Effects of Nozzle-Lip Length on Reduction of Transonic Resonance in 2D Supersonic Nozzle

doi:10.4236/ojfd.2013.32A011

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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

Email: [email protected]

Received May 28, 2013; revised June 5, 2013; accepted June 12, 2013

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

S. SHIN ET AL.

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

9.6 1

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.

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

NPR = 2.2

NPR = 2.0

NPR = 1.8

NPR = 1.6

NPR = 1.4

Psd (Pa

·S)

(

)

12u-D

0 1 2 3 4 56

NPR = 2.2

NPR = 2.0

NPR = 1.8

NPR = 1.6

NPR = 1.4

(

)

12u-u

0 1 2 3 4 5 6

NPR = 2.2

NPR = 2.0

NPR = 1.8

NPR = 1.6

NPR = 1.4

Psd (Pa

·S)

(

)

12d-D

0 1 2 3 4 56

NPR = 2.2

NPR = 2.0

NPR = 1.8

NPR = 1.6

NPR = 1.4

(

)

12d-U

0 1 2 3 4 5 6

NPR = 2.2

NPR = 2.0

NPR = 1.8

NPR = 1.6

NPR = 1.4

Psd (Pa

·S)

(

)

12ud-D

0 1 2 3 4 56

NPR = 2.2

NPR = 2.0

NPR = 1.8

NPR = 1.6

NPR = 1.4

(

)

12u

-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.

[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