Open Journal of Fluid Dynamics, 2013, 3, 69-74
http://dx.doi.org/10.4236/ojfd.2013.32A011 Published Online July 2013 (http://www.scirp.org/journal/ojfd)
Effects of Nozzle-Lip Length on Reduction of Transonic
Resonance in 2D Supersonic Nozzle
Seoungyoung Shin, Akira Matsunaga, Hiroyuki Marubayashi, Toshiyuki Aoki
Department of Energy and Environmental Engineering, Kyhu University, Fukuoka, Japan
Received May 28, 2013; revised June 5, 2013; accepted June 12, 2013
Copyright © 2013 Seoungyoung Shin et al. This is an open access article distributed under the Creative Commons Attribution Li-
cense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
It is known that the transonic resonance takes place, in divergent section of supersonic nozzle, similarly to the longitu-
dinal acoustic resonance of a conical section with one end closed and the other end open. And the “conical section” is
similar to the separation zone between shock wave and nozzle exit in divergent part of supersonic nozzle. The present
paper describes an experimental work to investigate a reduction of transonic resonance by change the lip length of 2-
Dimensional converging-diverging nozzle. In this study, the nozzle pressure ratio varied in the range between 1.4 and
2.2 as shock-containing flow conditions. And a Schlieren optical system was used to visualize the flow fields. Espe-
cially, by using a high-speed video camera, we obtained the shock position at that moment. And acoustic measurements
were employed to compare the sound spectra level of each experimental case. And it was found that the transonic reso-
nance was decreased when a large separation zone located at the side, where a nozzle-lip attached to nozzle exit addi-
tionally. In this case, the amplitude of shock oscillation and wall static pressure oscillation were also decreased.
Keywords: Transonic Resonance; Nozzle-Lip Length; Noise Reduction
1. Introduction
Supersonic jet noise is frequently encountered in many
diverse engineering applications such as supersonic air-
craft engine, jet propulsion thrust vectoring, fuel injec-
tion for supersonic combustion, soot blower devices,
thermal spray devices, etc. In general, it is known that the
supersonic jet noise consists of three major components:
the turbulent mixing noise, the broadband shock-associ-
ated noise, and the screech tones [1]. However, the tran-
sonic tone can occur independently of the general noise
components at low nozzle pressure ratios when a shock
wave occurs within the divergent section of convergent-
divergent nozzle without any abrupt area change. Con-
cerning the transonic tone, a great deal of experimental
and numerical research of the diffusion of the transonic
tone has been carried out. Zaman et al. investigated the
characteristics of the transonic tone in various nozzle
conditions [2], and provided correlation equations to pre-
dict the transonic tone frequency from a collection of
data for single round nozzles. Moreover, they showed
that transonic tone takes place similarly to the (no-flow)
longitudinal acoustic resonance of a conical section with
one end closed and the other end open. Accordingly, it is
called “transonic tone” or “transonic resonance”. How-
ever, it is poorly known under what process the transonic
tone can occur and how to reduce the transonic resonance
in actual flow complicated by shock oscillation and
shock wave/boundary layer interaction phenomenon. The
objective of this study is to investigate the effects of noz-
zle-lip length on reduction of transonic resonance in 2-
Dimensional supersonic nozzle. Especially, it takes ac-
count of not only nozzle-lip length but also the location
of large separation zone in parallel.
2. Experimental Procedure
2.1. Experimental Apparatus
This study had conducted in an anechoic test room which
is schematically shown in Figure 1. Preliminary acoustic
tests show that the test room is anechoic for frequencies
above approximately 120 Hz and the background noise is
at about 10 dB. And compressed air is stored in a high-
pressure tank which has a capacity of 5 m3, and is sup-
plied to the plenum chamber in which a honeycomb sys-
tem reduces flow turbulence. A convergent-divergent
nozzle with a design Mach number of 2.0 was placed into
the wall of the plenum chamber. And the supersonic
nozzle designed by characteristic method, has throat
C
opyright © 2013 SciRes. OJFD

S. SHIN ET AL. 70
height of 9.6 mm, exit height of 17.2 mm (H), width of
30 mm (W) and the length of divergent section was 46
mm (L), as shown in Figure 2. The sidewalls of the su-
personic nozzle have optical grasses to allow flow visu-
alization by a schlieren optical system. To measure the
position of the shock wave in the nozzle-divergent sec-
tion while the transonic resonance occurs, visualization
was performed by schlieren method with high-speed
video camera [Photron FASTCAM SA5]. The movie was
recorded as the frame rate was 10,000 fps with 5 μs-
shutter speed. And measurement time and pixel count are
1.6 s, and 256 × 512, respectively. Acoustic measure-
ments were made by using a condenser microphone
[Ono-Sokki MI-6420] that has a diameter of 1/4 inch.
And the microphone which shown in Figure 3, was lo-
cated at angles (θ) of 60 degrees from the jet flow direc-
tion, and a radial distance of 516 mm from the exit of the
nozzle (r/H = 30). The acoustic signals were analyzed
using the FFT analyzer [Ono-Sokki DS0221]. The FFT
analysis provided the noise spectra, in the range from 0
to 40 kHz, with a frequency bandwidth of 25 Hz. And the
pressure measurements were done by setting up the
pressure ports at x/L = 0.87 from the nozzle throat, using
the semiconductor pressure sensor [TEAC XCS-190].
The sampling frequencies of condenser microphone and
semiconductor pressure sensor are the same with 50 kHz.
2.2. Experimental Procedure
In this paper, the nozzle pressure ratio (NPR) is defined
as the ratio of the pressure inside the plenum chamber p0
to ambient back pressure pb. According to the one-di-
mensional analysis for the present nozzle, the correct
expansion state at the nozzle exit is obtained at NPR =
7.8. And experiment was carried out for different nozzle
pressure ratios from 1.4 to 2.2. And nozzle-lip length was
varied to study its effect on the transonic resonance by
attaching cuboid tips on the nozzle exit. The tip has 6mm
height, 30 mm width and 6 mm (I) or 12 mm (I) length.
Also the location of large separation zone (or flow direc-
tion) was varied at each experimental case. Table 1
shows detail of experimental conditions about all cases.
In Table 1, subscript “n”, “u”, “d” and “ud” mean
“no-lip”, “upper side”, “bottom side” and “both side” at-
tached condition, respectively. And “U” and “D” mean
flow direction or the opposite side of large separation zone
location.
Mirror
Light source
Pin hole
Knife edge
Camera
Supersonic
nozzle
Pressure
transducer
Plenum
chamber
Amplifier
A/D
converter
Personal
computer
Signal
controller
Pressure
control valve
Reservior
3.0MPa, 5m3
Compressor
325
160
5250
1000 4900
Absorption
material
Supersonic jet
Air outlet
Figure 1. Experimental apparatus and measuring sy ste m.
Figure 2. Supersonic nozzle geometry.

S. SHIN ET AL. 71
Microphone
Pressure Transducer
jet
r = 516
(r/H = 30)
flow
Laval Nozzle
72°
L = 46
H
=
D
=
9.6 1
7.
2
Figure 3. Measurement point of sound pressur e level.
Table 1. Experimental sets.
6 mm 12 mm 6 mm 12 mm
6n-D 12n-D 6u-U 12u-U
6u-D 12u-D 6u-U 12u-U
6d-D 12d-D 6d-U 12d-U
6ud-D 12ud-D 6ud-U 12ud-U
3. Results and Discussion
3.1. Sound Spectra and Tone Frequency
Figure 4 shows the sound pressure spectra in case of
normal nozzle. And the red and blue solid line mean
downside and upside flow direction. In Figure 4, there
are some peak value of sound pressure level at about 800
Hz and 2.5 kHz which is known as transonic resonance
of stage 1 (solid arrow) and stage 2 (open arrow), respec-
tively. According to Zaman et al., standing one-quarter,
three-quarter waves exist between the shock wave and
nozzle exit. And the frequency of transonic resonance is
proportional to NPR because the shock wave in the di-
vergent section moves to the downstream as the NPR
increases, and the distance between the shock wave and
nozzle exit shorten. And each difference of sound pres-
sure level between “n-D” and “n-U” is less than 2 dB. In
Figure 5, the frequency of the transonic resonance and
calculated value by Zaman’s empirical formula are plot-
ted with nozzle pressure ratio. As shown in Figure 5,
there are some gaps between broken line of Zaman’s for-
mula and each transonic tone frequency. However a
similar tendency is seen that the transonic tone increases
with increasing of NPR.
3.2. Reduction of Transonic Resonance
It is shown comparisons of sound pressure level ac-
Figure 4. Variation of sound pre ssure level for n-D and n-U.
Figure 5. Comparison of transonic tone frequency between
experiment and Zaman’s empirical formula.
cording to nozzle-lip length and flow direction at 1.8
NPR in Figure 6. And it is clearly shown that the stage1
transonic resonance is reduced at the case of (a), (d), (e)
and (f). In case of “d-D” at Figures 6(b) and (c), how-
ever, there are little effects of nozzle-lip length. Mean-
while, in Figures 6(e) and (f), the transonic resonance is
reduced both cases and each sound pressure spectra are
almost same with (a) and (d), respectively. Therefore it
can be considered that the effect of reduction is valid for
stage 1 when the large separation zone locates at the side
of nozzle-lip attached. And effects of reduction are larger
at 12 mm nozzle-lip length than 6 mm. Each amount of
transonic resonance reduction is plotted in bar chart in
Figure 7. The same tendency like 1.8 NPR reviewed in
Figure 6 is shown at every case. That is, the amount of

S. SHIN ET AL. 72
Figure 6. Comparison of sound pressur e level for 1.8 NPR.
Figure 7. Amount of transonic tone reduction (red bar:
stage 1, blue bar: stage 2).
tone reduction is remarkable at stage1 and larger at
longer lip attached in most case. Also, the case of “u-D”
and “d-U” have similar tendency to “ud-D” and “ud-U”,
respectively. Figure 8 shows variation of amount of
transonic resonance reduction with various nozzle-lip
lengths at 1.8 NPR. At the case of 1.8 NPR, it is clearly
shown that the transonic resonance sharply reduced until
0.4 I/W, and gradually reduced. There are some differ-
ences between “u-D” and “d-U” but the tendency is al-
most same at stages 1 and 2.
3.3. Wall Static Pressure
Figure 9 shows the variation of power spectral density of
wall static pressure oscillation in case of 12 mm-nozzle-
lip attached. For the case of the transonic resonance emit-
ting, there are high power spectral density at about 800
Hz and 2.5 kHz, mostly. However, at the Figures 9(a)
and (d) which are transonic resonance reduced conspicu-
ously, each power spectral density is gradually distri-
buted. Also the same tendency is found as sound pres-
sure level that the power spectral density of “ud-D” and
“ud-U” are similar to “u-D” and “d-U”, respectively.
3.4. Amplitude of First Shock Wave Oscillation
In Figure 10, Schlieren images are shown for the case of
corresponding to the condition of the transonic resonance
emitting and 12 mm nozzle-lip attached. And by analyz-
ing the Schlieren images, the amplitude of first shock
wave oscillation was compared with no-lip attached noz-
zle’s results which are shown in Figure 11. From the
Figure 11, we can recognize that the amplitude of first
shock wave oscillation is also decreased as the transonic
resonance reduces.
4. Conclusions
In this study, to investigate the effects of nozzle-lip
length on transonic resonance reduction in 2-Dimen-
sional supersonic nozzle, experiments were performed in
divers conditions which were considered in the location
of large separation zone (or flow direction), nozzle-lip
Figure 8. Variation of reduction amount of transonic reso-
nance with various nozzle-lip lengths at 1.8 NPR.

S. SHIN ET AL. 73
0 1 2 3 4 5 6
10
4
10
4
10
4
10
4
10
4
NPR = 2.2
NPR = 2.0
NPR = 1.8
NPR = 1.6
NPR = 1.4
Psd (Pa
2
·S)
(
a
)
12u-D
0 1 2 3 4 56
10
4
10
4
10
4
10
4
10
4
NPR = 2.2
NPR = 2.0
NPR = 1.8
NPR = 1.6
NPR = 1.4
(
b
)
12u-u
0 1 2 3 4 5 6
10
4
10
4
10
4
10
4
10
4
NPR = 2.2
NPR = 2.0
NPR = 1.8
NPR = 1.6
NPR = 1.4
Psd (Pa
2
·S)
(
c
)
12d-D
0 1 2 3 4 56
10
4
10
4
10
4
10
4
10
4
NPR = 2.2
NPR = 2.0
NPR = 1.8
NPR = 1.6
NPR = 1.4
(
d
)
12d-U
0 1 2 3 4 5 6
10
4
10
4
10
4
10
4
10
4
NPR = 2.2
NPR = 2.0
NPR = 1.8
NPR = 1.6
NPR = 1.4
Psd (Pa
2
·S)
(
e
)
12ud-D
0 1 2 3 4 56
10
4
10
4
10
4
10
4
10
4
NPR = 2.2
NPR = 2.0
NPR = 1.8
NPR = 1.6
NPR = 1.4
(
f
)
12u
d
-u
Figure 9. Variation of power spectral density of wall static
pressure oscillation in case of 12 mm nozzle-lip length.
(a)
(b)
(c)
Figure 10. Schlieren images for typical nozzle pressure ra-
tios (12 mm nozzle-lip length). (a) 1.6 NPR; (b) 1.8 NPR; (c)
2.0 NPR.
Figure 11. Amplitude comparison of oscillating first shock
wave.
length and nozzle pressure ratios.
And the conclusions are summarized as follows: The
transonic resonance was reduced about 5 dB in stage 1
when the large separation zone located at the side, where
the nozzle-lip was attached additionally. And at that mo-
ment, power spectral density of the wall static pressure
and the amplitude of first shock wave oscillation were
also decreased.
REFERENCES
[1] C. K. W. Tam, “Supersonic Jet Noise,” Annual Review of
Fluid Mechanics, Vol. 27, No. 1, 1995, pp. 17-43.
doi:10.1146/annurev.fl.27.010195.000313

S. SHIN ET AL. 74
[2] K. B. M. Q. Zaman, M. D. Dahl, T. J. Bencic and C.Y.
Loh, “Investigation of a Transonic Resonance with Con-
vergent-Divergent Nozzles,” Journal of Fluid Mechanics,
Vol. 463, No. 1, 2002, pp. 313-343.
doi:10.1017/S0022112002008819