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OCR for page 331
The Dynamics and Acoustics of
Travelling Bubble Cavitation
S. Ceccio, C. Brennen (California Institute of Technology, USA)
ABSTRACT
Individual travelling cavitation bubbles gener-
ated on two axisymmetric headforms were detected
using a surface electrode probe. The growth and col-
lapse of the bubbles were studied photographically,
and these observations are related to the pressure fields
and viscous flow patterns associated with each head-
form. Measurements of the acoustic impulse generated
by the bubble collapse are analyzed and found to cor-
relate with the maximum volume of the bubble for
each headform. These results are compared to the ob-
served bubble dynamics and numerical solutions of the
Rayleigh- Plesset equation. Finally, the cavitation nu-
clei flux was measured and predicted cavitation event
rates and bubble maximum size distributions are com-
pared with the measurements of these quantities.
1. INTRODUCTION
Though the dynamics and acoustics of travelling
bubble cavitation have been extensively studied both
experimentally and theoretically, the behavior of nat-
urally occurring cavitation bubbles near surfaces has
not been examined in great detail. It has been known
for some time that cavitation bubbles generated near
surfaces are usually not spherical (as often assumed
in theory) but hemispherical caps (Knapp and Hollan-
der (1948) and Parkin (1952~), and a cavitation bubble
collapsing near a solid boundary may produce a micro-
jet of fluid which has been speculated to cause surface
cavitation damage (Benjamin and Ellis (1966), Plesset
and Chapman (1970), Lauterborn and Bolle (1975),
Kimoto (1987) and, for a review, Blake and Gibson
(1987~. The complex shapes that travelling bubbles
assume will clearly be influenced by macroscopic flow
phenomena such as pressure gradients, boundary lay-
ers, separation, and turbulence. Researchers have at-
tempted to study these effects by observing cavita-
tion bubbles induced in a venturi (Kling and Hammitt
(1972~) or above a surface (Chahine et. al. (1979), van
der Meulen (1989~. Yet detailed, systematic studies
of hydrodynamically-produced cavitation bubbles are
almost non-existent. The random nature of naturally
occurring cavitation is the primary reason why investi-
gators have focused on integral measurements in their
study of cavitating flows, leaving the detailed behavior
of individual cavitation bubbles unexamined.
Analyses of cavitation noise have generally been
based on the theoretical behavior of single, spherical
bubbles following the work of Fitzpatrick and Stras-
berg (1956~. From this data base, researchers have
synthesized the acoustic emission from cavitating flows
331
with multiple events (Blake (1986~. Many experi-
ments have attempted to extract the actual behavior
of individual bubbles from the integral measurement
of the noise produced by cavitation (Mellon (1956),
Blake, Wolpert, and Geib (1977), Hamilton (1981),
Hamilton, Thompson, and Billet (1982), and Marboe,
Billet, and Thompson (1986~. Although trends are
seen in the measured spectra which may be related to
theoretical predictions, the difficulty of obtaining free
field acoustic spectra in the confines of most water
tunnels has always made interpretation of experimen-
tal spectra problematic.
Researchers have also attempted to treat cav-
itation as a stochastic process.
The spectral emis-
sion of a cavitating flow will depend not only on the
noise produced by single bubbles but also on the cav-
itatior~ rate and event statistics (Morozov (1969) and
Baiter (1986~. Furthermore, cavitation noise scaling
like that suggested by Blake, Wolpert, and Geib (1977)
will be significantly influenced by changes in the cavi-
tation event rate. As the number of cavitation events
increase, bubble interactions will affect individual bub-
ble volume histories and their acoustic emission (e.g.
Morch (1982), Arakeri and Shanmuganathan (1985),
and d'Agostino, Brennen, and Acosta (1988~. Analy-
ses of multiple bubble effects depend upon a knowledge
of the nuclei distribution in the flow and the dynamics
causing the nuclei to cavitate.
Yet, the effect of nuclei number distribution on
the total cavitation process is poorly understood, and
this is due largely to the difficulty of accurately mea-
suring this quantity. In fact, most cavitation studies
neglect to include any measure of the nuclei number
distribution. As we shall demonstrate, the number
and size distribution of cavitation bubbles, and the
resulting noise emission, can vary substantially over
the course of an experiment, even at a nominally fixed
operating point. Although the mean cavitation event
rate may be approximately determined by the acous-
tic pulse rate (Marboe, Billet, and Thompson (1986~),
cavitation bubble size distributions have only been de-
termined in very rough form (Baiter (1974) and Meyer,
Billet, and Holl (1989~. Although knowledge of the
cavitation rate and bubble size distribution is essen-
tial, no simple method has been found to count and
measure cavitation bubbles.
The above observations indicate a need to study
the dynamics and acoustic emission of individual cavi-
tation bubbles. A method of detecting and measuring
cavitation bubbles was needed, and this paper presents
OCR for page 332
data obtained through the use of a new electrical probe
developed for this purpose. Using this new instrument
experiments were performed to study individual cavi-
tation events and their statistics in an attempt to ad-
dress the above issues.
2. NOMENCLATURE
A (RO) streamtube capture area for given nuclei
Cp pressure coefficient, (P-Po) / ( ~ pU2)
CPM minimum pressure coefficient
on body surface
f frequency
I measured acoustic impulse
I* dimensionless acoustic impulse
N (RO) free stream nuclei distribution
PrO (RAT) max. bubble volume distribution
associated with nuclei of size RO
Pr (RM) maximum bubble volume distribution
PA acoustic pressure
PO freestream pressure
Pv water vapor pressure
r acoustic path length
R (t) calculated bubble radius
Rc critical nuclei radius
RB headform radius at CPM
RH headform radius
RL bubble radius along trajectory
RM cavitation bubble maximum radius
RMR cavitation bubble maximum reduced radius
RO nuclei radius
Re Reynolds number, UD/u
S water surface tension
SP acoustic pressure spectral coefficients
t time
integration limits for experimental impulse
acoustic pulse duration
calculated dimensionless pulse duration
free stream velocity
calculated bubble volume
Weber number, pU2RH/S
constant, pulse width relationship
constant, nuclei stability relationship
headform radius of curvature at CPM
water viscosity
water density
cavitation number, (P-Pv) / (2pU2)
bubble cavitation inception index
attached cavity formation index
cavitation event rate
to ~ t2
T
T*
U
V (t)
We
ct
IJ
p
ai
~ac
3. EXPERIMENTAL SETUP
The experiments were conducted in the Caltech
Low Turbulence Water Tunnel (LTWT),a full descrip-
tion of the facility is presented by Gates (1977~. For
all experiments, the test section free stream velocity
was set and the tunnel static pressure lowered until
the desired cavitation number was reached. The oper-
ating air content was generally between 6 - 8ppm, and
the tunnel water was well filtered. The free stream
nuclei number distribution of the upstream fluid was
measured using in-line pulsed holography. A detailed
description of the holographic system is presented by
Katz (1981~.
Two axisymmetric headforms were used in the
present experiments. The first was a Schiebe head-
form with an ultimate diameter of 5.08cm. (Gates
et al (1979~; the second, which has a modified ellip-
soida1 shape with a diameter of 5.59cm, is known as the
tJ
'_ 0.2
z
~O
O -o .2
~ - O . 4
-
u' -0.6
c
-0.8 _
r-~)
I.T.T.C. BODY 1 2.0
X/R
1 o.8
0.4
I ' I 10
0.6 o.a
o.`n ; , j , , , , , 1 2.2
SCHIEBE BODY I
~ 2.c
0.2 ~
1
0 1
C -o
- 0.
0 . 6
-0.8
1 ~
40.8
~' C P~n ' - 0 ?S
0 0.2 o.. 0.6 0.8
%/R
Figure 1. Surface pressure distributions and profiles
of the I.T.T.C body alla the Schiebe body.
I.T.T.C. headform (Lindgren and Johnsson (1966)).
Surface pressure distributions for the Schiebe body
(Gates et al (1979)) and the I.T.T.C. headform (Hoyt
(1966)) are availa61e in the literature. The headform
contours and surface pressure distributions are pre-
sented in Figure 1.
The headforms were fabricated out of lucite, a
material whose acoustic impedance is a fair match to
that of water. The hollow interior of both bodies was
filled with water in which a hydrophore was placed.
The hydrophore, an ITC-1049, has a relatively flat
response out to 80kHz. Except for ultralow frequen-
cies (<< lHz), the hydrophore signal was not filtered.
All acoustic signals were digitized at a sampling rate
of lMHz. Because of the relatively good acoustic
impedance match between lucite and water, the in-
terior hydrophore allows the noise generated by the
cavitation bubbles to reach the hydrophore relatively
undistorted; reflected acoustic signals from other parts
of the water tunnel only make their appearance after
the important initial signal has been recorded.
In addition to the hydrophore, each headform
was provided with novel equipment developed from
instrumentation which had previously been used to
measure volume fractions in multiphase flows (Bernier
(1981~. This instrumentation consisted of a series
of electrodes arrayed on the headform surface which
were used to detect and measure individual cavitation
bubbles. A pattern of alternating electric potentials is
applied to the electrodes and the electric current from
each is monitored. When a bubble passes over one of
the electrodes the impedance of the local conducting
medium is altered, causing a change in the current
from the electrode. This change, which is detected
and recorded, permits the position and volume of the
bubble to be monitored.
332
OCR for page 333
One specific electrode geometry consisted of
patches arrayed in the flow direction to cover the ma-
jor extent of the cavitating region. Another consisted
of electrodes which encircled the entire circumference
of the headform in the region of maximum bubble
growth. These two electrode geometries were used for
different purposes. Signals from the patch electrodes
indicated cavitation at a specific location on the head-
form, and, by electronically triggering flash photog-
raphy, simultaneous plan and profile photographs of
individual bubbles could be taken at a prescribed mo-
ment in the bubble history. Thus, a whole series of
bubbles could be inspected at the same point in their
trajectory. Furthermore, by simultaneously recording
the acoustic signal from the hydrophore, one could
correlate the noise with the geometry of the bubbles.
The circular geometry was used to detect the oc-
currence of every cavitation bubble at a particular lo-
cation on the headform. This position was chosen to be
near the location of maximum bubble volume, and for
relatively moderate event rates only one bubble would
occur over the electrode at any given time. Because
almost all the cavitation bubbles maintain the same
distance above the electrodes (this will be discussed
below), the output of the circular electrode system is
directly proportional to the area covered by the bub-
ble, and the peal; of the signal is proportional to the
major diameter of the bubble base. This system was
calibrated photographically and found to be quite lin-
ear. The volume of the bubbles was then determined
from a measure of the base diameter using a functional
relationship derived through the photographic study of
many individual bubbles (Ceccio (1990~. Two kinds
of experiments were performed with the circular elec-
trode system. The first involved the measurement of
event statistics and bubble maximum size distribu-
tions. In the second, the acoustic emission of indi-
vidual cavitation bubbles was analyzed and the result
correlated with the bubble maximum volume.
4. OBSERVATIONS OF SINGLE CAVITA-
TION BUBBLES
PROFILE VIEW
. v ~ ~
~ "PYRAMID
/ SHAPE
' ~ " WE DGE "
- ~ ~ SHAPE
~ HEADFORM SURFACE
PLAN VIEW
- 5 mrn
r sussLE
/ FISSION
~ 000
- ROUGH ~ SURFACE
" BUBBLE WAVE
DIRECTION
OF FLOW
Figure 2. Schematic diagram of typical bubble evo-
lution on the Schiebe headform.
Cavitation bubbles were observed on both the
Schiebe and I.T.T.C. headforms over a range of cav-
itation numbers. The cavitation number was var-
ied between the traveling bubble cavitation inception
value, hi, and the value at which attached cavitation
occurred, Sac. The inception index on both bodies
was strongly dependent on the ambient nuclei num-
ber distribution (Ooi (1981~. Inception occurred on
the Schiebe body at cavitation numbers as high as
Hi = 0.65, and on the I.T.T.C. body at Hi = 0.58
for tunnel water of 6 - 7ppm air content. However on
both bodies the inception index was reduced to about
Hi = 0.50 immediately after deaeration. Any definition
of the bubble cavitation inception index must there-
fore be associated with a particular free stream nuclei
number distribution. The attached cavitation forma-
tion index for the Schiebe body was aaC = 0.40 and for
the I.T.T.C. body arc = 0.41. These values were al-
most constant over the fairly narrow range of Reynolds
numbers of the experiments (Re = 4.4 x 105 - 4.S x 105 ).
Before detailing the results from each headform
one observation can be made for both geometries. For
a given tunnel velocity and cavitation number, the
maximum bubble volumes were quite uniform. Al-
though the incoming nuclei diameter ranged over al-
most three orders of magnitude, the maximum cav-
itation bubble volume varied over only one order of
magnitude. The reason for this is given below.
For both headforms, the growth phase of the nu-
clei was very similar to that described in the original
observations of Knapp and Hollander (1948) and El-
lis (1952~. For most of their evolution, the bubbles
take on a hemispherical or "cap" shape and move ex-
tremely close to the headform surface; only very oc-
casionally would quasi-spherical bubbles be observed
at a distance above the surface. Small waves could be
observed on the bubble surface in many instances. As
the bubbles reach their maximum volume they become
somewhat elongated in the direction normal to their
motion while their thickness normal to the surface re-
mains relatively constant. At this point, the difference
in the flows around the two bodies begins to cause
differences in the bubble dynamics.
The Schiebe body was designed to suppress lam-
inar separation in the region of cavitation (Schiebe
(1972~. It possesses a sharp pressure drop with a min-
imum pressure coefficient of-0.75 (Figure 1~. Figure
2 represents a schematic of the typical bubble evolu-
tion, and Figure 3 consists of a series of photographs of
bubbles at various stages during this process. After the
bubble has reached its maximum volume, it begins to
lose its cap-like shape and becomes elongated progress-
ing into a pyramid-lilte shape; the bubble thickness
normal to the headform surface consistently decreases
after reaching its maximum. The bubble then collapses
rapidly and develops an elongated shape. The elonga-
tion of the bubble and the formation of tubes is proba-
bly due to rotation of the bubbles caused by the shear
in the boundary layer. As the bubble collapses it may
fission into two or three tubes of collapsing vapor, and
the residual gas in these tubes may cause a rebound
to produce a rough bubble or group of bubbles after
collapse.
The I.T.T.C. headform has a relatively smooth
pressure drop with a minimum pressure coefficient of
-0.62. A distinguishing feature of this headform is
that, unlike the Schiebe body, it possess a laminar
333
OCR for page 334
-A
- ~ -
L
.
.
_ 11~ 1 11' ~
_ 1h 1 ~ ~
Twirl
:::
warty
_~_~ ~ ~
- _
~ __ ~ ~ ~ ~ ~ ~ ~
~ . l ~ __ ~ ~ ~ ~ ~ ~ ~ ~
~ Id_
~ ~ ~:~ ~. :~ ~ ~ ~ ~ ~ ~ ~
,, ~
. ~
~ _
1
fir
:_ ~
_:
_,
.
- . ~ i....
- ' r .
...~...
a.
.
:
it_
it_
. ~ . . ...
Profile View
_]
Plan View
Figure 3. Series of photographs cletailing typical bubble evolution on the Schiebe
hea(lform, U 9m/s and ~ 0.45.
334
OCR for page 335
PROFILE VIEW
"SNOUT"
\ SHAPE ~ "WEDGE"
~ \ SHAPE
~ ~ =-~ ~ _
14FAnFORM RII~FAr~
DIRECTION
OF FLOW
~-
PLaN VIEW
r ROUGH
\ UNDERSIDE ~ SURFACE
\ \ WAVES
(D o
ROUGH 'TRAILING
BUBBLE STREAM E R
- 5 non
~ 1
Figure 4. Schematic diagram of typical bubble evo-
lution on the I.T.T.C. headform.
separation region (Figure 1~. Figure 4 is a schematic
of the typical bubble evolution, and Figure 5 presents
a series of photographs of bubbles at various stages
of this development. The bubble has a cap-like shape
until it reaches its maximum volume where it then
becomes further elongated evolving into the wedge-
lil;e shape. However, unlike the bubbles on the Schiebe
body, the cavity starts to lift off the surface and begins
to roll up into a snout-like shape. This may be due to
recirculating flow associated with the separation region
or the stretching of the bubble in the velocity gradient.
As it collapses, the "snout" continues to role up into
a vapor tube eventually collapsing to produce a rough
bubble after collapse.
On both the Schiebe and I.T.T.C. headforms
the rough bubble or group of bubbles which is formed
after collapse is sheared by the surface flow and usually
disperses into smaller bubbles on the order of 50pm,
although a second collapse and rebound is not uncom-
mon. The mean lifetime of a bubble depends upon the
tunnel velocity, cavitation number, and initial nuclei
size, but, for most of the observed bubbles on both
headforms, it is approximately 3ms.
The laminar separation on the I.T.T.C. body
has been carefully studied in the context of its effect
on attached cavitation (Arakeri and Acosta (1973~.
Clearly, the separated flow also influences bubble cav-
itation for cavitation bubbles were observed riding over
the separation "bubble". As seen in Figures 4 and 5
the underside of the bubbles become roughened as they
pass over the region of turbulent reattachment. These
local flow disturbance seem to shear vapor off the un-
derside of the bubble, leaving a trail of much smaller
bubbles. This phenomenon was not observed on the
Schiebe body.
Furthermore, some bubbles were seen to cause
local attached cavitation. When the operating cavita-
tion number was close to the attached cavity formation
index, trailing "streamers" were often observed down
stream of the cavitation bubble (Figure 6~. These
streamers were generally associated with the larger
bubbles on the I.T.T.C. body (and occasionally on the
Schiebe body) and were seen to develop gradually at
the location of the laminar separation point (Arakeri
and Acosta (1973~. As the bubble is swept down-
stream, the streamers continue to grow, and in may
cases persist even after the bubble has collapsed. Why
these bubbles cause the attached cavitation streamers
at the lateral extremities of the bubble is unclear. This
phenomena has also been observed with travelling bub-
ble cavitation on hydrofoils (van der Meulen (1980)
and Rood (1989~. The process could be considered
an inception mechanism for attached cavities.
The classic observations of Knapp and Hollan-
der (1949) may be compared those of this study. Both
experiments revealed that bubbles travelling near sur-
faces are cap shaped' and the gross characteristics of
growth and collapse are similar. However, the pres-
sure distribution on the ogive of Knapp and Hollander
generated a long and steady growth, and the bubbles
often retained a quasi-spherical shape even near the
final stages of collapse. These bubbles would often re-
bound many times maintaining their quasi- spherical
shape after each collapse. The bubbles observed in
this study usually rebounded only once and lost most
of their coherent shape after the first collapse. This
difference may be explained by noting that the water
tunnel facility used by Knapp and Hollander was not
equipped with any deaeration system, and extremely
bubbly flows were used to increase the odds of pho-
tographing a cavitation event. Consequently, the cav-
itating nuclei observed by Knapp and Hollander were
large, containing more undissolved gas. Increasing the
amount of residual gas reduces the violence of the bub-
ble collapse making coherent rebounds possible. On
the other hand, the nuclei populations of the present
study were quite small, and the cavitation bubbles ob-
served were almost entirely vaporous. Such bubbles
collapse violently and therefore coherent rebounds are
less likely.
Photographs of bubbles presented by Ellis (1952)
show many of the features in the present study. Prin-
cipally, bubbles formed close to the headform also pro-
gressed from a cap shape to a wedge shape before col-
lapse, although the collapse mechanism is difficult to
distinguish in Ellis' silhouette images. He observed
that the bubble surface profile approximately coin-
cided with lines of constant pressure for bubbles near
the point of maximum volume. This accounts for the
wedge shape of the bubble. Examination of the iso-
baric lines computed for flow around the Schiebe body
(Schiebe (1972~) also show the bubbles observed in this
study are being shaped by the pressure gradients close
to the surface.
Returning to the present study, the collapse
mechanisms for bubbles on both headforms were dis-
cerned through the study of many photographs. A
composite mechanism is presented in Figure 7 for the
Schiebe body with sample photographs in Figure 8.
For the I.T.T.C. body similar results are included in
Figures 9 and 10. Previous researchers have noted the
generation of a liquid microjet in bubbles collapsing
near a solid surface (Lauterborn and Bolle (1975) and
Kimoto (1987), for example), and this microjet is of-
ten identified as the main cause of cavitation erosion
damage. Although many photographs were taken dur-
ing the present investigation, a reentrant microjet was
335
OCR for page 336
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· i ~ - ~ ~ ~ ~ ~ ~
1 ~ 1 ~ ~ _
. ~ 1 ~ ~ ~111 __ _
:~ -. ~ ~ l
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ - ~ ~ ~ ~ ~ ~ ~
:::~
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:~ ~ ~ ~ ~ ~
- ~ ~ ~ ~ ~ -
:~:~::~::~:~::~:::~:~:~:~::::~:~::~:~ ~
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-
.*^ *r*. - .'~:~.# 5 # # 2i.' ~ g# :~
~:~
~ ~ ~ ~'~'~'~'~'~'~'~ I, ~ I., A.
_ ~.~' :.: ~.~.~.~.~.~'~'.""" ~22~2.2~.~'~.~.~'~_
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-
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ill_
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_ 2##x.~.:c.#.:.: ~:*~# ~.~.~.~.~. ~.~.~.~.~.~.~_ _ ~ ~
~ ~ ~ ~ ~ ~_~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
my' _
_ -_
_, _ ~
~ ~..~::.#.*:~:#~ _ ~
Profile View
Plan View
Figure 5. Series of photographs detailing typical bubble evolution on the I.T.T.C
1l( n.(lforln, ll-8.71n/.Y nlld a ~ 15.
336
OCR for page 337
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~ ~ ~ .~-
1~.~.~ If.: ~ ~ ~ ~!
~l)~l~i Hi
:=~ ~ ~"
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Flgure8. Ser~sofpbotogr~bsdetadingbubbles~hbt~UstbeLl.T.C.beud~rm,
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an,
OCR for page 338
not observed in any of the present photographs of bub-
ble collapse, although the jet may have occurred too
rapidly to be detected. The observed bubbles lack the
compact geometry we might expect to be associated
with coherent microjet formation.
5. MEASUREMENT OF THE ACOUSTIC
EMISSION OF SINGLE CAVITATION BUB-
BLES
The detailed relationship between the collapse
mechanism of hydrodynamic cavitation bubbles and
the resulting noise generation is not completely clear
but some features are suggested by the present work.
First, as other investigators have concluded (for ex-
ample Harrison (1952) and Chahine, Courbiere, and
Garnaud (1979~), the majority of the noise is gener-
ated by the violence of the first collapse; the growth
phase contributed no measurable noise signal. The
rebound produces a rough bubble which may also col-
lapse to produce a second noise pulse of lesser mag-
nitude. However, noise was not necessarily generated
by every bubble collapse. Smaller bubbles would often
collapse without an acoustic pulse, and larger bubbles
would sometimes produced a muted collapse.
Figure 11 presents two examples of the initial
noise pulse generated by the collapse of a bubble on
the I.T.T.C. headform. The first pulse has only one
peak, but the second trace is an example of a multiple
peal; event. Multiple peaks suggest bubble fission
prior to collapse, and the photographs presented in
the previous section reveal that many bubbles have
undergone fission.
Although some researchers have used the peak
acoustic pressure to characterized cavitation noise in-
tensity (e.g. Van der Meulen (1989~), in this study the
magnitude of acoustic pulses will be characterized by
the acoustic impulse defined as
It2
I= PAdt (1)
Jt1
PROFILE VIEW
OR \ r Bt~ BUBB' F COLLAPSES
REBOUND \ \ REBOUNDS NEAR SURFACE
~ ~ -~( _
~ HEADFORM SURFACE
Pl;AN VIEW
_ 5 mm
BUBBLE FISSION
~ O
ROUGH BUBBLE
MAY REBOUND
DIRECTION
OF FLOW
Figure 7. Schematic diagram of typical bubble col-
lapse mechanism on the Schiebe headform.
PROFILE VIEW
AFTER -, BEFORE BUBBLE LIDS
REBOUND/ r REBOUND ~ OFF SURFACE
~ ~ ~ ~-W~ ~
~ HEADFORM SURFACE
Plan VIEW
DIRECTION
OF FLOW
/ _
~_
C: ~ Al ~ ~
_ VAPOR DISSIPATES
ROUGH BUBBLE ~ SHEARED
MAY REBOUND VAPOR
Figure 9. Schematic diagram of typical bubble col-
lapse mechanism on the I.T.T.C. headform.
The times to and t2 were chosen to exclude the
shallow pressure rise before collapse and the reverbera-
tion produced after the collapse. Experimentally mea-
sured impulses for the Schiebe body at a tunnel veloc-
ity of U = 9m/s and cavitation numbers of a = 0.55
and a = 0.42 are presented in Figure 12 and 13. The
data all appear to lie below an envelope which passes
through the origin. The existence of this well-defined
impulse envelope suggests that a collapsing bubble can
generate, for a certain maximum volume, a specific
impulse if it collapses in some particular but unknown
u)
15-
10
5F
O .
-5 _
-10 _ _
TIME (AS )
1 5
10 _
5 _
O
- 5 _
- 1 0 _
o
TIME (AS)
500
Figure 11. Two examples of typical cavitation ini-
tial noise pulses. The bubbles were generated on the
I,T.T.C. headform at a = 0.45 and U = 8.7m/s.
338
OCR for page 339
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::: :::
~ -
~.~1
Figure 8. Series of photographs detailing typical bubble collapse mechanism on
the Schiebe headform, U-9m/s and <:r 0.45.
339
OCR for page 340
~ ~ - ~ ~ ~
` l - ~ ~ ~ ~ ~:~; ~::
~1 ~`~ ~ 1 ~ ~_
- ~A:: - ~ -: ~-
:: :~ - ~:: --~- ~-
~ - ~ - - ~ - - ~ - ~-
~: ~ : : ~I: ::::: ::
: :: i::: ::::: :~ ~ :::::::: : :~T~ i: :~ ~
_I
:
- ~
- - .~
- it
~ - ~
- ~
~ ~ - Am
- ~ ::~: ~ ~
#a
;::
-
3~
_ ~....11.1
: ~- ~ :
- ~ -
- -
~ma -
a~a, ~ma=
~- -
- -
Figure 10. Series of photographs detailing typical bubble collapse mechanism on
the I.T.T.C. heaciform, U 8.7m/s and a 0.45.
340
OCR for page 341
0.20 L
In
0.10
0.00
0.1
l l l 0.20
SO BODY Number of
U -9 - k Peaks
a - Q42 + O ~
x 2 ~.
· O>2
x x x
~Y X ~X ~
./ b °
, A.
6!. . x x
At.' ·
As
11! . .. .: . .: .
~I ·;l i- I I 0.00
0 40.00 80.00 120.00 160.00 0
MAGNUM VOLUME. 3
Figure 12. Acoustic impulse plotted against the
maximum bubble volume for the Schiebe body at
U = 9m/s and a = 0.42.
way. It can, however, produce less than this maximum
impulse if it collapses in other ways.
The different symbols represent the different
number of acoustic peaks which are generated upon
collapse. As shown in Figure 12, the probability that
a collapse will produce multiple peaks increases for
larger bubbles. Yet, even as the number of peaks in-
creases, the impulse often reaches its maximum possi-
ble value implying that, in some collapse mechanisms,
fission does not decrease the total stored energy avail-
able to produce noise. Other large bubbles collapse to
produce almost no acoustic impulse. The production
of noise upon collapse is the result of violent changes
in bubble volume near the point of minimum bubble
volume, but- larger bubbles may be sheared apart and
dissipate thus losing their organized shape and pre-
venting a coherent and concentrated collapse. Fur-
thermore, larger bubbles may contain more contam-
inant gas (as a result of dissolution) and this would
cushion the collapse and reduce the acoustic emission.
At higher cavitation numbers such as that of Fig-
ure 13 the number of larger bubbles is reduced, and
most bubbles collapse to produce only one acoustic
pulse. However a large number of very small bub-
bles will collapse and produce no significant impulse,
and these cases are represented by the "0" symbols.
Mute events are generally not examples of "pseudo-
cavitation" as observed by Dreyer (1987) but distinct
cavitation events with a near-silent collapse mecha-
nism.
The general trends in the data for the Schiebe
body are also evident in the results from the I.T.T.C.
headform. Significantly, however, the average acous-
tic impulse is about three times larger than that of
the Schiebe body. This will be discussed further be-
low. Furthermore, as the cavitation number is low-
ered to near the attached cavitation inception index
of the I.T.T.C. body, the impulse data changes sig-
nificantly. Figure 14 presents an example of data
from the I.T.T.C. body taken at a tunnel velocity of
U = 8.7m/s and a cavitation number of a = 0.42
at near the attached cavitation formation index. The
impulses generated by smaller bubbles are much more
uncertain, and, for many larger bubbles, no significant
impulse is generated. Since these larger bubbles gen
scHIEs 0 Number of
E B DY Peaks
u -9m/s
a ~ 0.55 + I
x 2
0 >2
x . .. x xx
~,.~.
t...
0 40.00 80.00
MAXIMUM VOLUME, mm3
Figure 13. Acoustic impulse plotted against the
maximum bubble volume for the Schiebe body at
U = 9m/s and a = 0.55.
erally have trailing streamers, it would seem that the
streamers interfere with the collapse in a way which
decreases or eliminates the noise.
The average number of peaks for a given average
diameter is plotted in Figure 15 for both headforms.
For smaller bubbles, the average is less than unity, re-
flecting the influence of muted bubbles, and for larger
bubbles, multiple peaking produces an average above
unity. For the case of the I.T.T.C. body, however, the
muting effect of the trailing streamers causes a reduc-
tion in the average number of peaks for the data set
with the largest average volume. This data set occurs
at the lowest cavitation number, near the attached cav-
itation inception point.
6. COMPARISON WITH ANALYTICAL RE-
SULTS
In order to place the above experimental results
in some analytical perspective, calculations were made
of the bubble sizes and acoustic impulses predicted by
integration of the Rayleigh-Plesset equation starting
`,0.40- l
LT.T.C BODY
U-U-h
o-~
~ x
0.20 ~O . x
A .lK .
0~00
N~ of
Cot
O
. ~
X 2
O >2
A O
o o
· ...... ............... I
.. 0 40.00 80.00 1 20.00 1 60.00
hWOM~ VOWb~. ~,
Figure 14. Acoustic impulse plotted against the
maximum bubble volume for the I.T.T.C. body at
U = 8.7m/s and ~ = 0.42.
341
OCR for page 342
with various sizes of freestrea~n nuclei. The known
surface pressure distributions for both headforms were
employed to construct the pressure-time history which
a nucleus would experience while passing near the
headform. No slip between the bubble and the liquid
and a small offset from the stagnation streamline are
assumed. Calculations were performed with various
free stream velocities, cavitation numbers, and offsets
from the stagnation streamline. Figure 16 provides
an example of the dependence of the maximum bub-
ble radius on the original nucleus size for the I.T.T.C.
headform and various cavitation numbers. Note that
nuclei below a certain size (which depends on the cavi-
tation number) hardly grow at all and would therefore
not contribute visible cavitation bubbles. This critical
size is predicted by the stability analysis of Johnsson
and Hsieh (1966) and Flynn (1964~. Bubbles below the
critical size grow quasistatically, whereas larger bub-
bles grow explosively. A bubble is critically unstable
if
RL, > 8 5 1
RH 3 pRHU2 ~-a-CPM)
where CPA.! is the minimum pressure coefficient
(-0.62 for the I.T.T.C. headform) and Ret is the local
bubble size. The computations show that so long as
the bubble remains stable, then Rat; is somewhere in the
range RO < RI, < 2Ro for the common circumstances
of interest here. Consequently, the critical nucleus size
Rc is given by
RC > 8 /3S ~ (~3)
where ~ is a constant. The results of this simple
expression are presented in Figure 17 along with data
on the critical nucleus size obtained from the Rayleigh-
Plesset solutions. The qualitative agreement is excel-
lent and suggests a value of ,B slightly greater that 0.5.
Note that the higher the velocity, U. the smaller the
critical size, and therefore the larger the number of
nuclei that will be involved in cavitation.
u'
o
111
I' ~
Iii
to ·.
^~°
1 - O ~ ~
0
c,
.
·
.
.
.
0 · I1lC
o ° Schiebe
0 . · . , . I . ,
0 10 20 30 40 50
AVE. MAX. BUBBLE VOLUME (mm3)
Figure 15. Average number of peaks as a function
of average maximum bubble volume for bubbles gen-
erated on the Schiebe body and the I.T.T.C. body.
~ ~ 0
o
IL
LO 1 0;
u,
10
_~ ''
· :1 n
\ 04 ~:
~ ~ ~ ~ ~ R.,. = Ro
1 0 , ~
I'
1 ~
I 0~ 2 1 0-1
NUCLEI RADIUS/ HEADFORM RADIUS, Ro/RH
Figure 16. Numerical calculation of the bubble max-
imum radius as a function of nucleus radius for nuclei
passing near the I.T.T.C. headform.
The other feature of Figure 16 which is impor-
tant to note is that virtually all nuclei greater than the
critical nucleus size grow to approximately the same
maximum size. The asymptotic growth rate of an un-
stable cavitating bubble is a function only of the pres-
sure and not the initial nucleus size. Consequently
the maximum size achieved will be approximately in-
dependent of the nucleus size. This accounts for the
uniformity of cavitation bubbles observed experimen-
tally. Similar calculations were performed for nuclei
experiencing the Schiebe body pressure distribution,
and the results were qualitatively similar to those of
the I.T.T.C. body.
The above calculations yield the volume-time
history for a cavitating bubble, and the acoustic pres-
sure generated by the bubble may be approximately
given by
PAtr,t) = 4P dt2 (4~)
u,
-
c~
o
is
I
i_ _
C)
fir
_
2 0.0004 ~
S/PLRHU { 0.000036 ~
0 0.1
CAVITATION NUMBER, 0-
Figure 17. Crital nuclei radius as a function of flow
parameters for nuclei passing near the I T.T.C. head-
form.
342
OCR for page 343
0.4
0.3
-
J
0.2
In
U)
At
lo
In a..
-
S/pRHU2- 0.0004. 0.000036 /
a= 0.5 /
0.~
I.T.T.C. ~,/
^~' SCEIIE~E ~
~ MY
0 0.04 0.05 0.06
~UIUUIU BUBBLE VOLUIVIE / RH3
Figure 18. Numerical calculation of the acoustic
impulse as a function of the maximum bubble volume
for bubbles generated on the Schiebe body and the
I.T.T.C. body.
were V (t) is the bubble volume, p is the fluid
density, and r is the distance from the center of the
bubble. This relationship is valid in the acoustic far-
field and for subsonic wall velocities. The acoustic
impulses, I, were calculated from the definition (1)
where to and t2 were taken to be the times when
d2V/dt2 = 0 before and after the first collapse.
For those nuclei which become unstable and ex-
plosively cavitate the non-dimensional impulse, I*, is
defined as
I*= R U (5)
where we have assumed r = RH since this is
the location of the hydrophore in the experiments.
The impulse I* is plotted in Figure 18 against the
maximum volume of the bubbles non-dimensionalized
by RH. A number of investigators (i.e. Fitzpatrick
and Strasberg (1956) and Hamilton et.al. (1982~) have
suggested that the magnitude of the acoustic signal
should be related to the maximum size of the bubble,
and this is born out in Figure 18 where the data for a
range of cavitation numbers and two Weber numbers,
We, are contained within a fairly narrow envelope.
The median line was converted to dimensional
values and is plotted in Figure 19 where it is com-
pared with data sets from the Schiebe and I.T.T.C.
experiments. It is strilting to note that the envelope of
the maximum impulse from the experiments is within
a factor of two of the Rayleigh- Plesset calculation for
the I.T.T.C. body and within a factor of six for the
Schiebe body. This suggests that, despite the depar-
ture from the spherical shape during collapse, the in-
compressible Rayleigh-Plesset solutions correctly pre-
dict the order of magnitude of the noise impulse gen-
erated by individual bubbles.
It is not surprising that the predicted impulse
is greater than the experimental value. In fact, the
theoretical impulse may be considered the maximum
0.40
0.00
impulse possible for a given bubble volume since a
spherically symmetric collapse is probably the most
efficient noise producing mechanism. The difference
between the measured impulses and the theoretical
impulse is an indication of the inefficiency of the ac-
tual collapse mechanism. Furthermore the average
impulses are closer to the theoretically predicted val-
ues for the I.T.T.C. body than for Schiebe body, and
this is consistent with the photographic evidence that
the I.T.T.C. collapse mechanism is more compact than
that on the Schiebe body.
The duration of the impulse (as opposed to the
magnitude) is much better understood. Here, the du-
ration is defined as T = to-t2. This time is simply
related to the total collapse time derived by Rayleigh
(1917) which is used by many authors (e.g. Blake,
Wolpert, and Geib (1977) and Arakeri and Shanmu-
ganathan (1985~. Like the collapse time, it will be
approximated by
U (a) (6)
where or is some constant of order unity. It
follows that the dimensionless impulse duration T* =
TU/RH should be primarily a function of RM/RH,
and this is confirmed by the results of the Rayleigh-
Plesset solutions shown in Figure 20. Also plotted
are typical experimental data from the Schiebe body.
Note that the calculated results lie within a narrow
envelope for a range of cavitation numbers and that
the slope of the narrow envelope is close to unity. The
experimental data is about one third the predicted
magnitude. Note, however, that the definitions of to
and t2 are somewhat arbitrary.
Figure 21 presents spectra of the noise measured
in the experiments. A series of individual acoustic
pulses were recorded at a particular velocity and cav-
itation number. The resulting spectra were averaged
to produce the composite spectra in the figure; the
0.60- ~ / /
~ at/ T.C. ] MAY
~ ~ ~ ~ ~ I.T.T.C DATA U .8.7 As o -0.45
ic~oo~fic:
~SHE DATA U -90 ~O .0.42
0.00 40.00
_
80.00 t 20.00 160 .00
MAXIMUM VOLUME, mm3
Figure 19. Comparison of theoretically predicted
and experimentally measured acoustic impulse as a
function of the maximum bubble volume for bubbles
generated on the Schiebe body and I.T.T.C. body.
Experimental data for a = 0.45 and U = 9m/s for
the Schiebe body and U = 8.7m/s for the I.T.T.C.
body.
343
OCR for page 344
-
o'
-
-
-
signals were not altered to remove the erects of tun-
nel reverberation. Such a composite spectrum will be
equivalent to the spectrum derived from a measure-
ment of a long series of cavitation noise pulses, pro-
vided the cavitation events occur randomly (Morozov
(1969~. The measured spectral shape varies little with
cavitation number; only the overall spectral magnitude
changes. A decrease of approximately-12dB/decade
is noted until about 100kHz where a sharp falloff oc-
curs. This cut-off frequency corresponds to the fre-
quency response limit of the hydrophore.
Asymptotic analyses of the Rayleigh-Plesset
equation (Blake (1986~) predict a spectral shape of
f-2/5 for frequencies in the range of 10~^Hz to 100kHz.
The experimental spectrum has a shape of approxi
mately f-3/5 which is similar but not identical to the
predicted trend. Hamilton (1981), on the other hand,
observed an almost completely flat spectrum in this
range based on his integral measurement of bubble
cavitation noise. The high frequency roll-off associ-
ated with fluid compressibility was not observed below
100kHz, and this is consistent with the observations
of Hamilton (1981) and Barker (1975~.
7. OBSERVATIONS OF CAVITATION
EVENT RATES AND BUBBLE MAXIMUM
SIZE DISTRIBUTIONS
Experiments were performed to measure the cav-
itation event rate and bubble maximum size distribu-
tion on both headforms along with the freestream nu-
clei number distribution. Furthermore, an analytical
model was derived to study the relationship between
the nuclei flux and the resulting cavitation statistics.
The cavitation event rate and bubble maximum
size distribution were measured for several thousned
events at various operating conditions, and examples
of these measurements for the Schiebe headform are
given in Figure 22. Note that the bubble maximum
sizes are presented as reduced radii. The reduced bub-
ble radius is the radius of a sphere of volume equal to
the measured bubble volume. Although the four bub-
ble size distributions presented are all at the same cav-
itation number and tunnel velocity, their event rates
and size distributions are quite different. Since the
200.00
/\-TIEORY
150.001 /
_ 1 oo.oo
so.oo
o.oo
o.
SEE BODY
U-9m/t
O-Q42
0.10
tar
0.05
o
Cl
UJ
· . . . . ~
1 . · ,· ~· · cn
i: . . ~O. ~ 5
~! . in
Fat . . · · ~
.... . . . .
r - I- - I
10 40.00 80.00 120.00 160 00
BUBBLI? MAXIMUM VOLUME, mm3
Figure 20. Comparison of theoretically predicted and
experimentally measured pulse width as a function
of the maximum bubble volume for bubbles on the
Schiebe body at U-9m/s and ~ = 0.45.
30
10 _
-
E
L
-
L o~
0..
0.03 1 0'3 ; ~- ~o jo 1
to
Frequency t Adz]
~oO
Figure 21. Averaged acoustic spectra derived from
acoustic pulses generated by bubbles on the Schiebe
body at average U = 8.7m/s and ~ = 0.45,0.50, and
0.56m/~.
cavitation bubble maximum volume distribution is di-
rectly related to the incoming nuclei number distribu-
tion these results clearly indicate that the nuclei num-
ber distribution can be quite different for the same
tunnel operating conditions. Weak control of the num-
ber of nuclei was affected through deaeration and nu-
clei injection. But, as Figure 22 indicates, the nuclei
number distribution is a highly variable factor which
influences travelling bubble cavitation and cavitation
noise. The time between cavitation events was Pois-
son distributed, as would be expected for randomly
distributed nuclei. Consequently, the total noise spec-
tra produced by these flows should be equivalent to
the composite specrtra presented in Figure 21.
A relationship between the nuclei flux and the
resulting cavitation event rate and bubble maximum
size distribution can be developed as follows. Whether
a nucleus cavitates or not is strongly determined by
the local minimum pressure it experiences. On the
surface of the headform, this pressure is given by the
minimum pressure coefficient. On streamlines above
~ q ~ n 1 2
BUBBLE MAXIMUM REDUCED RADIUS, R&.4R (mm)
3 4
Figure 22. Example of four bubble maximum size
distributions for a particular free stream velocity and
cavitation number for cavitation on the Schiebe body.
344
OCR for page 345
\
id' ~
-
z
1010
o
m
-
in
1'
UJ
Jo
t, 1 0.
Expanmental polats
with best fit line
.
V 'I '1 \
10 100 200
NUCLEI RADIUS, R (p m)
Figure 23. Example measurement of the free stream
nuclei number distribution, U = 9m/s and a = 0.45.
the body surface, the fluid pressure may still be low
enough to cause a nucleus to cavitate provided that
the minimum pressure it experiences is below the crit-
ical pressure, derived from Equation (3~. An incorn-
ing streamtube may therefore be defined for a nucleus
of specific size such that the nucleus will always en-
counter a pressure low enough to cause it to cavitate
during its flow around the body. The fluid capture
area of this streamtube will be a function of the nuclei
radius, RO, the free stream cavitation number, and the
flow geometry. By assuming that the pressure gradient
normal to the surface corresponds to the centrifugal
pressure gradient caused by the radius of curvature
a, of the surface at the minimum pressure point, and
by assuming no slip between the nuclei and the fluid
the following expression for the nuclei capture area
A (RO), may be readily obtained (Ceccio (1990~:
A(RO) = RBC ~-a-CpM) (1 RO)
where RO is the original nuclei radius, RB is the
headform radius at the point of minimum pressure,
and RC is the minimum cavitatable nucleus given by
Equation (3~. Equation (7) may be rewritten as
( RO ) (8)
where Av is the capture area enclosing all
streamlines which involve pressures less than vapor
pressure; note that Av is a function only of the flow
geometry and free stream conditions. Finally, the to
tal flux of cavitatable nuclei or total cavitation event
rate, E), is
Ioo
O= A(Ro)N(Ro)UdRo (9)
RC
where N (RO) is the free stream nuclei number
distribution.
Now consider the distribution of bubble maxi-
mum sizes which this process will produce. This distri-
bution is the result of different nuclei trajectories and
sizes. Cavitating nuclei travelling on streamlines far-
ther away from the headform will not grow to the same
maximum volume as those travelling near the surface.
Consequently, a flux of uniform nuclei, RO, will yield
a probability distribution distribution of bubble maxi-
mum sizes, RM, denoted by Pro (\RM). Because of the
slight dependence of bubble maximum size upon nu-
cleus size, Pro is a function of RO. A flux of nuclei rep-
resented by the nuclei number distribution, N (RO),
will therefore produce a distribution of maximum bub-
ble sizes, Pr, given by
Pi (Ro) = (~' ~ ProA(Ro) N (Ro)UdRo (10)
If no relationship existed between nuclei size and
the maximum bubble size, Pr would be independent
of the nuclei number distribution; changes in N (RO)
would merely change the total event rate. The exper-
imental data indicate, however, that the bubble max-
imum size distributions are influenced by the nuclei
number distribution. The varying event rates reported
in Figure 22 indicate different nuclei populations, and
each example is accompanied by a unique bubble size
distribution. The small influence of nuclei size upon
the maximum bubble size will ultimately have a sig-
nificant influence upon the bubble maximum size dis-
tribution.
We shall now compare the measured cavitation
event rates and bubble maximum size distributions
with the predicted quantities based on holographically-
determined free stream nuclei number distributions.
The nuclei populations were measured at the same
time tliat the cavitation statistics were recorded, and
the smallest nucleus which could be detected with cer-
tainty was approximately 20,um in diameter. An ex-
ample nuclei distribution is presented in Figure 23.
Table 1 presents the measured event rates and the
predicted event rates based on Equations (7) and (9~.
The measured event rates fall within the range of the
predicted values, with the uncertainty in the predicted
event rates resulting from uncertainty in the measured
1
PREDICTED
(3 (events/sec)
128 ~ 25
164 st 25
1 47 t 25
MEASURED
(events/sec) l
156
147
162
1 _ _ _
Table 1. Comparison of measured and predicted
cavitation event rates for cavitation generated on the
I.T.T.C. body at U = 9m/s and a = 0.45.
345
OCR for page 346
0 . 1 0
o
3
G
-
~ G
r~ m 0~50 -
cnp
UJ
m
m
3
CALCULATED EVENT RATE . 128 events / see
MEASURED EVENT RATE _ 156 evens / see
CALCUlATED
...... MEASIRED
BUBBLE MAX. REDUCED RADIUS, RM (mm)
Figure 24. Calculated and measured event rate and
bubble maximum size distribution for cavitation on
the I.T.T.C. headform at U = 9m/s and ~ = 0.45.
nuclei number distributions. The close match between
the predicted and measured event rates indicates that
the nucleus stability criteria from Equation (3) ad-
equately models the actual cavitation process. The
ninimum cavitatable nucleus for this flow is calculated
to be approximately 20pm in radius, and the measured
nuclei number distribution indicate that most of the
cavitating nuclei are in the range 20 to 100,um. The
success of the model suggests that the quantities Av
and Rc may be used to adequately characterize the
nuclei capture area for flows over more complicated
bodies.
The calculated bubble maximum volume distri-
butions, however, depart substantially from the mea-
sured size distribution in terms of its details. Fig-
ure 24 presents a measured bubble maximum size dis-
tribution along with the predicted distribution based
on Equations (7), (9), and (10), the results of Figure
16, and the measured free stream nuclei distribution.
The calculated size distribution departs substantially
from the measured distribution in its details. The pre-
dicted bubble size range is about twice the observed
size range, and the number of larger bubbles predicted
is much smaller than the observed percentage. These
discrepancies may be the result of several phenomena.
First, the maximum size achieved by a nucleus sub-
jected to a specific pressure history may not be ad-
equately predicted by the Rayleigh- Plesset equation
since bubble growth may be limited by the positive
pressure gradients above the headform surface. Once
the bubble has grown sufficiently, the mean pressure on
the bubble surface will be larger than the surface pres-
sure used in the Rayleigh-Plesset calculation, reducing
the driving force for bubble growth. Furthermore, the
experimental bubble maximum size distributions often
show several maxima which were repeatable for nom-
inally fixed operating conditions. These distributions
cannot be simulated with simple, smooth nuclei dis-
tributions with several well defined peaks. It seems
likely that these maxima are the result of a compli-
cated nuclei number distribution. Such detail could
not be ascertained using the current holographic nu-
clei distribution methodology; its existence was only
revealed by the electrode system which permits very
large quantities of data on bubble size distributions.
8. CONCLUSION
Although theories of individual bubble cavita-
tion abound, this study demonstrates that a great
deal may still be learned through the observation of
naturally occurring cavitation bubbles, especially bub
bles formed in flows near surfaces. Cavitation bubbles
are significantly affected by the viscous flow near sur-
faces, and this in turn effects their noise production
and possibly their damage potential. Yet, numerical
integration of the Rayleigh-Plesset provided a reason-
able base for comparison with the experimentally mea-
sured data. The relationship between the nuclei flux
and the resulting cavitation was successfully predicted
based upon simple parameters derived from the non-
cavitating flow around the body, although estimation
of the bubble maximum size distribution was more dif-
ficult.
By combining the results of this study, cavitation
noise may systematically be synthesized. Analysis of
cavitation event statistics and size distributions can
relate the freestream nuclei distribution to the cavita-
tion process. And, once the number and size of the
cavitation events are known, the total noise emission
may be estimated based on the single bubble measure-
ments. The results presented here are useful for the
case of limited cavitation, but multiple bubble effects
must be included to characterize flows in which the
bubbles interact with one another. The importance
of the nuclei number distribution as a parameter in
cavitation studies cannot be overemphasized, although
simple and accurate methods are still needed to mea-
sure this quantity with speed, ease, and precision.
ACKNOWLEDGEMENTS
The authors would like to thank Professor Allan
Acosta for his advice and considerations. We would
also like to acknowledge the assistance of Sanjay Ku-
mar and Douglas Hart. This work was supported by
the Office of Naval Research under contract number
N-00014-85-I(-0397.
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DISCUSSION
William B. Morgan
David Taylor Research Center, USA
This paper presents a very interesting investigation of cavitation
acoustics and the authors are congratulated for such a fine and
thorough piece of work. I have one question concerning Fig. 19.
This figure shows a significant difference between the acoustic
impulses from the ~I.T.T.C.. headform and the ~SchiebeW headform.
Do the authors feel this difference is due to the difference in the way
the bubbles collapse relative to the headform or do you think there
would be an actual difference in the radiated noise?
AUTHORS' REPLY
The authors would like to thank Dr. Morgan for pointing out this
phenomena. The significant difference in the average acoustic
impulse measured for the two headforms prompted the authors to
investigate several factors which could explain the difference. Care
was taken to accurately measure the true bubble maximum volume,
since bubbles on the I.T.T.C. body were often larger than those on
the Schiebe body. Yet, bubbles of equal maximum volume on the
two headforms were found to produce significantly different impulses.
In fact, a listener standing near the tunnel could easily detect the
difference in the acoustic emission between the two headforms.
Consequently, the authors have concluded that different acoustic
impulses generated by bubbles of equal maximum volume result from
the significant difference in the bubble collapse mechanisms, in turn
influences the radiated noise.
348
Representative terms from entire chapter:
schiebe body
