NASA Technical Reports Server (NTRS) 19980037002: Design and Use of Microphone Directional Arrays for Aeroacoustic Measurements

26 Pages·1.4 MB·English

by  NASA Technical Reports Server (NTRS)

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AIAA 98-0471
Design and Use of Microphone
Directional Arrays for
Aeroacoustic Measurements
William M. Humphreys, Jr.
Thomas F. Brooks
William W. Hunter, Jr.
Kristine R. Meadows
NASA Langley Research Center
Hampton, VA 23681-0001
36st Aerospace Sciences
Meeting & Exhibit
January 12-15, 1998 / Reno, NV
For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics
1801 Alexander Bell Drive, Suite 500, Reston, Virginia 20191-4344

AIAA-98-0471
DESIGN AND USE OF MICROPHONE DIRECTIONAL ARRAYS
FOR AEROACOUSTIC MEASUREMENTS
William M. Humphreys, Jr.*
Thomas F.Brookst
William W.Hunter, Jr.*
Kristine R. Meadows_
Fluid Mechanics andAcoustics Division
NASA Langley Research Center
Hampton, Virginia 23681-0001
Abstract flap. Representative data obtained from these
measurements is presented, along with details of the
An overview of the development of two microphone array calibration and data post-p_ing procedures.
directional arrays for aeroacoustic testing is presented.
Nomenclature
These arrays were specifically developed to measure
airframe noise in the NASA Langley Quiet Flow
Facility. A large aperture directional array using 35 Superscripot source location
flush-mounted microphones was constructed to obtain
high resolution noise localization maps around A shearlayer amplitude correctiodnB,
C constant
airframe models. This array possesses a maximum
diagonal aperture size of 34 inches. A unique co speedofsound,IVsec
D SADA clustearpertures,eeeqn.(16)
logarithmic spiral layout design was chosen for the
targeted frequency range of 2-30 kHz. Complementing steerinmgatrixs,eccqn.(13)
the large array is a small aperture directional army, f frequency, cycles/scc
constructed to obtain spectra and dircctivity d
cross spectral matrix
information from regions on the model. This array,
cross spectra between ithandj _
possessing 33 microphones with a maximum diagonal microphones, see eqn. (6)
aperture size of 7.76 inches, is easily moved about the k wavenumber (=c0/co),ft"l
model in elevation and azimuth. Custom microphone
M total number of microphones in array
shading algorithms have been developed to provide a Mo Math number (--v/co)
frequency- and position-invariant sensing area from
P pressure, Pascals
10-40 kHz with an overall targeted frequency range for
radialdistance, fl
y
the array of 5-60 kHz. Both arrays are employed in
t time, sec
acoustic measurements of a 6 percent of full scale
velocitfyt,/sec
1/
airframe model consisting of a main element NACA
arrayshadingmatrix
632-215 wing section with a 30percent chord half-span
w microphonedusterweighting
*Research Scientist, Measurement Science and Technology W(k, £,£o) theoreticaarlrayresponseat
Branch, Senior Member AIAA. wavenumberk,dB,seeeqn.(4)
*Senior Research Scientist, Aeroacoustics Branch, Assc_ate
spectrawlindowweightingconstant
Fellow AIAA.
ke_FFT datablockforis'andjth
*Senior Research Scientist, Measurement Science and
Technology Branch. microphones
1Researdt Sdentlst, Aeroa_ustics Branch, Member AIAA.
locationf,l
Copyright O1998 bythe American Institute of_cs and
Astronautics, Inc. No copyright is asserted in the United States locatioonfphasecenterofarrayR,,
under Title 17, U.S. Code. The U.S. Gov_t has aroyalty-flee
see eqn. (3)
liceme to exercise all rights under the copyright claimed herein for
govenunent _. All other rights are reserved bythe copyright
OWt'ler.
American Institute ofAeronauticasnd Astronautics
acoustic wavelength, R microphones. As such, they can be considered one of
G SADA arrayweighting control the precursors to the current generation of microphone
C0 frequency, rad/sec directional arrays.
coat shear layerphase correction for co, Modem microphone directional arrays for
radians,seeeqns.(9)and(13) aeruaconstic research have as their origin early radio
andradarantennaarraysandU.S.Navy hydrophone
Introduction arrays(used for the detection of submarines as early as
World War 11)._'s Soderman and Noble were among
Over the past several years a growing need has the first researchers to adapt this earlier work for
emerged for accurate and robust noise measurement aeroaconstics when they constructed a one-dimensional
instrumentation in aerospace research facilities. This end-fire arrayto evaluate jet noise in the NASA Ames
need ispartly driven by research programs such as the 40- by 80-foot Wind Tunnel.9"1° At the same time
NASA Advanced Subsonic Technology (AST) Billingsley and Kinns constructed a one-dimensional
Program,which has setas one of itsgoalsthe linear arrayof microphones for real-time sound source
achievingofa greaterthan10 dB reductioinntotal location on full-size jet engines, n More recently _ch
aircraft effective perceived noiseby the year 2000 directional arrays have beenextended to include two-
(referenced to levels measured in 1992). This goal dimensional microphone layouts with the work of
requires the collection of experimental databases of Brooks, Marcelini and Pope 12"13, Underbrink and
various noise generation mechanisms from which DoughertyTM, and Watts and Mosher. 15q6
accurate and efficient noise prediction tools can be Two different state-of-the-art, two-dimensional
developed to guide noise reduction design. Recently, microphone directional arrays are described in this
emphasis has been placed on the measurement and paper. These aredesigned to provide broadband source
modeling of airframe noise, defined as the non- localization and directivity information needed to
propulsive component of aircraft noise which is due to characterizaeirframe noiseand noise reduction
unsteady flow about the airframe components (flaps, concepts. Both arrays have been successfidly used by
slats, undercarriage, etc.). the authors to obtain data for a wing / flap model. 17
One of the databases desired by computational This paper expands onthe previouwsork by providing
airframe noise modelers isfarfield noise datameasured detailed descriptions of the design and construction of
on various baseline and modified aircraft components. the two directional arrays. The philosophy
Traditional single microphone measurements of this surrounding their design as well as development of
noise have been hampered by poor signal-to-noise unique data processing algorithms to allow accurate
characteristics, spurring the development of a variety noisespectraand source imagestobe obtainedare
of new measurement techniques. Early techniques discussedF.inally, severarlepresentatievxeamplesof
employed the concept of an "acoustic mirror", where a data collected with the instruments areillustrated.
large concave elliptic mirror and an associated
microphone were positioned in the acoustic far field.1"_ Directional Array Development
SuchmL,xorswere capable of locating individual sound
Concept
sources accurately, but suffered the drawback of
requiring mechanical movement to determine source
distributions around models. The mirrors also became The basic principloef a microphonedirectional
excessively large when measurements of lower array can be simply illustratedA.ssume a simple
monochromatic acoustic point source is located in
frequencies (< 2 kHz) were required. Nevertheless,
such mirrors continue to have applicability in some of quiescent space at location _ (see Figure 1). A
the larger research facilities. 4 solution for r>O representing the propagation of a
In addition to acoustic mirrors, distributions of pressure wave radially in all directions isgiven by
individual microphones have been employed to
determineairframenoisesourcecharacteristicIsn.
p(r,t) = Cei(_'-k') (1)
particulasru,chsystemshaveprovenvaluableinthe
r
understandingofsingle-elemenatirfoislelfnoise5.6
Whilenotstrictlcyonsidereda directionaarlray(the
where C isa constant, r is the radialdistance from the
outputsofallmicrophoneswerenotcombinedasin
source origin, cois the frequency of the wave, and k is
beamforming),such systems capitalizedon the
the corresponding wavenumber. Assume now that an
amplitudeandphaserelationshibpestweenclusterosf
arrayofM microphones isplaced afinite distance from
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the source. Each microphone senses a slightly
different phase-s_ wave.form depending on its
distance from the source. The pressure pro(t)measured
atthe m-th microphone isdenoted as
(5)
C ya,(t-_)
This response isplotted as a contour map with contour
p.(t) = --e Co (2)
rm level proportional to O_(x-), representing the
computation of equation (5) over a large number of
where rmrepresents the distance from the location to steering locations lying on a surface a finite distance
the m-th microphone. The (t-rJCo) term is the from the array. Such plots represent the spatial
retarded time from the source to the microphone. In filtering ofthe array graphically at wavenumber k, and
order to focus on a source, the individual microphone allows one to examine the beamwidth and lobe
outputs can be phase shifted an amount equal to their structure.
propagation delay and then summed together (or
stacked). This yields a single output signal for the Array Desien Criteria for Airframe
arrayin aprocess commonly referred to as delay-and- Noise Measurements
sum beamforming. By adjusting the propagation
delays, one is able to electronically steer the array to Test Model and Facility: The test program is
points in space, selecting regions of interest to intended to investigate the mechanisms of sound
ascertain noise production while providing noise generation on high-lift wing configurations. In
rejection not found in individual microphone Figure 2, the test model apparatus and the Large
measurements. This steering can provide the same ApertureDirectional Array, to be discussed, axe shown
capability as the earlier acoustic mirror techniques but mounted in the Langley Quiet Flow Facility (QFF).
without the necessity of physically moving the array to The QFF is a quiet open-jet facility designed
measure source distributions. specifically for anechoic acoustic testing. 19 For the
present airframe model testing, a 2 by 3-foot
Array Response rectangular open-jet nozzle is employed. The model is
a NACA 632-215 main element airfoil with a 30
The phasecenter of the arrayisdefined as_s percent chord half-span Fowler flap. In the photo, the
model is visible through the Plexiglas windows located
1 M onthe side plates. The model section isapproximately
(3)
6 percent of a full-scale configuration, with a main
m=-I element chord length of 16inches, a flap chord length
of 4.5 inches, and a full span of 36 inches. The main
Using this, the ideal array response for a simple source element and flap are fully instrumented with static
canbe expressed as pressure ports and unsteady pressure transducers. To
hold the model in place, the vertical side plates are
M ¥o fastened rigidly tothe side plate supports of the nozzle.
W(k,£,£°) -- _ wm-- ej_[(?-')-(r_-r-)]
Appropriate acoustic foam treatments areapplied to all
(4)
edges and supports to reduce acoustic reflections from
these surfaces. More model and facility details can be
where x is an arbitrary Cartesian location in space to found inReference 17.
which the array is electronically steered, £°is the
source location, r° and rmoarethe distances from the Array Design Criteria: In choosing an array
design, specifically the microphone layout with respect
source to _¢and the m-th microphone, respectively,
tothe noise source to be studied, one must be aware of
and r and r., are the distances from the steering the character of the source distributions. The basic
location to _¢and the microphone. The term wm delay-and-sum beamformer procedure, described
represents a microphone weighting factor which can be above, renders an array output which assumes any
used to modifythe array response. single source to be an omni-dircctional simple
The array response is normally expressed in monopole, or any distribution of sources to be that of
incoherent (uncorrelated) simple monopoles. But,
decibels referenced to the level obtained at ,_o :
when the sources are multi-pole and/or coherent over a
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spatialsourcedistributiont,he noiseis not omni- arraywas constructed to be movable aboutthe model in
directionaFl.orsuchdirectional sources, variations in both elevation and azimuth, as opposed to the LADA
noise field coherence, amplitude, and phase can occur which was fixed in location. The SADA results can
over the face of the array. Major difficulties occur also be used to evaluate the degree of directivity
when the directivity has an oscillatory sweeping or uniformity the LADA encounters to add confidence to
rotational phase behavior. Still, even when source the LADA results.
directivity is stationary, which is assumed to be the
case for the airframe noise problem, spatial variations Description of Two Directional Arrays
can cause moderate to severe errors in source
amplitude, resolution, and localization. This is Large Averture Directional Array (LADA): The
because the phase variations are interpreted as retarded LADA is shown tothe left in Figure 2, on the pressure
time delays, and amplitude/coherence variations side of the model, positioned 4 feet from the mid-span
modify the relative contribution of each microphone to of the airfoil main element trailing edge. A 4-foot
the array output. Indeed, the effect of limited spatial diameter fiberglass panel provides a flat surface to
coherence for the noise directivity is to effectively flush mount all microphones. The panel is attached to
breakan arraywith too large an aperture (overall width a pan-tilt unit secured to a rigid tripod support. This
of the array of microphones) into a group of smaller allows precise alignment changes in the elevation and
sub-arrays whose individual steered output spectra are azimuth of the face of the array. A small laser diode
summed together. This is "pressure-squared" pointer is place at _,, corresponding to the center of
summing rather than the desired "linear-pressure"
the fiber glass panel. The LADA incorporates 35 B&K
summing (operation indicated by equation (4)), thereby
model 4135, _A-inch microphones placed in a two-
modifying the desired "design" characteristics of the
dimensional pattern consisting of logarithmic spirals.
array. To avoid such errors, all array microphones
The microphone layout, shown in Figure 3, consists of
should be placed within approximately the same source
five spirals of seven microphones each with the inner-
directivity (producing generally a small array), where
most microphones lying on a 1-inch radius and the
amplitude and phase appear as ff the source were
outer-most on a 17-inch radius. The locations of the
omni-direotional. However, as will be seen, this design
microphones, viewed from the front of the array, are
constraint cannot always be fully met and still have the
listed in Table 1. This design is very similar to a
desired arrayresolution atthe frequencies of interest.
multi-arm logarithmic spiral arraywith linearly spaced
Airframe noise measurements present an array
spiral elements described in Reference 14. This design
design challenge in that not only is source directivity
results in acceptable beamwidth and peak sidelobe
information required (necessitating the use of a small
height over a targeted design frequency range of
aperture arrayto satisfy the concerns discussed above), 2-30 kHz.
butalso accurate localization ofthe source distributions
Figure 4 shows a series of contour plots showing
is desired down to the order ofthe smallest wavelength
LADA array responses using equations (4) and (5) for
of interest, typically one to two tenths of an inch. This
6, 10, 20, and 30kHz. The contour plots cover a planar
latter need requires that the array aperture be large in
area measuring 4 feet on edge at a distance of 4 feet
order to minimize the array beamwidth, defined here
from a simulated point source, matching the mounting
as the width across the main response lobe over which
configuration shown in Figure 2. Note that the
the sensing level is within a given dB level from the
response contour features for the different frequencies
peak level. However, the required spectra and
arc almost identical with a linear scaling factor being
directivity information dictate the use of a small array
inversely proportional to frequency. The contour
aperture to ensure that all microphones are at
features would be more nearly identical ffthe arraysize
approximately the same directivity angle.
were vanishingly small compared to the planar
R was decided to address the two conflicting
measuring area. However, given its 17-inch radius, the
aperture requirements through the construction of two
array encompasses 39 degrees of solid collection angle
array designs. A Large Aperture Directional Array
at this distance. Included in Figure 4 are a series of
(LADA) was designed to produce high spatial
line plots obtained by scanning through the contour
resolution (narrow beamwidth) noise source
plots in the xo direction for each 3,0 location and
localization maps over a defined surface on the model.
selecting the maximum dBlevel. Itcan be seen that a
To obtain quantitative spectra and directivity
plateau-like sidelobe structure exists at all frequencies,
information, particularly for the dominant noise
with the minimum sidelobe height approaching -6 dB
sources identified with the LADA, a Small Aperture
ata frequency of 20kHz.
Directional Array (SADA) was also designed. This
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American Institute of Aeronautics and Astronautics
A study of the beamwidth characteristics of the not done in the calculations of Figure 8. The contour
LADA can be achieved by observing a series of array plots cover an area measuring 4 feet on edge at a
responses for a number of frequencies spanning a distance of 5 feet from a simulated point source,
range of 2-30 kHz and measuring the width of the matching the mounting configuration shown in
main lobe at various dB levels. Figure 5 shows a Figure 7. A series of line plots obtained from the
family of curves where the main lobe width is contour plots in a process similar to thatfor the LADA
measured atthe -0.5, -1, -3, and -6 dB level. Itcan be are also shown in Figure 8. It can be seen that the
seen from the curves that a typical -3 dB beamwidth sidelobe patterns again exhibit a plateau-like structure
for the LADA is approximately 1.5 times the source at all frequencies, with the maximum sidelobe level
wavelength. approaching -8dB atafrequency of 40kHz.
A study of the beamwidth characteristics of the
SmallApertureDirectionaAlrray(SADA): The SADA can be performed similarly to that for the
SADA isdesignedtocomplementthecapabilitioefs LADA by observing a series of array l"¢sponsesover a
the LADA by providingdirectivitaynd spectral frequency range and measuring the width of the main
informatioansafunctioonfpositioanroundthemodel. lobe at various dB levels. Figure 9 shows such a
Theaperturoefthearrayiskeptsmallwiththeintent beamwidth plot. A family of curves is shown where
to keep all microphonesin the arraywithin the main lobe width is measured at the -0.5, -1, -3, and
approximately the same source directivity regardless of -6 dB level. It can be seenfrom these curves that a
elevation orazimuth position. The arraypattern which typical 3 dB beamwidth for the SADA is
was chosen to achieve this can be seen in Figure 6, approximately 11times the source wavelength. It will
with the locations of the microphones given in Table 2. be seen subsequently that this beamwidth can be
The SADA consists of 33 B&K model 4133, 1/8-inch radically altered through the use of microphone
microphoneswith ¼-inch preamplifierpsrojecting shading (orweighting).
from an acousticaltlryeatedaluminum flame. The
arraypatterinncorporatfeosurirregulacrircleosfeight Measurement System
microphoneseachwithonemicrophoneplacedatxc,
DataAcquisitionT:he dataacquisitio/nanalysis
correspondintgothecenterofthearray.Eachcirclies
systememployedforboth arraysis illustratiend
twice the diameter of the circle it encloses. The
Figure 10. Acquisition hardware consists of a NEFF
maximum radiusofthearmyis3.89inchesg,ivingthe
495 transient data recorder which is controlled by a
SADA only5.25%ofthesurfacaereaoftheLADA.
DEC AXP3400 workstation. Sampling rate is
Two smalllaserdiodepointerasreincorporateidnto
controlledby an externalclock operatingat
thearraymount on oppositesidesof the center
142.857kHz. Themaximum allowablcelockrateisI
microphone for use inalignment.
MI-Iz. The use of an external clock allows
The SADA is mounted on a pivotal boom designed
simultaneous acquisition with other instrumentation
toallow ittobepositioned to awide range of elevation
suchasthe model unsteady surface pressuresensorsa,s
and azimuthangleswhilemaintaininga constant
described in Reference 17. The NEFF system
distancteothecenterofthetrailinegdgeofthemain
incorporates 36 12-bit (including sign bit) acquisition
elementairfoi(lanassumednoiseproductiornegion).
channels with each channel possessing a 4 megabyte
Thisisachievedby maintainingtheboom's pivot
buffer, allowing up to 2 million 2-byte samples to be
centeratthetrailinegdgeofthemainelementairfoil.
collected per acquisition. The signals from each
Rotationoftheboom isperformedusingprecisioDnC
microphone channel are conditioned by passing them
servo rotation stages mounted on the outer edges of the
through high pass filters set to 300 Hz (to remove DC,
side plates holding the model and boom. This is
60Hz linenoise,andlowfrequenciynterferenncoeise)
illustratiend Figure7, which shows the SADA
andthrough anti-aliasing filters set at 50 kI-Izwhich is
mountedintheQFF onthesuctiosnideofanairframe
substantially below the 71.43 kHz Nyquist frequency.
noisemodelata 5-footworkingdistance.At this
Custom software isused to control all aspects ofthe
distancethearrayencompasses7.5degreesofsolid
data acquisition. The output files generated by the
collectiaonngle.
acquisition system are written in NetCDF format to
Figure8 showsa seriesofcontourplotsshowing
provideplatform-independesnttorageof thedata,a
SADA array responses using equations (4) and (5) for
featuremandated by the distributed data analysis
10, 20, 30 and 40 kHz. Subsequently, a processing
system.2° The NetCDF files arearchived on the NASA
procedure is used to maintain constant spatial
Langley Distributed Mass Storage Subsystem for post-
resolution, independent of frequency; however, this is
testretrieval and processing. 21
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A typical acquisition run consists of collecting 36 a Hamming window, each of these blocks of data is
channels (array microphones pins additional reference Fourier transformed into the frequency domain. The
microphones) of dataundernoflow conditions. This is individual upper triangular matrix elements plus the
followed bythe actual data nm under aspecific flow or diagonal (representing auto spectra for each array
calibration condition. As will be seen, _ecwa obtained microphone) are formed by computing the
from the background runs are subtracted from spectra corresponding block-averaged cross spectra from the
obtained from data runs to remove the noise floor in frequency datausing
the measurements.
Data Analysis: It was desired to build a highly
distributed processing configuration to handle the
problem of array analysis given the volume of data = G22 • :
involved (greater than 500 Gbytes) and the amount of *°
time requiredtoprocess asingle test point ofdata from
(6a)
start to finish (typically 30-60 minutes per set on a
200-MHz Pentium-Pro machine). There are a number with
ofvarious platforms and operating systems used in the
processing of the array data, including a cluster of
N
three 200-MHz NT-based Pentium-Pro workstations, a = l zt=l[X_(f)Xit(f) ]
(6b)
500-MHz Alpha workstation running UNIX, and the
Langley SP2 supercluster consisting of 48 IBM
RS/6000 workstations. This heterogeneous cluster of where W_is the data window weighting constant, N is
hardware systems is controlled from a single Pentium- the number of blocks of data, andA_"represents an FFT
Pro workstation using a custom control panel program data block. The lower triangular elements of the
and a series of device independent configuration files matrix areformed by taking the complex conjugates of
readable bythe individual processing codes located on the upper triangular elements (allowed because the
each ofthe various hardware platforms. cross spectralmatrix isHermitian).
All cross spectral matrix elements are employed in
Data Post-Processing Procedure subsequent processing, with no modification of the
diagonal terms. Note that for in-flow arrays, the
Processing steps common to both arrays include the diagonal terms can be removed to improve the spectral
construction of cross spectral matrices from the raw dynamic range by subtracting off seLf-noise dominated
time data and the calculation of amplitude and time auto-spectra during the beamforming process, as
delay corrections to account for shear layer refraction. described in References 14 through 16. However, for
Classical beamformer processing algorithms are the airframe noise measurements described here, this
utilized in the generation of noise images, spectra, and step was not required since all array microphones are
directivity information. In addition, the SADA outside of the flow.
processing incorporates a unique shading algorithm
which provides a constant beamwidth independent of 3-D Shear Layer Refraction Correction: Testing in
frequency. an open-jet facility requires that the effect of the shear
layer on the propagation of the noise (both intensity
Computation of Cross Spectral Matrices: An and retarded time) from sources located in the jet to
M byM cross spectral matrix, where M is the total microphones located outside the jet be accounted for.
number of microphones in the array, is first The first challenge was to develop a technique for
constructed for each data set (both background and dealing with the highly three dimensional, curved
_e component test condition). The formation of shear layer present in the installation. The approach
the individual matrix elements is achieved through the taken was to acquire five-hole pitot probe
use of Fast Fourier Transforms (FFT). This is done measurements on boththe pressure and suction sides of
after convening the raw data to engineering units the airframe model to map out the velocity field. The
(Pascals) using sensitivity data based on a microphone shear layer position was defined to be the half mean
calibration using a frequency of 1kHz. Each channel velocity position. This data was then fitted with a
ofengineering unit datais then segmented into a series three dimensional surface to provide a continuous
of non-overlapping blocks each containing 8192 representation of the shear layer for each of the flow
samples, yielding a frequency resolution of 17.45 I-Iz conditions examined. With the shear layer position
for the 142.857 H-Izacquisition sampling rate. Using defined, amplitude and phase corrections were
6
American Institute of Aeronautics and Astronautics
determineudsingthe approachof Sctdinkearnd with
Amie=t andAmie_.
=3/(1_ Mo c0s(_2))2 _c0s2(_2 )
Thekeytofindingthe retarded time and phase
corrections isto find the intersection of the source ray
sin0_c
path with the shear layer, as illustrated in Figure 11.
O_1--
An iterative process is used, using the following sin _2
relationship between the source emission angle, qh,the
E/ 3I]
ray angle, 0, and the free jet Mach number,Mo
h -1 +1
6 2 =
r_c sin0_c
tan(O)= sin(_,_)
Mo+cos(¢,_)
(7)
and SneU's law
(II)
cos(_h)
cos(q,2) = wherepcisthe correctedpressure,]7=is the measured
1+Mo cos(_])
(8) pressure,h is the distance from sourceto shearlayer,
and 0.,_ is the measuredangle of the microphone
where the subscripts 1and 2 refer toangles inside and relative tothe flow direction.
outside of the jet, respectively, and the sound speeds Forthe low frequency correction, the reflected wave
inside and outside the jet are assumed equal. Once the amplitude cannot be neglected when the wavelength is
ray path-shear layer intersection isknown, the retarded of the same length as the shear layer thickness. In this
time difference and hence the phase can be computed case the amplitude correction isfound tobe
from
_ Pc _] 2
P=
k co )
(9) [_@_ +(1- Mocos(¢,O)21
(12)
where r_=r_+r2 is the wavefront travel distance
Examples of the calibration and use of the shear
(relative to the convecting flow inside the je0, and r=i¢
correction algorithms are shown subsequently.
is the line-of-sight distance from the source to the
microphone.
Beamforming: A classical beamforming approach
The amplitude corrections are based upon analysis
is used for the analysis which eliminates instabilities
of arectangular shear layer. There aretwo corrections
and potential matrix singularity problems found in
provided in Reference 22, namely a thick shear layer
adaptive techniques. The basic procedure consists of
(high frequency) correction and athin shear layer 0ow
electronically steering the array to a predefined series
frequency) correction. The appropriate correction is
of locations in space, as shown in Figure 12. These
determined by the ratio of the source acoustic
locations define aplane which canbe positioned in any
wavelength to the shear layer thickness. The
orientation in front of the array. For each selected
assumption in developing the thick shear layer
steering location, a steering matrix containing one
correction isthat the shear layer issufficiently thick for
entry for each microphone in the arrayis computed as
geometricalacousticstoapplysothat (1) the acoustic
follows:
energy is conserved along the ray tube, and (2) sound
pressure is the result of outgoing waves only since
reflections are absent in the geometrical acoustics
limit. As supplied in References 22 and 23, the ratioof
the corrected to measured sound pressure for
microphone m, including the astigmatism and distance (13)
correction, isfound tobe
where x is the distance from the steering location to
each microphone, Am is the shear layer amplitude
P= ".'_w2 ,',"_ _in(,,2) (10) correction formicrophone musing either equation (10)
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American Institute of Aeronautics and Astronautics
or (12),and oJdt_,s,_, is the shear layer phase
W1= 0-0.875
correction for microphone m at frequency oJ. The
W2 = 1-- 00.875 0 <o-_ <1
factor (r°/r,°) is included to normalize the amplitude
w3=0
An, to that of the array xc position. Using
equation (13) and the cross spectral matrix computed wl=0
p_ciously, the steered array output power spectnLm at W2 ----0-0.875 0<or 2<1
the steering location isobtained via
W3 = 1-- 0-O.875
w_=l
P(_) =
M" (14) W2 =0 0-1>1 and 0-2> 1
w3 =0
(15)
where the T denotes the conjugate transpose of the
matrix. Note that abackground subtraction process is withthe shading coefficients defined by
explicitly denoted in equation (14). The background
spectra is that obtained without tunnel flow, where the kD2- kDo
acquisition system noise dominates the recorded _=
output. The division by the number of microphones M
serves to reference the array output spectrum levels to
0-2=
equivalent single microphone output levels.
(16)
Equation(14) represents the steered response power
spectrum over the full range of single narrowband Thevalue of kD0for this studyis 36.38, corresponding
frequencies. If a wider bandwidth is desired (such as to frequencies of 10, 20, and 40 kHz for clusters 3, 2,
an Octave Band), the power (pressure-squared values) and 1, respectively (assuming a speed of sound of
of the narrowbands is summed. Note that wider
1126fl/sec). This causes the SADA to yield the same
bandwidths are not formed prior to the completion of
effective resolution for all frequencies hetween 10 and
the vectorial (or complex) operations of equation (14).
40 kHz, with smooth blending among frequencies.
This prevents possible significant bias errors in
The exponent of the coefficients, 0.875, was found to
summing across phase-shifted cross spectral bands. differslightly from the arrayofReferences 12and 13.
Figure 13 illustrates modified theoretical array
SADA Shading Algorithm: The use of the SADA
responses forthe SADA forfrequencies of 10, 12.5, 15
for directivity and spectral measurements requires that
and 17.5 kHz, using equations (4) and (5) with the
the beamwidth he invariant under steering angle and
shadings of equation (15) substituted for thew,_ term.
frequency changes, thereby providing a constant
Comparing the responses with those shown in
sensing area over noise source regions. The method
Figure 8, note that the responses for 10, 20, and
used to accomplish this is similar to previous
40 kHzare now identical, as are the ones for 12.5 and
techniques described in Reference 12 and 13. The
25, 15 and 30, and 17.5 and 35 kHz. This clearly
SADA microphones are divided into three clusters
illustrates the fiequency-invariant main and side lobe
containing 17microphones each. These clusters along
structurenow exhibited bythe array. Figure 14 shows
with their maximum diagonal aperture sizes areshown
in Table 3. Each cluster exhibits the same directional a beamwidth plot for the shaded array. At higher
frequencies the beamwidth, while invariant, now takes
characteristics for a given wavenumber-length product
on the value exhibited at the kDs wavenumber-length
kD_,where kisthe wavenumber and D, is the diagonal
distance between the elements of the n-th cluster. The product. In a sense the higher frequency beamwidths
have been sacrificed to achieve frequency invariance.
method used to achieve the invariant sensing area
This isan acceptable trade-off; however, since accurate
consists of shading (or weighting) the arrayclusters as
source directivity data can only be obtained over a
a function of frequency. The microphone cluster
broad frequency range ff the sensing area of the array
shadings arecalculated asfollows:
isheld constant.
To extract noise spectra and directivity from data
obtained with the SADA, the classical beamfonning
w2 =0 0-1<0 and ty2 <0 technique is employed with minor variations. First, a
wt =0 ]
w3 =1 single steering location is chosen for the array, which
is itself positioned at various elevation and azimuth
8
American Institute of Aeronautics and Astronautics