aiaa 98-0471 design and use of microphone …mln/ltrs-pdfs/nasa-aiaa-98-0471.pdfjanuary 12-15, 1998...

36st Aerospace SciencesMeeting & Exhibit

January 12-15, 1998 / Reno, NV

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AIAA 98-0471Design and Use of MicrophoneDirectional Arrays forAeroacoustic Measurements

William M. Humphreys, Jr.Thomas F. BrooksWilliam W. Hunter, Jr.Kristine R. Meadows

NASA Langley Research CenterHampton, VA 23681-0001

American Institute of Aeronautics and Astronautics1

Abstract

An overview of the development of two microphonedirectional arrays for aeroacoustic testing is presented.These arrays were specifically developed to measureairframe noise in the NASA Langley Quiet FlowFacility. A large aperture directional array using 35flush-mounted microphones was constructed to obtainhigh resolution noise localization maps aroundairframe models. This array possesses a maximumdiagonal aperture size of 34 inches. A uniquelogarithmic spiral layout design was chosen for thetargeted frequency range of 2-30 kHz. Complementingthe large array is a small aperture directional array,constructed to obtain spectra and directivityinformation from regions on the model. This array,possessing 33 microphones with a maximum diagonalaperture size of 7.76 inches, is easily moved about themodel in elevation and azimuth. Custom microphoneshading algorithms have been developed to provide afrequency- and position-invariant sensing area from10-40 kHz with an overall targeted frequency range forthe array of 5-60 kHz. Both arrays are employed inacoustic measurements of a 6 percent of full scaleairframe model consisting of a main element NACA632-215 wing section with a 30 percent chord half-span

flap. Representative data obtained from thesemeasurements is presented, along with details of thearray calibration and data post-processing procedures.

Nomenclature

Superscript o source location

A shear layer amplitude correction, dB C constant co speed of sound, ft/sec D SADA cluster aperture, see eqn. (16)

$e steering matrix, see eqn. (13) f frequency, cycles/sec$G cross spectral matrix

Gij cross spectra between ith and jth

microphones, see eqn. (6) k wavenumber (=ω/co), ft

-1

M total number of microphones in arrayMo Mach number (=v/co) p pressure, Pascals r radial distance, ft t time, sec v velocity, ft/sec$W array shading matrix

w microphone cluster weighting

W k x x o( , , )r r

theoretical array response atwavenumber k, dB, see eqn. (4)

Ws spectral window weighting constantXik , Xjk kth FFT data block for ith and jth

microphonesr

x location, ftr

xc location of phase center of array, ft,see eqn. (3)

AIAA-98-0471

DESIGN AND USE OF MICROPHONE DIRECTIONAL ARRAYSFOR AEROACOUSTIC MEASUREMENTS

William M. Humphreys, Jr.*

Thomas F. Brooks�

William W. Hunter, Jr. Â

Kristine R. Meadows�

Fluid Mechanics and Acoustics DivisionNASA Langley Research CenterHampton, Virginia 23681-0001

_________________*Research Scientist, Measurement Science and Technology

Branch, Senior Member AIAA.�Senior Research Scientist, Aeroacoustics Branch, Associate

Fellow AIAA.ÂSenior Research Scientist, Measurement Science and

Technology Branch.�Research Scientist, Aeroacoustics Branch, Member AIAA.Copyright �1998 by the American Institute of Aeronautics and

Astronautics, Inc. No copyright is asserted in the United Statesunder Title 17, U.S. Code. The U.S. Government has a royalty-freelicense to exercise all rights under the copyright claimed herein forgovernment purposes. All other rights are reserved by the copyrightowner.


λ acoustic wavelength, ftσ SADA array weighting controlω frequency, rad/secω∆t shear layer phase correction for ω,

radians, see eqns. (9) and (13)

Introduction

Over the past several years a growing need hasemerged for accurate and robust noise measurementinstrumentation in aerospace research facilities. Thisneed is partly driven by research programs such as theNASA Advanced Subsonic Technology (AST)Program, which has set as one of its goals theachieving of a greater than 10 dB reduction in totalaircraft effective perceived noise by the year 2000(referenced to levels measured in 1992). This goalrequires the collection of experimental databases ofvarious noise generation mechanisms from whichaccurate and efficient noise prediction tools can bedeveloped to guide noise reduction design. Recently,emphasis has been placed on the measurement andmodeling of airframe noise, defined as the non-propulsive component of aircraft noise which is due tounsteady flow about the airframe components (flaps,slats, undercarriage, etc.).

One of the databases desired by computationalairframe noise modelers is farfield noise data measuredon various baseline and modified aircraft components.Traditional single microphone measurements of thisnoise have been hampered by poor signal-to-noisecharacteristics, spurring the development of a varietyof new measurement techniques. Early techniquesemployed the concept of an “acoustic mirror”, where alarge concave elliptic mirror and an associatedmicrophone were positioned in the acoustic far field.1-3

Such mirrors were capable of locating individual soundsources accurately, but suffered the drawback ofrequiring mechanical movement to determine sourcedistributions around models. The mirrors also becameexcessively large when measurements of lowerfrequencies (< 2 kHz) were required. Nevertheless,such mirrors continue to have applicability in some ofthe larger research facilities.4

In addition to acoustic mirrors, distributions ofindividual microphones have been employed todetermine airframe noise source characteristics. Inparticular, such systems have proven valuable in theunderstanding of single-element airfoil self noise.5-6

While not strictly considered a directional array (theoutputs of all microphones were not combined as inbeamforming), such systems capitalized on theamplitude and phase relationships between clusters of

microphones. As such, they can be considered one ofthe precursors to the current generation of microphonedirectional arrays.

Modern microphone directional arrays foraeroacoustic research have as their origin early radioand radar antenna arrays and U.S. Navy hydrophonearrays (used for the detection of submarines as early asWorld War II).7-8 Soderman and Noble were amongthe first researchers to adapt this earlier work foraeroacoustics when they constructed a one-dimensionalend-fire array to evaluate jet noise in the NASA Ames40- by 80-foot Wind Tunnel.9-10 At the same timeBillingsley and Kinns constructed a one-dimensionallinear array of microphones for real-time sound sourcelocation on full-size jet engines.11 More recently suchdirectional arrays have been extended to include two-dimensional microphone layouts with the work ofBrooks, Marcolini and Pope12-13, Underbrink andDougherty14, and Watts and Mosher.15-16

Two different state-of-the-art, two-dimensionalmicrophone directional arrays are described in thispaper. These are designed to provide broadband sourcelocalization and directivity information needed tocharacterize airframe noise and noise reductionconcepts. Both arrays have been successfully used bythe authors to obtain data for a wing / flap model.17

This paper expands on the previous work by providingdetailed descriptions of the design and construction ofthe two directional arrays. The philosophysurrounding their design as well as development ofunique data processing algorithms to allow accuratenoise spectra and source images to be obtained arediscussed. Finally, several representative examples ofdata collected with the instruments are illustrated.

Directional Array Development

Concept

The basic principle of a microphone directionalarray can be simply illustrated. Assume a simplemonochromatic acoustic point source is located inquiescent space at location

r

x (see Figure 1). Asolution for r>0 representing the propagation of apressure wave radially in all directions is given by

p r tC

re j t kr( , ) ( )= −ω (1)

where C is a constant, r is the radial distance from thesource origin, ω is the frequency of the wave, and k isthe corresponding wavenumber. Assume now that anarray of M microphones is placed a finite distance from


the source. Each microphone senses a slightlydifferent phase-shifted waveform depending on itsdistance from the source. The pressure pm(t) measuredat the m-th microphone is denoted as

p tC

rem

m

j tr

c

m

o( )( )

=−ω

(2)

where rm represents the distance from the location tothe m-th microphone. The (t-rm/co) term is theretarded time from the source to the microphone. Inorder to focus on a source, the individual microphoneoutputs can be phase shifted an amount equal to theirpropagation delay and then summed together (orstacked). This yields a single output signal for thearray in a process commonly referred to as delay-and-sum beamforming. By adjusting the propagationdelays, one is able to electronically steer the array topoints in space, selecting regions of interest toascertain noise production while providing noiserejection not found in individual microphonemeasurements. This steering can provide the samecapability as the earlier acoustic mirror techniques butwithout the necessity of physically moving the array tomeasure source distributions.

Array Response

The phase center of the array is defined as18

r r

xM

xc mm

M

==

∑1

1

(3)

Using this, the ideal array response for a simple sourcecan be expressed as

W k x x w

r

reo

m

o

mo

m

Mjk r r r ro

mo

m( , , ) [( ) ( )]r r

≡ ∑=

− − −

1 (4)

where r

x is an arbitrary Cartesian location in space to

which the array is electronically steered, r

x o is the

source location, r o and rmo

are the distances from the

source to r

xc and the m-th microphone, respectively,

and r and rm are the distances from the steeringlocation to

r

xc and the microphone. The term wm

represents a microphone weighting factor which can beused to modify the array response.

The array response is normally expressed in

decibels referenced to the level obtained at r

xo :

dB xW k x x

W k x x

o

o o( ) log

( , , )

( , , )

r

r r

r r

=�

!

"

$##20 10

(5)

This response is plotted as a contour map with contourlevel proportional to dB x( )

r

, representing the

computation of equation (5) over a large number ofsteering locations lying on a surface a finite distancefrom the array. Such plots represent the spatialfiltering of the array graphically at wavenumber k, andallows one to examine the beamwidth and lobestructure.

Array Design Criteria for AirframeNoise Measurements

Test Model and Facility: The test program isintended to investigate the mechanisms of soundgeneration on high-lift wing configurations. InFigure 2, the test model apparatus and the LargeAperture Directional Array, to be discussed, are shownmounted in the Langley Quiet Flow Facility (QFF).The QFF is a quiet open-jet facility designedspecifically for anechoic acoustic testing.19 For thepresent airframe model testing, a 2 by 3-footrectangular open-jet nozzle is employed. The model isa NACA 632-215 main element airfoil with a 30percent chord half-span Fowler flap. In the photo, themodel is visible through the Plexiglas windows locatedon the side plates. The model section is approximately6 percent of a full-scale configuration, with a mainelement chord length of 16 inches, a flap chord lengthof 4.5 inches, and a full span of 36 inches. The mainelement and flap are fully instrumented with staticpressure ports and unsteady pressure transducers. Tohold the model in place, the vertical side plates arefastened rigidly to the side plate supports of the nozzle.Appropriate acoustic foam treatments are applied to alledges and supports to reduce acoustic reflections fromthese surfaces. More model and facility details can befound in Reference 17.

Array Design Criteria: In choosing an arraydesign, specifically the microphone layout with respectto the noise source to be studied, one must be aware ofthe character of the source distributions. The basicdelay-and-sum beamformer procedure, describedabove, renders an array output which assumes anysingle source to be an omni-directional simplemonopole, or any distribution of sources to be that ofincoherent (uncorrelated) simple monopoles. But,when the sources are multi-pole and/or coherent over a


spatial source distribution, the noise is not omni-directional. For such directional sources, variations innoise field coherence, amplitude, and phase can occurover the face of the array. Major difficulties occurwhen the directivity has an oscillatory sweeping orrotational phase behavior. Still, even when sourcedirectivity is stationary, which is assumed to be thecase for the airframe noise problem, spatial variationscan cause moderate to severe errors in sourceamplitude, resolution, and localization. This isbecause the phase variations are interpreted as retardedtime delays, and amplitude/coherence variationsmodify the relative contribution of each microphone tothe array output. Indeed, the effect of limited spatialcoherence for the noise directivity is to effectivelybreak an array with too large an aperture (overall widthof the array of microphones) into a group of smallersub-arrays whose individual steered output spectra aresummed together. This is “pressure-squared”summing rather than the desired “linear-pressure”summing (operation indicated by equation (4)), therebymodifying the desired “design” characteristics of thearray. To avoid such errors, all array microphonesshould be placed within approximately the same sourcedirectivity (producing generally a small array), whereamplitude and phase appear as if the source wereomni-directional. However, as will be seen, this designconstraint cannot always be fully met and still have thedesired array resolution at the frequencies of interest.

Airframe noise measurements present an arraydesign challenge in that not only is source directivityinformation required (necessitating the use of a smallaperture array to satisfy the concerns discussed above),but also accurate localization of the source distributionsis desired down to the order of the smallest wavelengthof interest, typically one to two tenths of an inch. Thislatter need requires that the array aperture be large inorder to minimize the array beamwidth, defined hereas the width across the main response lobe over whichthe sensing level is within a given dB level from thepeak level. However, the required spectra anddirectivity information dictate the use of a small arrayaperture to ensure that all microphones are atapproximately the same directivity angle.

It was decided to address the two conflictingaperture requirements through the construction of twoarray designs. A Large Aperture Directional Array(LADA) was designed to produce high spatialresolution (narrow beamwidth) noise sourcelocalization maps over a defined surface on the model.To obtain quantitative spectra and directivityinformation, particularly for the dominant noisesources identified with the LADA, a Small ApertureDirectional Array (SADA) was also designed. This

array was constructed to be movable about the model inboth elevation and azimuth, as opposed to the LADAwhich was fixed in location. The SADA results canalso be used to evaluate the degree of directivityuniformity the LADA encounters to add confidence tothe LADA results.

Description of Two Directional Arrays

Large Aperture Directional Array (LADA): TheLADA is shown to the left in Figure 2, on the pressureside of the model, positioned 4 feet from the mid-spanof the airfoil main element trailing edge. A 4-footdiameter fiberglass panel provides a flat surface toflush mount all microphones. The panel is attached toa pan-tilt unit secured to a rigid tripod support. Thisallows precise alignment changes in the elevation andazimuth of the face of the array. A small laser diodepointer is place at

r

xc , corresponding to the center of

the fiber glass panel. The LADA incorporates 35 B&Kmodel 4135, ¼-inch microphones placed in a two-dimensional pattern consisting of logarithmic spirals.The microphone layout, shown in Figure 3, consists offive spirals of seven microphones each with the inner-most microphones lying on a 1-inch radius and theouter-most on a 17-inch radius. The locations of themicrophones, viewed from the front of the array, arelisted in Table 1. This design is very similar to amulti-arm logarithmic spiral array with linearly spacedspiral elements described in Reference 14. This designresults in acceptable beamwidth and peak sidelobeheight over a targeted design frequency range of2-30 kHz.

Figure 4 shows a series of contour plots showingLADA array responses using equations (4) and (5) for6, 10, 20, and 30 kHz. The contour plots cover a planararea measuring 4 feet on edge at a distance of 4 feetfrom a simulated point source, matching the mountingconfiguration shown in Figure 2. Note that theresponse contour features for the different frequenciesare almost identical with a linear scaling factor beinginversely proportional to frequency. The contourfeatures would be more nearly identical if the array sizewere vanishingly small compared to the planarmeasuring area. However, given its 17-inch radius, thearray encompasses 39 degrees of solid collection angleat this distance. Included in Figure 4 are a series ofline plots obtained by scanning through the contourplots in the xo direction for each yo location andselecting the maximum dB level. It can be seen that aplateau-like sidelobe structure exists at all frequencies,with the minimum sidelobe height approaching -6 dBat a frequency of 20 kHz.


A study of the beamwidth characteristics of theLADA can be achieved by observing a series of arrayresponses for a number of frequencies spanning arange of 2-30 kHz and measuring the width of themain lobe at various dB levels. Figure 5 shows afamily of curves where the main lobe width ismeasured at the -0.5, -1, -3, and -6 dB level. It can beseen from the curves that a typical -3 dB beamwidthfor the LADA is approximately 1.5 times the sourcewavelength.

Small Aperture Directional Array (SADA): TheSADA is designed to complement the capabilities ofthe LADA by providing directivity and spectralinformation as a function of position around the model.The aperture of the array is kept small with the intentto keep all microphones in the array withinapproximately the same source directivity regardless ofelevation or azimuth position. The array pattern whichwas chosen to achieve this can be seen in Figure 6,with the locations of the microphones given in Table 2.The SADA consists of 33 B&K model 4133, 1/8-inchmicrophones with ¼-inch preamplifiers projectingfrom an acoustically treated aluminum frame. Thearray pattern incorporates four irregular circles of eightmicrophones each with one microphone placed at

r

xc ,

corresponding to the center of the array. Each circle istwice the diameter of the circle it encloses. Themaximum radius of the array is 3.89 inches, giving theSADA only 5.25% of the surface area of the LADA.Two small laser diode pointers are incorporated intothe array mount on opposite sides of the centermicrophone for use in alignment.

The SADA is mounted on a pivotal boom designedto allow it to be positioned to a wide range of elevationand azimuth angles while maintaining a constantdistance to the center of the trailing edge of the mainelement airfoil (an assumed noise production region).This is achieved by maintaining the boom’s pivotcenter at the trailing edge of the main element airfoil.Rotation of the boom is performed using precision DCservo rotation stages mounted on the outer edges of theside plates holding the model and boom. This isillustrated in Figure 7, which shows the SADAmounted in the QFF on the suction side of an airframenoise model at a 5-foot working distance. At thisdistance the array encompasses 7.5 degrees of solidcollection angle.

Figure 8 shows a series of contour plots showingSADA array responses using equations (4) and (5) for10, 20, 30 and 40 kHz. Subsequently, a processingprocedure is used to maintain constant spatialresolution, independent of frequency; however, this is

not done in the calculations of Figure 8. The contourplots cover an area measuring 4 feet on edge at adistance of 5 feet from a simulated point source,matching the mounting configuration shown inFigure 7. A series of line plots obtained from thecontour plots in a process similar to that for the LADAare also shown in Figure 8. It can be seen that thesidelobe patterns again exhibit a plateau-like structureat all frequencies, with the maximum sidelobe levelapproaching -8 dB at a frequency of 40 kHz.

A study of the beamwidth characteristics of theSADA can be performed similarly to that for theLADA by observing a series of array responses over afrequency range and measuring the width of the mainlobe at various dB levels. Figure 9 shows such abeamwidth plot. A family of curves is shown wherethe main lobe width is measured at the -0.5, -1, -3, and-6 dB level. It can be seen from these curves that atypical 3 dB beamwidth for the SADA isapproximately 11 times the source wavelength. It willbe seen subsequently that this beamwidth can beradically altered through the use of microphoneshading (or weighting).

Measurement System

Data Acquisition: The data acquisition / analysissystem employed for both arrays is illustrated inFigure 10. Acquisition hardware consists of a NEFF495 transient data recorder which is controlled by aDEC AXP3400 workstation. Sampling rate iscontrolled by an external clock operating at142.857 kHz. The maximum allowable clock rate is 1MHz. The use of an external clock allowssimultaneous acquisition with other instrumentationsuch as the model unsteady surface pressure sensors, asdescribed in Reference 17. The NEFF systemincorporates 36 12-bit (including sign bit) acquisitionchannels with each channel possessing a 4 megabytebuffer, allowing up to 2 million 2-byte samples to becollected per acquisition. The signals from eachmicrophone channel are conditioned by passing themthrough high pass filters set to 300 Hz (to remove DC,60 Hz line noise, and low frequency interference noise)and through anti-aliasing filters set at 50 kHz which issubstantially below the 71.43 kHz Nyquist frequency.

Custom software is used to control all aspects of thedata acquisition. The output files generated by theacquisition system are written in NetCDF format toprovide platform-independent storage of the data, afeature mandated by the distributed data analysissystem.20 The NetCDF files are archived on the NASALangley Distributed Mass Storage Subsystem for post-test retrieval and processing.21


A typical acquisition run consists of collecting 36channels (array microphones plus additional referencemicrophones) of data under no flow conditions. This isfollowed by the actual data run under a specific flow orcalibration condition. As will be seen, spectra obtainedfrom the background runs are subtracted from spectraobtained from data runs to remove the noise floor inthe measurements.

Data Analysis: It was desired to build a highlydistributed processing configuration to handle theproblem of array analysis given the volume of datainvolved (greater than 500 Gbytes) and the amount oftime required to process a single test point of data fromstart to finish (typically 30-60 minutes per set on a200-MHz Pentium-Pro machine). There are a numberof various platforms and operating systems used in theprocessing of the array data, including a cluster ofthree 200-MHz NT-based Pentium-Pro workstations, a500-MHz Alpha workstation running UNIX, and theLangley SP2 supercluster consisting of 48 IBMRS/6000 workstations. This heterogeneous cluster ofhardware systems is controlled from a single Pentium-Pro workstation using a custom control panel programand a series of device independent configuration filesreadable by the individual processing codes located oneach of the various hardware platforms.

Data Post-Processing Procedure

Processing steps common to both arrays include theconstruction of cross spectral matrices from the rawtime data and the calculation of amplitude and timedelay corrections to account for shear layer refraction.Classical beamformer processing algorithms areutilized in the generation of noise images, spectra, anddirectivity information. In addition, the SADAprocessing incorporates a unique shading algorithmwhich provides a constant beamwidth independent offrequency.

Computation of Cross Spectral Matrices: AnM by M cross spectral matrix, where M is the totalnumber of microphones in the array, is firstconstructed for each data set (both background andairframe component test condition). The formation ofthe individual matrix elements is achieved through theuse of Fast Fourier Transforms (FFT). This is doneafter converting the raw data to engineering units(Pascals) using sensitivity data based on a microphonecalibration using a frequency of 1 kHz. Each channelof engineering unit data is then segmented into a seriesof non-overlapping blocks each containing 8192samples, yielding a frequency resolution of 17.45 Hzfor the 142.857 kHz acquisition sampling rate. Using

a Hamming window, each of these blocks of data isFourier transformed into the frequency domain. Theindividual upper triangular matrix elements plus thediagonal (representing auto spectra for each arraymicrophone) are formed by computing thecorresponding block-averaged cross spectra from thefrequency data using

$G

G G G

G

G

M

MM

=

�

!

"

$

####

11 12 1

22

L

M

O M

(6a)

with

G f

NWX f X fij

sik jk

k

N( ) ( ) ( )*= ∑

=

1

1 (6b)

where Ws is the data window weighting constant, N isthe number of blocks of data, and X represents an FFTdata block. The lower triangular elements of thematrix are formed by taking the complex conjugates ofthe upper triangular elements (allowed because thecross spectral matrix is Hermitian).

All cross spectral matrix elements are employed insubsequent processing, with no modification of thediagonal terms. Note that for in-flow arrays, thediagonal terms can be removed to improve the spectraldynamic range by subtracting off self-noise dominatedauto-spectra during the beamforming process, asdescribed in References 14 through 16. However, forthe airframe noise measurements described here, thisstep was not required since all array microphones areoutside of the flow.

3-D Shear Layer Refraction Correction: Testing inan open-jet facility requires that the effect of the shearlayer on the propagation of the noise (both intensityand retarded time) from sources located in the jet tomicrophones located outside the jet be accounted for.The first challenge was to develop a technique fordealing with the highly three dimensional, curvedshear layer present in the installation. The approachtaken was to acquire five-hole pitot probemeasurements on both the pressure and suction sides ofthe airframe model to map out the velocity field. Theshear layer position was defined to be the half meanvelocity position. This data was then fitted with athree dimensional surface to provide a continuousrepresentation of the shear layer for each of the flowconditions examined. With the shear layer positiondefined, amplitude and phase corrections were


determined using the approach of Schlinker andAmiet22 and Amiet23.

The key to finding the retarded time and phasecorrections is to find the intersection of the source raypath with the shear layer, as illustrated in Figure 11.An iterative process is used, using the followingrelationship between the source emission angle, ϕ1, theray angle, θ, and the free jet Mach number, Mo

tan( )

sin( )

cos( )θ ϕ

ϕ=

+1

1Mo (7)

and Snell’s law

cos( )

cos( )

cos( )ϕ ϕ

ϕ21

11=

+ Mo (8)

where the subscripts 1 and 2 refer to angles inside andoutside of the jet, respectively, and the sound speedsinside and outside the jet are assumed equal. Once theray path-shear layer intersection is known, the retardedtime difference and hence the phase can be computedfrom

ω ω∆t

r r

cpath mic

o

=−�

�� (9)

where rpath=r1+r2 is the wavefront travel distance(relative to the convecting flow inside the jet), and rmic

is the line-of-sight distance from the source to themicrophone.

The amplitude corrections are based upon analysisof a rectangular shear layer. There are two correctionsprovided in Reference 22, namely a thick shear layer(high frequency) correction and a thin shear layer (lowfrequency) correction. The appropriate correction isdetermined by the ratio of the source acousticwavelength to the shear layer thickness. Theassumption in developing the thick shear layercorrection is that the shear layer is sufficiently thick forgeometrical acoustics to apply so that (1) the acousticenergy is conserved along the ray tube, and (2) soundpressure is the result of outgoing waves only sincereflections are absent in the geometrical acousticslimit. As supplied in References 22 and 23, the ratio ofthe corrected to measured sound pressure formicrophone m, including the astigmatism and distancecorrection, is found to be

A

p

pMm

c

mo

Mo= = − +α α α ϕ ξ ξϕ1 2 3 2

112 2

2( cos( )) ( )

sin( )(10)

with

ξ ϕ ϕ= − −( cos( )) cos ( )1 22 2

2Mo

α θϕ1

2

= sin

sinmic

αθ

ϕξ2

23

1 1=��

�� −

�!

"$## +h

rmic micsin

sin

αθ

ϕξ3

2 1 1=��

�� −

�!

"$##

+h

rmic micsin

sin

(11)

where pc is the corrected pressure, pm is the measuredpressure, h is the distance from source to shear layer,and θmic is the measured angle of the microphonerelative to the flow direction.

For the low frequency correction, the reflected waveamplitude cannot be neglected when the wavelength isof the same length as the shear layer thickness. In thiscase the amplitude correction is found to be

Ap

pM

M

mc

mo

o

= = + ×

+ −

12 1 2 3

2 2

22

1

12

α α α ξ

ϕξϕ[ ( cos( )) ]sin( ) (12)

Examples of the calibration and use of the shearcorrection algorithms are shown subsequently.

Beamforming: A classical beamforming approachis used for the analysis which eliminates instabilitiesand potential matrix singularity problems found inadaptive techniques. The basic procedure consists ofelectronically steering the array to a predefined seriesof locations in space, as shown in Figure 12. Theselocations define a plane which can be positioned in anyorientation in front of the array. For each selectedsteering location, a steering matrix containing oneentry for each microphone in the array is computed asfollows:

$

exp{ [( ) ]}

exp{ [( ) ]}

,

,

e =

− ⋅ +

− ⋅ +

�

!

"

$

####

A j k x t

A j k x t

rr shear

Mrr M M shear

o

mo

o

Mo

1 1 11

rr

M

rr

ω

ω

∆

∆ (13)

where r

x is the distance from the steering location toeach microphone, Am is the shear layer amplitudecorrection for microphone m using either equation (10)


or (12), and ω∆tm,shear is the shear layer phasecorrection for microphone m at frequency ω. Thefactor (ro/rm

o) is included to normalize the amplitudeAm to that of the array

r

xc position. Using

equation (13) and the cross spectral matrix computedpreviously, the steered array output power spectrum atthe steering location is obtained via

P eG G

M

Tdata background( $)

$ ( $ $ ) $=

−e e

(14)

where the T denotes the conjugate transpose of thematrix. Note that a background subtraction process isexplicitly denoted in equation (14). The backgroundspectra is that obtained without tunnel flow, where theacquisition system noise dominates the recordedoutput. The division by the number of microphones Mserves to reference the array output spectrum levels toequivalent single microphone output levels.Equation (14) represents the steered response powerspectrum over the full range of single narrowbandfrequencies. If a wider bandwidth is desired (such asan Octave Band), the power (pressure-squared values)of the narrowbands is summed. Note that widerbandwidths are not formed prior to the completion ofthe vectorial (or complex) operations of equation (14).This prevents possible significant bias errors insumming across phase-shifted cross spectral bands.

SADA Shading Algorithm: The use of the SADAfor directivity and spectral measurements requires thatthe beamwidth be invariant under steering angle andfrequency changes, thereby providing a constantsensing area over noise source regions. The methodused to accomplish this is similar to previoustechniques described in Reference 12 and 13. TheSADA microphones are divided into three clusterscontaining 17 microphones each. These clusters alongwith their maximum diagonal aperture sizes are shownin Table 3. Each cluster exhibits the same directionalcharacteristics for a given wavenumber-length productkDn, where k is the wavenumber and Dn is the diagonaldistance between the elements of the n-th cluster. Themethod used to achieve the invariant sensing areaconsists of shading (or weighting) the array clusters asa function of frequency. The microphone clustershadings are calculated as follows:

w

w

w

and1

2

3

1 2

0

0

1

0 0

===

()K*K

≤ ≤σ σ

w

w

w

1 10 875

2 10 875

3

11

0

0 1

== −=

()K

*K< ≤

σσ σ

.

.

w

w

w

1

2 20 875

3 20 875

2

0

1

0 1

=== −

()K*K

< ≤σσ

σ.

.

w

w

w

and1

2

3

1 2

1

0

0

1 1

===

()K*K

> >σ σ

(15)

with the shading coefficients defined by

σ

σ

12 0

2 1

23 0

3 2

= −−

= −−

kD kD

kD kD

kD kD

kD kD (16)

The value of kD0 for this study is 36.38, correspondingto frequencies of 10, 20, and 40 kHz for clusters 3, 2,and 1, respectively (assuming a speed of sound of1126 ft/sec). This causes the SADA to yield the sameeffective resolution for all frequencies between 10 and40 kHz, with smooth blending among frequencies.The exponent of the coefficients, 0.875, was found todiffer slightly from the array of References 12 and 13.

Figure 13 illustrates modified theoretical arrayresponses for the SADA for frequencies of 10, 12.5, 15and 17.5 kHz, using equations (4) and (5) with theshadings of equation (15) substituted for the wm term.

Comparing the responses with those shown inFigure 8, note that the responses for 10, 20, and40 kHz are now identical, as are the ones for 12.5 and25, 15 and 30, and 17.5 and 35 kHz. This clearlyillustrates the frequency-invariant main and side lobestructure now exhibited by the array. Figure 14 showsa beamwidth plot for the shaded array. At higherfrequencies the beamwidth, while invariant, now takeson the value exhibited at the kD3 wavenumber-lengthproduct. In a sense the higher frequency beamwidthshave been sacrificed to achieve frequency invariance.This is an acceptable trade-off; however, since accuratesource directivity data can only be obtained over abroad frequency range if the sensing area of the arrayis held constant.

To extract noise spectra and directivity from dataobtained with the SADA, the classical beamformingtechnique is employed with minor variations. First, asingle steering location is chosen for the array, whichis itself positioned at various elevation and azimuth


angles with respect to the model. A modified versionof equation (14) is used to compute the weightedsteered response power for the array at the fixedsteering location via

P eW G G W

w

Tdata background

T

mm

M( $)

$

$ ( $ $ ) $

$

=−

∑=

e e

1 (17)

where $W is a row matrix containing the set ofshadings computed in equation (15). The sum over themicrophone shading terms in the denominator isobtained from equation (15) as a function of frequency(this sum always equals 17 for the present SADAapplication). Note that this formulation of thebeamformer equation is identical to that for the LADA

if one assumes an identity matrix for $W .

Array Calibration and Applications

Careful calibrations are conducted for both arraysystems. These tests are designed to check fordeviations between experimental and theoretical arrayresponses which can be attributed to microphonesystem response differences, installation effects, orproblems in the data analysis algorithms.

Injection Calibration: Injection calibrations areperformed for the SADA. These calibrations consist ofinserting a known signal simultaneously into allmicrophone channels in order to detect microphonesensitivity and phase drift. Both pure tones and whitenoise are used. This is accomplished without physicaldisruption of the system. Inspection of cross spectralphase between all pairs of microphones allowsdiscrepancies to be easily identified and corrected.Also, sensitivity drift can be corrected without the needto perform a full microphone calibration before eachrun. Nevertheless, standard SADA microphonecalibrations are also performed daily because of readyaccessibility.

Isolated Point Source: A series of static calibrationtests are performed by placing an isolated point sourcedirectly in front of the array at the operational workingdistance (4 feet for the LADA, 5 feet for the SADA).The point source consists of a tube with one or moreacoustic drivers mounted on the back end. The openend of the tube is intended to provide an omni-directional sound source. Noise measurements areobtained across a broad frequency band though the useof white noise. These are compared with

corresponding theoretical array responses usingequations (4) and (5).

Figure 15 shows a series of LADA point source noiseimages taken at identical frequencies to the theoreticalones shown in Figure 4. Figure 16 shows thecorresponding measured beamwidths which can becompared with Figure 5. At the higher frequenciessome discrepancies were indicated between thetheoretical and experimental sidelobe shapes (mostlikely due to installation effects); however, themeasured beamwidths and peak sidelobe levels agreewell with theory. Figures 17 and 18 show a series ofSADA noise images and beamwidth line plotscorresponding to the blended theoretical ones shown inFigures 13 and 14, respectively. The shadingalgorithm is seen to be validated.

In-Situ Point Source: In addition to the staticcalibrations using an isolated point source, tests areconducted using the point source mounted in the QFFat the midpoint of the trailing edge of the main elementairfoil. These measurements include:

• Background acquisition runs for no tunnel airflow.The corresponding spectra is subtracted from theother spectra to remove the noise floor, asdescribed previously.

• Acquisition runs with no flow and point sourceturned on to verify processing accuracy and theeffect of the test apparatus on the acoustic field.

• Acquisition runs with flow and point sourceoperating to evaluate the shear layer correctionalgorithms.

Figure 19 shows a series of noise image maps takenwith the SADA on the pressure side of the model foran elevation angle of 107 degrees and an azimuthangle of zero degrees. At this location the face of thearray is parallel to the chord of the main elementairfoil. Figure 19(a) shows a photograph of the pointsource mounted in the QFF pointing toward thepressure side of the model. Figure 19(b) shows a30-kHz noise image map of the point source under noflow conditions. Figure 19(c) shows a 30-kHz noiseimage map for the point source operating in aMach 0.17 flow with no shear layer correction applied,while Figure 19(d) shows a similar map withcorrections. Notice that the apparent location of thesource moves approximately 3 inches downstream ofits actual position without shear layer correctionsapplied. The shear layer algorithm returns the sourceto its proper position, as verified by the no flow case.Other SADA elevation angles, producing larger


position corrections, also find success using thesealgorithms.

Test Application

LADA Measurements: Acoustic noise image mapsare obtained by steering the LADA over a planeparallel to the main element chord on the modelpressure side. Because of limitations in the dataacquisition process in the early test stages of theprogram (of which this particular LADA data wasobtained), background noise spectra have not beensubtracted. However, the effect of background noisewas determined to be negligible for these results.Figure 20 shows typical acoustic image maps taken atfrequencies of 5, 8, 12.5, and 20 kHz. The flow isfrom bottom to top and an outline of the wing and flapprovide a reference for the noise sources that arepredominant. Note that the location and strength ofthe sources are dependent on frequency, with the leveldiminishing with frequency.

The benefits of using a larger aperture withcorresponding narrow beamwidth can be seen inFigure 21. This figure shows the position of the locallydominant noise source location, defined by the centroidof the source on the image maps in Figure 20. Thisfigure shows that along the flap-side edge, a trendexists for the lower frequency sound sources to belocated near the flap trailing edge with the sourcelocation moving to the flap mid chord and flap mainelement juncture at higher frequencies. Suchinformation is only obtainable using an array with asufficiently large aperture size and correspondinglynarrow beamwidth.

SADA Measurements: Figure 22 shows the SADAelevation angles which were employed for directivitystudies in the QFF. Figure 23 shows flap edge spectrataken at an elevation angle of 107 degrees. The SADAazimuth angle is at zero degrees, corresponding to theplane of the flap side edge surface. The model flapangle condition is 29 degrees. The array is focused onthe flap region, which for this flap angle is by far themost intense noise producing region. Shown on theplot, along with the SADA beamformed-outputspectrum, is the spectra obtained from a singlemicrophone in the array. The difference in levelsbetween these represents the removal of unwantednoise emanating from regions other than those presentat the steering location. As previously indicated, theSADA spectrum represents that noise emitted from aregion of constant size for frequencies between 10 and40 kHz. At lower frequencies, the noise emission

region measured is larger; for higher frequencies, theregion is smaller.

Figure 24 shows the elevation angle sourcedirectivity in terms of a series of noise spectra obtainedfor the SADA at a number of elevation angles aboutthe model. The model flap angle is now 39 degrees.With the exception of the most downstream position,the spectra are within 2 to 3 dB of one another forfrequencies from 10-30 kHz. Larger deviations indirectivity occur over the lower and upper frequenciesdue to differences in source characteristics, asdescribed in Reference 17.

It is noted that the LADA’s 39 degrees of solidcollection angle sets well within the SADA elevationangle range shown here. The degree of directivityuniformity found over the 10-30 kHz range offrequencies suggests that measurements with theLADA should have quantitative accuracy, in additionto it having source positioning accuracy. This is true,as long as the azimuthal directivity (not determined forthis paper) is likewise uniform and that the spatialsource-noise coherence is high. As previouslyindicated, any lack of spatial uniformity over the arraymicrophones would effectively shade the microphone’sresponse in the beamforming and, thus, would changethe array response characteristics.

Summary

This paper presents an overview of the design andconstruction of two complementary microphonedirectional arrays used for aeroacoustic testing. ALarge Aperture Directional Array (LADA) has beenconstructed to obtain high resolution noise localizationmaps. A Small Aperture Directional Array (SADA)has also been made to be moved about the model toprovide localized spectra and directivity from selectednoise source regions. Calibration tests havedemonstrated their accuracy and functionality. Botharrays have been used to successfully measure the farfield acoustics on a main element / half-span flapmodel. The LADA was able to detect small changes inlocation of dominant noise sources emanating from theflap edge region, while the SADA was able to obtainspectra and directivity measurements from this region.

Acknowledgments

The authors wish to acknowledge Dave Devilbiss ofLockheed-Martin and Stuart Pope of ComputerSciences Corporation for data processing and softwaredevelopment support. The authors also gratefullyacknowledge Phil Grauberger and Ron Verhapen ofWyle Laboratories for data acquisition system support.


References

1. Kendall, J.M., Jr., “Airframe Noise Measurementsby Acoustic Imaging”, AIAA Paper 77-55, AIAA15th Aerospace Sciences Meeting, Los Angeles,CA, January, 1977.

2. Grosche, F.R., Stiewitt, H., and Binder, B.,

“Acoustic Wind-Tunnel Measurements with aHighly Directional Microphone”, AIAA Journal,Volume 15, Number 11, pp. 1590-1596, 1977.

3. Schlinker, R.H., “Airfoil Trailing Edge Noise

Measurements With a Directional Microphone”,AIAA Paper 77-1269, 4th AIAA AeroacousticsConference, Atlanta, GA, October, 1977.

4. Grosche, F.R., Schneider, G., and Stiewitt, H.,

“Wind Tunnel Experiments on Airframe NoiseSources of Transport Aircraft”, AIAA Paper 97-1642, 3rd AIAA/CEAS Aeroacoustics Conference,Atlanta, GA, May, 1997.

5. Brooks, T.F., Marcolini, M.A., Pope, D.S.,

“Airfoil Trailing-Edge Flow Measurements”,AIAA Journal, Volume 24, Number 8, pp. 1245-1251, 1986.

6. Brooks, T.F., Pope, D.S., Marcolini, M.A.,

“Airfoil Self-Noise and Prediction”, NASAReference Publication 1218 , July, 1989.

7. Elliot, R.S., “The Theory of Antenna Arrays”,

Microwave Scanning Antennas, R.C. Hansen, ed.,Academic Press, 1966.

8. Burdic, W.S., “Underwater Acoustic System

Analysis”, Prentice-Hall, Inc., Englewood Cliffs,NJ, 1984.

9. Soderman, P.T., and Noble, S.C., “A Four-

Element End-Fire Microphone Array for AcousticMeasurements in Wind Tunnels”, NASA TechnicalMemorandum X-62, 331, January, 1974.

10. Soderman, P.T., and Noble, S.C., “Directional

Microphone Array for Acoustic Studies of WindTunnel Models”, Journal of Aircraft, pp. 169-173,1975.

11. Billingsley, J., and Kinns, R., “The Acoustic

Telescope”, Journal of Sound and Vibration,Volume 48, Number 4, pp. 485-510, 1976.

12. Brooks, T.F., Marcolini, M.A., and Pope, D.S., “ADirectional Array Approach for the Measurementof Rotor Noise Source Distributions withControlled Spatial Resolution”, Journal of Soundand Vibration, Volume 112, Number 1, pp. 192-197, 1987.

13. Marcolini, M.A., and Brooks, T.F., “Rotor Noise

Measurement Using a Directional MicrophoneArray”, Journal of the American HelicopterSociety, pp. 11-22, 1992.

14. Underbrink, J.R., “Practical Considerations in

Focused Array Design for Passive BroadbandSource Mapping Applications”, Master’s Thesis,The Pennsylvania State University, May, 1995.

15. Mosher, M., “Phased Arrays for Aeroacoustic

Testing: Theoretical Development”, AIAA Paper96-1713, 2nd AIAA/CEAS AeroacousticsConference, State College, PA, May, 1996.

16. Watts, M.E., Mosher, M., and Barnes, M.J., “The

Microphone Array Phased Processing System(MAPPS)”, AIAA Paper 96-1714, 2nd AIAA/CEASAeroacoustics Conference, State College, PA,May, 1996.

17. Meadows, K.R., Brooks, T.F., Humphreys, W.M.,

Hunter, W.W., and Gerhold, C.H., “AeroacousticMeasurements of a Wing-Flap Configuration”,AIAA Paper 97-1595, 3rd AIAA/CEASAeroacoustics Conference, Atlanta, GA, May,1997.

18. Johnson, D.H., and Dudgeon, D.E., Array Signal

Processing, Prentice Hall, 1993. 19. Hubbard, H.H., and Manning, J.C., Aeroacoustic

Research Facilities at NASA Langley ResearchCenter, NASA Technical Memorandum 84585,1983.

20. Rew, R., Davis, G., Emmerson, S., and Davies, H.,

“NetCDF User's Guide - An Interface for DataAccess”, University Corporation for AtmosphericResearch - Unidata Program Center, Boulder,CO, 1996.

21. Pao, J.Z., and Humes, D.C., “NASA Langley

Research Center’s Distributed Mass StorageSystem”, 14th IEEE Symposium on Mass StorageSystems, 1995.


22. Schlinker, R.H., and Amiet, R.K., “Shear LayerRefraction and Scattering of Sound”, AIAA Paper80-973, 1980.

23. Amiet, R.K., “Refraction of Sound by a ShearLayer”, Journal of Sound and Vibration, Volume58, Number 3, pp. 467-482, 1978.

Table 1 - LADA Microphone Coordinates (Viewed from Front of Array)Mic # X location Y location Z location Mic # X location Y location Z location

(in) (in) (in) (in) (in) (in)1 0.03 -1.02 0.00 19 -9.99 5.66 0.002 0.97 -0.32 0.00 20 -8.47 -7.78 0.003 0.61 0.80 0.00 21 10.57 -8.60 0.004 -0.57 0.81 0.00 22 11.44 7.37 0.005 -0.93 -0.30 0.00 23 -3.47 13.14 0.006 -5.13 0.88 0.00 24 -13.56 0.75 0.007 -2.42 -4.63 0.00 25 -4.89 -12.69 0.008 3.67 -3.75 0.00 26 14.55 -5.15 0.009 4.71 2.30 0.00 27 9.39 12.22 0.0010 -0.73 5.17 0.00 28 -8.73 12.68 0.0011 -2.34 -8.63 0.00 29 -14.74 -4.38 0.0012 7.50 -4.91 0.00 30 -0.39 -15.42 0.0013 6.99 5.59 0.00 31 17.01 -1.12 0.0014 -3.16 8.35 0.00 32 6.32 15.81 0.0015 -8.92 -0.42 0.00 33 -13.08 10.89 0.0016 4.80 -10.49 0.00 34 -14.39 -9.09 0.0017 11.45 1.30 0.00 35 4.21 -16.52 0.0018 2.31 11.28 0.00

Table 2 - SADA Microphone Coordinates (Viewed from Front of Array)Mic # X location Y location Z location Mic # X location Y location Z location

(in) (in) (in) (in) (in) (in)1 0.00 0.00 0.00 18 0.00 -1.80 0.002 0.00 -0.45 0.00 19 1.37 -1.37 0.003 0.34 -0.34 0.00 20 1.80 0.00 0.004 0.45 0.00 0.00 21 1.37 1.37 0.005 0.34 0.34 0.00 22 0.00 1.80 0.006 0.00 0.45 0.00 23 -1.37 1.37 0.007 -0.34 0.34 0.00 24 -1.80 0.00 0.008 -0.45 0.00 0.00 25 -1.37 -1.37 0.009 -0.34 -0.34 0.00 26 0.00 -3.60 0.0010 0.00 -0.90 0.00 27 2.75 -2.75 0.0011 0.69 -0.69 0.00 28 3.60 0.00 0.0012 0.90 0.00 0.00 29 2.75 2.75 0.0013 0.69 0.69 0.00 30 0.00 3.60 0.0014 0.00 0.90 0.00 31 -2.75 2.75 0.0015 -0.69 0.69 0.00 32 -3.60 0.00 0.0016 -0.90 0.00 0.00 33 2.75 -2.75 0.0017 -0.69 -0.69 0.00

Table 3 - SADA Cluster GroupingsCluster Number Microphone Grouping Diagonal Cluster Aperture

(in)1 1 - 17 1.942 1, 10-25 3.883 1, 18-33 7.76

Mic 1Delay

Mic 2Delay

Mic 3Delay

Mic 4Delay

M1

M2

M3M4

Source

ArraySpherical Wave

Propagation

Figure 1. Basic Principle of DirectionalArray Operation.

20

15

10

5

0

5

10

15

20

0

30

60

90

120

150

180

210

240

270

300

330

Rad

ius,

inch

es

Figure 3. Large Aperture Directional ArrayMicrophone Layout.

Figure 2. Large Aperture Directional ArrayMounted in QFF for Testing.

13American Institute of Aeronautics and Astronautics

-0.5 -0.25 0 0.25 0.5-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

-3-6

-12

Yo (ft)

Xo

(ft)

-0.5 -0.25 0 0.25 0.5-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

-3

-6

-12

Yo (ft)

Xo

(ft)

-2 -1 0 1 2-14

-12

-10

-8

-6

-4

-2

0

OA

SP

L, d

B

Yo (ft)

Figure 4. LADA Theoretical Array Responsesfor 6, 10, 20, and 30 kHz.


6 kHz 10 kHz

-2 -1 0 1 2-14

-12

-10

-8

-6

-4

-2

0

OA

SP

L, d

B

Yo (ft)

<-13 dB <-13 dB

<-13 dB<-13 dB

-0.5 -0.25 0 0.25 0.5-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

-8

-8

-8

-8

-8

Yo (ft)

Xo

(ft)

-3 dB

-6 dB

-0.5 -0.25 0 0.25 0.5-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

-8

-8

-8

Yo (ft)

Xo

(ft)

-3 dB

-6 dB

Figure 4 (continued). LADA Theoretical Array Responsesfor 6, 10, 20, and 30 kHz.


20 kHz 30 kHz

-2 -1 0 1 2-14

-12

-10

-8

-6

-4

-2

0

OA

SP

L, d

B

Yo (ft)-2 -1 0 1 2

-14

-12

-10

-8

-6

-4

-2

0

OA

SP

L, d

B

Yo (ft)

<-9 dB

<-9 dB

<-9 dB

<-9 dB

Figure 5. LADA Theoretical Beamwidthas Function of Frequency.

Figure 6. Small Aperture Directional ArrayMicrophone Layout.

4

3

2

1

0

1

2

3

4

0

30

60

90

120

150

180

210

240

270

300

330

Rad

ius,

inch

es0 5 10 15 20 25 30

0.0

0.5

1.0

1.5

2.0

2.5

3.0

-0.5 dB level-1.0 dB level-3.0 dB level-6.0 dB level

Bea

mw

idth

(ft)

Frequency (kHz)

Figure 7. Small Aperture Directional ArrayMounted in QFF for Testing.


Figure 8. SADA Theoretical Array Responsesfor 10, 20, 30, and 40 kHz.


-2 -1 0 1 2-16

-14

-12

-10

-8

-6

-4

-2

0

OA

SP

L, d

B

Yo (ft)

-2 -1 0 1 2-16

-14

-12

-10

-8

-6

-4

-2

0

OA

SP

L, d

B

Yo (ft)

-2 -1 0 1 2-16

-14

-12

-10

-8

-6

-4

-2

0

OA

SP

L, d

B

Yo (ft)

10 kHz

20 kHz

30 kHz

Figure 8 (continued). SADA Theoretical Array Responsesfor 10, 20, 30, and 40 kHz

Figure 9. SADA Theoretical Beamwidthas Function of Frequency.

Figure 10. Data Acquisition / Analysis Block Diagram.


-2 -1 0 1 2-16

-14

-12

-10

-8

-6

-4

-2

0

OA

SP

L, d

B

Yo (ft)40 kHz

0 10 20 30 40 50

0

1

2

3

4 -0.5 dB level-1.0 dB level-3.0 dB level-6.0 db level

Bea

mw

idth

(ft)

Frequency (kHz)

Array Microphones

12-bitNEFF

SamplingClock

DEC AXP 3400(Acquisition)

Pentium-Pro WorkstationCluster (Analysis)

DEC Alphastation 600(Analysis)

48-node LaRC SP2Parallel System

(Analysis)

Ethernet / FDDI

36 Channels

27 GB LocalDisk Storage

27 GB LocalDisk Storage

Local TapeBackup

LaRC DistributedMass Storage System

(50 TB Capacity)

Figure 12. Array Steering.Figure 11. Geometry Showing Angles Utilizedin Shear Layer Correction. Dashed Line Denotes Ray Path.

Velocity Triangle is Shown.

Figure 13. Frequency-Invariant SADATheoretical Array Responses.


Array

Defined Grid

-2 -1 0 1 2Yo (ft)

-2

-1

0

1

2

Xo

(ft)

-3-6

-18

-21-21

-21 -21

10, 20, 40 kHz

-2 -1 0 1 2Yo (ft)

-2

-1

0

1

2

Xo

(ft)

-3-6

-18

-21-21

-21 -21

12.5, 25 kHz

-2 -1 0 1 2Yo (ft)

-2

-1

0

1

2

Xo

(ft)

-3-6

-18

-21-21

-21 -21

15, 30 kHz

-2 -1 0 1 2Yo (ft)

-2

-1

0

1

2

Xo

(ft)

-3-6

-18

-21-21

-21 -21

17.5, 35 kHz

Nozzle

Curved ShearLayer Midpoint

Position

Source

Source

Microphone

rmic

Tangent to ShearLayer at Ray Path

InterceptCo

vθmic

θ

r2

r1

θφ1

φ1

φ2

<-21 dB

<-21 dB

<-21 dB

<-21 dB

<-21 dB

<-21 dB

<-21 dB

<-21 dB

Figure 14. SADA Theoretical Beamwidths Using Shading.Compare with Figure 9.

Figure 15. Noise Image Maps from LADAIsolated Point Source Calibration.

Compare with Figure 4.


0 10 20 30 40 50

0

1

2

3

4

5


Bea

mw

idth

(ft)

Frequency (kHz)

Figure 16. Measured LADA Beamwidth fromIsolated Point Source Calibration.


Figure 17. Noise Image Maps from SADAIsolated Point Source Calibration.



0 5 10 15 20 25 30

0.0

0.5

1.0

1.5

2.0

2.5

3.0


Bea

mw

idth

(ft)

Frequency (kHz)

-2 -1 0 1 2Yo (ft)

-2

-1

0

1

2

Xo

(ft)

-3-6

-18

-21 -21-21

-21 -21 -21

10, 20, 40 kHz

-2 -1 0 1 2Yo (ft)

-2

-1

0

1

2

Xo

(ft)

-3-6

-18

-21-21

-21 -21

12.5, 25 kHz

-2 -1 0 1 2Yo (ft)

-2

-1

0

1

2

Xo

(ft)

-3-6

-18-21-21

-21 -21

15, 30 kHz

-2 -1 0 1 2Yo (ft)

-2

-1

0

1

2

Xo

(ft)

-3-6

-18-21

-21

-21

-21-21

-21

-21

-21

17.5, 35 kHz

<-21 dB <-21 dB

<-21 dB

<-21 dB

<-21 dB

<-21 dB

<-21 dB

<-21 dB

Figure 18. Measured SADA Beamwidths fromIsolated Point Source Calibration.



Figure 19. Example of In-Situ Point Source Measurementsfor Shear Layer Correction Verification.

(a) Photograph of Experiment(b) Noise Image Map of Point Source With No Flow

(c) Noise Image Map of Point Source - No Shear Correction Applied(d) Noise Image Map of Point Source with Shear Correction

(a)

Mo = 0.17, Freq = 30 kHz (c)

Mo = 0.0, Freq = 30 kHz (b)

Mo = 0.17, Freq = 30 kHz (d)

0 10 20 30 40 50

0

1

2

3

4

5


Bea

mw

idth

(ft)

Frequency (kHz)

Figure 20. Sound Source Localization Maps forLADA Airframe Noise Model Measurements.

Mo=0.17, Angle-of-Attack=16 deg, Flap=39 deg


Figure 21. Locally Dominant Noise Source CentroidLocations on Airframe Noise Model Flap.

Origin Denotes Flap and Main Element Juncture.Mo=0.17, Angle-of-Attack=16 deg

Figure 22. SADA Elevation Anglesfor Directivity Measurements.


Figure 23. Typical Noise Spectra fromSADA Using 87 Hz Bandwidth.

Mo=0.17, Angle-of-Attack=16 deg, Flap Angle=29 deg

Figure 24. Directivity of Spectra Using87 Hz Bandwidth for Mo=0.17.

Angle-of-Attack=16 deg, Flap Angle=39 deg

Flap

-0.5 0.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 18.00.5

yo (in)

xo (in)

Flap/Main Element Overlap

4

3

2

1

0

-1

1 kHz

1 kHz27 kHz13 kHz

32 kHz2 kHz

8 kHz

11 kHz

7 kHz9 kHz

5 kHz6 kHz

4 kHz

3 kHz2 kHz

5 kHz

8 kHz

12 kHz7 kHz

6 kHz 4 kHz

3 kHz

11, 12, 14, 17, 21 & 24,26 kHz

15, 16, 22 & 23 kHz10 kHz9 kHz

-90

-107 107

-124 124

141

-73

-56

-39

73

flap

SADAmainelement

nozzleside plate

90

aiaa 98-0471 design and use of microphone …mln/ltrs-pdfs/nasa-aiaa-98-0471.pdfjanuary 12-15, 1998...

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