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OCR for page 639
On the Flow Structure, Tip Leakage Cavitation Inception
and Associated Noise
Shridhar G opalan', H enry L Liu2, Joseph K atop
('The Johns H op kins U Diversity, U S A N aval Surface W arfare C enter, U S A)
ABSTRACT
Th objective of 6 is study is to investigate
the effect of gap size on She flow tructure md on She
inception of tip leakage cavitation Conholled
cavitation tests w ye performed after de~ercting She
water m the tunnel md usi g electrolysis to generate
cavitation m lei Th experiments consisted of
simultmeously detecting cavitation inception c
200 fps digital camera (visual) md two
accelerometers ("acoustic") mo mted on th test-
section windows Good cg cement between These
methods was achieved when the visual observations
w re performed carefully Po nom of the signal
containmg cc itation noise w re analyzed using
Hilbe t md Wavelet t msforms in order to obtain She
time depende t pectra, rates of cavitation events es c
fixation of the cavitation index (a) for She 3 gap sizes
(O 6, 1 4, 2 6mm) w re measured The observations
clearly demonshate that high amplit de noise spkes
are generated when the bubbles are disto ted md
"sh edded" broken to several bubbles following thei
g owth in th vortex cme Mbre chmg s to bubble size
md shape ceased sigmiScmtly low r noise High
resolution Particle mcge Velocimetry (c Rector
spacing of 180 m) was used to measure be flow,
especially to ccptme the slender tip vortices where
cavitation inception was observed Seventy
imt mhneous realizations for the 0 6mm gap md 65
for She 1 4mm gap w re crurly:D:d to obtain
di tobutions of circulation of She leakage vortex Prv
experiments for She 2 6mm gap are presently
mde way md only mstmtmeous samples are
presented The vortex cme diameter was fo md to be
3-4 vector spacings Minim m p~essme coefhcients in
th cores of th se vortices w re estimated using c
h~nlnne model These coefhcients show d c why
good cg cement with th mecsmed cavitation
inception indices
INTRODUCTION
Cavitation occurs m liquid flows whey c
m lens Bubbles, particles etc ) is ccptmed m c region
where She pressure is low r or equal to the vapor
pressure lAmdt 1981, Brenren 1995, Joseph 1998)
Such low-pressure legions could be et the cores of
vorticcl ml need which occur very frequently m
shear flows Lutz & Cat Hem 1986, Cat Hem 1991, Han
& Kilt 1994, Gopahm et cl 1999, Bekhadji et cl
1995) in such cases inception of cavitation is marked
by mtemmittent eve ts Experimental tudies on tip
vortex formation md cavitation have l en add essed
(for e g ) by Mames md A ndt (1997), Higuchi et al
(1989) md c m mericcl st dy of stecdy-state tip vortex
has been reported by Hsico & P mley (1998) Several
papers in recent y ars have dealt with cavitation in tip
leakag or tip clearance flows As c result of the gap, c
tip leakage vortex develops which is prone to
cavitation Farrell & Billet 1994, Boulon et al 1999)
Farrell md Billet (1994) examined She effect of gap
sine on tip leakage cavitation md fo md that th
cavitation inception mdices increased with demecsmg
gap sins They also fo md c cavitation inception index
minima near ~ ~0 2 (\ is th ratio of the tip gap side to
the maxim m tip thickmess) Cormersely, experiments
perfommed by Boulon et cl (1999) do not show c
minim m in She cavitation inception index Their
observations could be e Shined using c potential flow
model (elaborated in Boulon et cl md briefly m
section 4 of 6 is paper)
In She present tudy the 13110 in g issues will
be add essed (i) cc itation inception measurements
using bodh isual md acoustic techniques, (ii) bubble
dynamics during ca vitation using c high- peed camera,
(iii) c comparison hen al th acou tic signal md She
~ me of cavitation, including detailed spectral
analv is of She signal, (iv) shuctme of She leakage
flow using Particle hmege Velocimeby PPV) md th
effect of gap size on leakage flow characteristics Plots
of cavitation index, t august rate of cavitation events
(r,) are obtained m m lei co trolled conditions Thl ee
gap sins of 0 6, 1 4 md 2 6 w re st died (\ = 0 12,
0 28, 0 52) Cavitation events w re record d using
accelerometers attached to so mdoss s of the test section
A high- peed camera et 200 d,hs was used to record
the motion of bubbles es Hey interacted with She core
of She tip vo tex Th observations demonshete clearly
OCR for page 640
that high noise spikes occur when the bubbles break
up in the vortex core. Oscillation in bubble size and
shape cause significantly lower amplitude signals. PIV
experiments were conducted using an inclined light
sheet so that a cross-section of the tip leakage vortex
could be captured. One purpose of these
measurements is to estimate minimum pressure
coefficients from the circulation and compare it to the
experimental cavitation indices. The results show a
very good agreement.
(a)
surface:
turning
vanes
filtering
Ullit:
floor la el ~~;~
15 HP pumps
(b)
0.4~
0.3:
~ to vacuum pump / compressed al
_ _honeycomb root
_ ~ test section r
flown
O _
Side view ,
\\\\1
2~0" - ~ \\
~ ~ art''
Top view
~ =
Figure 1: (a) Experimental facility and (b) close-up
of the test-section.
EXPERIMENTAL SETUP AND PROCEDURE
The experiments were performed in a
specially designed water tunnel located at Johns
Hopkins University (figure la). The 6.35 x 5.08 cm2
test section has a minimum length of 41 cm and
./
/
0.2
0.1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0.25 0.5 0.75
tip
Figure 2: Lift distribution for the hydrofoil,
span=50mm.
maximum entrance velocity of 13 m/s. It has windows
(made of optical grade lucite) on four sides to enable
easy access for PIV and holographic measurements.
The constant chord hydrofoil with a chord length of
50mm (and a span of 50 mm) was attached to a side
window and its tip had a small clearance with the
other side window (figure lb). The maximum tip
thickness was 5mm (at mid-chord) and was loaded
towards the tip. Figure 2 shows the lift coefficient for
this hydrofoil at 0° incidence angle. The clearance (or
gap) size was varied by varying the thickness of the
side window. Boundary layer suction and tripping
were installed on the wall near the tip as shown in
figure lb (side view) to generate a fully developed
turbulent boundary layer on the wall. The flow was
driven by two 15 HP centrifugal pumps located about
4 m below the nozzle in order to prevent pump
cavitation. In this study the free stream velocity in the
test-section was fixed at 5 m/s (Rec. based on chord (c)
equal to 2.5x105) and the cavitation index was
controlled by varying the ambient pressure in the test
chamber. The air content was reduced to about 3 ppm
by keeping the facility under vacuum for extended
periods and the dissolved oxygen content determined
using an oxygen meter. The cavitation nuclei were
supplied by electrolysis with two vertical wires,
located upstream of the test section next to the
honeycombs shown in figure 1 a. The bubble
generation rate (approximately 2500/s) could be
controlled by varying the current through the
electrodes. The nuclei size distribution generated by
this setup was measured (figure 4) and varied between
50-250~m with a median at approximately 100~m.
Two accelerometers (PCB309A) with a resonant
frequency of 120kHz were used to detect cavitation
events (figure 3a); one was attached to the side
window and the other to the bottom window, both at
the vicinity of the blade trailing edge. A high-speed
OCR for page 641
(a)
(b)
..
Y~ c24/-t~.Y - .1.~
~A~,,~
1~"~" ~-~}
_ 1~
\ (7)~
\ FIDC ~ h~ 1.~/
\/,<\ C~-I
\ \
7K,~g ~or~wib \ \
\/
Figmre 3: Setup for (a) visual and aeousde detection
of cavitation e\peri ments j fh) PIV e\peri ments.
camerz Kodak Ekbpro M Motion Analyzer, Model
1012) zt 2000fps was used to record cavibting
bubbles m fhe tip leakage vortex These fiames w re
coupled with the acelerometer signals, providmg z
good conelation between fhe physical zppearance of
the bubb le s du mg cz itat i on md fhe ace ler ometer
signals A Dztz Trmshtion A-D board capable of
sampling rates up to 1 33M a was used, md datz was
aqui cd zt 250kHz/chumel usmg LzbView software
Th acelerometer signals were arudy:osd usmg m m-
house code, so that cavitation events could be coumted
(z sample m figme 5) md high-speed fmmes could be
tagged wifh th noise signals (z sample m flgme 7b)
PIV experiments were pe formed wifh z dual-
head Nd:YAG laser mted zt 30mJ/pulse (flgure 3b)
A inclmed iight sheet (show m figme 3b) was
0 2m 500
lame er (~m)
Figmre 4: Cavitation mmelei 7ize dflstribudon
mrasured just upstream of the Iradflng edge of the
hydr of oil.
necessary to measue fhe shengh of fhe leakage
vortices Wh n m mgled sheet (zt m mgle a) is u cd
in z medium (i e water md boumded by material of
diffe~ent refiative ind:x, i e lu ite) fnat is different
thm fnat of fhe recording device (i e armerz m zir), z
proper mte fae at m mgle, Y. given by
tmyltma=n,-~/n~ (whre n is th refrative
index) needs to be created Th trimgmlar cmister
zttsched to fhe side wmdow is made of Lu ite md
filled with Dow Coming 550 fluid, which has z
refiative mdex of I 5 (same zs lu ite), creatmg fhe
interfaes show in flgme 3b A 2K x 2K pi el~
camerz with hardwmebased image shfftmg was u cd
to record doubly exposed pulse separation, 51us),
dff~sely seeded P V imag s A color filter zs indicated
in flgure 3b was used to minimi:os 6he mcide t light,
zllowing only the emitted hfht fiom the flumescent
traer particles to be recorded (SridEsr & Kztz 1995,
Gopz m & Kztz 2000) A m-hou e developed code
Do g et zl 1992, Roth et zl 1995, Roth & Kzt
2000) was used to arudyze 6he images, indially with z
64 x 64 pi el~ mtenogation wmdow md 32 pixel
spamg Thff~ using 6he ouput of 6he flr t rum as z
"gmess mput" for 32 x 32 pi el~ mterrogation wmdows
md 16 pi cl spai g, denser velocity dishibutions
w re obtzmed Such m zpproah is feas~ble only when
the~e is enough i formation in z 32 x 32-pixel
window, ~equiring deme particle seedmg Wi6h suh
m aproah, very high~esolution velocdy flelds wi6h
vector spamg of 180 m could be obtzmed Such
OCR for page 642
Figure 5: A sample accelerometer signal showing
spikes caused by cavitation.
CAVITATION INCEPTION INDICES AND
BUBBLE DYNAMICS
Accelerometer signals like the one shown in
figure 5 were analyzed to obtain plots of cavitation
index vs. rate of cavitation events (rc) for the three gap
sizes, all at a 1° incidence angle. The results are
plotted in figure 6. The cavitation index is defined as
c;=(PO-Pv)/0.5pV2 (PO is the ambient pressure in the test
section, Pv is the vapor pressure, V is the free-stream
velocity, 5 m/s, and p is the density of water). The
code used to count cavitation events (in a lOs long
signal sampled at 250kHz), first identifies points
greater than 1.2V then searches for amplitudes 2 3.3 V
in a time interval of 0.06ms from the original point. In
order to avoid counting the same event several times,
the program would jump 1.4ms after finding an event
and then continue. It can be seen from figure 6 that for
'\ ~ ~
11.51
11,
1OI
9.51
9[
_ 5-~6= 1 1 .¢ ~ ~
- \7 i' :1 \ A
-T ~
_ iV WN ~
~ /\$ `~78 rC078
_ _ _~_r\\ 6=l U.l ~ ~ 6=1 6-56 rc
- V s I ~ /\ gap=0.6mm
- %7, ~ ~ ~ gap=1.4mm
- 6=42.67 rats ~ ~ ~ gap=2.6mm
_ _ 6-9.0 _ _ ~ `~ 6=10.3 r-04
rc (so)
p(~
Figure 6: Rates of cavitation events.
all three cases the event rate increases with decreasing
c; and both the inception indices and event rates
increase with decreasing gap sizes. As an example at
OCR for page 643
t
3~ time' ms
x ~04 Hz
I....;.;.
Figure 7: (a) A high-speed series (frames 1493-
1498) at 2000fps (gap=0.6mm). Flow is from left to
right with suction surface visible (c,~104; (b)
corresponding accelerometer and strobe signals; (c)
Wavelet and Hilbert transforms of the
accelerometer signal. Frame timings are indicated
by dashed lines.
10 events/s, c; for the 0.6mm gap is 11.5 as compared
to 10.1 for the 1.4mm gap and 9.0 for the 2.6mm gap.
The slope of the 0.6mm gap is also quite different than
the 1.4 and 2.6mm gaps. Since all experiments are
performed with the same nuclei distribution, the
substantial differences in event rate indicates that the
probability of finding low-pressure regions for the
0.6mm case is significantly higher than the 1.4mm and
2.6mm gap sizes. It is worthwhile to observe that in
later stages of cavitation for the 2.6mm gap, the curve
becomes much flatter (data for 1.4mm gap at these
pressures were not recorded but one may expect a
similar trend). This trend occurs due to the increased
concentration of nuclei from prior cavitation events, a
self-feeding phenomenon. Equations of power fit
curves for the three gaps are also shown in figure 6.
In this project we have verified that the
acoustical and visual detection of cavitation match
OCR for page 644
8 ~~ i. ~~ ~~:~ He'd ~~— if. I:? ~, ~~ ~~ ~~:~
I'd ~..7'~'~", A.:) 'I.. '.:.... ~~ ~.~ A..:'....'.. ~ A. ';:~.'.~".Q >.~'f..~ - ~ I'd
:::: g~
Figure 8: (a) A high-speed series (frames 729-734)
at 2000fps (gap = 1.4mm). Flow is from left to right
with suction surface visible (c,~104; (b)
corresponding accelerometer and strobe signals; (c)
Wavelet and Hilbert transforms of the
accelerometer signal. Frame timings are indicated
by dashed lines.
reasonably well. In almost all cases the acoustic spikes
appeared when we could detect bubbles some where in
the vortex core. Three random samples of high-speed
image series at time intervals of 0.5ms are presented in
figures 7, 8 and 9 (top views) for the three gap sizes.
The corresponding accelerometer signals are shown in
figures 7b, 8b and 9b. We have carefully examined
several matches between "acoustically" sensed
cavitation and visually observed cavitation. The
differences in bubble size and noise signals are not
characteristic to their respective gap sizes, i.e. bubbles
of all sizes in the range shown appeared in all gap
sizes. In figure 7a, the cavitation noise begins at frame
1495, where high amplitude noise is emitted by the
bubble on the left as it grows gets distorted and
fragmented along the vortex core (frame 14964. The
bubble on the right also experiences a similar
condition in frame 1497, resulting in further noise
emission. Later the bubbles are merely convected with
substantial reduction in the amplitude of the noise. In
figure 8b the cavitation signal occurs for a very short
time and is tagged to frame 733. We do not get a large
signal for the bubbles shown in frames 730-732,
although the bubbles clearly change shape and size.
Conversely, frame 733 shows the bubble quite
distorted and fragmented and a corresponding high
amplitude noise. Figure 9 shows a high-speed
.... ~~
...............
................. . ~
1
OCR for page 645
~Hilber1
~ :: ~~
.. in: ::
: ~~ :
I.::.
~~ :. ~:i:
Figure 9: (a) A high-speed series (frames 1299-
1304) at 2000fps (gap = 2.6mm). Flow is from left to
right with suction surface visible (c,~10); (b)
corresponding accelerometer and strobe signals; (c)
Wavelet and Hilbert transforms of the
accelerometer signal. Frame timings are indicated
by dashed lines.
series for the 2.6mm gap. One can observe that the
bubble moves towards the wall (consistent with the
trajectory of the leakage vortex for the 2.6mm gap)
while changing its shape. Cavitation starts at frame
1303 and continues on till frame 1307. The peak in
noise occurs at frame 1304, where the bubble is highly
distorted and fragmented again similar to previous
series.
Thus, several such high-speed series
examples indicate clearly that high amplitude noise
during cavitation is primarily due to the growth,
distortion and fragmentation of bubbles. Merely
changes in shape or volume of the bubble generate
substantially weaker noise signals. Spectra of noise
signals using Wavelet and Hilbert transforms (Huang
et al. 1998) are shown in figure 7c, 8c and 9c. In the
spectra of figure 7c several distinct peaks at 8, 12, 17,
22, 28 and 48kHz are observed whereas, in figure 8c
the energy is concentrated in a very narrow band
between 22-28 kHz range, with a sharp peak at 25kHz.
The multiple bubbles in figure 7a apparently
·.......
Figure 10: A 0.25s exposure showing the trajectory
of the bubbly tip leakage vortex as seen in a side
view (figure lb), for gaps of (a) 0.6mm; (b) 1.4mm;
(c) 2.6mm. Flow is from left to right. The hydrofoil
with its trailing edge and tip is visible on the left
edge of the images.
1
~ _
8.5 _
~ _
~ 7
-
>,6.5
6
_ _
7.5 _
5.5 _
~ _
4.5 _
~ - 1 1 1
ma..
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 0.5 1 1.5
gap size (mm)
1 1 1 1 1 1 1 1
2 2.5
N:
Figure 11: Vertical distance of the tip leakage
vortex trajectory from the trailing edge (by).
OCR for page 646
contribute to more complex spectrum. In figure 9c
peaks at lOkHz, 22-25kHz and 30 kHz can be
observed. Background noise measurements showed
extremely weak peaks at the bubble resonant
frequencies that disappeared when the bubble
generation was stopped. There were no other external
noise sources in the 10-40kHz range.
free-stream velocity = 5 m/s
(a)
0.1
0.05
O .
-0.05
$-0.1
-0.15
-0.2
-0.25
-0 3 ~ ~
~ _ ==, =_=. ~ ~
1 ~==~ = Li
wall 0.1 0.2 0.3 0.4 0~5
X'/C
,. \
. ._ . . ~
-0.1
Figure 12: (a) A sample instantaneous velocity field
(vector spacing of 180~m); (b) Zoomed-in portion
of (a), highlighting the cross section of the tip
vortex.
Figure 10 shows an extended exposure image
of the trajectory of the bubbly tip leakage vortex as
seen in a side view for the three gap sizes. The
hydrofoil is visible on the left side of the images. The
following points can clearly be noted: (a) The vortex
trajectory becomes closer (vertical distance) to the
hydrofoil as the gap size is increased (results shown in
figure 114; (b) the trajectories in the 0.6 and 1.4mm
gaps do not show the "bump" that is clearly evident in
the case of the 2.6mm gap; (c) The cause of this bump
is the interaction (merging) of two vortices, one being
shed from the trailing edge and the other is the tip
leakage vortex. Thus, increasing the gap to 2.6mm
causes shedding and interaction between multiple
structures, a phenomenon that cannot be observed
distinctly in the smaller gap. Realizing again the
outward trajectory of the bubbles in figure 9, this
motion is most likely associated with this complex
flow structure.
PIV RESULTS
Figure 12a shows a sample instantaneous
velocity field in the inclined plane (x'y, figure 3b)
with a vector spacing of approximately 180~m for the
2.6mm gap (only one velocity map is shown as an
example). The zoomed-in portion of this image (figure
12b) highlights the flow in the vicinity of the tip
vortex. The object on the left in this map is the
hydrofoil with portions of the trailing edge and tip
visible. Sample vorticity distributions derived from
such velocity fields are shown in figure 13 for tat
three gap sizes. The cross-section of the tip leakage
vortex is clearly visible at x'/c=0.12; y/c=-0.18 for the
0.6mm gap, x'/c=0.1; y/c=-0.16 for the 1.4mm gap
and x'/c=0.13; y/c=-0.06 for the 2.6mm gap. Keeping
in mind that the local flow is generated by an
interaction of a wing tip with a turbulent boundary
layer, it is not surprising that instantaneous realizations
contain multiple vorticity peaks. However, unlike the
tip vortex peak the others are intermittent and appear
in different locations in different images. The tip
vortex peak appears consistently although its exact
location varies slightly (figure 154. Furthermore,
clearly the tip vortex cores have substantially higher
overall circulation. Also, just below the hydrofoil
emerging from the gap (figure 13a and b only), we see
a trail of vortical structures that are weaker than the
primary leakage vortex. These secondary vortices are
similar to those seen by Farrell & Billet (19944. Figure
13c for the 2.6mm gap shows a vortex core quite close
to the hydrofoil as expected from figure lOc. Another
high vorticity region can be also observed at x'/c=0.2;
y/c=-0.12 that could very well be part of the structure
from the trailing edge interacting with the tip vortex.
We analyzed 70 and 65 instantaneous realizations for
the 0.6mm and 1.4mm gaps respectively (PIV data
analysis for the 2.6mm gap is currently in progress).
The regions with peak vorticity where the tip leakage
vortices dissect the sheet were selected and regions
with vorticity higher than 500 1/s considered to be part
of the vortex core. The circulation was computed from
~ = ~ ~' dA, where ~ is the vorticity in an elemental
area dA (= 180 x 180 ~m24.
OCR for page 647
(a)
0 1
0.05
o
-0.15
-0.2
-0.25
20:
0.1 0.2 0.3 0.4 0.5
(C) X'/C
o
n
-n no
-0.15
-o 2
-n2.S
-0.3
1
wall 0.1 0.2
0.3 0.4
X'/C
Figure 13: Sample instantaneous vorticity
distributions for gaps of (a) 0.6mm; (b) 1.4mm and
(c) 2.6mm.
| circulation r, gap=0.6mm
circulation r, gap=1 .2mm
~ Cpmin for d=3 spacings(540,um)
/\ Cpmjn for d=4 spacingsP171 t~)
15
~10
_
n l
_ \ ~ \ _ \
\ 1
\ ]
I ~ L
_
_
_ _ _ _ _ _ ~
-2 4 6 8 10
(r/vc) x 1 00
Figure 14: Distribution of circulation
corresponding minimum pressure coefficients.
_ -5
-6
_ cat
-7 ~
-8 2
_
con
_9
CN
-1 0 11
c
-11 a"
-12
-13
-14
-15
and
4. EFFECT OF GAP SIZE ON THE STRENGTH
DISTRIBUTION OF TIP VORTICES AND
PRESSURE MINIMA
Distributions of the measured circulation
normalized by the free-stream velocity and chord
length are presented in figure 14. Strength analysis for
the 2.6mm gap has not been completed by the paper
deadline, but will be available soon. It is evident from
figure 14 that the characteristic vortex strength of the
0.6mm gap is much higher than that of the 1.4mm gap.
Similar trends have been observed by Boulon et al.
(19994. Figure 14 also shows the estimated pressure
minima coefficients (Cpmin) computed for a Rankine
vortex, Cpmin = 2/~2 (~/Vd)2 where d is the diameter
of the vortex core. The vorticity distributions show
that d mostly varies between 3-4 vector spacings (i.e.
540-717~m) and sometimes 5 spacings. No significant
differences in the core sizes were seen between the
two gap sizes, although this statement is greatly
affected by our coarse resolution. Increased resolution
would clarify this point in addition to the 2.6 mm gap
data. Consequently, we show the magnitudes of Cpmin
for 3 and 4 vector spacings as a function of F.
The following points can be noted from
figure 14: (1) the measured cavitation indices (figure
6) are of the same magnitude as the estimated
minimum pressure coefficients. (2) Clearly, the
characteristic circulation of the 0.6mm case is
significantly higher than that of the 1.4mm gap,
explaining both the differences in Hi and the trends in
event rates as the pressure is reduced below the
inception level. For every selected pressure below the
inception level the fraction of vortices with strengths
OCR for page 648
causing the core pressure to be below that level is
much higher for the 0.6mm gap. The locations of the
vortex cores in all the instantaneous realizations
(points of maximum vorticity in the cross-section of
the vortex) are shown in figure 15 for two gap sizes
(data for the 2.6mm gap is not available yet).
0.15
01 _
. .
0.05
o
-n
-n 1~
0.15
0.1
0.05
n
~,-0.05
-n
-n 1.~
-n2
-0 25
(a)
I jinx = 0.6mm
. i
~ Az = 1.5mm
n
By = 9.3mm
0 0.1 0.2 0.3 0.4
(wall) X'/C
-at r
~~ i 7.28mm
.. — co A-—.
LO
__1 - I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 0.1 0.2 0.3 0.4
(wall) X'/C
(b)
Figure 15: Locations of the vortex cores in the
plane My for gaps of (a) 0.6mm (b) 1.4mm.
Both show substantial meandering over ranges that are
much larger than the core size. This meandering is
considerably larger in the 1.4mm case than that of the
0.6mm case, where it is confined to a region with
diameter of 3.7mm (in the x'y plane). Even in the
latter the meandering range is 7.4% of the
chordlength. In most cases the y-distance of the cores
from the trailing edge of the 1.4mm gap is smaller
than that of the 0.6mm gap in agreement with the
results presented in figures 10 and 11. Similar trends
have been observed by Boulon et al. (1999) who
explain this trend using a potential flow model. A
vortex near a wall has an "image" that causes an
induced velocity with direction from the pressure side
to the suction side. With decreasing gaps the induced
velocity increases, increasing as a result the y-distance
of the vortex from the hydrofoil. The higher induced
velocity also increases the effective incidence angle,
which would in turn increase the lift. However the
presently measured 24% difference in the vortex
strengths for the two gaps seems to be much larger to
be purely an effect of the induced velocity. Also, the
presently observed increased circulation will also
cause an increase in the strength of the "image" and as
a result an increase in the induced velocity. Thus, both
the increasing strengths and decreasing distance from
the wall affect the location of the vortex.
SUMMARY
Tip leakage cavitation is studied in detail
with three tip gap sizes of 0.6, 1.4 and 2.6mm (\ =
0.12, 0.28, 0.524. Cavitation inception indices and
event rates are highest for the smallest gap size and
decreases with increasing gap size. High-speed image
series (at 2000fps) of cavitation in the tip vortex
showed good agreement between acoustic and visual
cavitation. High amplitude noise peaks were observed
when bubbles were highly distorted and fragmented.
Much weaker signals (by an order of magnitude) when
the bubbles merely change shape or size. Cavitation
noise is consistently observed in the 10-40kHz range.
High resolution PIV data (180 lam distance
between vectors) is used for measuring the circulation,
estimate the size and location of the tip leakage vortex.
The results show a core size of 3-4 vector spacings,
i.e. 540~m-717~m. Minimum pressure coefficients
calculated using a Rankine vortex model and the
measured strengths and core diameters, lead to results
that are consistent with the measured cavitation
indices. Increasing the gap causes reduction (by 24%)
of the tip leakage vortex strength and its vertical
distance from the hydrofoil. Analysis for the 2.6mm
gap is underway. Observations reveal that the flow
structure for the 2.6mm gap is quite different than the
1.4 and 0.6 gaps. Meandering of the vortex core is
substantial in all cases.
ACKNOWLEDGMENTS
This project has been graciously supported by the
Naval Surface Warfare Center- Carderock Division.
The authors would like to thank Yury Ronzhes, Yi-
Chih Chow, Brian McFadden, Dr. Ed Malkiel and Dr.
Jacob Karni for their contributions.
OCR for page 649
REFERENCES
A tNDT, R. E A 1981 Cavitation m fluid mcchinery
md hyd mlic shuctmes Ann Rev Fhid Mech 13,
273-328
BELAHADll, B. FRANC, J. P. & MCH L, J. M
1995 Cavitation in 6he rotational shuctmes of c
turbulent wake J. Fhid Mech, 287, 383-403
BOULON, O. CALLENAEtE, M, FRANC, J. P.
M CH L, J. M 1999 A e perime tcl insig)~t mto the
effect of co fmement on tip vortex cc itation of m
elliptical hydrofoil, J. Fhid Mech, 390
BRENNEN, C E 1995 Covit tion and Bubble
ynomics O fordUniversityP'ess
DONG, R. CHU, S. KATZ, J. 1992 Q mtitative
Visuclization of Th Flow Shuctme Wi6hin The
Volute of c C ntrif gal P mp, Part A: Techmique, J.
FhidsEng, 114, 390-395
FARRELL, K J. & BILLET, M L 1994 A
conelation of leakag vo tex cc itation m axicl-flow
p mps,JomnolofFhid Engineening, 116
GOPALAN, S. KATZ, J. KN O. O. 1999 The flow
shuctme in the near field of jets md its effect on
cavitation inception, Jouxnol of Fhid Mechonics, 398,
I -43
GOPALAN, S & KATZ, J. 2000 Flow shuctme md
modelmg issues in the closure region of cttached
ca vitation, Physics of Fhid, 12, 895-9 1 1
HIGUCHI, H. ARNDT, R E A, ROGERS, M F.
1989 Characteristics of tip vortex cavitation noise, J.
FhidsEngng, 111, 495-501
HUANG, N E et cl 1998 The empi iccl mode
decomposition md the Hilbert spech m for non-linear
md non- tatiorury time series crurly is Pnoc R Soc
L~ndon 454, 903-995
HS AO, C T. & PAULEY, L L 1998 N mericcl
st dy of the tecdy- tate tip vortex flow over c fmite-
sp m hyd of oil Journol of Fhid Engineenng, 120
JOSEPH, D D 1998 Cavitation md 6he state of t~ess
in c flowing liquid J. Fhid Mech 366, 367-378
KATZ, J. & OHERN, T. J. 1986 Cavitation in large-
sccle shear flows J. Fhid Engng 108, 373-376
MANES, B. H. & A tNDT, R. E A 1997 Tip vortex
formation md cavitation, Journol of Fhid
Engineening, 119
O HE tN, T. J. 1 990 A experimentcl investigation of
turbulent shear flow cavitation J. Fhid Mech 215,
365-391
RhN, B. & KATZ, J. 1991 The response of
microscopic bubbles to mdden chmg s in cmbient
p~essure JFhidMech 224, 91-115
ROTH, G. HART, D & KATZ, J. 1995 Fecs~bility of
usmg 6he L64720 ideo motion estimation processor
MEP) to inxecse efhciency of velocity map
generction for PIV, ASME/EA A Six6h Intennotionol
Symp slum on laserAn mom t y, HiltonHecd S C
ROTH G & KATZ, J. F'v techm q s for mcr i g
h pe d md cccuracy of PIV mterrog,atim
submitted to Meos Sci Technol (June 2000)
SR DHAR, G & KATZ, J. 1995 Lfft md d cg fmces
on microscopic bubbles enbained by c vortex Phys
Fhid 7, 389 399
OCR for page 650
DISCUSSION
Georges L. Chahine and Chao-Tsung Hsiao
D YNAFLOW, INC.
We are grateful to Dr. Rood and the authors of
the very interesting paper"On the Flow Structure,
Tip Leakage Cavitation Inception and Associated
Noise", for requesting a discussion. The authors have
conducted careful experiments to investigate
cavitation inception in the gap region between a foil
and a solid wall. They visualized the cavities in the
vertical regions and detected the acoustic signal
emitted during the dynamics. They generated bubble
nuclei using electrolysis. They then modified the gap
size and deduced trends in cavitation inception
curves. We are particularly interested in two
conclusions the authors draw:
1. "High amplitude noise during cavitation is
primarily due to the growth, distortion and
fragmentation of the bubbles".
2. "The acoustical and visual detection of
cavitation match reasonably well".
The first conclusion confirms our orignal early
numerical predictions for bubble dynamics in a
vertical structure t14. Commonly used spherical
bubble models predict that the bubble continuously
grows during capture until it reaches the"vortex
axis", then collapses later when the vortex diffuses.
To the contrary, our 3D BEM numerical simulations
show that bubbles larger than
some characteristic size
significantly distort while
being captured, form re-
c entrant 'jets', stretch,
elongate, and get split into
two or more smaller bubbles.
This occurs when the pressure
gradient the bubble sees is
large and when various parts
of its surface grow with
differing velocities. At some
point some parts see a
pressure rise while the rest of
the bubble is still growing.
(See Fig. 1,24. Once a bubble
becomes centered on the
vortex axis it can continue to elongate and subdivide
t14 producing further noise. This leads to liquid
liquid impact on some part of the bubble that can be a
significant noise source. Unfortunately, this part of
the problem is difficult to compute, and is a subject
of our on-going efforts for ONR. The conclusions in
this paper give us further confidence in our
. .
slmulatlons.
Figured. Bubble shape
at four instances.
Initial bubble center
location is at 0.2 core
railing.
The second conclusion could be misinterpreted if
one does not underline that optical and acoustical
. . . . .
crlterla -or cavLtahon
inception lead to the same
answer only when one uses
sophisticated techniques such
as used in the paper,
involving appropriately
triggered micro-photography.
Since this is rarely the case in
practice, the acoustic
criterion gives higher values
for s. In addition, the
authors have used an
additional factor to call
inception, which is the use of
the number of events per
second. We believe this to be a very useful approach.
An additional comment to add is the great
importance of the initial nuclei size on the bubble
dynamics in a vortex and on the generated acoustic
signals and
spectra. Our
study t21 shows,
albeit for
spherical
bubbles, that it
is difficult to
find a simple
scaling to
describe all
bubble sizes.
Instead, there
appears to exist
for a given
vortex flow
field several
families of
behaviors (see Fig. 34. We would like the authors to
discuss this aspect of the problem since they have
restricted themselves to relatively large nuclei.
References
1. G.L. Chahine, "Bubble Interactions with Vortices,
Chapter 14, Vortex Flows Ed., S. Green Kluwer
Academic, 1995.
C-T HsiaO, G. L. Chahine, and H.L. Liu,"Scaling
Effects on Bubble Dynamics in a Line Vortex Flow
Prediction of Cavitation Inception and Noise,"
DYNAFLOW, INC. Technical Report 98007-1, Aug.
2000.
A?'
$<
as;
~ ~.; .:
~.:~
~.i ~
~ ~~.
~#:
.~ '.::2
':
lo"'
a:
T.,
'a:
I,,:
.,
2.
Figure 2. Bubble wire-
frame shapes during its
capture by a vortex.
t~ A-:;
.~
Figure 3. Normalized frequency
spectra for various bubble sizes in a
line vortex.
~ ~,)~.,~
-of ~:~0,:~
------- b ~-0 ~
..: ~ .. ;~
OCR for page 651
AUTHOR'S REPLY
We f mk He discussers for reading the paper Ed
offering se- end comments Ed suggestions it is also
nice to see that some of then mmmericcl simulations
sh wed similar results as observed m om
experiments
In re ponse to specific que tions:
First He discussers are conect to point out that He
optical Ed acou ticcl detecti m of cavitation match
w 11 only when appropriately triggered, high-speed
high mcgmfcati m ph tog tphv is used
In f is tudy w mte tiomtlly focus on bubbles Nat
r pure little tension to cmse cavitation inception
(~1001tm diameter) These initial bubble sizes are
smeller f m He vortex core (about l/5tt of He core
diameter) We have not looked et the effect of
various imticl bubble si es on bubble dynamics
duri g cavitati m But as indicated by Clhthme we
Tree that various bubble si es will behave
differently For very small bubbles the critical
pressure leading to cc itation inception is d pend nt
on bubble si e Larger bubbles will be deformed,
disto ted Ed fragme ted by He local p~essme non-
unfformities In the present study w use bubbles Nat
r pure little tension to initiate cc itati m, but are still
signifcmtly mcller thm He core Once cc itation
starts He bubble grows substantially lecdmg to odd
shapes, ficgmentation et
OCR for page 652
DISCUSSION
K J. Farrell Ed W. A St zkz
Pemmsyl mid State University, USA
I welt to thmkfhe mthors for contobutmg this mo t
i toasting paper to the Naval Hyd odynamics
symposium The collection of detailed :' V flow
field measurements, visual observations of individual
bubble dynamics, Ed cone pondng t msient
acoustic measurements are comprehensive Ed
unprecedented It this small scale it is intere ting
that She higher zmplit de noise peaks w re associated
with bubble disto non Ed fizgmentation rath r th m
shme or size charge
In my opmion, She intended relevance of She
subject Investigation to th "effect of gm si e on She
flow stmctme Ed on the inception of tip leakage
cz itation" is limited Ed somewhat misleading d e
to the omission of :eserrl impo t mt features of tip
leakage flows Pa t, She rektive moti m of She tip
Ed end-wall is omitted in z pump, She relative
motion zugme ts the leakage flow; m z t rhine She
motion opposes it The so-called scraping vo tex
conhibutes Toni it to the leakage vortex; Ed this
co tobution is ce thinly z f notion of gap size
Additionally, centrifugal lorces conh~bute to
secondary flows, which c m interact with the leakage
so tex at the tip Pmth rmore, She contemporary
practice of unloadi g She blade tip is not z feat re of
the test hyd of oil Rasher, th low r half of the sp m
is linearly unload d fr m z con t mt Ifft coefficient
along She upper half-sp m of She hyd of oil Given
these omitted featmes of z tip leakage -I .., th tudy
is more ~elevmt to She effect of confinement m tip
Rolex cavitation mceptim Ed associated noise
This is import mt distinction rektive to the
observation of z cavitation inception Index minimum
It some value of nommali ed clearance The an hors
conectly point out that Boulon et al (1) do not
observe z cavitation minimum, while Powell Ed
Billet (2) Ed Gentlrrt Ed Ross (3) do On the basis
of total p~essme loss, m optimum clearance exi ts
when th scr mm , secondary, Ed leakage sources of
ci cuhrion it th tip have z zero net sum (4) or me
identically zero [th motivation of She c mp~essor
"squealer" tip, e g (5)] Conversely, the data of
Figure 14 sugge t higher loss with the smaller
clearance
Prom She measured cavitation event rates plotted
in Figure 6, it would Up or that for se y low event
rates Fiat gap si e may not be z signfficmt
discriminator in cavitation pe formance The
observation begs She often tsked question what is
th definition of cavitation? The ITTC round-robin
tests clearly identified both flow Ed water quality Is
conhibutors to scale effects, but certainly She
threshold of Inception is imp nmt is w 11 in
colkpsmg data Cm th mthors c mme t on His
generally Ed m the se y I w event rate behavior
observed m Heir experime t?
The statistical nat re of cavitation re ts
signif Fitly on She probability of m appropriately
si ed mcleus entering the lo..- pressrun zone m She
vo tex Accordingly, would the m thors comment on
th uniformity of the mclei di tribution Ed the
method Ed location of measurement?
I Boulon, O. Cnllenze~e, M, Pranc, J. P. Ed
of t h 1, J. M "A E perime tal insight mto She
E feet of Co lineme t on Tip Vo tex Cavitation
of m Elliptical Hyd of oil," J f i,i:d Mechmni~,
Vol. 390, 1999
2 Ftnell, K J. Ed Billet, M L "A Conekti m of
L zkage Vo tex Cavitation in A ial-Plow
Pumps," J Fluid Engineering, Vol. 116
3 Gearhart, W. S. mdRoss, J. R. "Tip Lzkage
E Sects," Applied Research Laboratory Penn
State TM 33-20, 23 Pebmary 1933
4 LskshmirLtr trot, B. "Methods of Predicting
the Tip Clearance Plow in A ial Plow
Turbomachinery," J Basic Engineering,
September 1970, 467-432
5 Wisler, D C, "Advanced C mp~essor Ed P m
Systems," General Elechic Aircraft E me
Business Group," presented It the VK Penn
State Sho t Course on "Tip Clearance Effects in
A ial Turbo-Mzchines," April, 1936
AUTHOR'S REPLY
We thank She discussers for reading She paper Ed
offering several comments Ed suggestions
Th discussers me correct to pomt out that several
features of z tip leakage flow in z rotating
tmbomachine are omitted She motion of She tip
relative to She end wall, effect of cenhffugal lorces
Ed unloading of the tip (ours is intentionally loaded)
The differences may explain why some Investigators
To m wet sp civic q estions of She discussers:
First the water in the te t facility is deserved Ed we
record it elerometer signals without generating My
mmclei Under such conditions we may observe one or
two czntztion events m z ten t cond period,
OCR for page 653
indicating flat the flee stream mmclei are limo t
eliminated Then w "flood" She tip region with
bubbles (~lOOlrm diameter - size distribution md
details are provid d in th papery et approximately
2500 bubbles/s The measur me ts w He made ju t
up cream of the leading edge md had c field of vi w
of about 3mm The images w re crurlyzed using c
blob analysis sof wme Bubbles in good focus w re
used for size dishibution All the Laces including
those that me not exactly m focus were used for
computing She bubble flmc
Bubble with diameters of Worm Aqua little tension
to initiate cavitation, Thus bubble size is not c critical
issue m th present study Also al non of 2500
bubbles per second makes cavitation inception less
sensitive to bubble populations How ver, being c
se y t rbulent flow with large coherent struct res,
i fr que t cavitation events Jess f m 2 per second)
me c result of "extreme" flow conditions md not
Hopi 91 of She flow Wish ins sing events per second
c Rend c m be conectly identified Thus, She slope of
She cavitation eve t rate curve is importmt in
addition to its absolute values
Representative terms from entire chapter:
cavitation inception
