NASA Technical Reports Server (NTRS) 20040086840: Effect of Directional Array Size on the Measurement of Airframe Noise Components

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by  NASA Technical Reports Server (NTRS)

AIAA
EFFECT OF DIRECTIONAL ARRAY SIZE ON THE
MEASUREMENT OF AIRFRAME NOISE COMPONENTS
Thomas F. Brooks and William M. Humphreys, Jr.
NASA Langley Research Center
Hampton, Virginia
AIAA Paper No. 99-1958
Presented at the
Fifth AIAA/CEAS Aeroacoustics Conference
May 10-12, 1999
Bellevue, Washington
AIAA-99-1958
Effect of Directional Array Size On The Measurement of Airframe Noise Components
Thomas F. Brooks*
William M. Humphreys, Jr.†
NASA Langley Research Center
Hampton, Virginia 23681-0001
A BSTRACT purpose diagonal-removal processing in obtaining inte-
grated results is apparently dependent in part on source
A study was conducted to examine the effects of
distribution. Also discussed is the fact that extended
overall size of directional (or phased) arrays on the
sources are subject to substantial measurement error,
measurement of aeroacoustic components. An airframe
especially for large arrays.
model was mounted in the potential core of an open-jet
windtunnel, with the directional arrays located outside S YMBOLS
the flow in an anechoic environment. Two array sys-
A shear layer refraction amplitude correction
tems were used; one with a solid measurement angle m
that encompasses 31.6(cid:176) of source directivity and a for mth microphone
smaller one that encompasses 7.2(cid:176) . The arrays, and co speed of sound, ft/sec
sub-arrays of various sizes, measured noise from a C normalizing factor in integration equation,
l,n
calibrator source and flap edge model setups. In these Eq.(5)
cases, noise was emitted from relatively small, but dB sound pressure level, (ref. to 2· 10- 5 Pa)
finite size source regions, with intense levels compared
D dB reduction in level due to array/source size
to other sources. Although the larger arrays revealed L
much more source region detail, the measured source effect
levels were substantially reduced due to finer resolution D dBS reduction in level due to turbulence
compared to that of the smaller arrays. To better under- scattering
stand the measurements quantitatively, an analytical eˆ steering matrix, see Eq. (2)
model was used to define the basic relationships
f frequency, cycles/sec
between array to source region sizes and measured out-
ˆ
G cross-spectral matrix
put level. Also, the effect of noise scattering by shear
layer turbulence was examined using the present data G cross spectra between i th and jth
ij
and those of previous studies. Taken together, the two microphones, see Eq. (1)
effects were sufficient to explain spectral level differ- k wavenumber (=w /c ), ft- 1
o
ences between arrays of different sizes. An important
l integer
result of this study is that total (integrated) noise source
levels are retrievable and the levels are independent of L analytical model source length, ft
the array size as long as certain experimental and proc- m total number of microphones in array
0
essing criteria are met. The criteria for both open and
M tunnel free-jet Mach no. (=tunnel
closed tunnels are discussed. The success of special velocity/c )
o
n integer

*Senior Research Scientist, Aeroacoustics Branch, Associate N number of blocks of data
Fellow AIAA. p pressure, Pascals
†Research Scientist, Advanced Measurement and Diagnostics P array output power, mean square pressure,
Branch, Senior Member AIAA.
(cid:230) (cid:246)
Copyright © 1999 by the American Institute of Aeronautics and Ł p2ł
Astronautics, Inc. No copyright is asserted in the United States under
Title 17, U.S. Code. The U.S. Government has a royalty-free license Ql¢,n¢ sum of unit influences over integration
to exercise all rights under the copyright claimed herein for
region, see Eq. (5)
government purposes. All other rights are reserved by the copyright
owner. r radial distance, ft
1
American Institute of Aeronautics and Astronautics
r distance to center of array, ft, see Eq. (2) determining source distributions about models requires
c
R distance from source to array surface, ft mechanical movement of these sometimes very large
systems. These systems are still found to be useful
t time, sec
even today, especially in some larger test facilities6,7.
w microphone weighting Also in the 1970’s, measurements involving directional
Wˆ array weighting or shading matrix (or phased) arrays of microphones were examined8,9
Ws spectral window weighting constant using time delay and sum techniques. By adjusting for
propagation time delays from particular source loca-
X , X kth FFT data block for ith and jth
ik jk tions to the microphones, one is able to localize noise
microphones
r production in basically an equivalent fashion to that of
x location, ft the acoustic mirror approach, without the requirement
x, y coordinates of scanning plane, ft to mechanically move the system. In the 1980’s and
d free-jet shear layer thickness, ft early 1990’s, an array technique using a frequency
domain processing approach was introduced10,11 for a
f elevation (or streamwise) angle, deg
rotor noise application. Additional array applications
l acoustic wavelength, ft for aeroacoustic measurements were made using time
q array size in terms of solid collection angle domain12 and frequency domain13,14 approaches. In
DA
with respect to the source position, deg the mid 1990’s, the use of arrays expanded. Using a
q offset angle of array with respect to the ground array in a field study, flyover noise measure-
0
center of the analytical line source, deg ments of airframe noise have been made on landing
aircraft in spite of the presence of engine noise15. For
w frequency, rad/sec
windtunnels, sophisticated array acquisition and proc-
wD t shear layer phase correction for w , radians, essing systems were built for Boeing and NASA for
see Eq. (2) closed16 and open17 tunnel facilities. Efforts have been
y azimuthal (or sideline) angle, deg made to optimize array design and processing18,19,20,
particularly to suppress array sidelobe interference in
S ubscripts and Superscripts: order to increase signal-to-noise and to reduce ambigu-
ity in array results. Processing presently uses classical
L lower limit
beamforming approaches in the frequency domain
T subscript denotes complex transpose of
using cross-spectral matrices and robust steering algo-
matrix rithm codes16,17,21. Recent array applications have been
U upper limit conducted in the NASA Ames 40· 80 ft.7 and 7· 10 ft.22
tunnels, as well as in Boeing-Seattle’s LSAF23 tunnel.
I NTRODUCTION
The studies, sited above, address array
Single microphone measurements of aeroacoustic
development and methodology as well as the measured
sources can be naturally hindered by poor signal-to-
results of aeroacoustic testing. However, the array
noise and by the inability to distinguish contributions
literature fails to address how one obtains correct
from different source locations. This is especially true source amplitude. Mosher24 pointed this out in an
for model tests of airframe noise because the sources
extensive review of methodology. In aeroacoustics, the
are non-propulsive and their magnitudes are similar in
absolute level is important. A “perfect” array system
intensity level to test setup and tunnel noise sources. In
would be able to determine correct location and
the case of single airfoil-elements, it was found possible
amplitude of all sources under all conditions. Of course,
to localize and quantify trailing edge noise using distri-
such an array is impossible. For example, a proposal
butions of individual microphones—but with process-
that arrays, given enough microphones and expanse,
ing techniques involving cross-spectral and coherent-
can reconstruct the noise source distribution within a
power-output methods1,2. However, these techniques
region of space by surveying grid points electronically
become cumbersome when studying multiple element
within the region is simply incorrect. Based on the
sources. Starting in the same time frame (in the late Kirchhoff integral equation25 from fundamental
1970’s) “acoustic mirror” systems3,4,5 were able to
acoustics theory, one cannot uniquely define interior
localize and, in number of cases, quantify the noise
noise sources knowing only what occurs at the
produced. For elliptic mirrors, a microphone is fixed at
boundary of the region. Then, certainly, neither could
one elliptic focal point and the other focal point is
an array that encompasses only a small portion of such
placed in the source region of interest. However,
a boundary. In aeroacoustics, source distributions can
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be combinations of monopole, dipole, and quadrupole In the following sections, the testing and process-
type sources. In order to construct a source ing approaches are defined and the processed data are
distribution, one must hypothesize source types and then presented for three noise source configurations.
geometry. Normally this is taken as a distribution of Analyses are then given.
simple monopoles—with the additional provision that
A IRFRAME COMPONENT TEST AND
the monopoles be broadband-random and mutually
P ROCESSING
independent. The array data is then processed using
such assumptions. The extent to which such T est Setup and Method
assumptions are true, or can be modeled as being true
The tests were conducted in the Quiet Flow
for a particular noise source, should determine whether
Facility (QFF) at Langley Research Center. The QFF is
the array gives a true measure of the phenomena under
a quiet open-jet facility designed for anechoic acoustic
study.
testing. For the present airframe model testing, a 2 by
Calibrations of arrays typically involve measuring 3-foot rectangular open-jet nozzle was used. The 3-foot
noise from a small source (to approximate a point span model was mounted between two side plates that
source) in an anechoic field.26 It is then established were attached to sides of the nozzle exit. In Fig. 1, the
that the processed output of the array, when focussing model is visible through the Plexiglas windows located
or beamforming directly on the source, gives the same on the side-plates. The high-lift wing model is an
output as would a single microphone. Other focus instrumented NACA 63 -215 main element airfoil with
2
points would give the output predicted from linear the- a 30 percent chord half-span Fowler flap. This is
ory for the array geometry and source location. With approximately a 6 percent of a full-scale configuration,
this, it would appear that correct source levels could be with a main element chordlength of 16 inches and a flap
measured if the sources are small, separate, incoherent, chordlength of 4.5 inches. For the data presented, the
omni-directional and without high noise contamination. main element was aligned at 16(cid:176) angle of attack to the
Others, such as distributed incoherent sources, have undisturbed flow and the flap was at 39(cid:176) relative to the
been taken (assumed) as being able to be measured cor- main element. The noise source configurations studied
rectly24. Even this basic proposition has not been vali-
dated. An illustration of uncertainty in amplitude
measurement is contained in a study by Storms, et al.22
Spectra are presented from a large and a small array for
a series of flap edge and slat noise phenomena. The
levels measured by the small array were consistently
higher (by some 6 dB at about 13 kHz). The spectra
were obtained by volume integrations about the noise
producing regions. The difference in levels were
attributed to the difference in array size and a noise
scatter effect from turbulence within the boundary layer
of the wall, where the microphones are mounted.
The purpose of the present study is to help estab-
lish the effect of array size on the quantitative meas-
urement of aeroacoustic sources. The arrays are
mounted outside the flow in the anechoic free field.
Noise directivity field variations over arrays of different
sizes are determined. The measured noise sources are
small but finite sized, with sufficient intensity com-
pared to extraneous sources, so that the effects of rela-
tive size of the arrays and the source are clear. An
analytical model of the array to source size effect is
studied, as well as the effect of scatter due to shear
layer turbulence. By using an integration approach over
the noise regions, the degree to which each array can
recover the energy of the source regions is determined. Figure 1. LADA mounted in the QFF on pressure side
Implications of the results of the analysis are discussed. of model.
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American Institute of Aeronautics and Astronautics
are flap edges, with flat and contoured geometries, and 33 B&K model 4133, 1/8-inch microphones projecting
a calibrator source placed next to the flap edge. from an acoustically treated aluminum frame. The
Additional model, facility, and array details can be array pattern incorporates four irregular circles of eight
found in Refs. 27 and 17. microphones each and one microphone at the center of
the array. Each circle is twice the diameter of the circle
The Large Aperture Directional Array (LADA)
it encloses. The maximum radius of the array is 3.89
was developed to identify dominant noise sources by
inches. With the SADA positioned 5 foot from the
producing high spatial resolution noise source localiza-
model, solid collection angles of q =1.8(cid:176) , 3.6(cid:176) , and
tion maps along the airfoil surface. In Fig. 1, the DA
7.2(cid:176) are defined by the inner, middle, and outer sub-
LADA is shown mounted on the pressure side of the
arrays. Because of the need (for the directivity meas-
model—positioned 5 feet from the mid-span of the air-
urements) to keep the array resolution constant and
foil main-element trailing edge. It is constructed of a
independent of frequency, special blended processing is
4-foot diameter fiberglass panel to provide a flat surface
used for the SADA. This effectively makes q a
to flush mount all microphones. The LADA incorpo- DA
function of frequency (inversely proportional to
rates 35 B&K model 4135 1/4-inch microphones,
frequency).
spaced logarithmically in spiral patterns. The pattern
design was based on one by Boeing20. It has five In Fig. 3, the SADA measurement positions for
spirals of seven microphones each with the innermost zero azimuthal angle (y = 0(cid:176) ) are drawn in a side view
microphones lying on a 1-inch radius and the outer- (opposite side to that of Fig. 2) of the test setup. The
most on a 17-inch radius. With this radius, the array position of SADA in the photo of Fig. 2 corresponds to
encompasses 31.6(cid:176) of solid collection angle. The solid elevation angle f = - 124(cid:176) in the drawing. For this
angle, designated as q DA, is a key parameter of this paper, measurements for the pressure side are pre-
study. Sub-array groupings of the microphones of sented. In Fig. 3, the SADA is seen positioned at
different radii are used in the analysis of the present f = 107(cid:176) and an inset of the microphone-coverage
study. The sub-array sizes are q DA= 2.0(cid:176) , 9.9(cid:176) , 16.9(cid:176) , region of the LADA is shown superimposed at its own
25.5(cid:176) , and 31.6(cid:176) , which are defined by LADA’s inner 5, f = 106(cid:176) position. In practice, the two systems were
10, 15, 25, and 35 microphones, respectively. never operated together. The open jet shear layer
boundaries (defined at 10 and 90 % of the potential core
The Small Aperture Directional Array (SADA) is
velocity) are shown as measured along the y = 0(cid:176)
used to measure the acoustic directivity and spectra of
plane. A mean shear line or surface is shown, which is
selected portions of the wing-flap model. SADA is
part of a curved three-dimensional mean shear surface
shown in Fig. 2 mounted on a pivotal boom on the suc-
defined mathematically from the shear layer
tion side of the model. The pivotal boom is moved to
position SADA about the model for the directivity
f = –39°
measurements. The aperture of the array is small in
order that all microphones in the array remain within –56° f = 56°
approximately the same model noise directivity at any
elevation or azimuth position. The SADA consists of –73° 73°
TURBULENT POTENTIAL
–90° SHEAR LAYER CORE MEAN 90°
REFLECTED
RAY PATH
MEAN SHEAR
LINE
SADA
–107° MODEL SCARTATYESRED 107°
LADA
–124° SIDE PLATE 124°
NOZZLE
141°
Figure 3. Scale drawing of test setup and shear layer.
Figure 2. SADA mounted on pivotal boom in the QFF Noise ray paths from the source to the microphones are
on suction side of model. illustrated.
4
American Institute of Aeronautics and Astronautics
measurements. This is mentioned with regard to the where W is the data-window weighting constant, N is
s
beamformer solution to follow. Also illustrated, in Fig. the number of blocks of data, and X represents an FFT
3, are scattered noise ray paths, which are dealt with in data block. The full matrix is, with m being the
0
the analysis section. number of microphones
D ata Acquisition and Post-Processing Ø G G L G ø
11 12 1m
Œ 0 œ
G M
As described in Ref. 17, both arrays employed Gˆ =Œ 22 œ (1b)
Œ O M œ
acquisition hardware consisting of transient data
Œ œ
recorders controlled by a workstation. All data channels ºŒ Gm0m0ßœ
were simultaneously recorded with a 14-bit dynamic
range at a sampling rate of 142.857 kHz. Two million The lower triangular elements of this Hermitian matrix
2-byte samples were taken for each acquisition. The are determined from taking the complex conjugates of
signals from each microphone channel were condi- the upper triangular elements.
tioned with high pass filters set to 300 Hz and with anti- B eamforming
aliasing filters set at 50 kHz, which is substantially
below the 71.43 kHz Nyquist frequency. A conventional beamforming approach is used to
electronically “steer” the array to chosen noise source
Microphone calibration data were accounted for in locations. For each selected steering location, a steering
post-processing. For the SADA, regular pistonphone vector containing an entry for each microphone in the
and injection calibrations were made for all the individ- array is defined as
ual microphones. The manufacturer specifications for Ø r { [(r r ) ]} ø
frequency responses, based on mounting technique, Œ A1 1 exp j k(cid:215) x1 +w D t1,shear œ
were used for both the SADA and LADA. For the Œ rc œ
LinAdiDvAid,u bale cpaiustsoen opfh othnee dciaflfiibcrualttiyo nosf apnedrf oarcmcoinugn trineggu floarr eˆ=ŒŒ A rm0 exp{j[(kr(cid:215) xMr )+w D t ]}œœ (2)
Œ m m m ,shear œ
flush-mounting details of the microphones, a calibration º 0 rc 0 0 ß
procedure somewhat similar to that of Ref. 26 was r r
used. Here, the in situ responses to reference sources where k is the acoustic wave vector, x m is the distance
were compared to isolated free-field measurements. vector from the steering location to each microphone m,
The phase response, for all individual microphones, and w is the frequency, in radians/sec, (=2p f ).
was adjusted by small time delay offsets in the beam-
Equation (2) contains terms to account for mean
form processing. For the amplitude response, a single
amplitude and phase changes due to refracted sound
amplitude calibration adjustment was used, for all
microphones and frequencies, based on comparison of transmission through the shear layer to the individual
matched single and multiple microphone groups of the microphones of the arrays. A mean refracted ray path
acoustically treated SADA.
is illustrated in Fig. 3. The correction terms are
Post processing of the data begins with the com- calculated17 by the use of Snell’s law in Amiet’s
putation of the cross-spectral matrix for each data set.
method28,29, adapted to a curved three-dimensional
The computation of the individual matrix elements is
mean shear surface defined in the shear layer. In
performed using Fast Fourier Transforms (FFT) of the
original data ensemble. This is done after converting Eq. (2), the ratio (rm / rc) is included to normalize the
the raw data to engineering units. The time data is seg- distance related amplitude to that of the center
mented into a series of non-overlapping blocks
microphone at r . A is the refraction amplitude
c m
(244 blocks for the present data) each containing
correction. Correspondingly, wD t is the phase
8192 samples. Using a Hamming window, each of these m,shear
blocks of data is Fourier transformed into the frequency correction for microphone m. (D tm,shear is the additional
domain with a frequency resolution of 17.45 Hz. The time (compared to a direct path) it takes an acoustic ray
individual cross spectrum for microphones i and j are
to travel to a microphone from the steering location,
G (f)= 1 (cid:229)N[X*(f)X (f)] (1a) due to the convection by the open jet flow and
ij ik jk refraction by the shear layer.) Equation (2) corrects
NWs k=1
details of the corresponding equation in Ref. 17.
5
American Institute of Aeronautics and Astronautics
The output power spectrum (or response) of the A modified form of Eq. (4) is commonly used24 to
array at the steering location is obtained from
improve dynamic range of the array results in bad
signal-to-noise tunnel applications. The primary intent
( ) eˆTGˆeˆ
P eˆ = (3) is to remove microphone self noise (or pseudo-noise)
m2
0 contamination. This involves removing the diagonal
ˆ
terms of G and accounting for the change in the
where the subscript T denotes a complex transpose of ˆ
( ) number of terms of G in the denominator. For this
the matrix. Here P eˆ is a mean-squared-pressure
case, the beamform patterns are modified from that of
quantity. Note that the cross-spectral matrix normally
Eq. (4). This “diagonal-removal” method is, at least as
has a corresponding background matrix subtracted from
it to improve fidelity17. The division by the number of defined in this paper.
microphones-squared serves to reference levels to an
equivalent single microphone measurement. P(eˆ) is P(eˆ)= eˆTWˆGˆdiag=0WˆTeˆ (4a)
determined for each narrowband frequency (here at (cid:230) m (cid:246) 2 (cid:230) m (cid:246)
17.45 Hz resolution bandwidth) of interest. Wider Ł(cid:231) (cid:229) 0wmł(cid:247) - (cid:229)Ł(cid:231) 0wmł(cid:247)
m=1 m=1
bands are obtained by summing power, after the
operations of Eq. (3) are performed.
S ource Region Integration
For the SADA, a special shading algorithm is nor-
mally used when directivity and spectral measurements For this paper, the array response is determined,
are made. This keeps the array beamwidth invariant, using Eq. (4), for a range (grid) of steering (or scan-
thereby providing a constant sensing area over noise ning) locations over a plane that is positioned through
source regions17,10. This prevents the need to correct the airfoil main element. For particular frequencies,
measured levels, because resolution (sensing area) does contours of the response levels are plotted over the
not change with frequency and it is large enough to plane. In the case of an ideal point source in the plane
enclose the source regions of interest. In this blending (in free space without reflections), the contour would
application, the inner microphone groups (or sub- have the appearance of the theoretical array beampat-
arrays) are made inactive at low frequencies and the tern projected onto the plane. The point source location
outer microphones are made inactive at high frequen- would exhibit the maximum level, representing the total
cies. The resultant shaded or blended steered response output of the source. In the case of distributed sources,
is the total output must result from an integration over a
specified source region. However, in the integration the
( ) eˆTWˆGˆWˆTeˆ
P eˆ = (4) mutual summed influence of the distributed sources,
(cid:230)Ł(cid:231) m(cid:229) 0wm(cid:246)ł(cid:247) 2 etaakcehn winittho iatcsc oowunnt a(orrra nyo rremlaatleizde db eoaumt)p.a tTtehrins, cmouulsdt bbee
m=1
viewed as a way to avoid “double-counting” of source
where w is the frequency dependent shading (or contributions. The following integration approach
m
ˆ accounts for these influences in a systematic way by
weighting) for each microphone m. Wis a row matrix
incorporating the beamformer algorithm.
containing the w terms. For the blended case of the
m
SADA, the number of active microphones is always 17, We define the coordinates of grid points in a scan-
so the denominator is (17)2. Note that for the present ning plane as (x,y)=(x +(l)D x,y +(nD) y), where D x
0 0
paper, the weighting terms are used for both the SADA and D y are grid spacing and l and n are integers.
and LADA to define sub-arrays of different sizes, The integration region covers the area de-
( ) ( ) ( )
although frequency invariant beamforming was not fined by x + l D x to x l D x and y + n D y to
0 L 0 U 0 L
( )
applied to the LADA. When all w terms are set to one y + n D y. The integration approach is readily
m 0 U
and W becomes an identity matrix, all microphones are accomplished over a volume but is introduced here over
fully active in the beamforming. a plane for simplicity. At these grid points, let P
l,n
6
American Institute of Aeronautics and Astronautics
( )
represent P eˆ . Let P be the integrated (mean- integration by simply expanding the summation to
T
stacked multiple scanning planes.
squared-pressure) output of the region, which is
P = (cid:229)lU n(cid:229) U[P C ] An equivalent to Eq. (4a) can be obtained for
T l,n l,n Eq. (5). For this “diagonal-removal” method, P is
l=l n=n T
L L obtained by Eq. (5), except that Q becomes
Ø l¢ n¢ ø l¢,n¢
Cl,n =ºŒŒ lØ¢(cid:229)=UlL¢ n¢(cid:229)=UnLQ¢ l¢,n¢ ßœœ lø,n Ql¢,n¢ =ØŒŒŒŒ (cid:230)eˆTmWˆ(Gˆl¢(cid:246),n2)dia(cid:230)g=m0WˆTe(cid:246)ˆøœœœœ (5a)
Œ œ Œ (cid:231) (cid:229) 0w (cid:247) - (cid:229)(cid:231) 0w (cid:247) œ
Ql¢,n¢ =ŒŒŒ eˆT(cid:230) WmˆGˆl¢,nW(cid:246)ˆ2Teˆœœœœ (5) º Ł m=1 mł Ł m=1 mł ß l¢,n¢
Œ (cid:231) (cid:229) 0w (cid:247) œ In the analysis of results section, Eq. (5) and its related
Ł mł
º m=1 ß l¢,n¢ simplified method are used and evaluated.
Ø ( )- 1 ( -) 1 ( - ) 1 ø M EASURED RESULTS
Œ e1*e1 e1*e2 L e1*em œ
Œ ( )- 1 0 œ S ADA Free-Field Directivity
Gˆl¢,n =ŒŒ e2*e2 O MM œœ For the SADA at the f = 107(cid:176) position, Fig. 4 shows a
Œ ( )- 1œ theoretical contour plot over the model of the spatial
Œ e* e œ noise admittance (or negative rejection) in dB level.
º m m ß
0 0 l,n
The array is steered to the intersection of the airfoil
It is seen that P is determined by summing the values main element and the flap edge. The effective sensing
T
P after being normalized by corresponding C area is defined as that region within the - 3 dB contour
l,n l,n on the main beampattern lobe. The rejection of
values . C accounts for the integrated beampattern
l,n
characteristics of the array over the region with respect
to the l,n location. It is the sum of unit influences
Ql¢,n¢ from all other locations in the region. The use of --1188
--1188
inverses of the l,n-location steering vectors in the
Sideplates
synthesized cross-spectral matrix Gˆ¢ accounts for the
l,n
beamform characteristics, including side lobe inclusion
and shear layer correction. A roughly uniform
distributed source strength is assumed over the
Flap
integration region, although the sides of the main
beampattern may extend beyond. One could simplify --1188
--33
the above calculations by using a representative --66
C to replace the individual values of C . This is
l0,n0 l,n --1188
especially appropriate for compact sources and reduces
computation time greatly. The use of C Airfoil
l0,n0 --1188
(simplified method) should be equivalent to integration
24
methods that have been employed by Mosher and
Flow
Dougherty. Equation (5) is not exact, but should
--99
produce good results as long as the integration area
--99
contains no significant contributions, including portions
--1188
of main lobes or side lobes, from sources outside the
area. The procedure implicitly assumes that the source Nozzle Opening
regions are comprised only of a distribution of
statistically independent (uncorrelated) point noise Figure 4. SADA admittance contour map over model
sources, where spatially pressure-squared summing is pressure side. This is a “bird’s eye” view of model test
apparatus from the SADA.
appropriate. Equation (5) can be used for volume
7
American Institute of Aeronautics and Astronautics
(extraneous) noise regions over the side plates and and contoured edge configurations are shown. The
nozzle opening is also shown. The contour is for the calibrator source is the open end of a one-inch diameter
frequencies 10, 20, and 40 kHz. For frequencies tube, which for low frequencies should approximate a
between these, the blended processing keeps the simple monopole source. When the calibrator source is
sensing area approximately the same as that shown27. not present, the edges are the noise producing regions
At lower and higher frequencies than this range, the of the flap (this edge noise is of primary interest in the
sensing area becomes wider and narrower, respectively. study of the airframe noise problem). In Fig. 6, the
Therefore, over a broad range of frequencies, the outlines of the SADA and the microphone-coverage
spectral output of the SADA should represent only that region of the LADA are superimposed. This is
noise which is radiated from the flap-edge region. intended to show the positions used for most of the data
Noise directivity is mapped by placing the SADA at a presented in this paper and the directivity variations
series of elevation and azimuthal angles. present over the face of the arrays.
Figure 5 shows the model with the flap-edge direc- For the calibrator source, both the M=0 and 0.17
tivity contour mapped over a spherical surface, defined directivities show “hot spots” on the azimuthal side
by the SADA positions. The measurements are for a which is opposite the flap. This is an apparent reflec-
flap, with a flat cutoff-shaped edge, placed at a 39(cid:176) tion/shielding effect due to the source position being
angle to the main wing element. For the 6.3 kHz one- next to and slightly behind the flap edge. Except at the
third octave frequency band shown, the directivity on high frequencies, the basic directivity characteristics do
the pressure (flyover) side of the model is most intense not seem to be substantially affected by the flow. This
“underneath” the model. On the suction side of the tendency will be used in the analysis of turbulent shear-
model, the levels are less but are seen to increase in the layer noise scatter subsequently. For the flat and
downstream direction. Figure 6 are pressure-side contoured flap-edge configurations, the directivities are
directivity maps for different frequencies. These maps generally uniform at lower frequencies. At higher fre-
are the flattened spherical surfaces shown in Fig. 5. The quencies, however, stronger variations are seen. In the
positive azimuthal angles y are on the flap side of the later sections, the spectral results from the LADA are to
model. The elevation angles f with the smaller values be compared to that of the SADA—to examine the
(at the top of the plots) are in the downstream direction. effect of array size. These directivity results, as well as
For each set of three one-third-octave directivity maps, those of the point source, suggest that such comparisons
sketches of the respective calibrator source, flat edge, are proper because the levels at the SADA appear to
approximate some “average” of levels over the face of
the LADA. This conclusion assumes that no significant
Pressure Side phase variations occur over the face of the LADA. A
limited review of phase data did not reveal any signifi-
70
69 cant variations.
FLOW 71
68 S ource Distribution and Spectra for Different Array
72 S izes
Flap
67 Edge Figure 7 shows SADA and LADA source distribu-
tion contour maps for the model configurations at dif-
66 72
ferent tunnel speeds. The levels shown are for the 40
65 Main kHz one-third octave band. The LADA is using all 35
64 Element 71 microphones, so q DA = 31.6(cid:176) , and at this frequency,
70 q DA = 1.8(cid:176) , for the SADA. The contours were created
63 by electronically steering (focussing) to predefined grid
points, spaced 1/4 inch apart, on a plane projected
Suction Side
through the chordline of the main-element model.
For the calibrator source for M=0, the LADA gives
Directivity
a well-defined contour that clearly locates the source
Surface
alongside the flap edge. The dynamic range over the
Figure 5. Directivity contour levels over “surfaces“ spatial region (about 13 dB) is good and side lobes are
defined by SADA measurements. One-third octave seen to be projected to within 4 inches of the main lobe
levels for f1/3 =6.3 kHz. at the source. The SADA contour is dominated by the
8
American Institute of Aeronautics and Astronautics
CALIBRATORSOURCE CALIBRATORSOURCE FLATFLAPEDGE CONTOURED
M=0.0 M=0.17 M=0.17 FLAPEDGE
M=0.17
FLAP FLAP FLAP FLAP
MAINELEMENT MAINELEMENT MAINELEMENT MAINELEMENT
56 56 12.5kHz 56 56 12.5kHz
74 63 72
65
73 77 73 68 73 66 73 74
78 75 79 67 73
f 90 79 74 90 61 FLOW f 90 68 90 72 FLOW
(deg) 81 (deg) 72 73
107 107 107 107
73
SADA 77 SADA 71
124 LADA 124 124 LADA 124
80 78 75 80 68 67 70
141 141 141 141
FLAPSIDE FLAPSIDE
-30 -15 0 15 30 -30 -15 0 15 30 -30 -15 0 15 30 -30 -15 0 15 30
56 56 20kHz 56 56 20kHz
66 60 62 70
73 68 73 74 61 73 64 73 73
70 65 70
73 67 62 67 71
f 90 90 f 90 90
(deg)107 76 1077678 63 (deg)107 67 66 107 69
75
64 68
124 124 124 124
74 67 66
74 66
141 141 141 141
-30 -15 0 15 30 -30 -15 0 15 30 -30 -15 0 15 30 -30 -15 0 15 30
56 56 40kHz 56 56 40kHz
56 54 49 59 65
69
73 58 73 58 73 73
69
60 61 63
f 90 63 90 f 90 63 90 68
(deg) 63 (deg)
107 65 107 107 107
59 71 63
60 64 62
124 61 124 124 73 124
66 64
59 55 66
141 141 141 141
-30 -15 0 15 30 -30 -15 0 15 30 -30 -15 0 15 30 -30 -15 0 15 30
y (deg) y (deg) y (deg) y (deg)
(a) calibrator source for M=0 and 0.17. (b) flat edge flap and contoured edge flap for M=0.17.
Figure 6. Directivity levels for calibrator source and flat-edge and contoured-edge flaps for three one-third octave
bands.
main lobe, which is properly centered at the source the image is more dispersed with increased speed. The
location. For non-zero Mach number, the LADA still SADA levels are less reduced and any dispersion is less
properly locates the source by the use of the shear-layer noticeable because of the broader beampattern. The
refraction corrections in the steering vector processing. contours for the flat and contoured flap edges suggest a
However, the maximum level drops and the dynamic concentrated source distribution of an inch or two for
range drops to about 7 dB for M=0.11 and 5 dB for this particular frequency. Note that the dynamic range
M=0.17. The LADA maximum levels are reduced and is poor at about 5 dB for M=0.11 and 2 to 3 dB for
9
American Institute of Aeronautics and Astronautics