Cavitation and its influence on induced hull pressure amplitudes - Recent research at the Institut für Schiffbau, Hamburg

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RSITAT HAMBUR

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CAVITATION AND ITS INFLUENCE ON INDUCED

HULL PRESSURE AMPLITUDES

-RECENT RESEARCH AT

_{INSTITUT FÜR}

CAVITATION AND ITS INFLUENCE ON

INDUCED HULL PRESSURE AMPLITUDES

-Recent Research at che

Institut für Schiffbau

Universität Hamburg

by

E.-A, WEITENDORF

Hamburg University / Hamburg Model Tank

Bib;ofheek van de

Sche?pvartkun

le h

H

Left

t;

- i o

Abstract

Introduction

Measurements and Calculations of Propeller-excited

Pressure-Amplitudes

Measurements and Calculations of the Pressure

?iels on Propeller Slaes

4

_{Influence of Undissolved}

Air Content

_{on Cavitation}

Phenomena at the Propeller Blades

iull Pressure Amplitudes

Theoretical Research

_{on Cavitation Inception}

with Application of Bubble Dynamics

Conclusion

References

Figures

Contents

ha

Nek&weg 2, 2628 cl)

i

Ab st ra c t

A critical review of the

_{following subjects is given:}

Measurement _adcacujatipQ of

_Propeller

_excited

Pressure-Ampli-tudes.

It was found that in the case of heavily cavitating frigate

pro-pellers a decrease of the pressure amplitudes occurs in front

_of

and directly above the

_{propeller compared with}

_{noncavitating}

condit-ions. Behind the propeller

_{plane the cavitating tip}

_{vortx with}

nooes having a mean diameter of

_{about 3 to 5 per cent of}

the screw

diameter amplifies the

_{pressure impulses. By means of}

_theoretical

and experimental investigations it could be proved

_{that the wave}

length (i.e. distance

_{between two nodes) of the}

_{cavitating tip}

vortex causes amplitudes of

_{discrete frequencies. The}

_{wave length}

itsSelf depends on the meandiameterof

_{the cavitating vortex}

_{and the}

cavitation number. If the wave lenght x attains

_{a value}

corres-ponding to the number of

_{propeller blades e.g.}

_{= 1200 for a three}

bladed propeller, the

_{amplitudes of the blade frequency will be}

amplified. Analog effects will

_{happen at twice the blade}

_frequency

with a wave length of

60°.

Measurement and Çcylton_of

_{the Pressure _Fields}

_{on Propeller}

Blades.

The measurement of the

_{instationary pressures at 235 points}

on the

blades of a 1.40

_{m model propeller were}

_{executed in a ship-like}

wake

in a wind tunnel at Göttingen. The results of these

_{measurements at}

Göttingen are compared

_{with the results of}

_{an instationary lifting}

surface theory. For

_{one case they agree}

_{very well, but from}

real

pressure distribution of the _{propeller investigated.}

3. _{Influence of Undissolved Air Content}

on Cavitation Phenomena _at

the Pro_pelTer Blades and on _{nuced_HilJ Pressure}

Amplitudes.

This investigation consisted of the

application of the Scatterad Light Technique for measuring the undissolved

air conteìt of a

cavi-tation tunnel and

simultaneous measurements of propeller-excited pressure amplitudes _{on a flat plate above}

the propeller.

The main results _{of the measurements}

are:

Increasing relative free gas volume for cavitation

tests and

higher revolutions _{of the model}

propeller in a wake causes earlier inception and

increase in the size of the cavity and

tnerefore increasing _{nondimensional}

pressure amplitudes. Cavitation tests for estimating the _{propeller-excited}

pressure amplitudes should _{include the simultaneous}

determination of the relative free gas content and later _{on its possible}

con-trol

4. _{Theoretical Research}

on

of Bubble _Dynamics.

The theoretical _{research on this}

subject uses _{as input the nuclei}

distribution measured _{in the above}

mentioned point 3. _{Not only} the pressure field for a two phase _{flow around}

a hydrofoil is

cal-culated but also _{the growth of single}

bubbles in this _pressure

field. The result

greater number of smaller bubbles _{with a diameter less than}

lO,Mm have an important influence _{on the cavitation phenomena, if}

the

1. Introduction

The paper presented here gives a review of propeller and cavi-tation research con ducted at the Institut für Schiffbau of the Hamburg University within the Special Research Pool "Schiffs-technik und Schiffbau" (SFB 98) during the last four years.

Since there were several activities in this field, it is _impossible to describe them all in detail. That is feasible only for _those topics which are directly implied by the title. _{Others an only} be mentioned by way of suggestion in this introduction.

For instance Laudan ti] has complemented the Wageningen

"four-quadrant" measurements of propellers f2) in open water. He per-formed the "four quadrant" propeller measurements in a quasi-steady manner using four typical ship models in front of the propellers.

In this way global statements about the wake _{fraction and thrust} deduction fraction were found: the wake fraction _{remains constant} from the condition of operation to the reversing point, afterwards decreasing to zero. On the other hand the thrust deduction fraction diminishes in a linear way from the point of operation to a

nega-tive value.

In an additional investigation Laudan (3] measured the influence of the cavitation on the propeller-forces occuring during crash stops on straight courses. The measurements _{were performed in a}

cavitation tunnel in a quasi steady way. For the propellers used here it was shewn that the influence of the cavitation was not excessive. But at least the result was that the stopping time was prolonged by 20 per cent and the stopping distance was increased by 15 per cent.

Furthermore this project "Safety against collision" of the SFB 98

investigated the influence of oblique flow on the propeller _having different advance angles

_{43

wake measure-ments during oblique towing of _{the ship model}

_[57.

But now results are to be presented,whose origin

concerns the author directly.

2. Measurement _{and Calculation of Propeller-excited Pressure}

iplitudes

2.1. Measurements of _{Pressure Arn2uitudes for heavil,}

cavitatinS

fr19

292!1

In order to study the _{influence of cavitation on the blade} fre-quency pressures for heavily cavitating

frigate propellers of different design, measurements _{with seven}

pressure pick-ups on a,

flate plate (Fig. 1) _{were carried Out in the medium sized cavitation}

F. I

tunnel of the Hamburg Model Basin (HSVA). _{These investigations}

E6]

para-meters of these three, four - and five bladed propellers

valid for homogeneous but also for inhomogeneous flow, can be

found in Fig. 2.

Here the nondimensional pressure amplitude

K z

p3

Ap

n D

is plotted against the coordinate in flow direction x/R. The figure concerns homogeneous flow. The upper diagram stands for a

propeller (HSVA-Propeller 1240), whose maximal _{circulation or}

loa-ding is drawn to inner radii, the lower stands for an optimal pro-peller (HSVA-Propro-peller 1283). Both propro-pellers possess three blades. Parameter of the curves is the cavitation number

VA I

4A

In this definition VA means the speed of advances of the propeller. The solid curves are valid for the cavitation free condition of the propeller, i.e. there was an _{open connection between the test} section of the tunnel and the atmosphere. _{The procedure of the tests} was that the pressure in the tunnel was reduced step by step. So

the cavitation numbers,given in the legend of the figure, were reached. For the optimal propeller the following _{result for the} cavitating condition was found:

In front of and directly above the _{propeller plane a decrease of} the pressure amplitude occurs when compared _{with the} cavitation-free condition. The decrease of the pressure amplitude by cavitation

i

can be explained in the following _manner:

The propeller excited pressure amplitude is caused by _two influ-ences, i.e. the thickness and the loading of the blade. _{Since in} case of heavy cavitation the thrust breaks down, the loading

in-fluence can be reduced more than the thickness inin-fluence _will

in-crease from cavitation. The smaller dein-crease of the amplitudes _for the "noiseless" propeller in the upper diagram is _{due to the greater} cavitation-free area of this propeller.

Behind the plane of propeller 1283 the increase of _{the amplitudes,} compared with the cavitation _{free condition (ATM),}

is caused by the cavitating tip vortex. Already

by observing the stroboscopic photographs of both propellers in

Fig.3 the influence of the

cavitating tip vortex on the _{pressure amplitudes can be detected:} The optimal propeller 1283 _{possesses a thick tip vortex and}

accord-ingl,y in Fig. 2 an increase of the _{amplitudes. On the contrary}

the noise-less propeller 1240 shows _{very little of a cavitating} tip vortex in Fig. 3 and correspondingly

no amplification of the amplitudes behind the propeller plane _{in Fig. 2. In order to avoid} misunderstanding at the end of this chapter, it must be stressed that this practice of unloading the _propeller

ip can only be applied for propellers in wake fields of fast ships, mainly _navy

-

6-2.2. InvestiSations of the Cavitatin _{Tip Vortex with nodes}

Looking more precisely in Fig. 4 at some cavitating tip vortices in homogeneous flow, the following can be discovered:

At constant advance coefficient, bu4iecreasing cavitation number

VA the cavitating tip vortex becomes more and more thick.

Finally this vortex shows nodes _{at regular intervals which are} marked by arrows in the photographs of Fig. 4. These notes are

stationary with respect to the running propeller. The poitions of the nodes are determined by the mean radius of the tip vortex and by the cavitation number

dVA. This was, already shown 1930 by

Ackeret [7J . Turning with the propeller, this cavitating tip vortex contracted at different positions _{causes pressure amplitudes of} discrete frequencies, depending on the wave length of the vortex,

i.e. the distance between two nodes.

In the theoretical investigations {8J of this physical phenomenon the pressure impulses,created by the cavitating tip vortex, _were regarded as an effect of displacement. This was simulated by suitable source-sink-distributions, arranged on the spiral line described by the propeller tip in operation. _{Now it is imaginable} that the pressure amplitude, created by the displacement of _{a body,} is proportional to the variation of the cross-section of this body,

namely

K

dx)

if z. _{is the circumferential coordinate.}

In the calculations the

Fcx

(R

9sin2(xr))

'1

R

/

(-x

J

is built up of two _{parts: the round bracket}

stands for the

wave-like and cavitati.ng hollow _{vortex (sketch No. 1), and}

the square

yort

bracket for the ellipsoidal hollowYThe

designations in the round

bracket for the wave-like hollow vortex are:

= _{tne nican radius of the}

cavitating tip vortex,

nD

Ram

vortex,

to be taken from _photographs,

=

wave length of the hollow vortex in the theory by Ackeret [7],

R.,

i/o'i

ç

RiRa

the propeller blade,

coefficient,

number of blades,

inner and outer radius of

= _thrust

Qfl

R0,

ir

m

- _{circumferential coordinate}

The designations in the square bracket for _{the ellipsoidal hollow}

vQ'rtL)( (scetci No2

kefcb W04

A initial value of the hollow vortex,

s

final value of the _{hollow vortex,}

m _{parameter of inclination.}

The cross-sections applied in the _{theoretical investigations} correspond to formula _{(2.1). Some examples}

of cavitating tip vortices used in the calculations are shown _{in Fig. 5.}

9

In the calculations the value _{- O}

lies at

the position

of

the propeller blade,

i.e. trie 1/4 _{- point of the propeller profile. The different}

in-fluences of the shape parameters in formula (2.1), namely

Rk the mean radius of the cavitating _{tip vortex,}

Ram

of

the cross-section of the tip

vortex,

a the wave length, the mitai value, the phase angle,

m = _{the parameter of inclination,}

were investigated in a computer program. In order to enable

com-parisons with the present _{measurements [6] ,}

the computer program contains all contributions of the propeller excited _pressure am-plitudes, namely the influence of _{the loading}

_of

the blades,

in-cluding the steady cavitation, _{the influence of the thickness}

of

the blades and the influence of the wave-like cavitating tip _vortex with its effect of displacement. _{In the detailed report}

8) all

re-sults of these calculations are given. But _{here the results of} the variation of the wave length _{only can be shown in}

This figure contains two diagrams, _{the upper results are valid} for the third harmonic order of the _{pressure fluctuations (blade} frequency) and the lower for twice the blade frequency. The non-dimensional pressure amplitudes K3 and _{K6 are plotted against} the flow direction x/R4. Behind the propeller plane in the region

> 1.0 the normal contribution of the propeller, _i.e. thick-ness and loading effects of the blades have vanished. _{This is the} reason for showing the results up to x/R _{= 2.0. Parameter of the} different curves in Fig. 6 _{is the wave length x0.If the}

wave length x attains the value = = 1200 _{for N = 3, then the}

third harmonic of the pressure will be the strongest amplitude. If the wave length

_x

frequency will

be thgreatest. This can clearly be found _{in Fig. 6. The} oscillat-ions of different curves in Fig. 6 _{are due to the wave length.} Since these contracted tip vortices leaving the different blades are stationary with the positionsof their _{nodes with respect to the} propeller, all respective nodes of different _{blades must be in one} plane. This plan is located parallel _{to the propeller plane. The} distances between two such planes, _{corresponding to the oscillation} ir Fig. 6, are equal to the value _{x/R = X =}

_X0.

As the theory by Ackeret

_[73

x depends on

the mean radius 0f the cavitating hollow vortex. In the _present

investigation

_[83

curved tip vortex of a propeller. Ackeret's result namely _{was valid} for a straight hollow vortex. The mean radius of _{the cavitating} tip vortex depends on the cavitation number, the _{propeller loading} and is inversely proportional _{to the blade}

u

-in formula (2.2). In this way all dependencies not only for the

t

wave length x0 but also forean diameter of the _{cavitating tip}

vortex are formulated. But the merely theoretical calculation of the pressure amplitudes of a cavitating tip vortex with nodes is not feasible, for the position of the first node, the initial and final value of the vortex and its shape amplitude

Rkam can only be

ob-tained from measurements. From photograph of corresponding _tests these value are gathered. The valuesare used for the calculations whose results are shown in Fig. 7.

For the purpose of comparison the results of the measurements are given additionally, obtained with the five pressure pick-ups located along the direction of flow (see Fig. 1). In Fig. 7 results of calculations and measurements for J _{0.72 up to the 9th}

har-monic order are given for the cavitation _numbers

p-pv

-2.0, 1.75, 1.50, 1.25 and 1.14.

VA

-

-Comparing the results of calculations and measurements, a quite satisfactory agreement can be found, especially for _{= 1.75.} For this case an exellent _{agreement occurs, above all}

at the

position p 4 and P5, where the

cavitating tip vortex is of do-ininating influence. For this _{case not only photographs but also}

coloured slides were available. _{These were used for determining} the shape parameters of the _{vortex needed for the calculations.} Here one can see, how important the accurate determination _of the shape parameters is. Only if the input values of the computer program conform to reality, an agreement between measurement and calculation can be obtained.

In order to avoid the drawback of every time having _{to take}

photographs for the input data of the computer program, empirical formulas for the shape parameters _{of the tip vortex were}

develop-ed . By means of these emperical

formulas, it seems possible to compute approximately the _{pressure fluctuations caused by} cavitating tip vortices without having to take photographs. At the er1d _{of this chapter the following}

13

-the influence of -the cavitating tip vortex with _{nodes shall be}

given:

Not only by measurements _{but also by calculation}

it was proved

that the cavitating tip vortex with nodes, having _{a mean diameter} of about 4 per cent of the propeller diameter,

causes greater am-plitudes of higher blade frequencies. These _{can be observed in full}

scale and model

measurements. The phenomenon of these nodes _occurs

in a ship wake too.

An additional aim should be the calculation _{of the cavitating}

tip

vortex with nodes in a ship wake. Preliminary

calculation of this problem are already carried out for single

screw container ships using the above mentioned

computer program in a quasi steady manner for different loadings

of the propeller in the wake. The result was that the pressure amplitude excited _{by the cavitating} vortex was of minor magnetude

compared with the _other con-tributions of the propeller. _{A concluding}

statement about the influence of the cavitating _{tip vortex with}

nodes in a wake can

only be drawn after having performed _{extensive theoretical}

in-stationary calculations. _{It is imaginable}

that the instationary variation of the shape of the cavitating

tip vortex in the wake

may generate pressure amplitudes of the _{same magnitude as the} other exitations of _{the propeller.}

3. _{Measurement and Calculation of the Pressure}

Fields on _Pro2elier

Blades

Concerning a realistic

the propeller, the

inflow condition at the stern as well as the pressure distribution on the pressure and

suction side of the blades is needed.

Regarding the pressures on the propeller, auxiliary means consist of calculations _{of the unsteady}

lifting

surface theory and _{measurements. In cooperation}

between the In-stitut für Schiffbau _{Hamburg (Special}

Research Pool 98) _{and the} Aerodynamische Versuchsanstalt (AVA) in Gottingen _measurements of the pressure

distributions on both _{side of a model}

prpeller

were carried out in a wind tunnel with

a cross-section of g m2 (10, 113. _{The tests were}

performed in a ship _{like wake flow.} On the 4 blades of the 1,4 meter wide _{model 235 orifices}

were

distributed, mostly concentrated at the _{leading edges and}

the

outer radii. _{The measurements}

were performed by _{means of the} so called "indirect

method", i.e. the 235 orifices _{were connected} to one pressure

pick-up using five _{scanning valves. In}

this way

'n

a calibration of _{plitude and phase}

was necessary for each _orifice. In the figures 8 to 10 for instance,

results of the measured

pressure distributions for the radii r/Ra - 0.50, 0.90 and 0,975 are shown. Here the nondimensional pressure coefficient

p _po

cpb)

QW2

R

is plotted against the relative position along the chordlength

xii (x . distance from leading edge, i chord length).

X/

of the inhomogeneous inflow (ship wake) is concentrated on the fore part of the chord, i.e. x/i 0.5. The influence becomes dominant at the leading edge. The lowest pressure, giving a

pressure coefficient c = -0,362 at the blade position y = 30° ra

at chord station xii = 0.007, was found on the radius _{r/Ra = 0.80.} The influence of the tip vortex can be seen in Fig. 10 for the suction side. The great pressure &ifferences between _pressure and suction side at the trailing edge indicate the threedimens-ionai flow around the blade tip, being typical for the tip vortex

roiling up.

The choice of air as fluid medium has the advantage _{that no} cavitation can occur. The eperimental parameters were such that the flow remained incompressible so that the incompressible lifting surface theory could be applied for the calculations. Hence suitab1e possibility for the comparison between the re-sults from theory and measurements is available. _Furthermore,

by using such a big model of 1.4 meter diajneter, _{the orifices}

for the measurements could be placed very near to the leading edge. On the other hand, a drawback of using air as the fluid

17

-medium was the lower density of air compared with water. This leads to smaller pressure difference between suction and pressure side, approximately 0.025 bar. Above all, using the "indirect method" of pressure testing, these small _{pressure differences} could only be obtained with a lowered accuracy. To some extent, the determination of the zero level for the _{pressure coefficient} gave rise to certain difficulties, which only could be overcome by most precise measurements of the atmospheric pressure during the repeat tests. All in all, the AVA in Göttingen estimates the error of the whole measurement at _{5 per cent with respect} to the experi ence with other measuring techniques. This _value

of ± 5 per cent seerr6 to be pretty good. Here it _{cannot be}

de-cided whether the pressure differences at the leading _{edge could} be measured with the necessary accuracy _{considering the} ine-vitable inaccuracies of manufacturing in the profiles of the model propeller. This is the occcasion to give the hint that the AVA in Göttingen at this moment is pursuing _{the fundamental} problem of measuring pressure differences _{on foils of rotating} systems. The result _{of this investigation may give an additional} insight into the accuracy of the propeller measuremnt reported here. Nevertheless this propeller measurement leads to the

possibility of comparing the results of lifting surface theories. For this reason these wind tunnel tests were ordered by the

Special Research Pool (SF8 98), in order to compare the results of a computer program [12] based on the lifting surface theory [13) developed at the Institut für Schiffbau of the Hamburg

University.

In Fig. 11 and 12a comparison is

19

-results from AVA [111 and the -results of the Hamburg calculation E123 for the position 00 (12 o'clock position) and - 3300

(starboard) at the radius r/R = 0.90. For this case the agreement between computation and test seems pretty good. But using the same computer program for the HSVA-propeller 1917 leads to a substantially different picture in Fig. 13. For both the blade

positions

°0

-

) 330° (starboard) the cavity lengths

at the radius r/R - 0.90 for the cavitation number

p _{- p}

C

n

,2 (nD)2

are shown. In the calculation the vapour pressure, corresponding

to = 0.211, is only obtained for ten per cent of the chord length, whereas the real cavity lenght of a corresponding

cavitation test is extended over 55 per cent of the chord _length

(see Fig. 18, upper row). This suggests that the _{mere application}

of the cavitation number of the prototype is insufficient. It could be important to take into consideration the dynamics of the cavitating gas bubbles additionally.

Corresponding to the blade position _{= 330° in Fig.13, the} vapour pressure corresponding 0.211, which is approximately necessary for the cavitation inception, is not attained in _the calculations. This statement gives rise to the assumption that the pressure distribution of the computer program [123 does not fit the real values of the propeller pressures of a cavitation

test.

21

-to compute the circulation distribution of the HSVA propeller 1917 in an axial _{model wake. This circulation can be used for the} cal-culation of the blade frequency pressure without cavitation on a

flate plate

[83.

the

the-oretical values do not match the measurements. Once more the suspicion rises that the computer program f123 gives too small pressure differences between pressure and suction side compared with the reality. On the other hand, it must be admitted that the calculated blade frequency pressures on a flate plate do not indicate whether the calculated pressure differences on the

blades _{are right or wrong. For instance, computations of the}

pressure differences on the blades of the _{HSVA-propeller 1917}

Hamburg

ordered by the Institut fUr SchiffbaJ'?rom

another institute gave unsatisfactory results, inspite of _{better agreement of the}

simutaneously calculated calculated blade frequency pressures on a flat plate with the measurements in Fig. _14.

Concerning the calculations of the pressure differences on the propeller blades in a ship wake by means of the lifting surface theory, it would be of utmost interest _{to see what the comparison} of different lifting surface theories proposed by the ITTC _would look like. Beside the AVA-model _{propeller the HSVA-propeller}

1917

(Zeise-design) would offer a suitable object for purposes of

at the ProEeller Blades and on Induced Hull Pressure Am2litudes In a paper on propeller-excited hull forces given in 1972 by

van Oossanen and van der Kooy 14J, it was evident that for equal nondimensional flow conditions but different absolute revolutions (i.e. n = 20 and n = 30 Hz),the nondimensional

propeller-excited pressure amplitudes were different. That means an uncertainty with respect to the evaluation of the vibratory behavior of a ship.

Two possible influences concerning these differences were taken

into account:

the influence of the neglected Froude law of similarity _and the free air content of the tunnel water.

Using the Froude law of similarity, the correct _pressure distribution on the propeller blades in radial direction _is guaranteed. But normally the revolution based on the Froude number can not be realized, because it is out of the range of a normal cavitation tunnel.

With respect to the free air content, this _{content of the tunne'} water, i.e. the free gas bubbles of test water, governs the cavitation inception.

Taking the above mentioned influences into account as much as possible, new tests were performed in the medium sized cavitation tunnel of the Hamburg Model Basin in November and December of 1974. The axial component of the flow field in the propeller plane

23

-was simulated by grids of varying density.

Three kinds of measurements were executed simultaneously:

Measurement of the undissoived air content by the laser light

scattering method.

Measurement of the propeller-excited pressure amplitudes on a fiat plate above the propeller.

Stereometric photography of the extension of the cavitation on the propeller blades.

In this lecture a short review of the above mentioned measure-ments under number 1) and 2) shall be given. A more detailed description of these measurements was given in the IfS-Report

312 A [15).

The scattered light technique _{was applied in close cooperation} with A. Keller of the Technical _{University Munich. He developed} this method up to practical _{application of cavitation}

tests [16].

(F

.1),

In our case of applRà Tàthe _{optical control volume defined}

by the cross-sectional dimensions of the light beam and the optics of the system detecting the scattered light had a cross-section of 1.2 m2. The control volume was located in front of the propeller plane. Directly behind the control _{volume, the flow velocity}

was

measured by a Prandtl tube. The flow velocity is required for the estimation of nuclei concentration of the fluid. The

ca-libration of the photomultiplier used as the scattered light detector was performed with latex spheres of known diameter. These were injected into the control volume. The _electrical

output pulses of the photomul tipi ier _{which are proportional} to

the "nucleus size were evaluated by an HP-computer in _an on-line mode. Thereby, it was possible to print a nucleus size histogram immediately after each test.

For the example of degassed water, _{a histogram is shown in Fig. 16.} The abscissa is the size o _{the bubbles measured in the range}

between 20 and 350 microns.

The recommendation of the ITTC Cavitation Committee, taken

into consideration in this case, is the following that the nuclei size should be measured from 10 to 250 microns _{in diameter.The} dashed line in Fig. 16 is the size histogram. _{Additionally,} the diagram contains the fraction of the relative _{free gas}

volume

d

unit to the volume unit of the fluid. As _{mentoned, the full line} represents the fraction of all measured relative free gas volumes per bubble range, i.e. between 20 and 69,6 microns. _{Summing up} all the fractions of the relative free gas volumes per range,

we obtain the total measured relative free _{gas volume, i.e.}

c= 0.118 x 10 in the figure.

By gassing and degassing, it was possible to vary the free air content of the test water in a rather wide range. For the case of gassed water, the respective figure like Fig. 16 contains

a greater number of bubbles and greater relative _{free gas volume.} After and before each test series the total _{air content c0 was} determined by a van-Slyke-apparatus.

25

-As mentioned before the propeller-excited pressure amplitudes were measured on a flat plate above the propeller. The _{sketch of}

the test setup and positions of pressure pickups were shown in Fig. 1. The first tests of the heavely _{cavitating frigate} propeller (HSVA-propeller 1283) with open water conditions were performed without artificially changing the free _gas

con-tent of the tunnel water. The purpose of this _{procedure was} to find the connection to experimental results gained in 1972

[6]. The free gas volume changed in a way which is probably normal during a testing duration of eight to ten hours. The

results of these tests are the following _{that in case of existing} cavitation the nondimensional pressure amplitudes of the blade

frequency are not affected by the free air content or by the chosen propeller revolutions. This result is confirmed by the extension of the cavitation photographed.

In contrast to this instance of existing cavitation the relative free gas vo1ume. has an extreme influence on the pressure

amplitudes K = of a propeller in a wake. In Fig. 17 some results of pressure amplitudes of the model propeller

of S.S. "Sydney Express" (HSVA-propeller 1917 _{- Zeise-design)} are shown. Here the nondimensional pressure amplitudes K5

of the middle pickup (position 3) are shown for the advance coefficient

KT 0.61 and the cavitation number

C. =

PPv

27

-The abscissa is the measured relative free gas volumec. The

pa-rameter of the diagram is the chosen number of revolutions, i.e.

n = 15, 20 and 30 Hz, that means different pressure conditions in the test section according to the law of similarity _{of equal} cavitation numbers. Mainly for the revolutions of n = 15 and n - 20 Hz, there are great influences _{on the pressure amplitudes} by the relative free gas vo1umec,. Stereometric _{photographs of} the blade in several positions

show that for a lower relafive free gas volume the cavity starts later than in case of the higher free gas volume. The

photographs underline the fact that the inception of the cavitation _{in the wake field and}

conse-quently its disappearance,

influenced by the free _{gas volume,} control the pressure _amplitudes.

In Fig. 18 two sets of photographs for the observed _propeller blaae in several positions are shown. The upper _{row is valid for} the speed of revolution

n = 30 Hz, the lower for n = 15 Hz. The reason for the great difference in _{inception and extent}

of the

ca-vitation is the fact that for the higher revolution _{the absolute} pressure is lower (sometimes below zero) than for n _{15 Hz; and}

the absolute pressure is responsible for the expansion _{of the free} gas bubbles. A more detailed _{explanation of this physical}

behaviour shall be given in the last chapter of this _paper.

Another interesting result of these investigations _{on the influence} of the free gas content shall be mentioned

briefly, though the corresponding photographs _{cannot be shown here}

because of

-29-more and -29-more stable, when the _{gas content was increased from} lower to higher values, _{i.e. the intermittend}

cavitation observed

here is a sheer model _effect.

Before finishing this chapter, it has to be _{mentioned that the} model speed of revolution _{o S.S. "Sydney Express"}

regarding the Froude law of similarity was n = 9.7 Hz. According to _{Fig. 17 this} influence of the free _{gas volume at this revolution}

would be extra-ordinary. This speed could _{not be used because of the too low}

tunnel pressure which is necessary for equal cavitation _numbers of model and full scaie

It is obvious that the influence of the free gas volume is compensated to a certain _{extent by the greater} revolutions, often used for cavitation tests.

The main results of the described measurements are as follows Increasing relative free gas volume for cavitation _{tests in a} wake field ¿auses earlier inception and stronger _{extension of} the cavity and therefore

increasing nondimensional _pressure

ampi i tudes.

Cavitation tests for estimating the

propeller-excited pressure amplitudes should include the simultaneous _{determination of} the relative free gas content and later _{on its possible control.} The last statement

involves the question of the correct _relative free gas volume in cavitation tests. The _{answer of this question} is of highest importance for all cavitation

facilities, especially those with a free surface.

Moreover the main results confirm that the free gas volume scaling the cavity is _{of the same}

importance as the correction of the wake field in the cavitation _test.

In connection with the free gas volume it is to be mentioned here that a research project of the Special Research Pool at Hamburg in cooperation with the HSVA, The Technical University of Munich and D n V is going on. Besides cavitation observation

L-and pressure fluctuation measurements the free air content of the seawater shall be measured as the maintask in this project.

5. Theoretical Research on Cavitation Ince2tion with

A22lication of Bubble 0namics.

In Fig. 17 it could be observed that for the higher _revolutions n = 30 Hz and additionally in all cases of the HSVA-propeller 1283

in homogeneous flow no dependence of the pressure amplitudes K

on the relative free gas volume ci. could be stated. On the other

hand for the lower revolutions (n = 15 Hz and n = 20 Hz) not only the pressure amplitudes on the plate but also the observed cavi-tation were dependent on the relative free _{gas volumec& to a high} extent. Trying to find an explanation for this dependence _{one has} to remind that, applying the value c, the behaviour of the single bubbles in a flow field with pressure gradient is neglected. Thus it was attempted to explain the differences in cavitation extent and pressure amplitudes for equal propeller loading and equal cavitation number, but different revolutions (e.g. Fig. 17) by means of a theoretical analysis of the dynamic expansion of single bubbles in a flow with pressure gradients. Such theoretical in-vestigations were carried out by Lederer (173 for steady hydrofoil flow in compressible water. The procedure was the following:

Iterative computations for the pressure distribution in compressible water with gas - content around hydrofoils were carried out accor-ding to the following formula

P

I

2rrp

-

-(x-x)

dr1

-

ì4

yd

The notation used can be found in sketch No. 3:

Skec'ì Wo3

The formula (5.1) is derived in a paper by Isay and Roestel _1183. in this connection gas means the _{content of free air in the water} as well as the vapour in the interior of the cavitation _bubbles.

The si ip velocity of these bubbles shall _{be, neglected and a further}

assumption is that the bubbles are moving along streamlines. Using these assumptions the dynamic behaviour of a single bubble

+

(5.1)

in a temporally changing pressure field is _{described by a} diffe-rential equation of the second order. This is thewell _known Rayleigh-Plesset equation .. 4 1

*

(5.2)

-

-4.RR

In this case R stands for the radius and _{R for the wall velocity} of the bubble. The indes i _{is the designation for water r vapour,} the index 2 for dissolved or undissolved air. The _{star belongs} to the gas phase and Ö is the surface tension.

The growth of different initial radii

R0 was calculated by Lederer

(173 applying equation (5.2), which was solved with a Runge-Kutta method. The streamlines, along which the bubbles are moving, were

substituted by straight lines y

= n parallel to the x-axis.

For

following ought to be mentioned:

During an air content measurement [153 Z _{= 1000 bubbles were} measured, flowing through a cross-section F0 with a velocity u

in a time ç. Dividing

_{the measured radii (e.g. Fig 16) into}

ranges

j

then the gas volume of the flow is

'f

-

-For the radii range R0 the number of bubbles is denoted by

o3

Ri

\I

\Vw

_co

L

j4

So the number n3 of bubbles per unit volume of the flow is

z05=>

oj

O O O

(5.5).

(5.6).

Comparing an initial state ck _{at a point x = xo with a state at a}

point x lying downstream and applying the conservation-equation, wnich means that the number of bubbles remains constant, one can

find

J

=

(M)

j'4

If the bubbles of the different bubble _{ranges contribute} uni-formly to the compressibility, equation (5.7) leads to

(5.4),

(5.7)

(5.8).

which is referred to unit volume. Using the gas volume ratio

vg0

of the flow, then one 't.

For a point x (dównstream from the point x0) one can determine

3 ₃

--

3

The expansion of the radius _{of the single bubble from the}

initial radius in the pressure field p(x) is calculated by means of the Rayleigh-Plesset equation (5.2). ¡f

s

(5.9)

R

=

B(R0,x)

B

is the solution of equation (5.2), the local _{gas volume ratio} in the hydrofoil flow can be derived from the equations (5.7) and (5.8) and it follows

3

3

(x,y)

3:4

(5.11).

As already mentioned, the precise determination of the streamline is neglected. Instead of this, the straight _{lines y = y parallel} to the chord (x-axis) are regarded.

Knowing the pressure distribution p(x, _{y) along the lines y}

=

according to equation (5.1) and using a nuclei distribution from a laser scattered light measurement (e.g. Fig. 16), the local gas volume ratio oc(x, y) of the flow can be calculated with the aid of equation (5.11).

The computations by Lederer _{L173 were carried out for two foil} sections, a curved and an uncurved section. _{For the latter section}

35

-results are shown in Fig. 19 to 21. The chordlengths for both were assumed to be ?A = lo cm.

The nuclei distributions of the computation were adapted to the results of the laser scattered light measurement[15J. _Since more-over the growth of a single bubble depends on the absolute value of the initial radius R0, the measure bubble histograms were divided

into four ranges:

s

R01

5,m;

These ranges were applied in two different nuclei distributions for the calculations:

Nuclei distribution No. 1:

= 50;

o2 = 20; o3 = 5; o4 = i with

-= number of bubbles of the range j) Nuclei distribution No.2;

oi

= 200;02 = 20;

o

The increase of the number.çof the small bubbles by a factor four means practically no change in the free gas volume ratio _{of the}

flow.

The occurrence of diffusion is neglected for _{this theoretical} investigations, since this phenomenon develops _{too slowly,} com-pared with the pressure changes on the foil _{section. Futherinore,} the interaction between the different bubbles was ignored.

VG0

z 1,3 10

In order to show clearly the influence of the nuclei present in the flow, the expansion of a single bubble in the pressure field is displayed in Fig. 19. There the results of calculations for the r smallest bubble R01 and the greatest one R04 are shown. Fig. 19

J

is valid for the cavitation number

p

- p

=

EO.3

V

The pressure Po = 1 kp/cm2 and Po = 0.2 kp/cm2 in the flow

corres-pond nearly to the revolutions n = 30 Hz and n = 15 Hz in the ex-periments from 1974 [15J . The results of the computation, given

in Fig. 19 and plottet against the chordlength 2A, show clearly that the smallest bubble R01 is expanded after a short distance from the leading edge, if the inflow pressure is Po = 1 kp/cm2. The same bubble R01 is not expanded, if the inflow pressure is

Po 0.2 kp/Cm2. The reason for the latter fact is that the

pressure on the foil section does not reach stronger negative values because of the lower inflow velocity for the constant cavitation number 0.3. This can be found in Fig. 20, if the

pressure distributions for the two inflow pressures p0 = 1 kp/cm2

'\

Trie strongly negative pressurés therefore lead to the expansion of small bubbles. On the other hand a difficult problem of substant-ial importance appears, if the question should be answeredto what values the pressure in real water with free gas content may drop.

37

-Nevertheless Keller (see p. 96 in [163) found that during cavitation inception the absolut pressure on a body in the flow decreased

to negative values, whose magnitude depended on the nuclei distri-bution, i.e. the pretreatment of the water.

From Figs. 19 and 20 it becomes understandable, why the cavity

extent in Fig. 18 for n = 30 Hz is greater than for n = 15 Hz: The first reason is that the absolute pressure at the foil section for

n = 30 Hz reaches stronger negative values than for n _{= 15 Hz,} and the second reason is that the number of small bubbles _(see Fig. 16) is always greater than that of the great bubbles.

Additionally the great bubbles are further displaced from _{the foil} section (screening effect).

The number of bubbles has in influence of the local free _gas

volume c«x, (see eq. 5.11). In this connection the results calculated by Lederer r173 for the local free _{gas volume K(x,}

on the suction side at a distance y/A = 0.005 _{are given in Fig. 21.,/'} Here the nuclei distribution No. 2 for Po = 1 kp/cm2 attains the

greatest value c..(x, _{since the number of small bubbles R01}

is four times as great as in the distribution No. 1. _{By the way,} in this theorie with spherical symmetry for the _{bubble, the value} c.= i means pure cavitation. This theory of the behaviour of single bubbles becomes meaningless, when the single bubbles grown and touch each other. In this relation of exspanding single _bubbles

a question concerning Fig. 17 emerges. There the nondimensional pressure amplitude K5 on the flat plate is plotted against the relative free gas volume .But the que'stion is, _{whether the value} c& is the right parameter for plotting the results, _{because,using}

is ignored. But a better presentation of the results like Fig. 17 needs the measurement of smaller bubbles _{as measured in Fig. .16.}

In this respect the recommendation given by the

ITTC-Cavitation-tö

Committee measure the bubble radii _{between 10,tm and 250,m should} be supplemented: Nuclei should additionally be measured between 5 and 10pm radius.

At the end of this chapter on cavitation inception and bubble dynamics questions on future work should _{be discussed.}

Normally the cavitation number and the thrust - or torque coefficient of model and prototype are kept equal for cavitation tests. This does not always lead to geometrically _{similar extent of cavitation} (see Fig. 18), since the number and _{size of nuclei are important} parameters in the reaction to the pressure field of the foil . Thus

geosim tests with hydrofoils _{or propellers should be performed with} simultaneous measurement and possibly control of the free air content.

of the

Supplementary investigations'b'theory of _{bubble dynamics described}

above should accompany the geosim _{tests. Furthermore for additional} similarity conditions of cavitation tests it is necessary to know

the nuclei distribution in seawater around a ship. Other important factors are the basic behaviour of the cavitation facilities and the effect of installed flow regulators upon the free air _content. These amount to a stronger consideration

of the quality of the flow medium for cavitation tests.

Efforts regarding these three tasks in cavitation research, namely geosim test for cavitating hydrofoils or propellers,

39

-tunnels and

determination of free air content in seawater

are being pursued in Hamburg at the Hamburg model tank (HSVA) and the Institute for shipbuilding (IfS) within the special research pooi for shipbuilding (SF8 98).

6. Conclusions.

The following conclusions can be drawn from the results presented

The hull surface forces excited on fast naval vessels by a cavitating tip vortex can be decreased by shifting the maximum circulation

to inner radii of the propeller. This method is probably useless for tankers and container ships, because of their wake distribution. In the theoretical field the estimation of the variation of the cavitating tip vortex in a ships's wake would be an interesting task. Afterwards it would be possible to account for the cavitating tip vortex in the total vibration excitation by the propeller.

Not only the technique for measuring the instationary pressure

distribution on propeller blades in a ship 's wake but also the three-dimensional lifting surface theory for the same purpose must be

improved. For the measuring technique the so-called direct method should be applied, i.e. pressure pick-ups mounted in the surface of the propeller blades.

The influence of the free air or _{gas content on cavitation}

in-ception makes it necessary to determine the _{nuclei distribution} during cavitation _{tests, where simultaneously}

propeller-excited pressure amplitudes are _{to be measured. The}

possible control of the free air content

_{would balueable}

tool for these _tests.

e

From the theoretical

investigations on bubble dynamics it can be

concluded that the theoretical model of _{the bubble and its} behaviour in _{pressure fields' should be}

checked by means of geósim tests. Another problem would be scale effects

on cavitation, which should be pursued with

7.

References

Lauaan, J.: Propellerkr.fte und

_{-vomente beim}

geradlinigen Stoppmanöver.

(Propeller forces and moments during a

straight-lined crash stop). HSVA-Bericht

3FB 98.

f2

van Larnmeren, W.P.A., vari Manen, J.D.,

Osterveld, M.W.C.: The Wageningen B-Screw Series.

Transactions

SNAME Vol.

₇₇

f3]

_{Laudan, J.: Einfluß der Kavitation auf die}

Propel-lerkcräfte und -momente beim

_geradlinigen

Stopp-manöver.

(The

influence

_{of the cavitation on the propeller}

forces and torque during a straight-lined crash

stop). HSVA-Bericht Nr. F

_8/76.

Laudan, J.: Einfluß der

_{Schrganströmung auf die}

Propelierkräfte und -momente bei

_{verschiedenen}

Fahrtsteigungswinkeln.

(Tne influence of the oblique flow on propeller

forces and torque for different advance angles.)

HSVA-Bericht Nr. F 9/76.

(Wake measurements with a series 60

_model.)

Institut f1r Schiffbau,

_{Bericht Nr.}

₃₄₀

(1976).

[63

_{Weitendorf, E.-A.: Experimentelle}

Untersuchungen

der durch kavitierende

Propeller erzeugteì

Druck-schwankungen.

(Experimental investigations on the pressure

fluctuations caused by cavitating

_propellers.)

Schiff und Hafen,

_{Heft 11 (1973),}

25. Bd.,

5. 1040-1060.

nj

_{Ackeret, J.: Ober stationäre Hohiwirbel.}

(On stationary

_{hollow vortices.)}

Ing.-Archiv (1930),

_399-402.

f

_{Weitendorf, E.-A.:}

KavitationseinflUsse

_{auf die}

vom Propeller induzierten

Druckschwankungen.

(Cavitation influences

_{ori the propeller}

induced

fluctuations.)

Institut fUr Schiffbau der Universität

_Hamburg,

bericht Nr. 338

_{(Sept. 1976).}

Chijupiri, A.I.; Weitendorf,

_{E.-A.: Berechnungen}

_von

Druckamplituden mittels einer verbesserten

Quellen-Senken-Verteilung

fur

einen

_{kavitierenden}

Spitzen-wirbel mit Knoten und Vergleich mit Messungen.

(Calculations of pressure amplitudes

_{by means of}

an improved source-sink distribution for a

cavita-ting tip vortex with nodes,

_{and comparison with}

measurements.)

Institut fUr Schiffbau der Universität Hamburg,

Bericht Nr. 339 (August

_1976.)

10;

_{Xienappel, K.; Triebstein, H.}

und Wagener, J.:

Messung der instationären Druckverteilung und der

Kräfte ari einem Propeller im

(Measurements of the instationary pressure

distri-bution and forces on a propeller in a ship'8 wake.)

Internal

_{DFVLR-AVA Report No. IB 253-76 C 04}

(March 1976).

11

_{Kienappel, K.: Wiederholungsrnessung}

der

instatio-nären

_{Druckverteilung eines Propellers im}

Schiffs-nachstrom.

(Repeated measurement of the instationary pressure

distribution on a propeller in a ship's wake.)

DFVLR-AVA Report No. IB 253-76

_{J 09 (Sept.}

Xrfte an Propellern

im Schiffsnachstrom.

(On the calculation

_{of the pressure distribution}

and the forces on propellers in a ßhip'8 wake.)

Rep. No 309 Institut

_{für Schiffbau der}

_Universität

Hamburg (Oktober 1974).

r13

Isay, W.-H.: Moderne

_{Probleme der Propellertheorie.}

(Modern problems

_{on propeller theory.)}

Berlin - Heidelberg

_{- New York, Springer-Verlag}

(1970).

van Oossanen, P., and

_{van der Kooy, J.: Vibratory}

null forces induced by

_{cavitating propellers.}

Trie Royal Institution of Naval Architects,

_Spring

Meeting (1972).

)15

_{Keller, A.?., and Weitendorf,}

_{E.-A.: Der Einfluß}

'- J

dea ungelösten

_{Gasgehaltes auf die}

Kavitations-erscheinungen an einem

_{Propeller und auf die}

_von

ihm erregten

_{Druckschwarikurigen.}

(Influence of undissolved

_{air content on cavitation}

phenomena at the propeller

_{blades and on induced}

hull pressure amplitudes.)

Rep. No 321 A Institut für Schiffbau der

L161

Keller, A.?.: Experimentelle und theoretische

Untersuchungen zum Problem der modellmßigeri

Behandlung von

_{Strömungskavitation.}

(Experimental and theoretical investigations on

the problem of cavitation in a flow with models.)

Versuchsanstalt für Wasserbau der T.U. München,

Bericht 26 (1973).

Lederer, L. :

_{Profilströmungen unter}

Berücksichti-gung der Dynamik von Kavitationsblasen.

(Hydrofoil flow with regard to bubble dynamics.)

F(ep. No 31 Institut für Schiffbau der Universitat

Hamburg (Oktober 1976).

Isay, W.-H., and Roestel, Th.: Berechnungen der

Druckverteilung an Flügeiprofilen in gashaltiger

Wasserst römung.

(Calculations of pressure distributions

_on

hydro-foils in water flow with

_{gas content.)}

Zeitschrift für angewandte Mathematik und Mechanik

Fi g.

Caption

i

_{Test setup for pressure amplitudes}

and

coordi-nates for measurements

2

_{Nondimensional blade frequency pressure}

amplitu-des K3 in x-direction for

_{two propellers in}

homogeneous flow

3

_{Cavitating propellers in homogeneous flow}

Optimal propeller 1283 in homogeneous flow

under different cavitation

_conditions

5

_{Different shapes of the}

cross-section of

cavi-tating tip-vortices used

_{for calculations}

6

_{Calculated pressure amplitudes}

with

variations of the wavelength

7

_{Calculated and measured pressure-amplitudes}

(including those owing to a cavitating tip vortex)

on a flat plate

8

_{Measured instationary pressureon the}

propeller-blades in a ship's wake

9

_{Measured instationary pressures on the}

propeller-blades in a ship's wake

Fig.

No Capt i on

10

_{Measured inatationary pressures on the}

propeller-blades in a ship's wake

11

_{Comparison between measured and calculated}

pressures on propeller blades

12

_{Comparison between measured}

_{and calculated}

pressures distribution on propeller

_blades

13

_{Comparison between calculated pressure and}

cavity extent at radius

riRa

0.90

14

_{Nondimensional blade frequency pressure}

amplitudes K5 in axial wake without

_cavitation

15

_{Test setup for laser light scattering}

method

16

_{Nucleus size histogram and fraction of relative}

free gas volume

17

_{Noridimensiona]. blade frequency}

_pressure

amplitu-des Xp5 in an axial wake dependent on measured

relative free gas volume

18 1-LSVA propeller 1917 in

a wake for two propeller

revolutions with low free gas volume

19

_{Calculated (in 117] ) growth of}

_{a single bubble}

20

_{Calculated (in}

_{fi7J )}

_{pressure distribution}

on a hydrofoil in stationary flow

21

_{Calculated (in}

_{j17j )}

_{local relative free gas}

volume

on a hydrofoil in stationary flow

Sketch No.

_{Wave-like hollow vortex}

Sketch No. 2:

_{Ellipsoidal hollow vortex}

Sketch No.

3:

Notation for hydrofoil in

water with gas-content

B5

BL.

Direction of

flow

e= 30mm

ig.1: Test setup for pressure am plitudes

and coordinates for measurements

0.06

fK3

..

in front of Prop.

-.05

Propeller 120; N'3

- Ratio J = 0.8 03

Max. Circulation drawn to inner radii

0.12

0.08

0.04

¡n front of prop.

Prop.-plane

-0.25

0.25

44

4J

0.5

_a.x/R

aIR' 0.109

a/Rs 0.109

g.2: Non dimensional

_{blade frequency}

pressure amplitudes Kp3

_Ifl

x-direction for two propellers in

homogeneous flow

-0.5

-0.25

₂₅

xIR

ATM

3.00

2.00

1.75

1.50

1.25

1.1b

PropelLer 1283 ;

Ns 3

Advance - Ratio

J a 0.803

Fig.3: Cavitating

_{propelters in}

homogeneous flow

P l283, Nz3

_{P 12h0}

_Nz3

Optimal distribution

Maximal circulation

of circulation

drown to inner radii

4 Optimut

propeLler

1283 in homogeneous

flow under

different cavitation

condition

Wavelength X0 = 600

ig. 5: Different shapes of the

cross

section of cavitating tip vortices

0 16

0.08

0.02

0.40

0.32

0.24

0.08

0.16

-0.02

- 0.5

Fig. 6: Calculated

_{pressure amplitudes}

Kp3 und Kp6 with variation of

the wavelength Xo

60°

45°

150°

2.0 xIR0

I

.1

I

150°

i.

TAj,A;A

p

HSVA-Prop. 1283; homog .flow

Cavitating tip-vortex

Advance Ratio J = 0.803

m 24; RK0m /R0 :0.0252

Tip-clearance aIR0

_{XA: 20°; X.t.p}

Cav.-num berGVA 1.14 .RK/RQ0.0143

0 24

90°

60°

<phri 0.2 0.1 O 0.2 0. 1 O 0.2 0.1 o 0.2 0.1 O 0.2 0.1 O

n

e

e

2.0

1.50

1.25

Fig. 7:

Calculated and measured

pressure amphtudes (in

-cluding those owing to

a

ccivitating tip vortex) on a flat plate

3. 5. 9. 3. 6. 9.

in front of prop.

Pos.

Pl

P2

HSVA-Prop.1283;N3

Homogeneous flow

Advance Ratio

Prop. plana

P3

P4

Calculations with

)(

6.harm Order

behind prop.

P5

RKam/Ra

Tip cearence a/R=O.1O9

660

410

0.010

1.75

700

_31°

_0.014

750

43°

0.017

Measurement U

1020

110°

20°

20°

41°

46°

0.018

0.018

o Q. Q.

3

-0.12

-0.16

nondirnens Rad. r/Ra 2 0.50

pressure side

suction side

0° 30° 90°

1800 2700 3300

o

o

_A

Fig.8: Measured instationary

_pressures

on the propeller-blades in

_{a ship's}

wake

ç

0 0.1 0.2 0.3 0.4 0.5

0.6

-i

_cp

-0.0/.

-0.12

-0.16

-0.20

-0.2/.

-0.28

-0.32

-0.36

pressure side

suction side

AVA Propeller

non-dimens. Rad. nR0 a 0.90

0° 30° 90°

180°

2700 330°

_A

0.5

chordtength

Fig. 9: Measured instationary pressures

on the propeller blades in a ship's

Q? Q. Q. u

3

-0.04

-0.08

-0.12

-0.16

-0.20

-0.24

nondimens. Rad. r/R

'0.975

pressu re side

.

suction side

..

_

lu

I,

j

0° 30

90°

2700 3300

0.7

0.9

chord length

Fig. 10:

Measured instationary

pressures on

the propeller

pressure

coefficient

-0.04

-0.08

-0.12

-0.1 6

-0.20

-0.24

-0.28

Fig.11: Comparison between

_measured

and calculated

pressure

distri-bution on propeller blades

nondimens. Rad. r/R' 0.90

\

o

/7

I

I

--e-- measured

po*0o

catcuLated

r

I

i

AVA-PropeUer

p-p-

Cpa

ÇW2R

0 6

-.. chordtength

coefficient

2

Ppw2R 2

0.08

0.04

o

-0.04

-0.08

-0.12

-0.16

-0.20

-0.24

-0.28

0

0.2

0.4

0.6

0.8

1.0

chord length

Fig.12: Comparision between measured

and calculated

_{pressures on}

propeller blades

£

L

Blade pos. p0:330°

JTw

AVA-Propeller

calculated

measured

I