4t
r
-3°b.
lab. y.
ReçortA
Date
ehruiryDC1th,
947
M A .P.VOT-1ffoD
AVG.ONOiP}.8
QkNELAL EPU'OO(I.ìT1C: c
1HIP
OPç
(&VTAT1C.
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
subjecthas
oeeri given, e
gby H
L e r b s
[1]We shall rather
reí'ex
otha
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
Wl3t
The conditions for thestart 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
correspondto the
.arp-edged egmerit.swith 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 presstreaid
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 onti.
'of an aerofoli
The most important
reauÏt
however)
f
ii
w8 the kow1ede that
ri mat aei th cvtatanat cie p7O)eAz,
which up to now was cois1Iered as ar 1zievitab1erawback,
ou1be
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 oftAe
propdlr the result wa veri 'convenient on account
of its
sim-plicityietirt 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 'HamburgisekieSchiffbau-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 trior1of the loaded ltn. thus the well-known
fact is..
explained that
broad-laded propeer
practically produce much less thrustarid absorb ]C83
power than might be expected according to t etheory 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. il44)
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] . Fromthese results the correction cf curvature
can
e interpolatedfor
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-bladedprollers 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
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 liestWOdileAslOTLal
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 thedynar
pressure
q . W2q 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:ltherthe value
6' can be measured in thecavitation
tank, where the first cavitation 18 observed to appear at a model blade or thepressure 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 beginningcavi-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 CLr
-4-of different tMcknes5 with straight pressure side and eircu1ar
arc suction sido. The thickneis ratio
is denoted.hy
8The curves are si.ib-dìvided into
tireebranches by two sharp
benda.
The upper
branchindicte
the limit for suction bide
cavitation
fromthe profile leading e&e.
Thecase 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 thejresure side. The middle
brandi holds for
therange wTiere the
stagnation point. is on
the leadn.g
edge itselfand the smallest jessure an
the suction
side occurs about
the middle oÍ' the profile chord.
Here the
cavi-tation nurnbero cliaracteriin
the cavitationstart 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
inb o
1 ddrew attention to the suitability of
representing the cavitation start
for profiles with stagnation
points at the 1eadn edge
in functiori of
and
_._ [7] . inFig. 2 the results of Fig.
iare plotted in
this form.
within
the range
wilere ft
stagnatitn point is at the leading
edge
the nenuremnts
f profiles of the set
Aof 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
____
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 reasons2 5 of stability, cavitation
5
451
3.2 neur the propeller hub7 52.9 2.2 can frequently he avoided
10
59.9
5 by approximatelybi-15 71 .0 0.3 convex diniensiortirig of
2 79,5
o
he profile. The reor30 92.0
o
will be discussed later40 98.5
o
(cf. Figs. 8 end9).
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, Is90 41 ,4 o 9traight only In the
95 25.2 o niddle part ol' the
ioo
300 3.0 profile At both theends, 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
(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
Aend
B.= O
means symetr1cally
hicon.vex profiles. For the
blretdy :nentione
3et of profiles
Awith 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 , ôBy 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
= iarid 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
Ccomputed
100
100-i-. measurements, we
the pressure minimum on
suctiOi aide
pressure side
the suction side of the
o
2.5
5 10 1533.3
52.8
61 .1 v'2I .80.0
set of profiles
Din 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 86.19 ,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 8589.8
75 .0 6 .5profile
f to the profile
0.5
thickness
dis 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
(
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 !. &'ein 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 displacementbut 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 aflow-with
stagnationooint 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 greaterlift values
cari be obtained with thinnerprofiles
than withthicket ones. With regard to a good lift-drag rstìo
ofthe 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 thedesign of propellers.
Finally the result of
Eqs. (2) arid (3) is plotted i*
CL e'
the form of - against
.
C
L0
f
,
4Z
or by combining these equations
0L
o
z,
8r
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
thatthe
theoretic curve comprases different valuasarid holds
specially for
Oor
-r -
4 x
Thus tfle
limits of cavitation
which
were observed for ¿ sat ofpro-files with given
within the range where ttke stagnation pointis at the
Jeading edge inthe cavltat.ioh tank1 un, strictly.speaking
only he compared with that point on the theore io
curve, whose
CLOis equal to
4 z
. AsF.g. 2 shows,
he
1tiit of
cavjtton
for the whole range o angles of a flowitn
stagnation pointìt
the leading edge ,hover, is
rather wellrepresented 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 byincrease 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 Care 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
pointt1 operation,
of course, 'ituet not be located on the limltB
forstarting
cavitationbut at
a certain distance from them towardshigher values of
f
.Starting
cavitation, indeed, hasnot yet
a rceptible effect on the forces of the biades, filth regard
to the
danger of blade damage, however, lt must be avoiued,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 Cdiffer from D, viz
by
a slightly increased convexity of thefront 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 onthe application
öl' the theory ofthe loaded une to
the particularcndi
ans of the propeller blade Thttheory 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 thereresults. an effective flow at the location of the blade, which deviateB
by the
induced angle of incidence from the geometricangle 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 sheetre
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 thecurvature of
the centre line of theproí'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 smallerthan its geometric camber.,
We denote theratio f
f by k.r
-On account of the great
atount of'
calculation required for conputirìg k when designing a propeller accordirxgto thetheory 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
theprofile 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. Figs15to 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 ofadvance
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 thecontour 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.etelybeen
neglected arid, moreover, some sintpliflceic'is of the theory are not always admissible there.The
inflnce of the blade number issmall 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
tof a three-bla
3flerwith
the sham Ic for each blade,Cdrisiderin. ho'
propllers with equa total area of theblades with var
ui
nurrbers, it is evident that there is aconsIderable 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 figuresil -- 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 represent this plotting for X1 0,3 as sii example. From these
diagrams the k-values for other pian
shapes, whichare
ffinous to the sets I or II, cari easily beinterpolated. 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
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-valuesfor 0.3
4. Descrition of the methcd of deßi&
The results of the two
receding
sections represent thefoundations for the calculation of a
propeller with large chordblades 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 forcompleteness.
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. diameterand
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
from the shaft becomes
(x)
B + (h - xR). y (kg
rn2)
Let
yhe the specific
of the water (kg m) .
With theseparation pressure
e(kg m2) the cavtatioñ
number relatedto the cruising speed becomes
(V,x)
=and
thcavitation
number related tothe
profile velocity wVi1
()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 toan 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 cavitationCL =
fr48
For e d drag coefi'icent (say, CD = 0.007) we get
the profile li
i'-
rtic
¿which is
based as meanvalue over th'
le aius. aerice he ideal power loading ratioaccording to
eden-Karruan
[8]cP
1
cP
2
First X1 =
must
be estimated since the idealefficiency 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 theprovided
number of blades z.x)
_.__1L_.
. v.
13
-The ordinate at this point
shows
in function of
Cor 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 idealefficiencies in thi.s
fori is rmede
bei K0N r am e r
19]0Now we detemine the chord for
x = 07 It is given
byZ
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 23to 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 remainscon-stitt in the case of
optimumthrust distributio*
over theradius,
pis known also for theother blade sections
xNow we choose
the remaining shape of the bladecontour the
chord of which is already kncn for
x0.7
Eq. (5) then
supplies the lift coefficients for all blade sections0 FtoiEq (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 leadingedge and obtain it for the
profile set
Dfor
«
O(related to the profile
chord), then the
increase becoies = x X tan zNow the
profile camber has still to be
ascertained,For
en-trance
without cavitation it is determined by
t C f CL
14
-We have alread' d cussed
the
csat;er correction k sufficientlyin section
3 .Now we do
not apply exactly the profile set Dwhich we have only investigated on account of the simpler
cal-culation. As already rneritoned in section
2 the front partof the true profiles will be
given a somewhat
greater convexityend. the profile
nose will he curved in about the same way as the profile set Bdiffers
'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 threeshafts 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 u22.3 ms'
aztd an inflow of
6 per cent. within the range of theside 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 pitchfor the side sc ew are
plotted. For
the blade section at x 0.45the caiculao
java a profile with straightpressure 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
pl
d1agraa
in axialand sectional elevation.The middle ac:
rs froc the side screws only by a
smallerpitch
(H/D =
Inteati
r that theside 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 reducedto cavitation. Th reason for the development of' cavitation in the
vicinity of the hub could no more be
stated
beforethe 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
- 15
two-dimensional paraflel flow. On these conditions the cavitatjø*
at rotating
propeller profile will already begin at higherce-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 profilesnear the hub,tbere
-fore, is better based on the second approximationaccording to
Fig. 10 thai on the firstapproxiriation according to Eq.(4).
Owi*g to the rotation of the jet,
the pressure
gradientin the propeller et was neglected when
the cavitation
numberwas calculated. Closely behird the serew it become for an
ele-ment at the
distance r from the axisR
Ap
-
$KW
dr
r
where
Wtis the tangentIal disturbing velocity In the trace
of a blade. For optilium
propellerswith
constant over therad"ia, it can b. written by means of non-dimensional quantities
i
2
- 8
(1 Z' 1)2j' (
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 thelocatlos.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 withinthe
range of smaller values xThe 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
. Perhapsthis l.a the reason why the flow with stagnation point at the
r
6,Ref e rences.
[i]
H. Lerba,
[2J
O; Waichner,
H.B. Ee
Tb. Beneri,
Tb .v .Karmri,
Eramer, 16Investigation 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).sdscrew.
L1M
3097
(1944).r
075 0,5 Q2 IO b CL C,-2
cfI
/
/
/
I-//
I
/
--0,07312
-20 25Start 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
Profile 8et
B¿.5
Q 01
02 03 24 0.5
r
Set of prof ilea
C18 0,6 0,7 0.8 0,9 1,0 cf =0.037 cf =0075 1
duo
: d0,1485 26 0,7St.''t of cavitaciok for the eet of profiles B (meurt
Start of cavitation for the set of profiles D
i
tkcaae of flow without shock waves (calculetjon)
08 0,9 1,0
-t
f-£1 O. o 2,5
StTt of cavitation
(measurement)
Stsrt of cavitation
in the case of flow
(ca1cu1t ion)
f f-
19
-III
o jTTTT 2--0,25 250for the set of profiles C
for the set of profiles
Dwithout 3hock waves.
0.75 f d 1,00 1,25
St ji: profiles
D f --25 10 f5r,
1,5 1. t'o 0,520
--Q50 ¶,O. -.----0O25
9:
Li.t't coefficients of the
profile set
Din
tXiof 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 0158: start of oavitatiori for the profile set
Din tk
case of flow without
shock waves according to Eq.
(2)
oto 0,15
'5 10
_ 21
-5 Oto,
15 20 1,25Start oÎ' cavitat.ou tor the profile
t D in
the 0b88 of flow without 8hoCk waves
Second approximation according to
qa. (2) and (3).
o 0,8 0,6 0,2 fc. O 'fl .2
N'
r
22
-t'o 08 a6 0,4iii - 14
Camb-er correction for the set of b1ade
iPP'«DI
W
kIe
Û JILi 0,2 04 06 08 1,0 0 lU2l 02 0,4 0,8 10ii.
L&gL.
Ftg
14.
Q6 08 1,0 0 Th10.2 Q4 G6 0,b tO 0,8 05 0,4 c2¿.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 i0Fi
16.
Fig, 17.
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
0,8 0 0,4 02
25
-f' Q 0,2 G4 0,6 0,820: Influence of the chord distribution c
thb
camber correction at
= 03.
r
20' Fu2:
.
w---.--Ào
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
asamai
asauusius
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 -- k1111
098 - a TuUL Lt
-'as....
uuiui
auii
RIiliIE
UU!IIII
XRUIfl
111111
Í.;:L
liii
VIUH
u Ii
'I.
Rami
a....
a...
guau.5LUu*
u.u.
aussiRIi'1 Wt&iVU
aiuuu
IIrII
lU
i00
HUIT
UNE 11111W9k\
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 3 227 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 UUUJ
-
-S--_U
I-
iIIii_
SSI'
flflUNhISXi
Il
sUiIWtIHH
'
. - -5....0
-T
11H&Ê
iHI
:lull
III'
rulliini
i.
uuuiù '.
ii
umili
Uil II
miiiia
Iii
I%IM
IIV% ilL%%i
lUVkU h
000? L122J Q005 0.01 0.05 0! 05 s loIdeal 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 2b '2 1 O Q8 »4 v.2
-
28
-ç.. 23
Factor of mean value Y for optiicurn prope.
t 6 2 (28 0.6 0, 0.2
-
29
-z. 324:
Factor of mean value x
for optimum propellers.
X
r
30
-2:
F,tot of ineiL vaiu.e g
Íor opt1inuì
2 3 4 5
1,6
7,4
4 10 0,8 0,6 Q 0,2