High-speed optical imaging and spatio-temporal analysis of sound sources of edge tone phenomena

Risako Tanigawa 1 Panasonic Holdings Corporation 1006, Oza Kadoma, Kadoma-shi Osaka, Japan

Kohei Yatabe 2 Waseda Research Institute for Science and Engineering, Waseda University 3-4-1, Ohkubo, Shinjuku-ku Tokyo, Japan

Yasuhiro Oikawa 3 Department of Intermedia Art and Science, Waseda University 3-4-1, Ohkubo, Shinjuku-ku Tokyo, Japan

ABSTRACT Aerodynamic sound is one of the noises of high-speed trains, automobiles, and wind turbines. To understand the characteristics of these noises, measuring sound sources is important. In general, microphones are used for measuring aerodynamic sounds. However, measuring the sound fields in- side flow fields is difficult for microphones because they disturb flows. Thus, optical measurement methods have been applied to visualize aerodynamic sounds. The optical method can measure the sound fields without installing devices inside measurement fields. Therefore, it can capture the sound around sources. In this paper, we performed visualization and spatio-temporal analysis of sound sources of edge tones using parallel phase-shifting interferometry (PPSI). We experimentally confirmed the difference in pressure fluctuations near the sound source depending on the frequency of the edge tones.

1. INTRODUCTION

Aerodynamic sound is one of the noises of high-speed trains, automobiles, and wind turbines. Edge tone is one of the aerodynamic sounds, which is generated by impingements of flow on a wedge- shaped edge [1]. Some researchers have been interested in the mechanism of edge tone generation. Brown proposed a predictive formula of edge tone frequencies based on experiments [2, 3]. After Brown’s proposal, experimental and theoretical investigations have been performed [4, 5], and they explained the basic mechanism of edge tone generation. In recent years, two approaches for investi-

tanigawa.risako@jp.panasonic.com 1

k.yatabe@asagi.waseda.jp 2

yoikawa@waseda.jp 3

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Figure 1: Experimental setup of edge tone visualization.

gations of edge tone, experimental investigations and numerical simulations, have been conducted. Experimental investigations have concentrated on the parameters of flow conditions such as the speed of jet [6], the nature of the gas [7], and the shape of the nozzle [8]. Numerical simulations have accomplished observations of flow and/or sound fields around the sources of edge tone [9–11].

These investigations have revealed the hydrodynamic sources of the edge tone. While numerical simulations performed based on ideal conditions have provided new insights into edge tone, the ac- tual conditions may be different from such ideal situations. In addition, the acoustic sound sources of edge tone have not been well investigated especially in experiment. For further understanding of the phenomena, experimental confirmation should be important. However, the measurement of aerodynamic sound sources is difficult because instruments such as microphones cannot be placed inside air-flow without disturbing the phenomena.

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Recently, the development of optical technology has enabled sound measurement without in- stalling any devices inside the measurement area [12–14]. These methods are based on the principle that pressure fluctuations of sound modulate phases of light. Sound fields are non-intrusively cap- tured by passing laser light through the fields. Therefore, these optical measurement methods are useful for measuring aerodynamic sound including edge tones.

In this paper, we experimentally observed the sound fields around the sources of edge tone. We used parallel phase-shifting interferometry (PPSI) for the observations of the edge tone phenomena so that the pressure fields are measured non-intrusively. By analyzing the approximate position of sound sources, the movement of the position of the sound sources between the nozzle and edge was confirmed.

2. EXPERIMENT

The experimental setup of edge tone visualization is shown in Fig. 1. Air-flow was supplied from an air-pump. The flow rate was controlled by a speed controller and measured by a flow meter. The size of the nozzle outlet was 1 × 25 mm. The edge was fixed on a traverse system in order to auto- matically control the nozzle-edge distance. The width of the edge was 50 mm, and the angle was 20 degrees. The nozzle-edge distance and the flow rate were set to 4 mm and 35 L/min, respectively, where this condition results in edge tone consisting of a single tone. A microphone was installed 100 mm above from the nozzle outlet for reference. PPSI, which can capture the pressure fields non-intrusively and instantaneously through observing the phase of light [14, 15], was used to visu- alize the sound sources of edge tone. The maximum size of the measurement area was a circle of diameter 100 mm, which was determined by the size of lenses and mirrors. The PPSI has a high-

Figure 2: Visualized images of the edge tone.

speed camera, whose maximum shutter speed is 1.5 M frames per second. In this experiment, the frame rate of the high-speed camera was set to 20 000 frames per second, which was enough sam- pling rate for measuring the edge tone. The image of the measurement area is shown in the bottom- left of Fig. 1. The circular area, whose size corresponds to that of the beam of light, was the mea- surement area. The nozzle and edge were located on the left and center of the measurement area. The microphone was placed outside the measurement area.

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3. RESULTS

Visualized images of edge tone are shown in Fig. 2. These data were calculated by applying a band- pass filter with a center frequency of 1970 Hz and a bandwidth of 200 Hz. The center frequency of the filter was determined by the data captured by the microphone. The color indicates the value of the phase of light. The positive/negative values correspond to that of the pressure difference from static pressure. Vertical stripes observed in the measurement area are optical noises. Dipole like sound pressure distributions over the entire area can be seen. The wavelength of the sound at 1970 Hz was 174.0 mm by assuming that the speed of sound was 342.8 m/s based on the room tempera- ture of 18.6 ◦C. Therefore, about half of a period of the sound wave was included in the 100 mm diameter visualized area. Pressure fluctuations between the nozzle and edge were also visualized. These pressure distributions were anti-phase at the upper and lower of the edge, whose features were also seen in the simulated results in Ref. [11]. Therefore the pressure fluctuations between the nozzle and edge would be caused by the air-flow, which generates the aerodynamic sound.

3.1. Analysis of the position of the sound sources of edge tones

Since the visualized pressure fields include the sources of the edge tone, the positions of the sound sources can be identified. Therefore, vertical and horizontal pressure distributions around the sound sources were analyzed. The pressure distributions in the vertical directions are shown in Fig. 3. Se- lected pixels are surrounded by a blue rectangle in the left-side picture. The pressure distributions averaged 10 pixels in the horizontal direction were displayed as blue lines. Two dominant peaks,

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Figure 3: Pressure distributions in the vertical direction.

Figure 4: Pressure distributions in the horizontal direction.

which correspond to the sound sources, were observed at 121st and 125th pixels. The pressure dis- tributions in the horizontal directions are shown in Fig. 4. The blue and red lines are the pressure fluctuations of the upper and lower sides of the edge, respectively. Extracted pixels are indicated as lines in the left-side picture. The pressure fluctuations of the upper and lower sides of the edge were extracted from 121st and 125th pixels on the vertical axis. The maximal/minimal points in the hori- zontal directions were pointed by the triangle indicators. The peak positions were moved from the nozzle to the edge with changing their amplitude values. Both the same and different peak positions were observed at the upper and lower sides of the edge.

3.2. Analysis of the amplitude modulations of edge tone We confirmed the variations of the amplitude of sound through observing visualized images of the entire measurement time. In order to investigate the local difference of these time variations of sound, the waveforms of the sound were extracted from the upper and lower sides of the edge as shown in Fig. 5. The blue and red lines represent the signals of the upper and lower sides of the edge, respectively. These waveforms are averages of 100 pixels, whose positions were surrounded by the rectangles in the left-side picture. The time variations were observed from the waveforms, and the amplitude modulations of the upper and lower sides of the edge were different. In ideal

Figure 5: Waveforms of the sound captured by the PPSI.

condition as in the simulation of Ref. [9], the positive and negative pressures appear symmetrically in the upper and lower tips of the edge. In contrast, our experimental result indicates that the sound source of edge tone in actual condition may not be a simple dipole, which might be caused by the imperfection of the edge, laminar flow, and positioning of them.

4. CONCLUSIONS

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We conducted experimental visualizations near sources of the edge tone using PPSI. In our experi- ment, the edge tone and pressure fluctuations caused by air-flow were observed. The pressure dis- tributions of the sound sources were investigated and the source positions were analyzed. The am- plitudes of the sound in the upper and lower sides of the edge differently changed through time. These results suggested that the sound source of the edge tone would not be a simple dipole source.

REFERENCES

1. K. Karamcheti, A. B. Bauer, W. L. Shields, G. R. Stegen, J. P. Woolley, Some Features of AN

Edge-Tone Flow Field, 207 , NASA, Washington, D.C., 275–304 (1969). 2. G. B. Brown, The vortex motion causing edge tones, Proc. Phys. Soc. , 49(5) , 493–507 (1937). 3. G. B. Brown, The mechanism of edge-tone production, Proc. Phys. Soc. , 49(5) , 508–521

(1937). 4. N. Curle, M. H. A. Newman, The mechanics of edge-tones, Proc. R. Soc. Lond. Ser. A. Math.

Phys. Sci. , 216(1126) , 412–424 (1953). 5. A. Powell, On the edgetone, J. Acoust. Soc. Am. , 33(4) , 395–409 (1961). 6. M. K. Ibrahim, Experimental and theoretical investigations of edge tones in high speed jets, J.

Fluid Sci. Technol. , 8(1) , 1–19 (2013). 7. J. Devillers, O. Coutier-Delgosha, Influence of the nature of the gas in the edge-tone phe-

nomenon, J. Fluids Struct. , 21(2) , 133–149 (2005). 8. J. L. Weightman, O. Amili, D. Honnery, D. Edgington-Mitchell, J. Soria, Nozzle external geom-

etry as a boundary condition for the azimuthal mode selection in an impinging underexpanded jet, J. Fluid Mech. , 862 , 421–448 (2019).

iil wl ii iil i ) iM i |

9. N. S. Dougherty, B. L. Lui, J. M. Ofarrell, Numerical simulation of the edge tone phenomenon,

Tech. Rep., NASA-CR-4581, NASA (1994). 10. G. Pa´al, I. Vaik, Unsteady phenomena in the edge tone, Int. J. Heat Fluid Flow , 28(4), 575–586

(2007). 11. S. Iwagami, T. Kobayashi, K. Takahashi, Y. Hattori, Reproducibility of mode transition of edge

tone with DNS and LES, in: Proc. Int. Congr. Acoust. , 5573–5579 (2019). 12. K. Nakamura, M. Hirayama, S. Ueha, Measurements of air-borne ultrasound by detecting the

modulation in optical refractive index of air, in: Proc. IEEE Ultrason. Sympo. , 1 , 609–612 (2002). 13. M. J. Hargather, G. S. Settles, M. J. Madalis, Schlieren imaging of loud sounds and weak shock

waves in air near the limit of visibility, Shock Waves , 20(1) , 9–17 (2010). 14. K. Ishikawa, K. Yatabe, N. Chitanont, Y. Ikeda, Y. Oikawa, T. Onuma, H. Niwa, M. Yoshii,

High-speed imaging of sound using parallel phase-shifting interferometry, Opt. Express , 24(12) , 12922–12932 (2016). 15. K. Yatabe, R. Tanigawa, K. Ishikawa, Y. Oikawa, Time-directional filtering of wrapped phase

for observing transient phenomena with parallel phase-shifting interferometry, Opt. Express, 26(11) , 13705–13720 (2018).

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