P. Naylor, A. fliliward
Department of 1echanical Engineering The University of Liverpool
P.O. Box 147
LIVERPOOL L69 3BX
THE EFFECT OF GAS CONTENT ON THE CAVITATION INCEPTION NUMBER
September 1981
Ta h e
o, DoLt
FP1/74/81D_CU,
TE :8- io t
A technique has been developed which allows the effect on the
cavitation inception number of the gas content in the water to be
predicted in cavitation experiments. The predicted results have
been compared with data obtained during experiments to measure
cavitation inception in the tip vortex of a low aspect ratio
hydro-foil and have shown good agreement.
The results showed that the gas content affected the cavitation
inception number significantly at low free stream speeds, particularly
Symbol Definition
P Absolute pressure at point of cavitation
res Residual gas pressure at cavitation inception
S Individual gas content at standard pressure
Smax Maximum residual gas content at standard pressure
U Free stream speed
p Water density
°ci Cavitation inception number
Contribution to due to vaporous cavitation
Suffixes
A Atmospheric pressure
N,O,C Quantities related to the gases nitrogen, oxygen and carbon dioxide
The present work on the effect of gas content on the cavitation inception number forms part of a larger project concerned with
predicting the inception of cavitation in the tip vortices shed
from a low aspect ratio hydrofoil. Although the effect of gases
in the water on cavitation inception has been described qualitatively
little information appeared to be available to allow this effect
to be predicted quantitatively despite its importance on the data
obtained in an experiment.
The gas content of the water can affect cavitation in two separate ways:
Discrete gas bubbles may cause momentary aeration or cavitation within the vortex shed from the hydrofoil,
a problem which is usually disregarded since in a
relatively bubble-free environment such as the open sea
or a towing tank, this effect is negligible. In other
facilities such as the water tunnel used in these
experiments, discrete gas bubbles are present but their
effect can be minimised by ignoring discontinuous
cavitation and by choosing the operating conditions
appropriately.
The gas dissolved in the water can affect the onset of
cavitation. In general water is a solution of gases
-usually those found in the atmosphere which are mainly nitrogen and oxygen. The quantity of these gases
present determines the onset of cavitation and it is
with this important topic that the present work is
The cavitation inception number °ci' was defined as: P -P
OV
Gd
-
1 2pU
where po was the undisturbed static pressure in the free stream at the
depth of the vortex core, P and p were the water vapour pressure
and density respectively at the relevant temperature and U was the free stream speed. From this definition the experimental values
of
°ci were calculated.
In order to predict this quantity an analysis was carried out
to find the effect on of varying the hydrofoil parameters such
as chord, aspect ratio etc. and also of the gas content of the water.
It was assumed that the effect of these various parameters on the
cavitation inception number could be separated into
°ci = °o + °res (2)
where and
°res were the contributions from the hydrofoil shape and the gas content respectively. An analysis will be presented
elsewhere showing the method of calculating o, but for these
experiments it was adequately assumed to be unity.
°res was known as the residual cavitation number and was defined as:
re s °res 1 2 pU where
res was the residual gas pressure in the vortex core.
A preliminary investigation suggested that at atmospheric pressure
cavitation in the tip vortex shed from the hydrofoil would not occur below free stream speeds of about 10 ni/s. Since the maximum speed
available in the cavitation tunnel described later was 6.4 rn/s the (3)
conventional approach was adopted of reducing the overall pressure
in the working section. In practice the lowest pressure that could
be obtained allowed the experiments to be conducted at a relatively
low free stream speed where, as might be expected from [qn. 3, the
effect of Gres was more pronounced.
The procedure was to perform experiments to measure as defined by Eqn. 1 and also measure the quantity of gas present in
the water usi ng the normal Van Slyke manometric apparatus. The experimental runs consisted of measuring the variation of with
free stream speed for different gas contents and these results were
used to show that a simple theory could be applied to predict the
effect for future use.
2. THE CAVITATION TUNNEL
The facility in which the experiments were carried out was the University of Liverpool recirculating water channel. This is
a versatile facility capable of allowing tests on submerged and free
surface devices to be carried out. It includes apparatus for generating
moving or standing waves. It can also be operated as a cavitation
tunnel and it was used in this configuration for these experiments.
A schematic diagram is presented in Fig. 1 and further details of
this facility can be found in Ref. 1.
The dimensions of the rectangular working section when operating
as a cavitation tunnel are: length 3.66 metres, width 1.37 metres
and depth 0.84 metres. The speed of the flume is continuously variable
up to 6.4 rn/s and is controlled with a calibrated vernier potentiometer.
When the cavitation work was undertaken the absolute pressure
pressure attainable was 30 mm of mercury absolute and this was measured with a mercury manometer. From this nieaurement po was
found in Eqrì. i since the depth of the cavitating vortex core and the free stream speed were known. Other required measurements were the water temperature and gas content. The fornier was measured
using the thermometer situated as shown in Fig. i and the latter
using the Van Slyke manometric apparatus with a water sample collected
via a tapping hole in the water channel. A syringe was used to draw
the water against the internal low pressure enabling gas content
measurements to be taken without re-pressurising the flume.
3. THE EXPERIMENTAL METHOD
For this sequence of tests when the interest was in the effect of gas content only it was thought sufficient to use only one hydrofoil blade and to fix the various parameters determiflinfl its performance.
A NACA 0015 symmetrical section hydrofoil was used with a chord
of 0.2286 metres and aspect ratio 2. The hydrofoil was in fact square and was mounted against a surface with only one exposed tip thus making the usual assumption that the surface acted as a reflection plane. The angle of incidence was chosen to be 10 degrees in order to generate a strong tip vortex without incurring the risk of stall. The
hydro-foil was mounted in the roof of the cavitation tunnel as depicted in Fig. 1 using securing bolts.
Cavitation was observed visually in the tip vortex with the aid of floodlights and the vantage point and lighting arrangements remained the same throughout the tests to achieve consistency. The results
could have been obtained in two ways, but only one was found to be practical.
The first and less successful method was to fix the flume speed
and reduce the absolute pressure gradually until cavitation was
seen to begin in the vortex core. This was perhaps the more desirable
method since the flow was steady, but the longer operating time
necessary while the pressure was reduced allowed large quantities
of gas to forni as discrete bubbles, rendering cavitation difficult
to observe. Also the longer operating time allowed the quantity of
gas dissolved in the water to be reduced thus altering the experimental
conditions.
The second methoi,which was the one used, was to fix the pressure
and then slowly increase the speed until cavitation occurred. This gave satisfactory results and was considered accurate providing the
flow was accelerated slowly in order to reduce unsteady effects. By choosing the pressures, cavitation was caused in a range of speeds from 1.5 to 4 rn/s.
The gas content of the water was varied from its saturation
quantity, which had been obtained by simply allowing the water to dissolve air over a period of time, down to less than 10% of this quantity. Unfortunately the flume did not have deaeration apparatus
fitted and so this gas content could only be randomly varied. The procedure was to operate the flume at a speed over about 4 rn/s while de-pressurised to about 40 mm of mercury absolute. This was carried
out for a short period of time, after which measurements showed that the gas content had fallen by the desired amount. An experimental run
was then performed before the air was re-dissolved taking care not to operate the flume for too long which would reduce the gas content further.
The measurement of the gas content was carried out using the
of many methods reviewed by Morgan (Ref. 2) and was chosen as
being a simple, cheap and accurate method for the tests. A history of the apparatus can be found in Ref. 3. The particular product
used here was provided by GallenKampf Suppliers as a clinical
apparatus. The way in which the equipment was worked was to seal a known volume of water - the sample - with a known quantity of
atmospheric air and then to agitate these under a much reduced pressure using a magnetic stirrer to release the dissolved air.
The pressure then necessary to return the water and the air to
its original volume could be used to calculate the volume of released air. Provided that the instructions were carried out and care was taken the measurements were consistent. The length of time required
to take a measurement - about 40 minutes - allowed several to be taken during the experimental run and so the values of gas content
given later represented mean results.
The cavitation within the vortex shed from the hydrofoil's exposed tip was visible in the floodlighting as a thin silvery trace about 4 mm in diameter. It originated suddenly and at about a half a chord length aft of the hydrofoil trailing edge. Owing to its
sudden appearance and the continuous nature of the cavitation little doubt was associated with measurements at the moment of cavitation inception and little scatter was thus evident in the results.
4. THE THEORETICAL PREDICTION
Water, as a solvent, can dissolve certain quantities of various gases depending on environmental factors such as temperature and
pressure. It has been established that the small quantities of gases dissolved in the water do not affect the water's capability to dissolve
another gas independently, acting as though the other gases were not present. Consequently the three main gases assumed to be
dissolved in the water (nitrogen, oxygen and carbon dioxide) can be treated separately. The maximum solubility of these three gases
in water has been tabulated in Ref. 4 for varying water temperature at a pressure of 760 mm of mercury as standard. Use was then made of
a well established result (Ref. 5, for example) to relate the
maximum solubility at a given water temperature to the absolute pressure. This is a linear relationship, the maximum solubility
for each gas, Smax at an absolute pressure P, being given by:
s = s
max maxA
where SmaxA is the maximum solubility of each gas at atmospheric pressure
In a practical case .here the quantity of gas dissolved in
water is less than the maximum amount possible at standard pressure, then gas is not released as the pressure is lowered until a pressure
is reached where the quantity of gas present becomes the maximum possible at this pressure. When that critical pressure is reached,
gas is released and aeration of the vortex core would be observed in
these experiments.
When the cavitation inception number was defined in the
introduction, [qn. 1, it discounted any effect of gas content in the water. To take account of this effect it was necessary to modify the definition slightly. This was achieved by replacing
v' the vapour pressure of the water, by a new quantity including a term dependent
on the residual gas pressure in the vortex core. The numerator of [qn. 1 was calculated as the difference between the station pressure
in the undisturbed flow at the same depth as the water and the water
vapour pressure, but in fact represented the difference between this
static pressure and a quantity dependent on the water vapour
pressure and the residual gas pressure in the vortex core. To
deter-mine analytically the cavitation inception number to compare with the experimental results, it was necessary to include the residual
gas pressure in the vortex core as shown in Eqns. 2 and 3.
The residual gas pressure in the vortex core when aeration was observed was recognised to be the critical pressure below which
gas was released.
Since there were three main gases present, the graph of the
total gas content of the water against the critical pressure was
separated into three linear regions, the sizes of which were dependent on the relative quantities of the three gases. By referring to
Fig. 3, it can be seen that the residual gas pressure in the vortex
core due to the three gases, nitrogen, oxygen and carbon dioxide
(quantities suffixed N, O and C respectively) was given by:
resN = (5)
presO = (6)
resC =
(7)
where SN, and S were the quantities of the three gases present at
atmospheric pressure and N, O and C were the gradients of the
solubility lines in Fig. 3. These lines were calculated from tabulated
values of the maximum solubilities at standard pressure and were:
N
SAN
etc. (8)
Aeration in the vortex core should be observed when the static
pressure in the core dropped below the highest value of 1res for
the gases present.
5. DISCUSSION
For the particular experiment carried out here, the water in the
flume was degassed steadily. It was to be expected that the relative
quantities of individual gases present would change with the total
gas content owing to the difference in slope of the
solubility-pressure lines. Also, the Van Slyke manometric apparatus in the
particular configuration used here found only the total gas content
of the water. Consequently, to match the experimental results
with the theory above, the graphs in Fig. 3 had to be summed, and
the relative quantities of the gases were estimated from the data.
From the experimentally obtained curves of cavitation inception
number against free stream speed, shown in Fig. 4, values for the
residual gas pressure, eres' were calculated by assuming that
was unity - in later work this was shown to be a simplification, but
within the experimental error expected for this experiment and by
plotting curves
°cj against 1
2' the gradients of which were values
pU
for 1res Equivalent values for the total gas content of the water
in the flume were averaged from at least eight results taken during
each run. On plotting these experimentally obtained values for 'res and the total gas content, S, three distinct regions were evident. These three regions could be fitted by lines assuming initial values,
that is, before the first run was performed, of the nitrogen, oxygen
and
so res0
= SmaxAO
water respectively as shown in Fig. 5. These values, representing
relative quantities of 51%, 36% and 12% respectively, do not exactly
match the tabulated values (Ref. 5) of 63%, 34% and 0% for the
constituent gases of air at the relevant temperature. This was
probably caused by prior agitation of the flow, thus reducing the
nitrogen content first and the absorption of some carbon dioxide
possibly via the flume feed water.
The above discussion explains how the experimental data were
matched to a theory describing the shape of the curve resulting
when the total gas content of the water was plotted against the
residual gas pressure in the vortex core. For practical application
to any given case, the quantities of each gas per unit volume of
water have to be measured. For most experimental purposes the amount
of carbon dioxide present can be ignored as negligible.. Should the
water being used for the experiment have not been exposed to any
unusual effects, for example, high temperatures, passage of any
gas through it, low pressure, etc., and consequently only absorbed
air from the atmosphere is present, then tabulated values can be
used to give the relative amounts of nitrogen and oxygen for a given
temperature since the noble gases can also be ignored. The total gas
content can be found using a relatively simple device like the Van
Slyke apparatus and hence the actual quantities of nitrogen and
oxygen can be found. Using then Eqns. 6 and 8 applied to each gas
gives:
sr» resN
Examination of Eqns. 2 and 3 shows the reason for the shape of
the cavitation inception number against free stream speed curves
shown in Fig. 4. For low free stream speeds, the quantity °res was large and dominated the right hand side of Eqn. 2. At speeds
above about 4 m/s in this case the effect was minimal, but was difficult to assess due to the difficulty of observing aeration or cavitation at higher speeds for relatively large gas contents. In a later series of experiments the gas content was much reduced to allow observation of aeration, if any, or cavitation at high speeds.
The probem of seeing the aerated vortex core at high speeds and
high gas content is pe aps peculiar to this cavitation tunnel
and should not occur if the experiments were performed in a de-pressurised towing tank, such as that at NSMB, or a water tunnel with air
re-absorption ducts.
In considering the overall result it is possible that some errors
could have occurred during the experimental analysis for several reasons. At low speeds, a small change in speed had a large effe::t
tne cavitation inception number and so some error may have resulted
in misreading the speed dial, observing the onset of cavitation
wrongly or adjusting the speed control too quickly. Other errors
could have been caused by missing the moment when cavitation or ven-tilation actually began. This could have been caused by distractions
such as a gas bubble momentarily aerating the vortex core. Such events however were not significant owing to the large quantity of experimental data collected over the whole test. Errors were not
large as the small amount of scatter shown in the experimental curves
in Fig. 4 bears out. In order to estimate the residual
in the vortex core, it was necessary to replace by unity as
dis-cussed earlier. This was shown later to be of the right order of
magnitude and as Fig. 5 shows, resulted in little error in the
correlation between residual gas pressure in the vortex core and the total gas content of the water.
A point that was considered is that previous work in this field has alluded to the onset of cavitation caused by nuclei in the flow. Such nuclei could be of several causes, dust and discrete gas
bubbles being the major ones. The flume had a filter fitted to
eliminate particles greater than fifteen microns in size. This was not used and was sealed off during the cavitation experiments
themselves because of a faulty seal on the pump. t was usrd between experiments however and this would have reduced the size and quantity of particles present. Further work might be carried
out with different filter sizes to test the dependence, if any, of particle size on the cavitation criteria. In this work, however,
no account was taken of the effect of nuclei and the theory produced
still described the experimental observations well. It is likely
that sufficient nuclei were present in the flow, causing the aeration
or cavitation of the vortex core to occur as soon as the necessary pressure was reached. Too few nuclei might have caused the delay
of cavitation although this was not observed.
Another point of interest was that for aeration especially the vortex core continued to aerate oc cavitate after the pressure was raised slightly above the critical point, or the speed was reduced,
quite often appreciably, below the critical value. The less gas
there was present in the water, the less this effect was apparent, implying that it was caused by the presence of gas probably not
was noted by McCormick (Ref. 6) and explained in the same way.
6. CONCLUSIONS
The effect of gas dissolved in the water on cavitation, was to allow cavitation or to be precise, aeration of the vortex core to occur at higher pressures or, conversely, lower free stream speeds
than otherwise would be possible with no gas present. This effect
was especially marked at low free stream speeds, in this case below about 4 rn/s.
The gas content of the water had a quantitative effect on the cavitation inception number described by:
P
Cl = O +
res
where at low free stream speeds was very small relative to the gas content effects and was approximated by unity.
The present work has shown that values of eres can be calculated from initial measurements of the gas content of the water thus
allowing the effect of the gas present in the water on the cavitation inception number to be predicted.
REFERENCES
1949.
1. J. -I. Preston 'Design of high speed free surface water channels'. Proc. NATO Advanced Study Inst., Surface Hydrodynamics, Bressanone, 1966. pp. 1-82.
2. W. B. Morgan 'Air content and nuclei measurements', 13th Tnt. Towing Tank Conf., Berlin, Hamburg, 1972.
3. J. P. Peters, and 'Quantitative clinical chemistry. Vol.
D. D. Van Slyke 2, Methods', Bailliere, Tindall and Cox, London, 1946.
4. C. D. Hodgman (Ed.) 'A handbook of physics and chemistry', Chemical Rubber Publ. Co. Ltd., 32nd Ed.
5. G. N. Sawyer and P. L. McCarty
'Chemistry and environmental engineering', McGraw-Hill, 1978.
6. B. W. McCormick 'On cavitation produced by a vortex trailing from a lifting surface', J. Basic Eng., Vol. 84, p. 369, 1962.
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Schematic
diagram of Van Slyke manometric
apparatus for evaluating the total
gas content
of a water sample.
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Thermometer
Water jacket
Extraction pipette
t'vlaynetícciuy stirred
water sample
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SmaxO
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Pressure in vortex core -*
FIG. 3
raph showing variation of the
gas content
of the water with pressure in the
vortex
core for the three gases. nitrogen,
oxygen
and carbon dioxide observed to be
present.
Standard
pressure
cl) E C C
