Exploring Noise Sources Using Simultaneous …web.mit.edu/hileman/www/Publications/AIAA2002.pdfdiagnostics in a fully anechoic environment. Thus, simultaneous optical measurements

AIAA JOURNAL

Vol 40 No 12 December 2002

Exploring Noise Sources Using Simultaneous AcousticMeasurements and Real-Time Flow Visualizations in Jets

James Hilemancurren Brian Thurowcurren and Mo Samimydagger

The Ohio State University Columbus Ohio 43210

Work was carried out as part of an ongoing effort to relate instantaneous large-amplitude features of the far- eld acoustic to the dynamic evolution and interaction of large-scale structures within the mixing layer of ideallyexpanded high-speed high-Reynolds-number jets It is believed that such information is essential for a betterunderstanding of jet noise sources and jet aeroacoustic modeling and control The acoustic measurements weretaken with a four-microphone inline array placed 30 deg to the jet axis Conditional sampling of the data from themicrophones was used to create characteristic waveforms for the large-amplitude far- eld sound pressure peaksThe frequency content of these phase-averaged waveforms compare very well with those of the overall acousticfar eld at 30 deg A vast majority of the large-amplitude sound events originated between four and nine jet exitdiameters downstream of the nozzle The acoustic measurements were taken simultaneously with real-time owvisualizations to determine the mechanisms that were responsible for the creation of individual far- eld acousticpeaks and these results have identi ed three noise-generation mechanisms intense cross-mixing-layer interactionthe tearing of large turbulent structures and the rollup of large turbulent structures The simultaneous data alsoshowed that large structures entrain more ambient air into the jet and the mixing layer extends farther into thejet core during intense noise production than during periods of relative quiet

Nomenclaturea = wavelet scaleb = wavelet translationc = speed of soundD = jet exit diameterSrD = Strouhal number based on jet exit diameters = radial distance from the jet centerline

to the microphone arrayuc = convective velocity of large structures within

the jet mixing layerx0 = downstream distance of the front microphone

within arrayplusmn = space between microphones within the arrayfrac34 = standard deviation of the sound pressure data

Introduction

O VER the past 50 years considerable effort has been madetoward reducingthe noise createdby jet engineexhaust In jets

with subsonicconvectivespeeds (averagespeed of large-turbulencestructures within the jet) this component of engine noise is knownas turbulent mixing noise because it is due to the mixing of the ex-hausting high-speed jet with the surrounding ambient air In spiteof much effort the mechanisms that are responsible for the gener-ation of turbulent mixing noise are still not well understood Manyof the average properties of turbulent mixing noise are well knownbut not the underlyingmechanisms responsible for its creationThegoal of this research effort is to gain a better understanding of theintimate relationship between turbulence and mixing noise in anideally expanded high-speed jet

Turbulent mixing noise is highly directional within the acousticfar eld The noise emission is the most intenseat anglesclose to thedownstream jet centerline The preferred angle has been measured

Received 29 October 2001 revision received 15 July 2002 accepted forpublication 19 July 2002 Copyright cdeg 2002 by the American Institute ofAeronautics and Astronautics Inc All rights reserved Copies of this papermay be made for personal or internal use on condition that the copier paythe $1000 per-copy fee to the Copyright Clearance Center Inc 222 Rose-wood Drive Danvers MA 01923 include the code 0001-145202 $1000 incorrespondence with the CCC

currenGraduate Student Gas Dynamics and Turbulence Laboratory Depart-ment of Mechanical Engineering Member AIAA

daggerProfessor Gas Dynamics and Turbulence Laboratory Department ofMechanical Engineering samimy1osuedu Associate Fellow AIAA

to vary from 25 to 45 deg with respect to the downstream jet axis1

An angle of 30 deg was measured with a peak frequencyof approxi-mately 3 kHz (SrD D 02) for the jet used in this study2 The majorityof turbulent mixing noise emanates from a region that includes theend of the potential coreThis determinationhas beenmade by mea-suring the noise intensity globally over the acoustic near eld134

By the use of the correlation between velocity uctuations insidethe jet and the far- eld acoustic pressure the noise source regionof a Mach number 098 jet was determined to be between 5 and10 jet diameters downstream of the jet exit5 By the utilization ofvariousmicrophone arrays several research groups have found thatthe high-frequencynoise from high subsonic jets is generated nearthe nozzle exit whereas lower-frequency noise originates fartherdownstream6iexcl8

In studies of low-speed jets and mixing layers the noise creationprocess has been linked to vortex pairing9iexcl11 A direct numericalsimulationof a low-Reynolds-numberMach 09 jet showed the far- eld noise originated from a region where the computed Lighthillnoise sources were both strong and rapidly changing in time (seeRef 12) Sarohia and Massier13 performed experiments with high-speed schlieren motion pictures that were synchronized with near- eld pressure measurements Their study of excited subsonic jetswith Mach numbers ranging from 01 to 09 and Reynolds numbersof up to 106 found that large instantaneous pressure pulses wereformed whenever two large-scale structures merged however thepassage of a large structure did not signi cantly change the near- eld pressure signal These results all indicate that a time-varyingsource is required to generate noise

In the rst phase of the current research Hileman and Samimy2

used a dual-microphonearray located 30 deg with respect to the jetaxis for noise source location as well as simultaneous ow visual-ization using a double-pulse laser with two charge-coupleddevice(CCD) cameras to explore the causes of noise emission within thesame high-Reynolds-number ideally expanded Mach 13 jet usedin this study The results showed that interactions between largestructures across the jet mixing layer and ldquotearingrdquo of large-scalestructures are two likely mechanisms of intense noise productionObviouslybothof these eventswouldcausea rapid temporal changein a large-scale turbulent structure This is consistent with the pre-viously mentioned studies

The convective velocity of large-scale structures within the jetmixing layer is a particularly important parameter in this study be-cause it is used to track the locationof noiseproducingeventsbeforeand after noise is generated Theoretical equations developed by

2382

HILEMAN THUROW AND SAMIMY 2383

Bogdanoff14 and Papamoschou and Roshko15 predict a convectivevelocity of 206 ms and a convective Mach number of 06 for thejet in this study The actual convective velocity of the large-scalestructures has been found to deviate substantiallyfrom the theoreti-cal value16 Detailed experimental results of Thurow et al17 whichwere obtained in the same jet facility as the current work with theuse of a megahertz rate ow visualization system indicate that theconvective velocity is much higher than the theoretical value Witha large data set of 320 measurements they founda broad probabilitydensitydistributionof convectivevelocitieswith a mean of 270 msBased on these ndings a convectivevelocity of 270 ms is used inthe current study

The examination of turbulent mixing noise in this study focuseson establishing a correlation between the large coherent structureswithin the jet mixing layer and the measured noise in the acousticfar eld This is commonly known as establishinga causalitycorre-lation In an unconventionalmanner the acousticdata are examinedin the time domain and are only taken to other domains as neces-sary when comparison between individual dynamic features andthe overall properties of the jet is desired The jet in this study hasa Mach number of 13 a nozzle exit diameter D of 254 mm (1 in)(a dimension that will be extensively used in this work as a refer-ence length scale) a Reynolds number based on the jet diameter of108 pound 106 and a potential core length of about six jet diameters2

The region around the potential core which is where the majorityof the far- eld acoustic radiation apparently originates will be thearea of primary interest in this work

Experimental ArrangementAll of the experiments were conducted in the optically accessed

anechoic chamber of the Gas Dynamics and Turbulence Laboratoryof The Ohio State University The facility allows for simultaneousacoustic measurements with real-time ow visualizationThis sec-tion describesthe pertinentcomponentsof the experimentthe noisesource localization routine and its validation using a known noisesource

Anechoic Chamber and Jet FacilityThe anechoicchamberfacility thatwas usedfor theseexperiments

is unique in it allows for the measurement of the jet ow with laserdiagnostics in a fully anechoic environment Thus simultaneousoptical measurements of the jet ow and its acoustic eld wereconductedThe inner dimensionsof the chamber from wedge tip towedge tip are 312 m in width and length and 269 m in height Thechamber was tested for compliance to American NationalStandardsInstitue (ANSI) Standard S123535 and the results from the testswere within the required tolerance over most of the distances alongthe microphonepaths18 The air for the jet was suppliedby two four-stagecompressorsit was ltereddriedandstoredin two cylindricaltanks with a total capacity of 425 m3 at a pressure of 165 MPa(1600 ft3 at 2500 psi) A stagnationchamber was used to conditionthe jet air before exhausting it through a 254-mm (1-in) nozzlewith a lip thickness of 25 mm (01 in) where the inner contourwas determined by the method of characteristics for uniform owat the exit The actual Mach number of the nozzle was measured as128Additionaldetailsof the anechoicchamberand jet ow facilitycan be found in Refs 2 and 18

Details of the Inline Microphone ArrayThe microphone array used in this work relies on the novel ap-

plication of acoustic principles that was developed with the dual-microphonearray describedby Hileman and Samimy2 In that workand this one as well the goalwas to relate the acousticfar eld of thejet to the dynamicsof coherentstructuresin the ow The large-scale ow structures are widely believed to create sound that radiates inthe preferentialdownstreamdirectionwhich for thecurrentjet wasmeasured as 30 deg with respect to the downstream jet axis2 There-fore the microphone array was placed in this direction Althoughthis unconventionalarray location is not optimal for the localizationof noise sources it was considered necessary to capture accuratelythe sources of the large-amplitude low-frequency noise tradition-ally associatedwith the turbulencemixing generated by large-scalestructures

Fig 1 Schematic of the inline microphone array used to determinenoise source location

The arraywas composedof four635-mm( 14 -in)4939Bruel and

Kjaer microphones that were separated by 381 508 and 635 mm(15 20 and 25 in) These separationsas well as the physical lo-cationof the array relative to the jet nozzleare shown schematicallyin Fig 1 An aluminum block surrounded by 5-cm-thick acousticfoam housed the microphones Based on the inherent tolerance inthe machining of the microphone holding block the uncertaintyin microphone separation was estimated as 005 mm (0002 in)All exposed surfaces within the chamber were covered in 15-cm-thick acoustic foam The sound data were acquired with a NationalInstruments PC-6110E data acquisition board at a rate of 1 millionsamples per channel per second This fast acquisition rate was cho-sen to maximize the accuracy in measuring the time delay betweenan acoustic signal peak reaching any two of the microphones

The time delay between an individual acoustic ldquoeventrdquo beingrecorded by two different microphones (phase lag) was combinedwith knowledge of the array geometry to determine the angle withwhich the event had approached the array This angle and the speedof sound in the ambientwere then used to determine the locationsofthe apparentnoise sources assuming they were all located on the jetcenterlineFurther detailscan be found in Ref 2 Segments of sounddata that were 035 ms in length (350 data points) were cross corre-lated with equal-lengthsegments from the othermicrophonesignalsto determine the time delay between the two microphonesrecordingthe event The use of four microphones provided for six differenttime delays that lead to six different estimates for the event originThese six locations were then averaged to determine the averagenoise source location Any of the six origins that were located out-side the range from iexcl5 to 25D with respect to the nozzle exit werenot included in the average because they were likely in error

Typical sound pressure data recorded by the microphones thatcompose the inline array are shown in Fig 2 The time origin corre-sponds to the rst laser pulse illuminating the ow The four micro-phones recorded peaks of similar shape and magnitude but thesepeaks are shifted in time that is phase shifted Even at the largesttime delay (between the rst and last microphones)the overallshapeof the sound wave remains substantially unchanged This mannerof determining noise source location is different than those using across-spectralmethod For that type of technique which computesan average noise source location and not an instantaneous sourcethe microphone spacing should not exceed one-half of the wave-length of the sound that is being located For the technique usedhere any microphone spacing can be used as long as there is ahigh correlation between the microphone signals for the event ofinterest

The large negative sound pressurepeak of Fig 2 recordedaround34 ms was cross correlated for the six different microphone pairsto determine the corresponding time delays and to show how thistechnique works Figure 3 shows the 035-ms data segments fromeach microphone that yielded the maximum correlation Figure 4shows the same segments shifted by the computed time delays Thetime delays between the peaks recorded by microphones 1 and 21 and 3 and 1 and 4 were used to shift the signals of microphones23 and 4 to overlapwith themicrophone1 signalcenteredon339msSimilarly the time separationbetween the signals of microphones2and 3 and microphones2 and 4 were used to overlap their signals to

2384 HILEMAN THUROW AND SAMIMY

Fig 2 Typical data recorded by the four microphones of the inlinearray time is relative to the rst laser pulse illuminating the ow andthe numbers correspond to each of the individual microphone signals

Fig 3 Time segments for each of the four microphones of the inlinearray that were used to determine the origin for a large-amplitudepeakportion of the time signature in Fig 2

Fig 4 Time segments of Fig 3 shifted by the computed maximumcorrelation times (time separations)

that of the microphone 2 signal forming the second group centeredon 347 ms Finally the separation between the peaks for micro-phones 3 and 4 was used to align the signals of the two microphonescentered on 360 ms As seen in Fig 4 all six time shifts give goodvisual correlation

The noise source location technique needs to be instantaneousbecause the source origins are going to be compared to real-timeimages of coherent structures and their interaction To do this onehas to relate the time of noiseemission to the time the ow imagewascaptured by laser ow visualization that is one needs to measurethe time lag between the ow visualization and the emission ofthe sound wave by the noise source Equations (7ndash9) of Hilemanand Samimy2 were used to determinethe streamwise locationof thenoise-emittingregion of the jet during the time of laser illuminationUnfortunatelythe laserwill oftennot be illuminating the ow whilethe peak sound generation is occurring thus one has to take manysets of data to capture a few noise-producingevents while they arecreatingsigni cant soundThis is clear if one considersthat the totalillumination time of the ow in the acquired movies is limited to150sup1s (approximately16convectivetime scalesof D=uc whereasthe period of the peak noise at the 30-deg location (3 kHz) is 333 sup1s(Ref 2) That is often the ow is illuminated during a period ofintermediate noise generationand not during the most intense noiseemission Ideally the ow visualizationimage set would span a timeperiod longer than 333 sup1s

Validation of the Inline Microphone ArrayA Hartmann tube uidic actuator (HTFA) was used to test the

ability of this inline array to locate sound sources19 A Hartmanntube consists of an underexpanded jet directed into a coaxial tubewhere the open end of the tube is placed within a compressionregion of the underexpanded jet and the other end of the tube isclosed20 The high-speed ow of the jet entering and exiting thetube generates a pulsating ow as well as an intense tonal soundAn HTFA is created by placing a cylindrical shield between thenozzle and the tube21 This shield covers a large portion of the openarea and creates a pulsating jet The HTFA used in this validationcreated a pure acoustic tone with a frequencyof 3662 Hz along with ve harmonics The opening of the HTFA was 4 pound 6 mm and theouterdiameterof the HTFA was 127 mm The noise-emittingregionof the HTFA was expected to be within a region close to its exitbecause this area has been found to be rich in vortical structures19

The HTFA was placed so that the exiting uid was aligned with thejet centerline and the back surface of the tube was next to the jetnozzle exit The inline array was then used to determine the originof all of the sound events that had amplitude in excess of 15 timesthe standarddeviationof the signal This was performed for 06 s ofacoustic data The predicted downstream locations are given in theprobabilitydensitydistributionofFig 5 The peakof thedistributioncoincideswith the exit of the actuator and 90 of the distribution iswithin sect05D of the actuator exit Another experiment conductedwith a lower pressure HTFA (the frequency content only slightlydifferent from that listed earlier) showed similar results Becausethis is a distributed source rather than a point source the resultsindicate that the accuracy of this inline microphone array must bebetter than sect05D

Flow Visualization (Pulse-Burst LaserUltrafast Camera System)The ow was visualizedvia scatteringof laser light by condensed

water particles within the jet mixing layer The warm moist air ofthe ambient is entrained into the cold dry jet air that is exiting thenozzle thus forming the jetrsquos mixing layer On mixing the mois-ture contained in the ambient air condenses into small particles thatscatter laser light and mark the majority of the mixing layer Thelight was provided by an in-house built pulse-burst laser and thescattered light was captured with a camera from Silicon MountainDesign [(SMD) now a subsidiary of Dalsa Inc] Both systems arecapableof operatingat a megahertz rate The camera was limited to17 frames and the ow visualizationimage sets in this work consistof 16 images Both a 5-sup1s (200-kHz) and a 10-sup1s (100-kHz) inter-pulse timing were used Details of this lasercamera system can befound in Ref 17


Fig 5 Probability density distribution of apparent noise source loca-tions for the HTFA used to validate the inline array the abscissa isrelative to the rear of the HTFA which coincides with the jet exit sup2calculated data points and mdashmdash curve t

There were 250 sets of simultaneoussoundand ow visualizationimages taken for both of the time separationsThe laser was locatedoutside of the anechoic chamber and its beam was redirected intothe chamber through a 25-cm opening A frame structure whichwas covered with acoustic foam and connected to the ceiling of thechamber held the optics that were used to create the laser sheet thatpassed throughthe jet centerlinealong the streamwisedirectionTheSMD camera was placed insideof the chamber perpendicularto thelaser sheet capturing the ow over a range of downstream locationsfrom 45 to 105D The camera could not be placed outside of theanechoic chamber due to limited laser power and poor sensitivityofthe camera Both the camera stand and the camera were wrapped inacoustic foam to minimize acoustic re ections

Results and DiscussionPhase-Averaged Waveform of Large-Amplitude SoundPressure Events

All of the sound pressure events with acoustic peaks in excess of20frac34 were phase averaged to create a representativewaveform Thestandard deviation of the sound pressure frac34 was 19 Pa To obtainthe phase-average waveforms 1 ms of data before and after ev-ery peak exceeding 20frac34 where the peaks had been phase alignedwere ensemble averaged This process was performed separatelyfor the positive peaks (910 events) and negative peaks (833 events)to get correspondingphase-averagedwaveforms The analysis wasthen repeated with a 15frac34 threshold In this case 2307 positive and2259 negative peaks were ensemble averaged from 20 s of data toget phase-averagedwaveforms The positive phase-averagedwave-forms for both threshold levels are shown in Fig 6 along with aMexican hat wavelet which will be discussed later All three havebeen normalized by the standard deviation of the acoustic data Thenegative waveforms not shown here bear enough similarity to thepositivewaveforms of Fig 6 that if they were rotated 180 deg aboutthe origin the correspondingpositive waveform would be created

The shapes of the waveforms are quite remarkable They havesharpdistinctpeakswith side lobesonboth sidesof thecentralpeakThe central peak of the 20frac34 threshold waveform has a magnitudeof about 26 whereas the side lobes have absolute values of about07 and 09 The main peak for the 15frac34 threshold waveforms has amagnitude of 22 whereas the side lobes have equal values of about06 Because the 15frac34 waveform has equal magnitude side lobesthe asymmetry in the side lobes of the 20frac34 waveform must be duein some way to the higher intensity of those sound waves

The phase-averagedwaveformalsosharesa strongsimilaritywiththe Mexican hat wavelet A wavelet analysis is often used to deter-mine how the frequency of a signal is changing with time In thistype of analysis a wavelet is convoluted with the signal of inter-est To determine what the frequency content is within the signal

Fig 6 Phase-averaged positive large-amplitude sound pressurewaveforms for all of the time trace segments with a peak amplitudelarger than 15frac34 and 20frac34 along with a Mexican hat wavelet (ampli-tude normalized by the standard deviation)

Fig 7 Overall spectrum and the spectrum for the 15frac34 average wave-form mdashmdashmdashmdash waveform spectrum

the wavelet is stretched or compressed by a multiplier known asthe scale The convolution is then performed with the wavelet forvarying time delay which is referred to as translation When thescale and the translationof the wavelet are changed the energy con-tained within various scales (frequencies) can be determined overthe duration of the signal There are an in nite number of waveletsavailable for study but a few are commonly used One of these isthe Mexican hat wavelet which got its name from its similarity toa Mexican sombrero The Appendix goes into further details of theMexican hat wavelet and its use in signal analysis As mentionedpreviouslyFig 6 also includes a Mexican hat wavelet that was cre-ated via Eq (A2) of the Appendix with a translation of 05 ms ascale of 84 sup1s and a multiplier of 47 The Mexican hat wavelet haslarger magnitude side lobes than either of the phase-averagedwave-forms Otherwise the match of the wavelet and waveform is goodBecause of these similarities the acoustic data from the simultane-ous measurements were transformed with the Mexican hat waveletto determine the time-varying frequency content of the sound data

The 15frac34 phase-averagedwaveform was transformed to the fre-quency domain and converted to a power spectral density plot Thisspectrum is given in Fig 7 along with the conventional spectrumThe frequency content of the spectrum around the peak frequencyfrom the 15frac34 threshold waveform has a remarkable similarity tothe conventionalspectrumThe strongmatch of the spectra from the


Fig 8 Probabilitydensity of the apparent large-amplitudesound eventsources (peak amplitude larger than 15frac34) calculated data pointsthat are spaced at 1D and mdashmdash curve t

Fig 9 Two-dimensional probability density distribution showing thedownstream locations for sound events of varying amplitude

Fig 10 Example of an image set showing cross-mixing-layer interaction near the origin of an intense sound event

phase-averagedwaveforms and the overall far- eld radiationshowshow well the average waveform is capturing the dominant noisecharacteristics of the jet at the 30-deg observation angle This hastremendous implications for understandingthe correlationbetweenturbulence structures and far- eld acoustic owacoustic controland aeroacousticmodeling Because the phase-averagedwaveformwas created by averaging many individual large-amplitude soundevents and its spectrum accurately recreates the overall spectrumfor the jet it would appear that the large-amplitudesound events areresponsible for the generation of the intense low-frequency soundthat is observed at shallow angles to the downstream jet axis

The phase-averagedwaveformbears several similaritiesto acous-tic pressuretracescreatedby the head-oncollisionof low-Reynolds-number vortex rings Kambe22 performed experiments where twovorticesweregeneratedand directedtowardeach otherfor a head-oncollisionThe resultingacousticpressuretime traces were recordedand the ensemble average of 10 such acoustic time traces was ob-tained The resulting waveform has some of the same character-istics as the phase-averaged waveforms given in this work Bothhave a large central peak with two side peaks of opposite sign Theside lobes in Kambersquos work also have unequal amplitude (as was

Fig 11 Far- eld acoustic time signature corresponding to ow imagesof Fig 10 time zero corresponds to the rst laser pulse


Fig 12 Example of an image set taken while the microphone array was recording a period of relative quiet

observed for the 20frac34 waveform) and the phase angle (time delay)between side lobes is on the order of that for the phase-averagedwaveforms Inoue et al23 performed a numerical simulation of thehead-oncollisionsof two low-Mach-numbervortex rings where theMach numbers of the two vortices were varied When the two vor-tices had equal Mach numbers the pressure trace did not resemblethat of Kambe22 or the phase-averaged waveform of the presentwork However when the ratio of the Mach numbers of the twovortices was two the shape was very similar to those of the presentwork Furthermore when the ratio was held at two the pressuretrace remained consistent in shape over a range of Mach numbersfrom015 to 03 for the faster vortexAlthoughthere is no directcon-nectionbetween the noise sources in the Mach 13 jet of the presentwork and the head-oncollision of two simple vortex rings there ap-pear to be similarities in the resulting acoustic waveform betweenrelativelysimple vortex ring interactionsand the more complexcaseof turbulent structure interaction in a high-speed jet This similaritymight shed light on how noise is being generated in high-speedjets

Origin of the Large-Amplitude Sound Pressure EventsThe probability density of the apparent noise emission locations

for all of the sound peaks in excess of 15frac34 has been plotted inFig 8 Data points that had a standard deviation in excess of 20Dwithin the locations determined by the six microphone pairs werenot includedThis left 5584 data points to be plotted in Fig 8 for the25 s of data analyzed The mean of the noise source locations was67D and the standarddeviationwas 23D The vastmajority (74)of the noise sources were located in the region between 4 and 9Dand 98 originated between 1 and 12D The lack of noise originsupstream of the jet exit gives further credibility to the accuracy ofthis noise localization technique

The absolute magnitude of each sound peak in excess of 15frac34has been plotted vs its origin in the form of a two-dimensionalprobability density distribution (Fig 9) Figure 9 was created fromthe same set of data that was used for Fig 8 The amplitude hasagain been normalized by the standard deviation of the acousticdata The contour levels give the percent of noise events within thetwo-dimensionalbins (the bins are 1D wide along the abscissa and025 units in length along the ordinate) Larger amplitude but lessfrequently occurring sound events apparently emanate from fartherdownstreamthan the weaker but more frequentlyoccurringeventsFor example one can see from Fig 9 that events with an amplitudelevel larger than 25frac34 originateddownstreamof 3D The number ofall events drops off considerably after 11D

Fig 13 Far- eld acoustic time signature corresponding to the owimages of Fig 12

Simultaneous FlowAcoustic ResultsAfter the locationsfor every large-amplitudepeak (usinga thresh-

old of 15frac34 within the 25-s data set were calculated they wereexamined to determine which noise generating events would haveoccurred during the ow visualizations Any large-amplitude peakthat 1) was created during or within a short period of time eitherbefore or after the ow visualizations 2) had an amplitude over20frac34 and 3) had an origin within the eld of view was further an-alyzed This increased amplitude was deemed appropriate becausethe phenomena that cause larger amplitude sound waves should bemore apparent These requirements reduced the number of soundpressure events to be analyzed from several thousand to 22 eventswith 5 sup1s between consecutive ow visualization images and 32events with 10 sup1s between ow images

To understand fully what phenomena are creating these largesound pressurepeaks it is also insightful to examine ow visualiza-tion movies that coincide with periods where the microphone arraywas not recording any large-amplitude events which is referred toin this work as a ldquorelatively quiet periodrdquo A period of relative quietwas de nedas onewhere the arraydid not recordany soundwaves inexcessof 15frac34 over a length of time of at least 06 ms This time span


Fig 14 Example of an image set that shows structure rollup near the origin of an intense sound event rollup is circled in image 8

is approximately six convective timescales of D=uc A convectivetimescale is a time period over which a large-scale structure wouldtravel a distancecomparable to the structurersquos length scale which istaken to be D here During such relatively quiet movies a minimalamount of sound reached the microphone array Practically speak-ing the time traces associated with relatively quiet movies have nolarge-amplitude peaks between 32 and 38 ms after the laser illu-minates the ow There were 12 relatively quiet movies with 10-sup1sspacingand 18 movieswith 5-sup1s spacing that met this requirementBecause of the space constraints and because the 10-sup1s separationmovies show more developmentof the jet none of the 5-sup1s moviesare presented in this work However they were examined in greatdetail and will be used in the average images that will be discussedin the next section

The presented data sets consist of images that are separated by10 sup1s and the simultaneously acquired acoustic time signatureFigures 10 and 11 form a typical simultaneousdata set The imagesof Fig 10 can be viewed as a movie of the developmentof the mix-ing layer of the jet In the ow visualization images of Fig 10 andothers to follow the scatteringof laser light via condensedmoistureparticlescreated the white cloudlikeareas that mark a major portionof the mixing layer The ow is from left to right and the imagesare numbered The last few images have poor quality because thelaser power dropped signi cantly toward the end of the set of laserpulses The apparent streamwise noise emission location (assumedto be on the jet axis) is marked with a closed squareAn open squaremarks the region of the jet that passed through the noise emissionlocation at the time the sound event was created This region of thejet was assumed to be traveling with a convective velocity of 270ms hence the open square is an estimate of the location of thenoise source in that frame The proximity of the squares to the topof the image was chosen to prevent clutter within the images andshould not be taken to mean the noise originated above the jet Aswas mentioned earlier the inline acoustic array cannot resolve thecross-stream location of the noise source and thus the noise ori-gin was assumed to be on the jet centerline The image where bothsquares are aligned was taken close to or at the time of peak noiseproductionAn acoustic time trace from the front microphoneof thearray is given in Fig 11 In all of the data shown the other three mi-crophones recorded phase shifted events similar to that of the frontmicrophoneThe time origin on the abscissa corresponds to the rstpulse of the laser illuminating the ow


Based on the ow image sets that capturednoisegenerationthreenoise-generationmechanismshavebeenobservedThe rst is cross-mixing-layer interaction where a large turbulence structure withinone side of the mixing layer interactswith another large structureonthe opposite side of the mixing layer across the jet core The secondmechanism is the rollup of large structures within one side of themixing layer The last mechanism involves a large structure beingtornapartTwo of thesemechanismscross-mixing-layerinteractionand tearing were observed with dual laser pulse illumination andwere presented by Hileman and Samimy2 In this work examplesof all three noise-generationmechanisms are given along with twoexamples of relative quiet

Cross-mixing-layerinteraction within the image set of Fig 10 isthe likely causeof the peak that is markedwith an ldquoordquo in the acoustictime signatureof Fig 11 (The threshold levels of sect20frac34 are shownin Fig 11) This peak was createdat a downstreamlocationof 79Dabout 70 sup1s after the rst image was taken The standard deviationfor the noise source location was 06D If the source of the soundmoved at a convectionspeed of 270 ms it would have been at 72Din the rst image and at 90D in the last as is marked with the open




squares It would appear that the interaction across the two sides ofthe mixing layer produced the large peak This interaction region isbetween7 and 10D in image number8 which was takenat about thesame time as the maximum sound generation There were severalother data sets that had similar cross-mixing-layer interaction inareas of noise production

Two other peaks have been marked in Fig 10 The one markedA was created at 87D 1010 sup1s before the rst image was takenThus the region of the jet that passed through the noise productionregion 87D at the instant of noise emission would be at 194D bythe time the rst ow image was taken Similarly the peak markedB was created at 57D 609 sup1s before the rst image The regionof the jet that passed through 57D during noise emission wouldhave convected to 122D when the rst image was taken In otherwords the regions of the jet which were responsible for creatingsoundpressurepeaksbeforeB were downstreamof the regionbeingimaged in the ow visualizationsFurthermore those regionsof thejet that caused the peaks recorded after o would be upstream of theimaged ow region

As mentioned in addition to the data sets that captured appar-ent large-amplitude sound emission there were also data sets thatcaptured the jet while the microphone array was recording a periodof relative quiet One such image set is shown in Fig 12 As can

be seen in the acoustic time trace of Fig 13 the period of relativequiet is over 18 ms long (raquo18 convective timescales) and the fewpeaks in excess of 15frac34 were all created long before or after theimage set in Fig 12 was taken The horizontal lines in the relativequiet acoustic time traces show the 15frac34 threshold levels Basedon the lack of large amplitude acoustic events there should not beany signi cant noise generating events present in the top portionof the mixing layer However in this image set there is interactionbetween the two sides of the mixing layer between 7 and 8D inimages 9 to 13 but this interaction appears to be much less intensethan that of Fig 10 This subjective interpretationwill be validatedto some degree in the next section

The ow visualization image set in Fig 14 shows the rollup of alarge structurewithin the top half of the mixing layer that appears tohave generated signi cant noise The structure is located between 7and 8D within image 8 (the structure is inside the white circle) andthe sound event that apparently originated from the same region ismarked in the time signatureof Fig 15 with a small o The apparentorigin of the marked peak of Fig 15 was estimated at 65D and itwas created about 70 sup1s after the rst (Fig 14) and 80 sup1s before thelast images were taken The standard deviation in the six individualnoise source locations was 14D When a convection velocity of270 ms is assumeda large structureat 58D in the rst frame wouldbe at 65D during noise emission this same structure (assuming aconstant convection velocity) would be located at 76D in the lastimage The sound wave was created approximately when image 8was taken By examinationof the rollup process in the ow imagesone can see the open square lags the large developing structureby about one jet diameter This is expected because the structureis above the jet centerline and the calculation assumes it to be onthe centerline If the noise origin were 05D above the centerlinethen the calculated noise emission location would be 08D fartherdownstreamThus there is very good agreementbetween the originof the marked large peak and the large structure rollup The rollupof large structures was determined to be the mechanism of soundgeneration in a large number of other image sets

During the time period when the images in Fig 16 were takenthe jet was in a period of relativequiet that started at 3 ms and lasteduntil 45 ms as is seen in the time signature of Fig 17 Throughanalysis of the array acoustic data it was determined that no noiseevents in excess of 15frac34 were produced during this movie set Therelativelyquietperiodusingtheaforementionedde nitionis 16mslong during which a large-scale structure convecting at 270 mscould travel 166D This period of relative quiet is quite remarkableconsidering the large rollup of successive large structures within


Fig 18 Example of an image set that shows structure tearing near the origin of an intense sound event region of tearing is circled in image 3

the bottom half of the mixing layer (in image 13 the structures arecentered at 7 and 9D) The structure at 9D in image 13 was createdby the mixing layer rst becomingwavy in appearance(frames 4ndash6between 7 and 9D) and then rolling up into a large round structure(frames8ndash14 between8 and 9D) This process is verymuch like thatdescribed by instability wave theory13 The upstream structure (at7D in image 13) forms between 5 and 7D over the course of themovie set by the merging of several structures

There were additional cases not shown here of large structurerollup within the bottom half of the mixing layer occurring withoutlarge-amplitude sound waves reaching the ceiling-mounted micro-phonearrayThesevorticeswhich roll up in eitherside of the mixinglayer are not axisymmetric If a source of noise were locatedon oneside of the jet then it is unlikelythat it would radiateuniformlyin allazimuthaldirectionsIn additionthemicrophoneslocatedon theop-posite side of the source relative to the jet centerlinewould receiveif they receive it at all acoustic radiation that has been refracted (forexample see Ref 24) Thus the instantaneous azimuthal radiationpattern caused by a sound source that is located on one side of thejet would probably be nonuniform and such nonuniformity mightexplain the inability of this acoustic array to detect the rollup on theother side of the mixing layer as an apparent noise source Furtherwork is needed to resolve this issue

The image set of Fig 18 shows the tearing of a large structurewithin the top half of the mixing layer that is the apparent cause ofthe marked peak in the far- eld acoustic signature of Fig 19 Thisacoustic event has been marked by an o The apparentorigin for theevent was at 80D and it was created about 60 sup1s after the rst and90 sup1s before the last images were taken Hence the apparent noisesourcewould havebeen at a locationof 74D in the rst frame and at92D in the last (constantconvectivevelocityassumption)The tear-ing event (marked with a circle in frame 3) is occurringover the rstfour frames of the image set and is distinguishableby the growingseparationbetween structures that are enclosed in the circle As wasthe case for the other two noise generation mechanisms structuretearing was also prevalent in other noise-capturingdata sets

To relate the large-amplitudefar- eldacousticeventsto thebroad-band frequency peak the time-varying frequency of the acousticsignal was computed for each of the cases given earlier by calculat-ing the energy density over time and frequency using the Mexicanhat wavelet transformation The Appendix discusses the Mexicanhat wavelet and its associated energy density The scales that werecomputed correspond to frequencies between 1 and 10 kHz Based


on the energy maps the large-amplitude peaks (those marked inthe preceding acoustic time traces) consistently had large energycontent between 2 and 4 kHz The energy density maps for the rela-tive quiet cases had less energy (as compared to the large-amplitudeevents) within the frequency range between 2 and 4 kHz during thetime of relative quiet Figure 20 shows these two phenomena It isthe energy density distributionfor the acoustic time trace of Fig 17The large-amplitude events (Fig 17) all have corresponding highenergy levels in the frequency range between 2 and 4 kHz (Fig 20)whereas the period of relative quiet lacks energy at any frequencyThis further supports the argument that these large-amplitudeeventsare in fact the time domain representation of the broadband peakin the frequency domain that occurs between 2 and 4 kHz

Average Noisy and Relatively Quiet ImagesAs mentioned earlier there were a large number of movies taken

during noise production as well as periods where the microphonearray was not recording any large-amplitude sound events Thusit made sense to compare the average state of the jet (in terms ofthe ow images) during these two conditions The average imagesof these opposing conditions as well as the unconditional average


Fig 20 Energy distribution for the Mexican hat wavelet transforma-tion of the time signature of Fig 17

Fig 21 Plots of the average image intensity for the noise creation(noisy) relatively quiet (quiet) and random (overall) images at vari-ous downstream locations

image of the jet (average of randomly selected images) were ob-tained to make the comparison

The random average image of the jet was created by ensembleaveraging the seventh ow image out of the 17 images from 77random ow visualizationsets An average ow image over a simi-lar range of downstream locations was given in Ref 2 Frames fromeach ow visualization set that had captured a noise event in theprocess of creating a large sound peak in excess of 20frac34 were alsoensemble averaged (54 sets in all) Images from each ow visual-ization image set that had acoustic signatures matching the relativequiet requirements (from the last section but with a quiet periodlonger than 076 ms raquo8 convectivetimescales)were also ensembleaveraged This set contained 29 images Before averaging each ofthe images was normalized so that its maximum intensity would beone This was done to eliminate problems caused by variations inshot-to-shot laser pulse intensity

Figure 21 shows the intensityof each of the three average images(noisy relative quiet and random) at select downstream locationsUpstream of 7D the three curves have nearly identical centerlineintensity However downstream of 8D the noisy image has thelargest centerline intensity Because the intensity is directly relatedto the amount of condensation particles in the jet and these parti-cles are a direct result of large structures entraining ambient uidinto the mixing layer there must be more large structures or thelarge-scalestructuresmust be more robust enabling them to entrainmore ambient air into the jet during the period of time the noisyimages were taken than during the relative quiet images This is notsurprising because cross-mixing-layer interaction and large-scalestructure rollup were considered to be causes of large-amplitude

noise production in this work as well as in the work of Hileman andSamimy2 Such an observationis impressiveconsideringthat it wasbased on an objective sampling of data and that it was not based ona subjective comparison of ow images to noise source locations

ConclusionsThe focus of this work was on exploring the correlation between

turbulence structures and the acoustic far eld of a high-Reynolds-number ideallyexpandedMach 13 axisymmetric jet Noise sourcelocalization measurements were made with an inline four-elementmicrophone array located at 30 deg and simultaneous ow visual-ization was made with a home-builtmegahertz rate imagingsystemThe unconventionalarray locationof 30 deg was chosen to measurethe preferential high-intensity acoustic radiation in that directionThis ow visualization system using a pulse-burst laserultrafastCCD camera system was operated at an imaging rate of either 100or 200 kHz

By phase averaging many large-amplitude sound pressure peaksfrom the far- eld microphones an average waveform was createdThis waveform possesses the same dominant frequency contentas the overall acoustic eld This should have tremendous con-sequences in modeling the acoustic sources This waveform alsoresembles a Mexican hat wavelet and as such the Mexican hatwavelet transformationwas used to analyze the acoustic signals fortheir frequency content

The noise source location was calculated for every sound wavewith intensity greater than 15frac34 and plotted in the form of a prob-ability distribution Three-fourths of the sound waves originatedbetween 4 and 9D This is consistent with the results from otherresearcherswho found the majority of the sound from a high-speedjet originates in the region surroundingthe end of the potential corewhich for the jet in this study was measured between 5 and 6D

Based on the simultaneous ow visualizationacoustic measure-ments three apparent noise generatingmechanisms were identi edwithin the Mach 13 jet They include cross-mixing-layer interac-tion large structure rollup and structure tearingPeriods of relativequiet (as recordedby the microphonearray) were also observedanddiscussed

Apparently asymmetric noise-producing events such as largestructure rollups one of the three identi ed noise sources havea pronounced nonhomogenous directivity For example when therollup occurred within the microphone array side of the mixinglayer the array recorded a large-amplitude sound wave whereaswhen it occurred within the other side the array did not record anysigni cant sound waves

The average state of the jet during noise emission was comparedto that duringperiodsof relativequietThe averagenoisy image wasobtained by ensemble averaging images taken during time periodsof signi cant noise emission (peak amplitude in excess of 20frac34 whereas the average relatively quiet image was obtained using theensemble average of the images taken while the microphone arraywas recordinga periodof relativequietwhich was de nedas havingno sound peaks in excess of 15frac34 Based on this comparison thereare more large and coherent structures in the jet that entrain theambient air into the jet duringnoise emission than periodsof relativequiet This further supports the idea that large structure rollup andcross-mixing-layerinteraction generate noise

Appendix Mexican Hat WaveletThe wavelet transformationallowsfor theanalysisof a signalwith

varying resolution in the time and frequency domains As is donewith a Fourier transformation the signal is weighted by a functionIn the case of the Fourier transformation the weighting function iseiexcl j2frac14 f t whereas a wavelet transformation uses a wavelet functionfor weighting In both transformations the weighting is performedvia a convolution in time The general equation for the wavelettransformation Xwava b is given as

Xwava b D 1p

a

Z 1

iexcl1xt9

sup3t iexcl b

a

acutedt (A1)

where xt is the signal that is being transformed Atilde is the motherwavelet being used to analyze the signal and the 1=

pa quantity


is used to conserve wavelet energy with wavelet scale After thetransformationthe signal is in a domainof translationb and scale aThe translationquantity is very similar to the shiftingof the windowof the short-termFourier transformdomainThe scale allows for thevarying resolution of frequency with varying lengths of time

The Mexican hat wavelet is a crude but commonly used waveletthat is especially well suited to analyze peak locations within a sig-nal because it has a central peak and two small side lobesThe nameof the wavelet comes from its resemblance to the cross section ofa Mexican sombrero It is also known as the g2 wavelet (secondGaussian wavelet) The Mexican hat wavelet Atildemexh can be derivedby taking the second derivative of the Gaussian probability den-sity function If normalized for energy conservation purposes theMexican hat wavelet is given by

9mexhiquest D21 iexcl iquest 2

p3frac14

14

exp

sup3iexcliquest 2

2

acute(A2)

where iquest is the modi ed time given by t iexcl b=a Equation (A2) isthe form of the Mexican hat wavelet used in this work and shownin Fig 6

For this analysis where the signal was not deterministic thewavelet equation was not solved analytically Instead the signaland Mexican hat function were both discretizedThe operation wasperformed within MATLABreg and the limits of integration wereset to the length of the signal The scale was varied from 25 to250 sup1s and the translation was scanned over the duration of theacoustic data The actual equationused for the Mexican hat wavelettransformation is

Xmexha b D1

pa

NX

n D 1

xnh

pound 2f1 iexcl [nh iexcl b=a]2gp

3frac1414

expfiexcl[nh iexcl b=a]2=2g (A3)

where h is the time resolutionof the data equal to 1 sup1s For plottingpurposes the scale was converted to frequency f by the followingrelationship

f Diexclp

5=2centmacr

2frac14a (A4)

which is only valid for the Mexican hat wavelet This relation canbe analytically obtained by matching the peak of the wavelet meanspectrum with the peak of the Fourier transformof the cosine waveIn the discussion of the results f is referred to as scale frequencybecause it is different from the commonly de ned frequency fromFourier analysis

The energy level at different scales and time can be determinedfrom the wavelet domain provided that the wavelet does not addenergy to the signal The energy distribution E a b over scale andtranslation is given by

Ea b D 1=frac14jXmexha bj2 (A5)

This equationis similar to thatof thepower spectraldensityobtainedfrom the Fourier transformation In the case of the power spectraldensity the energy contained in the signal can be obtained by inte-grating the spectrum over all frequencies The energy in the signalcould also be obtained by integrating the energy distribution overall translationsand scales Typically sound spectra are converted toa logarithmic quantity (sound pressure level) for analysishoweverthe energy distributionmapping in this study was given with a linearscale

Detailed informationon the Mexican hat wavelet and the wavelettransformation can be found in Refs 25ndash27

AcknowledgmentsThe support of this research by the Air Force Of ce of Scienti c

Research with John Schmisseur and Steven Walker as the Techni-cal Monitors is greatly appreciated The rst author would like tothank the Ohio Space Grant Consortium for his doctoralfellowshipThe second author is grateful for his National Defense Science andEngineering Graduate fellowship The authors would like to thankSatish Narayanan of United Technologies Research Center for thehelp in developing the microphone technique used in this work

as well as stimulating discussions in the eld of aeroacousticsThehelp of JeffreyKastner in researchingthe wavelet transformationaswell as in the use of the Hartmann tube uidic actuatorsand MarcoDebiasi in editing the manuscript is also greatly appreciated

References1Tam C K W ldquoJet Noise Generated by Large-Scale Coherent Motionrdquo

Aeroacoustics of Flight Vehicles Theory and Practice Vol 1 edited byH H HubardAcoustical SocietyofAmerica WoodburyNY 1991pp311ndash390

2Hileman J and Samimy M ldquoTurbulence Structures and the AcousticFar Field of a Mach 13 Jetrdquo AIAA Journal Vol 39 No 9 2001 pp 1716ndash1727

3Morrison G L and McLaughlin D K ldquoNoise Generation by Insta-bilities in Low Reynolds Number Supersonic Jetsrdquo Journal of Sound andVibration Vol 65 No 2 1979 pp 177ndash191

4Yu J C andDosanjh D S ldquoNoise Field of a SupersonicMach 15 ColdModel Jetrdquo Journal of the Acoustical Society of America Vol 51 No 5Pt 1 1972 pp 1400ndash1410

5Schaffar M ldquoDirect Measurements of the Correlation Between AxialIn-Jet Velocity Fluctuationsand Far-Field Noise near the Axis of a Cold JetrdquoJournal of Sound and Vibration Vol 64 No 1 1979 pp 73ndash83

6Simonich J C Narayanan S Barber T J and Nishimura M ldquoAero-acousticCharacterizationNoiseReductionand Dimensional ScalingEffectsofHigh SubsonicJetsrdquo AIAA Journal Vol 39 No 11 2001pp 2062ndash2069

7Ahuja K K Massey K C and DrsquoAgostino M S ldquoA Simple Tech-nique of Locating Noise Sources of a Jet Under Simulated Forward MotionrdquoAIAA Paper 98-2359 June 1998

8FisherM J Harper-BourneM and Glegg SA L ldquoJet EngineSourceLocation The Polar Correlation Techniquerdquo Journal of Sound and Vibra-tion Vol 51 No 1 1977 pp 23ndash54

9Kibens V ldquoDiscrete Noise Spectrum Generated by an Acoustically Ex-cited Jetrdquo AIAA Journal Vol 18 No 4 1980 pp 434ndash441

10Colonius T Lele S and Moin P ldquoSound Generation in a Mixing-Layerrdquo Journal of Fluid Mechanics Vol 330 Aug 1997 pp 375ndash409

11Mitchell B Lele S and Moin P ldquoDirect Computation of the SoundGenerated by Vortex Pairing in an Axisymmetric Jetrdquo Journal of Fluid Me-chanics Vol 383 Oct 1998 pp 113ndash142

12Freund J ldquoNoise Sources in a Low-Reynolds-Number Turbulent Jetat Mach 09rdquo Journal of Fluid Mechanics Vol 438 2001 pp 277ndash305

13Sarohia V and Massier P F ldquoExperimental Results of Large-ScaleStructures in Jet Flows and Their Relation to Jet Noise Productionrdquo AIAAPaper 77-1350 Oct 1977

14BogdanoffD W ldquoCompressibilityEffects in TurbulentShear LayersrdquoAIAA Journal Vol 21 No 6 1983 pp 926 927

15Papamoschou D and Roshko A ldquoThe Compressible TurbulentMixing-Layer An Experimental Studyrdquo Journal of Fluid MechanicsVol 197 1988 pp 453ndash477

16Murakami E and Papamoschou D ldquoEddy Convection in CoaxialSupersonic Jetsrdquo AIAA Journal Vol 38 No 4 2000 pp 628ndash635

17Thurow B Hileman J Samimy M and Lempert W ldquoCompress-ibility Effects on the Growth and Development of Large-Scale Structures inan Axisymmetric Jetrdquo AIAA Paper 2002-1062 Jan 2002

18Kerechanin C W Samimy M and Kim J-H ldquoEffects of NozzleTrailing Edges on Acoustic Field of Supersonic Rectangular Jetrdquo AIAAJournal Vol 39 No 6 2001 pp 1065ndash1070

19Kastner J and Samimy M ldquoDevelopment and Characterization ofHartmann TubeFluidicActuators forHigh-SpeedFlowControlrdquoAIAAJour-nal Vol 40 No 10 2002 pp 1926ndash1934

20Hartmann J and Trolle B ldquoA New Acoustic Generator The Air-JetGeneratorrdquo Journal of Scienti c Instruments Vol 4 1927 pp 101ndash111

21Raman G Kibens V Cain A and Lepicovsky J ldquoAdvanced Ac-tuator Concepts for Active Aeroacoustic Controlrdquo AIAA Paper 2000-1930June 2000

22Kambe T ldquoAcoustic Emissions by Vortex Motionsrdquo Journal of FluidMechanics Vol 173 1986 pp 643ndash666

23Inoue O Hattori Y and Sasaki T ldquoSound Generation by CoaxialCollision of Two Vortex Ringsrdquo Journalof FluidMechanics Vol 4242000pp 327ndash365

24Freund J B and Fleischman T G ldquoRay Traces Through UnsteadyJet Turbulencerdquo InternationalJournalof Aeroacoustics Vol 1 No 1 2002pp 83ndash96

25Daubechies I Ten Lectures on Wavelets Society for Industrial andApplied Mathematics Philadelphia 1992 pp 1ndash106

26Lewalle J ldquoWavelet Analysis of Experimental Data Some Methodsand the Underlying Physicsrdquo AIAA Paper 94-2281 June 1994

27Wang Q Brasseur J Smith R and Smits A ldquoApplication of theMulti-DimensionalWavelet Transforms to the Analysis ofTurbulenceDatardquoInternational Workshop on Wavelets Springer-Verlag New York 1991

P J MorrisAssociate Editor


Bogdanoff14 and Papamoschou and Roshko15 predict a convectivevelocity of 206 ms and a convective Mach number of 06 for thejet in this study The actual convective velocity of the large-scalestructures has been found to deviate substantiallyfrom the theoreti-cal value16 Detailed experimental results of Thurow et al17 whichwere obtained in the same jet facility as the current work with theuse of a megahertz rate ow visualization system indicate that theconvective velocity is much higher than the theoretical value Witha large data set of 320 measurements they founda broad probabilitydensitydistributionof convectivevelocitieswith a mean of 270 msBased on these ndings a convectivevelocity of 270 ms is used inthe current study

The examination of turbulent mixing noise in this study focuseson establishing a correlation between the large coherent structureswithin the jet mixing layer and the measured noise in the acousticfar eld This is commonly known as establishinga causalitycorre-lation In an unconventionalmanner the acousticdata are examinedin the time domain and are only taken to other domains as neces-sary when comparison between individual dynamic features andthe overall properties of the jet is desired The jet in this study hasa Mach number of 13 a nozzle exit diameter D of 254 mm (1 in)(a dimension that will be extensively used in this work as a refer-ence length scale) a Reynolds number based on the jet diameter of108 pound 106 and a potential core length of about six jet diameters2

The region around the potential core which is where the majorityof the far- eld acoustic radiation apparently originates will be thearea of primary interest in this work

Experimental ArrangementAll of the experiments were conducted in the optically accessed

anechoic chamber of the Gas Dynamics and Turbulence Laboratoryof The Ohio State University The facility allows for simultaneousacoustic measurements with real-time ow visualizationThis sec-tion describesthe pertinentcomponentsof the experimentthe noisesource localization routine and its validation using a known noisesource

Anechoic Chamber and Jet FacilityThe anechoicchamberfacility thatwas usedfor theseexperiments

is unique in it allows for the measurement of the jet ow with laserdiagnostics in a fully anechoic environment Thus simultaneousoptical measurements of the jet ow and its acoustic eld wereconductedThe inner dimensionsof the chamber from wedge tip towedge tip are 312 m in width and length and 269 m in height Thechamber was tested for compliance to American NationalStandardsInstitue (ANSI) Standard S123535 and the results from the testswere within the required tolerance over most of the distances alongthe microphonepaths18 The air for the jet was suppliedby two four-stagecompressorsit was ltereddriedandstoredin two cylindricaltanks with a total capacity of 425 m3 at a pressure of 165 MPa(1600 ft3 at 2500 psi) A stagnationchamber was used to conditionthe jet air before exhausting it through a 254-mm (1-in) nozzlewith a lip thickness of 25 mm (01 in) where the inner contourwas determined by the method of characteristics for uniform owat the exit The actual Mach number of the nozzle was measured as128Additionaldetailsof the anechoicchamberand jet ow facilitycan be found in Refs 2 and 18

Details of the Inline Microphone ArrayThe microphone array used in this work relies on the novel ap-

plication of acoustic principles that was developed with the dual-microphonearray describedby Hileman and Samimy2 In that workand this one as well the goalwas to relate the acousticfar eld of thejet to the dynamicsof coherentstructuresin the ow The large-scale ow structures are widely believed to create sound that radiates inthe preferentialdownstreamdirectionwhich for thecurrentjet wasmeasured as 30 deg with respect to the downstream jet axis2 There-fore the microphone array was placed in this direction Althoughthis unconventionalarray location is not optimal for the localizationof noise sources it was considered necessary to capture accuratelythe sources of the large-amplitude low-frequency noise tradition-ally associatedwith the turbulencemixing generated by large-scalestructures

Fig 1 Schematic of the inline microphone array used to determinenoise source location

The arraywas composedof four635-mm( 14 -in)4939Bruel and

Kjaer microphones that were separated by 381 508 and 635 mm(15 20 and 25 in) These separationsas well as the physical lo-cationof the array relative to the jet nozzleare shown schematicallyin Fig 1 An aluminum block surrounded by 5-cm-thick acousticfoam housed the microphones Based on the inherent tolerance inthe machining of the microphone holding block the uncertaintyin microphone separation was estimated as 005 mm (0002 in)All exposed surfaces within the chamber were covered in 15-cm-thick acoustic foam The sound data were acquired with a NationalInstruments PC-6110E data acquisition board at a rate of 1 millionsamples per channel per second This fast acquisition rate was cho-sen to maximize the accuracy in measuring the time delay betweenan acoustic signal peak reaching any two of the microphones

The time delay between an individual acoustic ldquoeventrdquo beingrecorded by two different microphones (phase lag) was combinedwith knowledge of the array geometry to determine the angle withwhich the event had approached the array This angle and the speedof sound in the ambientwere then used to determine the locationsofthe apparentnoise sources assuming they were all located on the jetcenterlineFurther detailscan be found in Ref 2 Segments of sounddata that were 035 ms in length (350 data points) were cross corre-lated with equal-lengthsegments from the othermicrophonesignalsto determine the time delay between the two microphonesrecordingthe event The use of four microphones provided for six differenttime delays that lead to six different estimates for the event originThese six locations were then averaged to determine the averagenoise source location Any of the six origins that were located out-side the range from iexcl5 to 25D with respect to the nozzle exit werenot included in the average because they were likely in error

Typical sound pressure data recorded by the microphones thatcompose the inline array are shown in Fig 2 The time origin corre-sponds to the rst laser pulse illuminating the ow The four micro-phones recorded peaks of similar shape and magnitude but thesepeaks are shifted in time that is phase shifted Even at the largesttime delay (between the rst and last microphones)the overallshapeof the sound wave remains substantially unchanged This mannerof determining noise source location is different than those using across-spectralmethod For that type of technique which computesan average noise source location and not an instantaneous sourcethe microphone spacing should not exceed one-half of the wave-length of the sound that is being located For the technique usedhere any microphone spacing can be used as long as there is ahigh correlation between the microphone signals for the event ofinterest

The large negative sound pressurepeak of Fig 2 recordedaround34 ms was cross correlated for the six different microphone pairsto determine the corresponding time delays and to show how thistechnique works Figure 3 shows the 035-ms data segments fromeach microphone that yielded the maximum correlation Figure 4shows the same segments shifted by the computed time delays Thetime delays between the peaks recorded by microphones 1 and 21 and 3 and 1 and 4 were used to shift the signals of microphones23 and 4 to overlapwith themicrophone1 signalcenteredon339msSimilarly the time separationbetween the signals of microphones2and 3 and microphones2 and 4 were used to overlap their signals to


















































































Xwava b D 1p

a

Z 1

iexcl1xt9

sup3t iexcl b

a

acutedt (A1)


pa quantity





p3frac14

14

exp

sup3iexcliquest 2

2

acute(A2)



Xmexha b D1

pa

NX

n D 1

xnh


3frac1414



f Diexclp

5=2centmacr

2frac14a (A4)























































































































Xwava b D 1p

a

Z 1

iexcl1xt9

sup3t iexcl b

a

acutedt (A1)


pa quantity





p3frac14

14

exp

sup3iexcliquest 2

2

acute(A2)



Xmexha b D1

pa

NX

n D 1

xnh


3frac1414



f Diexclp

5=2centmacr

2frac14a (A4)












































































































Xwava b D 1p

a

Z 1

iexcl1xt9

sup3t iexcl b

a

acutedt (A1)


pa quantity





p3frac14

14

exp

sup3iexcliquest 2

2

acute(A2)



Xmexha b D1

pa

NX

n D 1

xnh


3frac1414



f Diexclp

5=2centmacr

2frac14a (A4)

































































































Xwava b D 1p

a

Z 1

iexcl1xt9

sup3t iexcl b

a

acutedt (A1)


pa quantity





p3frac14

14

exp

sup3iexcliquest 2

2

acute(A2)



Xmexha b D1

pa

NX

n D 1

xnh


3frac1414



f Diexclp

5=2centmacr

2frac14a (A4)


























































































Xwava b D 1p

a

Z 1

iexcl1xt9

sup3t iexcl b

a

acutedt (A1)


pa quantity





p3frac14

14

exp

sup3iexcliquest 2

2

acute(A2)



Xmexha b D1

pa

NX

n D 1

xnh


3frac1414



f Diexclp

5=2centmacr

2frac14a (A4)
















































































Xwava b D 1p

a

Z 1

iexcl1xt9

sup3t iexcl b

a

acutedt (A1)


pa quantity





p3frac14

14

exp

sup3iexcliquest 2

2

acute(A2)



Xmexha b D1

pa

NX

n D 1

xnh


3frac1414



f Diexclp

5=2centmacr

2frac14a (A4)









































































Xwava b D 1p

a

Z 1

iexcl1xt9

sup3t iexcl b

a

acutedt (A1)


pa quantity





p3frac14

14

exp

sup3iexcliquest 2

2

acute(A2)



Xmexha b D1

pa

NX

n D 1

xnh


3frac1414



f Diexclp

5=2centmacr

2frac14a (A4)
































































Xwava b D 1p

a

Z 1

iexcl1xt9

sup3t iexcl b

a

acutedt (A1)


pa quantity





p3frac14

14

exp

sup3iexcliquest 2

2

acute(A2)



Xmexha b D1

pa

NX

n D 1

xnh


3frac1414



f Diexclp

5=2centmacr

2frac14a (A4)






















































Xwava b D 1p

a

Z 1

iexcl1xt9

sup3t iexcl b

a

acutedt (A1)


pa quantity





p3frac14

14

exp

sup3iexcliquest 2

2

acute(A2)



Xmexha b D1

pa

NX

n D 1

xnh


3frac1414



f Diexclp

5=2centmacr

2frac14a (A4)










































p3frac14

14

exp

sup3iexcliquest 2

2

acute(A2)



Xmexha b D1

pa

NX

n D 1

xnh


3frac1414



f Diexclp

5=2centmacr

2frac14a (A4)






































Documents

Exploring Noise Sources Using Simultaneous …web.mit.edu/hileman/www/Publications/AIAA2002.pdfdiagnostics in a fully anechoic environment. Thus, simultaneous optical measurements