2 2 SEP; 1q32

### ARCH1EF

### Lab.

### y. Scheepsbouwkund

### Technische HogeschooI

### Minimizing Hydrodynamic

### Deift

### Blade Spindle Torque by Ventilation"

### Con'f;oI!ebte-Pif ch Propellers

### By Ir. L. A. van Gunsteren 2)

The engineering effort and the costs needed for the reali-sation of a c.p.p. installation are directly dependent on the magnitude of the actuating forces. These are the forces to be produced by the actuating mechanism for the changing

of pitch during operation. The actuating forces are pro-portional to the blade spindle torque, that is the torque

with respect to the spindle axis required to change pitch. In modern large c.p.p. installations, with over 25,000 horse

power which is no longer exceptional, the blade spindle torque can easily raise the actuating force (e.g. in the

actuating rod) to over 200 tons. The immense engineering problems of such heavy loadings put a limit on the

reali-sation of the shipowners' wishes concerning the c.p.p. A

drastic decrease of the blade spindle torque, without affect-ing other aspects, could therefore mean an important step forward. How can this be achieved?

The blade spindle torque is made up of three parts (see Fig. 1): 1. a torque due to hydrodynamic forces: 2. a torque due Fig. 1. Basic pressure distributions.

MEAN LINE PRESSURE DISTRIBUTION

TRAILING EDGE C + + L EADING EDGE

### TE(

DIRECTION OF FREE STREAM C + LE, I.. D ES 1G N PR ESS U RE DISTRIBUTION FLAT PLATE PR. DISTR DISTORTION### 7

PR.OISTR. TOTAL" PP OtSTR') Abstract from paper presented at the Inrybprom' Exhibition,

Leningrad.

2) _{Lips NV., Drunen, Holland.}

to mechanical friction; 3. an inertia torque due to centrifugal

forces.

The inertia torque is much smaller than the hydrodynamic

and the frictional one, although it should be taken into

account in quantative calculations of blade spindle torque. The friction torque depends directly on the hydrodynamic torque which itself is roughly half the total blade spindle torque. Significant gains are thus only to be expected from a reduction in the hydrodynamic blade spindle torque.

Of course, many attempts have been made to reduce the

hydrodynamic spindle torque, but only the application of skew back has no significant additional disadvantages. It is not possible, however, to choose the skew in such a way, that a low hydrodynamic spindle torque is obtained over

the whole range of operation. A useful improvement is

therefore only to be expected from hydrodynamic means,

### which can be temporarily used and do not affect the

performance of the propeller in the design condition. Such a solution may be found in movable flaps, which involves, however, serious mechanical problems.

A more practical means for the control of the pressure

distribution over the blades may be the injection of air (or

other gases) through holes in the blades, the air being

supplied through tubes in the shaft and actuating mechan-ism. It is the aim of this paper to investigate and discuss this idea.

Nature of the blade spindle torque

With an ordinary right handed c.p.p. the entrance in the design condition will be nearly shock free, that is, the stagnation point is located on the nose of the profile and consequently the pressure distribution over the chord o a

blade element will have an elliptic character. The resulting lift force of this pressure distribution acts about mid-chord or slightly forward of it, as for instance when the N.A.C.A. a = 0.8 mean line is used. It is logical to select the skew in such a way that the maximum spindle torque encountered

SPIN OLE AX IS

### /

TE. Dl### \

D /O DESIGN POSITION AFTER DECREASING r PITCH LE.Fig. 2. Projected blade outline at different pitch settings. in the whole range of operation is minimized.

This requirement generally yields a moderate and negative hydrodynamic spindle torque in the design condition (out-wardly directed torque vectors are defined to be positive). Thus, the hydrodynamic loading 'tries' to put the blade in

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Le astern position. In this way the point at which the

dndle torque changes direction and flutter might occur, kept outside (above) the range of operation.

y decreasing the pitch, so that the effective angle of attack tnds to become negative, a pressure distribution is obtained

hich can be thought to be macle up of three parts: a basic pressure distribution associated with the camber of the section - the design pressure distribution. a pressure distribution of a non cambered profile (flat plate) under a negative angle of attack.

a pressure distribution associated with the distortion of the mean line due to pitch changing.

bese three pressure distributions are schematically

in-Icated in figure 1.

e nature of the distortion of the mean line due to the

icrease in pitch requires explanation. Fig. 2 gives the axial ojection of the outline of a propeller blade, looking from t in the sailing direction.

Dnsider the mean line of the secion C-T-A on radius X. r the sake of simplicity we assume this mean line to be

### at in the design condition. By a pitch decrease of an

igle A q, the section mean line on radius X becomes i-T-Bi. MEAN LINE IS TO PIED DECREASING ITCH C

g. 3. Mean line distortion.

he points B1 and D1 originate from the points B and D.

these points are situated more inward than the points

and C, their local pitch angles have to be larger. Conse-uently, the local pitch angles at the points B1 and D1, are

so larger than those of the points A and D.

ie resulting mean line is not flat any more, but has an

-shaped form as indicated in fig. 3. A second consequence

this effect is, that the nose-tail line has turned over a naller angle than the blade itself, as will be clear from specially at large pitch deviations, both the additional Itch angle of the nose-tal line and the distortion of the tean line have a considerable influence on the pressure

istribution. We developed a procedure, which can calculate 1ACTERI STIC OPERATING

lITIONS RO TRRIJST POINT LLANO AIIEAD LLANO ASTERN Et RUNNING AhEAD (E RUNNING ASTERN

MEAN LINE IN DESIGN POSITION

BL AC E

SPINDLE TORQUE

NOSE-TAIL LINE

AFTER DECREASING PITCH

PITCH ANGL E Q PI TCINCIIANG ING TOWARDS AHEAD ITHOUT FRICTION P lIC Ii CH ANGING TOWAROS ASTERN

Blade spindle torque versus pitch angle at nw.ximum tational speed.

lo

Fix advance ratio J and assume

Calculate effective angles of attack by iterative lifting Line procedure Calculate pressure distribution over the blades

uithin tolerance Integrate pressure distribution yielding six hydrodynonic force/ torque coefficients

Integrate centrifugal Force dustribution yielding sio

inertia force / torque codfficients

¿

Add hydrodyeanic and inertia loads and integrate consequent friction forces in the mechaniSm, yielding actuating forces.

Fig. 5. Flow chart of the calculation of actuating forces. the shape of the distorted mean line of a section at a given pitch angle deviation from the design position. This pro-cedure has been incorporated in all our computer programs concerning the hydrodynamics of controllable pitch

pro-pellers.

It will be clear from fig. 1, that both the 'flat plate' pressure distribution and the 'distortion' pressure distribution have

an increasing effect on the blade spindle torque. Conse-quently we may expect the hydrodynamic blade spindle torque to increase the more the angle of attack becomes

negative and the more the pitch is put astern.

In practice, however, the largest actuating forces are not met in the astern condition, but in the vicinity of the point

of zero thrust. This is caused by the effect of cavitation

which considerably affects the pressure distribution at

negative pitch settings. In particular the 'flat plate' pressure distribution is 'cut off' by the cavitation number.

As in the partially cavitating condition the lift is known

to be hardly effected, the cut off 'pressure area' at the nose will be compensated by an approximately equal additional

### area at the rear of the chord. The larger the region of

cavitation, the more favourable the pressure distribution

will be with regard to the blade spindle torque.

The characteristic curve of the blade spindle torque as a

function of the pitch setting at constant rotational speed of the propeller is indicated in fig. 4.

Non cavitating sections at negative pitch settings can be

met in practice when the blade area is exeptionally large. In such cases the maximum blade spindle torque occurs at maximum negative pitch, as is indicated with a dot-dash line in fig. 4.

The favourable effect of cavitation upon the magnitude of the hydrodynamic blade spindle torque already suggests that an important gain may be achieved by enlarging this influence.

The friction blade spindle torque is always directed against the movement itself. Thus, the largest (negative) spindle torques occur putting the pitch from astern to ahead. The total spindle moment is indicated by a thick line in fig. 4.

The friction spindle torque depends on all six force and torque components exerted by the blade onto the hub; it

may behave discontinuously if one of these components

Changes sign and the origin of the friction is abruptly changed from one surface in the mechanism to another.

### I

2 Calulote distortion

of mcxc Lines

3 Calcolate zero lift direction and lift gradient of distorted Sections 7 Correct 1'/D.7R 4 h 5 out of tolerance 6 8 9

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In fig. 4 five characteristic points are

indicated:-1. Point of zero thrust; 2. bollard condition ahead; 3. bollard condition astern; 4. free running ahead; 5. free running

astern.

Although more severe situations with regard to blade spindle torque are imaginable e.g. the manoeuvre from

ahead to astern and immediately again to ahead, we feel that these five conditions determine sufficiently the actual

### situation. For many cases the picture

### is even on the

pessimistic side, because mostly there is no need to run

through the zero pitch point at maxmum rotational speed of the propeller. Already a small reduction in r.p.m. at this point considerably lowers the blade spindle torque.

In our analysis of the merits of ventilation with respect to the actuating forces, we shall calculate these forces for the

CAMBER PITCH 1 ¿00 7.5 1X00 0,X9 9.6 1X00 01 14.6 1X00 01 19.0 1400 0.7 02.1 0400 0.6 15.3 1058 0,5 7.2 1209 0.4 0.0 lOSO 0.3

RADIUS EXPANDED BLADE OUTLINE

SII _L_4

602 210

6MO _.._4___.,,3l

five conditions defined above in both the non ventilatc

and the ventilated condition.

Calculation of actuating forces in non ventilated condition

Figure 5 shows a simple flow chart of the calculation

the actuating forces in one of the five characteristic ope

ating conditions. As it is beyond the scope of this pap.

to present a detailed description of the applied theories at methods, only the essence of them will be given.

### The distortion of the mean lines (box 2 of fig.

5),described above, is calculated assuming that the section flat in the design condition. The resulting S-shaped mez line is simply added to the design mean line and the turnii of the nose-tail line is incorporated in the pitch angle. The calculation of the two dimensional section characte

### /

PROPELLER 0F FIGURES ICALCUL PROPELLER B 3-SO 1 NEASUR! PIO :0.6Fig. 7. Open water diagram.

PEN WATER DIAGRA

SPINDLE

AX S DIAMETER 2300mm

NUMBER DF BLADES 3

EXPANDED BLAOE AREA RATIO 0,526

ENGINE OUTPUT 1290 B.H,P, 300 R.P.M.

SACA 0.0 MEAN LINE OIACA1STHICRNESS FORM

Stand E336 Europort 1968

Exhibition

stics (box 3 and box 5 of fig. 5) is done by the method

[escribed in section 4.5 of reference (2). In this method

he velocity distribution about the wing section is considered

o be composed of three separate and independent

corn-onents:

the distribution corresponding to the velocity

distri-bution over the basic thickness form at zero angle of

attack.

the distribution corresponding to the load distribution of the mean line at its ideal angle of attack.

the distribution corresponding to the additional load

distribution associated with angle of attack.

hese three basic velocity distributions have been tabulated n reference (2) for families of thickness forms and mean

ines, the tables being computed by conformal mapping

COMPUTED

MEASURED CULL SCALE) (TON

- Is (P ER AT IM ,ONO ilION -10 SKEW Da R IO FORCE N ACT U AT j NG ROD

---IO 2 4ig. 8. Computed and measured actuating forces. Amsterdam RAI-bu ilding November 12-16, 1968 15(D FOR E ES P11CM ANGLE E? R

### vuyk shipyards

### holland

techniques. When proper corrections for viscosity are applied, the pressure coefficients obtained by this method are considered to he very accurate. In order to be able to use the tables of reference (2), any mean line is thought to be made up of several tabulated meanline types.

The effect of cavitation is taken into account as follows. If the under pressure coefficient at any point of the suction side would exceed the cavitation number, the area cut off by the cavitation number at the entrance is distributed over the rear of the chord. This additional pressure distribution is assumed to decrease linearly over the rear of the chord

towards zero at the traiing edge.

The iterative lifting line procedure (box 4 of fig. 5) is similar to the method described in reference (3); it differs, however, basicafly in the application of correction factors.

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Basic assumption is, that the sections can be calculated independently. This is in fact only correct for propellers with an optimum radial load distribution. We got round this difficulty by introducing proper correction factors. Starting point is the well known equation of optimum

lifting line propellers (see reference (4) section 41):

47ED

C1, = z k sin 13' tan ((3,-13) (1)

### zC

where:

CL = lift coefficient of the section D = propeller diameter

y. = dimensionless radius Z = number of blades

### C = chord length

13 = pitch angle of undisturbed inflow direction

(3, = pitch angle of inflow direction corrected for velocities induced by the free vortex system K Goldstein factor, allowing for the effect of

finite number of blades

...-...---..NONVENTILATEO 5OEWO.Rll)I T SIDE VENTILATED 2 SIDES VENTILATED -IS OPERAI ING CONDITION P R PRESSURE COEFFICIENT 4 TRAILING EDGE - 1.2 x/C t SIDE VENTILATED SKEW o 1 7.6 /. O.S R NON VENTILAT D

I ACTUAl ING FORCE VERSUS PITCH ANGLE AT MAXIMUM ROTATIONAL SPEED

Fig. IO. Actuating force versus pitch angle at maximum

rotational speed.

PRESSURE DISTRI BUTIONS AT 0.7 RADIUS

Fig. 11. Operating condition I (zero thrust).

2 SIDES VENTI ATEO L E AO ING EDGE (DEGREES) PITCH ARELE 0.7 R

### Usually an additional correction - for instance that

ILudwieg und Ginzel - on camber is applied, allowing f stream curvature (lifting line-lifting surface correction). In our method neither Goldstein, nor Ludwieg und Ginz corrections are applied. Instead a correction on the inducE velocity is used, which includes:

effect of number of blades

effect of aspect ratio (lifting line-lifting surface correc ion)

effect of propeller load (slip stream contraction) The correction has been found by an extended regressic

analysis of systematic propeller series. Bringing the li gradient to the right side of equation (1), we can write

in form: a = f (u) (la)

where:

ci = angle of attack measured from zero lift direction.

This equation can conveniently be solved by Wegstein

iterative method (see reference (4) ).

It seems useful to give an impression of the accuracy of ti' methods described so far. Figure 6 gives the particulars a controllable pitch propeller of a trawler. We will use th

### propeller as an example throughout this paper. Fig.

presents the open water diagram of this propeller calcu

ated with the methods described above.

Also the characteristics of a comparable Troost propelh have been drawn. Not only from the agreement showed i fig. 7, but also from experience with this method in man other cases, it may be concluded that it possesses sufficier accuracy.

Once the pressure distribution is determined, the hydr(

dynamic forces and torques are obtained by chordwise an

radial integration (box 8 of fig. 5). As an example of ti'

expressions involved, we present in appendix i the formu]

for the hydrodynamic torque component with respect I the spindle axis. Expressions for the other five hydr( dynamic force torque coefficients are found in a similr

way. The numerical integration of the centrifugal forcE involves no particular difficulties (box 9 of fig. 5).

### Once the forces exerted by the blade onto the hub ai

determined, the consequent friction forces in the mechanist are calculated and added (box. 10 of fig. 5). Of course, tE choice of friction coefficients involves some uncertainty. Fig. 12. Operating conditions 2 and 4 (bollard ahead an free running ahead).

PRESSURE COEFFICIENT I

### '

OP ERAl ING a CONDITION 2 TRAILING EDGE SKEW_{o 17.1 /.}x/C PRESSURE DISTRIBUTIONS 4j O.7RADIU$.(IOENTICALIN

NÖN VENTILATED AND IN_ VENTILATED CONDITION

This completes the calculation of the actuating forces.

### In order to give an impression of the accuracy of th

procedure described above, the results cf calculations fc the propeller of fig. 6, as well as full scale measuremeni of it are presented in fig. 8.

In view of the many approximations involved, we feel thr

the agreement is sufficient, in any case for the preser analysis.

LEADIN

PRESSURE O E C I E N T P .2 TRAILING E DGE -1.0 - 1.2 I SIDE VENTILATED SKEW NON 0.SR VENTILATED PRESSURE DISTRIBUTIONS AT 0.7 RADIUS

1g. 13. Operating condition 3 (bollard astern).

r 175/. LEADING ED GE 2 SIDES VENT ILATED he ventilated condition

will be obvious, from the considerations of the second

### ection and our example presented in the preceeding

ction, that the severest condition is putting the pitch from

### stern to ahead, at about zero - or in some cases at

egative - pitch settings. The most significant contribution the negative hydrodynamic blade spindle torque can be

xpected to originate from the 'flat plate' pressure

### distri-ution at negative angle of attack. See fig.

1. We can duce the strength of this distribution by ventilating airrough the face of the blade, that is the nominal pressure de, now acting as a suction side. We assume air inlets to e located on the face at 5 % from the leading edge. The

### ir pressure is assumed to be equal to the free stream

ressure; that means tbat the cavitation number based on

avity pressure is zero and the cavity, starting from the

ose of the section, is infinite in extent. It is known from

e theory of fully cavitating flows that the lift gradient

only one quarter of that of the sub cavitating foil. This

### eans that the reduction in the effect of the flat plate

ressure distribution of fig.

### i may be expected to be of

e same order.

ased on the finding of reference (6), in which the

require-ents for ventilation inception are investigated, we may xpect that this point will not present any difficulties in

ractice. A very favourable circumstance in this respect is

at in the considered condition the angle of attack and

e camber have opposite sign, yielding a pronounced under ressure peak at the leading edge. In our calculations we

all assume arbitrarily the ventilation to start, if in the

on-ventilated condition the under pressure coefficient at e 5 % chord point exceeds 0.05.

nother point of practical importance consists of the air

quirements, because these will determine the air supply

easures such as the tubes in the blades and actuating

echanism. This problem has been investigated in refer-nce (7). In view of the results of this refererefer-nce, we may

### ate that also this point will not present any serious

oblems. In order to get an impression of the feasibility

of the air supply system, we made several designs of the hub mechanism with such systems built in.

The idea of ventilation being feasible at a first glance, we now have to make quantitative calculations of the reduction in blade spindle torque. This is not so easy, because a three

dimensional theory for the analysis of fully cavitating

propellers is not yet available. We therefore shall proceed as follows.

In the computer program the described test on ventilation inception is built in. If ventilation occurs, all two dimens-ional calculations of the considered section are replaced by

procedures for the analysis of ventilated lifting foils in

two dimensional flow.

This concerns box 3 and 5 of fig. 5.

Earlier design methods of supercavitating propellers were based on this principle, which has led, however, to over-optimistic predictions. The discrepancy can be explained by two important effects, namely cavity blockage and cavity-blade interference. See reference (8).

These effects influence the lift of the blade sections. But it

is not to be expected that they will have a strong effect

on the distribution of pressure along the chord, this being the key point of the present study. In view of this we shall

### neglect cavity blockage and blade interference in our

calculations.

We assume that the sections are only ventilated during

pitch changing. Consequently the pitch positions of the five characteristic operating conditions are identical in both the

ventilated and the non ventilated condition. Calculating

with the corresponding pitch settings of the non ventilated condition, we may therefore omit for the ventilated case the

iteration on horse power (box 6 of figure 5).

Also the procedures concerning partially cavitating con-ditions are skipped, because these regions are ventilated

now.

The pressure distributions in two dimensional ventilated

flow are calculated with the linearized theory for fully cavitating foils at zero cavitation number of Tulin and

Burkart (9). In this theory the fully cavitating hydrofoil is reduced to an equivalent airfoil, which can be analysed by classic thin airfoil theory.

PRESSURE CO EF F ICI E N T P R t TRAILING E OGE - 1.0-SKEW r 17.6 /. 0.8 R NON VENTILATED -t. . -t .9 .6 .2 i SIDE VENTILATED PRESSURE DISTRIBUTIONS AT 0.7 RADIUS

Fig. 14. Operating conditions (free running astern

LEADING EGG E

The results of reference (9) used in our study are reviewed

in appendix

### 2. We analysed the equivalent airfoil by

Glauert's method, taking 30 sinuscoefficients in the Fourier expansion throughout all calculations.

Test calculations for a flapped hydrofoil, which is obviously

### not very suited

to Fourier analysis, yielded pressuredistributions agreeing within a few percent with the meas-urements of Meijer (lO).

We have to deal with the case of a fully cavitating foil with negative camber and positive angle of attack. See fig. 9. This has some consequences. Analizing this configuration

-I OPERATING CONDITION s PR ESSURE COEFFICIENT P R

### I

### ----

### u

### I1_.=L

T RAIL I NG EDGE 1.0 SKEW o 8,8/. 0.8 R .8 I .6 NON VENTILAJED 1 SIDE VENTILATEDPRESSURE DISTRI BUTIONS AT 0.7 RADIUS

Fig. 16. Operating condition i (zero thrust).

I DEGREES) PITCA AMGL 0.3 R 2 L LEAD ING EDGE

we arrive at under pressures at the wetted side. In naturally fully cavitating flow this would be a physically impossible solution, because cavitation would occur at such points. In artificially cavitating flow such solutions are acceptable, provided, of course, that the under pressure coefficient does not exceed the cavitation number based on vapor pressure. The drag characteristics of such negative cambered fully

cavitating foils are very poor. We found indeed in our

calculations that by ventilating the blades, the drag coeffi-cients of the sections will increase considerably. This may

be a useful circumstance. In the ventilated condition the lii

is strongly reduced, so also the torque on the propelle

shaft will decrease considerably. This may be uníavourabl with regard to the characteristics of the machinery.

### The fact that fully cavitating foils are so much mor

sensible to profile form than subcavitating foils, work

also in an unfavourable sense.

Test calculations showed that the negative moment co

efficient of negatively cambered sections is in fully wette

flow only about 2/3 of that in fully cavitating flow. Thi

works out uníavourably with respect to the blade spindi

torque. The effect is

### stil enlarged by the fact that ih

negative camber of the wetted side of the fully cavitatin section is half the blade thickness larger than the cambe

### of the mean line of that section. Also the effect of th

S-shaped form of the section due to the distortion is in

creased in the ventilated condition.

### In view of these considerations, we also included th

possibility of ventilation on two sides of the blade. We proceeded as follows. If the considered section is alread ventilated on the face, the pressure coefficient at 70 % c the chord from the entrance is tested. If the under pressur coefficient exceeds 0.05, it is assumed that the back of th section is also ventilated. The free stream line is assume

to spring off from the 70 % chord point, so that the rea

of the section is over 30 % of the chordlength entirely witl in the cavity.

In order to establish this situation, extra air inlets have t

be provided on the back of the blade slightly behind th

70 % chord point. It should be noted that the conditions fo

cavitation inception are less favourable than at the inlet

on the face of the blade.

How serious this problem is, can only be explored by mean of experiments.

Results

Having available the tools for the calculation of the actual

ing forces both in non ventilated and in ventilated cor

### ditions, we are now able to present the results of th

SKEW r 0.8 R PRESSURE COEFFICIENT TRAILING EDGE LEADING EDGE PRESSURE DISTRIBUTION. AT 07 RADIUS (IDENTICAL IN NON VENTILATED AND IN VENTILATED CONDITION I

Fig. 17. Operating conditions 2 and 4 (bollard ahead a free running ahead).

3

### j

Fig. 15. Actuating force versus pitch angle at tmo.xiinum rotational speed.

SKEWØJ II .0.

NON VENTILATED FORCE IN

(TON) ACTUATING

----1 SIDE VENTILATED ROD 30 OPERATING COOITION 2 / OPERATING CONDITION R

### i

### LIPS'

### CONTROLLABLE

### PITCH PROPELLERS

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### WORKMANSHIP

### IN PROPELLER

### AND ADJUSTING

### MECHANI SM

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But LIPS have done something more too. They have reduced

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hydraulically and is entirely inboard. Reliability is at the maxi-mum - the propeller can take even higher loads than it will ever be called on to take at sea. The perfect hydrodynamic design of blades guarantees maximum efficiency.

### LIPS NV.

DRUNEN - HOLLANDPRESSURE C OEF F IDI ENTE

PR :2 T R4 I L N G EDO E -.' -1.0 PRESSURE CO E FF IC lE NT .2 TRAILING EDGE -Á -.8 - 1.0 NON VENTILATED B .6 x/c t SIDE VENTILATED SKEW r 1.8 /. 0.8 R PRESSURE DI STRIUTIQNS AT 0.7 RADIUS

Fig. 18. Operating condition 3 (bollard astern).

analysis of our example. The propeller is defined in figure 6, the radial wake distribution and the mean inflow velocities for the free running conditions are given in table 1.

The force in the actuating rod as a function of the pitch

angle at maximum rotational speed is presented in fig. 10. Four dimensionless constants Kû, K1, CR11, CR111, defining

1 -'.

### -

--X/c I SIDE VENTILATED SKEWO8R 8.8 /. NON VENTILATEDFig. 19. Operating condition 5 (free running astern).

LEADING EDGE

LEAD ING EDGE

the shaft torque, the thrust, the hydrodynamic blade spin

torque, the frictionless blade spindle torque (i.e. hydr

dynamic plus intertia torque) respectively, are given i table 2 for the five characteristic operating conditions i

ventilated and non ventilated cases. In particular the torqu constant Kq deserves attention, because it affects the wor ing of the main engine. The corresponding pressure distr butions at .7 radius are presented in fig.

### 11 up to an

including 14. At positive pitch settings we find of cours

approximately the design pressure distribution, being i

our example that of the N.A.C.A. a = .8 mean line. The result indicates a significant reduction in the magnitu

### of the actuating force at negative pitch settings in t

ventilated conditions over the non ventilated ones. As could be expected, the most advantage is obtained whe we ventilate at two sides. If we ventilate only the face

### the blade the reduction in blade spindle torque is

als considerable. This suggests that in the first place furthresearch could be limited to ventilation at one side.

### As can be seen from fig.

10 the largest forces in t ventilated conditions are not met at small pitch angles an### more, but at

positive pitch settings### (bollard and fr

running ahead). The blade spindle torque at positive pite

settings can be lowered by decreasing the design ske

Calculating with half the original skew, we get the resul presented in fig. 15 up to and including 19 and table 3.

As one sided ventilation seemed the most feasible, limited the calculation to that case. It can be seen fro fig. 15 that the zero thrust point again shows the large

spindle torque within the range of operation. This critic value is less than one half of the corresponding maximu torque in the non ventilated condition (fig. 10).

Conclusion

The following conclusions can be drawn from our i

vestigation.

The calculation of actuating forces of controllable pite

propellers with a digital computer seems to be sufficient accurate, provided that proper allowances are made for:

the effect of heavy loading in the three dimension analysis.

- the distortion of mean lines due to pitch changing. - the effect of cavitation on the chord-wise pressure

distribution.

Ventilation through holes on the face of the blade can low the actuating forces by more than 50 %. This seems ther

fore to be worth further research. In order to check promising results of this paper, model tests should

carried out, including the aspects of ventilation inceptio air requirements and optimum location of air inlets.

References

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Marine Engineers, Vol. 76, June 1964.

I. H. Abbott and A. E. von Doenhoff: 'Theory of wi

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No. 60. August 1959.

G. N. Lance: 'Numerical methods for high speed computer

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J. D. van Manen: 'Fundamentals of Ship resistance and pr pulsion'. Part B: Propulsion. Publication no. 132 a of t N.S.M.B., International Shipbuilding Progress 1960. R. A. Barr: 'Ventilation inception', Hydronautics, Inc., Tee

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R. A. Barr: 'Air requirements for ventilated propeller

Hyd.ronautics, Inc., Technical Report 127-5, March 1963.

M. P. Tulin: 'Supercavitating Propellers. History, Operati

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the Fourth ONR symposium and Naval Hydrodynami

(Government Printing Office), Washington, D.C. 1962.

M. P. Tulin and M. P. Burkart: 'Linearized theory for f10 about lifting foils at zero cavitation number', David Tayl

Model Basin, Report C-638, February 1955.

M. C. Meijer: 'Pressure measurement on flapped hydrofo in cavity flows and wake flows', Journal of Ship Resear