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NAVY DEPARTMENT
THE DAVID W. TAYLOR MODEL BASIN
WASHINGTON 7, D.C.
AN EXPERIMENTAL STUDY OF SiNGLE
BUBBLE CAVITATION NOISE
by
Mark Harrison, Ph.D.
November 1952
Report 815
TABLE OF dONTENTS Page ABSTRACT i INTRODUCT,ION . . .
...
fi
EERNTAL. PROCEDURE
. . 2Venturi Nozfle Bubbles - 2
Spai'k Bubbles . 4
RESULTS AND DISCUSSION 5
Venturi Nozzle BUbbles 5
Spark Bubbles 12
SUMMARY AND CONCLUSIONS ...
15ACKNOWLEDGINTS . . .
...
- 16REFEREHCES .
...
by
Mark Harrison, Ph.D.
ABSTRACT
An exper1ental. study óf the Íiolse produced by a single cavitation bubble
has been made. The noise consists principally of a transient pressure pulse
associ-ated with the collapse of thé bubble.
The motion of. the bubble has been photographed
sirnultaneoúsiy with the measurement Of the pressure pulse.
INTRODUCTION
Cavitation is a phenomenon that has attracted consIderable attention in the past thirty years. Its importance has been due largely to thé practical engineering consequences of cavitation occurring on propellers and in hydraülic machinery. In this connectiOn the intérest has been focused upon the resulting
damge and reduced effiiency.
There s, however, a more, fundamental interest In the dnamics and thermodynamics of the cavitation bubble Rayleigh1 treated the proble of the
ot'ion of an empty spherical bubble in an i±ifinite body
dr
incompressibleliquid. He showed that iheri this bubble'öollapses the radial velocity becomes infinite ând an in.finite pressure is developed. He also cons1deied the cavity filled with an ideal gas that is compressed isothermally., The assumption of an incompressible liquid, while satisfactory for the slow.phases of the motion; Is clearly untenable 'In the collapse phase of the motion wheré high radial velocities are encountered. (Also, it seenis clear that a more adequate
treat-ment of the bubble thermodynamics is required.) A considerable ¿moii.nt of: material on bubble dynamics and thermodyñamlcs can be found n Coie' book.2
Knapp and Hollander3 have made photographic studies of the ¿ollapse of a cavi-tation bubble-and their observations have led to fruitful speculations as to the role played by compressibility, condensation, heat conductIon,,, and air
content.
.*A dissertation subthitted to the faculty of the Graduate School of Arts and Sciences of the Catholic University of merica in partial fulfiJJient of the requirements for the degree of Doctor of Philosophy.
2
In recent years another aspect of cavitation has assumed importance. This is the noise associated with cavitation. There' does not appear in the available literature a systematic study of cavitation nólse. The studies that have been mae4'5'do nOt always consider the simplest case, i.e., the noise produced by a single cavitation bubble in free field conditions.
This article presets the resülts of simultaneous measurements of the noise ánd dynamics of collapsing cavitation bubbie in approximately free field conditions-or in afield where the conditions are clearly defined.
EXPERIMENTAL PROCEDURE ..
-Tzo experimental méthods were used. The first method gave'measùre-ments and observations on cavitation bubbles produced in a venturi nozzlé'. The bubbles were observed by high-speed photography and the pressure pulse
thàt arose when the bubble collapsed was measured by a pressure pickup and oscilloscope. In the second method bubbles were produced in a small tank of water by:a spark. These spark bubbles wére observed and their pressure pulse upon collapse measured by a technique similar to that employed on the
cavitä-tion bubbles.
VENTURI NOZZLE BUBBLES
The venturi nozzle and its associated equipínent are shöwn in Figure L The nozzle, has a circular. ¿ross section and is machined from à sblld piece
of lucite.. The diffuser part Of the nozzle 'is conical with an' erìclosd' angle
of 5 degrees.' Figure 2 shows the'nozzle assembly. Brass flanges are fitted
to 'each ,nd of the lucite. nozzle. and. are carefully sealed by O-rings at' the
lucité-to-brass joints. . The"piezometer taps consistof'holes 1/32 inch in diameter drilled normal to th tube boundary and located in pairs .6n opposite sides of the test section. The taps are connected by plastic tubing to a set
of. mercury manometers. A detailed account of the construction detail has been g'iven by S.F. Crunip.6'7 ' ., ' , ' , '
The nozzle has been calibrated so the readings' of these manometers give the pressure and velocity as a function öf the axial coordinate inside the nozzle.' A.detailed account of 'this calibration is given in Reference
7.
The bubbles are produced in the 1ow-p'resurè region shown in Figure
3.
The successive stages of the 'life history of a bubble are also illustratedIn Figure 3. In order' to make possible the measurement of the pressure pulse radiated fioth the' collapse of the cavitation bubble, the nozzle was immersed In a tank of water 3 by 3 by 3 feet The crystal pressure pickup was located In the tank of water near the point where the bubbles collapsed... It would
Topil Top2
\ \
/, \\SS\S s\ \
u
22Ç
Figure 2 - Details of the Venturi Nozzle have been desirable to place the pres- Externally Applied Air Pressure
sure pickup inside the nozzle but, un -
Air Bleeding Line fortunately, cavitation would have beeninduced on the pressure pickup.
r-
jSince the impedance of the
Venturi Nozzle
lucite nozzle is different from that Stifling Tank for water, it is necessary to measure
the transmission loss through the
lu-cite nozzle. Since this transmission g
loss is a function of frequency, single frequency measurements are of little
value. The technique used, therefore, t
Pump
was to produce a spark. bubble inside
the nozzle and to measure the reduc- Figure 1 - Schematic of Venturi Nozzle tion in the peak pressure of the pres- and the Associated Equipment sure pulse after it had passed through the nozzle. This is a reasonable pro-cedure since thepressure pulse radiated by the spark bubble should be quite similar to that of the cavitation bubbles. The correction factor obtained by
this method was )4.5. There is, of course, considerable uncertainty as to the accuracy of this factor for the cavitation bubble since it is not known how nearly alike are the original pressure pulses of the spark and cavitation
bubbles. All that can be said is that after transmission through the nozzle they are quite similar. As a matter of fact, there is a goôd indication that the pressure pulses from the cavitation bubbles were of shorter time duration than those from th spark bubble.
The pressure pulse was measured with a piezoelectric pressure pick-up. The pickup was constructed by paralleling four tourmaline wafers 3/8 inch
\ \\\ \'
\' \"
\\ \'S' \\Ç\'\S",.\'\'\
\
oOOOO&.
\
Figure
3 -
Sketch of the Pressure In the Venturi NozzleThe hißtory of a single bubble le illustrated.
in diameter and 1/2 inch thick. The
crystal assembly wa dippe n wax
and coated. q1th rubber cernent. The pressure pickup was mounted .sothat.
its diameter was normal .to the wave
front.. The output of th powp wa
fed. to .an oscilloscope and the ocil-loscopic presentation suitably
photo-graphed. The electron1.c system had a frequency response that was flat from 10 to 1,000,000 .cps to withIn iO
per-cent. io kinds of photQgraphy were. used. on the oscilloscope bec.ase of the type of information desired. One
experiment was simultaneously to photograph the bubb.le in the nozzle and to observe the pressure wave ra-diated by the collapsing bubble. In this Instance, the oscilloscope beam moved only vertically and the camera film was moved horizontally at a speed
of 100 fps. The filin then gave a pressure-time record. Suitable timing marks
were placed on both the pressure-time record and the bubble photographs to identify that part of the bubble motion thatresulted in radiated sound. The oscilloscope was calibrated so that the pressure.measurernerjts could be corre-lated with other available information about the bubble. Since the oscillo-scope camera film speed was only 100 fps it gave inaccurate information con-cerning the shape of the pressure pulse. In order to obtain this information the oscilloscope was used in a single sweep arrangement of loo niicroseconils duration and the shape of the pressure pulse photographed with an open shutter still camera. The bubbles were photographed with a Western Electr.c Fastex camera capable of a frame speed of 8000 frames per second. ..
It was possible to obtain water with a known amount of air contint. The water was deerated by producing a large steady-state cavity -in the
nozzle and the contents of the cavity drawn off by vacuum. The air content
could be reduced by this method to .30 percent of saturaÏ on at .1 atm. The air content ws measured by the Winkler method.
SPARK BUBBLES
The spark bubbles were produced br passing a large current of short duration through a 3-inch length of 5-.mil:copperWire. The wire had a 1-mil
(approximately) constriction that was made by nicking the wire with a specially modified pair of wire cutters. The current was obtained by discharging a
condenser charged to a high potential. The condenser sizes varied from 0.1 to 1.0 microfaradand its potential was varied up to 5000 volts. The duration
f the current was about 2 microseconds. When the current passed through the constriction in the wire, the wire parted and the resulting spark vaporized
the water. The spark bubble was phôtographed by the same technique used for the cavitation bubble.
The pressure pulses emitted by the spark bubble were observed by a different technique than was used on the cavitation bubble. The oscilloscope was set for a two-millisecond single sweep that was triggered by the condenser discharge current. The output of the pressure gage was fed to the vertical plates of the oscilloscope. The resulting pressure-time trace on the
oscillo-scope was then photographed. This technique gave good results. It Is un-fortunate that it was inapplicable to the cavitation bubbles in the venturi nozzle since the cavitation bubbles occur here in a random fashion. However, by the use of photocells to indicate the presence of the cavitation bubbles
it might be possible to use this technique.
For the spark bubbles the water was deaerated by boiling under
vacu-uni. Since it was awkward to work with an air tight system, some care had to be taken in order to prevent air from redissolving in the water during the course of the experiments. Good results were obtained by coating the water surface with deaerated castor oil. 'This kept the water from splashing about and retarded the re-entry of air into the water.
RESULTS AND DISCUSSION
VENTURI NOZZLE BUBBLES
The cavitation bubbles that appear in the venturi nozzle were formed about small air bubbles that were being circulated through the closed system of Figure 1. When one of the small bubbles entered the low-pressure region illustrated in Figure 3 lt served as a nucleus around which the cavitation bubble formed. A description of the expansion of the nucleus into a cavita-tion bubb-le has been given by Lamb8 who has treated the air content adiabati-cally but has neglected the evaporation of the water into the cavity.
It was possible to vary the size of the air nuclei'. The air nuclei were produced by forcing the water through the nozzle at such high speeds that a large quasi-steady cavity was produced on the wall of the 'nozzle. The be-havior of this quasi-steady cavity is very complicated, but It sufflòes here to say that lt formed many air bubbles that were circulated through the system
6
and served as nuclei about which cavitation bubbles were formed. The size of a nucleus when it produced a cavitation bubble depended upon the dissolved air content of the water and the time that had elapsed since the nucleus was formed by the above procedure.
The maximum size attained by the cavitation bubbles could be varied by the flow velocity of the water through the nozzle. Increasing the flow velocity increased the pressure shown in FIgure 3 and decreased the time during which the bubble was in the low pressure region.
When the cavitation bubbles were formed about a relatively large air nucleus (diameter of several millimeters) they would collapse to a small radius,
compressing the contents of the bubble, and then rebound to a fraction of the first maximum radius. Subsequently, they would rebound in this manner many
times. This process is quite similar to the nonlinear oscillations of the
gas globe in underwater explosions. Illustrations of this can be found in Cole's book.2 When the bubbles observed here were formed about a large air nucleus and in water close to being saturated with dissolved air, the motion of the bubble was similar to those observed by Knapp and Hollander3 and to those shown by Cole.2
However, when the air nucleus was so small as to be invisible, the
rebounds, are absent. A sequence of photographs revealing such a bubble in
the collapse stage of the motion is shown in Figure 4. The correspoid1ng radius-time curve is plotted in Figure
5,
where the experimental points are superimposed upon a theoretical curve computed from equations by Rayleigh.1 A discussion of how this may be done has been given by Knapp and Hollander.3 In Figure 5 the ratio of the radius r to the maximum radius r0 is plotted against the ratio of the elapsed time t to the total collapse time to. Rayleigh has shown that to and r0 are related to the equationp
1/2
to =
0.915
r0 (;)where p is the density of the fluid and P0 is the difference pressure between A and B in Figure 3.
The agreement between theory and experiment is surprisingly good in view of the fact that P is not constant during the collapse as specified by Rayleigh. Plesset9 has generalized Rayleigh's treatment so that the time variation of po may be included. Applying Plessetts ideas as a first order correction did not materially change the theoretical curve. This is because the pressure in the nozzle has increased to nearly its full value before the bubble begins to collapse.
e
12Figùre 4- Photographsof a Collapsing Bubble
0.8 0.6 D4 02 830microseconds 0.67 cm. P. :1.3 atmospheres - o
-02
4. - 0.6 0.8. 1.0 1.2tito
The pressure pulse produced
UQfl
collapse of the cavity was markedly different depending upon how much time was allowed for the nuclei to dissolve. The audible sound would progress from a dull crack of small 'amplitude to asharp crack not unlike the report of S rifle.. Eventually as the water con-tinues to circulate through the nozzle no more nuclei would beconie available and cavitation either ceased or became extremely intermittent. The pressure pulse was measured 10 cm främ the point of collapse. In Figure 6 the peak pressure of the pressure pulse is plotted as a function of the time that has elapsed since the nuclei were observable and were about 1 mm in diameter. It is to be noted that the radiated pressure pulse increases as the air bubbles, which serve as nuclei for the cavitation bubbles, dissolve.. This clearly indicates that when the air content of the cavitation bubble is high the air content is an important factor in determining the noise radiated upon collapse of the cavitation bubble. The bubbles for this case are about 1 cm in
diame-ter. It is to be noted that the pressure pulses seem to approach a limiting
value. It is possible that as the air content of the bubble becomes very small the influence of the compressibility of the liquid plays a more iinpor-tant role in determining thd' motions of the bubble in the collapse phase and hence the pressure pulses approach a limiting value. It is also possible the bubbles stopped dissolving due to some phenomena at the surface of the bubble such as an increased concentration of some dissolved impurity. In any case, these data are of only qualitative significance.
D. . D o
co
'XDO
a-8 020.
40 60 80 Time in secondsFigure 6
-
RadiatedPressure Pulse as.a Functionof the Time Life of the Nuclei
o o o o o loo 140
radiated when the cavity grew1 simultaneous pressure measurements and bubb].é
photographs were .thade of the growth part of the bubble motion.. It.was obser-ed that the bubble radiatéd a pressure pulse only upon collapse. In this. coñ-nect.ion it was observed that oöcasionally cavities, were fórmed on the wail of the nozzle.. When these cavities broke free of the wall, noise wa radiated.
This noisé probably as due to water-on-water impact that resulted from the closing of the cavity after tearing loose from the wall,.
At the sanie time the above theasurements were performed it was
pos-sible to obtain pressure measurements as-a funôtion of the maximum bubble radius; In-this case the air. content öf all the.bubbles was substantially the same; that is to say the air nuclei from which the cavitat.on bubbles were forme had all been ih existence aboüt the saine length of time. The
narrow spread of the data shwn -in Figure 6 gives confidenòe in the equality: of size of the air nuclei that eicisted at a specified time after the. formatiön of the air nticlei in watér with a constant amount of dissolved air The size.
of the bubbles was varied by.operating the nozzle at differert water. velocities
and hence d'ifferènt prñsures,4P, as shown in Figure 3. The-results
are presented 1n.Figue
7.:
Shown onFigure7 is the-pressure difference.?0that causes the collapse of the bubble. po is the differeñce presure
be-tween points A and B in. Figure 3. It. is this pressure Po that enters into
¡2 Q. o e
o
E28
E u o-Q.. o Et,4
C o Q. a. o o Ft2.l atmospheres 0.2 04 0.6 O8 Radius in cm.'Figure .7
-
Radiated Pressure Pulse Amplitude Fünetion òf. - the Maximum Radius of the Cavitation Bubb.lelo
Rayieighequations.
The air content of the.water.was 35 percent ofsatura-tion at i atm. it is -to be observed that the peak pressureof the pressure pu1sedöes not continue 'to Increase as the bubble size increases. . This Is probably due tothe characteristic of the apparatus. There are severaieffects
poss1bl here. One-. effect is that.. the bubble radius. is too large a. fraction
of the nozzle radius. so that the Surrounding medium isa poor approximationto. free field conditions because.of walL effects. Another effect'.Is:that the pressure field whIch causes thé.bubble' collapse is not. the same at.
the:differ-ent flow Velocities that were used to produce. differthe:differ-ent. bubble. sizes
-Itcannot be seen, in. the pictures of the bubble In Figure '4,.'but on. the original filin an interesting phenomenon could be' seen. Immediately after the bubble had disappeared the only thing visible on the film was a'gray. fdg
about, 0.05 cm,In,diameter. -This gray fog persisted for 'about one niillIsecond.
One conjecture is that this .fog is made up. of many minute air or vapor bubbles
at a, high temperature,. ',Iñ t'his connection, it is of Interest to' ask:what is
the minimum radius attained by the bubble. . High-speed photography to date
ha been unable to supply this information'. it is even doubtful'.'if a..factor
of 10 in the frame speed
woul4 'supply
the Information.. If the'above diàméterof 0.05 cm Is 'taken. to:be near th minimum radius, attained' :by the bubble,: thén the need-for including. compiessIbility effects .in.the: analysis can be.: indicated..
Ray1eIgh-.has.showthatth radial veIocity' of anempt.yspherical'bub'bie in: aninconipressiblefluid is 'given by
r
OQ)
-
i]where r0 is the' maxmmüinradius of'the bubble, ' ' . . '"
p is the fluid densitç and' ' .
P0 has been previöury defined.
' '
If ris taken to be 0.025 cm, r0 Is 1 cm and po Is i atm, then f' exceeds the
re,locity of sound ànd thé need for compressibility Is indicate&.
A further point of interest is to estimate the maxiinurn pressure at.
the bubble on the assumptIons that 0.025 ..cm is the minimum radius and thàt the
pressure varies inversely' with distance. Using 'he results o,f Figure 7 for the 1 cm radius bubble, the maximum pressure at the bubble is 4Ö00 atm. 'ThIs extrapólatlon is not valid near the bubble and the áb6ve igure fdr the pres-sure should be regarded as only an order of magnitude. .
.-I.t was stated. at, the first of this section that these,' bubbles were
different from-those of Knapp and Hollandér In that no rebound was oberved.
This statement appiies to the spherical bubbles -of, small air cQntert.. .The
a slight rebound of about 10 percent of the maximum radius in the direction corresponding to the axis of the nozzle. A typical sequence of photographs
is shown in Figure
8.
It should also be added that a weak pressure pulse was radiated from the subsequent collapses.The frequency spectra of the pressure pulses were not measured
di-rectly. The frequency spectrum can be computed by the use of Fourier trans-forms. The pressure pulse measured experimentally can be fitted very nicely
to the curve
p(t) = Po e_ItI
The time constant varied from 30 microseconds for bubbles formed about a large air nucleus down to 10 microsèconds for the bubbles in water of low air
content. The transform g(w) of p(t) is
a
[(1)2
2]
12
The 10-microsecond bubble should have an essentially flat spectrum UP to about
16 kc. It is probable that'the time constants of the shorter pressuré pulses are actually much shorter than those observed since the observed time constants aré near the resolution limit of the pressure pickup as computed from
consider-ations given in Cole!s book.2'
-A further point of intèrest on the radiation of sound is how much
of the bubble energy i's'radiated. The remainder of the energymay be dissi-pated by turbulence, heat conductioii, etc., or may remain in the. bubble to cause rebounds. The last circumstance is true for the spark bubbles arid for nozzle bubbles formed about large air nuclei but not true for the nozzle bbbles of low air content.
The total energy of the bubble is the same as the potential energy when the radius of' the bubble is a maxImum, = 0. The total energy Is
4irr
ET=
3 Po'The acoustifc energy radiated through a sphere of radius ,R which is the dis-taiice at which the pressure is measured is
EA=.fP2dt
It has been found that the pressure can e described by
p(t) = Po etVa
and if this expression Is used to' evaluate the expression for EA, wé obtain
4TB2p
EA Pc
The quantity EA/ET has'been' computed and is generally from O. to'
0.5 for bubbles of low aSir content. Attempts ,were made. to relate this
quan-tity to the vilue of r0 or thé'air content of the water but the attempt failed. The variation of the quantity EA/E with r0 was smaller than its probable
error. For bubbles of high air content, EA/ET was generally around 0.3. Since the errors were large it was not possible to establish a definite relation.
SPARK BUBBLES .
A sequence of photographs showing the bubble In various stages of mo tion is shown in Figure 9. The radius-time curve is shown in Figure 10. This
'-'bubble was formed in water with an air content of 15 percent at. i atm. It is :
of interest to note the. rebound In contrast to the venturi nozzle cavitátion
pulse each time the bubble collapsesto a minimum. The amplitude of these pressure pulses is roughly proportional to the maximum radius attained on
the rebound..
Another point of difference with the venturi nozzle bubbles is that these bubbles produce a.pressure pulse upon formation nearly equal to the pressure pulse radiated upon collapse of the bubble. Since the origin ofthe
spark bubble is at a region of extremely high local temperature and undoubted-ly high local pressure that is not too surprising. The origin of the spark bubble is quite similar to an underwater explosion.
The spark bubble when formed in water with practically no dissolved air behaved quite similarly to an underwater explosion gas globe. This is a little surprising since the underwater explosion gas globe is filled with the gaseous products of the explosion while the spark bubble formed in nearly deaerated water should be filled chiefly with water vapor. It might be expect-ed then that these spark bubbles would behave like the venturi nozzle cavita-tion bubbles In regard to rebound. When the venturi nozzle bubbles were formed about a large air nucleus they were Identical in their behavior to the spark
bubbles in regard to rebound, magnitude of pressure pulse, time duration of
1.0 0.8 06 -o 0.4 0.2 lL t0. 760 mIcroseconds r0
85cm..
P0 1.0 atmosphere X X Q2 0.4 06 0.8 IO titoìure 10
- Radius versus Time Curve of a Spark Bubblepressure pulse; etc. It appears, however, that it is not possible to make . spark bubbÏe even in water of extremely low air content that behaves like
the venturi nozzle bubbles that are formed about a small air nucleus. Per-haps the reason they 'do not'.is because of the higher temperatures in the spark
bubble.
When the spark bubble is produced in water of.low air dontent it can be seen in"Figure 9 that a de±nite air bubble is left over after the
-kinetic nergy.has been dissipated. it' is not entirely clear why this should.
be so in òontrast to. the vent un nozzle, bubbles where. only. the "gray fog" is the residue. One, conjecture is that 'since the spark bubble undergoes many rebounds t'here is sufficient opportunity for the air to diffusa into the spark
bubble. Anothet possibility is that the water was decomposed by lectrolysis. The'pre'sure pulse radlated'upon collapse is plotted as a function of bubble radius in 'Figum il. It should be noted that these pressures are. considerably smàiler than in the corresponding vénturi nozzle bubble.
The frequency spectrum produced. by the spark bubbles is quite simi-lar to that of the venturi nozzle bubbles. The preèsure pulses are, however, slightly longer in time duration The shortest pressure pulse was about 15 microseconds. This is consistent with the above remarks tothe effect that
the air cbntent of the spark bubbles is' usually higher than can be. acount'ed
for. .
The'efficiency of the spark bubble methodas a noisemaker is worth
comment. 'Even'thouh no attempt wàs made to mInimize ldsses, about 10 percent of the energy stored in the condenser is ultimatèly radiated as sound.
0
E0
o
6co
oc
0. 5 U) U)-0:E
u IO o 0.2 04 06 08 Io 12 14 Radius r0 In cm.Figure 11 - Radiated Pressure Pulse Amplitude as a Function of the Maximum Radius of the Spark Bubble
SUMMARY AND CONCLUSIONS
The noise in single bubble cavitation ds due to the pressure pulse associated with the first collapse of the bubble. If there are many bubbles present the resulting noise spectrum should be the complex sum of these
pres-sure pulses. In view of the high percentage of the total energy lost as radiation on the first collapse it is doubtful if the noise resulting from any subsequent motion of the bubble can make any appreciable contribution to the noise spectrum. However, there are many factors to be considered before the noise spectrum can be predicted when there are many bubbles present in close proximity. The pressure field surrounding one bubble influences the dynamics of the nearby bubbles. The pressure pulse radiated from one bubble is scattered and absorbed by the nearby bubbles. In addition, if there are rigid boundaries present they will influence the dynamics of those bubbles that are nearby. If the boundary is sufficiently flexible such as a thin steel plate, then it may well absorb energy from the bubble and the subsequent motion of the plate result in a radiated field from the plate. All of these
items are areas for fruitful research.
The size of the air nuclei around which a cavitation bubble is formed affects both the magnitude and the shape of the noise spectrum. It is
unfortunate that tnese experiments could not determine the size of these micro-scopie air nuclei. It would be very desirable to design an experiment where a known air nucleus could be introduced.
16
The pressure near the bubble .àt its minimuin is at least 4'OOO atm.
This is sufficiently close to the elastic limit of most materials that erosion by cavitation is not surprising. The temperatures existing inside the bubble would also be of interest- as a factor in erosion by cavitation. SInce the direct measurement of the minimum radiu, the radial velòcity, and the temperature and pressure inside the bubble near the minimum appears to. be an Insurmountablé experimental problem, a theoretical approäch is indicated. Since the radial velocities near the minimum radius are close to the velocity
of sound, compressibility of the liquidmust beconsldered. In thefirst
attempt it mightbe wise to consider the problem as Rayleigh did, i.e., an. empty spherIcal cavity, only with a compressible liquid.
Onequestion,then
that might be asked iswhether the radial velocity approaches aterththalveioc-ity Instead of becom1n irfinite as in the case of the incompressible liquid.The spark bübbles. were studied to see if the temperature of the contents was a factor in the collapse phase since'the :finite rate of conden-sation of the water vapor1s a funct-ion of tpe'atures. Thé resuitsare in
conclusive since the spark bubbles always eem tohave.more air content than
can be explained.
ACKNOWLEDGMENTS .
The aüthor wishes to thank Mx. Phillip Elsenberg of the
Hydrodynam-ics Division. of the David Taylor Model. Basin for hi.s continued interest In and
support of this problem while the aithor was assocIated with his group. Appreciation l's also expressed to Professors
F.E. Fox
andK.F.
Herzf.eld ofthe Catholic University ofArnerica for their continued encouragenent and
Ra1eigh, John William Strutt, baron, Phil. Nag.., Vol. 34,
i97.,
pp.94-98:
Cole., R.H., Press,
194a.
Knapp, Pbert:T.. and Ho ander, A.., Trans.. A.S.M.E., Vol.
70, 1948.
Osborne .'LF..M., Trans.. A.S..M.E.,.Vol. 69:, 194.7,
pp. 253-26.
Osborne, 4.F..M., J.A.S.A..., Völ..
19,
19U7pp. 13-25.;
:6. crump, s..?.., '"eterminaion'of Critical Presures for the Ïnception of Cavitation
ih
'Frésh and Sea Water as Thfluenc.ed by Air .Coñtent of theWater," .TP'Report 575., October
1949.
. . . -.7.'
Criimp, S..F., "Critical Preßsures for' the Inceptión of Cavitation in a 'Large-Sca3e Nunachi Nozzle as Influenced .by the Air 'Content of theWater," Report .7.70,
Júly
1951.
.8..,,Lamb,., Horace., Hydrodyniòs," .Doer Publications, cinc ,. 1,932,
p. 1.22. , .
'9 :Pieset., LS.., Journal of Applied 'Mech..., VoL '.16, 1,949,
3 Director, Iowa Institute Iowa, Iowa City, Iowa
DirectOr, Hydrodynamics Technology, Pasadena
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