A test apparatus was designed and constructed to observe the effect of sinusoidal pitching oscillations on the cavitation of three-dimensional hydrofoils.  The apparatus is capable of oscillating hydrofoils at a rate up to 50 Hz and provides for adjustments in oscillation amplitude and mean angle of attack.  Observations of the effect of pitching oscillation on cavitation have been made for a NACA 64-309 (modified) hydrofoil operating at its designed mean angle of attack of 7 degrees with an oscillation amplitude of 2 degrees.  Photographs illustrating the interaction between natural cavity shedding frequencies and the foil reduced frequency are included

Acosta, A. J.

Brennen, C. E.

Hart, D. P.

English

Caltech Authors - Main

OBSERVATIONS OF CAVITATION ON A THREE-DIMENSIONAL 
OSCILLATING HYDROFOIL 
D. P. Hart, C. E. Brennen, and A. J. Acosta 
California Institute of Technology 
Pasadena, California 
Abstract 
A test apparatus was designed and constructed to observe 
the effect of sinusoidal pitching oscillations on the cavitation 
of thredimensional hydrofoils. The apparatus is capable of 
oscillating hydrofoils at a rate up to 50 Hz and provides for 
adjustments in oscillation amplitude and mean angle of attack. 
Observations of the effect of pitching oscillation on cavitation 
have been made for a NACA 64-309 (modified) hydrofoil oper- 
ating a its designed mean angle of attack of 7O with an oscilla- 
tion amplitude of 2O. Photographs illustrating the interaction 
between natural cavity shedding frequencies and the foil re- 
duced frequency are included. 
Nomenclature 
c = Foil chord length, 0.154m (6in) 
j = Excitation frequency in Hz 
k = Reduced frequency = wc/2Um 
P, = Water vapor pressure in kPa 
Pm = LTWT test section pressure in kPa 
Re = Reynolds number = Umc/v 
U, = LTWT test section velocity in m/s 
w -= Foil excitation frequency in rad/s 
a! = Hydrofoil angle of attack in degrees 
v = Kinematic viscosity in m2/s 
p = Fluid density in kg/m3 
a = Cavitation number = (Pm - P , ) / ( O . S ~ U ~ )  
1. Introduction 
Oscillating foils provide a convenient means of simulat- 
ing the effects of freestream velocity fluctuations on cavita- 
tion. These fluctuations have a pronounced influence on the 
performance of propellers, hydrofoils and turbomachinery. It 
effects not only the inception of cavitation but also the form in 
which cavitation appears (Avellan et. al. [1989]). A number 
of theoretical, numerical, and experimental studies have been 
devoted to the subject of oscillating foils. However, these inves- 
ceived very little attention. In an effort to explore this area, 
we recently constructed a test apparatus to oscillate three- 
dimensional hydrofoils in the Low Turbulence Water Tunnel 
(LTWT) (Gates [1977]). 
2. Experimental Setup 
The oscillating foil mechanism, shown in Figure 1, was de- 
signed and constructed to mount to the underneath side of the 
working section of the LTWT. When in place, this mechanism 
is capable of pitching a hydrofoil in a sinusoidal fashion at  a 
rate variable from 0 to 50 Hz. It is driven by a one horsepower 
DC motor coupled to the hydrofoil by a three bar linkage. A 
slip collet at the hydrofoil end of this linkage allows the hy- 
drofoil mean angle of attack to be adjusted. The hydrofoil 
itself mounts to an aluminum plate recessed in the floor of 
the LTWT test section. It pivots about a stainless steel shaft 
mounted 0.38~ from the leading edge of the foil. The phase 
angle and oscillation rate of the hydrofoil are monitored by an 
optical shaft encoder mounted on the DC motor. The encoder 
output, 1024 pulses per cycle, is supplied to a digital tachome- 
ter and to a synchronizer which allows instrumentation to  be 
synchronized with the foil position. The oscillation rate is con- 
trolled in an open loop fashion by a Sabina motor control unit. 
The LTWT is capable of operating at  speeds up to 10 m/s 
and pressures down to 18 kpa. A Zenith 120 microcomputer 
has been adapted to continuously monitor the tunnel operating 
conditions including velocity, pressure, and temperature. 
Photographs of the hydrofoil cavitation were taken using 
two Strobotac 1531-A strobe lights mounted to the top of the 
LTWT test section. The camera shutter was opened and a 
single flash was triggered at a chosen moment during an os- 
cillation cycle using the output from the motor shaft encoder. 
The 10 microsecond flash duration of the strobes in combina- 
tion with Konica 3200 ASA film allowed the cavitation events 
to be captured clearly. 
tigations deal primarily with two-dimensional foils whereas the 
study of three-dimensional oscillating foils have, in the past, re- 
the oscillation of the hydrofoil. However, there exists a phase 
lag between the extent of the leading edge cavitation and the 
Figure 1. Oscillating Foil Mechanism. 
3. Observation and Discussion 
The present paper will describe preliminary observations 
made of cavitation on a reflection-plane mounted, aspect 2.3, 
NACA 64-309 (modified) hydrofoil oscillating in a sinusoidal 
fashion with an amplitude of 2O at  the design mean angle of 
attack of 7O. Comparisons are made for reduced frequencies, k, 
from 0.15 to 1.5, Reynolds numbers, Re, ranging from 11 x lo5 
t o  13 x lo5 and a dissolved air content of 6 ppm. In all cases, 
cavitation inception was first observed in the tip vortex about 
three chords downstream from the trailing edge and occured at 
a cavitation inception number, a, of about 2.1. This cavitation 
then moved upstream as the tunnel pressure was decreased 
until it attached to the foil tip on the suction side near the 
trailing edge. Leading edge cavitation did not appear until the 
cavitation number was approximately half that of tip vortex 
cavitation inception, about a NN 1.0. 
Leading edge cavitation first appears on the suction side 
of the hydrofoil as traveling bubble cavitation which, as the 
cavitation number is reduced, quickly becomes attached cav- 
itation near the base of the foil. With further reduction, the 
attached cavitation grows from the base outward towards the 
tip. The trailing edge of this attached cavity has a parabolic 
shape which follows the pressure contour characteristic of fi- 
nite aspect ratio foils. At the base of the hydrofoil, where the 
attached cavity initially forms, there is a strong interaction 
between the hydrofoil and the tunnel boundary layer. The 
result of this interaction is an increased pressure which s u p  
presses cavitation near the mid-chord and trailing edge of the 
foil. When the leading edge cavity collapses (due to the natu- 
ral shedding frequency of the cavitation, the oscillation of the 
foil or a combination of both), a bubbly cloud near the base 
of the hydrofoil is formed. A ring vortex often emerges from 
the  downstream side of this cloud and the cloud and vortex 
dissipate several chords downstream of the trailing edge. 
We now examine the response of the cavitation to the 
hydrofoil oscillation between angles of attack of 5" and 9". In 
general, the leading edge cavitation forms and collapses with 
foil oscillation which tends to increase with increased frequency. 
At lower reduced frequencies, leading edge cavitation forms and 
grows an appreciable amount before the hydrofoil has reached 
its maximum angle of attack. The cavitation then remains 
until the hydrofoil angle of attack is well below that at  which 
inception occurs. At the higher reduced foil freque~cies of 0.3 
or greater, leading edge cavitation does not grow significantly 
until after the hydrofoil has reached its maximum oscillation 
amplitude. Again, it remains until the hydrofoil angle of attack 
is well below the point of inception. 
In addition to the noticeable phase lag between the hydro- 
foil and the cavitation oscillations, a strong interaction between 
the hydrofoil reduced frequency and the natural shedding fre- 
quency of the leading edge cavitation exists. Cavitation on the 
leading edge of the foil sheds and reforms at  a frequency not 
only dependent on the excitation frequency but also on the 
Reynolds number of the flow. The photographs in Figures 2. 
through 4. illustrate this interaction between the natural shed- 
ding frequency and the excitation frequency. They show the 
suction side of the hydrofoil with rounded tip operating at  a 
Reynolds number of 12 x lo5 and a cavitation number of 0.5 as 
it oscillates from 9" to 5" in 0.5O increments. Figure 2 shows 
the hydrofoil at  a reduced frequency of 0.35 or an oscillation 
rate of 6 Hz which is slightly below the 8 Hz cavity shedding 
frequency observed when the hydrofoil is held stationary a t  
7" angle of attack. Notice the two distinct cavities that exist 
at 7.5O angle of attack and the ring vortex that remains from 
a previous cavity collapse. As the excitation frequency is in- 
creased to 8 Hz (Figure 3.) two separate collapses no longer 
occur. Observations at this frequency reveal that the points 
of cavitation formation and collapse during an oscillation cycle 
are very inconsistent. At a higher excitation frequency of 12 
Hz (Figure 41 the cavity formation and collapse remain very 
similar to  that at  8 Hz but the points during the oscillation 
Figure 2. Leading Edge Cavitation (Re = 12 x lo5, 
o = 0.5, k = 0.44). 
Figure 3. Leading Edge Cavitation (Re = 12 x lo5, 
a = 0.5, k = 0.57). 
cycle at  which they occur have now become quite consistent. 
Unlike the 6 Hz excitation case both the 8 Hz and the 12 Hz 
excitation cases result in a loud pounding sound as the cavities 
collapse. Note the phase lag between the hydrofoil angle of 
attack and the extent of cavitation that exists in all three sets 
of photographs. 
As one would expect, oscillating the hydrofoil significantly 
affects the cavitation number at  which inception occurs. Figure 
5 illustrates this by showing the leading edge cavitation incep 
tion index as a function of hydrofoil phase angle for reduced 
frequencies, k, ranging from 0.22 to 1.82. The hydrofoil phase 
angle shown in this figure corresponds to an angle of attack of 
5' at a phase angle of 0' increasing to 9' at  a phase angle of 
180' and then decreasing back to 5' at  a phase angle of 360'. 
ivote that as the excitation frequency is increased a phase shift 
develops and results in the largest cavitation inception index 
occuring later in the oscillation cycle. Moreover, even at  an 
excitation frequency of 4 Hz a significant asymmetry occurs 
in inception. This phenomena is better illustrated in Figure 
6. Here the data has been plotted in the form of a hysteresis 
diagram with the lower traces representing an increasing angle 
of attack and the upper traces representing a decreasing angle 
of attack. As the excitation frequency increases, there is an in- 
creased hysteresis between cavitation inception and desinence. 
This hysteresis, however, is largely due to kinematic effects 
which result in a difference between the hydrodynamic angle 
of attack of the leading edge moving relative to the freestream 
flow and the geometric angle of attack of the hydrofoil rela- 
tive to the tunnel floor. When the data is plotted relative to 
the hydrodynamic angle of attack (Figure 7.), it collapses to 
an extent which suggests a universal relationship between in- 
ception and the instantaneous hydrodynamic angle of attack. 
Stationary surface cavitation inception index for this foil as a 
function of angle of attack was documented by Green 119881 
and is included for comparison. The reason for the discrep 
ancy between this data and that of Green is unknown at  the 
present time. 
Figure 4. Leading Edge Cavitation (Re = 12 x lo5, 
rr = 0.5, k = 0.88). 
4. Conclusions 
The effect that freestream velocity fluctuations have on 
the cavitation of a hydrofoil of finite aspect ratio has been in- 
vestigated using a test facility designed to pitch a hydrofoil in 
a sinusoidal fashion about its center of pressure. Photographs 
taken with strobes synchronized to the hydrofoil motion show 
that there is a dependence of the observed cavitation formation 
and inception on the hydrofoil reduced frequency. Further- 
more, observations indicate that there can be a strong inter- 
action between the natural shedding frequency of the leading 
, 
0 9 0 1 8 0  2 7 0 3 6 0  
Hydrofoil Phase Angle 
Figure 5. Leading Edge Cavitation (Re = 12 x lo5). 
The maximum and minimum angles of 
attack correspond to phase angles of 180" 
and O0 (or 360°) respectively. 
.? 
.'I 
I4 ; 1.5 - 
2; 
g 1.0- 
.* Y 
m 
.% + Excitation Frequency 
0.5 - - 4 Hz (k=0.22) 
-.-. ,.-.- 8 Hz (k=O.46) 
Geometric Angle of Attack [degrees] 
Figure 6. Leading Edge Cavitation as a Function 
of Hydrofoil Geometric Angle 
(Re = 12 x lo5). 
edge cavitation and the hydrofoil excitation frequency leading 
to  irregular cavitation patterns and violent cavity collapses. 
However, investigations of leading edge cavitation inception 
indecates that within the range of reduced frequencies investi- 
gated, the increase in the cavitation number at which inception 
occurs is primarily due to the increase in hydrodynamic angle 
of attack resulting from the kinematics of the oscillating foil. 
5 .  Acknowledgments 
The authors are grateful for the support of the Office of 
Naval Research under grant number N00167-85-K-0165. We 
should also like to thank Professor S. Green a t  the University 
of British Columbia for his help in initiating this project and 
S. Ceccio for his continuing support. 
*05 
/ Excitation Frequency 4 Hz (k=0.22) + 8 Hz (k=0.46) A 12 Hz (k=0.68) 
24 Hz (k=1.37) 
Hydrofoil Angle of Attack 
Figure 7. Leading Edge Cavitation as a Function 
of Hydrofoil Hydrodynamic Angle of 
Attack (Re = 12 x lo5). The Solid 
line represents stationary leading edge 
cavitation data from Green [1988]. 
6. References 
Avellan, F., Dupont, P., Ryhming, I. 1989. Generation Mecha- 
nism and Dynamics of Cavitation Downstream of a Fixed 
Leading Edge Cavity Proc. of 17th Symposium on Naval 
Hydrodynamics, National Academy Press, Washington 
D.C., pp. 317-329. 
Avellan, F., Farhat, M. 1989. Shock Pressure Generated by 
Cavitation Vortex Collapse, Proc. of Int. Symp. on Cav. 
Noise and Erosion in Fluid Mech., San Francisco, pp. 119- 
125. 
Bartels, F. 1989. Model Tests on Noise Characteristics of Pro- 
peller Cavitation in Wake Flow, Proc. of Int. Symp. on 
Cav. Noise and Erosion in Fluid Mech., San Francisco, 
pp. 47-54. 
Gates, E. M. 1977. The Influence of Freestream Turbulence, 
Ekeestrearn Nuclei Populations, and Drag-Reducing Poly- 
mer on Cavitation Inception on Two Ansymmetric Bodies. 
Calif. Inst. of Tech., Div. of Eng. and Appl. Sci., Report 
NO. E182-2. 
Green, S. I. 1988. Tip Vortices - Single Phase and Cavitating 
Flow Phenomena Ph.D. Thesis, Calif. Inst. of Tech. Div. 
of Eng. and Appl. Sci., Report No. 183-17. 
Kato, H., Ye, Y. P., and Maeda, M. 1989. Cavitation Erosion 
and Noise Study on a Foil Section. Proc. of Int. Symp. 
on Cav. Noise and Erosion in Fluid Mech., San Francisco, 
pp. 7488. 


Observations of Cavitation on a Three-Dimensional Oscillating Hydrofoil

OBSERVATIONS OF CAVITATION ON A THREE-DIMENSIONAL 
OSCILLATING HYDROFOIL 
D. P. Hart, C. E. Brennen, and A. J. Acosta 
California Institute of Technology 
Pasadena, California 
Abstract 
A test apparatus was designed and constructed to observe 
the effect of sinusoidal pitching oscillations on the cavitation 
of thredimensional hydrofoils. The apparatus is capable of 
oscillating hydrofoils at a rate up to 50 Hz and provides for 
adjustments in oscillation amplitude and mean angle of attack. 
Observations of the effect of pitching oscillation on cavitation 
have been made for a NACA 64-309 (modified) hydrofoil oper- 
ating a its designed mean angle of attack of 7O with an oscilla- 
tion amplitude of 2O. Photographs illustrating the interaction 
between natural cavity shedding frequencies and the foil re- 
duced frequency are included. 
Nomenclature 
c = Foil chord length, 0.154m (6in) 
j = Excitation frequency in Hz 
k = Reduced frequency = wc/2Um 
P, = Water vapor pressure in kPa 
Pm = LTWT test section pressure in kPa 
Re = Reynolds number = Umc/v 
U, = LTWT test section velocity in m/s 
w -= Foil excitation frequency in rad/s 
a! = Hydrofoil angle of attack in degrees 
v = Kinematic viscosity in m2/s 
p = Fluid density in kg/m3 
a = Cavitation number = (Pm - P , ) / ( O . S ~ U ~ )  
1. Introduction 
Oscillating foils provide a convenient means of simulat- 
ing the effects of freestream velocity fluctuations on cavita- 
tion. These fluctuations have a pronounced influence on the 
performance of propellers, hydrofoils and turbomachinery. It 
effects not only the inception of cavitation but also the form in 
which cavitation appears (Avellan et. al. [1989]). A number 
of theoretical, numerical, and experimental studies have been 
devoted to the subject of oscillating foils. However, these inves- 
ceived very little attention. In an effort to explore this area, 
we recently constructed a test apparatus to oscillate three- 
dimensional hydrofoils in the Low Turbulence Water Tunnel 
(LTWT) (Gates [1977]). 
2. Experimental Setup 
The oscillating foil mechanism, shown in Figure 1, was de- 
signed and constructed to mount to the underneath side of the 
working section of the LTWT. When in place, this mechanism 
is capable of pitching a hydrofoil in a sinusoidal fashion at  a 
rate variable from 0 to 50 Hz. It is driven by a one horsepower 
DC motor coupled to the hydrofoil by a three bar linkage. A 
slip collet at the hydrofoil end of this linkage allows the hy- 
drofoil mean angle of attack to be adjusted. The hydrofoil 
itself mounts to an aluminum plate recessed in the floor of 
the LTWT test section. It pivots about a stainless steel shaft 
mounted 0.38~ from the leading edge of the foil. The phase 
angle and oscillation rate of the hydrofoil are monitored by an 
optical shaft encoder mounted on the DC motor. The encoder 
output, 1024 pulses per cycle, is supplied to a digital tachome- 
ter and to a synchronizer which allows instrumentation to  be 
synchronized with the foil position. The oscillation rate is con- 
trolled in an open loop fashion by a Sabina motor control unit. 
The LTWT is capable of operating at  speeds up to 10 m/s 
and pressures down to 18 kpa. A Zenith 120 microcomputer 
has been adapted to continuously monitor the tunnel operating 
conditions including velocity, pressure, and temperature. 
Photographs of the hydrofoil cavitation were taken using 
two Strobotac 1531-A strobe lights mounted to the top of the 
LTWT test section. The camera shutter was opened and a 
single flash was triggered at a chosen moment during an os- 
cillation cycle using the output from the motor shaft encoder. 
The 10 microsecond flash duration of the strobes in combina- 
tion with Konica 3200 ASA film allowed the cavitation events 
to be captured clearly. 
tigations deal primarily with two-dimensional foils whereas the 
study of three-dimensional oscillating foils have, in the past, re- 
the oscillation of the hydrofoil. However, there exists a phase 
lag between the extent of the leading edge cavitation and the 
Figure 1. Oscillating Foil Mechanism. 
3. Observation and Discussion 
The present paper will describe preliminary observations 
made of cavitation on a reflection-plane mounted, aspect 2.3, 
NACA 64-309 (modified) hydrofoil oscillating in a sinusoidal 
fashion with an amplitude of 2O at  the design mean angle of 
attack of 7O. Comparisons are made for reduced frequencies, k, 
from 0.15 to 1.5, Reynolds numbers, Re, ranging from 11 x lo5 
t o  13 x lo5 and a dissolved air content of 6 ppm. In all cases, 
cavitation inception was first observed in the tip vortex about 
three chords downstream from the trailing edge and occured at 
a cavitation inception number, a, of about 2.1. This cavitation 
then moved upstream as the tunnel pressure was decreased 
until it attached to the foil tip on the suction side near the 
trailing edge. Leading edge cavitation did not appear until the 
cavitation number was approximately half that of tip vortex 
cavitation inception, about a NN 1.0. 
Leading edge cavitation first appears on the suction side 
of the hydrofoil as traveling bubble cavitation which, as the 
cavitation number is reduced, quickly becomes attached cav- 
itation near the base of the foil. With further reduction, the 
attached cavitation grows from the base outward towards the 
tip. The trailing edge of this attached cavity has a parabolic 
shape which follows the pressure contour characteristic of fi- 
nite aspect ratio foils. At the base of the hydrofoil, where the 
attached cavity initially forms, there is a strong interaction 
between the hydrofoil and the tunnel boundary layer. The 
result of this interaction is an increased pressure which s u p  
presses cavitation near the mid-chord and trailing edge of the 
foil. When the leading edge cavity collapses (due to the natu- 
ral shedding frequency of the cavitation, the oscillation of the 
foil or a combination of both), a bubbly cloud near the base 
of the hydrofoil is formed. A ring vortex often emerges from 
the  downstream side of this cloud and the cloud and vortex 
dissipate several chords downstream of the trailing edge. 
We now examine the response of the cavitation to the 
hydrofoil oscillation between angles of attack of 5" and 9". In 
general, the leading edge cavitation forms and collapses with 
foil oscillation which tends to increase with increased frequency. 
At lower reduced frequencies, leading edge cavitation forms and 
grows an appreciable amount before the hydrofoil has reached 
its maximum angle of attack. The cavitation then remains 
until the hydrofoil angle of attack is well below that at  which 
inception occurs. At the higher reduced foil freque~cies of 0.3 
or greater, leading edge cavitation does not grow significantly 
until after the hydrofoil has reached its maximum oscillation 
amplitude. Again, it remains until the hydrofoil angle of attack 
is well below the point of inception. 
In addition to the noticeable phase lag between the hydro- 
foil and the cavitation oscillations, a strong interaction between 
the hydrofoil reduced frequency and the natural shedding fre- 
quency of the leading edge cavitation exists. Cavitation on the 
leading edge of the foil sheds and reforms at  a frequency not 
only dependent on the excitation frequency but also on the 
Reynolds number of the flow. The photographs in Figures 2. 
through 4. illustrate this interaction between the natural shed- 
ding frequency and the excitation frequency. They show the 
suction side of the hydrofoil with rounded tip operating at  a 
Reynolds number of 12 x lo5 and a cavitation number of 0.5 as 
it oscillates from 9" to 5" in 0.5O increments. Figure 2 shows 
the hydrofoil at  a reduced frequency of 0.35 or an oscillation 
rate of 6 Hz which is slightly below the 8 Hz cavity shedding 
frequency observed when the hydrofoil is held stationary a t  
7" angle of attack. Notice the two distinct cavities that exist 
at 7.5O angle of attack and the ring vortex that remains from 
a previous cavity collapse. As the excitation frequency is in- 
creased to 8 Hz (Figure 3.) two separate collapses no longer 
occur. Observations at this frequency reveal that the points 
of cavitation formation and collapse during an oscillation cycle 
are very inconsistent. At a higher excitation frequency of 12 
Hz (Figure 41 the cavity formation and collapse remain very 
similar to  that at  8 Hz but the points during the oscillation 
Figure 2. Leading Edge Cavitation (Re = 12 x lo5, 
o = 0.5, k = 0.44). 
Figure 3. Leading Edge Cavitation (Re = 12 x lo5, 
a = 0.5, k = 0.57). 
cycle at  which they occur have now become quite consistent. 
Unlike the 6 Hz excitation case both the 8 Hz and the 12 Hz 
excitation cases result in a loud pounding sound as the cavities 
collapse. Note the phase lag between the hydrofoil angle of 
attack and the extent of cavitation that exists in all three sets 
of photographs. 
As one would expect, oscillating the hydrofoil significantly 
affects the cavitation number at  which inception occurs. Figure 
5 illustrates this by showing the leading edge cavitation incep 
tion index as a function of hydrofoil phase angle for reduced 
frequencies, k, ranging from 0.22 to 1.82. The hydrofoil phase 
angle shown in this figure corresponds to an angle of attack of 
5' at a phase angle of 0' increasing to 9' at  a phase angle of 
180' and then decreasing back to 5' at  a phase angle of 360'. 
ivote that as the excitation frequency is increased a phase shift 
develops and results in the largest cavitation inception index 
occuring later in the oscillation cycle. Moreover, even at  an 
excitation frequency of 4 Hz a significant asymmetry occurs 
in inception. This phenomena is better illustrated in Figure 
6. Here the data has been plotted in the form of a hysteresis 
diagram with the lower traces representing an increasing angle 
of attack and the upper traces representing a decreasing angle 
of attack. As the excitation frequency increases, there is an in- 
creased hysteresis between cavitation inception and desinence. 
This hysteresis, however, is largely due to kinematic effects 
which result in a difference between the hydrodynamic angle 
of attack of the leading edge moving relative to the freestream 
flow and the geometric angle of attack of the hydrofoil rela- 
tive to the tunnel floor. When the data is plotted relative to 
the hydrodynamic angle of attack (Figure 7.), it collapses to 
an extent which suggests a universal relationship between in- 
ception and the instantaneous hydrodynamic angle of attack. 
Stationary surface cavitation inception index for this foil as a 
function of angle of attack was documented by Green 119881 
and is included for comparison. The reason for the discrep 
ancy between this data and that of Green is unknown at  the 
present time. 
Figure 4. Leading Edge Cavitation (Re = 12 x lo5, 
rr = 0.5, k = 0.88). 
4. Conclusions 
The effect that freestream velocity fluctuations have on 
the cavitation of a hydrofoil of finite aspect ratio has been in- 
vestigated using a test facility designed to pitch a hydrofoil in 
a sinusoidal fashion about its center of pressure. Photographs 
taken with strobes synchronized to the hydrofoil motion show 
that there is a dependence of the observed cavitation formation 
and inception on the hydrofoil reduced frequency. Further- 
more, observations indicate that there can be a strong inter- 
action between the natural shedding frequency of the leading 
, 
0 9 0 1 8 0  2 7 0 3 6 0  
Hydrofoil Phase Angle 
Figure 5. Leading Edge Cavitation (Re = 12 x lo5). 
The maximum and minimum angles of 
attack correspond to phase angles of 180" 
and O0 (or 360°) respectively. 
.? 
.'I 
I4 ; 1.5 - 
2; 
g 1.0- .* Y 
m 
.% + Excitation Frequency 
0.5 - - 4 Hz (k=0.22) -.-. ,.-.- 8 Hz (k=O.46) 
Geometric Angle of Attack [degrees] 
Figure 6. Leading Edge Cavitation as a Function 
of Hydrofoil Geometric Angle 
(Re = 12 x lo5). 
edge cavitation and the hydrofoil excitation frequency leading 
to  irregular cavitation patterns and violent cavity collapses. 
However, investigations of leading edge cavitation inception 
indecates that within the range of reduced frequencies investi- 
gated, the increase in the cavitation number at which inception 
occurs is primarily due to the increase in hydrodynamic angle 
of attack resulting from the kinematics of the oscillating foil. 
5 .  Acknowledgments 
The authors are grateful for the support of the Office of 
Naval Research under grant number N00167-85-K-0165. We 
should also like to thank Professor S. Green a t  the University 
of British Columbia for his help in initiating this project and 
S. Ceccio for his continuing support. 
*05 
/ Excitation Frequency 4 Hz (k=0.22) + 8 Hz (k=0.46) A 12 Hz (k=0.68) 
24 Hz (k=1.37) 
Hydrofoil Angle of Attack 
Figure 7. Leading Edge Cavitation as a Function 
of Hydrofoil Hydrodynamic Angle of 
Attack (Re = 12 x lo5). The Solid 
line represents stationary leading edge 
cavitation data from Green [1988]. 
6. References 
Avellan, F., Dupont, P., Ryhming, I. 1989. Generation Mecha- 
nism and Dynamics of Cavitation Downstream of a Fixed 
Leading Edge Cavity Proc. of 17th Symposium on Naval 
Hydrodynamics, National Academy Press, Washington 
D.C., pp. 317-329. 
Avellan, F., Farhat, M. 1989. Shock Pressure Generated by 
Cavitation Vortex Collapse, Proc. of Int. Symp. on Cav. 
Noise and Erosion in Fluid Mech., San Francisco, pp. 119- 
125. 
Bartels, F. 1989. Model Tests on Noise Characteristics of Pro- 
peller Cavitation in Wake Flow, Proc. of Int. Symp. on 
Cav. Noise and Erosion in Fluid Mech., San Francisco, 
pp. 47-54. 
Gates, E. M. 1977. The Influence of Freestream Turbulence, 
Ekeestrearn Nuclei Populations, and Drag-Reducing Poly- 
mer on Cavitation Inception on Two Ansymmetric Bodies. 
Calif. Inst. of Tech., Div. of Eng. and Appl. Sci., Report 
NO. E182-2. 
Green, S. I. 1988. Tip Vortices - Single Phase and Cavitating 
Flow Phenomena Ph.D. Thesis, Calif. Inst. of Tech. Div. 
of Eng. and Appl. Sci., Report No. 183-17. 
Kato, H., Ye, Y. P., and Maeda, M. 1989. Cavitation Erosion 
and Noise Study on a Foil Section. Proc. of Int. Symp. 
on Cav. Noise and Erosion in Fluid Mech., San Francisco, 
pp. 7488. 


Avellan, F., Dupont, P., Ryhming, I. 1989. Generation Mechanism and Dynamics of Cavitation Downstream of a Fixed Leading Edge Cavity Proc. of 17th Symposium on Naval Hydrodynamics, National Academy Press, Washington D.C., pp. 317-329.

Avellan, F., Farhat, M. 1989. Shock Pressure Generated by Cavitation Vortex Collapse, Proc. of Int. Symp. on Cav. Noise and Erosion in Fluid Mech., San Francisco, pp. 119-125.

Bartels, F. 1989. Model Tests on Noise Characteristics of Propeller Cavitation in Wake Flow, Proc. of Int. Symp. on Cav. Noise and Erosion in Fluid Mech., San Francisco, pp. 47-54.

Cavitation Erosion and Noise Study on a Foil Section.

Gates, E. M. 1977. The Influence of Freestream Turbulence, Ekeestrearn Nuclei Populations, and Drag-Reducing Polymer on Cavitation Inception on Two Ansymmetric Bodies. Calif. Inst. of Tech., Div. of Eng. and Appl. Sci., Report NO. E182-2.

Generation Mechanism and Dynamics of Cavitation Downstream of a Fixed Leading Edge Cavity

Green, S. I. 1988. Tip Vortices - Single Phase and Cavitating Flow Phenomena Ph.D. Thesis, Calif. Inst. of Tech. Div. of Eng. and Appl. Sci., Report No. 183-17.

Kato, H., Ye, Y. P., and Maeda, M. 1989. Cavitation Erosion and Noise Study on a Foil Section. Proc. of Int. Symp. on Cav. Noise and Erosion in Fluid Mech., San Francisco, pp. 7488.

Model Tests on Noise Characteristics of Propeller Cavitation in Wake Flow,

Shock Pressure Generated by Cavitation Vortex Collapse,

The Influence of Freestream Turbulence, Ekeestrearn Nuclei Populations, and Drag-Reducing Polymer on Cavitation Inception on Two Ansymmetric Bodies.

Tip Vortices - Single Phase and Cavitating Flow Phenomena Ph.D. Thesis,

http://authors.library.caltech.edu/211/1/HAR107.pdf

Observations of Cavitation on a Three-Dimensional Oscillating Hydrofoil

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