Propeller hull Vortex cavitation

JUtI 1971

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PROPELLER

HULL VORTEX

CAVITATION

by

E. HUSE

NORWEGIAN SHIP MODEL EXPERIMENT TANK PUBUCATION NO. 106 MAY 1971

PROPELLER-HULL _{VORTEX CAVITATION} by

E.

Huse Contents page Abstract. 2 List of symbols. 2 Introduction. 3

Experiments with afterbody represented by flat plate 4

above propeller.

Influence of J, and c. ₅

Influence of blade angular position. 6

Influence of section form above propeller. ₇

Influence of propeller geometry and wake distribution 9

Direction of rotation of vortex. ₁₀

Experiments with afterbody model. ₁₀

Possible physical explanations of PHV cavitation. 12

General discussion. ₁₅

Conclusions. ₁₈

Acknowledgement. ₁₉

References. ₁₉

ABSTRACT.

A special type of cavitation, here denoted as "pro-peller-hull vortex cavitation" (hereafter abbreviated PHV cavi-tation), has been investigated in the cavitation tunnels of The Norwegian Ship Model Experiment Tank.. This cavitation appears

in the form of vortices with cavitating cores extending from the propeller to the hull above and ahead of it. There are

indi-cations that such cavitation also takes place on certain ships in full scale, and that it may give rise to afterbody noise and vibrations.

Syst'ematic observations have been carried out to in-vestigate the effects of afterbody form, tip clearance, propeller loading and cavitation number. Small vertical fins fitted to the hull above the propeller have been found to be very effective in reducing PHV cavitation. Various hypotheses are suggested as possible physical explanations of PHV cavitation.

LIST OF SYMBOLS.

propeller tip clearance,

propeller diameter,

height of vertical fins on flat plate,

height of vertical fin on afterbody model,

advance coefficient,

propeller shaft revolutions pr. second,

tunnel pressure,

saturated vapour pressure,

mean velocity of axial inflow to propeller, C f hf n Po V a

propeller blade angular position,

section angle (Fig. 8),

probability of occurance of PHV cavitation,

density of water,

cavitation number.

INTRODUCTION.

Blade thickness and lift give rise to a pressure field surrounding. each blade of a rotating propeller. At a point

fixed in space this pressure field will be felt as a periodical pressure fluctuation of a fundamental frequency equal to blade frequency (propeller revolutions pr. second multiplied by blade number). This pressure fluctuation may be of importance ïn ex-citing. hull .vibràtion.

A considèrable amount of information is available from model-scale measuréments of propeller-induced _{pressures on the}

hull. Amplitudes calculated by free-space pressure field theory show, good correlation with model-scale measurements. _Correlation with full-scale measurements, however, is in many cases very poor. Measurements carried out by Det norske Ventas on a number of. ships show that, especially for ships suffering from, vibrations., the pressure amplitudes may exceed those predicted by free-space pressure field theory by a factor of up to about 40. In other cases, especially for ships with an unusually low level of vibra-tions, the deviation has been within the limits of measurement

accuracy.. Possible reasons for the poor correlation in certain cases may be

the occurence of cavitation in full-scale not accounted for in model-scale measurements or theöretical cal-culations, or

pressure fluctuations due to excessive vibratory motion of the hull plates in the vicinity of the préssure

ducers.

The second item above has been treated in Pressure

fluctuations induced by cavitating propellers are at present being investigated by the Norwegian Ship Model Experiment Tank. During these investigations it has become clear to the author that under certain circumstances a special type of cavitation may occur, which will probably give rise to extreme pressure amplitudes on

the hull.

This special type of cavitation consists of vortices with cavitating cores extending from the propellér disc to the hull above or ahead of the propeller. This type of cavitation has,

as far as the author is aware, not been described in any published

work. We shall here use the notation "propeller-hull vortex cavi-tation" (PHV cavitation) to denote the phenomenon.

EXPERIIENTS WITH AFTERBODY REPRESENTED BY FLAT PLATE ABOVE PROPELLER.

Experiments have been carried out in the Number one cavi-tation tunnel at The Norwegian Ship Model Experiment Tank. This tunnel has an open jet test section of 360 nan diameter. Fig. i shows the arrengement in the test section. A flat rectangular plate 295 iran wide and 250 mm long (in flow direction) is f itted above the propeller in such way that the tip clearancec can be readily adjusted without removing the cover from the test section. A vertical

strut

with streamline section is positioned ahead of

the propeller. By fitting wire mesh to this strut a region ot high wake is produced in the upper part of thepropeller disc. The stçut can be removed to obtain homogeneous inflow. Strobo-scopic light is applied for visual observation of cavitation

pheno-mena. Fig. 2 shows the propeller, P-700.

With certain combinations of J, a and. c the typical

propeller-hull vortex cavitation can be observed. A vortex with cavitating core is formed, extending from the propeller to the

plate. Fig. 3 shows a photograph of it. The photograph also shows .a pitot tube protruding from the plate. The PHV cavity appears and disappears in a random way. When ôbserving visually

Fig. 4 shows results obtained by systematic variation of J, a,'and c. The cavitation number is here' defined by

ov

by stroboscopic light, the cavity can be seen for periods of time ranging from a few tenths of a second (corresponding to two or three propeller revolutions) to ten seconds or more. The most realistic parameter to describe the occurence of P1W cavitation is thereföre the probability 11 which is here defined as the per-centage of total time the phenomenon can be seen in stroboscopic

light.

Thus 11=100%

means

that P1W cavitation can be seen all thetime, while 11 = 0% means that it cannot be observed at all.

Observations have been carried out by first adjusting tip clearance and advance coefficient. Thén by starting at atmospheric pressure' the tunnel pressure has been gradually decreased, and 11 has been estimated by visual observation at various cavitation numbers.

All the results presented in the subsequent section have been obtained, by running the propeller at 18 revolutions pr. second, and with a relative air content in the water of about 20%.

INFLtJENCE OF J, a PND c.

p (V2

'(0.7 rrnD)2)

where

= static tunnel pressure in undisturbed flow,

= pressure of saturated vapour at the temperature of tunnel water,

p density ofwater,

V=.mean

vélocity of axial inflow to propeller (based on thrust Identity),

D = propeller diameter.

J is advance coefficient V

J

=-nD

The points plotted in Fig. 4 represent the values at which 11 values of about 1% were first obtained by gradual reduction of tunnel pressure. This observation was carried out for tip

clearances c equal to 0.1 D, 0.25 D and 0.4 D, ànd for advance coefficients J equal to 0.15, 0.30 and 0.45. Fig. 5. shows the

velocity distribution due to the actual wire mesh configuration. The conclusion to be drawn from Fig. 4 is that for each tip

dea-ance there exists a limiting curve in the a0-J diagram above which no PHV cavitation could be observed. With c=0.1 D II values of 1%

could be obtained for advance coefficients up to 0.45. With c=0.25 D and 0.40 D it could be obtained at J values only up to 0.15.

When reducing a to values below the limiting points shown in Fig. 4, the occurence of PHV cavitation becomes more

fre-quent. This effect is shown in Fig. 6, where II has been plotted as a function of At an advance coefficient of J=0.15 II was Observed to increase continually with decreasing

. For J=0.30, however, II reaches a maximum at a=0.5 and from there it decreases

again with decreasing a. It is also interesting to notice that the highest value of II (most stable PNV cavitation) was not ob-tained at the lowest J value, but at J=0.30.

INFLUENCE OF BLADE ANGULAR POSITION.

The ability of PNV cavitation to induce excessive blade frequency pressure fluctuations on the hull is expected to be very dependent upon the stability of the PNV cavï\ty. If the cavity is stable in the sense that it is constant in time and space close to the hull, it will not give rise to pressure fluctuations on the

hull. If its position on the hull is changing, however, it will be felt as pressure fluctuations at given points on the hull. The

worst case will probably be when the PNV cavity is presènt only during the short time intervals when each blade pases through the

directly on the hull. Such implosions, if they occur, will give rise to excessive pressure fluctuations at blade frequency.

The strobosáope can be triggered with the propeller at any angular position. Observations have been carried out to investigate if there is any dependence of TI upon blade angular position a. If for instance the value of II is considerably higher for a=0 (blade vertical pointing upwards) than for a=45 degrees, this may be taken as a proof that the PHV cavity

dis-appears between each blade's passage through the high wake

region, possibly leading to blade frequency implosion pressures on the hull.

Results of the observations in the tunnel are that. under most circumstances there is no significant dependence of .11 upon a. What happens when the blade passes out of the high wake region is

that the PHV cavity appears as an extra branch twisting around the ordinary tip vortex, and finally, terminating on the plate. This appearance is shown in Fig. 7. When the next blade has re-ached the high wake region (OE=0) the PHV cavity seems to jump to this blade, leaving the tip vortex of the previous blade for good.

Under certain circumstances, however, it has been observed that TI depends upon a. in such a way that TI is consider-ably higher for a values in the range O-20 degrees than for a values around 60-70 degrees. This seems to occur most frequently at the lowest tip clearances and at cavitation numbers where P1W cavitation is just starting.

INFLUENCE OF SECTION FORM ABOVE PROPELLER.

In order to investigate the influence of the form of the sections of the afterbod above the propeller special plates were fitted to the borizontal flat plate. The arrangement is shown in Fig. 8 where A ïndicates this extra plate. The plate

forms a tube open at both ends so that water can flow through it. The axial wake distribution will thus be influenced to the

smallest possible extent.

Plates have been tested having section angles equal to 45, 60 and 75 degrees. (90 degrees is represented by he flat plate). The height h shown in Fig. 8 was the sanie for all three

of fl at various combinations of c, J and cY,.

The results of the observations can be summarized as

follows:

With =45 degrees no PHV cavitation could be observéd at any combination of c, J and a0

With =6Odegrees the value.of n was about one third of its flat plate value at corresponding c, J and a0

With ß=75 degrees the value of n was only slightly less than Its flat plate value.

A possible explanation of the reduction of n with decreasing is that a sharp corner at the lower part of the section effectively prevents the rotational motion of water close to the hull. This immediately leads to the idea that a small vertical fin fitted to the hull in axial direction above the propeller might be sufficient to prevent PHV cavitation.

This idea has been tested experimentally. Fig. 9 shows 'the arrangement with a vertical fin F fitted to the plate above the propeller. Fins of three different heights were tested

Observations were made for a large number of combinat-ions of J and a values, and for c values ranging from c=0.40 D to c=0.03 D. The results were as follows:

Forf = 0.20 D and for f = 0.10 D no PHV cavitation could be observed at any a0 and J.

Fcr f = 0.05 D PNV cavitation could be observed at certain J and a0 values, but only for large tip clear-ances, c being in the range of 0.25 D to 0.40 D. In

this case the cavity appeared as shown in Fig. 9, ter-f = 0.20 D

f = 0.10 D

minating on the plate in an area about 0.20 D to the starboard side of the fin, For tip clearances below 0.25 D no PHV cavitation could be observed .at any J

and

a0.

With one single fin above the propeller PHV cavitation could under certain conditions be observed as shown in Fig. 9.

In order to prevent rotational motion of the water at larger distances from the fin, two more fins were fitted to the

hori-zontal plate as shown in Fig. 10. The sanie test program was carried out as had been previously done for the single fin. The same range of tip clearances and the same three heights of the fins were tested. The result was now that no definite P1W cavi-tation could be observed under any conditions.

INFLUENCE OF PROPELLER GEOMETRY AND WAKE DISTRIBUTION.

A few comparative tests with various propellers, in the cavitation tunnel with horizontal, plate above them have been carried out. The results indicate that ali propellers are not

subjected to P1W cavitation to the same extent. The experiments carried out so f arare not sufficiently extensive arid systematic to tell what geometrical parameters are of importence in producing P1W cavitation. This is a subject of further investigations at The Norwegian Ship Model Experiment Tank.

All experiments described so far have been carried out with wire mesh producing the wake distribution shown in Fig. 5. As a preliminary test to investigate the effect of wake dis-tribution propeller P-700 was run with the horizontal plate above it but without any wire mesh .to produc inhomogeneous

inflow. Even in this case P1W cavitation could be observed, but

now only for J values belöw 0.15. More details about the effect of wake distrioution is a subjectof further investigations.

DIRECTION OF ROTATION OF VORTEX.

By suspending wool tufts from the plate above the propeller the direction of rotation of the vortices between propeller and plate have been observed. _{Propeller P-700 is} right-handed. A left -handed propeller has also been tested. For both propellers, there was a predominent direction of

rota-tion. _{This direction was not the same for the two propellers.}

It was in both cases opposite to the diréction of the bound circulation around the propeller blades in their vertical up-'

wards position (direction indicated in Fig. 7). This direction was predominant to such an extent that it could. be observed

about 80 percent of the time that P1W cavitation could be _seen.

EXPERIMENTS WITH AFTERBODY MODEL.

As described in a previous section. it was possible to suppress P1W cavitation on the horizontal plate above the pro-peller by means of Small vertical fins fitted to the 'plate. in

order to investigate the effect of such fins under more ship-like conditions a few simple experiments were carried, out with a complete afterbody model in the Number two cavitation tunnel at The Norwegian Ship Model Experiment Tank. _{This tunnel has a} closéd circular test section of 1200 mm diameter.

Model M-910 and propeller P-746 were used to test the fin. _{M-910 was chosen because on this mödel P1W cavitation had}

been observed previously. _{As a matter of fact, of the five} afterbody models hitherto tested in the Number two cavitation. tunnel at The Norwegian Ship Model Experiment Tank, _{this is the} only model. on which P1W cavita.tion has been _observed.

Fig. 11 shows the afterbody plan of M-910 with pro-peller P-746. Fig. 12 is the open water characteristics of

P-746. Main partidulars of the propeller _are,

number of blades: 4

diameter: 222,8 nmi

expanded blade arêa ratio: 0.507

Fig. 13 shows the arrangement with the afterbody-model

in thé cavitation tunnel. Wire mesh fitted to the surface of the model was used to obtain the correct wake distribution. This

is shown in Fig. 14.

Observations were carried out fór advance coefficients ranging from 0.28 to 0.60. A range of cavitation numbers was tested, starting at atmospheric pressure and gradually reducing the tunnel pressure.

Figs. 15, 16 and 17 show examples of PHV cavities that could be observed. It should be noted that when these pictures were taken the wake distribution was not exactly equal to that

of Fig. 14. The wake peak in the upper part of the propeller disc was higher. Fig. 18 shows in a a0-J dIagram curves of constant 11 equal to 1% and 50% respectively. As can be seen it

is of the same general appearance as in the case of the flat plate described in a previous section.

In order to investigate the effect of propeller geometry, the propeller P-746 was replaced by other propellers, one 4-bladed

and then a 5-bladed one, both of them having about the same dia-meter and pitch as P-746. The occurence of PHV cavitation with

these two propellers turned out to be roughly the same as with

P-746. This indicates that the PNV cavi.tation is mainly caused

by special properties of the hull geometry and flow field rather than the propeller geometry. However, the experiments carried out so far do not allow definite conclusions to be drawn regarding the influence. òf propeller geometry.

All experiments with afterbody model described so far were carried out without any fins .f.itted to the hull. In order to investigate the effect of vertical fins, such a fin was f i.tted to the hull above the propeller as shown in Fig. 19. The fin was

made of a 1 mm thick brass plate. Its extension in longitudinal direction was from the leading edge of the rudder to a point on the skeg ahead of the propeller at the same height from the base line as the propeller tip. - Along its whole length the fin

protruded by a distance hf from the hull surface. Fins of three different hf were tested,

hf =0.05 D

hf = 0.03 D

With propeller P-746 and with the sàxne wake field as before, observations were made for the saine range of J values and the same range of ac values as before. The results of these observations were that with a fin of this _{type, even with a hf} value of only 0.03 D, no PHV cavitation _{could be seen. The ex} periments with afterbody model thus _{indicate that fins of this} type are extremely effective in preventing _{PHV cavitation.}

POSSIBLE PHYSICAL EXPLANATIONS OF PHV _CAVITATION.

Our understanding of the physical phenomenon, _or pheno-mena, giving rise to PHV çavitation is at _{present incomplete.}

However, certain hypoteses _{may be suggésted.}

1. Hypotesis based on "starting vortex".

The blade of a propeller operating in _{an inhomogeneous} wake field are subjected to fluctuating _{lift due to changing} angle of attack. _{This means that the circulation of the blades} is also fluctuating. _{According to Kelvin's theorem of the} con-stancy of circulation a vortex must be either closed or termi-nate on the boundary of the fluid. _{n the case of a ship} pro-peller it is generally accepted _{that the fluctuating part of the} circulation form closed loops by _{the shedding of radial vortices} from the trailing edge. _{Fig. 20 shows the corresponding vortex} line representation of a propeller blade. _{The radial vortices} represent the same phenomenon as the. "starting vortex" created by an aeroplane durig.. take-off, _{or the spanwise vortices shedded} from the trailing edge of _{an aerofoil moving through gusts.}

The main idea of the present hypothesis _{is that with} a hull above and ahead of the propeller the _{fluctuating part of} the blade circulation may instead _{terminate on the hull. It} may be thought of as forming an imaginary _{closed loop inside the}

hull as shown in Fig. 21.

under what circumstance? the fluctuating circulation will tend to terminate on the hull, forming the vortices necessary for

PIv cavitation. One assumptiön which might seem obvious is that the circulation will be closed the shortest possible way. This means that one necessary condition would be thát the tip

clearance is less than the blade length (distance from hub to blade tip). Another necessary condition is evidently that the

axial flow velocity in the region between hull and blade tip is close to zero. This is very ofteñ the casebacause, first, the wake is usually high in this region, secondly the velocity in-duced by the propeller is directed forwards.

One argument that P1W cavitation is not due to a "starting vortex't is that the sharp trailing edge facilitates

the shedding. of "normal" startiig vortices frorn. hub to tip (see [2]). In the region between hull andblade tip, however, there

is no such mechanism to stimulate vortex formation.

Observations carried out in the cavitation tunnels do not directly support the hpothesis that P1W' cavitation is caused by "starting vortices". Observations with wool tufts suspended

frOm the hull of the afterbody model and from the horizontal

plate in the smaller tunnel show in both cases that the direction 'of rotation of the vortex is somewhat random, but mainly opposite

to the direction of circulation around the blades in their vertical 'upwards pósition. This shows 'that if' it ïs 'a "'starting vortex" it

is usually createdby 'the reduction of blade circulation when the

blade passes out of..the high wake' region', and not so'often due to

increase of circulation when the blade enters the high wake region. P1W cavitation could be observed on the.. horizontäl plate

even without any. wiremsb to produce inhomogeneous'iflf low. At a first glance this might be taken as a proof that P1W cavitation öannot be. caused by a "starting vortex" since this requires wake inhomogenity. Howevere the image effect of the plate will induce

a velocity. component direçted forwards which will be felt as an

effective'wake peak 'by the proe1ler. Thus the hypothesis that P1W cavitation "is due to a "startïng vortex" still connot be

Hypothesis based on vortices created by shear flow in the wake f i el d.

A high wake peak in the upper part of the propeller disc gives rise to intense shear flow in the regions of highest velocity gradient (see Fig. 22). This represents a vorticity in the flow field which may "curl up" to form the concentrated vortices

necessary for PHV cavitation. This hypotesis, however, cannot explain the fact that PHV cavitation could be observed without wire mesh. Even the velocity field induced by the "image

pro-peller" cannot produce such vorticity because it is mainly

irro-tational.

Hypothesis based on vortices created in other regions of the flow field.

The basic idea of this hypothesis is that the cores of vortices created in other regions of the flow field will cavitate when entering the low pressure region between propeller and hull. The vortices may be created by certain flow phenomena around the

afterbody model (or wire mesh and horizontal plate) or in other parts of the.cavitation tunnels.

Hypothesis based on "pirouette effect".

The type of flow disturbañce giving rise to PHV cavi-tation may possibly be explained as follows. _{Fig. 23 shows}

schematically the flow field of a heavily loaded propeller. Outside the blade tips the propeller induces _{an axial velocity} component directed forwards. _{In the vicinity of thé plate this} component will be further increased by the "image effect" _{of the}

plate. _{Especially when there exists a high wake region in the}

upper part of the proeplier disc and.close to the plate, the axial velocity induced by the propeilér may become equal to the inflow velocity so that a stagnation point _{is formed on thè plate} above the propeller (point A in Fig. 23). Now consider the fluid contained in an imaginary closed volume V1 in a thin circular

layer close to the plate. _{Due to turbulence and other flow} distur-bances the fluid in V will have a net moment of momentum about a vertical axis through the stagnation point. _{After some time}

the fluid originally in V1 will occupy volume V2 (Fig. 23). Neglecting viscous forces the moment of momentum of the fluid

in V2 has to be the same as it was originally in V1. The radius of gyration is, however, only a small fraction of wht it was originally in V1. This means that the rotational velocity has to increase considerably in order to keep the moment of momentum constant, thus forming a vortex. (This is the same effect as made use of by a ballet dancer performing a piroue.tte).

GENERAL DISCUSSION.

It is the author's opinion that of the 4 hypotheses presented in the previous section, the one based on "pirouette effect" is probably the most correct. By this hypothesis the following characteristic features of P1W cavitation can be

satisfactorily explained:

Effect of vertical fins:

By the hypothesis it may be concluded that flow dis-turbarices in a thin fluid layer close to the hull

(or plate) aré most important in producing P1W

cavi-tation. This is in excellent agreement with the ex-perimental observation that even very small vertical

fins fitted to the hull (or plate) above the pro-peller are very efféctive in reducing P1W cavitation

(by reducing flow disturbances in the most critical region of the flow field).

Effect of tip clearance:

With increasing tip clearance the forwardly directed velocity compoment induced at the plate by the pro-peller is reduced. This means that a correspondingly lower inflow velocity (J value) is necessary to obtain a stagnation point on the plate. This is in agreement with the experimental results of Fig. 4.

Randomness:

The random way in which P1W cavitation occurs may be explained as a consequence of the random flow

disturbances on the plate initiating the vortices.

Effect of blade angular position :

If the vortices are due to the "pirouette effect" their strength should not be müch influenced by c. However, in the cases where 11 has been observed to vary with ct, this may be explained in the following

way:

If a vortex between propeller and hull is not strong enough to cavitate continuously it may still cavi-tate during the short periods of lowest ambient pres-sure occuring when each blade passes through its

vicinity.

Effect of o upon II:

Fig. 6 shows that for J=O.30 II is a maximum at

and is from there reduced with decreasing c0. This may possibly be explained as a consequence of the blade

cavitation influencing induced velocities at the plate, thus affecting the formation of stagnation point there.

The predominant direction of rotation of the vortices between propeller and plate cannot be explained by the hypothesis based on "pirouette effect" alone. If the distrubances on the plate were completely random, the direction of rotation of the vortices would also be completely random, which is not the case. So far the author has been unable to find a satisfactory ex-planation of the predominant direction of rotation.

One question naturally put forward now is , does PIN cavitation occur in full scale, or is it only a specific tunnel phenomenon. And if it does, how common is it and how serious is it in producing hull vibration and noise?

As far as the author is awarePHV cavitation has never been observed visually on any full scale ship. However, there are certain indications that it does occur. First, there is the type of propeller noise that can be heard in the afterbody of certain ships suffering from severe vibrations. It is described as an extremely sharp, hammering noise, exactly the noise one

.,ould expect from cavities imploding directly on the outer surface of the hull. In [3J (páge 771) the noise is "likened to the noise

of a sledgehammer striking the hull with the passage of each pro-peller blade".

Secondly there is thé more convincing indication to be read from certain records of propeller-induced pressure f

luctu-ations meásured on sorne full scale ships. Fig.. 24 shows an

ex-ample of such a record, taken by Det nörske Ventas on a tanker of about 230 000 TDW. At transducer positiön a the blade f

re-quency pressure amplitude is at certain times suddenly increased to 3 or 4 times its "normal" value. This seems to occur in a

completely random way. It can not be due to sudden outbursts of severe cavitation on thé propeller blades, since this would also give rise to an increase in the pressure. singnal at transducer positions b andc. It must be due to some sort of hydrodynamic phenomenon occuring locally over relatively small areas of the

hull. At present it is hard to find any other explanation than PHV cavitation.

The next question concerns scale effects. Can model tests be used to predict PHV cavitation in full scale, and,

eventually, what model laws should be applied? Since our under-standing of the physical phenomena giving riSe to such cavitation is f ar from complete, it is hard at present to answer these

questions on a theoretical basis. If the hypothesIs based on flow disturbanòesòn the plate and "pirouette effect" is correct, this means that first the modél law govérning the generation of disturbances (vortices) must be satisfied. Since viscosity is probably an important f actòr in this process, a natural require-ment would be equality in Reynolds nunthçr. Having achieved a vortex of given circulation the factors determining whether or not its core will open to forma cavity are the ambient pressure and the surface tension (and also such factors as the content of

cavitation nuclei and dissolved air in the water). This means that the tests shouid.be carried out under conditions of

equ1ity

in Weber's number and cavitation number too.

- Regardïng generation of vortices it should be remembered

that in full scale there exists a lot of flow disturbances due to waves, the ship moton in waves, and the use of rudder. On the other hand, in the cavitatiOn tunnels there i-sa background turbulence level not found in full scale.

In the author's opinion the conclusion must be that PHV òavitation is subject to considerable scale effects so that direct

application of for instance the observed II values to full scale is probably very uncertain. However, general trends observed such as the influence of vertical fins, section form above pro-peller, tip clearance, etc. are probably correct also in full

scale.

-As a last item in the general discussion it should be mentioned that the vortex-forming mechanism of PHV cavitation is possibly closely related to the mechanism of ventilation (pro-peller drawing air from the surface). Thus the vertical fins fitted to the hull above the propeller might be effective in re-ducing ventilation too. Preliminary investigations of this idea carried out at .The Norwegian Ship Model Experiment Tank confirm that such fins are indeed, under certai.n conditions, effective in reducing ventilation.

CONCLUSIONS.

A special type of cavitation, here denoted as "pro-peller-hull vortex cavitation", has been investigated .in the cavitation tunnels of The Norwegian Ship Model Experiment Tank. This cavitation appears in the form of vortices with cav.itating

cores extending from the propeller to the hull above and ahead

of it. There are indications that such cavitation also takes place on certain ships in full scale.

Experimental observations with a flat, horizontal plate above the propeller in a cavitation tunnel show that PIN cavitation is most pronounced. for small tip clearances. The

phenomenon has been observed for tip clearances up to 40 percent of propeller-.diameter but then only for very low advance coeff j_

cients. The form of the afterbody section above, the propeller is an important parameter. Large section angles (sections with flat bottom) tends to increase the probability of PHV cavitation. A most important conclusion is that small, vertical fi,ns fitted to the hull above the propeller are very effective in reducing

PHV cavitation.

The physical phenomena giving rise to PIiV cavitation are not completely understood. It is therefore at present not possible to know what scale effects are involved.

ACKNOWLEDGEMENT.

The investigation presented in this report have been financially supported by The Norwegian Concil for Scientific and Industrial Research.

The author wishes to express his thanks to the Director and staff of The Norwegian Ship Model Experiment Tank for their cooperation and support. Special appreciation is extended to Mr.

Svein Eggen for his assistance in carrying out and analysing the experiments, and for many useful discussions regarding their

interpretation.

The author is also indebted to Mr. T SØntvedt of Det norske Ventas for his interest in the project and fôr making

available the results of full scale pressure measurements carried out by Det norske Ventas.

REFERENCES.

[i] Huse, E: "Hull vibration and measurements of propeller-induced pressure fluctuations". International Ship-building Progress, Vol. 17, No. 187, 1970.

Prandtl, L. and Tietjens, O.G., "Applied Hydro- and .Aero-mechanics", Dover Publications 1957.

Nichols, W.O., Rubin, M.L., and Danielson, R.W., "Söme Aspects of Large Tanker Design", Transactions SNAME, Vol. 68, 1960.

Flow direction

Fig. 2. Propeller P-700, 4-bladed, pìtch=147.6 mm (constant). I 1.0 81.7

0.0 049

0.95 77.6 40.5 0.17 0.9 73.5 49.4 106 I I 0.8 653 55.2 1.70 0.7 57.2 55.4 21.2 0.6 49.0 53.5 3.28 -0.5

40.8 503 4.29

0.4 32.7 46.0 5.50 0.3

245 412

7.01 _____ 0.2 16.3 363 8.31

(

i [mn] [mCrn]

1.5 1.0_ 0.5

-o 0 0.1 ¿

c0.25D

Q

c=0.40D

Fig. 4. Experimentally determined c0-J conbinations giving

11=1%. Arrows indicate a rough estimate of standard

deviation.

0.5

0.4

0.3

60 50

o

30

-20

-lo

-00

Fig. 6. Observed values of II versus Arrows in-dicate a rough estimatè of standard deviation.

J 0. 5

o G s I f

Fig. 7. _{Photograph and sketch showing PHV cavity}

Arrangement for Investigating effect of

o

Ñ

o

o

Fig. 10. _{Arrangement with 3 parallell fins fitted}

i'

7'

'h 1h 2 2h 3 5 s 7 9 9h9 10

Fig. 11.

Afterbody model M-910.

01, 0.3 02 0.1 o 1OKq0 Fig. 12. Open water I characteristics I I of propeller P-746. o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Jo 0.8 0.9 0.6 K0 lo Kq0 11, 0.5

Arrangement of mOdel M-910 in Number

Fig. 15. Example of PHV cavitation on afterbody model M-910 with propeller P-746. J=0.395, a00.327.

Fig. 18. Experimentally observed a0-J combinations giving

11=1% and 50%. M-910, P-746. Arrows indicate a rough estimate of standard deviation.

Arrangement of vertical fin F fitted to

Fig. 20. _{Vortex line representation of propeller}

blade operating in inhomogeneous flow.

fLuct uating.part

of bound vortex

PHV- cavity_

-hub vortex

Imaqinary_part of closed

vortex (oop__.

I

Fig. 21. _{Idea of "starting vortex" forming}

imaginary closed loop inside hull.

veLocity

/

\

distribution

Jci

vorticity due to.

G

veLocit

gradient

propeLLer seen from above

Vol u me V4

3W

VoLume Vz

Fig. 23. Flow around heavily loadèd--.propeller

ff

il

It

it

f

f

'Vf

I

3/

1/

¡

Transducer posit n a (starboard)

Transducer

sitlon b(port)

f

I

_f

f

Transducer position c(starboord)

peaks occurring with blade traguency_.

/11

t

1\J1\t\t\f\

1w

Fig. 24.

Simultaneous records of full scale pressure

fluctuations on 230 000 TDW tanker. 0.2 KpIcm2 1.0 Kpicm3

JI

"J pzgpeller aperture Transducer position a G-. Transducer position b N. Transdúcer position C