Experimental Application of Aeroacoustic Time-Reversal

__________American Institute of Aeronautics and Astronautics

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Experimental Application of Aeroacoustic Time-Reversal

Akhilesh Mimani1,†, Danielle J. Moreau2, ‡ and Con J. Doolan2, §

1School of Mechanical Engineering, The University of Adelaide,

South Australia – 5005, Australia2School of Mechanical and Manufacturing Engineering, University of New South Wales,

New South Wales – 2052, Australia

This paper presents an experimental application of the Time-Reversal (TR)source localization technique to investigate the flow-induced noise generationmechanisms due to a benchmark aeroacoustic problem of a flat-plate.Experiments were conducted in an Anechoic Wind Tunnel (AWT) for thetest-case of a full-span symmetric flat-plate located in subsonic cross-flow.The far-field acoustic pressure was sampled using two Line Arrays (LAs) ofmicrophones located above and below the test-case. It was shown that thePower Spectral Density (PSD) spectrum for a flat-plate exhibits a broadbandnature. The TR simulations were implemented using the time-reversed signalsat the two LAs and the superposition technique whereby the spatio-temporalevolution of the time-reversed acoustic pressure fields and the TR sourcemaps indicate the dipole nature (with axis perpendicular to cross-flow) of theflow-induced noise source throughout the frequency range. In particular, theTR source maps reveal that beyond the low-frequency range (givenby 1000 Hzcf ), the predicted location of the dipole source is near theTrailing Edge (TE) of flat-plate; indeed, the TE dipole was shown to be thedominant noise source in the high-frequency range (given by 2500 Hzcf ),

cf denoting the center frequency of a rd1 3 octave band. Furthermore, theaverage transverse and longitudinal focal-resolution of the flow-induceddipole sources due to the flat-plate (using the present LA configuration) werefound to be c and 0.4 ,c respectively, c denoting the wavelength at cf .

I. Introduction

Acoustic Time-Reversal (TR) proposed by Fink et al.1 is a robust method operating in thetime-domain used for solving inverse problems of sound source localisation. The TR methodfinds application in various fields such as ultrasound medical imaging1, diagnostic and non-destructive testing1, long-range communication in deep underwater acoustics2, in structuraldynamics for health monitoring3, electromagnetic wave propagation4 and recently, in

† Post-Doctoral Research Associate, E-mail: [email protected], AIAA member‡ Lecturer, E-mail: [email protected], AIAA member§ Associate Professor, E-mail: [email protected], AIAA Senior member


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Computational Aeroacoustics (CAA)5. The superior focusing quality of TR over ConventionalBeamforming6 (CB) techniques is because TR simulates the back-propagation of acoustic wavesby solving the same set of differential equations (taking into account, the properties of thepropagating medium and the geometrical features such as reflective surfaces, reverberatingenvironments, scatterers, etc.) of the propagation that govern their emission from the source(s),without making any a-priori assumptions on the source nature unlike CB. While CB may beimplemented in time-domain7, classically, it is carried out in the frequency domain; hence, it isunable to provide valuable temporal information on the evolution of acoustic fields near thesource region. TR on the other hand, being a time-domain approach, enables visualisation of thespatio-temporal evolution of acoustic field near the source, thus providing critical insight into thenoise-producing physics.

A unique blend of numerical CAA simulation and data from aeroacoustics experiments,therefore, gives TR a potential advantage over CB to understand flow-induced noisemechanisms; however, such an experimental application of aeroacoustic TR has received onlylimited attention. For instance, Padois et al.8 presented an application of the TR technique to asimulated-experimental aeroacoustics problem. They used the acoustic pressure time-historymeasured over one Line Array (LA) of microphones located above a wind tunnel test-section(and outside the flow) to localize loudspeaker source(s) (modeling a time-harmonic monopole ora dipole source) in a non-uniform shear mean flow field. The present authors have previouslypresented the first demonstration of the aeroacoustic TR technique to an experimental flow-induced noise problem of a circular cylinder located in a subsonic cross-flow9. Through their TRsimulation, the authors studied the spatio-temporal evolution of the acoustic pressure field in thesource vicinity and subsequently, accurately localized and characterized the lift-dipole nature ofthe flow-induced noise source generated at the Aeolian tonal frequency10-13. Indeed, the TRsource maps were shown to be similar to those obtained using the CB with the same LAconfiguration. In a recent communication14, the present authors demonstrated the effectiveness ofthe super-resolution technique termed as the Point-Time-Reversal-Sponge-Layer15,16 (PTRSL) toenhance the focal-resolution of the flow-induced lift-dipole source generated at the Aeolian toneof a circular cylinder. Despite the aforementioned advancements, further work is required todevelop the TR technique as a practical diagnostic tool (possibly, as a useful alternative to CBand a superior source localization technique) to analyze the flow-induced noise productionmechanism of more complicated experimental test-cases such as a finite wall-mounted cylinder17

or airfoil18 (wherein the end effects are not negligible), an airfoil or flat-plate at non-zero angleof attack19, a flat-plate serrated trailing edge20, poro-elastic trailing edge21 or due to a rod-airfoilinteraction22. However, before attempting the use of TR to solve such class of problems, it isnecessary to first consider simpler benchmark aeroacoustics problem of a practical importancenot studied using TR method as yet.

In view of the background provided above, this work, therefore, considers the benchmarkproblem of a full-span symmetric flat-plate23,24 located in subsonic cross-flow field with a viewto demonstrate the suitability of the aeroacoustic TR method for localizing/characterizing thenature of flow-induced noise.

The paper is organized as follows. Section II briefly describes the experimental set-up, i.e.,the wind tunnel, its operating conditions, the test-case (full-span flat-plate) considered and theconfiguration of two LAs of microphones for recording the far-field acoustic pressure. SectionIII presents the far-field acoustic spectra generated due to subsonic cross-flow over the flat-plate.


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Section IV describes the methodology for implementing the aeroacoustic TR simulations andcomputation of the TR source maps. Section V analyzes the experimental results: the spatio-temporal evolution of the time reversed acoustic pressure fields (especially near the sourceregion), the TR source maps and comments on the predicted location (and the likely error in thesame), characteristics and resolution of the flow-induced noise source. The important findings ofthis investigation are then summarized in Section VI with directions for future work.

II. Experimental set-up and the flat-plate test-case

A full-span symmetric flat-plate23,24 with a sharp Trailing Edge (TE) located in a low Machnumber flow 0 0.09M is considered in this work. Experiments were conducted in the

University of Adelaide’s Anechoic Wind Tunnel (AWT) which is nearly cubic having internaldimensions 1.4 m 1.4 m 1.6 m and its walls are acoustically treated with foam wedgesproviding a near reflection-free environment above 250 Hz. The AWT contains a contraction-outlet of rectangular cross-section of height h = 75 mm and width w = 275 mm that produces aquiet, uniform test-flow. The maximum free-stream velocity of the jet and turbulence intensity atthe contraction-outlet is 140 m sU

and 0.33%, respectively17,18,20,23,24.

In this work, experiments were carried out at 132 m sU with the flow issuing out

from the contraction-outlet towards the positive x direction as indicated in Fig. 1.

Figure 1 Schematic diagram showing the experimental set-up (in the side-view) of a full-span symmetricflat-plate secured between the mounting frame attached to the contraction-outlet flange in the AWT testsection. (Not shown to scale.)

Figure 1 shows a schematic of the experimental set-up (in side-view) of the flat-plate test-case secured between the two side-plates (mounting frame) attached to the contraction-outletflange in the AWT test section. A zero angle of attack was considered between the mean flowdirection and the flat-plate. Furthermore, the end-effects were minimized by extending the span


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of the test-model sufficiently beyond the width of the contraction-outlet24. The origin

0x y is fixed at the opening of the contraction-outlet on its axis as indicated in Fig. 1.

The flat-plate has a chord length C of 200 mm, span of 450 mm, 5 mm thick, and issymmetric with the Leading Edge (LE) being semi-circular (of radius 2.5 mm) and the TEhaving an apex angle of 12 , see Moreau et al.23,24. As shown in Fig. 1, the flat-plate is mountedat a pivot-hole which is 60 mm downstream of the origin and the TE to the pivot hole distance is155 mm which implies that the stream-wise extent of the flat-plate is between

15 mm LE 215 mm TE .x Two line arrays (LAs) of microphones (schematically shown in Fig. 1) arranged parallel to

the stream-wise direction, i.e., the x direction, one above the test-model and another below wereused to measure the acoustic pressure time-history generated due to cross-flow over the flat-plate. Each microphone LA consists of 32 GRAS 40PH 1/4” phase matched microphonesmounted in a timber frame. The microphones were positioned with a unit-to-unit spacing of 30mm, therefore, the total length of each LA is 930 mm. The two LAs are located 700 mm apartand equidistant from the test-model, i.e., the top and bottom LAs are located at

350 mm,yy L respectively, as indicated in Fig. 1. The 64 microphones in the two LAs

were connected to a National Instruments PXI-8106 data acquisition system containing 4 PXI-4496 simultaneous sample/hold ADC cards9,14. Data from the 64 microphones were acquired at asampling frequency of 162 Hzsf for a sample time of 10 s. It is noted that the two LAs of

microphones extend from 1 2 ,x xL x L where 1 96 mmxL and 2 834 mm.xL It is noted that

four microphones in each of the two LAs are located upstream of the origin with the microphonenearest to the contraction-outlet being 6 mm upstream.

Figure 2(a) shows the photographs of the front-view of the flat-plate test-case taken underexperimental conditions in the AWT, whilst part (b) of Fig. (2) shows the photographs of theside-view of this test-case.

(a) (b)

Figure 2 A full-span symmetric flat-plate test-model held in a two-sided mounting frame attached to thecontraction-outlet in the AWT (a) Front-View and (b) Side-View. The angle of attack of the flat-plate(with respect to the mean flow direction) is 0 .


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III. Power-Spectral Density of acoustic pressure signals measured at LAs

Figure 3 depicts the Power Spectral Density (PSD) in dB Hz of the acoustic pressure

p t signal Pa measured at the microphone located below the flat-plate test-model at 24 mm

downstream of the origin at free-stream velocity 132 m s .U It is observed from Fig. 3 that a

broadband PSD spectrum is generated by the flat-plate23,24.

Figure 3 Acoustic Power Spectral Density (PSD) of the full-span symmetric sharp-edged flat-plate atflow speed 132 m s .U

The acoustic pressure signals at each of the 64 microphones were first band-pass filtered inrd1 3 octave bands with center frequencies Cf given by (a) 630 Hz, (b) 800 Hz, (c) 1000 Hz, (d)

1250 Hz, (e) 1600 Hz, (f) 2000 Hz, (g) 2500 Hz, (h) 3150 Hz and (i) 4000 Hz using a high-orderFinite Impulse Response (FIR) filter. It is noted that the background noise level generated by thefree-stream jet is insignificant in comparison to the spectrum generated due to flow-inducednoise throughout the broadband frequency range of interest23,24. Therefore, it is expected to havea negligible contaminating effect on the TR simulation and hence was not removed from thespectrum prior to band-pass filtering.

IV. Methodology: Summarized implementation of Time-Reversal (TR)

The TR simulation was implemented by numerically solving9,25,26 the 2-D Linearized EulerEquations (LEE) using the Pseudo-Characteristic Formulation27,28 (PCF) in reverse time t on arectangular domain 1 3 2 ,x x x y yL L x L L y L shown as follows.


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0 0linear linear linear linear

0 0 0linear linear

0 0 0

linear linear 0

,2

1,

2

1,

2

p cX X Y Y

t

u U U p UX X v u

t y c c x

v vY Y U

t x

(1-3)

where linear 0 00 0

1 p uX c U

ρ c x x

and linear 00 0

1 .

p vY c

ρ c y y

(4-7)

The Anechoic Boundary Conditions29,30 (ABCs) were used at all computational boundariesduring TR whilst enforcing the time-reversed acoustic pressure30 , ,p x y t (recorded during

experiments) at boundary nodes corresponding to the two LAs back-propagates acoustic wavesin the domain. It is noted that 3 150 mm,xL therefore, the upstream length of the domain for

implementing 2-D TR simulations is greater than the upstream length of the LAs.

In Eqs. (1-3), u and v denote acoustic velocities -1m s along the x and y directions,

respectively, linearX and linearY denote a pair of opposing fluxes25-28 propagating towards the x and

y directions, respectively, the sound speed 10 345.75 m sc (at ambient temperature

0 297.47 KT ) whilst 10 m sU represents the spatially-developing shear mean flow of a

free-jet modeled by14

0 0 max

1, 1 cosh sech sech ,

2 2 2y y y

y yU U x y U

L L L

(8)

where 1max max , 32 m s ,U U x U x

and x are the maximum mean flow,

steepness of the shear-layer and half-thickness of the potential-core, respectively; their variationalong x direction (from contraction-outlet) is modeled by an appropriate polynomial-fit usingconstrained least-squares optimization. Figure 4 depicts the variation of this spatially-developingshear mean flow profile of the free-jet at 132 m sU

over the computational domain based

on the model given by Eq. (8). It is noted that the mean flow direction was reversed towards thenegative x direction, i.e., 0 0U U during TR, thereby ensuring the TR invariance8,25,26,28,30 of

the governing LEE.The spatial derivative of acoustic pressure and velocities in the opposing fluxes

linear linear,X Y of the PCF were computed using an overall upwind-biased Finite-Difference

(FD) scheme26,30 that is formulated using a fourth-order, seven-point optimized upwind-biasedFD scheme31 at interior nodes and a seven-point optimised backward FD scheme at the boundarynodes32. In order to increase the mesh-resolution, two equally spaced nodes were added betweeneach pair of nodes corresponding to the microphone locations. The acoustic pressure time-history


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at these two extra nodes (required during TR) were obtained by interpolating the experimentaldata, (i.e., the band-pass filtered acoustic pressure signals) between each pair of microphonesusing Lagrange polynomial interpolation33, resulting in a mesh-size 10 mmx along the xdirection. Equal mesh-size 10 mmy was also considered along the y direction. Themaximum frequency that may be accurately propagated on this mesh is approximately 8255 Hzas determined from the Dispersion-Relation-Preserving31,32 (DRP) range 1.5DRP of the

fourth-order optimized upwind-biased FD scheme and 10 345.75 m s .c The third-order Total-

Variation-Diminishing Runge-Kutta scheme34 is used for time-integration with a time-step51 1.5259 10 sSt f implying that the Courant–Friedrichs–Lewy number or 0.58CFL

for 132 m sU for the mesh-size considered which ensures accuracy of the TR simulations.

Figure 4 Spatially-developing (evolving) non-uniform shear mean flow profile modeling a subsonic free-jet issuing out of the contraction-outlet in the AWT with the free-stream velocity 132 m sU

at thecontraction-outlet opening. The top-hat profile (shown in black) occurring at and near the contraction-outlet opening 0x gradually evolves within the mixing region wherein the potential-core collapses

and the jet rapidly spreads into the ambient stationary fluid producing a developing free-shear layer(shown in red).

The superposition technique26 is used to implement the TR simulations. To this end, thetime-reversed acoustic pressure fields given by Top , ,p x y t and Bottom , ,p x y t obtained by

implementing the TR simulations using a single LA located at the top and bottom boundaries,respectively, are superposed, i.e.,

Top Bottom, , , , , , ,p x y t p x y t p x y t (9)

to obtain the total time-reversed acoustic pressure field , ,p x y t which is equivalent to using

two LAs simultaneously. The superposition technique completely suppresses the formation of


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spurious local maxima region (which deteriorates the quality of TR source localization) in thesource map without making use of the Time-Reversal-Sponge-Layer26 (TRSL) at and near theLAs. However, in comparison to the use of TRSL, its computational cost is high because itsolves the same set of governing equations twice to obtain , ,p x y t field26. Nevertheless, in

this work, the superposition technique is consistently used in all rd1 3 octave bands for TRsimulation. Indeed, its use is preferred over the TRSL method, especially, in the low-frequency

range (the first two rd1 3 octave bands) because the primary side-lobes occur near the LAs andthe use of TRSL in such low-frequency range for the test-case considered generates spuriouslocal maxima region near the LAs which tend to overwhelm the focal spots, thereby affecting thesource localization.

The TR simulation was implemented over 0, 10000t t whereby the aeroacoustic

source location/characteristics were obtained by determining the focal spots in the Root-Mean-Square8,9,25,26 (RMS) time-reversed acoustic pressure field (computed over the time-intervalwhen a steady-state acoustic field is observed throughout the domain) denoted by , .TR

RMSp x y

The focal spot maximum is termed the focal point. The ,TRRMSp x y field is converted to dB scale

(with respect to 52 10 Parefp ) and the source map denoted by dB ,TRp x y is expressed relative

to the focal point(s) whose magnitude is taken as 0 dB, see Mimani et al.15,16,26.

V. Results and Discussion

The spatio-temporal evolution of the time-reversed acoustic pressure field , ,p x y t due

to the full-span symmetric flat-plate23,24 obtained using time-reversed signals at the two LAs isstudied in the (1) low-frequency range 800 Hz ,cf (2) mid-frequency range 2000 Hzcf

and (3) high-frequency range 3150 Hz .cf Figure 5 shows the spatio-temporal evolution of

the , ,p x y t field using the band-pass filtered signals in the rd1 3 octave band with

800 Hzcf at reverse time-instants (a) 40 ,t t (b) 80 ,t t (c) 160 ,t t (d) 380 ,t t

(e) 640t t and (f) 1300 .t t The two LAs, contraction-outlet, its flanges and the flat-platemodel are shown by white lines, whilst the reversed direction of mean flow is indicated by anarrow; the same symbolic convention is followed henceforth in the time-snapshots as well as theTR source maps.


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Figure 5 Spatio-temporal evolution of the time-reversed acoustic pressure field , ,p x y t due to full-

span symmetric flat-plate23,24 obtained using the time-reversed signals (recoded at the top and bottom LAs

during experiments) filtered in rd1 3 octave band with 800 Hzcf (low-frequency range) at reverse time-

instants: (a) 40 ,t t (b) 80 ,t t (c) 160 ,t t (d) 380 ,t t (e) 640t t and (f) 1300 .t t


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It is observed from Figs. 5(a) and (b), that during the initial time-instants, a simultaneousemission of acoustic fluxes from the top/bottom LAs is observed that propagate into the domainand are about to converge or undergo constructive interference. Figure 5(c) shows that this isfollowed by formation of two instantaneous maxima regions (henceforth, referred to as the focalspots) on the opposite sides of the flat-plate (in its vicinity) of nearly the same strength butopposite phase, indicating a dipole-source. The simulations reveal that at the source region, thewidth of the wave-fronts diminish whilst their amplitude significantly increase. However, due tothe conservation of energy8,26 and absence of an acoustic-sink15,16,35 during TR, the convergingwave-fronts do not stop at the source but propagate beyond. By virtue of the superpositiontechnique26 and the use of ABCs29,30, the interference problem near the LAs is prevented. Figures5(d-f) indicate a continuous formation of two instantaneous focal spots throughout the TRsimulations, although their instantaneous geometrical center (taken as the dipole location)slightly varies over time. Furthermore, it is noted that the size of the instantaneous focal-spot islarge because of the low-frequency content of the time-reversed signals.

Figure 6 depicts the spatio-temporal evolution of the , ,p x y t field due to the flat-plate

test-case using the band-pass filtered signals in the rd1 3 octave band with 2000 Hzcf at

reverse time-instants (a) 60 ,t t (b) 120 ,t t (c) 240 ,t t (d) 480 ,t t (e) 960t t and

(f) 1680 .t t The initial time-instants of the spatio-temporal evolution of the , ,p x y t field in

this case is similar to Figs. 5(a-c). However, with the course of TR simulations, i.e., at later time-instants, formation of instantaneous pair of focal spots is observed near the Leading Edge (LE)which are slightly weaker then the focal spots present near the TE of the flat-plate. The LE focalspots can possibly be a weaker dipole source near the LE; however, in order to establish thishypothesis, a further investigation is required to establish that the signals at the LE and TE focalspots are incoherent. Alternatively, the LE focal spots may also be due to the scattering of theback-propagated acoustic waves due to the flat-plate model and/or contraction-outlet flanges.


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during experiments) filtered in rd1 3 octave band with 2000 Hzcf (mid-frequency range) at reverse

time-instants: (a) 60 ,t t (b) 120 ,t t (c) 240 ,t t (d) 480 ,t t (e) 960t t and (f) 1680 .t t


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Figure 7 depicts the spatio-temporal evolution of the , ,p x y t field due to the flat-plate

test-case using the band-pass filtered signals in the rd1 3 octave band with 3150 Hzcf at the

noted reverse time-instants. The initial time-instants of the spatio-temporal evolution in Fig. 7 issimilar to Figs. 5 and 6; however, the instantaneous focal spots at the LE formed during the latertime-instants are somewhat weaker that those formed near the TE. Furthermore, it is noted thatsize of the TE focal spots are smaller in comparison to those observed in Figs. 5 and 6 due to the

higher frequency content of the signals in this rd1 3 octave band.


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during experiments) filtered in rd1 3 octave band with 3150 Hzcf (high-frequency range) at reverse

time-instants: (a) 60 ,t t (b) 120 ,t t (c) 320 ,t t (d) 660 ,t t (e) 1260t t and (f) 2240 .t t


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Figure 8(a-i) depicts the TR source map (RMS acoustic pressure field) over the dynamic

range 0, 10 dB due to the sharp-edged full-span symmetric flat-plate23,24 in rd1 3 octave

frequency bands with (a) Cf 630 Hz, (b) Cf 800 Hz, (c) Cf 1000 Hz, (d) Cf 1250 Hz,

(e) Cf 1600 Hz, (f) Cf 2000 Hz, (g) Cf 2500 Hz, (h) Cf 3150 Hz and (i) Cf 4000 Hz.

The predicted location of the dipole source is taken as the geometrical center of the two focalspots8,9,25,26 (formed on the opposite sides of the flat-plate) and is indicated by a cross X. Thesame dynamic range and symbolic convention of the predicted dipole location is used in theremaining TR source maps presented in this work.

Figure 8 Source map (RMS acoustic pressure fields) of a sharp-edged symmetric full-span flat-plate23,24

obtained using aeroacoustic TR in the one-third octave frequency bands with center frequency Cf givenby (a) 630 Hz, (b) 800 Hz, (c) 1000 Hz, (d) 1250 Hz, (e) 1600 Hz, (f) 2000 Hz, (g) 2500 Hz, (h) 3150 Hzand (i) 4000 Hz.


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The formation of two focal spots (of nearly the same relative magnitude) located inproximity in subparts (a) to (i) of Fig. 8 indicate the dipole nature of the flow-induced noisesource generated due to the flat-plate located in subsonic cross-flow36,37. The TR source mapshown in Figs. 8(a-c) indicate that the flow-induced dipole sources are located between the mid-span of the flat-plate and the TE in the low-frequency range whilst in the mid-frequency andhigh-frequency regions, the dipole sources are located slightly downstream of the TE. Thepredicted location 0 0,x y of the dipole source are noted in the 2nd and 3rd columns of Table 1,

the average Sound Pressure Level (SPL) at the two focal spots is indicated in the 4th column ofTable 1 wherein it is observed that a high SPL is predicted (or alternatively, the dominant noiseis) in the low-frequency range. It is however, known that at low-frequency, the expected locationof the dipole source is towards the mid-span of the flat-plate whereas at high-frequency, thedipole is expected to be located exactly at the TE. Therefore, the predicted dipole location notedin Table 1 indicates a small error which may be attributed to partial angular aperture of the LAs.

Table 1 Predicted location of the dipole source generated by cross-flow over a sharp-edged symmetricfull-span flat-plate and average SPL at the focal points in one-third octave frequency bands obtained fromaeroacoustic TR. The LE of the flat-plate is located at 15 mm, 0x y whilst the TE is located at

215 mm, 0 .x y

Predicted location of Dipolerd1 3 Octave Band

(Hz) 0x (mm) 0y (mm)

Average SPL at the

focal points

(in dB)630Cf 194 20 69.7

800Cf 194 5 71.4

1000Cf 174 0 71.0

1250Cf 234 5 66.9

1600Cf 234 10 67.8

2000Cf 234 5 65.2

2500Cf 234 5 64.2

3150Cf 234 5 61.0

4000Cf 234 5 59.7

Of particular interest, is the beginning of bifurcation of the elongated focal spots observedin Fig. 8(d) which gradually evolves to a complete separation of the LE and TE focal spots inFig. 8(f). As noted earlier, further work is required to comment on the source nature of LE focalspots. Nevertheless, Figs. 8(g-i) indicate that the relative strength of the LE focal spotsdiminishes with increase in frequency band whereby the TE dipole (denoted by X) is thedominant noise source in the high-frequency range.

Figure 8 indicates that with an increase in frequency band, the longitudinal and transversesize of the dipole focal spots decreases and a more compact orientation of the focal points isobtained. Indeed, the size of the focal spots is quantified in terms of the following two metrics;the transverse spatial resolution (parallel to the LAs) and longitudinal spatial resolution


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(perpendicular to the LAs) and is taken as Full-Width at Half-Maximum (FWHM) given by sumof the distances corresponding to the 6 dB level considered on either side of the focalpoint15,16. The average transverse and longitudinal focal-resolution of the TE focal spots is

quantified in the 2nd and 3rd columns, respectively, of Table 2 for different rd1 3 octave bands in

terms of the wavelength c corresponding to .cf

Table 2 Transverse and longitudinal focal-resolution of the dipole source due to sharp-edged symmetricfull-span flat-plate in one-third octave frequency bands obtained from aeroacoustic TR.

Average Size of the Focal Spots (relative to 6 dB)rd1 3 Octave Band

(Hz)Transverse Resolution

(Parallel to the LAs)

Longitudinal Resolution

(Perpendicular to the LAs)

630Cf 0.8511 c 0.4383 c

800Cf 0.9660 c 0.3653 c

1000Cf 1.0060 c 0.4276 c

1250Cf 1.4079 c 0.4167 c

1600Cf 1.1517 c 0.4337 c

2000Cf 0.8987 c 0.4204 c

2500Cf 0.9386 c 0.4349 c

3150Cf 0.8402 c 0.4018 c

4000Cf 0.8813 c 0.3479 c

Table 2 indicates that the average transverse and longitudinal size of the focal spots are

nearly commensurate with respect to the rd1 3 octave frequency band; their average values are

given by 0.9935 c and 0.4096 ,c respectively, for the given LA configuration. These average

values of the focal-resolution signify the conventional half-wavelength diffraction limit (at thesource vicinity) of the TR method15,16,35.

VI. Conclusions

This paper has presented the first experimental application of aeroacoustic Time-Reversal(TR) source localization technique to analyze the flow-induced noise generation mechanisms ofa benchmark test-case of a full-span symmetric flat-plate in subsonic cross-flow. The spatio-temporal evolution characteristics and corresponding TR source maps indicate the dipole nature(with axis perpendicular to flow) of the aeroacoustic source generated due to cross-flowthroughout the broadband frequency range of the flat-plate. This observation is consistent with


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the classically known result that the interaction of a rigid body (typically, smaller than orcomparable to a wavelength) with a flowing medium induces local surface stresses which are ofequal magnitude but act in opposite direction to the surrounding fluid resulting in a dipole sourcenature36,37, thereby demonstrating the suitability of TR technique to such aeroacoustics problems.In particular, the TR source map indicates that the flow-induced dipole sources are locatedbetween the mid-span of the flat-plate and the Trailing Edge (TE) at low-frequency whilst in themid-frequency and high-frequency region, the dipole sources are located slightly downstream ofthe TE. This observation signifies a small error in the location of the dipole source predicted bythe TR method which may be attributed to the partial angular aperture of the two LAs orpossibly, the use of computationally simpler 2-D LEE solver that under-represents theexperimental noise generation phenomenon (more accurately modeled by numerical simulationof 3-D LEE).

The average transverse and longitudinal TR focal-resolution of the flow-induced dipolesources due to the flat-plate in cross-flow (obtained from Table 2) given by c and 0.4 ,crespectively, signify the conventional half-wavelength diffraction limit of the TR method. In afuture work, the Point-Time-Reversal-Sponge-Layer (PTRSL) damping technique developed bythe present authors14-16 will be implemented (at the predicted dipole location) to enhance the TRfocal-resolution of the flow-induced dipole sources. An investigation to examine the effect ofrigid-wall boundary conditions due to the contraction-outlet, its flanges and the model geometryof the flat-plate on the TR source maps (and spatio-temporal evolution of acoustic pressurefields) will also be carried out. In addition, the future work will also include a comparison of theTR source maps with those obtained using the Cross-Spectral Conventional Beamforming (CB)and the Deconvolution Approach for the Mapping of Acoustic Sources6 (DAMAS) method withthe same LA configuration considered here.

Acknowledgments

This work was supported by the Australian Research Council (ARC) under grant DP120102134 ‘Resolving the mechanics of turbulent noise production.’

References

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2 Shimura, T., Watanabe, Y., Ochi, H., Song, H. C., “Long-range time reversal communication in deep water:Experimental results,” The Journal of the Acoustical Society of America, 132 (2012) EL49-EL53.

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Experimental Application of Aeroacoustic Time-Reversal

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