This paper presents the details of the collapse process for single bubbles generated in travelling bubble cavitation around two axisymmetric headforms.  The details of the bubble collapse process have been examined acoustically to understand the phenomena of rebounding and multipeaking.  We find that both rebounding and multipeaking increased with reduction in the cavitation number for the ITTC headform.  However with the Schiebe headform rebounding increases and multipeaking is decreased with reduction in the cavitation number.  Some possible physical explanations for these phenomena are presented

Brennen, Christopher E.

Kumar, Sanjay

English

Caltech Authors - Main

FED-Vol. 109, Cavitation and Multiphase Flow Forum 
ASME 1991 
STATISTICS OF NOPSE GENERATED 
BY TRAVELLING BUBBLE CAVITATION 
Sanjay Kumar and Christopher E. Brennen 
California Institute o f  Technology 
Pasadena, California 
ABSTRACT 
This paper presents the details of the collapse process for 
single bubbles generated in travelling bubble cavitation around 
two axisymmetric headforms. The details of the bubble col- 
lapse process have been examined acoustically to understand 
the phenomena of rebounding and multipeaking. We find that 
both rebounding and multipeaking increased with reduction in 
the cavitation number for the ITTC headform. However with 
the Schiebe headform, rebounding increases and multipeaking is 
decreased with reduction in the cavitation number. Some pos- 
sible physical explanations for these phenomena are presented. 
1. INTRODUCTION 
This paper presents some observations on the details of the 
bubble collapse process in travelling bubble cavitation. These 
observations were made for the purpose of improving under- 
standing of the bubble collapse process and its effect on the 
spectra of the resulting noise. Fitzpatrick and Strasberg (1956) 
were the first to model cavitation noise based on Rayleigh's 
analysis. Since Rayleigh's analysis of the collapse of spherical 
bubbles does not consider the effect of the presence of a solid 
wall or the interaction of collapse process with local flow struc- 
tures such as separation and vortices, it may be inadequate 
for the modelling and prediction of travelling bubble cavitation 
noise. Baiter (1974, 1986) has povided a framework for the 
synthesis of the cavitation noise from single bubble cavitation 
noise once the details of the latter are known. 
A number of researchers have acousticallg and photo- 
graphically studied travelling bubble cavitation noise. These 
include studies of a hydrofoil (Blake e t  al. 1977) and a Schiebe 
headform (Marboe e t  al. 1986, Hamilton e6 al. 1982 and Hamil- 
ton 1981). The bubble dynamics have been documented photo- 
graphically for both the Schiebe (Hamilton 1981, Hamilton e t  
al. 1982, Ceccio and Brennen 1991) and the ITTC (Ceccio and 
Brennen 1991) headforms. Recently Ceccio and Brennen (1991) 
found that a single cavitation event can produce an acoustic sig- 
nal which consists of more than one pulse, each of which may 
consist of more than one peak. These phenomena are the result 
of interaction between the bubble and the local flow structure. 
The present paper reports on an investigation of the bubble 
collapse process with particular attention to rebounding and 
multipeaking and their impact on the noise generated by the 
cavitation event. The effect of these phenomena on the spec- 
trum of the resulting noise has also been investigated and will 
be pesented at the forum. 
2. NOMENCLATURE 
I,  acoustic impulse (see Fig. 3) 
I ,  a measure of strength of the pulse 
P peak amplitude of the main or the rebound 
pulse (see Fig. 3) 
Lucite 
Headform 
ITC - 1042 
Water Hjdrophone 
Cavity 
Digital Data 
Acquisition System 
Figure 1. 
headform. 
T 
tl 
t 2  
U 
c7 
T 
r3 
T I  
Schematic illustrating the instrumentation of the 
ratio of maximum peak of the rebound pulse 
to maximum peak of the main pulse 
time of begining of the main or the rebound 
pulse 
time of end of the main or the rebound pulse 
flow velocity 
cavitation number 
duration between maximum peak of the main 
pulse and maximum peak of the rebound 
pulse (see Fig. 3) 
peak separation (see Fig. 3) 
duration of main or rebound pulse (see Fig. 3) 
3. EXPERIMENTAL METHODS 
The experiments were conducted in the Low Turbulence 
Water Tunnel (Gates 1977) at  the California Institute of Tech- 
nology. The experimental equipment and installation used by 
Ceccio and Brennen (1991) was employed in these experiments. 
All the experiments were conducted at a fixed velocity with the 
desired cavitation number obtained by lowering the static pres- 
sure in the water tunnel. The air content was measured using 
a Van Slyke apparatus and was maintained between S and 10 
ppm. Travelling bubble cavitation was produced on the two 
axisymmetric headforms used by Ceccio and Brennen (1991), 
namely a Schiebe headform and a ITTC headform with diame- 
ters of 5.08 and 5.59 cm respectiveiy. The signal emitted during 
bubble collapse was recorded using an ITC-1042 hydrophone 
which has a flat frequency response up to about 80 kHz. The 
hydrophone was placed inside the headforms which were made 
of lucite in order to make them acoustically transparent. The 
interior of the headforms werc filled with water to produce a rel- 
atively reflection-free path between the cavitation bubbles and 
the hydrophone. An experimental schematic is included as Fig. 
1. 
The signal from hydrophone was amplified and extremely 
low frequencies ( << 1 Hz ) were removed by a high pass filter. 
The filtered signa! wa-s rl;gita!!y szq?!ed rrt 500 Efi. P.re~nd 
500 acoustic traces were collected for each operating condition, 
namely for 3 cavitation numbers ( 0.45, 0.50 and 0.55 ) and 
two flow velocities ( S and 9 m / ~ e c ) .  The signal sampling dura- 
tion was adjusted to capture one complete acoustic trace from 
a bubble collapse. These records were then digitally processed 
in following way. First peaks were detected and classified as 
belonging to a main or a rebound pulse. Then quantities such 
as the peak amplitude and the time intervals between the peaks 
were evaluated. In addition, the following quantities were ob- 
tained: 
Here I ,  is the acoustic impulse, tl and t 2  being the times of 
the begining and the end of main pulse or of the rebound pulse. 
The integral I, is an alternative measure of the strength of the 
pulses and T,  is the duration of each pulse. Also measured were 
the time between maximum peaks in the main and the rebound 
pulses, d, and the ratio of the amplitude of maximum peak in 
the main pulse to the maximum peak in the rebound pulse, r .  A 
typical acoustic trace is shown in Fig. 2 and a sketch illustrating 
the definition of some of the parameters is included as Fig. 3. 
4. EXPERIMENTAL RESULTS 
The probabilities of occurrence of the phenomena of re- 
bounding and multipeaking were examined statistically in order 
to gain some insight into these phenomena. The dependence of 
these probabilities on cavitation number, a , and, to a limited 
I ,  I I I I I I 
1.8  2.0 2.2 2.4 2.6 2.8 3.0 
Time ( msec. ) 
Figure 2. A typical amplified and filtered signal for a single cayitation event 
illustrating multiple peaks and a rebound. Inset shows the complete acoustic 
trace. 
Time Between the 
Main Pulse and the 
Rebound Pulse, z 
Main Pulse . I I I 
~ e b o u n d  Pulse I---$ Pulse D ration, z 
W 
extent on flow velocity, u, are presented in Fig. 4 for the ITTC 
headform and in Fig. 5 for the Schiebe headform. Consider 
first the phenomenon of multipeaking in the main pulse. The 
following trends can be clearly seen in the data. First note that 
changing the flow velocity from 8 to 9 m/sec  has little eEeci on 
the results. Secondly, the probability of rebounding increases as 
o is reduced and this appears to be the case for both the head- 
forms. It is particularly evident that rebounding almost never 
occurs at highest of three cavitation numbers tested, o = 0.55. 
TI,,, --A A : C  ----"- L-b --.--- & --.- L--.lS--- :- ' LL- ---L 
Lub u L a u  uuLxx-zuLc u c b w c c u  the t,wu u c a u ~ u ~ ~ u a  la iii LUC p ~ u u -  
ability of occurrence of multipeaking. For the ITTC headform, 
the probability of occurrence of double-peaked events is almost 
independent of a . However, the probability of occurrence of 
events with more than two peaks increases as the cavitation 
number is reduced. Events with more than two peaks almost 
never occur for the Schiebe headform. The probability of oc- 
currence of both multipeaking and rebounding is higher for the 
ITTC headform than for the Schiebe headform. 
The probability of occurrence of multipeaking in the re- 
bound pulse was also examined and exhibited trends similar to 
Figure 3. Sketch of a typical acoustic trace with definition of 
those for the main pulse. Rebounds are predominantly single 
some measured quantities. 
peaked ( approximately 80 % for the ITTC headform and 90 '?& 
for the Schiebe headform ). It is convenient to classify the events 
headform 9 m/sec IlTC headform 8 m/sec 
" .  
0.45 0.50 0.55 0.45 0.50 0.55 
Cavitation Number Cavitation Number 
Figure 4. Probabilities of different types of cavitation events on the ITTC head- 
form indicating the occurrence of multiple peaks or a rebound. R and NR respec- 
tively denote events with and without rebound. The number alongside indicates 
the number of peaks in the main pulse. 
Schiebe headform 8 m/sec Schiebe headform 9 m/sec 
0.45 0.50 0.55 0.45 0.50 0.55 
Cavitation Number Cavitation Number 
Figure 5. Probabilities of different types of cavitation events on the Schiebe 
headform indicating the occurrence of multiple peaks or a rebound. R and NR 
respectively denote events with and without rebound. The number alongside 
indicates the number of peaks in the main pulse. 
with a rebound by a of two letters, where the first rebounds with ms type rebounds also present about 20 % of the 
letter represents the number of peaks in the main pulse and the time. 
second letter the number of peaks in the rebound pulse. We use Obviously, the nature of the events are quite different for 
m to denote multiple peaks and 3 to denote a single peak. It the two headforms because of differences in the interaction be- 
is found that the ITTC headform has mostly ms type d m u n d s  tveen the bubble dynamics and the flow structure for the two 
150 %I but mm and sq3 type rebounds are also present in signifi- headforms. Specifically, the presence of boundary layer sepa- 
cant numbers [25 %I. The Schiebe headform has mostly 33 type ,ation on the ITTC headform and its absence on the Schiebe 
Figure 6. A typical photograph from Ceccio and Brennen (1991) 
illustrating the bubble breaking up into two or more pieces 
during the collapse. 
x ITIT - ss - 9 A Schiebe - ss - 9 
w I ~ C  - ms - 8 . Schiebe - ms - 8 1 
Cavitation Number 
Figure 7. Ratio of peak pressure amplitude of the rebound pulse 
to peak pressure amplitude of the main pulse. r ,  as a function 
of cavitation number. 
headform is probably responsible for the observed effects. The 
rebound pulse indicates a second collapse separated by a growth 
phase from the first collapse. The multipeaking, on the other 
hand, could be result of several mechanisms: 
hlult i~le ~ e a k s  map be the result of several shock waves 
emitted during the collapse process (Mellen 1955 and 1956. 
Iiimoto 1987 and Vogel et al. 1989). Iiimoto (1987) has 
separately measured the pulses resulting from microjet im- 
pact as well as a shock wave emitted from the final bub- 
ble collapse. It can be seen from those obsermtions that 
pressure resulting from the shock wave is the larger one. 
Also. the peaks from the microjet and the shock-*me ap- 
pear 0.1 msec apart whereas in present experiment peak 
separation was roughly 0.015 msec. Using Schlieren tech- 
nique, Vogel e t  al. (1989) have observed two shock waves 
emitted due to non-spherical bubble collapse. Hence, the 
multiplicity of peaks could also be result of a number of 
shockwaves due to the non-spherical bubble collapse. 
The bubble can breakup into several pieces while collapsing 
(as seen by Ceccio and Brennen (1991) and shown in Fig. 
6) and therefore generate two or more peaks. Considering 
the two bubble pieces to be roughly 1 mm apart (as seen 
from the photographs in Ceccio and Brennen 1091) the 
resulting peaks could be roughly 100 msec apart. Here, 
the bubble may breakup during the collapse as a result 
of the onset of higher order surface oscillations due to 
presence of the solid wall or due to the shearing action 
of the local flow. 
Volume oscillations during the collapse process could cause 
multiple peaks. By comparison with observed peak sepa- 
ration of roughly 0.015 msec, the natural period of oscil- 
lation for a 20 pm microbubble is also 0.015 msec. Thus. 
volume oscillations during the collapse may be a plausible 
reason for the multiple peaks. 
We now examine other features of the results. The ratio of 
the maximum main pulse amplitude to maximum rebound pulse 
amplitude, r ,  is presented against the cavitation number in Fig. 
5 for two velocities and various types of events. It is seen that 
most of the data is clustered around the value of 3. With a 95 % 
confidence level, we find that the mean value of r will lie between 
1.5 and 2 .5 .  It seems that bubble fission observed by Ceccio and 
Brennen (1991) happens in such a way that the remnant nucleus 
generates approximately half the maximum pressure. This may 
mean that during the first collapse certain nonlinear modes of 
surface oscillation are set up which cause the bubble to breakup 
0.44 0.46 0.48 0.50 0.52 0.54 0.56 
Cavitation Number 
Figure 8. Dependence of time between the main and rebound 
pulses, T on the flow condition and the type of rebound. The 
legend indicates the headform, type of rebound and the f i o ~  
velocity. Type of rebound is indicated by 2 letters; the first 
letter indicates the number of peaks in the main pulse and 
the second letter the number of peaks in the rebound ~ u l s e ;  
m indicates multiple peaks and 3 indicates a single peak. 
in a repeatable way. The present observations differ from those 
of Hamilton (1981) who found that the acoustic energy emitted 
by the main and the rebound pulses were roughly the same. 
The time interval between the main pulse and the rebound 
pulse, r. is presented as a function of cavitation number in Fig. 
Q r ~ , -  ..--.-..- -r .---.- 
rvL r a i u u a  bypc UL w w t s  and two fiow veiocities. It can 
be seen that T is in the range of between 0.3 to 1.3 msec and 
generally increases as a is reduced. Multiple peaks appear to 
delay the rebound. This feature and the differences between 
two flow velocities are not easily explained. 
The quantities P, I,, I,, T,, T, and spectra were also 
examined to understand their dependence on the flow condi- 
tion and multipeaking and rebounding. These results will be 
presented at  forum and in a later publication. 
5 .  C O N C L U S I O N S  
On the basis of above observations it may be concluded 
that multipeaking and rebounding increase with the reduction 
in the c~v;\lit,..tion u=.,ber for the ITTC headform. Kuwe-ver for 
the Schiebe head form, multipeaking decreases and rebounding 
increases as the cavitation number is reduced. Also, both the 
multipeaking and rebounding occur more frequently for the 
ITTC headform compared to the Schiebe headform. The flow 
velocity seems to have little effect on these results. Most events 
with rebound for the ITTC headform are of m s  type whereas 
they are mostly 3s type for the Schiebe headform The ratio of 
the peak amplitude of the rebound pulse to the peak amplitude 
of the main pulse is close to 2.0 for d l  flow conditions and 
types of events. This may indicate a fairly repeatable process 
of bubble fission and rebound. The time between the main pulse 
and the rebound pulse, T ,  is seen to decrease with increase in 
a . Multiple peaks in the main pulse are observed to delay the 
rebound. 
6. ACKNOWLEDGEMENTS 
The authors are grateful for the support of the Office of Kaval 
Research under contract N 000167 - 85 - I< - 0165. We also 
thank Dr. Steven L. Ceccio and Yan Kuhn de Chizelle for their 
assistance. 
7 .  R E F E R E N C E S  
Baiter, H. J. 1974. Aspects of Cavitation Noise. Symp. on High 
Pewered Propulsion of Ships, Wageningen, The Netherlands, 
Fubiication No. 490, pp. 1-33. 
Baiter, H. J. 1986. O n  Diflerent Notions of Cavitation Noise 
and W h a t  T h e y  Imply.  Int. Symp. on Cavitation and hfulti- 
phase Flow Noise, ASME FED Vol. 45, pp. 107-118. 
Brennen, C. E. and Ceccio, S. L. 1990. Recent Observations o n  
Cavitation and Cavitation Noise. Proc. Third Int. Symp. on 
Cavitation Noise and Erosion in Fluid Systems, San Francisco, 
CA, Dec. 1989, pp. 67 - 78. 
Blake, W. K., Wolpert, M. J. and Geib, F. E. 1977. Cavitation 
Noise and Inception as Influenced b y  Boundary Layer Develop- 
m e n t  o n  a Hydrofoil. J .  of Fluid Mech., Vol. 80, pp. 617 - 
640. 
Ceccio, S. L. and Brennen, C. E. 1991. The  Dynamics and 
Acoustics of l+avelling Bubble Cavitation. To appear in the J.  
of Fluid Mech. 
Fitzpairi&, TT l b  . - 3  O L _ - - L - _ .  h l  ? n C C  =..I-..I '. n. M. itl~u abrasutxp, i v l .  LY.JU. IIB~LIUUTJILUIILZL 
Sources of Sound. First Symp. on Naval Hydrodynamics, 
Washington D. C., pp.241 - 280. 
Gates, E. M. 1977. The influence of Free Stream Turbulence, 
Free Stream Nuclie Populations and Drag Reducing Polymer 
on Cavitation Inception on Two Axi.~ymmetric Bodies. Rep. 
E182-2, Cal. Inst. of Tech., Div. of Engg. and Appl. Sci. 
Hamilton, M.F. 1981. Travelling Bubble Cavitation and Result- 
ing Noise. Appl. Res. Lab., Penn. State, Tech. Mem. TM 
81-76. 
Hamilton, M. F., Thompson, D. E. and Billet, M. L. 1983. A n  
Experimental Study of Travelling Bubble Cavitation and Noise. 
ASME Int. Symp. on Cavitation Noise, pp.25 - 32. 
Kimoto, H. 1987. An  Experimental Evaluation of the Effects of 
a Water  Microjet and a Shock Wave by a Local Pressure Sensor. 
T-‘ 1 1 1 b .  c..-- i l Y I I I p .  on Cavitation Research Facilities and Techniques. 
ASME FED Vol.57, pp.217-224. 
Marboe, M. L., Billet, h l .  L. and Thompson, D. E. 1986. Some 
Aspects of Travelling Bubble Cavitation and Noise. Int. Symp. 
on Cavitation and Multiphase Flow Noise, ASME, FED Vol. 
45, pp. 119 - 126. 
Mellen, R.H. 1955. An Experimental Study of the Collapse 
of Spherical Cavity i n  Water.  Underwater Sound Laboratory. 
Report No. 279, Oct. 3, 1955. 
Mellen, R.H. 1956. Spherical Pressure Waves of Finite Ampli- 
tude'from Collapsing Cavities. Underwater Sound Laboratory, 
Report No. 326, Sept. 17, 1956. 
Vogel, A., Lauterborn, W. and Timrn. R. 1989. Optical and 
Acoustic Investigations of Dynamics of the Laser-produced Cav- 
itation Bubbles Near a Solid Boundary. J .  Fluid Mech., Vol. 
206, pp.299 - 338. 


Statistics of Noise Generated by Travelling Bubble Cavitation

FED-Vol. 109, Cavitation and Multiphase Flow Forum ASME 1991 
STATISTICS OF NOPSE GENERATED 
BY TRAVELLING BUBBLE CAVITATION 
Sanjay Kumar and Christopher E. Brennen 
California Institute o f  Technology 
Pasadena, California 
ABSTRACT 
This paper presents the details of the collapse process for 
single bubbles generated in travelling bubble cavitation around 
two axisymmetric headforms. The details of the bubble col- 
lapse process have been examined acoustically to understand 
the phenomena of rebounding and multipeaking. We find that 
both rebounding and multipeaking increased with reduction in 
the cavitation number for the ITTC headform. However with 
the Schiebe headform, rebounding increases and multipeaking is 
decreased with reduction in the cavitation number. Some pos- 
sible physical explanations for these phenomena are presented. 
1. INTRODUCTION 
This paper presents some observations on the details of the 
bubble collapse process in travelling bubble cavitation. These 
observations were made for the purpose of improving under- 
standing of the bubble collapse process and its effect on the 
spectra of the resulting noise. Fitzpatrick and Strasberg (1956) 
were the first to model cavitation noise based on Rayleigh's 
analysis. Since Rayleigh's analysis of the collapse of spherical 
bubbles does not consider the effect of the presence of a solid 
wall or the interaction of collapse process with local flow struc- 
tures such as separation and vortices, it may be inadequate 
for the modelling and prediction of travelling bubble cavitation 
noise. Baiter (1974, 1986) has povided a framework for the 
synthesis of the cavitation noise from single bubble cavitation 
noise once the details of the latter are known. 
A number of researchers have acousticallg and photo- 
graphically studied travelling bubble cavitation noise. These 
include studies of a hydrofoil (Blake e t  al. 1977) and a Schiebe 
headform (Marboe e t  al. 1986, Hamilton e6 al. 1982 and Hamil- 
ton 1981). The bubble dynamics have been documented photo- 
graphically for both the Schiebe (Hamilton 1981, Hamilton e t  
al. 1982, Ceccio and Brennen 1991) and the ITTC (Ceccio and 
Brennen 1991) headforms. Recently Ceccio and Brennen (1991) 
found that a single cavitation event can produce an acoustic sig- 
nal which consists of more than one pulse, each of which may 
consist of more than one peak. These phenomena are the result 
of interaction between the bubble and the local flow structure. 
The present paper reports on an investigation of the bubble 
collapse process with particular attention to rebounding and 
multipeaking and their impact on the noise generated by the 
cavitation event. The effect of these phenomena on the spec- 
trum of the resulting noise has also been investigated and will 
be pesented at the forum. 
2. NOMENCLATURE 
I,  acoustic impulse (see Fig. 3) 
I ,  a measure of strength of the pulse 
P peak amplitude of the main or the rebound 
pulse (see Fig. 3) 
Lucite 
Headform 
ITC - 1042 
Water Hjdrophone 
Cavity 
Digital Data 
Acquisition System 
Figure 1. 
headform. 
T 
tl 
t 2  
U 
c7 
T 
r3 
T I  
Schematic illustrating the instrumentation of the 
ratio of maximum peak of the rebound pulse 
to maximum peak of the main pulse 
time of begining of the main or the rebound 
pulse 
time of end of the main or the rebound pulse 
flow velocity 
cavitation number 
duration between maximum peak of the main 
pulse and maximum peak of the rebound 
pulse (see Fig. 3) 
peak separation (see Fig. 3) 
duration of main or rebound pulse (see Fig. 3) 
3. EXPERIMENTAL METHODS 
The experiments were conducted in the Low Turbulence 
Water Tunnel (Gates 1977) at  the California Institute of Tech- 
nology. The experimental equipment and installation used by 
Ceccio and Brennen (1991) was employed in these experiments. 
All the experiments were conducted at a fixed velocity with the 
desired cavitation number obtained by lowering the static pres- 
sure in the water tunnel. The air content was measured using 
a Van Slyke apparatus and was maintained between S and 10 
ppm. Travelling bubble cavitation was produced on the two 
axisymmetric headforms used by Ceccio and Brennen (1991), 
namely a Schiebe headform and a ITTC headform with diame- 
ters of 5.08 and 5.59 cm respectiveiy. The signal emitted during 
bubble collapse was recorded using an ITC-1042 hydrophone 
which has a flat frequency response up to about 80 kHz. The 
hydrophone was placed inside the headforms which were made 
of lucite in order to make them acoustically transparent. The 
interior of the headforms werc filled with water to produce a rel- 
atively reflection-free path between the cavitation bubbles and 
the hydrophone. An experimental schematic is included as Fig. 
1. 
The signal from hydrophone was amplified and extremely 
low frequencies ( << 1 Hz ) were removed by a high pass filter. 
The filtered signa! wa-s rl;gita!!y szq?!ed rrt 500 Efi. P.re~nd 
500 acoustic traces were collected for each operating condition, 
namely for 3 cavitation numbers ( 0.45, 0.50 and 0.55 ) and 
two flow velocities ( S and 9 m / ~ e c ) .  The signal sampling dura- 
tion was adjusted to capture one complete acoustic trace from 
a bubble collapse. These records were then digitally processed 
in following way. First peaks were detected and classified as 
belonging to a main or a rebound pulse. Then quantities such 
as the peak amplitude and the time intervals between the peaks 
were evaluated. In addition, the following quantities were ob- 
tained: 
Here I ,  is the acoustic impulse, tl and t 2  being the times of 
the begining and the end of main pulse or of the rebound pulse. 
The integral I, is an alternative measure of the strength of the 
pulses and T,  is the duration of each pulse. Also measured were 
the time between maximum peaks in the main and the rebound 
pulses, d, and the ratio of the amplitude of maximum peak in 
the main pulse to the maximum peak in the rebound pulse, r .  A 
typical acoustic trace is shown in Fig. 2 and a sketch illustrating 
the definition of some of the parameters is included as Fig. 3. 
4. EXPERIMENTAL RESULTS 
The probabilities of occurrence of the phenomena of re- 
bounding and multipeaking were examined statistically in order 
to gain some insight into these phenomena. The dependence of 
these probabilities on cavitation number, a , and, to a limited 
I ,  I I I I I I 
1.8  2.0 2.2 2.4 2.6 2.8 3.0 
Time ( msec. ) 
Figure 2. A typical amplified and filtered signal for a single cayitation event 
illustrating multiple peaks and a rebound. Inset shows the complete acoustic 
trace. 
Time Between the 
Main Pulse and the 
Rebound Pulse, z 
Main Pulse . I I I 
~ e b o u n d  Pulse I---$ Pulse D ration, z 
W 
extent on flow velocity, u, are presented in Fig. 4 for the ITTC 
headform and in Fig. 5 for the Schiebe headform. Consider 
first the phenomenon of multipeaking in the main pulse. The 
following trends can be clearly seen in the data. First note that 
changing the flow velocity from 8 to 9 m/sec  has little eEeci on 
the results. Secondly, the probability of rebounding increases as 
o is reduced and this appears to be the case for both the head- 
forms. It is particularly evident that rebounding almost never 
occurs at highest of three cavitation numbers tested, o = 0.55. 
TI,,, --A A : C  ----"- L-b --.--- & --.- L--.lS--- :- ' LL- ---L 
Lub u L a u  uuLxx-zuLc u c b w c c u  the t,wu u c a u ~ u ~ ~ u a  la iii LUC p ~ u u -  
ability of occurrence of multipeaking. For the ITTC headform, 
the probability of occurrence of double-peaked events is almost 
independent of a . However, the probability of occurrence of 
events with more than two peaks increases as the cavitation 
number is reduced. Events with more than two peaks almost 
never occur for the Schiebe headform. The probability of oc- 
currence of both multipeaking and rebounding is higher for the 
ITTC headform than for the Schiebe headform. 
The probability of occurrence of multipeaking in the re- 
bound pulse was also examined and exhibited trends similar to Figure 3. Sketch of a typical acoustic trace with definition of 
those for the main pulse. Rebounds are predominantly single 
some measured quantities. 
peaked ( approximately 80 % for the ITTC headform and 90 '?& 
for the Schiebe headform ). It is convenient to classify the events 
headform 9 m/sec IlTC headform 8 m/sec 
" .  
0.45 0.50 0.55 0.45 0.50 0.55 
Cavitation Number Cavitation Number 
Figure 4. Probabilities of different types of cavitation events on the ITTC head- 
form indicating the occurrence of multiple peaks or a rebound. R and NR respec- 
tively denote events with and without rebound. The number alongside indicates 
the number of peaks in the main pulse. 
Schiebe headform 8 m/sec Schiebe headform 9 m/sec 
0.45 0.50 0.55 0.45 0.50 0.55 
Cavitation Number Cavitation Number 
Figure 5. Probabilities of different types of cavitation events on the Schiebe 
headform indicating the occurrence of multiple peaks or a rebound. R and NR 
respectively denote events with and without rebound. The number alongside 
indicates the number of peaks in the main pulse. 
with a rebound by a of two letters, where the first rebounds with ms type rebounds also present about 20 % of the 
letter represents the number of peaks in the main pulse and the time. 
second letter the number of peaks in the rebound pulse. We use Obviously, the nature of the events are quite different for 
m to denote multiple peaks and 3 to denote a single peak. It the two headforms because of differences in the interaction be- 
is found that the ITTC headform has mostly ms type d m u n d s  tveen the bubble dynamics and the flow structure for the two 
150 %I but mm and sq3 type rebounds are also present in signifi- headforms. Specifically, the presence of boundary layer sepa- 
cant numbers [25 %I. The Schiebe headform has mostly 33 type ,ation on the ITTC headform and its absence on the Schiebe 
Figure 6. A typical photograph from Ceccio and Brennen (1991) 
illustrating the bubble breaking up into two or more pieces 
during the collapse. 
x ITIT - ss - 9 A Schiebe - ss - 9 
w I ~ C  - ms - 8 . Schiebe - ms - 8 1 
Cavitation Number 
Figure 7. Ratio of peak pressure amplitude of the rebound pulse 
to peak pressure amplitude of the main pulse. r ,  as a function 
of cavitation number. 
headform is probably responsible for the observed effects. The 
rebound pulse indicates a second collapse separated by a growth 
phase from the first collapse. The multipeaking, on the other 
hand, could be result of several mechanisms: 
hlult i~le ~ e a k s  map be the result of several shock waves 
emitted during the collapse process (Mellen 1955 and 1956. 
Iiimoto 1987 and Vogel et al. 1989). Iiimoto (1987) has 
separately measured the pulses resulting from microjet im- 
pact as well as a shock wave emitted from the final bub- 
ble collapse. It can be seen from those obsermtions that 
pressure resulting from the shock wave is the larger one. 
Also. the peaks from the microjet and the shock-*me ap- 
pear 0.1 msec apart whereas in present experiment peak 
separation was roughly 0.015 msec. Using Schlieren tech- 
nique, Vogel e t  al. (1989) have observed two shock waves 
emitted due to non-spherical bubble collapse. Hence, the 
multiplicity of peaks could also be result of a number of 
shockwaves due to the non-spherical bubble collapse. 
The bubble can breakup into several pieces while collapsing 
(as seen by Ceccio and Brennen (1991) and shown in Fig. 
6) and therefore generate two or more peaks. Considering 
the two bubble pieces to be roughly 1 mm apart (as seen 
from the photographs in Ceccio and Brennen 1091) the 
resulting peaks could be roughly 100 msec apart. Here, 
the bubble may breakup during the collapse as a result 
of the onset of higher order surface oscillations due to 
presence of the solid wall or due to the shearing action 
of the local flow. 
Volume oscillations during the collapse process could cause 
multiple peaks. By comparison with observed peak sepa- 
ration of roughly 0.015 msec, the natural period of oscil- 
lation for a 20 pm microbubble is also 0.015 msec. Thus. 
volume oscillations during the collapse may be a plausible 
reason for the multiple peaks. 
We now examine other features of the results. The ratio of 
the maximum main pulse amplitude to maximum rebound pulse 
amplitude, r ,  is presented against the cavitation number in Fig. 
5 for two velocities and various types of events. It is seen that 
most of the data is clustered around the value of 3. With a 95 % 
confidence level, we find that the mean value of r will lie between 
1.5 and 2 .5 .  It seems that bubble fission observed by Ceccio and 
Brennen (1991) happens in such a way that the remnant nucleus 
generates approximately half the maximum pressure. This may 
mean that during the first collapse certain nonlinear modes of 
surface oscillation are set up which cause the bubble to breakup 
0.44 0.46 0.48 0.50 0.52 0.54 0.56 
Cavitation Number 
Figure 8. Dependence of time between the main and rebound 
pulses, T on the flow condition and the type of rebound. The 
legend indicates the headform, type of rebound and the f i o ~  
velocity. Type of rebound is indicated by 2 letters; the first 
letter indicates the number of peaks in the main pulse and 
the second letter the number of peaks in the rebound ~ u l s e ;  
m indicates multiple peaks and 3 indicates a single peak. 
in a repeatable way. The present observations differ from those 
of Hamilton (1981) who found that the acoustic energy emitted 
by the main and the rebound pulses were roughly the same. 
The time interval between the main pulse and the rebound 
pulse, r. is presented as a function of cavitation number in Fig. 
Q r ~ , -  ..--.-..- -r .---.- 
rvL r a i u u a  bypc UL w w t s  and two fiow veiocities. It can 
be seen that T is in the range of between 0.3 to 1.3 msec and 
generally increases as a is reduced. Multiple peaks appear to 
delay the rebound. This feature and the differences between 
two flow velocities are not easily explained. 
The quantities P, I,, I,, T,, T, and spectra were also 
examined to understand their dependence on the flow condi- 
tion and multipeaking and rebounding. These results will be 
presented at  forum and in a later publication. 
5 .  C O N C L U S I O N S  
On the basis of above observations it may be concluded 
that multipeaking and rebounding increase with the reduction 
in the c~v;\lit,..tion u=.,ber for the ITTC headform. Kuwe-ver for 
the Schiebe head form, multipeaking decreases and rebounding 
increases as the cavitation number is reduced. Also, both the 
multipeaking and rebounding occur more frequently for the 
ITTC headform compared to the Schiebe headform. The flow 
velocity seems to have little effect on these results. Most events 
with rebound for the ITTC headform are of m s  type whereas 
they are mostly 3s type for the Schiebe headform The ratio of 
the peak amplitude of the rebound pulse to the peak amplitude 
of the main pulse is close to 2.0 for d l  flow conditions and 
types of events. This may indicate a fairly repeatable process 
of bubble fission and rebound. The time between the main pulse 
and the rebound pulse, T ,  is seen to decrease with increase in 
a . Multiple peaks in the main pulse are observed to delay the 
rebound. 
6. ACKNOWLEDGEMENTS 
The authors are grateful for the support of the Office of Kaval 
Research under contract N 000167 - 85 - I< - 0165. We also 
thank Dr. Steven L. Ceccio and Yan Kuhn de Chizelle for their 
assistance. 
7 .  R E F E R E N C E S  
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Statistics of Noise Generated by Travelling Bubble Cavitation

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