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The contribution to the design of ship propellers without cavitation

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(1)

4t

r

-3°b.

lab. y.

ReçortA

Date

ehruiryDC1th,

947

M A .P.

VOT-1ffoD

AVG.

ONOiP}.8

QkNELAL EPU'O

O(I.ìT1C: c

1HIP

OPç

(&VTAT1C.

(2)

r

by O

her

.

..t,&jJijçt.1Oi 01

LigL-cdU tha

tLe..e LL

...er

of ppei1ers.hus

to

tILggle against

the cavitb(ion

its disadvantageous

consequences

ie ahaU not

describe

j

detail how

.t has been

tried to explain

the nature of ca. .

tation at the

propeller arid to

investigate the

conditions in

order to avoid lt. list of references on

thib

subject

has

oeeri given, e

g

by H

L e r b s

[1]

We shall rather

reí'ex

o

tha

rivestigations

arricci out i.

this direction

at Goettinn

A s

vey on the

de

lopment of the

invstignttons arid

their

stai

at tl

end of the war

is given below

In the suhsequet

xs the

foundations required

for the desigii

of a orcpeHr

with it

cavItation will be discussed in detail.

according to

the present

state of

knowledge and in a

form suited for practi

.'sl use

üuxirtg the yea.s

93i to 1934

several profiles in

two--diine:siona1 now

were

inuebtigated ta the cavitation tank

of the

Wl

3t

The conditions for the

start of cavitation

and ita exparislozA over the profile were observed

Its influenoc

on

drag arid lift was

deternined by force

rneaurements

The

shape of profiles

first

correspond

to the

.arp-edged egmerit.s

with straight pressure

83.de and arc-shaped

suction side, which

were generafly

uscd at that time

A further. set

of profiles

dIffered fron it by a

somewhat greater

convexity of the

profile

frot part and by

the curved

shape of the nose. Their presstre

aid

was also

straight, Profiles

with convex or concave pressurc

sic)

andcavitatiori were not investigated since at that time,

ori account of a

manufacturing as simple as possible the German

".Mrir-e1eItung" (Admiriistratiox-i of txie

Navy) by wnose order

these experIments vere

made; was only

interested in profiles

with straight pressure

aide

The main purpos.e

of these tests

to

et acuatnted with

trie in.fluerice of the cavitation on

ti.

'

of an aerofoli

The most important

reauÏt

however)

(3)

f

ii

w8 the kow1ede that

ri mat aei th cvtatanat cie p7O)eAz,

which up to now was cois1Iered as ar 1zievitab1erawback,

ou1

be

avoided when the b1ade

have te 5tanation poirt at the 1eadIri

edge

Sothe further experimental arid nuruerical ir1Va8tiat1OrS,

tharerore, referrea isere1y to tne atudy of tke start of

cavIa-tion daper1ihg on

the profi.Le etape Profties with convex and

con-cave pieasure side were also considered. Por the design of

tAe

propdlr the result wa veri 'convenient on account

of its

sim-plicity

ietirt attes;pt, wer, to design on mis basi's Q

pro-pel 1r wiiout cavltati)L for e 3eatoyei oi the riegsmariL4e failed in the cavitation tark of the 'Hamburgisekie

Schiffbau-VersucIsanatalt (HSVA) (H6mburg ship-building research

institute)

a model of this design showed widespread cavitation startiRg

from the leading edge of the blade. This fact

showed that the

stagnation point was aót et the leading ed

The reason was

that the curvacure of the streauìl.inalong the profile cnord

is not considered ty

the propeller calculation based on the trior1

of the loaded ltn. thus the well-known

fact is..

explained that

broad-laded propeer

practically produce much less thrust

arid absorb ]C83

power than might be expected according to t e

theory of t.ue lsded ine r4]

With regard to

ne crvatute of trie strttn lines for the

case when the sta

c1n point isat the load'ing edge and

opti-mum thrustdistributor LGize1 and H.Ludwieg

have further deveT. øed tie ,)ropeLler theory

LJ

(cf. il

44)

In pursuanceof th .ape 1. S t r a s s i calculated tne

factor for sereral n shapes ox' the blades and ratios of advtace by wLic a profile t the propeller rnust bave a greater camber

than an

equivalent profile in two-dimensional flow

E6] . From

these results the correction cf curvature

can

e interpolated

for

rost of the conditions

f design occurring in practice,

Tnere

is

til] too little experience in order to

judge conclusively

the

reliability of the theory of

broad-bladed

prollers after

Giriel end Ludwieg. khan teated,

a propeller dsigaed for

an

E boat

of the Rrieg8rnarirle without the help

of modei experiments

or ay empiric factor1 produced the desired

power at the

re-quireo iotationai speed. This result

points to thefact that

the

size ol the curvature correction must he at

leest summarily

correct

(4)

On the other hand, hcwe,ver, ccnsiderabie damage which will be

due to cavitation, was stated on the blades near the hub ox'

this propelle

The reaon could not be found before the end

of the war Thus the aim of designing a propeller without cavi-tation by calculatioa onJy was riot obtained'

comp1etely

2. Condition for

the

start of cavitation at £rof lies

tWOdileAslOTLal

flow.

AccOrdinß to tne aeroftl thoory the knowledge of th operties of the individual blade profiles in two-dimensionai

flow is necessary for the degn of a propeller The, study of the condition for the start of cavitation on

nrofiles in

two-dimension.al flow is of fundamental importance for the calculation

of a propeller

operstin

without cavitation. If the pressure

In the undisturbed tlow is denoted by p the pressure variation on the profile at the locatión of the greatest supervelocity

by p and the separation

pressure by

e , then the condition for b -innlng separation is p + p e or re'ated to the

dynar

pressure

q . W2

q q

(i)

In wate.r free of aira e is the steam pressure corresponding

to the respective temperature, 1f tha possibility of à boilIng delay is left out of consideration. With water containing air

however, e is greater than the steam pressure. The pressure

coefficient

_-

e

is e characteristic value of the undisturbed

flow arid is denoted es separation or cavitation

number 5

Iii order

to find the liita for

the beginning separation,e:lther

the value

6' can be measured in the

cavitation

tank, where the first cavitation 18 observed to appear at a model blade or the

pressure distribution around the profile is determined by ex-perimente or by ciculatio*,.

On the Occasion of' the already mentioned profile

measure-ments with cavitation

12]

f]

, the limits for the beginning

cavi-tat ion were also observed.. The test8 were made with Reynolds

numbers of about 5 1O

related to the profile chord

Fig.

i representa the reeult in fuiction of the lift coefficient CL

(5)

r

-4-of different tMcknes5 with straight pressure side and eircu1ar

arc suction sido. The thickneis ratio

is denoted.hy

8

The curves are si.ib-dìvided into

tireebranches by two sharp

benda.

The upper

branch

indicte

the limit for suction bide

cavitation

from

the profile leading e&e.

The

case occurs wíie

the ang1

of intcidenìce is so great

that the stagnation point lies

on the préssure side

3nd the 1eadin

edge of the profile is

surrounded by a flow coming

from the

jresure side. The middle

brandi holds for

the

range wTiere the

stagnation point. is on

the leadn.g

edge itself

and the smallest jessure an

the suction

side occurs about

the middle oÍ' the profile chord.

Here the

cavi-tation nurnbero cliaracteriin

the cavitation

start obtain their

smallest values possible.

The start of the pressure side-cavitation

from the leading

ede is represented by the lower branch.,

H.B. H e i

in

b o

1 d

drew attention to the suitability of

representing the cavitation start

for profiles with stagnation

points at the 1eadn edge

in functiori of

and

_._ [7] . in

Fig. 2 the results of Fig.

i

are plotted in

this form.

within

the range

wilere ft

stagnatitn point is at the leading

edge

the nenuremnts

f profiles of the set

A

of various thic'tees

will CO1Cd for t-b plotting.

The limits for the suction or

preure oI(1e cav tion,

starting from the leading edge, however,

do not cntisfy the si»'ip1e rule of affinity. Tie dashed curve is

the result of a

c 1i ion for circular arc

profiles in the range

where the stgnat.

is c

the leading edge, with differt

ratio of the crnhe

e&-'t

f tê centre line of the profile

to the profHe t'n'

cness, 'ich wl later he

discussed in detail.

An enl3refeL t of

the rare of the angle of incidence

without cavitation, is ired at with the set of profiles B

accord-ing to Fig.

3.

Te straight preaure side and

the position of the

rreatest thickness In

the profile centre were inaintained. Compared,

with the set of

profiles

,

however, the forward half of

the

profile wa

designed with a soinewhat greater convexity and

the

nose was gi7erì a curs.red

shape. The ordinates of the profiles

related to the greatest tlickriess are

given in the following

tahle. Four affinous profiles

with

= 0.037,0.075, O.11O,and

C.1485 of this set, al' profiles were investigated. Fig. 4 shows

t'ne start of the cavitation in function

of

and

____

(6)

o profiles

r

loo

loo

Fsuction side

5

the range of the angle of incidence without cavitation, a dis-placerrYnt of the cavitation limit towards smaller cavitation numbers as against set A was also obtained in this range.

This is simply explained by the fact that with the same

pressure minimum on the suction side on account of the greater. convexity of the forward half of the profile; the set of

pro-files B produces greater lift coefficients than the set of

profiles A It must still be mentioned that the limits of

cavitation of the profile sot B comply rather well with the rule of affinity even for entrdnce without shock waves

During the developchent

of propellers it was empirically stated that pressuie side with profiles, which

O 14.4

144

are thicker for reasons

2 5 of stability, cavitation

5

451

3.2 neur the propeller hub

7 52.9 2.2 can frequently he avoided

10

59.9

5 by approximately

bi-15 71 .0 0.3 convex diniensiortirig of

2 79,5

o

he profile. The reor

30 92.0

o

will be discussed later

40 98.5

o

(cf. Figs. 8 end

9).

50 100 0 The pressure side of

60 96.6 0 the set of profiles C

70 85.6 0 represented diagrama.

80

676

o tically by Pig. 5, Is

90 41 ,4 o 9traight only In the

95 25.2 o niddle part ol' the

ioo

300 3.0 profile At both the

ends, however, it is lifted, so that a bicon-vex shape is practi-cally ohtsined

Accoruing t the rnehures of the tab'e In the margin three affinous profiles with the ratios of thickness ¿ = 012,

0.15, and 00181 were constructed and Investigated in the cavi-tation tank. In the range where the stagnation point is t the leading edge the measurements verity again the rule of affinity and can be determined by a curve when is plotted against

(7)

(Wy2

On account of the sal1ar ratto of the camber height of the

centre line of the profile to the profile thickiiesa,

the flow

with stagnation point lies in the rance of smaller

lift

co-effi'cienta than in the case of the above mentioned sets o!

profiles

A

end

B.

= O

means symetr1cally

hicon.vex profiles. For the

blretdy :nentione

3et of profiles

A

with straight pressure aide1

we have

0.5,

hreas poriie with concave pressure aide

are determineI by

? ).5

Moreovei', the ratio of camber

not only depenis on

but also on

ô , ô

By confornal

representation of the circu]ar flow wtth the help of the

Karinari -

Trefftz'represeritation, the maximum velocity

w'

in the centre of the 'uct lori side ws calculated for the oase

of entrance without shock waves (« = 0). The essure varistion

st this location compared with the pressure of the undisturbed

flow then becomes

= i

arid the cavitation number,

with which we have to calculate at the start of the cavitation

according to Eq. (i)

-

In addition of these

Set of profiles

C

computed

100

100

-i-. measurements, we

the pressure minimum on

suctiOi aide

pressure side

the suction side of the

o

2.5

5 10 15

33.3

52.8

61 .1 v'2I .

80.0

set of profiles

D

in a

33.3

potential Liow with

stag-18.3

nation point at the leading

l3.3

edge. The maximum profile

7.2

thickness is sgat

on half

3.6

20 30 40 50 86.1

9 ,5

98 5

loo

'the profile chord,

suction-1 .6

and pressure side consist

o

of cimilar arcs. The retto

o

of the camber height of

o

6c

.97.2

o.

the centre line of the

70

80 85

89.8

75 .0 6 .5

profile

f to the profile

0.5

thickness

d

is aeTheted

2,2

as profile parameter. Some

3.9

90

54.5

6.6

.shapes with

0, 0.25,

95 41 t

11.1

0.5, 0.75, LO, and 1.25

(8)

(

8J)

+

and for the lift coefficient

-7

The cacuìatiort for the start of cavitation gives as an

appro-ximation of Ô 80

r

8) 24 (f)2 ) 2 +

....

(2) = 4 6 +

i6

b + .

(3)

. n !. &'e

in Fig. 8, according to Eq. (2), the cavitation nuiûers

characterizing the start of cavitation In tne cese where the stagnation point is at the leading edge ere plotted for various values in function of the ratio of thickness 6 (curves plotted with full lines) In addition some curves

fo

equal camber ratios are plotted with dashed lines. The curves

= O arid = O coincide. Considering profiles with given camber ratio, the cavitation number indicating the start of cavitation increus3 with growing 6 chiefly by the increase

of the displacement. For = conat. the cavitation number

increes more with

8 , hecausenot only the displacement

but also the ratio of camber. and thus the circulation

increasès Moreover, FigS 8 demonstrates clearly how the camber with equal cavitaticrn number must be iøceased when the

thick-ness ratio is icreased The curve O represents the limit for the greatest possible thickness in a flow without cavitatio*, There is no profile vkiich is surrounded bye flow without

cavitation within the range between the curve = O and

the axis of the abscissa0 In Fig0 9, the curves plotted in full

'ines represent the

lift

coefficient for a

flow-with

stagnation

ooint at the leading edgefunction

of

6 and according' to Eq. (3). The dashed lines again correspond to constant camber ratios. The dash-dotted linea of equal cavitatioh number are taken from Fig, 8 arid demonstrate that with given d greater

lift values

cari be obtained with thinner

profiles

than with

thicket ones. With regard to a good lift-drag rstìo

of

the pro

-file or a small power-loss in order to overcome.the pro-file drag the aim will be to use profiles as thin as possible for the

design of propellers.

Finally the result of

Eqs. (2) arid (3) is plotted i*

CL e'

the form of - against

.

(9)

C

L0

f

,

4Z

or by combining these equations

0L

o

z,

8

r

If the terme with 2 in Eqs. (2) and (3) are neglected we find

8

(2a)

(3e)

(4)

This simple relation is plotted in dasLe.i.lines in Figs .2,

,

6, and 10. When comparing with the ineasuierneits wehare to

consider

that

the

theoretic curve comprases different valuas

arid holds

specially for

O

or

-r -

4 x

Thus tfle

limits of cavitation

which

were observed for ¿ sat of

pro-files with given

within the range where ttke stagnation point

is at the

Jeading edge inthe cavltat.ioh tank1 un, strictly.

speaking

only he compared with that point on the theore io

curve, whose

CLO

is equal to

4 z

. AsF.g. 2 shows,

he

1tiit of

cavjtton

for the whole range o angles of a flow

itn

stagnation point

ìt

the leading edge ,

hover, is

rather well

represented by the x

lation

= .

(f -

)

Conequently

it does not make any differEnce for the limits of cavitation within the same :ane, whether we assume a SmaLl lift increase

to be produced y an inr'rease of the

angle

of Incidence or by

increase of thE. value

with unchanged arle of incidence.

Within this range, the limits of caïitation stated

experi-mentally for

the sete of

profiles B and C

are a litt'e shlfte

as against the set of profiles A for reasons already mentionet and they lie

at smaller values of

than the theory for the set gives In the firstapproximation (Figs. 4 and 6).

When designing a propeller without cavitation,

the

point

t1 operation,

of course, 'ituet not be located on the limltB

for

starting

cavitation

but at

a certain distance from them towards

higher values of

f

.

Starting

cavitation, indeed, has

not yet

a rceptible effect on the forces of the biades, filth regard

to the

danger of blade damage, however, lt must be avoiued,

(10)

V

Moreover, we must conicie that the propeller at the ship not always operates witxi the ratio of ai'ïance or lift coefficient

for which it has been deigned A variation of the ratio of advance can he expected if tk coeffici.ent of the drag of the

ship alters, eg by variatioii of the displacement ox by

grith

on the skin rd the like By alterirg the shape at' the profi set D in the sare sense in which the profiles sets B and C

differ from D, viz

by

a slightly increased convexity of the

front part and by the

curved shape of the nose,

then freedom

from cavitation can be. expected with sufí'icent certainty on

account of the present easurernen s. if the calculation of the design with given - is based on , corresponding to q.(4).

3 Consiìeiation of the curvature

of

streamiinesalon

the chord

The usual rnthd for

calculating propellers is based on

the application

öl' the theory of

the loaded une to

the particular

cndi

ans of the propeller blade Tht

theory of loaded line

suhst.. .uts the blade the chord of which is asuined to be small

by a vortex filament

Corresporidin

to the variable strength of

the vortice in direction of the span, vortices detach backwards along the span. At the location of the loaded vortex filament

these vortices

produce an additional downward velocity. By super-posing these induced velocities with the undisturbed flow there

results. an effective flow at the location of the blade, which deviateB

by the

induced angle of incidence from the geometric

angle of incidence

For great chords. the bade can no longer be replaced by

a vortex filament bL;t by a vortex sheet1 from which also

vor-tices detch backwards.. The

downward velocities thus produced

are variable along the chord. The blade or the vortex sheet

re

placing it, therefore, really are in a flow which, compared with the undisturbed flow, is deflected by the Induced angle of in-cidern3, and curved in addition. In a curved flow, however merely the excess of the

curvature of

the centre line of the

proí'Ue, against the curvature of the streamlines, is decisive

for the lift of a thin profile in a flow with stagnation point

at the ]eading edge. Thus, in

the

three-dimensional flow around a propeller blade the effective camber of a profile is smaller

than its geometric camber.,

We denote the

ratio f

f by k.

(11)

r

-On account of the great

atount of'

calculation required for conputirìg k when designing a propeller accordirxgto the

theory of 1. G i n. z e i and H. L u d w i e g, H. S1t r a ssl

has computed the correction of the curvature for some blade con-tours with different ratios of

advance. In Figs. 11 to 14

the

profile chords of four affinous plan shapes of the t ada

(Ia, Ib, Ic and Id) are plotted against the radius x =

Moreover, the k-values calculated by Strassi, for the ideal

ratlos of advance

= O2, O4,

and Ob are recorded. Figs15

to 17 hold for another set of three affinous plan shapes of

blades (lIa, lIb, lic), the greatest chord of which is more out-side than for the set i In both cases the calculation was

carried out for the blade number z 3 k decreases with

in-creasing chord cf

blades0 An increase of the rEitio of

advance

also results in a decrease of k Finally k decreases with x

at all investigated blade contours. The fact that k disappears completely when x =

unity is

based upon the propositions for the

contour of the blades arid the distribution of the circulatlon,

The calculations are uncertain for small values of x since the

presence of a hub nas

comp.etely

been

neglected arid, moreover, some sintpliflceic'is of the theory are not always admissible there.

The

inflnce of the blade number is

small when

tL.

individual blades are equal in shape und s4ze. The k-value of a four-blade' propeller with the sham Ic for each bJade,

e 0g f or x = dighe r. by only at out 3 pe r cent. than

tha

t

of a three-bla

3fler

with

the sham Ic for each blade,

Cdrisiderin. ho'

propllers with equa total area of the

blades with var

ui

nurrbers, it is evident that there is a

consIderable ln nce the blade numbr on account of the different chord the individual hlades

The tritrpuIatin of the k-values for her plan: shapes

and ratios

of advance is very simple when the plan shape is affinous to the investigated sets I or II . In the figures

il -- 14 or 15 17 the k-values for the desired ideal

ratios ot

advance must be interpolated and

p)otted for the individual plan

shapes of set I and II against 1/D. Figs. 18 and 19 re

present this plotting for X1 0,3 as sii example. From these

diagrams the k-values for other pian

shapes, which

are

ffinous to the sets I or II, cari easily be

interpolated. The

lnter.-polatlon for plan shapes which do not belong to set I or II,

is more difficult becau"e the plan shape of the blade consideraUly Influences the progress of the camber correction against x

(12)

Fig. 20 e.g. shows two plan shapes of set I arid II which,

at x 0.7 have the sar!e chords

and the

apperteinin, k-values

for 0.3

4. Descrition of the methcd of deßi&

The results of the two

receding

sections represent the

foundations for the calculation of a

propeller with large chord

blades arid without cavitation. according to the state of know -ledge irt Germany at the end of the war. The method of design

itself does not

anything

new arid ta mentioned here only for

completeness.

Let the undisturbed speed V(ris1), the number of

revo-lu.tiori(s1), the diameter D 2R (m) or the ratio of advance

V be

knòwn,

ioreover

the power P(rnkg 1)

arid the

density of the water p (kg m a ) Thus the power loading

ratir P is given too,

D

vvith ship propellers endangered by cavitation the number of blades depends on the solidity. With regard toan efficiency as good as possible a ¿reat nuaber of blades would be more

favourable than e small one

If we compare

two propellers with equa. diameter

and

equal tbru4t but different bladé numbers z then the chords of the individual blades arid the forces actizi on them aré inversely proportional to the number of blades.

In both cses, however, the thickness ratio of the blade profiles must be equal for the saine danger of cavitation.

Under this presupposition the1moment of resistance of the profiles will decrease with and the stresses wilt in-crease with z when the blade number increases. As a rule

the propellers of fast ships for the

German Kriegsmarine

were constructed with three blades. The increase of the blade number to z = 4 was not possible on account of the

in-creased stress of the material. Tests withtwo-blade propellers have not been brought to the tuthor's notice, but should not

be neglected0

With consideration of

the stern wave of the moving 8h3.p ,'

let the low position of the propeller shaft below the water surface be h(m) and the air preasure B (kg m2), then the

(13)

from the shaft becomes

(x)

B + (h - xR). y (kg

rn2)

Let

y

he the specific

of the water (kg m) .

With the

separation pressure

e(kg m2) the cavtatioñ

number related

to the cruising speed becomes

(V,x)

=

and

th

cavitation

number related to

the

profile velocity w

Vi1

()2

becomes

=

__!LLL....

x 2

1 +

After having determined

the cavitation numbers coordiiated

to the individual profiles by this method, we choose the

pro-file thickness ratio E for x 0.7,

say, with

reference to

an already tested propeller. As has already been discussed iR detail in the prevIous section, the thickness ratio must not be

chosen gredter than

it appears to be indispensable for reasons

of solidity

- cm Eq. (4) we now obtain the lift coeffleiet

still attainah_e without cavitation

CL =

fr48

For e d drag coefi'icent (say, CD = 0.007) we get

the profile li

i'-

rtic

¿

which is

based as mean

value over th'

le aius. aerice he ideal power loading ratio

according to

eden-Karruan

[8]

cP

1

cP

2

First X1 =

must

be estimated since the ideal

efficiency i not1 yet knowm. The efficiency can be

taken from

Fig. 21 where is xepresented in function of X ,

C(j)

and

z for B e t z - o i d s t.e i n'a optimum screws. When the dj.-gram is used, the efficiency X Is plotted on the lowest ab-scissa. Then WP proceed in a direction parallel to the oblique curves as far as the axis with the

provided

number of blades z.

x)

_.__1L_.

. v.

(14)

13

-The ordinate at this point

shows

in function of

C

or the case that

riot the rete of power loading is give*

but

the rate of tkrust loading CT

---,

is

deter-V D

isined by

Fig0

22, where CT(i) = CT Tb.

repre-sentation of

the ideal

efficiencies in thi.s

fori is rmede

bei K0N r a

m e r

19]

0Now we detemine the chord for

x = 07 It is given

by

Z

L

s in t ( p) x

(5)

The Goldstein

factor

considers the influence of the fi*ite

blade rturiber ori the thrust distribution along the radius.

It is represented in

function cf , z and x i* Fige 23

to 26 = arc tan -4...

is the angle of advanc and

arc tan

-i---

the effct

angle of

dv&riee. The difference

- p

i

the induced

angle of incidence. Let us dispenae with the derivation of Eq. (5),

since the literature gvee

su

icient irtforriation (cf0, saya

4 ). Since remains

con-stitt in the case of

optimum

thrust distributio*

over the

radius,

p

is known also for theother blade sections

x

Now we choose

the remaining shape of the blade

contour the

chord of which is already kncn for

x

0.7

Eq. (5) then

supplies the lift coefficients for all blade sections0 Ftoi

Eq (4), moreover,

we obtain the highest possible thickness

ratios for flow without cavitation

CL

5

_4___ .- w

The pitcrì angle for the individual

profiles becomes

+ «

Since we

presuppose a flow with stagnation point at the leading

edge and obtain it for the

profile set

D

for

«

O

(related to the profile

chord), then the

increase becoies = x X tan z

Now the

profile camber has still to be

ascertained,

For

en-trance

without cavitation it is determined by

t C f CL

(15)

14

-We have alread' d cussed

the

csat;er correction k sufficiently

in section

3 .

Now we do

not apply exactly the profile set D

which we have only investigated on account of the simpler

cal-culation. As already rneritoned in section

2 the front part

of the true profiles will be

given a somewhat

greater convexity

end. the profile

nose will he curved in about the same way as the profile set B

differs

'rcm the sharp-edged segaient.

5.

Results of atotype

eller

According to the above described method the

propellers for

n E-hoat cf the

Kriegsmarine were designed.

The .ß-hoat had three

shafts with

a performance of 195 000

rnkg s

each with a nuaher

of revolutions n =

16.3

s'',

The diameter was

D =1.1 ,

and

the tip speed xr D = 56.4 ais , At a ship speed of 43..5 knotS u

22.3 ms'

aztd an inflow of

6 per cent. within the range of the

side screws, the cruising speed of the latter amounted to

V = 21 For the middle screw ari inflow of

10 er cent. ws

aseumd, In F±g. 27. the chord of the blades, the thjcknes

ratio of the profiles arid their camber, as

well as

the pitch

for the side sc ew are

plotted. For

the blade section at x 0.45

the caiculao

java a profile with straight

pressure aiLe

(f/a

0.5)

.

T'-'

ure aide becomes concave for

x > 0.45

(f/d > 0,5)

and .. vex for

x

< 0.45 (f/d < 0.5)

Fig. 28

represents

a pi

p

l

d1agraa

in axialand sectional elevation.

The middle ac:

rs froc the side screws only by a

smaller

pitch

(H/D =

Inteati

r that the

side screw

abaorb the

desired power

iei:ed nu-er of revolutions, The number

of revoiuti. a .. iddle screw slightly differed floR the

requested vaue

..

because the assumed in!low did not

coripletely corresnd. tc the real conditions, in this respect

the design oarae up co thi' expectations. Considerable daege,

however, was stated at t e blades near

the hub, wiich was reduced

to cavitation. Th reason for the development of' cavitation in the

vicinity of the hub could no more be

stated

before

the end of the

war. There are the following proseihilities which cari quickly be

cleared b

tests with

model propellers in the cavitation tank,

a) At the rotating propeller the boundary layer is flung

away and the qualities of the profiles approach more the ideal

(16)

- 15

two-dimensional paraflel flow. On these conditions the cavitatjø*

at rotating

propeller profile will already begin at higher

ce-vitatio* numbers than we could observe with profile measurements

in the cavitation tank, The ret io between start of cavitation

and lift coefficient for the thick profiles

near the hub,tbere

-fore, is better based on the second approximation

according to

Fig. 10 thai on the first

approxiriation according to Eq.(4).

Owi*g to the rotation of the jet,

the pressure

gradient

in the propeller et was neglected when

the cavitation

number

was calculated. Closely behird the serew it become for an

ele-ment at the

distance r from the axis

R

Ap

-

$KW

dr

r

where

Wt

is the tangentIal disturbing velocity In the trace

of a blade. For optilium

propellers

with

constant over the

rad"ia, it can b. written by means of non-dimensional quantities

i

2

- 8

(1 Z' 1)2

j' (

xi&

xd'x

(6)

I

X

Closely before the screw the

jet is

non-rotational, Thus, there is no pressure drop yet towards the middle of the jet. For the

locatlos.a 1* the middie of the chords we can assume about half the velue of Eq. (6).

We

hare already pointed to

the uncertainty of the camber correction k within

the

range of smaller values x

The variability of the inflow over the radius has not been considered in designing. For want of sufficient testing material

we assumed a mean inflow constant over

x

. Perhaps

this l.a the reason why the flow with stagnation point at the

(17)

r

6,Ref e rences.

[i]

H. Lerba,

[2J

O; Waichner,

H.B. Ee

Tb. Beneri,

Tb .v .Karmri,

Eramer, 16

Investigation of the ca1tatioz

t screw propellers.

131 . Mitt. d. Harnburglschen

Sciiiffbu-Versuchsanste1t (i 936)

Profile measurements in the case

of cavitation.

Hydromechauische Probleme dea

Schiffsantriebes (1932),pg. 256.

profiles.

AVA 45,4i/08 (1 945).

Contribution to the discussion

to

[2].

Hydromechartische Prob1e

des

Schiffssntriebes.

(1932),

pg. 338.

On the theotyof air screws.

Z. VDI volume 68 (1924),

pg.,923

and 1315.

Induced efficiencies of optium

ii screws of finite blade nmbe

Jahrb. d. DL (1938)

1, pg. 357.

L-' Waichner,

Report on the

profile

measure-ments with cavitation, carried out by order of the Marineleitu.n. in the Goettingen

Kaiser-WilheirT

Institut fir Strörnurigsforschung.

KWI-report ('1934) .

[4] F. Horn, Tests with wing-ship screws.

Jahrb. d.

schiffbautechn,

Gesch

schaft 28. Volume

(1927).

[5] I. Ginze,

H. Ludw

On the theory of

the broad b).sd

screw.

L1M

3097

(1944).

(18)

r

075 0,5 Q2 IO b CL C

,-2

cf

I

/

/

/

I-/

/

I

/

--0,073

12

-20 25

Start of cavitation for the set of profiles A

(measurement)

Start of cavitation for the set of profiles

in

'the case of flow without shock waves.

(calcul3t ion)

3 (;5 1,0 1,5 2,0 2,5

i 1

Start of cavitation for the set of profiles A

(19)

Profile 8et

B

¿.5

Q 01

02 03 24 0.5

r

Set of prof ilea

C

18 0,6 0,7 0.8 0,9 1,0 cf =0.037 cf =0075 1

duo

: d0,1485 26 0,7

St.''t of cavitaciok for the eet of profiles B (meurt

Start of cavitation for the set of profiles D

i

tk

caae of flow without shock waves (calculetjon)

08 0,9 1,0

-t

(20)

f-£1 O. o 2,5

StTt of cavitation

(measurement)

Stsrt of cavitation

in the case of flow

(ca1cu1t ion)

f f

-

19

-II

I

o jTTTT

2--0,25 250

for the set of profiles C

for the set of profiles

D

without 3hock waves.

0.75 f d 1,00 1,25

St ji: profiles

D f

--25 10 f5

(21)

r,

1,5 1. t'o 0,5

20

--Q50 ¶,O. -.-

---0O25

9:

Li.t't coefficients of the

profile set

D

in

tXi

of flow without shock wave according to

Eq.

(3)

I

r

4.)

-A

-I

-_Q05O --0,025 f-i-0

-o r:

0.05 0,10 015

8: start of oavitatiori for the profile set

D

in tk

case of flow without

shock waves according to Eq.

(2)

oto 0,15

(22)

'5 10

_ 21

-5 O

to,

15 20 1,25

Start oÎ' cavitat.ou tor the profile

t D in

the 0b88 of flow without 8hoCk waves

Second approximation according to

qa. (2) and (3).

(23)

o 0,8 0,6 0,2 fc. O 'fl .2

N'

r

22

-t'o 08 a6 0,4

iii - 14

Camb-er correction for the set of b1ade

i

PP'«DI

W

k

Ie

Û JILi 0,2 04 06 08 1,0 0 lU2l 02 0,4 0,8 10

ii.

L&g

L.

Ftg

14.

Q6 08 1,0 0 Th10.2 Q4 G6 0,b tO 0,8 05 0,4 c2

(24)

¿.0 0,8 0,6 0, 0.2

Fige

23

-Fig15- 17:

Camber correctton for the set of

blades II.

'f

- o

P@

A s' O rj 0,2 0,6 0,8 1,0 O r.TJ73 0,2 0,4 Q6 0,8 i0

Fi

16.

Fig, 17.

(25)

I0

48

02 0,4 06 0.8 1.0

CainLr correction for the set of blades

at

O.3.

-

24

-A,. (

19: 4Jarabe

orretiori for the set of bJ.ies il

xi = 0.3.'

02 0,4 0,6 08 10

fA C3

(26)

0,8 0 0,4 02

25

-f' Q 0,2 G4 0,6 0,8

20: Influence of the chord distribution c

thb

camber correction at

= 03.

(27)

r

20' Fu

2:

.

w---.--À

o

Ideal

fuictenctes for optimum prope11xa in

function of the ratio of advance1 number of

biades, and ideal power loading ratio,

-1111111

I7°°-!".

H __

..*u ,,i

ui

-&auiuaus

t

asama

i

asauu

sius

aunsuauus

:

!!!!!

!!Ip5

____.u..________0,70 ______

!!MiIII'IIffI

UiIiuìaU1III

-uai.ii'..iu.i

_...u''____...

L

::J

I

-, -030 '

j

.1!!L

----R..

-.

UI

Dii

r -- t

-- k

1111

098 - a T

uUL Lt

-'

as....

uuiui

auii

RIiliIE

UU!IIII

XRUIfl

111111

Í.;:L

liii

VIUH

u Ii

'I.

Ra

mi

a....

a...

guau.

5LUu*

u

.u.

aussi

RIi'1 Wt&iVU

aiuuu

IIrII

lU

i

00

HUIT

UNE 11111

W9k\

I II

I 11111

III

I

liii

1IIF'

tsuiia

'%

as

u a

'*

0,007 17J 0005 QQ? Ql 05 5 J0 8 6 4 0,6 0,4 0.2 8 6 4 2 -JI 8 6 4 3' 8 3 2

(28)

27 A

II

_tIF

_1 J

Ii-_

fil

it4

5!!:::

11111.: :

111111

075 _aso 'u1!

-.

l

U

S

______

m

.u.i

.

&IlU

92-__ul

__

I L. . -. ' j ______-

_______

S t UUU

J

-

-

S--_U

I

-

iIIii_

S

SI'

flflUNhISXi

Il

s

UiIWtIHH

'

. - -

5....0

-

T

11H

iHI

:lull

III'

rulliini

i.

uuuiù '.

ii

umili

Uil II

miiiia

Iii

I%IM

IIV% i

lL%%i

lUVkU h

000? L122J Q005 0.01 0.05 0! 05 s lo

Ideal efficienciea for optimum propellers

in fu.nction of the ratio of advance, number of

blades, and ideal rate of thrust loading.

2 lo 8 6 4 08 0,6 0:4 0,2 0.? 8 6 4 00? 8 6 4 2 0001 c) 8 3 2

(29)

b '2 1 O Q8 »4 v.2

-

28

-ç.

. 23

Factor of mean value Y for optiicurn prope.

(30)

t 6 2 (28 0.6 0, 0.2

-

29

-z. 3

24:

Factor of mean value x

for optimum propellers.

(31)

X

r

30

-2:

F,tot of ineiL vaiu.e g

Íor opt1inuì

2 3 4 5

1,6

7,4

(32)

4 10 0,8 0,6 Q 0,2

-

31 ç

Fi,26: Factor of mean value

for optimum propellers

Cytaty

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