Bubble nuclei populations in the wake of a circular cylinder under cavitating and noncavitating conditions were measured using a Phase Doppler Anemometry (PDA) system.  In addition, the mean velocity defect and the turbulent fluctuations were monitored in order to try to understand the nuclei population dynamics within the flow.  At the Reynolds numbers of these experiments (20000->33000) the laminar near-wake is fairly steady and under very limited cavitation conditions nuclei accumulate in this wake so that the population there is several orders of magnitude larger than in the upstream flow.  Further downstream the population declines again as nuclei are entrained into the wake.  However at fifteen diameters downstream the population is still much larger than in the upstream flow

Brennen, C. E.

Liu, Zhenhuan

Sato, K.

English

Caltech Authors - Main

FED-Vol. 153, Cavitation and Multiphase Flow 
ASME 1993 
THE MICRO-BUBBLE DISTRIBUTION IN THE WAKE 
OF A CAVlTATlNG CIRCULAR CYLINDER 
K. Sato, Zhenhuan Liu, and C. E. Brennen 
California Institute of Technology 
Pasadena, California 
ABSTRACT 
Bubble nuclei populations in the wake of a circular cylinder 
under cavitating and noncavitating conditions were measured us- 
ing a Phase Doppler Anemometry (PDA) system. In addition, 
the mean velocity defect and the turbulent fluctuations were moni- 
tored in order to try to understand the nuclei population dynamics 
within the flow. At the Reynolds numbers of these experiments 
(20000 + 33000) the laminar near-wake is fairly steady and under 
very limited cavitation conditions nuclei accumulate in this wake 
so that the population there is several orders of magnitude larger 
than in the upstream flow. Further downstream the population 
declines again as nuclei are entrained into the wake. However at  
fifteen diameters downstream the population is still much larger 
than in the upstream flow. 
1. INTRODUCTION 
Ever since the watershed experiments of Lindgren and Johns- 
son (1966) it has been widely accepted that cavitation inception 
and patterns of flow are dependent on the population of micron- 
sized "cavitation nuclei" present in the flow. Yet progress toward 
establishing the relationship between these nuclei and the cavi- 
tation they produce has been relatively slow, in part because of 
the difficulties in measuring the nuclei population in a water tun- 
nel environment. The pioneering efforts of Keller (1972, 1974) 
in developing optical scattering methods have been followed by 
other valuable contributions (for example, Ahamed and Hammitt 
(1975), Gates and Bacon (1978), Peterson et al. (1975), O'Hern et 
a]. (1988)). Yet as Billet (1985) has indicated in his review, per- 
haps the only reliable methods of obtaining the nuclei number den- 
sity distribution function (defined as N ( R )  where N(R)dR is the 
number of nuclei per unit sample volume with radii between R and 
R + dR) are the holographic methods in which the nuclei present 
in a reconstructed hologram are directly counted. The difficulty 
with this approach is that it is laborious and time-consuming and 
does not permit on-line monitoring of the changes in the water 
tunnel nuclei population during an experiment. 
In our laboratory, Liu (1992) has cooperated jointly with Dan- 
tec in developing and calibrating a light-scattering instrument for 
nuclei population measurement. These results and the investi- 
gation of nuclei population dynamics will be reported later. The 
present paper presents the results of an investigation into the vari- 
ation of the nuclei population within a typical flow and we have 
chosen to examine the classic case of flow around a circular cylin- 
der. The motivation is to gain some understanding of how the 
nuclei population varies from one location to another within such 
a flow since the cavitation inception and flow pattern may well de- 
pend on the details of that distribution. Of course, the nuclei are 
sufficiently small that most are simply convected along as would 
be particles of fluid. But it is also possible for nuclei to accu- 
mulate in a wake, in a separation bubble or, perhaps, in a vortex 
and such concentrations may have important consequences. Kato 
(1985) has also demonstrated that cavitation itself supplies nuclei 
to the water tunnel population: he also used a PDA instrument 
to show that the population downstream of a cavitating foil was 
about two orders of magnitude larger than the population density 
upstream. In this paper we simultaneously measure the velocity, 
the turbulent fluctuations and the nuclei population in the wake 
of a circular cylinder in order to provide some evidence of nuclei 
population dynamics. 
2. EXPERIMENT 
The experiments were conducted in the Caltech Low Turbu- 
lence Water Tunnel (LTWT), shown in Figure 1. A full descrip- 
WORKING SECTION 
O.3m SOUARE X 2.5 
1 I R  R E U O V I L  
Figure 1 Diagram of the Low Turbulence Water Tunnel 
(LTWT) (not to scale) 
HP 
MOTOR 
tion of the tunnel, which has a 31 [cm] x 31 [cm] working section, 
is presented by Gates (1977). A circular cylinder with a diameter, 
D , of 6.35 [mm] was installed vertically on the centerplane of the 
tunnel. A Phase Doppler Anemometer (PDA) made by Dantec 
(see Saffman, Buchhave and Tanger [1984]) was used to simul- 
taneously measure the mean fluid velocity, turbulent fluctuations 
and bubble number density distribution. This instrument utilizes 
an Argon-ion laser and was mounted on the LTWT as shown in 
figure 2. The transmitting optics are mounted horizontally and 
focused on the centerplane of the tunnel. The receiving optics 
collect light scattered at  an angle of 87" to  the incident beams. 
The  processing program of the PDA used a validation level of -4 
[dB] and a band width of 4 [Hz]. It  was adjusted to  focus on 
nuclei in the diameter range of 5 lpm] to 100 [pm]. 
Most of the results reported here were obtained a t  two tunnel 
operation conditions, namely tunnel velocities, U , of 3.1 and 5.2 
[m/sec], a t  a pressure of 40 [kPa]. The corresponding cavitation 
numbers, u , are 7.3 and 2.8, respectively. By varying the velocity 
and pressure it  was established that cavitation inception occurred 
about u % 2.9 so that the flow at  3.1 [m/sec] was non-cavitating 
while that  at 5.2 [m/sec] exhibited very limited cavitation. 
Measurements of the mean velocity, turbulent fluctuations and 
nuclei number distributions were made at a series of locations on 
the  centerline, namely at a point 15 diameters upstream and at  
locations 5, 10 and 15 diameters downstream ( X/D=-15, 5, 10 
and 15). Here X is the axial coordinate; the coordinate perpen- 
dicular to  X and the axis of the cylinder is Y. A second series of 
measurements was conducted to explore the variations with YID. 
The population dynamics of cavitation nuclei in a water tunnel 
are not well understood. Because of the difficulties of making reli- 
able measurements there have been very few efforts to understand 
how the nuclei population in a water tunnel change with time, 
or with pressure, velocity and air content. A notable exception 
were the efforts of Keller (1972, 1974). However many questions 
remain. Concurrently with the present tests and effort is be- 
ing made to study the nuclei population in the LTWT using the 
PDA. These studies will be reported later. In the present context 
it is however important to report that the nuclei population can 
change with time when the tunnel is run for an extended period 
of time of the order of hours. This was a concern in conducting 
the  present experiments. However several centerline nuclei popu- 
Figure 2 Schematic diagram of Phase Doppler Anemometry 
(PDA) system. 
U [ m / s l  X/D 
0 : 5 . 2  5 
0 : 5.2 1 5  
0 ' 3 . 1  5 
: 3 . 1  1 5  
-. . Numerical Result 
Figure 3 Mean velocity deficit in the wake. 
( P=40 [kPa]). 
lations (at X/D=5) were repeated both before and after a series 
of measurements and showed relatively little discrepancy. We 
therefore believe that any temporal drift in the nuclei population 
in the present experiments was fairly small and does not alter the 
qualitative conclusions. 
3. RESULTS AND DISCUSSION 
We begin by showing in figure 3 the mean velocity deficit in the 
wake of the circular cylinder under the condition of P=40 [kPa]. 
The parameter, b, used in this figure is defined as the half width 
of the mean velocity deficit. It should be noted that in the case 
of U=5.2 [m/s], the cavitation could be observed by the human 
eye. On the other hand, no cavitation could be observed visually 
Figure 4 Oscillations and histograms in the velocity on the centerline. ( U=5.2[m/s] ; P=40[kPa]). 
(a), (a') : X/D=-15 ; (b), (b') : X/D=5 ; (c), (c') : X / D = l O ;  (d), (d') : X/D=15. 
Figure 5 Variation in u/U and (';liZ)i / U with distance 
downstream along the centerline. ( P=4O[kPa]). 
0 ,O : U=5.2[m/s] ; 0 , A  : U=3.l[m/s]. 
25 o : U=~ .Z [~ /S I  
o : U=3.I[rn/sl 
'1 
: N u m e r i c a l  Result E 20 
10 f l5 
5 
at  U=3.1 [m/s]. Clearly the influence of cavitation on the mean 
velocity deficit is small. In this and other later figures we shall 
include numerical predictions obtained using a two-dimensional 
discrete vortex method in which the time step was 0.1 and the 
separation angle was assumed to be  84'. 
Typical oscillations in the velocity in the X direction, u, mea- 
sured on the centerline, are shown in figure 4 for U=5.2 [m/sec], 
P=40 [kPa], and various X/D.  Clearly the turbulence level is 
largest at the location X/D=5 and declines with the distance 
downstream; the level of turbulence in the free stream is less than 
8 % . The corresponding histograms of the nuclei velocities are 
also shown in figure 4. Clearly the turbulence in the wake has 
created a distribution in the nuclei velocity but this distribution 
begins to  narrow as one proceeds further downstream. 
The variation in u /U and ( p ) ;  / U with distance downstream 
along the centerline is shown in figure 5, which shows similar trends 
at  both the U=3.1 and U=5.2 [m/sec] speeds and indicates that 
the level of cavitation at  U=5.2 [m/sec] had little effect on the 
basic features of the flow. The variation in (p)h / U with Y/D 
is shown in figure 6 which also includes the numerical prediction 
by means of the discrete vortex method. In the same figure we 
BOOO , I 1 I 
BOOO 
- 5000 
0 
0 
\ - 
d 
4000 
0 
2000 
0 
Figure 6 Variation in (F);/U and concentration with Y/D. ( P=4O[kPa]). 
show the variations in the total nuclei concentration. In the lat- 
ter graphs it is very clear that the cavitation occurring at Uz5.2 
[m/sec] has caused a -major increase in the bubble population in 
the wake (at X/D=5) but that turbulent mixing with the free 
stream has substantially diluted this concentration of nuclei by 
X/D=15. 
The lateral and longitudinal variations in the nuclei popula- 
tion are illustrated in figure 7 in which the volume fraction of the 
bubbles (calculated from the nuclei number density distribution ) 
is  lotted against Y/D (for X/D=5 and 15) and against X/D (for 
Y/D=O). The data for U=3.1 [m/sec] clearly exhibits a uniform 
population with a void fraction of about 0.0005 % throughout the 
flow field. On the other hand, the cavitation at U=5.2 [m/sec] has 
substantially increased the void fraction in the wake and one can 
see the effects of dilution further downstream in the wake. The 
right-hand graph of figure 7 also includes some data at U=5.54 
[m/sec] and P=40 [kPa] or a cavitation number, o , of 2.45 and 
the decrease in a from 3.0 to 2.45 clearly can be seen to cause a 
more than fourfold increase in the volume fraction of the bubbles. 
Having examined some global measures of the bubble pop- 
ulation (concentration and volume fraction) we now turn to the 
size distribution of the nuclei/bubbles. Typical distribution are 
shown in figures 8,9 and 10 where N(R) is plotted against the ra- 
dius R in pm. Figures 8 and 9 present bubble size distributions in 
the centerline with and without cavitation. Figure 9 is obtained 
without cavitation and exhibits only small changes in the nuclei 
distribution. However there does appears to be a higher popula- 
tion of small bubbles in the wake than upstream which may be the 
result of a tendency for nuclei to accumulate in the wake. How- 
ever, as illustrated in figure 8, the onset of very limited cavitation 
causes major changes which overwhelm any of the differences in 
figure 9. Note that there is a major increase in the number of 
nuclei over the entire range of radii and that figure 9 shows the 
same tendency for dilution with distance downstream of the cylin- 
der. It is also important to observe that the cavitation supplies 
a larger increase in the number of smaller nuclei so that the slope 
of the N(R) distribution in the wake is significantly larger than 
that in the upstream flow. Indeed the slope of the wake nuclei 
distributions is more characteristic of the N(R) observed in wa- 
ter tunnels at higher speeds having a behavior like N(R) = RR-" 
where n=2.5 -+ 3. In contrast the low speed nuclei upstream of 
the cylinder in the present tests have n = 1 or less. Other tests 
(Liu [1992]) have shown that allowing the LTWT to run under 
de-aerated conditions for a long period tends to cause the value of 
n to decrease. 
4. CONCLUSIONS 
Bubble nuclei populations in the wake of a circular cylinder un- 
der cavitating and noncavitating conditions have been measured 
using Phase Doppler Anemometry (PDA) system to make sure the 
interaction between the nuclei distributions and a circular cylin- 
der or the turbulence. It has been shown that the population 
in the wake with cavitation is several orders of magnitude larger 
than the population density upstream. Although at fifteen diam- 
eters downstream the population is still much larger than in the 
Figure 7 Volume fraction of bubbles against Y/D and X I D .  
upstream, it declines again as nuclei are entrained into the wake. 
ACKNOWLEDGEMENTS 
The authors wish to thank Professor Allan Acosta for helpful 
advice. This work was carried out with the support of the Office 
of Naval Research under Grant N00014-91-5-1295. 
' I   
lo 5 10 50 
R [W"l  
Figure 8 Bubble size distributions on the centerline 
with cavitation. 
( U=5.2[m/s] ; P=$O[kPa]). 
Figure 9 Bubble size distributions on the centerline 
without cavitation. 
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The Micro-Bubble Distribution in the Wake of a Cavitating Circular Cylinder

Acosta, A.J., O'Hern, T . and Katz, J . 1986. &quot;Some Recent Trends in Cavitation Research,&quot; Intl. Syrnp. Cavitation, Sendai, Vol.l, pp. 1-7.

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Simultaneous Measurements of Size, Concentration and Velocity of Spherical particles by a Laser Doppler Method,&quot;

Some Recent Trends in Cavitation Research,&quot;

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The Micro-Bubble Distribution in the Wake of a Cavitating Circular Cylinder

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