Experimental Investigation of the Acoustic Characteristics of Shock-Vortex Ring Interaction Process

Thangadurai Murugan and Debopam Das

Department of Aerospace Engineering, Indian Institute of Technology, Kanpur, 208016, India

murugan@iitk.ac.in and das@iitk.ac.in

The acoustic waves generated during the interaction of shock wave with a compressible vortex ring are studied experimentally. All experiments are performed in a short driver section shock tube with helium as a driver section gas for shock Mach numbers 1.30, and 1.55. The effect of different shock Mach numbers and reflected shock strength on the generation of acoustics waves is studied for different ring velocities. The far field noise generated during the interaction of the shock wave with the vortex ring is identified in addition to the sound generated during the evolution of vortex rings using Discrete Wavelet Transform. It has been found that the intensity of acoustic disturbance generated during the interaction of vortex ring with shock is dominant as compared with the sound generated during other key processes such as formation, jet interaction and pinching off noise. The intensity of acoustic fluctuation by shock vortex interaction is dominant in the direction of shock wave which also increases with Mach numbers.

Nomenclature

M = Mach number at the exit of the shock tube F = Frequency Vs = Velocity of shock V0 = Speed of sound Ub = Velocity behind the shock D = Diameter of the shock tube DWT = Discrete Wavelet Transform t = Time where t=0 refers to the shock at exit CTA = Constant Temperature Anemometry CCD = Charge-Coupled Device Keywords: Shock-vortex interaction, compressible vortex rings, shock tube, vortex sound, shock diffraction, flow visualization.

I. Introduction

N

oise is a major concern in modern day flight mainly due to the fact that the most commercial plane are operated by jet engines. In incompressible flows, the sound generated by the flow is mainly due to continuous

formation, interaction, and pairing of vortices. Aerodynamic noise is due to interaction of vortices with shear layers that emits small amplitude pressure fluctuation in all directions (Lighthill1, 2). The generation of sound in an ideal and stationary medium is predominantly by the Reynolds stress fluctuations which analogy was given by Lighthill1, 2 who derived the analytical expression for sound generation from the exact governing equations of the flow. There has been a lot of study on sound generated by vortices interactions at low Mach number where the vorticity play major role in sound generation1-6. The far field sound radiation in free space by vortices producing acoustic pressure is linearly dependent on the flow vorticity3, 4 for low Mach number incompressible flows.

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13th AIAA/CEAS Aeroacoustics Conference (28th AIAA Aeroacoustics Conference) AIAA 2007-3422

Copyright © 2007 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

In compressible flow, the sound generation is mainly due to the interaction of shock wave with vortices which

is much more dominant than the sound generated from the interaction of vortices in incompressible flow. The shock-vortex interaction noise includes the scattered wave generated due to inhomogeneity, interaction of shock with vortex core, the scattered waves generated during shock wave interaction with trailing jet and so on. Acoustic disturbance produced by momentum fluctuation is of great interest in designing the efficient and reliable supersonic intakes, combustion chamber and nozzle where the shock-vortex interaction plays a major role. The extension of Lighthill formulation for acoustic disturbances for compressible flow was developed by Weeks and Dosanjh7 which was verified with the shock-vortex interaction experimental results. They observed the interaction of shock wave and a columnar vortex using the Mach-Zhender interferometer. The two dimensional shock-vortex ring interactions and their acoustic wave generation were studied mathematically by Ribner8 who obtained the quadrupolar pressure distribution. Minota9 studied experimentally the interaction of a spherical shock wave and a vortex ring for low shock Mach numbers. Takayama et al.10 studied the shock wave and vortex ring interaction computationally for shock Mach number 1.4 and verified the flow field using shadowgraph method. They found that during the passage of shock wave over the vortex ring, the part of the wave propagating through the inside of the vortex ring is intensified spontaneously.

Ellzey et al.11 study has clarified the appearance of a triple point by the interaction of a shock wave and a

columnar vortex, and the quadrupolar nature of the scattered waves in the far field. The mechanism responsible for the creation of acoustic wave when a shock interacts with a vortex was discussed by Ellzey12. The interaction of shock wave with a vortex ring is investigated experimentally using shadowgraph method and verified with computational results for shock Mach number 1.23 by Tokugawa et al.13. Inoue14 found numerically that the nature of sound produced by shock vortex interaction was closely related to the generation of reflected shock waves. Simizu et al.15 studied the scattered waves generated during the interaction of vortex rings with shock experimentally and theoretically for shock Mach number 1.23 and measured the directivity of the scattered wave. This scatted wave consists of the diffracted shock wave, the acoustic wave generated by the velocity interaction, and the backward scattering by density inhomogeneity.

In the present study, the acoustic waves generated during the interaction of vortex ring with the shock wave are studied experimentally for shock Mach numbers 1.30, and 1.55. In order to reduce the sound generated by many number of components, the author has used single shock tube along with smooth plate which is used to reflect the incident shock wave. This reflected shock is used to study the shock-vortex interaction. The present work is the extension of work carried out by Arakeri et al.16- 17. Discrete Wavelet transform (DWT) is used along with curve fitting technique for synthesizing the acoustic signal obtained from the microphone. The sound generated during the interaction of shock wave with the vortex ring is clearly identified in addition to the sound generated during the formation and pinching of process of vortex rings using DWT. It shows that the intensity of acoustic disturbance generated during the shock-vortex interaction is more dominant as compare to the sound generated during other key processes of vortex ring evolution. The directivity of the acoustic waves produced by shock vortex interaction is also obtained.

II. Experimental setup A short driver section cylindrical shock tube is used for generating the compressible vortex ring at the open of

the shock tube which is shown in Fig. 1 along with CCD camera, pulsed laser and microphone. The shock tube has a driver section length of 115mm and the driven section length of 1200mm with inner and outer diameter of 64mm 100mm respectively. The exit of the tube has 70° tapering with the axis of the tube to make sharp opening. The phenomenon of shock vortex interaction is takes place in few milliseconds hence, the shock tube is kept at a height of 1.70m from the ground to avoid any ground reflection of shock during the measurement time. The shock tube stand angles are covered using foam to avoid any significant reflection of shock wave from them. ¼ inch B&K 4939 2478630 microphone is used for far field acoustic measurements. The data acquisition is done with the sampling rate of 100KS/sec using NI 4472 24 bit sound and vibration DAQ card which has eight simultaneous channels. All experiments are performed with the helium as a driver section gas for Mach numbers 1.3 and 1.55. The Mylar sheet is used as a diaphragm for all experiments which is ruptured using heated nichrome wire which is kept in the driven section. The shock speed is calculated from the arrival time of shock in two pressure transducers which are kept 300mm apart inside the shock tube. A smooth aluminum plate with the cross section of 450mm x 450mm is used for

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reflecting the incident shock wave which is kept at a down stream location of 300mm. For flow visualization, a pulsed laser along with a CCD camera is used. Vortex ring translational velocity and shock speed variation along the radial and downstream direction are calculated using hot wire anemometry and these results are verified from the flow visualization images. These two velocities are used to fix the location of shock vortex interaction. The laser is triggered and synchronized with the camera using external trigger unit to capture the supersonic flow field.

Fig. 1 Experimental setup

III. Results and discussion The following section shows the results obtained from the experiments and its wavelet analysis. The wavelet

analysis of the signal gives the discontinuity presents in the system, the time of occurrence of a phenomenon and the self similarity presents in the signal. The DWT split the entire range of frequencies into two parts. The low frequency part contains the frequency up to Fmax/2. The high frequency part contains the frequency from Fmax/2 to Fmax. Experiments are performed at each location 10 times and their average is used for analysis.

A. Consistency of experimental results The fluctuating pressure signal obtained from the microphone consists of pressure rise due to incident shock,

vortex ring evolution sound, reflected shock, and the acoustic waves generated during the vortex ring-shock interaction. Fig. 2 shows the results obtained from four consecutive experiments for shock Mach number 1.55 at 1.5m from the plate at an angle 135o from the plate.

Incident Shock Reflected Shock

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Fig. 2 The fluctuating pressure signal obtained for four consecutive experiments from the microphone for

shock Mach number 1.55

Shock-Vortex Interaction

The first peak shows the pressure rise due to incident shock wave whose amplitude is less due to the diffraction and spreading of planar shock wave at the exit of the shock tube into a spherical wave (See Fig. 1). The second peak shows the reflected shock wave from the smooth plate which is kept at 300mm from the exit of the shock tube. The strong pressure rise followed by this reflected shock is due to shock vortex interaction. This is due to the generation of scattered waves during the interaction of shock waves with vortex rings.

B. Identification Shock Vortex Interaction Noise Fig. 3 shows the pressure signal obtained without the shock vortex interaction phenomenon for shock Mach

number 1.30 where the microphone is kept at 110o and 1m location from the plate. The detail procedure of obtaining the fluctuating pressure signal from this microphone signal is explained by Murugan and Das18. The pressure signature due to the passage of the shock is filtered out with curve fitting technique from the microphone signal. The obtained fluctuating acoustic signal is then processed and analyzed with wavelet transform to get the sound generated during the different processes of vortex rings evolution namely formation, interaction of secondary and tertiary vortices with trailing jet and pinching off respectively. Fig. 3(b) shows the amplitude of sound generated during formation and interaction of vortices with trailing jet. Fig. 3(d) shows the exact time of generation of acoustics waves during vortex ring evolution and these results are verified with flow visualization which is given in Ref. 18.

(b) (a) Incident shock

(c) Vortex ring formation sound

(d)Trailing jet interaction

Fig. 3 (a) Microphone signal and filtered shock signal (fitted curve) for shock Mach number 1.30. (b)

Fluctuating pressure signal. (c) Low and (d) High frequency contents of fluctuating pressure signal obtained using debauches mother wavelet.

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Fig. 4(a) shows the far field pressure signal obtained from microphone with the presence of reflected shock wave. Fig. 4(b) shows the fluctuating pressure signal obtained after removing the incident and reflected shock wave from the microphone signal. This shows the amplitude of scattered waves generated during shock vortex interaction which is much more dominant than the vortex ring evolution sound which is shown in fig. 3(b). When the vortex ring start to interact with shock, the outer portion of the shock which is passing through the ring is locally get accelerated due to the motion of fluid in the same direction. Whereas the shock passing through the centre of the vortex ring is get decelerated due to the strong opposing velocity. So, the shock passing through the rotational core of the vortex ring and through the axis of the vortex ring is deformed substantially. This cause the origin of additional waves along with waves generated due to inhomogeneity of flow. The shock is continued to interact with the trailing jet, secondary and tertiary vortices which also generates the scattered waves. These scattered waves look similar to the shock wave which was numerically found by Inoue14. The other peaks followed by the vortex shock interaction are due to interaction shock waves with secondary and tertiary vortices. Fig. 4(c) and Fig. 4(d) shows the low and high frequency contents which exists in the fluctuating acoustic pressure obtained using the discrete wavelet transform of second order Debauches family mother wavelet. Fig. 4(d) shows three distinct high intensity peaks which correspond to the incident shock, reflected shock, and acoustic disturbance generated during the interaction of vortex ring with shock. The sound generated during the evolution of vortex ring is very small compare to the strength of the incident shock wave (Fig. 3(a) and Fig. 3(b)). The sound generated during the vortex ring formation and the interaction of secondary and tertiary vortices with trailing jet are of the same order for small shock Mach number 1.30 (Fig. 3(b)). The sound generated during the evolution of vortex ring is much smaller than the acoustic waves emitted by shock vortex interaction (see Fig. 3(b) and Fig. 4 (b)).

Location of reflected Shock

Reflected Shock Incident Shock

(b) (a)

(d) Shock vortex interaction Shock vortex interaction

(c)

Fig. 4(a) Microphone signal and filtered shock signal (fitted curve) for shock Mach number 1.30 with

reflected shock (b) Fluctuating pressure signal. (c) Low and (d) High frequency contents of fluctuating pressure signal obtained using debauches mother wavelet.

C. Radial variation of shock strength and propagation velocity of vortex ring The location of shock vortex interaction is calculated from the radial shock speed variation and vortex ring

translational velocity. Fig. 5(a) shows the radial variation of shock speed obtained using hot wire anemometry for incident shock Mach number of 1.30. The incident planar shock wave diffracted at the open end of the shock tube and forms a spherical wave whose strength is large along the direction of axis and gradually reduces as the angle increases which is shown in Fig. 5(a). The speed of reflected shock is also calculated to find the location of shock vortex interaction. Fig. 5(b) shows the translational velocity of vortex ring for shock Mach numbers 1.30 and 1.55. The translational velocity during the formation is less due to the propagation and expansion of vortex ring in lateral

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direction. After the formation, the radial acceleration is zero and the ring starts to translate with high velocity. This ring is attached with the trailing jet before it pinches off. After the pinching off, it translates smoothly along the downstream direction with nearly constant velocity. The translational velocity after pinching off for shock Mach number 1.30 is 70m/sec. The exact location of shock vortex interaction is calculated from these two shock and vortex ring velocities.

Vortex ring formation

Pinching off

(b) (a)

Fig. 5(a) Shock strength variation along the radial direction for shock Mach number 1.30 where angle 0o is along the axis of the shock tube (b) Vortex ring translational velocity for shock Mach number 1.30 and 1.55

D. Flow visualization Fig. 6 shows the smoke flow visualization pictures obtained using CCD camera and pulsed laser which are used

to verify the translational velocity obtained from mini CTA measurements. Fig. 6(a) shows the formation of vortex ring at the open end of the shock tube. Fig. 6(b) shows the vortex ring pinching off process. Fig. 6(c) shows the free traveling stage of the vortex ring. These pictures give the clear flow field of a vortex ring which interacts with the shock. These pictures are not revealing the structure and nature of the scattered wave generated during the shock vortex interaction because of the small change in density across those waves. The vortex ring translational velocity after the pinching off of vortex ring from the trailing jet for shock Mach numbers 1.3 and 1.55 are 70m/sec and 175m/sec respectively. The exact location of shock-vortex interaction is calculated using these time dependent velocities and microphone is kept accordingly.

Fig. 6 Flow visualization pictures for shock Mach number 1.30 for time 467μs, 1867μs, and 3110μs where t=0 refers the shock at exit

E. Shock vortex interaction Fig. 7 show the fluctuating acoustic signal obtained after removing the incident and reflected shock waves from

the microphone for shock Mach number 1.30 and 1.55 at different angular locations. Fig. 7(a) to Fig. 7(c) show the far filed acoustic signal obtained at 135o, 110o, and 80o and at 1m location from the point of shock vortex interaction for shock Mach number 1.30. The strength of the reflected shock wave is very strong as the angle is close to 180o (the tube exit plane) whereas the incident shock has less strength. The scattered waves followed by the shock is mainly due to inhomogeneity in density at the axial flow region of the vortex ring, vorticity generation at the core of the vortex ring, and the interaction of shock with secondary and tertiary vortices.

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The strength of the scattered wave reduces as the angle move close to the perpendicular direction of the shock tube. Scattered wave strength at 110o is less than the strength at 135o. The strength of the scattered waves reduces as the angle reduces (See Fig. 7(a) to Fig. 7(c)). So, the scattered waves have directivity whose strength is large along the direction of shock (Reflected). The vortex ring has a long trailing jet, as a result scattered waves generated from the secondary and tertiary vortices also important. It is very difficult to find the directivity of the secondary and tertiary vortices because of its interaction with shock and other scattered waves generated during primary vortex ring and shock interaction. Fig. 7(d) shows the scattered waves generated at 2m and 135o for shock Mach number of 1.55. The strength of this scattered wave (2m) is much larger than the strength of the scattered wave generated for shock Mach number 1.30 (1.5m). Because of strong reflected shock wave, the microphone is kept at 2m for shock Mach number 1.55. The strength of the scattered waves increases with the shock Mach numbers.

(a) (b)

(c) (d)

Shock-Vortex Interaction

Shock-Vortex Interaction

Shock-Vortex Interaction

Shock

Shock-Vortex Interaction

Shock

Shock

Shock

Fig. 7 The shock vortex interaction sound at (a) 135o (b) 110o (c) 80o for shock Mach number 1.30 at 1m

(d) 135o for shock Mach number 1.55 at 2m

IV. Conclusions The shock-vortex ring interaction for shock Mach number 1.35 and 1.55 is studied experimentally using

microphone and flow visualizations. The exact location of shock vortex interaction is calculated using the shock speed and the vortex ring translational velocity which are measured using CTA and from time series flow visualization pictures. Discrete Wavelet Transform analysis is used to find the shock discontinuities, sound generated from various sources present in the microphone signal. When the vortex ring interacts with shock, the shock at the surface of the primary vortex ring gets accelerated due to the favorable velocity at the surface (outer region of vortex ring). Whereas at the inner part of the vortex core and the axis of the vortex rings, the shock wave get intensified due to strong adverse velocity.

The part of the shock waves which moves at the outer region get accelerated and the part of the shock wave

which moves through inner region get decelerated. This shock wave is further decelerated by strong trailing jet and the primary and secondary vortices. Scattered waves are generated during all these interactions. So, the shock wave get scattered due to strong gradient in density, in addition to the acoustic waves generated at the core due to strong gradient. The scattered waves generated for high Mach number is very intensified as compare to the low shock Mach number. The microphone signal has few additional scattered waves which are generated because of the secondary and tertiary vortices interaction with shock wave. The far field acoustic pressure measurement at 80o, 110o and 135o from the axis of shock tube shows that the scattered waves are very strong at 135o. The present study

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focuses on the variation of acoustic waves intensities along the reflected shock wave propagation direction. The strength of the scattered waves increases with increase in shock Mach number.

Acknowledgments

The authors would like to thank Indian Space Research Organization, India for providing partial financial support for this work. We are grateful to Mr. Ajay Panday and Mr. Akshaya for helping us performing the experiments.

References

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