Cavitation and its influence on induced hull pressure amplitudes

3 SEP.

₈₄

ARCHIEF

SYMPOSIUM ON

"HYDRODYNAMICS OF SHIP AND OFFSHORE PROPULSION SYSTEMS"

H0VIK OUTSIDE OSLO, MARCH 20. - 25. 1977

"CAVITATION AND ITS INFLUENCE ON INDUCED HULL PRESSURE AMPLITUDES"

By

E. A. WEITENDORF

Hamburg University/Hamburg Model Tank

SPONSOR: DET NORSKE VERITAS

PAPER 9/2 - SESSION 3

(ç)

Lab. y. Scheepsbouwkijnde

Technische Hogeschool

Abstract

Introduction

Measurements and Calculations of Propeller-excited

Pressure-Amplitudes

Measurements and Calculations of the Pressure

Fields on Propeller Blades

Influence of Undissolved Air Content ori Cavitation

Phenomena at the Propeller Blades and on Induced

Hull Pressure Amplitudes

Theoretical Research on Cavitation Inception

with Application of Bubble Dynamics

Conclusion

References

i

Abstract

A critical review of the following subjects is given:

Measurement and Calculation 9f_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 vortex with nodes 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 lenght0 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 Calculation 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 another

case of comparison (HSVA-Propeller 1917) it seems, that the results of the lifting surface theory do not reach the values of the real pressure distribution of the propeller investigated.

3. Influence of Undissolved Ajr_Conten on Cavitation Phenomena at

the Propeller Blades and on nquced_Hyl] Pressure Amplitud_es.

This investigation consisted of the application of the Scatterad Light Technique for measuring the undissolved air content 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 therefore 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 CavitationjnceptionwithApplication

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 complementing the above point _{3. is that the}

greater number of smaller bubbles with a diameter less than 1Ojrn

have an important influence on the cavitation phenomena, if the

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 can only

be mentioned by way of suggestion in this introduction.

For instance Laudan [1] has complemented the Wageningen "four-quadrant" measurements of propellers

12)

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

2

Furthermore this project "Safety against collision" of the SFB 98 investigated the influence of oblique flow on the propeller having different advance angles [4 and made threedimensional wake measure-ments during oblique towing of the ship model [5]. But now results are to be presented,whose origin concerns the author directly.

2. Measurement and Calculation of Propeller-excited Pressure

Ampi itudes

2.1. Measurements of Pressure Amplitudes for heavil, cavitatinS

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

tunnei of the Hamburg Model Basin (HSVA). These investigations [6] contain numereous results with a wide variation of the main para-meters of these three, four - and five biaded propellers having a

blade area ratio of about AE . 0.72. The essential results of

the experimental investigat9ons, which are qualitively not only

valid for homogeneous but also for inhomogeneous flow, can be

found in Fig. 2.

Here the nondimensional pressure amplitude

K -

IP

P3 -

Qn

Da

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

9VA

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

O-VA Pv

4

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 fluence can be reduced more than the thickness influence 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-ingly in Fig. 2 an increase of the amplitudes. On the contrary

the noise-less propeller 1240 shows very little of a cavitatirig

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

ships.

-2.2. Investigations of the Cavitating Ti2 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, buecreasing 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 positions 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

d. F'x)

K"'p-'-

_p

if x is the circumferential coordinate. In the calculations the

r

area of the cross-section F(x) of the cavitating tip vortex

-

2.

F)

sin2(i

(-XA)(-)

R R _"-e

/

_L'

(_XA)a

is built up of two parts: the round bracket stands for the

wave-like and cavitating hollow vortex (sketch No. 1), and the square

bracket for the ellipsoidal hollowYThe designations in the round

kec

No'f

T

kec No'f

bracket for the wave-like hollow vortex are:

number of blades,

inner and outer radius of the propeller blade,

= _{thrust coefficient,}

= advance coefficient,

nD

amplitude of the cross-section of the tip vortex,

to be taken from photographs,

= _{wave length of the hollow vortex in the theory}

m

(2.1) RcL Z)»

XAxL

rn RcL Z)»

XAxL

rn L rn N = =

Ram

= a

r-

T iv

RK = the mean radius of the cavitating tip vortex,

RK '16 K. '1 (2.2) (2.2) K K V 'u

= circumferential coordinate

The designations in the square bracket for the ellipsoidal hollow

vortex (ketc.b

P.Io2') are

-r

Skcch Wo

2

= initial value of the hollow vortex

A

XE = 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.

i In the calculations the value x= O lies at

the position of the lifting line vortex of the propeller blade, i.e. the 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

= the amplitude of the cross-section of the tip

vortex,

= 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 Ç8J all re-suits of these calçulations are given. But here the results of the variation of the wave length only can be shown in Fig. 6.

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

x/R > 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 lengtn x0 attains the value = = 1200 for N = 3., then the

third harmonic of the pressure will be the strongest amplitude. If the wave lengthx0 is equal 600, twice the blade frequency will

be th91greatest. 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 positionof 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 in Fig. 6, are equal to the value x/R = =

x0.

As the theory by Ackeret

[73

shows, the wave length x depends on the mean radius of the cavitating hollow vortex. In the _present

investigation [8] this statement was also confirmed for the spiral

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 number, as can be seen

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

for

the

wave length X0 but also formean drnet'r

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 va1uesare used for the calculations

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-manic order are given for the cavitation numbers

p-pv

- 2.0, 1.75, 1.50, 1.25 and 1.14.

VA

- Q

_V

-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 P 5, where the cavitating tip vortex is of do-minating 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

{3

. 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 end of this chapter the following concluding remarks on

3 13 3

-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 inin-stationary 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 Calculatlon of the Pressure Fields on Pro2eller

Blades

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 n 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 Göttingen measurements of the pressure distributions on both side of a model propeller were carried out in a wind tunnel with a cross-section of

g m2 [10, iiJ. 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 a calibration of àlitude and phase was necessary for each orifice. In the figures 8 to 10 for instance, results of the measured

-15-pressure distributions for the radii r/R = 0.50, 0.90 and 0,975

are shown. Here the nondimensional pressure coefficient

p-p0

CPI CU

P _QW

R

is plotted against the relative position along the chordlength

xii (x = distance from leading edge, 1 = chord length).

X/

With the exception of the blade tip (see Fig. 1O),the influence

of the inhomogeneous inflow (ship wake) is concentrated on the fore part of the chord, i.e. xii < 05. The influence becomes dominant at the leading edge. The lowest pressure, giving a

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

at chord station x/l = 0.007, was found on the radius r/R = 0.80.

The influence of the tip vortex can be seen in Fig. 10 for the suction side. The great pressure differences between pressure and suction side at the trailing edge indicate the threedimens-ionai flow around the blade tip, being typical for the tip vortex

rolling 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 suitable possibility for the comparison between the re-suits from theory and measurements is available. Furthermore, by using such a big model of 1.4 meter dianeter, 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. AU in all, the AVA in Göttingen estimates the error of the whole medsurement at ± 5 per cent with respect to the experience with other measuring techniques. This value

of 5 per cent seerî 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 (SFB 98), in order to compare the results of a computer program [121 based on the lifting surface theory [13] developed at the Institut für Schiffbau of the Hamburg

University.

19

-results from AVA [u] and the -results of the hamburg calculation

[12] 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° and = 3300 (starboard) the cavity lengths

at the radius r/Rq = 0.90 for the cavitation number

n

p - p Q12 _(irnD)

= 0.211

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 p0 = 330° in Fig.13, the vapour pressure corresponding Ön = 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 [8). The result is shown in Fig. 14. Again the

the-oretical values do not match the measurements. Once more the suspicion rises that the computer program [123 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 für Schiffbaifrom 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

f 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 Propeller Blades and on Induced Hull Pressure Amplitudes In a paper on propeller-excited hull forces given in 1972 by van Oossanen and van der Kooy [14], it was evident that for equal nondimensional flow conditions but different absolute

revolutions (i.e. n = 20 and n = 30 Hz), the nondiriiensional

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 tunnel 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 undissolved air content by the laser light

scattering method.

Measurement of the propeller-excited pressure amplitudes

on a flat 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 1163.} In our case of applicatiothe 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 mm2. 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 tne scattered light}

detector was performed with latex spheres of _{known diameter.}

These were injected into the control volume. _{The electrical}

output pulses of the photomultiplier which are proportional to

the unucleusl 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 of 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

volumec4. per bubble range (full line). The relative free gas

volumek is the ratio of all measured _{gas bubbles per volume} 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 volumec..}

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

161. 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 volumed,. 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 = 0.61 and the cavitation number

=

PPv

_=0.211

n

Ç/2 (TrnD)2

27

-The abscissa is the measured relative free gas volume.. -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 volumec. Steréometric photographs of the blade in several positions show that for a lower relative 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 blade 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 shor-tage of time: The cavitation sheet on the propeller blades became

-29-more and -29-more stable, when the gas content was increased from lower to higher values; i.e. the intermitterd cavitation observed

here is a sheer model effect.

Before finishing this chapter, it has to be mentioned that the model speed of revolution of 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 cavitatìon numbers of model and full scale. It is obviou _{that thé 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 causes earlier inception and stronger extension of

the cavity and therefore 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 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

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 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 A2lication

of Bubble Dynamics.

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 K1, on the relative free gas volume c 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 volume oc. to a high

extent. Trying to find an explanation for this dependence one has

to remind that, applying the value oc, 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 (17J for steady hydrofoil

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

A r o Q

hr

co

-

31

-+

I ()+y

J

1J(x+y?

2°

-A

(x-.x) dr

(5.1) (

x.

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

Sfçekch Wo3

The formula (5.1) is derived in a paper by Isay and Roestel [18]. 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 slip velocity of these bubbles shall be neglected and a further assumption is that the bubbles are moving along streamlines.

in a temporally changing pressure field is described by a diffe-rential equation of the second order. This is the well known

Rayleigh-Plesset equation

'7f

*

R

=

R

(5.2)

In this case R stands for the radius and R for the wall velocity of the bubble. The indes 1 is the designation for water or vapour,

the index 2 for dissolved or undissolved air. The star belongs to the gas phase and is the surface tension.

The growth of different initial radii R0 was calculated by Lederer

(uJ

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 further understanding of the procedure of Lederer {l7Jthe

following ought to be mentioned:

During an air content measurement f153 Z = 1000 bubbles were measured, flowing through a cross-section F0 with a velocity u0

in a

time tcr Dividing the measured radii (e.g. Fig 16) into ranges

j = 1,2 J, if the number of bubbles in a range is equal to Z0,

then the gas volume of the flow is

a

(5.3).

4 ç

veo

zoi (R0)

33

-For the radii range R0 the number

of

bubbles is denoted by

(5.4),

COj

which is referred to unit volume.

V

Using the gas volume ratio =

fl

of the

flow,

then one Vw can define

(R0)3

=

) -7 1

(5.8).

't',

So the number n3 of bubbles per unit volume

of

the flow is

>a

j4

(5.6).

Comparing an initial state at a point x = x0 with a state at a

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

find

(44

i0)

=

(1c

(5.7)

4

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

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

J

-- 3

The expansion

of

the radius Rxj

of

the single bubble from the

initial radius R0 in the pressure field p(x) is calculated by

means

of

the Rayleigh-Plesset equation (5.2). If

R

= .BCR0,x)

(510)

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

J

(x,y)

0(.B(R

, X,

_(5.11).

A

As already mentioned, the precise determination of the streamline

-is neglected. Instead of this, the straight lines y

= n parallel

to the chord (x-axis) are regarded.

Knowing the pressure distribution p(x, Yn) 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 c&(x, y) of the flow can be calculated with the aid

of equation (5.11).

The computations by Lederer E173 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 2 A = 10 cm.

The nuclei distributions of the computation were adapted to the results of the laser scattered light measurementElsj. 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:

R01

= 5rn;

R02 =

35,rn;

R03 = 651wr; R04 =

95,,m.

These ranges were applied in two different nuclei distributions

for the calculations: Nuclei distribution No. 1:

V

= 50;

'o2 = 20; o3 = 5; co4 = 1 with

= V_w

1,3 10

= number of bubbles of the range j)

Nuclei distribution No.2,

= 200;c02 = 20; co3 = 5; _o4 = 1 with

K

= 1,3 . 10

The increase of the number,çof the small bubbles by a factor four

means practically no change in the free gas volume ratio K0 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. Futhernìore,

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 1

smallest bubble R01 and the greatest one R04 are shown. Fig. 19 is valid for the cavitation number

p-p

=0.3

V

(iu

The pressure p0 = i 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 [15] . 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

and Po = 0.2 kp/cm2 are compared in the region 0.01

_2A

0.06.

The strongly negative pressures 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 answered.1 to what

values the pressure in real water with free gas content may drop.

J- ')P

37

-Nevertheless Keller (see p. 96 in 116]) 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 r&(x, n) (see eq. 5.11). In this connection the results calculated by Lederer (17] for the local free gas volume c&(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 = i kp/cm2 attains the

greatest value c(x,

n'

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 *= 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 Kp5 on the flat plate is plotted against the relative free gas volume .But the que'stion is, whether the value

'& 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-ç t Ô

Committee' measure the bubble radii between iO,&m and 250,um should

be supplemented: Nuclei should additionally be measured between 5 and 1O»m 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'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

pool for shipbuilding (SF3 98).

Conclusions.

The following conclusions can be drawn from the results presented

Reardin chapter 2:

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 thepropeller.

Regarding chapter 3:

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

Reardin chapter 4

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.

Regarding chapter 5

From the theoretical investigations on bubbie dynamics it can be

concluded that the theoretical model of the bubble and its

behaviour in pressure fields' should be checked by means of gebsim

tests. Another problem would be scale effects on cavitation, which should be pursued with a combination of experiment and theory.

7. References

.

iJ

Laudan, J.: Propellerkräfte und -imente beim

geradlinigen Stoppmanöver.

(Propeller forces and moments during a

straight-lined crash stop). HSVA-Bericht F 14/7k für den

SFB 98.

12]

van Larnrneren, W.P.A., van Manen, J.D.,

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

Transactions SNAME Vol. 77 (1969)

3]

Laudan, J.: Einfluß der Kavitation auf die

Propel-lerkräfte 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 Schräganströmung auf die

Propellerkräfte und -momente bei verschiedenen

Fahrt steigungswinkeln.

(The influence of the oblique flow on propeller

forces and torque for different advance angles.)

(Wake measurements with a series 60 model.)

Institut fUr Schiffbau, Bericht Nr. 34O (1976).

163

Weitendorf, E. -A.: Experimentelle Untersuchungen

der durch kavitierende Propeller erzeugten

Druck-schwankungen.

(Experimental investigations on the pressure

fluctuations caused by cavitating propellers.)

Schiff und Hafen, Heft 11 (1973), 25. Bd.,

s. ioo-iO6o.

Ackeret, J.: Über stationäre Hohiwirbel.

(On stationary hollow vortices..)

Ing.-Archiv (1930), S. 399-4O2.

L8i

Weitendorf, E.-A.: Kavitationseinflüsse auf die

vom Propeller induzierten Druckschwankungeri.

(Cavitation influences on the propeller induced

fluctuations.)

Institut für Schiffbau der Universität Hamburg,

Bericht Nr. 338 (Sept. 1976).

i 9

Chljupin, A.I.; Weitendorf, E.-A.: Berechnungen von

Druckamplituden mittel8 einer verbesserten

Quellen-Senken-Verteilung für 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 für Schiffbau der Universität Hamburg,

Bericht Nr.

₃₃₉

(August

_1976.)

10]

Kienappel, K.; Triebstein, H. und Wagener, J.:

Messung der instationären Druckverteilung und der

Kräfte an einem Propeller im Schiffsnachstrom.

(Measurements of the instationary pressure

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

Internai

DFVLR-AVA Report No. IB

253-76 C 0

(March

1976).

[iJ

Kienappel, K.: Wiederholungsmessung 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.

_1976).

im Schiffsnachstrom.

(On the calculation of the pressure distribution

arid the forces on propellers in a ship's wake.)

Rep. No

₃₀₉

Institut für Schiffbau der Universität

Hamburg (Oktober

_1974).

Isay, W-H.: Moderne Probleme der Propellertheorie.

(Modern problems ori propeller theory.)

Berlin - Heidelberg - New York, Springer-Verlag

(1970).

1114f

van Oossanen, P., and van der Kooy, J.: Vibratory

hull forces induced by cavitating propellers.

The Royal Institution of Naval Architects, Spring

Meeting

(1972).

115;

Keller, A.?., and Weiteridorf, E.-A.: Der Einfluß

des ungelösten Gasgehaltes auf die

Kavitations-erscheinungen an einem Propeller und auf die von

ihm erregten Druckschwankungen.

(Influence of undissolved air content on cavitation

phenomena at the propeller blades and ori induced

hull pressure amplitudes.)

Rep. No 321 A Institut für Schiffbau der

Universi-tät Hamburg (Sept.

_1975).

116]

Keller, A.?.: Experimentelle und theoretische

Untersuchungen zum Problem der modellmäßigen

Behandlung von Strörnungskavitatlon.

(Experimental and theoretical investigations on

the problem of cavitation in a flow with models.)

Versuchsanstalt für Wasserbau der T.U. München,

Bericht

26 (1973).

f17j

Lederer, L.: Profilströmungen unter

Berücksichti-gung der Dynamik von Kavitationsblasen.

(Hydrofoil flow with regard to bubble dynamics.)

Rep. No

31

Institut für Schiffbau der Universität

Hamburg (Oktober 1976).

f18j

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

Druckverteilung an Flügelprofilen in gashaltiger

Wasserströmung.

(Calculations of pressure distributions on

hydro-foils in water flow with gas content.)

Zeitschrift für angewandte Mathematik und Mechanik

54 (19714).

Fig.

Caption

No

i

Test setup for pressure amplitudes and

coordi-nates for measurements

Noridimensional 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

and K6 with

variations of the

wavelength c

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 ori the

propeller-blades in a ship's wake

r

Fig.

No

Caption

10

Measured instationary pressures on the

propeller-blades in a ship's wake

il

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

p.90

114

Nondimensional blade frequency pressure

amplitudes K,5 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

Nondimensional blade frequency pressure

amplitu-des K5 in an axial wake dependent on measured

relative free gas volume

18

HSVA propeller

1917

in a wacè for two propeller

revolutions with low free gas volume

19

Calculated (in

117] )

growth of a single bubble

on a hydrofoil in stationary

flow

21

Calculated (in

_{¡17J )}

local relative free gas

volume

on a hydrofoil in stationary flow

Sketch No. 1:

Wave-like hollow vortex

Sketch No. 2;

Ellipsoidal hollow vortex

Sketch No.

3:

Notation for hydrofoil in

B5

BL,

Direction of

flow

e 30mm

B2

Fig.1: Test setup

for pressure amplitudes

0.12 0.08 0.04 s

¡p

o in front of Prop. Prop.-plane b,

\

aIR

0.109

aIR: 0.109

in front of prop. Prop. plane

-0.5 -0.25 0 0.25 0.5

x/R-Fig.2: Non dimensional blade frequency

pressure

amplitudes Kp3

ifl

x-direction for two propellers in

homogeneous flow

-.05

-0.25 à 0.25

0.5 .a-x/R

Pos. 1 2 3 4

Propelter 1240; N:3 Advance - Ratio J :0.803

Max. Circulation drawn to inner radii

ATM

PropeLler 1283 N 3 _3.00

Advarce - Ratio J: 0.803 _2.00

Circulation distribution OptimaL

.eVA_ 1.75

VA 1.50

= 1.25

Lib

Pos. 2 3 /4 5 0.06 0.01. 0.02 o

Fig.3: Cavitating propellers in

homogeneous flow

P 1283, N3

P 121.0

N=3

Optimal distri bution

Maximal circulation

of circulation

drawn to inner radii

OJ4

1,50

dVA.-2JOO

a'VA_

1,2

'VA175

OVA 1,14

Tipclearctnce a/R0.109

Advance Ratio J

0.72

Wave(ength X0

600

Fig. 5: Different shapes of the cross

-section of cavitating tip vortices

used for caLculatioñs

0°

20°

/400

_60°

800 ¡ i i I 1000 i i

120°

i

X

m24

m2/4

XA

XA2O° x0°

z2Q

m8

photograph

20

X

X0

from

No

XAO° XLp°°

00 I I I I I

20°

40°

60°

80°

t I I

1000

I I

120°

1/.0°

0.1 o 0.2 o. i o 0.2 0.1 O 0.2 0.1 O 0.2 0.1 O

flgg

g

g

3. 6. 9.

n front of prop.

HSVA -Prop. 1283; N 3

Homogeneous flow

Advance Ratio

J 0.72

Tip clearence al ROEZ 0.109

Measurement

g

e

e

3. 6. 9. 3. 6. 9. Prop. plane g

e

g e

e

n

n

e

e

Calculations with

1.14 H

n

g 3. 6. harm Order

behind prop.

Fig. 7:

CalcuLated and measured

pressure amplitudes (in

-cluding those owing to a

cavitating tip vortex)on a flat plate

VA

o

XA

)(

RKam/Ra

2

66°

10° 141°

0010

1.75

70°

15°

31°

0.014

1.50

75°

15° 143°

0.017

1.25

102°

20°

41°

0.018

1.14

110°

20°

46°

0.018

Pos.

Pl

P2

P3

P4

P5

g

e

e

g

e

e

n

3. 6 9.

e

4-,

2.0

1.75 1.50 1.25

o

o-cp

0.16 CN 0.12

3

0.08 0.04 a) o L)

I0

-0.04

-0.08

-0.12

-0.16

00 30° 90°

180°

270°

330°

o

o

.

A

AVA- Propeller

noridimens Rad. r /R

0.50

pressure side

suction side

,po90°

Fig.8: Measured instationary

pressures

on

the propeller-blades in

a ships

wake

0 01 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 c ho rd length

pressure side

suction side

00 300

90°

180°

270°

330°

D O

s

_A 90° 00

w

0 0.1

0.2

0.3

0./.

0.5

0.6

0.7

0.8

0.9

chordlength

Fig. 9: Measured instationary

_pressures

on the

propeller blades in

a

ship

o a. Q-a) (N ç'J

3

o-a. o

cp

0.08 0.0 L O

-0.04

o

-0.08

-0.16

-0.20

pressure side

suction side

I

AVA -Propeller

nondimens. Rad. r/R

:0.975

Fig. 10:

Measured instationary

pressures on

the propeller

blades in a ship's wake

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

08

o 9

chordlength

-0.24

00 300 900

180°

2700 330°

90

0.0/4 o

-0.04

-0.08

-0.12

-0.16

-0.20

-0.24

-0.28

Fig.11: Comparison between

_measured

und calculated pressure

distri-bution on propeller blades

A

-

7-/

/

00

I

r

----o----measured

pelter

caLculated

AVA-Pro

P Pr

' W2 R

0.12 0.08 0.6

0 6

0.8

-

chordlength

0 0.1 0.2

pressure

coefficer'it

-p-p0

Cp_

pw2R2

012

0.08

0.04

O

-0.04

-0.08

-0.12

-0.16

-0.20

-0.24

-0.28

0

0.2

0h

0.6

0.8

1.0

chord (ength

Fig.12: Compansion

between measured

and cacuEated pressures on

propeller blades

I

nondimens.Rcid.

i I

nR =0.90

£

t.

Blade pos. Lp0330°

J

measured

caLculated

--A--AVA-Propeller

I I J

0.10

0.08

-0.06 0.04 0.02 O

-GO

2--0.04

-0.06

-0.08

-0.10--0.12

pressure side

suction side

cavity

t e n gi h

calculated pressure

-A av i ty press ure a cc o rd ng

s

0.211

Model -Prop.

HSVA 1917

(Zeise-Design

Fig. 13:

Compurision between calcuLated

pressure and cavity extent at

radius r/RaO.9O

caLculated pressure

p0330°

rd i n g 0.211

;re

ccc o =

cavity length

100./o

__!_ 0.1

02

0./. _0.6

08

_{chord length}

0.06 0.04

0.02-O - 0.0 2

-0.04

-0.06

-0.08

-0.10

K5

0.012 0.0 08 0.004

0.002

O

-0.48

-0.24

HSVAFrcp. 1917

Advance Ratio j

_Kl

0.61 Tip

clearance a/R

0.60

Measurement

Theory

Fig.14: NondimensionaE blade frequency

pressure

amplitude K5 in

axial wake without

cavitation

x ,flow

0 0.24 0.48

_'direction

Ra

7

deviation

of measurement

Contr1 volume

Test section

Slit aperture

/

t

PhotornultipLier

Fig.15: Test set up for laser light

scattering method

0.1 _0.001

20

Test No l5

Degassed Water

Rel. Free Gas Volume

loo

Q'-O.11&-1U

Diameter of nucleus D C,Lm2

0.0 01

3L O

Fig.16: Nucleus size histogram

and fraction of relative

free gas volume

1

L____..1

Nuclei per cm3

Relative free gas volume

n-1

L..

i

r-1 r

-

r

i I i i I LO C) 0.1 0.01 200 300

0.04

0.03

0.02

0.01 -O ¶

20 Hz

K5:

pn2D2

C Uy,

fl: 15Hz

Advance ratio

J Kl

0.61

Cavitation number d

:0. 211

Pressure pick up pos. 3, directly ab. prop.

HSVA -Prop. 1917, number of blades N: 5

usual cavitation test

-0.01 _0.02 0.04 0.06 0.1 0.2 0.4 0.6 1

Rel. free gas volume oC

---O n

«

15 Hz

n

20Hz

: 30 Hz

Fig.17: Nondimensional blade frequency

pressure amplitudes Kp5 Ifl Qn

axial wake dependent on

mea-sured relative free

gas volume

n

.30 Hz

0.12 10 n

15Hz

= 0.25 -KT 0.61

6'

=0.211

Fig.18: HSVA Propeller 1917 in

a wake for two

propeller revolutions with low

free gas

Y,4

0.005

-9U2

4----3 i o2 3 2

lo

6

i kp

Po

smaflest bubble R01

Po :1

kp/cm2

0.3

smallest bubbte R

greatest

bubble R04

r _t\ P

''

.U.h

cm 0.004 0.01 0.02 0.04 0.1 0.2

chordlengih 24

Fig. 19: Calcu [ci ted(in [17]) growth of

ci

p

[kpicm2]

04

0.2 o - 0. 2

-0.4

-0.6

Fig. 20: CcUculated(in[171)pressure

distribution on a hydrofoil

in stationary flow

n u c 1. d i st r. No 2 p

1 kp/cm2

nuci . d istr. No. I

kp/cm2

/

Jnuclei.distrib.

1nuclei.distrib.

I

p0-0.

2kp

cm2 p_o

0.2

No 1 and No 2

--.

-/

/<Po

-7--/

/

/

lkp/cm2

-

Vp2

P0 - Pv

2°

distance from

suction side

I J I Y/A 0. 005 I I 001 0.02 0.04 0.06 0.1 0.2 0.4 0.6 1.0

chord(ength 2A

o_2 distr.No 1

p z i

kp/cm2

p0zO.2

Çnuclei distr.

Lnuclei disir.

kp/cm2

I

No 1 and

No 2

,I liii

I

p0 - P;

-0.3 I

III

T

U0

distance from

suction side

Y/A z 0.005

I I ü. 01

002

_{0.0/. 0 1 0.2 0./. 1.0}

chordlength 2A

Fig. 21: CaLculated (in[17])loccil

_relative

free

gas volume o( on a hydrofoil

r

2RK

xo

X0

Xo

x

2(RKRKam)

Sketch No2 :

Ellipsoidal hollow vortex

T

U,X

2y(x

Shock

y

X

Sketch N 3 : Notation for hydrofoil in water with gas-content

o

Xst