Open Journal of Fluid Dynamics, 2013, 3, 14-21
http://dx.doi.org/10.4236/ojfd.2013.32A003 Published Online July 2013 (http://www.scirp.org/journal/ojfd)
Experimental Study of the Response of Transonic Diffuser
Flow to a Piezoceramic Actuator at Diffus e r Throat
Minoru Yaga1, Yusuke Uechi2, Hiroaki Ozono3, Masaaki Ishikawa1, Isao Teruya1
1Department of Mechanical Systems, Faculty of Engineering, University of the Ryukyus, Okinawa, Japan
2Mie Metal Industry Co. Ltd., Mie , Japan
3Graduate School of Engineering and Science, University of the Ryukyus, Okinawa, Japan
Received May 28, 2013; revised June 5, 2013; accepted June 12, 2013
Copyright © 2013 Minoru Yaga et al. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
An experimental study of the response of a piezoceramic actuator set at the throat to a transonic diffuser is carried out
by measuring wall static pressure fluctuations and by visualizing the flow field using schlieren technique. The visual-
ized flow fields are captured with a digital still camera and a digital high speed video camera. The piezo ceramic actua-
tor is attached at the throat of the diffuser and driven by sinusoidal amplified voltage signals. The diffuser used in this
experiment is circular arc half nozzle with the height h* and width w of 3 mm and 25 mm, respectively. The blockage
factor of the piezoceramic actuator to the diffuser throat is 9.2% assuring the effect of change in the throat area rather
than the boundary layer d isturbances. The piezoceramic actuator is driven at the frequency of 100 Hz, 200 Hz, and 300
Hz and its amplitude is about 1 mm. It is found that the wall static pressure fluctuations and the behavior of the shock
wave clearly correspond to the vibration of the piezo ceramic actuator for all the frequency ranges whereas the averaged
shock position remains almost unchanged. All the results mentioned above suggest that driving the piezo ceramic ac-
tuator at the diffuser throat can be one of the promising techniques to control unsteady transonic diffuser flow.
Keywords: Compressible Flow; Shock Wave; Transonic Diffuser; Piezoceramic Actuator; Throat
1. Introduction
The unsteady flow field in a transonic diffuser has at-
tracted a great deal of interest not only because of the
practical industrial importance but also because of the
complexity of the flow itself. It is well known that a
shock wave in a transonic flow is basically unsteady due
to the interaction between a shock wave and other flow
phenomena, i.e., the shock wave oscillation is triggered
and maintained by a local interaction between the shock
foot and the boundary later developed along the wall
surface or upstream and downstream propagating distur-
bances. Meier [1] reported that shock-induced separation
causes the large-amplitude, unstable oscillation of a
shock wave. In addition to the sh ock-induced separation,
the effects of propagating disturbances toward the shock
waves on the oscillations have been analytically, nu-
merically and experimentally investigated [2,3], includ-
ing forced oscillations by some functions or rotating rods
as a forcing function to drive the shock waves. Accord-
ing to previous studies, several factors affect unsteady
shock behavior in transonic diffusers. Therefore, in addi-
tion to revealing the causes of the shock oscillations,
there have also been attempts to eliminate or reduce these
unfavorable unsteady shock oscillations both for internal
and external devices. It is quite difficult to deal with
these types of oscillation s unless the disturbances around
the shock wave are attenuated or canceled by some tech-
niques because th e longitudinal and boundary layer asso -
ciated disturbances cannot be separated.
The approach to stabilize the unsteady flow fields is
divided into two major controls, which are active control
with jets [4,5] and passive control with a porous cavity [6]
or vortex generators. These controls are expected to gen-
erate the opposite phase of signals or to retard separa-
tions of boundary layers. However, the causes of the os-
cillations include pressure disturbances in a core flow
and unsteady phenomena associated with the shock-
boundary layer interaction, as mentioned above, the fu-
ture trend for the oscillation controls might be a combi-
nation of passive and active controls.
Although the effect of the pressure disturbances in a
core flow and disturbances associated with the boundary
C
opyright © 2013 SciRes. OJFD

M. YAGA ET AL. 15
layer should be considered individually in order to clarify
the factors affecting the oscillations, both effects cannot
be divided because they interact with each other. Thus, in
the present paper, we focus primarily on the mechanical
disturbances by changing cross sectional area at the
throat of a transonic diffuser, which is expected to affect
the location of shock waves according to the isentropic
flow relations between the throat area and local cross
sectional area at a location of the shock wave.
2. Experimental Apparatus and Procedure
2.1. Wind Tunnel Facility
Figures 1(a)-(c) show the wind tunnel, the detail of the
test section, and the driving circuit of the piezoceramic
actuator, respectively. The experimental apparatus con-
sists of a 0.7 MPa compressor, a settling chamber, a
regulator valve, and a circular arc transonic half diffuser
in a blow down wind tunnel discharging to the atmos-
phere. The throat height of the diffuser and its radius are
h* = 3 mm and R = 500 mm, respectively. The span of
the diffuser is 33 mm. The flow field in the diffuser is
visualized by the schlieren technique and captured with a
digital still camera or a digital high-speed video camera,
which enables images of the flow field to be captured at a
rate of 41,000 frames per second. Unsteady wall static
pressure fluctuations are measured using semiconductor
pressure sensors at the settling ch amber, at the throat, and
at positions x = 20, 30, 40, and 50 mm downstream of the
throat. The signals from the pressure transducer are digi-
tized at a sampling frequency of 10 kHz with 16-bit ac-
curacy and are analyzed to evaluate the effect of the pie-
zoceramic actuator on the diffuser flow fields. The reso-
nance frequency of the transducers is 50 kHz assuring the
accuracy of monitoring the pressure fluctuations. The
total pressure at the settling ch amber is monitored during
the experiments by a computer, which controls the tim-
ing of the pressure measurements and flow visualiza-
tions.
2.2. Piezoceramic Actuator
The piezoceramic actuator is set at the diffuser throat, as
shown in Figure 1(b). In order to achieve sufficient dis-
placement by the actuator, a bimorph type piezoceramic
(a)
Bimorph Piezoceramic Actuato
r
DC Amp.
F.G.
DC Amp/ADC
Computer
Diffuser throat
Prs. sensor
U
f
0
Us
PZT pl ate
(b) (c)
Figure 1. Experimental apparatus: (a) Wind tunnel and measure ment system; (b) Detail of test section; (c) Driving circuit for
iezoceramic actuator. p

M. YAGA ET AL. 16
actuator is adopted and driven by the circuit as shown
n images of the
of the interaction region.
e shock waves appear to move
ck
Figure 1(c). The length, width, and thickness of the pie-
zoceramic actuator are 33 mm, 11 mm, and 0.8 mm, re-
spectively. During the experiment, the piezoceramic ac-
tuator is conn ected to a DC typ e amplified vo ltage source
and then bent in order to change the cross sectional area
at the diffuser throat. The maximum input voltage from
the signal source, displacement, and natural resonance
frequency of the piezoceramic actuator are 60 Vp, 0.7
mm, and 400 Hz, respectively. Accordingly, the exciting
input frequency to the piezoceramic actuator is li mited to
300 Hz. From preliminary experiments, the displacement
of the piezoceramic actuator is found to be sufficiently
large compared to that with a layer type piezoceramic
actuator. In this report, only sinusoidal signals are input
into the DC amplifier to achieve simplicity of the fre-
quency analyses.
3. Experimental Results and Discussion
3.1. Results of Flow Visualization
Figures 2(a)-(d) show typical schliere
flow fields and shock positions for th e input frequ ency of
fp = 200 Hz. It is clear that some quite weak Mach waves
are generated near the throat due to the effect of the
moving piezoceramic actuator. At the same time, at a
pressure ratio of p0/pb = 1.20, the starting shock wave
appears to be very weak near x/h* = 6.0, which is fol-
lowed by some weak shock waves due to the interaction
between the shock wave and the boundary layers along
the diffuser walls. Although the flow field downstream of
the normal shock wave is supposed to be subsonic, Fig-
ure 2(a) and subsequent figures illustrate the occurrence
of the shock wave downstream of the first normal shock
wave.
The second shock wave or multiple shock waves are
generated by the acceleration of the main flow due to the
change in the effective cross sectional area of the diffuser
and the disturbances approaching from downstream of
the shock wave. As reported in several previous studies,
the shock wave near the throat is unstable, so that the
shock wave observed in Figure 2(a) change its position,
as will be discussed later herein. Figure 2(b) shows that
the slight increase in the pressure ratio causes the down-
ward displacement of the shock wave. Figure 2(c) illus-
trates the lambda-foot type shock wave on the upper and
lower walls due to a typical moderate interaction be-
tween the shock wave and the boundary layer. Other
shock waves downstream of the first shock position also
correspond to the varying throat height. Then, the dis-
tance between the throat and the averaged shock posi-
tions increases with the pressure ratio. Figures 2(c) and
(d) show that the clear shock waves cause boundary layer
separation followed by multiple shock waves down stre am
3.2. Shock Locations for Various Frequencies
According to Figure 2, th
gradually in th e previous section. Then , it is necessary to
check the relation between rough locations and sho
waves for various input frequencies of the piezoceramic
actuator. Then, their positions are plotted with respect to
the pressure ratio and are shown in Figure 3 as a pa-
rameter of the input frequencies of 0 Hz, 100 Hz, 200 Hz,
and 300 Hz.
2.0
1.0
y/h*
p0 / pb = 1.20
0.0
0246810 12 14 16 18 20-2 x/h*
(a)
2.0
1.0
0.0
y/h*
20181614121086420-2 x/h*
p
0
/ p
b
= 1.40
(b)
2.0
1.0
0.0
y/h*
20181614121086420-2 x/h*
p
0
/ p
b
= 1.60
(c)
2.0
1.0
0.0
y/h*
20181614121086420-2
x
/h*
p
0
/ p
b
= 1.80
(d)
Figure 2. Schlieren images for frequency 200 Hz: (a) p0/pb =
1.2; (b) p0/pb = 1.4; (c) p0/pb = 1.6; (d) p0/pb = 1.8.
20
15
10
5
0
x
s
/ h*
2.42.22.01.81.61.4
Input Frequency
0 Hz
100 Hz
200 Hz
1.21.0
p
0
/ p
b
300 Hz
Figure 3. Relation between shock wave position and pres-
sure ratio.

M. YAGA ET AL. 17
Figure 3 shows the relation between the positions of
shock waves xs divided by throat height h* and the pres-
sure ratio p0/pb the shock locations are measured in the
schlieren images for various input frequencies of 0 Hz
through 300 Hz. The shock wave is found to move mo-
notonically downstream with the increase in the pressure
ratio. However, the gradient of the shock displacement to
the pressure ratio decreases with the pressure ratio be-
cause the shock-induced separation causes displacement
delay. Considering the effect of the piezoceramic actua-
tor, it is easily expected that the location of shock waves
corresponds to the throat height because the Mach num-
ber just upstream of the shock wave depends on the ratio
of the local cross sectional area to the throat area. From
the viewpoint of small-scale observatio n, the shock wave
oscillates around its averaged position at the fixed fre-
quency of the piezoceramic actuator, which will be dis-
cussed in the following section based on images captured
by a high-speed video camera. The behavior of the shock
wave is critical to the generation of large pressure fluc-
tuations under the various pressure ratios.
3.3. Wall Static Pressure Fluctuation
Figures 4(a)-(d) show the time series pressure fluct uat i ons
at the throat x/h* = 0.0 and at x/h* = 10.0 for a frequency
of 200 Hz. The wall static pressure pw divided by the
back pressure pb at the throat exhibits a clear sinusoidal
time history, which is considered to correspond to the
behavior of the piezoceramic actuator. On the other hand,
the pressure fluctuation at x/h* = 10.0 indicates a severe
large amplitude fluctuation. The large amplitude fluctua-
tion suggests that the shock wave passes back and forth
over the measurement position corresponding to the mo-
tion of the piezoceramic actuator. The increase in ampli-
tude can be explained by Figure 3, which shows that the
shock wave is located around x/h* = 10.0. Then, in case
of a pressure ratio of 1.50, the shock wave is expected to
stand slightly downstream of the pressure measurement
position at x/h* = 10.0.
The influence of the shock wave could reach the pres-
sure measurement position through the subsonic layer in
the boundary layer which develops along the diffuser
wall. The pressure remains relatively low compared to
that shown in Figure 4(a), which indicates that the shock
wave stands further downstream than that for p0/pb =
1.45. However, the effect of the piezoceramic actuator
can be still detected. Finally, in the case of p0/pb = 1.55,
the shock wave moves far downstream of the pressure
0.7
0.6
0.5
0.4
0.3
0.2
p
w
/p
b
0.15s0.100.050.00 time [s]
p
0
/p
b
=1.45
x/h* = 0.0
x/h* = 10.0
0.7
0.6
0.5
0.4
0.3
0.2
p
w
/p
b
0.15s0.100.050.00 time [s]
p
0
/p
b
= 1.50
x/h* = 0.0 x/h* = 10.0
(a) (b)
0.7
0.6
0.5
0.4
0.3
0.2
pw / pb
0.15s0.100.050.00 time [s]
p0 / pb = 1.55
x/h* = 0.0
x/h* = 10.0
(d)
0.6
0.5
0.4
0.3
0.2
p
w
/ p
b
0.15s0.100.050.00 time [s ]
p
0
/ p
b = 1.55
x/h* = 0.0
x/h* = 10.0
(
c)
Figure 4. Wall static pressur p0/pb = 1.45; (b) p0/pb
1.50; (c) p0/pb = 1.55; (d) p0/pb
e fluctuations at throat and x/h* = 10.0 for input frequency 200Hz: (a)
= 1.55. =

M. YAGA ET AL. 18
measurement position. This is also con firmed in Figure 3,
which showing xs/h* = 10.0 at a pressure ratio of 1.55.
Both the fluctuating and averaged pressure are much
lower due to the downstream displacement of the pres-
sure measurement position. These figures contain infor-
mation about the shock position and the shock wave be-
havior. In other words, Figure 4(a) shows the severe
pressure fluctuation at x/h* = 10.0, whereas the fluctua-
tion at the throat does not. This means that the shock
wave stands between the throat and the measurement
position at x/h* = 10.0. As the pressure ratio increases,
the fluctuation at x/h* = 10.0 gradually decreases the
pressure fluctuation, ach
s the supersonic state
stream of the shock wave.
d compared
a) shows
quency
of fp throat shows almost no increase in
ieving the smallest pressure
fluctuation, as shown in Figure 4(c). The pressure fluc-
uation as shown Figure 4(c) denotet
at x/h* = 10.0.
However, the sudden change in the average pressure
was observed as shown in Figure 4(d) under the same
condition, which is caused by the flow separation down-
stream of the shock wave. The increase in the pressure
fluctuation indicates the shock wave displacement up-
stream due to the flow separation. However, some time
after the increase in pressure, the average value and fluc-
tuation decrease, denoting the shock wave located down-
stream of the position at x/h* = 10.0. The pressure fluc-
tuations at the throat are found to oscillate sinusoidally
for all pressure ratios. Figure 4(d) also reveals that the
wall pressure fluctuation at a pressure ratio of 1.55 sud-
denly chan ges its level at time t = 0.03 s, which suggests
that the flow has just recovered from an unexpected
separation down
3.4. Root Mean Square of the Pressure
Fluctuation
It is well known that wall static pressure fluctuations
greatly decrease when a flow becomes supersonic. In
other words, monitoring the wall static pressure fluctua-
tions clarifies whether the flow is supersonic or subsonic.
In the previous section, the pressure fluctuations also
indicate the rough shock wave positions. Then, for a
more quantitative evaluation of the pressure fluctuations,
the root mean square of pressure fluctuations is one of
the indices of the shock wave position and its behavior.
Figures 5(a)-(d) show the root mean squares prms di-
vided by the atmospheric pressure pb for three different
frequencies 100 Hz, 200 Hz, and 300 Hz an
to the case for 0 Hz as a reference. Figure 5(
that the root mean square prms/pb for the input fre
= 0 Hz at the
prms/pb with the increase in the pressure ratio p0/pb. On
the other hand, activation occurs at the throat, the rms
increases with the pressure ratio. This indicates that the
piezoceramic actuator always affects the pressure fluc-
0.10
0.08
0.06
0.04
0.02
0.00
p
rms
/ p
b
2.42.22.01.81.61.41.21.0
p
0
/ p
b
0Hz
100Hz
200Hz
300Hz
x/h* = 0 (throat)
(a)
0.10
0.08
0.06
0.04
0.02
0.00
p
rms
/ p
b
2.42.22.01.81.61.41.21.0
x/h* = 6.67
p
0
/ p
b
0Hz
100Hz
200Hz
300Hz
(b)
0.10
0.08
0.06
0.04
0.02
0.00
prms / pb
2.
4
2.22.01.81.61.41.21.0
p0 / pb
x/h* = 10.0
0Hz
100Hz
200Hz
300Hz
(c)
0.10
0.08
0.06
0.04
0.02
0.00
p
rms
/ p
b
2.42.22.01.81.61.41.21.0
p
0
/ p
b
x / h* = 13.33
0Hz
100Hz
200Hz
300Hz
(d)
Figure 5. RMS of wall static pressure fluctuations: (a) x/h*
= 0.0; (b) x/h* = 6.67; (c) x/h* = 10.0; (d) x/h* = 13.33.
tuation at the throat. When the rms reaches approxima-
tely zero, the state of the measurement position is con-
sidered to be supersonic. This indicates that the hock
wave is located downstreaof the measurement posi-
tion.
s
m

M. YAGA ET AL. 19
In Figure 5(b), the clear peaks at a pressure ratio p0/pb
of approximately 1.2 show that a single and relatively
weak shock wave appears and moves downstream with
the increase in the pr essure ratio. The sudden drop in the
rms indicates the completion of the process from the
subsonic-to-supersonic transition due to the downstream
displacement of the shock wave. This process is inde-
pendent of the input frequencies of the piezoceramic ac-
tuator.
Figure 5(c) shows that the rms at a pressure ratio of
approximately 1.7 suddencreases, which is caused
by the unexpected separation of a boundary layer, as
mentioned in the previous section. This also indicate the
shock wave existence around the position of x/h* = 10.0.
However, for a pressure ratio greater than 1.8, the rms for
all input frequen cies becomes approximately zero, which
suggests that the flow is completely supersonic. Note th at
the source of the signal originates at the throat, and then
even if the flow measurement position is supersonic, the
signal from the throat can be detected. Figure 5(d) indi-
cates the same variations that is all the rms for each input
frequency suddenly decrease at the pressure ratio at 2.0
denoting the supersonic sta this postion.
on
ly in
te at
3.5. FFT Analyses of Wall Pressure Fluctuati
The rms of the pressure fluctuation usually becomes
large when the oscillating shock wave approaches the
monitoring position. It is also important to examine the
unsteady behavior of the shock wave in detail, especially
in this case, in order to confirm the response of the flow
field to the piezoceramic actuator.
One of the best ways to evaluate the effect of the ac-
tuation is to check the contributions of every frequency
by means of FFT analysis of the pressure fluctuations at
x/h* = 6.67. Figures 6(a)-(d) show the results of the FFT
analysis of the pressure fluctuations for each pressure
ratio. Figure 6(a) shows no dominant frequency and al-
most no frequency output for pressure ratios greater than
p0/pb = 1.25, as deduced from the results for the rms
shown in Figure 5(b). This indicates that the shock wave
oscillates with no dominant frequency for all of the
pressure ratios and that the state of the flow at x/h* =
6.67 becomes supersonic at pressure ratios greater than
1.25. Moreover, the levels of each spectrum are not so
large because the shock wave at this position is not so
strong.
On the other hand, Figures 6(b)-(d) clearly show the
dominant frequencies for each pressure ratio, which cor-
responds to the input frequency to the piezoceramic ac-
tuator. Note that even in the supersonic state, the fre-
quency of 200 Hz can be observed. These figures indi-
cate the effect of the piezoceramic actuator on the flow
fields. In addition to the results of the visualization,
100
80
60
40
20
0
Power Spect rum
500Hz4003002001000
Frequency
1.8
1.6
1.4
1.2
1.0
p
0
/p
b
f
p
=0Hz
(a)
100
80
60
40
20
0
Power Spect rum
500Hz4003002001000
Frequency
1.8
1.6
1.4
1.2
1.0
p
0
/p
b
f
p
=100Hz
(b)
100
80
60
40
20
0
Power Spectrum
500Hz4003002001000
Frequency
1.8
1.6
1.4
1.2
1.0
p
0
/p
b
f
p
=200Hz
(c)
100
80
60
40
20
0
Power Spectrum
1.8
1.6
1.4
1.2
1.0
p
0
/p
b
f
p
=300Hz
100 200 3000
Frequency
400 500Hz
(d)
Figure 6. FFT analysis of wall static pressure fluctuations at
x/h* = 6.67: (a) fp = 0 Hz; (b) fp = 100 Hz; (c) fp = 200 Hz; (d)
fp = 300 Hz.
monitoring the wall static pressure fluctuation is a quan-
titative way to confirm the effect of the actuator.
Figures 7(a)-(d) show the FFT analysis of the pres-
sure fluctuation at x/h* = 10.0 for the same input fre-
quency as that in Figure 6. Figure 7(a) shows no domi-
nant frequency but only a relatively low frequency,
which has the same tendency as that in Figure 6(a)
Figures 7(b)-(d) show cleominant frequencies. This
indicates the possibility of reducing the pressure fluctua-
tion by controlling the shock position, which is expected
to cancels the pressure fluctuation. In the figures, a wide
range of frequencies are observed at a pressure ratio of
approximately 1.7 due to the unexpected shock-induced
separation of the boundary layer. All of the figures show
a sudden decrease in the power spectrum at a pressure
ratio of approximately 1.4. This implies that the shoc
.
ar d
k

M. YAGA ET AL. 20
100
80
60
40
20
0
Power Spectrum
500Hz4003002001000
Frequency
1.8
1.6
1.4
1.2
1.0
p
0
/p
b
f
p
=0Hz
(a)
100
80
60
40
20
0
ower SpectrumP
500Hz4003002001000Frequenc y
1.8
1.6
1.4
1.2
1.0
p
0
/p
b
f
p
=100Hz
(b)
100
80
60
40
20
0
Power Spectr um
500Hz4003002001000
Frequency
1.8
1.6
1.4
1.2
1.0
p
0
/p
b
f
p
=200Hz
(c)
100
80
60
40
20
0
Power Spectrum
500Hz4003002001000
Frequency
1.8
1.6
1.4
1.2
1.0
0 b
p/p
f
p
=300Hz
(d)
Figure 7. FFT analysis of wall static pressure fluctuations at
x/h* = 10.0: (a) fp = 0 Hz; (b) fp = 100 Hz; (c) fp = 200 Hz; (d)
fp = 300 Hz.
wave completely passes the measurement position, re-
sulting in a chan ge in state from subsonic to supersonic.
3.6. FFT Analysis of Shock Positions
The wall static pressure fluctuations prov ide us with only
local information on the shock wave behavior around th
measurements positions. Ardingly, in order to clarify
the entire flow field, the variations in unsteady shock
positions are also important because the shock wave al-
ways contains all of the information on its upstream and
downstream conditions regardless of its position.
Figures 8(a)-(d) show the results of the FFT analyses
of the shock positions under the influence of the piezo-
ceramic actuator as well as with no control. In case of no
control, there is no domi frequency, as shown i
e
cco
nantn
500
400
300
200
100
0
Power Spectrum
500Hz4003002001000
Frequency
1.8
1.6
1.4
1.2 p
0
/ p
b
f
p
= 0 Hz
(a)
500
400
300
200
100
0
Power Spectrum
500Hz4003002001000
Frequency
1.8
1.6
1.4
1.2 p
0
/ p
b
f
p
= 100H z
(b)
500
400
300
200
100
0
Power Spectrum
500Hz4003002001000
Frequency
1.8
1.6
1.4
1.2 p
0
/ p
b
f
p
= 200Hz
(c)
500
400
300
200
100
0
Power Spectrum
500Hz4003002001000
Frequency
1.8
1.6
1.4
1.2 p
0
/ p
b
f
p
= 300Hz
Figure 8. FFT analysis of Shock positions: (a) fp = 0 Hz; (b)
fp = 100 Hz; (c) fp = 200 Hz; (d) fp = 300 Hz.
Figure 8(a). The relatively low-frequency spectrum is
observed as long as the pressure ratio is smaller than 1.4.
This shows that the shock wave passes the measurement
position monotonically as the pressure ratio increases. In
contrast, for a shock wave frequency of 100 Hz, a domi
nant frequency is observed until a pressure ratio of 1.5.
The peak value of the dom frequency decreases as
the pressure ratio increases. This decrease in the peak
value of the dominant frequency is explained by the be-
havior of the shock wave, as shown in Figure 3. That is,
the gradient of the shock wave displacement decreases as
the pressure ratio increase as shown in Figure 3 due to
the expansion rate of the cross sectional area of the diffuser.
(d)
-
inant

M. YAGA ET AL. 21
This implies that shock wave located downstream is in-
sensitive to the pressure fluctuation compared with that
located upstream position. Then, the oscillation of the
shock wave gradually decreases as it moves downstream.
The diminishing of the dominant frequency for higher
pressure ratios might be due to the relative increase in
other frequencies.
On the other hand, when the higher frequency is ap
plied to the throat, the cleareaky dominant frequency,
which is the exact same frequency as that input to the
piezoceramic actuator, can be observed. Note also that
the applied frequency remains, even for the higher pres-
sure ratio, which suggests that the shock wave is always
under the influence of the piezoceramic actuator. The
tendencies observed in Figure 8(c) also appear in Figure
8(d). In other words, the input frequency of 300 Hz is the
dominant frequency for all pressure ratios. Then, actua-
tion at the throat is a promising method for controlling
shock wave behavior.
Transonicum II, Springer, Berlin, 1976, pp.
d Oscillations in a Diffuser Flow,” AIAA Journal,
-
ly p
4. Conclusions
A piezoceramic actuator is applied to the throat of a cir-
cular arc diffuser with various driving frequencies in
order to clarify the response of the flow field and shock
wave behaviors to the piezoceramic actuator. The piezo-
ceramic actuator, which moves periodically as a refer-
ence signal, is considered to be a driving force for oscil-
lation phenomena. The conclusions are summarized as
follows:
1) The starting shock wave moves downstream mono-
tonically with the increase in the wind tunnel pressure
ratio, regardless of the input frequencies to the piezoce-
ramic actuator.
2) The rms values of the wall pressure fluctuations d e-
crease suddenly just after the shock wave completely
passes over the measurement position for all driving fre-
quencies.
3) The pressure fluctuations at the throat and down-
stream of the throat correspond to the exact same fre-
quencies of the input frequencies to the piezoceramic
actuator in both cases that the position is supersonic and
subsonic state.
4) Shock wave behaviors are also confirmed to corre-
spond to the piezoceramic actuator behaviors.
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