vo!. 2 ( Iq'q)
STEARTHE
MEdIANISM
OF CAVITATIONE. G. RI('IIAI(ISON
king's College, \ewcaslle upon Tyne (Grial Rn/am)
S U M M A R Y
Measurements are made of the numl)er and size of the gaseous nuclei which exist in water and
utlit'r li(lui(ls and give rise to cavitation and consequent erosion in hydraulic machinery. lt is shown
that the nuclei may be remove(l by long standing or l)V application (1f pressure. The nuclei are detected by the absorption of an acoustic signal which they produce in a ''reverberation vessel" containing the liquid. The distinction between air nuclei and vapour nuclei is brought out in the
experiments.
Z USA MM EN FA SS UNG
DER MECHANISMUS DER KAVITATION
\nzahl und Grösse von Gaskernen, (lie in \Vasser und anderen Flüssigkeiten auftreten,
Kavita-tintI und schliesslich Erosion mn hydraulischen Maschinen verursachen, wurden gemessen. Es zeigt
sich, dass die Kerne bei längerem Stehen der l'lüssigkeit oder bei .\nweridung von Cberdruck verschwinden. Die Kerne werden (lurch Absorption cines akustischen Signals, das sie in einem Echiogefäss'' mit der Flüssigkeit erzeugen, nachgewiesen. Der Unterschied zwischen Gaskernen und Dampfkernen wird durch die Versuche verdeutlicht.
Much attention has been given to the phenomenon of cavitation, since its effects OU propeller efficiency were first studied by Sir CHARLES PARSONS in 1894. It is now
known that not only is the operation efficiency of many hydraulic machines reduced if cavities arc produced in the water, but the solid surfaces on which they usually collapse can be seriously eroded either by the first action of sudden pressure impulses or by the shock waves which are also set up.
It lias also been known for some time that cavitation is more easily produced in vater that has been saturated with air than in water which has been deaerated by stirring it up in a partially evacuated chamber and it has been supposed that minute air bubbles in the former case act as nuclei on which regions of low pressure act if, for example, the water is accelerated round a sharp bend or over the backs of blades of aerofoji section.
In order to study this mechanism and to be able to detect and, if possible, count tue number of nuclei in a given specimen of water, some research lias been SI)onsorcd by tue Mechanical Engineering Research Laboratory of the Department of Scientific and Industrial Research and carried out by the author in conjunction with I)r. I. S.
IVENGAR in time Physics L)epartmnent of this College.
l/een-es p. zoó
i:. (.. R1(ÎIARI)SON
\o!. 2 (Is'/5)
I'lie hydraulic engineer is usually concerned to remove, as far aspossible, all nucleifrom the water he is going to through a machine hut, in Or(lcr to study the
probleiiì lundamentally, we started by seeing if we could add nuclei to water. This we did h' dropping a few grains of common salt into freshly distilled water.
APPARATUS FOR MEASURING THE SOUND ABSORPTION DUE TO NUCLEI
The apparatus is copied from a well-known technique in architectural acoustics. A glass or aluminium vessel of several litres capacity contains a liquid which is set in reverberation by the "pinging" of an ultrasonic quartz or barium titanate crystal stuck to the wall. A similar crystal connected to an amplifier and oscillograph picks up the decaying signal. From a plot of the logarithm of the signal with time, the "absorption" due to the liquid and container are calculated in the same fashion as in the aerial sound experiment. The "reverberation time" is the time for the signal picked up to fall to a small fraction of that when the source is turned up. It is inversely proportional to the total sound absorption. This method has been used by STRAS-BERG' and by us.
The output from the receiving crystal was amplified and detected. The signal was applied to the I).C. amplifier of the oscilloscope and the receiver gain was adjusted until a full-scale deflection as obtained for pure water. (Fig. i is a photograph of
the apparatus.)
Ittte e I1( t f) i ()
Fig. i Iht' reverl)erati( tu apparatus.. \ noise generator. H alu minium vessel (' receiver,
I I nìtiltiviltrator, E mixer network, F power packs.
À weighed i ¡iiantitv of salt particles was added to the \vater surface tin oughi the neck of tiR experimental vessel. These fell afl(l rapi(llv produced a diffuse cloud whichi occupied ¡ui st of t lit Vollinhi' of the vessel. The particles (IiSSOI ved (Illickiv and
ti ir rate f fall as rapi( 11v rt' luced. ()l1It ui in appeared to hc coin plete hcf ire any
u.. 2 i qS ,q) M l(LIANISM OF (AVITATEON
U) Incaur( Oint' froiiì the instant at which the salt was added and the oscilloscope
d{lect fl)lI Vas recorded at intervals of several seconds.
2 4) L L 4) 24 E o o 22 s-Is' ftH . f) ¡of) 40 30 ax10' cm 20 X )o t 200 Kc/s OKcJs
NX
o0 Kc/s X 800 Kc/s X XFig. 2. Absorption uf ultrasonics () for various frequencies in 2.2 1 distilled water at various times
after the addition uf 0.1 g commun salt.
Fig. 2 shows specimen curves of the excess absorption a- over pure water - with time. At first the absorption goes up as the air carried in with the salt is released, hut it subsequently falls as the bubbles either (IiSSO1Ve or rise to the surface. Bubbles which have a natural pulsation frequencv,10, near that of the source absorb the sound energy fastest. The resonant frequency is related to the diameter d (iii cm) by the
formula /0d = 657.
The process was followed by measuring in a van Slyke apparatus the air content in samples of water which liad been saturated in air. Fig. 3 shows how the air
dis-Long sordng water
lig, j. ( 1ìaiig of air content uf water after standing.
24 r'» 'höurSl L 4) o E L 4) a L o o 4) C n C .4 -3 1.x10 50 100 Seconds 200 20 o
1? ! ;i rS p. io6
/
I )( i. ;. RICHARDSON VOL. 2 (1958,
200 400 600 800 1000
Frequency (kC)
Fig. 4. Decay of ultrasonics of various frequencies in aerated water (a) at start (b) after 30 min (c) after i hour (W after 20 hours.
appears on standing and Fig. 4 gives results in the reverberation chamber at corre-sponding times.
CAVITATION OF WATER SUBMITTED TO CONTINUING PRESSURE
HARVEY2 and his colleagues have reported that water when subjected to large hydrostatic pressures for a short time does not cavitate even in intense sound fields.
According to them this process of "pressurisation" eliminates air hubbies, which act as cavitation nuclei, by driving them into solution. A study of the air hubbies in
pressurised water using the reverberation technique was therefore made. Pressures
UI) to 20,000 lb. 5(1.111. (7o4i atmospheres approximately) were employed using an equi)fl1cflt basically consisting of an hydraulic pressure intensifier connected to a pressure cvhimler in which the reverberation is placed for pressurisation. A reservoir
provides a reserve source of vater an(i the pressure is monitored with a standard
Bourlon gauge. A thin glass CVlifl(ler was USe(l as the reverberation vessel since it could convenientl be introduced into the pressure apparatus. The experimental procedure consists of initially filling the glass cylinder with tap water and determin-ing it5 reverberation time. lt is then placed in the pressure cylinder and subjected to a known pressure for some time. The pressure is then released and the reverbera-tion time of tut li(lui(l again determined. Çurve (a) of Fig. shows the condition of water before, the curves (h) and (C) after pressurisation. The decrease in absorption in(Iicatc(l by curves (h) and (C) is due to the entrained air going into solution. the interesting feature of these curves is tue finite amount of absorption still present, particularl in the neighbourhood of i Mc/sec. This shows that the largest bul)l)ICS
present have a radius of 3 (3 1 cm).
\n tilt noiuic cavitation test vas carried out on the Pressurised samples of \vatcr. Fhitse aiììiiles WCfl cofltaint(l ill thin glass test-tuil)es and subjected to tite same
/', fi ,e¡IN f). ¡ut'j
Fig. . I )ecav factors in aerated water; (a) nurnial (h) compressed at 5000Ik/in. (350 kg/ciiì)
(c) at 10,000 IL/in. ( oo kglcm) fur . h nirs.
Fig. b. I Tltras 4I1ic huwl tran.diicer irradiating water in test-tube shi)Wiii caVitation.
fii.h I was a spherical bowl of barium titanate approximately i ¡ cm (liameter and ° iniìì thick (Fig. 6). This was immersed in a light oil and when operated at 3o volts alÌ(l at a frequency of 442 kc1sec, produced a fairl' intense field at the centre of cur-Vat nrc. By regulating tuìe voltage on the transducer this intensity could be brought huiler control. A calibration of the intensity at the focus was carried out by
measur-1I1 t lii.' ra(liation pressure exerted by the sound field on a small steel bea(l SUSI)cfl(le(l
in a fuie wire froiìì one arm of a sensitive balance.
11 test-t tibes containing tite j)ressuriscd samples ol water were held at the focus ut tiic soitni I field and t in VIiltagc of t lic transducer was gradually increased in small
VOI.. 2 i ( MI;(IL\IsM 0F CAVITATION
io'
240 80 LI V C 40 (b>
:---20C) 400 bOO 800 loon Frequency >kc/16 u, o > 12 D o
r
u, Lr8
c o o o o 100 120 oir Saturationt"ig. 7. \ariation ot cavitation threshold for samples of water.
THE TWO TVI'ES OF CAVITATION
The bubbles that appear at tlìe onset of cavitation are generally of two kinds;
gas(air)-filled bubbles and vapour-filled bubbles. Gas-filled bubbles grow to visible size and then remain stable while vapour-filled bubbles expand and collapse explo-sively in a sound field. The appearance of the former (also referred to as degassing) is
not considered to be tite true sign of cavitation. The term cavitation is normally applied to the formation of vapour-filled bubbles because most of the theoretical
work in cavitation has been related to vapour-filled cavities. Such cavities are the ones whose collapse causes erosion. But this distinction is not critical since both kinds of cavitation must in the last analysis originate from microscopic cavities cavita-tion nuclei already existing in liquids. When the liquids contain dissolved gases these will diffuse into the growing nucleus and give rise to gaseous cavitation. L)uring the progress of titis cavitation, vapour-filled bubbles are also seen to grow and col-lapse so that the two cavitations exist side by side.
The bowl transducer of Fig. 6 was now set to beam horizontally in a tank filled
vitlì tue liquid under investigation. A short-focus telescope was focussed on the
region in which tite sound 1111(1 is concentrated.
\Vhcn tite tank is filled with aerated water (taj) water) and the transducer set going in it, a small rise in tite sound intensity is enough to cause the generation of a large number of cavitation hubbies at the focus. The focus is thus easily located. f the
sound prsslir' is further increased, cavitation bubbles appear on either side of the
focus and a cone of bubbles is formed vithì the apex at the focus. In dc-aerated water these l)tll)l)lt'5 do not appear.
\Vinn t lie tank is fillid with aerated water and the sound intensity is gradually
Ii' /tre flees p. i (
Io. J. (.. Ri('IIAIO)SON VOL. 2 (i5/59)
steps until the sample showed traces of cavitation by the sudden appearance of air l)Ui)l)h'S. hit \ ltage at titis instant was taken as the threshold for cavitation. 19g. 7 si tows how ti n' t Itresitolti de1)cn(ls on t lie air content.
increased, gaseous cavitation sets in at the focus. The onset of cavitation was recog-iìised by two nwtlìods. The first method was based on visual observation. A micro-sCOpe was used to observe the bubbles. The smallest bubble that could be seen through
it was of a radius of io¡. At the onset of cavitation, hubbies of this size suddenly appear one after another in rapiti succession at a region of the focus which is a
pressure antinode. They start rising in an oblique direction towards a pressure node. On the way the smaller bubbles coalesce to form larger ones, but more often the individual bubbles grow in size as they move forward and finally join a large bubble which remains trapped at one of the pressure nodes. These large bubbles grow larger
until their buoyancy enables them to escape the traps. When the sound field is
reduced in intensity below the threshold level, the small bubbles at the pressure anti-node decrease rapidly in size and disappear, while the larger bubbles, which
main-tain a steady size, either rise to the surface of the liquid and disappear or remain
supported by the sound field.
(i) (2)
Fig. 8. Records of noise (i) with, (2) without cavitation at 400 kc/sec.
The second method of detecting the onset of cavitation was through the noise the bubbles make while they are growing in a sound field. These noises are picked up by the same howl transducer which provides the incident sound field for cavitation, and are detected by a method which will be described under vaporous cavitation. Fig. S (i) is an oscillograph trace of the noise. Fig. 8 (2) shows the same trace
when the noise is absent. The frequency of the noise is in the region of 400 c/sec. As this is in the audible range, a pair of headphones may be used for aural detection.
This method of detecting gaseous cavitation is quite sensitive. Even before the
bubbles become visible in the microscope, the noise indicates the onset of cavitation. This method was found to be of great help in detecting gaseous cavitation in under-saturated vater, since in this water the bubbles sometimesnever grow to visible size. In taj) water vaporous cavitation starts at S volts, which corresponds to a pressure t hiresliold of 4.1 atmospheres. The individual bursts are just perceptible and they
occur roughly at the rate of one per minute. The amount of dissolved air has no
effect whatever on the threshold. The pressurisation of water increases its capacity to resist cavitation. The threshold for vaporous cavitation goes up quite considerably even for such small applications of pressure as 50 to zoo lb./sq.in. ( to 7 kg/cm2).
/t't/erent.s p. ioó
1. G. RI(11'iII )SON voi. 2 (z
f)
li lias 1l( t, lìowtver, lR'efl ¡ ' t precisely, as in the case of gascons cavil a-tfl)1l at vhat j)n'ssures tile cavitation starts again. ibis is l)eCatlSe 1u)t only is tue
lllilnl)ur o! cavitatim counts greatly (lecreased but the intensity of cavitation bursts is also very mud i reduced after a t jim.
(AVLT:VFION IN O'I'IIIR LIÇUI1)S
Many other samples of w ater vcre investigated. All natural waters contain more or less solid matter in suspension as well as (IiSSO1 ved gases and salts. '[hey all
reseni-bled tap water in cavitation behaviour with and without pressurisation. 1)istilled
vater which contains far less solid in susi)ension than tap water behaved in a similar manner. Sea water was very much the same. However, some interesting features of this water came to light during the experiments.
wo samples of sea water collected near the shore at different places were sub-jected to cavittion. They showed a low threshold, lower than tap water. The water was allowed to remain undisturbed for a few days. But once again at the end of the period, they showed the same threshold. The air content of the samples was examined. They showed undersaturation, the percentage saturation being 85. It was therefore obvious that sonic air in undissolved form existed in these samples. Inorder to detect its presence the reverberation method was employed. Fig. 9 is a graph of the excess decay against frequency. lt was obvious that a certain size distribution of bubbles existed, probably as gas entrained by the action of waves or produced by organisms near the surface.
50 1) 50 ' 40 L) 30 20 u X
Ui.
X/
200 400 600 800 1000 1200 1400 Frequercy Kc/sFig. 9. I )ccav factors in surface sea water.
X-Tite sea vater samples were pressurised at loo and 200 lh./sq. ill. (7 to x kg/cm2).
At the lower pressure they cavitated at 24 volts, while at the higher 'ssiire no cavitation could be effected.
h n tite present investigation nine organic liquids have been StU(lie(l and work is in hand on sonic commercial oils. They vcrc chosen from tIte point of view of their differing vapour pressures. The spherical glass 1)1111)5 referred to earlier were usen as
Coiìtainers of these hi(Juids. The' were placed at the sound focus and tite sound
inteii-sitv was gratlualiv increased to the cavitation level. hie onset (1f cavitation iii
t liese hi 1iiids is su(ld(n. At the threshold pressure a cavity sud(h'nhV apiRars iii tlit
V i.. 2 ( i5S '5g) MF(IIANISM OF (A1TAT10N
luniv of tlU' liiiii&I right at tut' SOIifl(l fOCUS, V('1V iìitich rescrnl)ling the vaporous
cavit at ioiì ii water L t I iii i ()LI11(l h\el. this is accolllpanie(l by a ¡)roflisi( n of air l)l11)l)1'-. H n ti irtslìoitl j)rcsslirts P1 art' giv'n in Tal le I. I'lnsc pressures are tift' ¡neail of at least teli OI)servatiOfls. lin' letter N (leflOtes ''110 cavitation''. ( )ften the
cavitation would start on tin' wall of tin bull) containing the li(iUi(I at 10W thresholds
and 1uicklv spread uit tt t lu 1i juid. \Vlìeiievcr this liai )pened the sound fiel(l would
be corn pleteiv shut off ami t lie li(1ui(l left undisturbed for a tjuarter to half an hour. 1f the sound field vas theiì (luickiv turned on, the cavitation in the interior was
observed to take place much before the cavitation at the vessel surface.
Lquzd (at o"C)
ï'.BLE I Pi, -t a 21 mío' 2.23 PC i.Acetaltlehv(le N 2. Is()pentallt.' oo ¡4 7. N 3. Ethyl etht'r 475 17 2.3 19.5 4. l'entan 400 2.3 ¡3.7 ..\ceton&' 20() 23 3.3 ¡5 6. Hexane ¡20 iS 3.2 10
7. Carbon tetracltl ritte loo 2(1 9 19
8. Benzene 50 2g 6.4 N
q. Tolut'ne 20 30 .5 N
va ¡n u r pressu n' in ni in ir surface tension (dynes/cru); 1 viscosity in poise: Pc cavitation t hreslu I in atm ispheres.
An attempt vas made to supersaturate the liquids with air and study the influence
of such saturation on cavitation thresholds. Tue liquid was placed in a flask and
with the help of an air pump the pressure on the surface of the liquid was increased to a desired value. While maintaining this pressure the liquid was kept under
con-stant mechanical agitation. In a few seconds the saturation went up, as could be
proved by using the air-content apparatus. A cavitation test of such a liquid showed no change of threshold. Under-saturation of the liquid aise (lid not affect the thresh-01(1.
As with water, the organic liquids contained in glass bulbs were subjected to
hydrostatic pressures from three minutes to half an hour. The maximum pressures employed were in the neighbourhood of 350 atmospheres. After releasing the pressure
the liquids t'cre introduced into the tank for a cavitation test. They showed no
cl ìange of cavi t at ion ti ireshold after pressurisation.
DISCUSS ION
urveving all these results, one can say that the existence of nuclei of the order of 50 u in diameter which encourage cavitation is definitely established in water
anti given a sanl1)h' we can give an estimate of their size aiid number, though if the range of size is large - it may IR' difficult to disentangle tite size-number
function. \\t' lìtve also estai)lishied t hat truly dissolved air lias no effect oiì the
iilCt1)t it iii of cavitation; t lie air imist be in discrete bubbles.
Received July 21, 19S
J)
E. G. R!C1LRI)SONvai. 2 (ig58/5)
1'1ìe frequency rangc of tli' reTrlXratiOfl rflethO(1 can he extendcd to cover small
bllI)l)1CS ami (k'tCCt them, j)r\1(((l their nh1I111)&r is sufficicntly large. For exaniple,
l)11l)l)lt'S of i
. ra(lius IÌdVC t volume v1ìiclì (>1 the order of ¡y12 cni3. Accor(ling to
CLICl1lttiO1i iii&1t' of t lic tltrt'slìold of (lctcCtiOfl, tue reverberation apparatus is
Cal)aI)l(' of detecting these l)U1)hlCS when at Icast a lìiindrcd of theiri are prescnt in each cubic centinmt'r of vater. The 'a1uc of this ii'iiniiinim increases quite rapidly as the l)ubl)le size (lecreases. Wíhcn the size falls to o.r u the number of bubbles needed for detection is of the order of io6 or even Io7 per cm3 when account is also taken of the fact that the threshold is a function of the frequency of the apparatus. Measurcnients of tlw excess (over the I)ure-\vatcr value) decay rate with the rever-heration apparatus were not possible in long-standing water. Evidently the number of nuclei in such water is far below these figures. There is
thus a limitation to the
usefulness of the method as a means of detecting nuclei below a certain size.That the nuclei below a micron size are fairly numerous in water may be inferred from the results of the many investigations carried out on cavitation. The effect of prolonged pressure seems to be to drive the nuclei into solution.
According to the organic skin theory3, when a pressure is applied to vater the larger nuclei are first crushed leaving the smaller ones intact. If these pressurised samples are subjected to cavitation, the threshold for cavitation will be determined mainly by the size of the largest nucleus present. Experiments show that the cavita-tion threshold is quite repeatable for a given sample pressurised in a given manner. This could be so only if a large number of nuclei of the same size were J)resent.
Organic liquids have few nuclei. If air is pumped in, it either dissolves or escapes. These results with organic liquids receive- from the point of view of their being
due to absence of nuclei - confirmation from other sources. PATTLE4 produced
bubbles of gas from a glass tip immersed in a liquid, and 1w photographing them as they rose determined the rate at which they vanished as the gas dissolved. Whereas bubbles of 50 or less could only be formed with difficulty in oil, and in clean de-aerated water disappeared within 3 mm, if the water contained protein they often reached a limiting size at which they became stable. At the other extreme, a so bubble in carbon tetrachioride had a life-time of only 15 sec.
Some investigators claim to have found a correlation between the electric break-down voltage and the presence of gaseous nuclei in oils. It is for this reason that we
are now extending the acoustic measurements on organic liquids to samples of
transformer oils.
REFERENCES
I
\I. STRASHERG, i'hesis, Catholic tniversitv, \Vashington 1). ('., I96. E. N. I I.RVEY, J. Am. (hem. Soc.,
b7 (5) ih.
.1 k. 1ox
Nt) K. 1. IIERZFELD, J.Acm,sf. Soc. Amer., 26 (1954) 9S4.
- R. E. I'\TTLE,