economical restraints tend to chtnge by

technical progress and economical developments. Physical

restraints are far less subject to changes, although the relation which often exists with both other categories, might affect also here a shift of boundaries. The physical restraint to speed and power of marine propellers is the occurrence of cavitation. The

transition from the sub-cavitating to the super-cavitating

operat-St,uerrs S tarin

e -I i

Mauretania

ing condition in hydrodynamics is comparable to breaking

through the sound barrier in aerodynamics. Like in aerodynamics,

operation in the range of transition should be avoided, although here on penalty of catation erosion on the propeller instead of

an ear deafening noise. Since super-cavitating propellers are not

yet feasible for large ships, our problem is to establish to what extent power and speed can be increased without occurrence of

cavitation beyond the allowable level in view of erosion. Counter-rotating propellers are also considered because of their particular suitability for high speed and large power.

The analysis starts from the present world records which are

indicated at the ends of the curves in Fig. 1. These record

propellers both pertain to fast twin screw container ships.

Therefore, when circumstances are principally different, our results are no longer valid. For instance, the mission profile of naval ships is generally such that far more cavitation can be allowed at full power than in case of merchant propellers. The limits imposed by cavitation to the power of tanker propei1er

are much higher than the values below, because of the relatively low ship's speed.

The result of the analysis is, that cavitation is expected to impose limits to the power per shaft line and the speed of fast container ships in the order of:

- 70 000 lip at 35 knots for controllable pitch propellers

(c.p.p.)

100 000 hp at 39 knots for ft'ed pitch propellers (f.p.p.)

- I 50 000 hp at 45 knots for counter-rotating propellers

(c.r.p.). Basis of analysis

The particulars of both record propellers are given in Tables I and 2. Photo impressions of the propellers are shown in Figs. 2

and 3. At first it will be assumed that the fictitious power increase

will be used exclusively to raise the ship's speed, assuminga

parabolic resistance curve. Actually, the resistance varies in the considered speed range s'ith a higher power than two, but this can be compensated by a slight decrease in displacement. Since the draught is the same, the propeller diameter also remains unchanged. To remain in the range of optimum efficiency, the

advance ratio J has to be kept approximately constant. By means

of systematic calculations with computer programs for the

design of fixed pitch, controllable pitch and counter-rotating

propellers, the limits to the power and the speed due to cavitation

then can be found. Only speed, power and rev/mm have been

varied in the calculations. All other design parameters, suchas

allowable static stresses, margins against cavitation at OE7 radius,

etc., have been taken the same as in the design of both record

propellers. ¡ri. addition to the systematic computer calculations, a general non-dimensional analysis is made.

Table 1Paiticulartj of Sied pileb record propeHer

Propeller:

Power, ht, ₆₀₀₀₀

Shaft speed, revlmin 135

Diameter, _7'00

Number of bladez S

Blade area r4tiO O'91

Ship (twin !Crew):

Length, bpp, m 26750

Beadth. m 3216

Draught, m 914

Speed, iaiots 33 Table 2Particaalar of coatrolitible pitch record propeller

Propdller

Power, Lp 35 000

Shaft speed, revlmut 135

Diameter, ut 620 Hub diameter, rn

Number o bladeg 4

Blade ara rath, 0-69

11

Ship (twin screw):

length bpp en _fl5.

Breadth, en 3000 Draught, ut 10-70

PLL

y I fr ,, i.;; ;- - .

&-Fig 2Photo impression of 600GO

propeller Back cavitation

Cavitation occurs whenever the pressure on the blade section

drops below the vapour pressure of the fluid. In non-dimensional

form:

Where:

= underpressure ori profile

q = dynamic pressure,

q = pV2

p = density

V = main Stream velocity

a = cavitation number,

Pa, - e

a=

Poe = static pressure

e = vapour pressure

The difference between a and (p/q), presents the margin Aa

against cavitation:

Aa

a

-\ q /

The maximum underpressure (Ap/q) and the associated cavitation margin Aa depend, for shockfree entrance, on the

lift coefficient CL and the thickness-chord ratio i/c (see ref. 2):

(é)

_{=(1+C1.CL+C2.!)2_l}

q _max C

The constants Ci and C2 depend on the selected type of

section. The operation of the propeller can be characterized by the section at OE7 R (R = propeller tip radius). For high speed

propellers (large blade area) with approximately optimum

diameter, minimum values for CL and tic at the OE7 R section can be indicated 4)

¿I.

5

'

Lr -J

(

q )max

<a

hp fixed pitch record

(1)

(2)

(3)

Fig 3Photo impression of 35 000 hp controllablo pitch record

propeHer

In words: a propeller blade must not be paper thin and to

let the propeller fulfil its function, the blades should carry some load. The constants C1 and C2 are for section types that are usual for high speed propellers:

C1 = OE278 (N.A.C.A. a = OE8 mean line)

C2 = i O6 (elliptic-parabolic thickness distribution). This yields a cavitation number at OE7 R:

aO.7ROIO

(6)

A margin has to be added to allow for deviations for

shockfree entrance operation, manufacturing tolerances, etc. A

usual value is Aa = OE2 a which gives:

aO.7R=Ol2 (7)

In view of the results of the systematic calculations, calcula-tions have been made with:

ao.7R= 014 (8)

The velocity V is determined by the intake velocity VA and

the shaft speed n. The cavitation number at radius x R is:

Po - e ± pg h - xR)

p [VA2 ± (xnD)2] Where:

Po = atmospheric pressure g = acceleration of gravity

h = distance from centre line of shaft to water surface x = non-dimensional radius

D = propeller diameter

n = revolutions per unit of time.

The cavitation number ao, defined on the intake velocity V4 is:

Fo - e + pg/i

PVA2 (10)

The relation between both cavitation numbers is:

I

(

gxD'\

Il)

- I + (rxiJ)2

ao VA° J Where: J = advance ratio, VA nD

For the sake of completeness, it is mentioned that

super-cavitating operation is only possible if:

a().7 R

<005

(12)

The boundaries (6), (7), (8) and (12) combined with equation.

dL REGION OF LOW EFFICIENCY FOR ANY PROPELLER Oì I 0.08:

006-30

R/h=052

2O\ \.

1.5\

\.

N.

..

N.

k

04

-

03-U

i

SUPERCAVITATINIG PROPELLERS I T I I I I I I I C?p A 1 2 CPp_' R 0-065 (9) 0-8 10 1-2 1-1. 1.6. ADVANCE COEFFICIENT.

Fig 4Limits to sub and super-cavitating operation of

propellers-(for typical cases see Table 3)

16 MARINE ENGINEERS REVIEW . JANUARY

0 04 O4 OS t/co.7R > 002 CLO.7R O1 50 I I I I I 40 _{SURCAVITATING PROPELLERS} b° ° 08 Ui

-m R

06-z

-(Il) are graphically shown in Fig. 4. The numbers in circles

refer to seveñ specific cases which are listed in Table 3. Tablé 3--Typical cases regarding limits of sub-caitating

operation of propellers (see Figs. 4 and 7)

f.p.p.: 60000hp; 33 knots; 135 rév/min; D = 7-00m;

manufactured in 1971.

C.p.p. :35 000 hp; 277 knots; 135 rev/mm; L) = 620m;

manufactured in 1971 as four blader; feasibility as

five blader checked with Lips design programme for controllable pitch propéllets.

c.p.p.: 40 000 hp; 192 rev/mm; tested on blade root cavi-tation in cavicavi-tation tunnel.

f.p.p.: 84 000 hp; 37 knots; 151 rev/mm; D = 700 m;

feasibility checked with Lips design programme for fixed pitch propellers.

c.p.p.: 54000hp; 32 knots; 156 rev/mm; D = 620m;

limiton bladé root cavitation ¿Oo.325 R = 0065.

151 000 hp; 45 knots; 136 rev/mm; Dfarword prop

700 m; feasibility checked with Lips design

programme for counter-rotating propellers.

100 000 hp; 39 knots; 120 rev/mm; D = 700m;

feasibility checked with Lips design programme for fixed pitch propellers.

It app ars that the limit GO-7 R = OE14 is too optimistic for

fixed pitch propellers, in the range of high J-values. According

to our computer program for the design of solid propellers, case

7, resultirigin 100000 hp at 39 knots, represents the maximum

that,. at J = l3, can be reasonably realized (blade area ratio AE/Ao = 115). With counter-rotating propellers the limit

o7 R = OE14 can be attained at both low and high advance coefficients. Calculation with our computer Progräm for the

design of counter-rotating propellers,(5) gives for case 6: J = 13;

151 000hp.at 45 knots; AE/Ao = 112 for the forward propeller

and AE/Ao = OE95 for the aft propeller. Blade root cavitation

The foregoing analysis pertains to propellers where no limits are imposed on the length of the Sections at the roots of the blades. This holds true for fixed pitch, counter-rotating and overlapping propellers,but not for controllable pitch propellers. The condition

that the blades can pass each other at zero pitch, gives:

(13) Where:

c = chord length Z = number of blades

= ratio of the length of the S-shaped section ¡ri the zero pitch position to the corresponding arc,

f103

The strength calculation gives a required section modulus of the considered section, characterized by 12c:

c(x).t2(x)=C3(x)

(14)

The hydrodynamic load at the root sections can be made

nearly zero, so Ci. 0, by selecting a suitable radial pitch distri-bution. Equation (3) then becomes:

I

_'

(15)

(

t(x)

j

q 'max

\

c(x)

The cavitation margin ic (x) can be obtained from equa-lions (3), (13), (14) and (15) by elimination of t (x) and c (x). Whenever the margin becomes negative, cavitation will occur. In practice we have to maintain a positive margin of at least

= 005, because of the assumptions made in thi simple analysis:

- viscous effects are neglected

- tWo-dimensional flow is assumed; accordingly, the hub

is assumed to give a pure mirror effect

- blade interaction due to thickness is neglected.

The cavitation margin ¿a (x) is for a given configuration a

function of the non-dimensional radius x, which means: the margin at the root is a function of the hub diameter ratio. A

large hub-diameter ratio is favourable in this respect.(6) However,

weight and capital costs of a controllable pitch propeller are

proportional to the hub-diameter ratio to a power between

JANUARY . MARINE DGINEERS REVIEW

b 04 03 02 0.1 O -01 27 28 CONDITIONS: 9,-e=15720kg1 m2 p=lO4kgf s2m' R/h = 062 w=0112 t=0908 BLADE ROOT CAVITATION (AO325 R<0065) 29 30 31 32 33

SHIP SPEED V5 (knots)

Fig 5Margins against blade root cavitation of 5-bladed c.p.

propellers 2 and 3.

The hub-diameter ratio in the calculations is therefore restricted to:

dID = OE325. (16)

Since it is not convenient to treat the strength calculation in

non-dimensional form, we start from the dimensional values, derived from the controllable pitch record propeller, as given in

Fig. 5. For the original advance ratio J OE908 and a cavitation

margin o325 R = 0065, the limit W= 32 knots at t7 = OE231

is found. At arbitrary J and V3, the thickness-chord ratio is

approximately:

-

v ri + (J/O7v)27o.25

t/c=r/c.f,.Ll+(_jIO7)2J

(17)

The boundary ao as a function of J can then be obtained

from equations (1), (11), (15) and (17). This limit in view of blade

root cavitation on controllable Pitch propellers has also been

indicated in Fig. 4. Blade root cavitation turns out to be the

determinant factor for controllable pitch propellers, since the

limiting cavitation numbers are higher than the boundary

regarding suction side cavitatiOn at OE7 R as established in the preceding section.

The effect of the hub-diameter ratio on blade root cavitation

has been investigated experimentally (6) from which Fig. 6

has been taken. The cavitation inception number o' is defined:

Poe+pgh

p(nD)2 (18)

The influence of propeller loading is charàcterized by the

thrust coefficient KT. It may be concluded from Fig. 6 that

freedom from blade root cavitation must be possible for

= 14, provided a suitable pitch distribution

is chosen

(reduced at the root). The limit 072 = 14 has also been indicated in Fig. 4.

Discussion

-The limits in non-dimensional form as given in Fig. 4 have been converted into knots and horsepowers and the result is presented

in Fig. 5. As already mentioned, the systematic computer

cal-culations indicate that the limit°o?R = OEl4 is too optimistic for

solid propellers in the range of high J-values , but for counter-rotating propellers this limit can be attained at both low and

high advance ratios. The explanation can be found in the relation

that exists between strength and cavitation. Increasing the

ad-vance ratio results in a shift of the cavitation linit towards higher

speeds and larger powers. The blade thickness required for suf-ficient strength of the propeller then also increases, this having

an adverse effect on the cavitation margin; see equations (3) and

(2). In case of counter-rotating propellers, thrust and torque are distributed over two propellers. Accordingly, the effect of

pro-peller strength on the cavitation limits is roughly half as large as

in case of solid propellers. Since it is not convenient to

in-corporate the effect of strength in the non-dimensional analysis,

the cavitation limits have been determined with systematic cal-culations. The resulting limits are characterized in Fig. 7 by case 7 (100000 hp; 39 knots) for fixed Pitch propellers and by

case 6 (151 000 hp; 45 knots) for counter-rotating propellers As

a corollary, the prospective range of application of counter-17 34 35 4 ii c.r.p.: f.p.p.:

09

012 013 014 015 046 017 018 019

K1

Fig 6Inception of bubble cavitation on pressure and suction

side of blade root sections as function of KT, for three values

of the hub diameter ratio d/D

rotating propellers is at powers between 100 000 and 150 000 hp

and speeds between 39 and 45 knots. Since conventional pro-pulsors fail in these ranges, one may accept the risks and costs due to the considerable mechanical complications which will

neyer be justified by a gain in efficiency only, regardless of how

substantial thi gaiñ may be

The analysis for controllable pitch propellers has been made for five blades, for. we expect that in many cases considerations regarding vibrations will require five or six blades. However, the lirhits for four bladed controllable pitch propellers turn out to be only slightly more favourable.

Finally, we emphasize that the limits that have been found,

are only valid for normal optimum propellers with large blade areas and a missiOn profile of nearly 100 per cent full power.

Uñusual conditions, such as non-optimum design point, excessive

blade areas, extremely large hub diameters in the case of

controllable pitch propellers, non-uniform inflow due to considerable shaft inclination, etc., have not been considered. Conclusions

The following limits are imposed by cavitation to the speed and

the power of propellers for fast container ships with two shaft

lines (see Fig. 7 and Table 3):

I) Controllable pitch propellers: 70 000 hp per shaft;

35 knots.

Fixed pitch propellers: 100 000 hp per shaft; 39 knots. Counter-rotating propellers: 150 000 hp per shaft line;

45 knots. References

\VrND, J. "Principles and mechanisms used in controllable

pitch propellers", International Shipbuilding Progress, February 1971.

ABB0rr, I. H. and VON DoENHoFF, A. E. "Theory of wing

sections", Dover Publications Inc., New Yòrk, 1959.

KRUPPA, C. F. L. "Hìgh speed propellers, Hydrodynamics and Design", Post-graduate course, University of Michigan,

October 1967.

Cox, G. G. and MORGAN,. W. B. "Application of theory to propeller design", International Symposium on Fluid Mech-anics and Design of Turbomachinery, Pennsylvania State

College, September 1970.

VN GUNsTEREN, L. A. "Application of momentum theory in counter-rotating propeller design", International Shipbuilding Progress, October 1971.

VAN DER MEULEN, J. H. J. "The effect of the hub diameter

ratio on blade root cavitation for the DD 963 propellers," N.S.M.B Report No. 70-216 SP, February 1971.

020

60

SUBCAVITATING OPERATION

T

KT=D42

revolutions per unit of time

pressure

atmospheric pressure static pressure dynamic pressure;

q=pV2

propeller tip radius thickness

thrust

inflow velocity with respect to section propeller intàke velocity

wake fraction number of blades margin against cavitation density

cavitation number;

Pcce

cavitation number defined on rotational speed;

_Poe+Pgh

(nD)2

cavitation number at non-dimensional radius x;

Poe+pg(h±xR)

= +P[VA2 + (xD)2]

cavitation number defined intake velocity;

Poe+pgh

G

4PVA2

18 MARfl4E ENGINEERS REVIEW . JANUAflY

10

06 08 10 12 14 16 18

ADVANCE COEFFICIENT, t

Fig 7Limits to the ship's speed for sub-cavitating operation of

propellers (for typical cases see Table 3)

List of symbols

A E/AO blade area ratio

c chord length

CL lift coefficient

Ci coefficient relating maximum mean line induced

velocity to lift coefficient

C2 coefficient relating maximum thickness induced

vIocity to thickness-chord ratio

constant (inverse of allowable static stress)

hub diameter

propeller diameter vapour pressure

ratio of section length to corresponding àrc

acceleration of gravity

distance from oentre line of shaft to water surface advance ratio;

Jr

_'u)

thrust coefficient; 50 u' o C 40 o LU Ui o-30 Q-X u, 20 C3 d

D.

e fc g h

J

n p po Poe q R t T V VA w

z

p G an ax '50