Measurements of the radiated noise from various forms of lifting surface cavitation

-NOV. 1982

ARCH1F

SYMPOSIUM ON

"HYDRODYNAMICS OF SHIP AND OFFSHORE PROPULSION SYSTEMS"

HØVI K OUTSIDE OSLO, MARCH 20. - 25., 1977

"MEASUREMENTS OF THE RADIATED NOISE FROM VARIOUS FORMS OF LIFTING SURFACE CAVITATION"

By Steven J. Barker

University of California, Los Angeles

Ref.: PAPER 2/3 - SESSION 4

Lab. v.

Scheepsbouwkunde

Technische Hogeschool

'.jIiotheek

van de

Measurements of the Radiated Noi eAfcheepsb

'

-vrthijnde

ICe

Various Forms of Lifting Surface C

V _TE

DATUM!

I

ABSTRACT

This paper describes the results of a regent series

of noise

measurements in the CaltechFiigh-Speed

Water Tunnel.

Model

hydro-foils of 15 cm span were mounted in the rectangular

test section of

the tunnel and run atvelocities from 600. to

1,500cm/sec.

The

static pressure was varied independently of the velocity to

produce

a wide range of cavitation parameter.

.

Radiate.d noise was measured.

by a hydrophone mounted flush with the tunnel wall.

Cavitation noise

spectra were measured in the frequency range

from 200 Hz to 160 kHz.

Three distinct types of cavitation were studied: partial or

"blade surface" cavitation, full cavitation, and tip.vortex

cavita-tion.

For partial cavitation, vibrations of the hydrofoil mo4el

exéited by the cavity collapsearefound tobe an important source

of noiSe.

In full cavitatiOn this is not the case, although the

broad .band.nOise intensity is apparently greater.

Both partial and

full cavitation produce a strong spectral peak at a Strouhal

num-bér based upon cavity length of 0.5.

Noise from trailing vortex

cavities is found to be of. lower intensity than that of the

other

forms.

This is due to the fact that the vortex cavitation as i.t

occurs in the water tunnel is gaseous rather

than vaporous. .

The

vortex cavities do not show the same behavior with cavitation

parameter as the other forms.

Submitted by: Steven J. Barker, Assistant Professor

University of California

CONTENTS

Page

Introduction _i

Experimental Geometry ₅

Blade Surface Cavitation ₈

Wake Cavitation ₁₅

Trailing Vortex Cavitation ₁₇

Summary and.Conclusions ₁₉

REFERENCES ₂₂

MEASUREMENTS OF RADIATED NOISE FROM VARIOUS FORMS OF LIFTING SURFACE CAVITATION

1.. Introduction

Cavitation on lifting surfaces in the ocean is often unavoidable,

particuiar].yin.high speed hydrofoils and screw propellors. The

noise generated by cavitation has thus been a subject of interest

for manyyears. However,, efforts to predict this noise fom. theory

have met with little success, and laboratory measurements of the

noise have been.incoinplete and unsatisfactory. Lifting surface

'cavitation occurs in several forms,' and in this study noise from

,eaóh of these fors. was measured independently. The measurements

of the study were made in a water tunnel that is unique in its low.

background noise level. . .

Cavitation produced noise is almost always of much greater

intensity than fully wetted turbulent flow noise at the same flow

velocity. The reason for the greater intensity is as follows.

Lighthill [1] showed that the momentum equation in ,a single-phase

flow, can. be written as . . .

4 -.

aVp

=

_

_ T .

,:

where the tensor T1 'is defined by

= PU1U - pj - (2)

In these equations, u _{is the i-component of the instantaneous}

fluid velocity, p is the fluid density, _{is the stress tensor,}

a0 is the local iseitropic speed of sound, and

i.j is the kroneker

momentum equation as a wave equation for the density with the

double divergence of the tensor T1 appearing as a forcing

fimc-tion on the right hand side. called the "fluctuating

Reynolds stress tensor," is quadrupole in nature since its

second derivative appears in the wave equation. The acoustic

quadrupole is. a relatively inefficient means .of converting

kinetic energy to sound. Most of the energy goes into near field

terms, representing localized reciprocating motions wh.ich do. not

propagate to infinity. To use Lighthili's example1 if a sphere

vibrates in a quadrupole fashion such that the acoustic

wave-length is twice the circumference, only 1/1000 of the energy of

the vibration is radiated as sound. For a corresponding dipole

motion of the sphere, 1/13 of the energy is radiated as sound.

The application of Lighthill's

analogy

to boundary layer flows

hasbeen investigated by Curle [2] an4 Phillip.s [3].

For the case of cavitating flow, the: continuity equation.

can be written as . ..

pu. zh(x,t) . (3)

where th(x1t) is a distribution of mass sources representing the

rate of change in volume of cavitation bubbles. This would add

another .term to the right hand side of equation (1), namely

/at.

This term is a simple acoustic. SOurce, which is much more efficient

than either the dipole or quadrupole. Because of its greater

acous-tic efficiency, weexpec.t.a cavitating flow to radiate sound at

a higher. intensity than a fully. wetted flow of the same energy

Each of these different acoustic source. types will produce a

different dependence of. the noise intensity upon flow veloäity.

Lighthiil showed that the acoustic quadrupoles of his equation

should yield a dependence of noise intensity upOn U8. _Similarly,

acoustic dipoles will result in a U6 dependence and simple _sources

a U dependence. The assumptions made. in reaching these

conclu-sions are that the amplitude of the fOrcing function scales with

pU2 _{and that the frequencies present in the turbulent flow scale}

with U. _{Previous experimenters have compared the behavior of}

various frequency bands in a measured noise spectrum with these laws and made inferences about dipole, quadrupole, and even

octu-pole radiation. _{However, the velocity dependence predict-ions for}

the different sources are for the total noise intensity and not

for the spectrum level at a particular frequency. _{Since these}

predictions were made under the assumption that frequencies

pre-sent in the flow scale with velocity, the velocity dependence _of

the spectrum level cannot be interpreted, in this way..

Cavitation on bodies moving through water. _{appears in Several}

forms, and these may generate noise by different _{mechanisms. For}

the purposes of the present experiment we shall discusS blade

sur-face cavitation, wake cavitation, and tip _{vortex cavitation.}

Blade surface cavitation, also known. as "partial. cavitation,"

consists of a vapor cavity which begins near the leading edge of the suction side of a hydrofoil and collapses on the surface

of the foil somewhere further aft. _{Blade surface cavitation may}

travelling bubble cavitation, the cavity is a mixture of liquid

and small vapor bubbles which change rapidly in size. Such a

cavity has a cloudy or diffuse _{appearance. On the other hand, a}

stationary cavity has a well defined interface with _{a glassy}

ap-pearance, within which the pressure is essentially vapor pressure.

Wake cavitation, also referred to as "full" cavitation,

occurs when the cavity collapses downstream of the trailing edge

of the mode]... _{The cavities generally have the glassy appearance}

of a stationary cavity near their upstream end.,, changing _{to the}

frothy look of travelling bubble cavitation further aft. _Between

partial. and full cavitation there. is a region of 11unsteady"

cavi-tation,.'in which thecavity collapse occurs very near the trailing

edge of' the model.. In this case. the cavity fluctuates rapidly

in length, causing the forces on the foil to vary by more than

100% _{Any type of measurement is difficult to make in this}

re-gime, and none were made in these tests.

The trailing vortex wake of a lifting three 'dimensional

hydro-fOil has .a low pressure core which can cavitate. Trailing vortex

cavities occur not only at the erds of hydrofoils, _{but more}

conmion-ly at the tips of ,screw propellers. _{These cavities usually have a}

glassy appearance, and are found to behave very differently from

the other forms mentioned above. _{They will be discussed below in}

Section 5. . '

It might be. asked why further measurements of cavitation

,rioise are important, since there have been several such

proper-ties of the CaItech High-Speed Water Tunnel, which will be

brief-ly described below. In addition, past measurements have not

characterized the noise from the different forms of cavitation

described above. SOme of the previous experiments have employed

rotating blades as' the Source of cavitation [4], [5].. Such

mea-surernents are of limited use since the cavitation parameter sigma

is not constant along the length of the blade. '(Sigma is defined

by a=(p_P)/½Pu2, where pis free stream pressure,

PC is cavity

pressure, and U is free stream velocity.) _{There have also been}

other water

tunnel

_{measurements [6], [7], but these differ}

great-ly from the present study.

2. Experimental Geometry

2.1 High-Speed Water Tunnel.

These experiments were conducted in the Caltech 'High-Speed

Water Tunnel, which is deScribed in detail in Reference [8]. _This

tunnel has two features that are very Important to the measurement

of cavitation noise. One is its extremely low background noise

level, which makes it possible to measure radiated noise _from

even fully wetted boundary layers under. some conditions. _The

higher intensity of cavitation noise is far above the background.

The other relevant feature of th _{tunnel is the. "resorber" section.}

The resorber' is a vertical Oylinder 12 ft . in diameter and 58 ft

high whose top is located about 20 ft below the test section.

The volume of the resorber is approximately 45,000 gallons. _Water

leaving the test section passes first through the drive _{pump and}

then through the .resorber. _{The time required for the. water to pass}

at its bottom causes complete re-absorption of entrained air

bubbles generated by cavitating flow in the test Section.

The test section of the tunnel is rectangular; 6 inches x 30

inches in cross section and 48 inches in length. The maximum

velocity is a.bout 80 ft/sec and the static pressure can be varied

independently of velocity from vapor pressure to about three

at-mospherés. .. . .

2.2 Transducer Geometry

The chief difficulty in measuring radiated noise in ,a steady

state flow is to distinguish radiated sound from the wall

pres-sure fluctuations (also called "self noise" or "pseudo-Sound")

created by the turbulent boundary layer over the face of the

transducer itself.. This was done in the past in this tunnel by

placing a focusing acoustic reflector outside of the test

sec-tiôn and locating the. transducer at its focus [9). However the

test section wall through which the sound must pass before

reach-ing this reflector is a very poor acoustic window. . The

config-uration . used in the present study employs a thin diaphragm

mounted.

flush with the tunnel wall, with a flooded cavity behind it (See

Figure 1).. A piezoelectric transducer is located at the back of

this cavity. The diaphragm transmits nearly all sound into the

cavity, but has .the effect of averaging the boundary layer wall

pressure fluctuations over its full area. _{(The diaphragm is 1½}

inches in diameter, which is much larger than the tunnel wall

boundary layer thickness.) Thus the wall pressure fluctuations

detailed

explanation

_{of thismechanism, see Reference (10].)} The lowest resonant frequency of the flooded transducer

cavity is 25 kHz, but prominent peaks in the noise spectrum _are

not observed at this frequency or any. of its harmonics. A more

likely source of reverberation is the 6 inch spacing between the

two largest parallel walls, of the test section. The fundamental

frequency of this

standing

wave is between 4 and 5 kHz, where 'a

mild peak is observed in the clear tunnel spectrum. _{Due to 'the}

reverberant nature of the test section, the absolute measured

acoustic lee1s may not be' significant. _{However, the goal of}

these tests is to establish trends of, the noise spectrum,

in-cluding its variation with velocity, cavitation number, and model

configuration. ' .

The transducer output is coupled to a .high input impedance

preamplifier, and then to a pre-whitening amplifier. _The

out-put of this is fed into a Bruel and Kjaer Audio Spectrometer,

which reads out 1/3 octave band levels for bands whose _center

frequencies range from 100 Hz to 160 kHz. The band levels are

converted to spectrum levels' in decibels referred to I dyne per

square centimeter, and the resulting spectra are plotted by

computer. _{To establish the background noiSe level of the}

tun-nel, power spectra were measured in the clear tunnel

configura-tion and are shown in Figure 2. _{Spectra are plotted for test}

section velocities of 20, 25, 30, 35, 40, 45, and 50 ft/sec.

The clear tunnel Spectra are independent of the static _pressure

.3. Blade Surface Cavitation

Noise measurements on blade surface cavitation were made

over a wide range of sigma and angle of attack. Test section

velocity was varied from 20 to 50 ft/sec. One of the hydrofoil

models used was an NACA 66-210 section with a six inch chord.

The model spanned the six inch width of the test section, so that

the mean flow was nearly. two dimensional. The model was made of

aluminum, and its surface was painted and polished to a mirror

finish. A xnicroflash photo of blade surface cavitation on this

model is

shown.in

Figure 3.

Let us consider first the effect Of varying sigma while

holding velocity, and angle of attack constant. (The cavity

pres-Sure is assumed to equal vapor pressure in all measured values

of siqta.) Figure. 4 shows four spectra measured at eight degrees

angle of attack and 20 ft/sec tunnel velocity. In the lowest

spectrum, labeled sigma co the pressure is high enough that no

Oavitation occurs; this establishes, a background level. In the

spectrum for sigma = 6.6 there is no visible cavitation, but the

spectrum level for frequencies above 10 kHz has increased by.

between. 2 and 7 db.. This increase at high frequencies is not

detectable to the ear. There is still no visible cavitation at

sigma = 4.9, but the spectrum level at the highest frequencies

has been increased by about 40 'db. The low, frequency part of

the spectrum remains unchanged, and the change in sound is. barel.y

audible. At sigma = 4.2 the cavity is clearly visible and. about

48 db, but the changes at the low frequencies are still relatively

small.

Figure 5 shows the fully wetted spectrum again plus two _spectra

for still, lower values of sigma. At sigma = 3.5 the cavity length

is 2. mm and the significant increases in spectrum level _{now extend}

to frequencies belOw 1 kHz. For the lowest sigma of 2.2, the

cavity is 30 mm long and the spectrum level increases extend down

to 300 Hz. Beginning with sigma = 3.5, the spectrum level _{at the}

highest frequencies decreases as the pressure is lowered. The 30

mm long cavity actually produces less noise at 100 kHz than _the

invisible incipient cavitation at sigma = 4.9. All of these

vapor cavities have, the cloudy. or' diffuse appearance of travelling

bubble cavitation, as seen in Figure 3.

For the first visible.cavitatjon (sigma =.4.2) _{we can form 'a}

frequency based upon the flow velocity, and the observed cavity

length' of 1 mm. _{This frequency is approximately 6 .kHz. At. sigma =}

4.2 there is very little increase in, the radiated _{sound (relative}

to sigma = _{) for frequencies below 6 kHz, and it is near this}

frequency that. the spectrum begins to deviate from that of the

fully wetted flow. _{This suggests that, at. least for incipient}

cavitation, the sound may be produced by acoustic sources created

by the growth and collapse of very small bubbles passing _through

the region of cavitation. _{For larger cavities we shall Se below}

that another mechaniam becomes important:. the forces exerted by

Note that the spectra in Figures 4 and 5 are of dissimilar

shapes. Each spectrum has prominent peaks occurring at different

frequencies. The general trend is that as sigma decreases, energy

content shifts to lower frequencies and the broad band nOise level

increases.

We now consider noise spectra measured for a model

configura-tion run at different speeds for a fixed value of, sigma. Speed

is. varied over the range from 20 to 40 ft/sec in these runs, and

sigma is held constant by raising the static pressure as speed

is increased. The size and appearance of the cavity are observed

to be constant over this speed range. Two very interesting

char-acteristics can be seen in these spectra. One of theseis shown

in Figure 6, which is a plot of spectra for 20, 25, 30, 35., and

40 ft/Sec at sigma 2.46. Here the cavity forms near the leading

edge of the mOdel and is about 5 mm long. The spectra for the five

different speeds are remarkably similar in shape, with peaks occur-i

ring at the same frequencies over the entire speed range. Figure

7. shows another series of spectra for sigma =. 2.15; the cavity

length is. .8 mm. Again the spectra have the. same shape at all

speeds, with the major peaks occurring at the same frequencies.

However, the shapes of the spectra in Figure 7 are quite

differ-ent from those of. Figure 6.

The similarity in the Spectral "signature" at different speeds

is not

consistent

with the concept of the noise being produced

directly by the

expansion

and collapse of cavity bubbles. For a

scale with the velocity. The fact that. they do not in the above

cases suggests the following. A well developed (as opposed to

incipient) blade surface cavity will exert large fluctuating

forces on the surface of the hydrofoil in the region of collapse.

These fOrces can be expected to excite the normal modes of

oscil-lation of the foil itself. The resulting vibrations of the

hydro-foil would then be a very efficient noise generating mechanism.

The frequencies of these vibrational modes are iüdependent of

the flow velocity, hence the similarity in spectral signatures

at all speeds. Increasin.g the speed only increaSes the energy

being 'fed into these vibrations, so that the whole spectrum moves

upward rather uniformly.

bn

the other hand, a change in sigma will

change the Spectral, signature because for a different cavity length

the fluctuating forces are being applied on a different part of the

foil. This would tend to excite different modes,: or tO excite the

same modes in different propgrtions.

Further evidence ui support of this

explanation

of the

con-stant spectral. Signature can be obtained. Measurements

on two

models, of identical shape but very different vibrational

charac-teristics Should yield different results for the same flow

condi-tions.' An effective way to change the vibrational characteristics

of a model is.to vary the

mounting

_{configuration. Hydrofoil}

models in the water tunnel are normally cantilevered from the

test section wall 'opposite the waIl in which the transducer is

located. A plug was constructed to f it into the latter wall Such

this way the same model could be studied when cantilever mounted

or when fixed at both ends. Spectra for the two different

con-figurations are different in shape, Supporting the hypothesiS

that cavitation-induced foil vibration is a mechanism of noise

production.

The variouS sets of spectra discuSSed. above were chosen

be-cause they exhibited the characteristic of constant spectral

sig-nature In many other spectra we observe: peaks which Shift to a

higher frequency as velocity is increased for

constant

sigma. This

is the behavior we would expect for the mechanism of direct

radia-tion from the expansion an collapse of cavitation bubbles. The

spectra of Figure 8 are for a piano-convex hydrofoil with a four

inch chord at a. five degree angle of attack. Sigma is 1.74. and

the velocities shown are 20, 25, 30, 351 and 40 ft/sec. The

most prominent peak

in

these spectra occurs at 500 Hz for 20 ft/sec

and 1,000 Hz for 40 ft/sec. We can form a Strouhal number based

on the observed cavity length (L) of 6 nun, the free stream

velo-city. U, and the frequency

n of

the spectral peak. The resulting

values of nL/U for the four different velocities are 0.52, 0.53,

0.54, .0.48, and 0.52. These values are constant to within the

resolution of. the spectrum analyzer, and they are all very

close to 0.5. This indicates that the time required for a

cavita-tion bubble to traverse the length of the cavity is one half the

period of the fundamental noise frequency.

Similar data for a lower sigma value of 1.54 are shown in

Figure 9. In this case the cavity length is 10 mm and the

0.50, 0.47, 0.45, and 0.49. Thus the Strouhal number is again

about 0.5, in this case for a much larger cavity. Data for a

very small cavity, L = 3 xtn, are shown in Figue 10. Here the

primary peak in the spectrum occurs between 1 and 2 kHz.. The

Strouhal numbers are 0.50, 0.50, 0.53, 0.46, and 0.50. In these

spectra we also see two prominent peaks whose freqi.iencies do not

vary with Speed, at 5 kHz and. 31.5 kHz. The appearance of both

constant Strouhal number and cOnstant frequency peaks is seen

in much of the data. The former generally occur at lower

fre-quencies than the latter., The constant Strouhal number. peaks do

not exhibit strong harmonics, while the conStant frequency peaks

often. do. .

Noise measurements made for incipient blade surface

cavita-tion show some very different properties. Incipient cavitation

refer. to flow at a value of sigma such that cavitation is just

beginning, and the vapor cavity or bubbles may not be visible: at

all. The :incipient cavitation nimiber a1 refers to the value of

sigma at which cavitation begins as sigma is lowered. The

"desi-nent" cavitation number ad is the value at which cavitation ceases

as sigma .is increased. This. is generally slightly greater than.

the incipient value. Both a1 and ad are found to be weak functions

of velocity, increasing with the velocity in most. cases. Measured

values for a particular model configuration depend on the facility

in which the measurements are made, and the Caltech water tunnel

yields lower values of a than most other tunnels [11]. This is

described above. There is some ambiguity in the definition of

inq.pient cavitation number, since there is' no universally

ac-cepted criterIon for what defines the onset of cavitation.

As was Shown in Figure 4, incipient cavitation is first

detected acoustically, at very high frequencies.. High intensity

noise will be radiated at frequencies above the audible band

before there is any visual indication of cavitatIon. _{Figure 11}

shows spectra at four different speeds for a cavitation number of

305, which is slightly below the incipient value. These

àpec-tra'have two interesting characterist-ics: _{(1) at frequencIes}

above 1 kHz, the spectra are relatively flat, that is, the noise

is nearly "white." and. (2) at frequencies abov 6 kHz a change

in flow velocity has very little effect _{on the spectrum. The}

flatness of the high frequency part of the spectrum indicates

that mOdel vibrations are not important in this case. The lack

of dependence of spectrum level upon velocity is difficult to

understand. Even for simple source radiation, the total energy

radiated should vary as U4.

The explanation for this anomalous behavior of the spectrum

level may lie in the fact that all velocity dependence predictions

from Lighthill's equation are for the total sound intensity and

not for the spectrum level at a particular frequency. As stated

above., an assumption in these predictions is that the _frequencies

present in the flow scale with the flow velocity. _{The effect}

that. this scaling has upon a particular part of the spectrum

by Figure 12.

This figure. shows spectra for incipient

cavita-tion on a different. model, and has the same characteristic region

of velocity independence above 10 kHz.

However., at 100kHz the

spectra begin to diverge rapidly and have developed a 13 db spread

at the highest frequency of 160 kHz.

This behavior again points

out the errors that can be made in drawing concluSions from the

velocity dependence of the spectrum level at a particular frequency.

4.

Wake Cavitation

If the cavitation niznber is low enough in flow over the models'

described above, the cavity length will exceed the ôhord length and

the collapse of,the cavity will occur downstream of the trailing

edge.

.

The cavitation then changes from partial or.blade surface

cavitation to full cavitation.

.

In the case of certain

bluff-based shapes, the collapse of the cavity occurs downstream of the

trailing edge for all values of sigma.

We now consider the noise

radiated from a model of this type.

The model used for these stud-.

ies was a 7.5° wedge with a six inch span and six inch chord,

run

at zero angle. of 'attack with the sharp edge pointing upstream.

The base or trailing edge of. this wedge was 0.78 inches thick.

Vapor cavities formed with this model have a different

appear-ance from the blade surface cavities discissd above.

Here the

cavity has a more vagtie outline; its boundaries are not well

defined, as seen in Figure 13.

.

The reasoh for this appearance

can be seen in microf'lash photographs, such as Figure 14..

The

cavitation is of the travelling bubble type, and the bubbles

occupy a relatively low volume fraction of the cavity region.

A

dis-tribution suggests the shedding of von Karxnan vortices from the

base. Globular masSes of bubbles can be seen in the cores of

these vortices (Figure 14). The Reynolds ntirnber based upon the

thickness of the model is about 200,000.

Figure 15 shows a series of spectra measured with the wedge

for a sigma of 2.27. Several features. of these spectra. should be

pointed out. (1) The broad band noise level for this form of

cavitation is 5 'to 10 db higher than for a blade 'surface .cavity

of 'the same

dimensions

and at the same velocity. (2) Much higher

levels are seen in the 100. to 500 Hz band than for blade surface

cavitation. (3) The spectra are "whiter" at the higher frequencies

and there are no constant frequency peaks, indicating that model

vibration is not a factor. The average downward slope of the

spectrum is about 3 dbpr octave, which is a (frequency)

be-havior of spectrum level. (4) The prominent peak occurring

be-twèen 100 and 200 Hz has constant Strouhal number. The value of

nL/U based on the best estimate of the cavity length L is 0.5, th

same value found for blade surface cavitation.

Figure 16 shows results from the same model at a lower value

of sigma, 1.79. The appearance of tIe cavity is.much more dense

than in the higher sigma case, and photographs show .a higher

den-sity of bubbles distributed over the sameregion of space. The

visible length of the. cavity is about the same. As shown in

Figure 16, there is only a slight change in the radiated noise

spectrum. The broad band level is about

I

db higher for the

lower sigma, and there is a very slight shift of'energy toward

It is a

well known

fact that "ventilating" a base cavity by bleeding atmospheric air into it has some effect upon the

noise.. Figure 17 shows this effect quantitatively for the wedge

model at a sigma of 1.79. We see that the effect of vent-ilation

at ow frequencies, below 300 HZ, is not very significant. At

the high frequency end of the spectrum, noise reductions on the

order of 24 db result from ventilation. The downward slopE of

the spectrum rezfla-ins uniform with ventilation, but is increased

.frorn about 3 db per. octave, to 5 db per octave. The reduction .

in the broad band noise, level is from 4 to, 7 db, depending on

the Speed. .

5. -Trailing Vortex Cavitation

- Trailing vortex cavitation is observed to occur both on

hydro-foils and submerged screw propellers.. A trailing vortex wake is.

formed behind any three dimensional lifting surface, and the

dy-namics of these vortices have, been studied extensively, both in

theory. [12W) and experiment [13]. The Static pressure distribution

across a trailing vortex has a minimum at the center of the

vor-tex core, and this presSure minimum can be low enough to produce

cavitation.

Trailing vortex cavitation was produced in the Caltech water

tunnel in the following way. An MACA 4412 section hydrofoil with

a three. inch span and three inch chord was mounted on the test

section wall. The moel planform extended halfway across the six

inch width of the test eotion. This model developed sufficient

cay-ity at Static pressures high enough that no blade surface

cavita-tion occurred, as can be seen in Figure 18. Thus the.noise

pro-duced by the trailing vortex cavity could. be measured in a flOw

with no other significant noise sources.

The. characteristics Of the vortex cavities produced in this

study run completely counter to those of the other forms of

cavi-taton.

The most significant difference is the failure of

trail-ing vortex cavities to scale with sigma. In the previous cases,

the size, and appearance of the vapor öavity depended only on sigma,

and were nearly independent of velocity or time. For, trailing

vortex cavities the size and shape do not depend solely on sigma,

nor are they constant in time.

When the trailing vortex cavity is first formed, it is

cylin-drical in shape and about ¼ inch in dianieter. The cavity may

be-gin right at the tip.ofthemodel, or at'higher pressures it may

begin a foot or more downstream of the model. If the cavity

be-gins downstream of the model, its upstream end. will oscillate back and forth in 'the streantwis.ê. direction over a distance of

several inches. The' cavities have no visible downstream end,

ex-tending far into the diffuser section of the water tunnel. _The

surface of' a vortex cavity is glassy in appearance except at its

upstream end. _{If constant. flow conditions are maintained for}

sev-eral minuteS, t'e' cavity gradually thickens and. develops a twisted

ribbon shape.. The width of this ribbon is about 3/4 inch and its

thickness about ¼ inch. The twisting wavelength of the ribbon is on

'the order of a foot and is inverSely proportional to the angle of

These properties of the trailing vortex cavities suggest that

they are largely gaseous rather than vaporous. Instead of being

composed entirely of water vapor, these cavities are mostly gases

which have been taken out of solution. The measured dissolved air

content

of the water tunnel is about. 10 parts per million, and

varies very little.

Noise measurements of the trailing vortex cavities support

the conclusion that they are gaseous. Figure 19 shows spectra

for vortex cavitation at a sigma of 1.70 and an angle of attack

of seven degrees. The signal to noise ratio is greater than one

only .at frequencies above 600 Hz. The trailing vortex cavities

produce much less noise at all frequencies than the other forms.

of cavitation. The downward slope of the spectrum is greater for

vortex cavitation; in the example of figure 19 it is 7 db per

oc-tave. _{The low noise levels are further evidence of gaseous}

cavi-tation because gas bubbles do not undergo the violent collapse of

vaporous cavitation bubbles. If both blade durface and vortex

cavitation take place simultaneously in the water tunnel, the

vortex cavitation will contribute little to the noise spectrum.

The same will be true of vortex cavitation on full scale hydrofoils

and propellers if the cavities in those cases are also gaseous.

6. Suzmnary and Conclusions

Cavitation-produced flow noise is inherently more intense than

fully wetted boundary layer noise because the kinetic energy of the

flow is more.efficiently converted to acoustic energy. The ratio

The water tunnel is thus an effective means of studying this _type

of flow noiSe. The major limitation of _{a water 'tunnel study is}

that. the closed test sectiOn geometry makes it difficult to

mea-sure absolute acoustic levels. However, in these tests we have

been interested in relative changes in noise resulting from ôhanges

in flow parameters or model configuration.

in blade surface or partial cavitation two different mechanisms

of noise production were. Observed. One of these is direct radiation

from, the rapid expansion and collapse of _{vapor bubbles in the}

cav-ity. _{This is characterized by spectral peaks which occur at a}

constant Strouha]. number as velocity is varied with sigma held

constant. _{The Strouhal number based on cavity length of the low-.}

est of these peaks is consistently 0.5. _{The second noise}

genera-tion mechanism is vibragenera-tion of the hydrofoil model excited _{by the}

collapse of the vapor cavity. _{This type of noise is}

character-izedby spectral peaks occurring at constant frequency _{for all}

velocities. _{Changing the structural"properties of the hydrofoil}

model has a measurable effect on these spectral peaks.

Wake cavitation produces noise with _{a whiter spectral}

distri-bution than that of blade surface cavitation. _{The total intensity}

is higher for wake cavitation, and there is a high energy content

at very high frequencies. _{Node]. vibration does not appear to be}

a factor in this type of cavitation. _{The cavitation of trailing}

vortex wakes, as it occurs 'in the water tunnel, is _apparently

gaseous in nature. _{The violent collapse characteristic of vapor}

cavities does, not occur, and as a result _{the radiated noise levels}

noise is detectable only at frequencies above 5 _kHz.

In comparing the relative importance of various mechanisms of producing flow noise, it can be said that cavitation noise

will predominate over boundary layer _{radiated. noise under almost}

any conditions. _{Incipient cavitation produces high intensities}

at very high frequencies, so that in _{some frequency bands small}

cavities will radiate more noise than large _{ones. Under partial}

cavitation, foil vibrations are important and the structural

pro-perties of the hydrofoil will affect the _{radiated noise. Full}

cavitation produces high levels throughout the measured spectrum,

but these can be reduced a great deal by _{ventilation, particularly}

at high frequencies. Tip vortex caviation _{may not be an}

Curie, N., 1955 dynamic Sound," Phillips, O.M., Plane Turbulent p. 327'. REFERENCES

.1. Lighthili., N.J., 1952 "On _{ound Generated Aerodynamically,"}

Proc. Roy.Soc. London,A, 211, _{p. 564.}

"The Influence of Solid Boundaries upon,

Aero-PrOc. ROy. Soc. London A,231, p. 505.

1956 "On the Aerodynamic Surface Sound from a

Boundary Layer," Proc. Roy. Soc. London A, 234,

Meilen, R.H., 1954 "Ultrasonic Spectrum Of _{CavitationNoise}

in Water1" J. Acous. Soc. Am. 26. '

Ross, D. and' McCormick, B, 1948 "Propeller Blade-Surface Cavitation Noise," Penn. State College report NOrd 7958-115.

Song, S.C. and Silberman, E., 1961 "Experimental _{Studies of}

Cavitation, Noise in a Free-Jet Tuine1,":St. _{Anthony F411$}

Hydraulic Lab., U. of Minn., Tech, paper No. 33, series B.

Ripken, J.F.-and Killen, J.M., 1959 "A Study _{of: the' Influence}

of Gas Nuclei on Scale Effects and Acoustic Noise for mci-pient Cavitation in a Water Tunnel," St. Anthony Fails

Hydrau-ho Lab., U. of Minn., Tech, paper No. 27, series B.

'8'. _{Knapp, R.T. and Levy, J., 1948 "The Hydrodynamics Laboratàry}

of the California Institute of Technology," _{Trans. ASNE 70,}

p. 437. '

'

Knapp, R.T., 1945 "Cavitation NoiSe from Undeqater Projectiles,"

California Institute of Technology, report No. _{6.l-sr207-19]O'.}

Corcos,G.lvl., 1963 "Resolution of PreSsure in Turbulence," _J.

Acóus. Soc'.Axn. 35, p. 192.

il. _{Arakeri, V.H. and Acosta, A.J., 1974 "Cavitation Inception}

Observations on Two Bodies at Supercritical _{Reynolds Numbers,"}

Calif. Institute of Technology, Div. of Eng. report No. E183.2.

Moore, D.W. and Saffman, P .G., 1973 "Axial Flow in _Laminar

Trailing VorticeS," Proc. Roy. ,Soc. London A, _{p. 491.}

Baker, G.R., Barker, S.J., Bofah, K.K., _{andSaffman, P.G.,'1974}

"Laser Anemometer Measurements of Trailing _{Vortices inWater,"}

ACKNOWLEDGMENT

The author would like to acknowledge the

-24-List of Figures

1.. Transducer Geometry.

2. Clear Tunnel Noise Spectra:

0

20 ft/sec.;

0

25 ft/sec;

30 ft/sec;

_V

35 ft/sec; 40 ft/sec; 45 ft/sec;

50 ft/sec.

3 Hydrofoil blade Surface Cavitation.

NACA 66 Model

06.6;

4.9; . NACA 66 Model o 3.5;

A

2.2. NACA 66 Model o 25;L 30;

_V

NACA 66 Model

at 20 ft/sec. Sigma.

= 0

fully wetted;

V'4.2.

-at 20 ft/sec. _Sigma

.0

_{fully wetted;}

at Sigma =2.46. U = 020 ft/sec.;

3.5; 40.

at Sigma = 2.15. Velocity - same as Figure

_6.

Piano-Convex Model at Sigma = l.74. _{Velocity -same as}

Figure. 6.. .. . .

Piano-Convex Model

at

Sigma = 1 54. Velocity - same as

H _{Figure 6.}

NACA 66 Model at Sigma= 2.41. . Velocity - same as. Figure 6.

ii. _{InOipient Cavitation, sigma = 3.05..}

30;

V

3.5.

Incipient Cavitation, sigma 1.40.

V35; 40.

Hydrofoil Wake Cavitation.

Wake Cavitation - Micrôflash photograph.

Wake Cavitation Spectra,

Figure 6.

16. Wake Cavitation Spectra,

Figure. 6. .

Trailing Vortex Cavitation.

Trailing Vortex Cavitation Spectra,

0

30 ft/sec;

0

U

= 0

20 ft/sec;

0

25;

U = Q25 .ft/s,ec; 30;

Sigma .= 2.27.. Velocity - saite as

Sigma 1.79. _{Velocity = same as.}

Sigma = 1.70.

17. _{Effect of Ventilation, on Wake Cavitation Spectr}

U=20

U=25

Unventilated

0

Ventilated

/,/i/, / /////////////

Metal Wail

1/32" Diaphragm

Figure 1.

Transducer Geometry.

Plexiglass Wall

Flooded Cavity

1/4" Transducer

6"

U

FREQUENCY (KHZ)

Figure 2.

Clear Tunnel Noise

Spectra: El 20 ft/sec;

0

25 ft/sec;

A

30 ft/sec; S735 ft/sec; $40 ft/sec; 045 ft/sec;

so

ft/sec.

-S

FREQUENCY (KHZ)

Figure 4.

NACA 66 Model at 20 ft/sec.

Sigma

= 0

fully wetted; Q6.6; Lt4.9; c74.2. 10 100

FREQUENCY (KHZ)

Figure 5.

NACA 66 Model at20

ft/sec.

Sigma = Ufully wetted;

0

3.5;

40,-

20

zD

Figure

111111

I I

1111111

I I

1111111

FREQUENCY (KHZ) ,.10. 100

NACA 66 Model at Sigma

2.46..

U' = 1320 ft/sec;

.0 25

3,0; V 35;

.4.0. .

.20

-Cl)

-40 -

-60 I I

40 20 w

>0

w -J 20 _.60: L FREQUENCY (KHZ). Figure 7.

NACA 66 Model at Sigma =2.15.

Velocity - same as Figure 6.

I.. 'I .I. I. I F I I i i I 10. 100

FREQUENCY (KHZ)

Figure 8.

Piano-Convex Model at Sigma = i.74.

Veiàcity - same as

40 -

V

0

-40 -

-60'

1.1

I

11111

I I

1111111

I I I

111111

FREQUENCY (KHZ). Figure 9...

Piano-Convex Model at Sigma = 1.54.

Velocity - same as

40 -

.

20

0

10

2O

60 I I I

ii ii

I I I I i i

ii

I I I I i i

ii

1

10

100 FREQUENCY (KHZ) FigurelO.

NACA66 Model at Sigma = 2.41.

40 -

V

0

20

-)

0

0

J

C.)

UJi20 -

a- Cl) I

1.111111

I I

1111111

-40 - 60 I I

I

I

iii,

I 1 10 100 FREQUENCY (KHZ) Figure 11.

Incipient Cavitation, sigma = 3.05.

U = 1] 20 ft/sec;

0 25;

40 20 _{-40 -60} 1 10 100 FREQUENCY (KHZ)

Figure

12.

Incipient Cavitation, sigma = 1.40.

U

.Q 25 ft/sec; L 30;

Figiire' 14.

Wake Cavitation

40 20

-j

LU

>

LU -J

D

I- C-) LU C,) -20 -40 -60

11,1111

I I

.11.11111

1 I

1111111

10 100 FREQUENCY (KHZ) Figure 15.

Wake Cavitation Spectra, Sigma = 2.27.

Velocity - same as

10

FREQUENCY '(KHZ)

Figure

16.

Wake Cavitation Spectra., Sigma

1.79.

Velocity - same as

Figure 6.

:

-40 -60 I I

111111

I I I

111111

FREQUENCY (KHZ) Figure 17.

Effect of Ventilation on Wake Cavitation Spectra.

U=20

U=25

Unventilated [1

0

Ventilated I I i

ui1

100 1 10

Figure

18.

40 20 _{-40 -60}

FREQUENCY (KHZ)

Figure

19.

Trailing Vortex Cavitation Spectra, Sigma

= 1.70. 0 30 ft/sec;

0

40. 1 10 100