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For permission to copy or republish, contact the American
Institute of Aeronautics and Astronautics1801 Alexander Bell Drive,
Suite 500, Reston, VA 20191
6th AIAA/CEAS Aeroacoustics Conference
June 12-14, 2000 / Lahaina, Hawaii
AIAA 2000-1975
Flap Edge AeroacousticMeasurements and Predictions
Thomas F. Brooks and William M. Humphreys, Jr.NASA Langley
Research CenterHampton, VA 23681-0001
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American Institute of Aeronautics and Astronautics
1
AIAA-2000-1975
Flap Edge Aeroacoustic Measurements and Predictions
Thomas F. Brooks*
William M. Humphreys, Jr.
NASA Langley Research CenterHampton, Virginia 23681-0001
ABSTRACT
An aeroacoustic model test has been conducted toinvestigate the
mechanisms of sound generation onhigh-lift wing configurations.
This paper presents ananalysis of flap side-edge noise, which is
often the mostdominant source. A model of a main element
wingsection with a half-span flap was tested at low speeds ofup to
a Mach number of 0.17, corresponding to a wingchord Reynolds number
of approximately 1.7 million.Results are presented for flat (or
blunt), flanged, andround flap-edge geometries, with and
withoutboundary-layer tripping, deployed at both moderate andhigh
flap angles. The acoustic database is obtainedfrom a Small Aperture
Directional Array (SADA) ofmicrophones, which was constructed to
electronicallysteer to different regions of the model and to obtain
far-field noise spectra and directivity from these regions.The
basic flap-edge aerodynamics is established bystatic surface
pressure data, as well as byComputational Fluid Dynamics (CFD)
calculations andsimplified edge flow analyses. Distributions
ofunsteady pressure sensors over the flap allow the noisesource
regions to be defined and quantified via cross-spectral diagnostics
using the SADA output. It is foundthat shear layer instability and
related pressure scatter isthe primary noise mechanism. For the
flat edge flap,two noise prediction methods based on
unsteady-surface-pressure measurements are evaluated andcompared to
measured noise. One is a new causalityspectral approach developed
here. The other is a newapplication of an edge-noise scatter
prediction method.The good comparisons for both approaches suggest
thatmuch of the physics is captured by the prediction
* Senior Research Scientist, Aeroacoustics Branch,
AssociateFellow AIAA.
Research Scientist, Advanced Measurement and
DiagnosticsBranch, Senior Member AIAA.
Copyright © 2000 by the American Institute of Aeronautics
andAstronautics, Inc. No copyright is asserted in the United States
underTitle 17, U.S. Code. The U.S. Government has a royalty-free
licenseto exercise all rights under the copyright claimed herein
forgovernment purposes. All other rights are reserved by the
copyrightowner.
models. Areas of disagreement appear to reveal whenthe assumed
edge noise mechanism does not fullydefine the noise production. For
the different edgeconditions, extensive spectra and directivity
arepresented. Significantly, for each edge configuration,the
spectra for different flow speeds, flap angles, andsurface
roughness were successfully scaled by utilizingaerodynamic
performance and boundary layer scalingmethods developed herein.
SYMBOLS
a0 medium speed of soundc flap chordlengthCN normal force
coefficient with respect to cCp static pressure coefficientCOPs
coherent output power spectrum of unsteady
surface pressure with respect to far-field noised distance from
one sensor to anotherD directivity factor, Eq. (13)dS( )y elemental
surface area at yf frequencyf 1/3 one-third octave band center
frequency∆f spectrum frequency bandwidthGa auto-spectrum of noise
measured by SADAGs auto-spectrum of unsteady surface pressure
at
sensorGa s, cross-spectrum between outputs of SADA and
surface pressure sensori pressure sensor location numberj −1k
acoustic wave number = ω / a0 l1 correlation length scale in
chordwise edge
direction
l3 correlation length scale in spanwise directionfrom edge
L length of chordwise section that a sensorrepresents
′L lift per unit spanMc convective Mach number, U ac / 0McAVG
average Mc , see Eq. (8).
M0 tunnel Mach number, U a0 0/n normal vector to surface at
y
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American Institute of Aeronautics and Astronautics
2
Rc Reynolds number based on c and U0pa acoustic pressure time
historyps surface pressure time historyPa Fourier transform of paPs
Fourier transform of psqc dynamic pressure based on convective
speed
Ucq0 tunnel dynamic pressurer distance = r′r effective
source-to-observer distance for
quiescent field radiation, see Fig. 19r vector distance = x
y−SADA small aperture directional arrayt timeusu inboard velocity
along suction sideupr inboard velocity along pressure sideuv
velocity at radius r0 from center of vortex, see
Fig. 9(c)Uc convection velocityUh hydrodynamic convection speed
from the
pressure to suction side, see Fig. 13′Uh hydrodynamic convection
speed over the
suction side, see Fig. 13Up flow velocity at edge on pressure
side, Eq. (4)Us flow velocity at edge on suction side, Eq. (4)U0
tunnel velocityx chordwise distance from the flap leading edgex
noise observer location vector
′x effective observer location vector for radiationin quiescent
field, see Fig. (19)
y spanwise distance from the flap edgey surface noise source
location vectorz height above surface sensor, see Fig. 8α flap
angle with respect to the main elementβc edge convective-flow skew
angle, see Fig. 8γ circulation densityγ a s,
2 coherence function, see Eq. (9)Γ vortex circulationδ boundary
layer thicknessδ0 boundary layer thickness at airfoil zero
angle
of attackς coherence decay factor for l3η coherence decay factor
for l1θ angle between n and x , see Fig. 19
′θ angle between n and ′x , see Fig. 19ϑ observer azimuth angle
defined for Eq. (21)ρ medium densityτ retarded time, Eq. (12)τ a s,
noise transmission time from sensor to SADAφ SADA elevation
(flyover) angle, see Figs. 5
and 24
ϕ a s, cross-spectral phase between SADA andsensor outputs
ψ SADA azimuth angle, see Fig. 24ω radian frequency = 2πf
INTRODUCTION
Airframe noise can be dominant during airportapproach and
landing when the engines are at lowpower and the high-lift systems
and landing gears aredeployed. This becomes particularly true as
present-day propulsive systems become quieter1. As a result,there
has been an increased emphasis placed on themeasurement and
modeling of non-propulsivecomponents such as flaps, slats, and
undercarriage.
As reviewed by Crighton2, a number of studies ofairframe noise
were conducted in the1970's and early1980's. An early evaluation
was performed by Hardin3.Empirical airframe noise studies and
predictiondevelopments include those of Fink4 and Fink
andSchlinker5. A series of airfoil self-noise experimentswere
performed by Brooks and Hodgson6 and Brooksand Marcolini7,8,9 for
trailing edge noise and wing tipnoise. The results of these studies
formed the basis of acomprehensive self-noise prediction method10
forisolated airfoils. As part of a wing and flap high-liftsystem,
the flap is much more loaded aerodynamicallythan it would be if
isolated. Because of this, it has beenfound capable of producing
much more intense noise.Block11 in wing, flap, and landing gear
interactionstudies found flaps to contribute significantly to
theoverall noise. Kendall12 and Kendall and Ahtye13,using an
elliptical acoustic mirror, found stronglocalized flap edge noise.
This was confirmed by Finkand Schlinker5 in component interaction
studies.McInerny et al.14, Ahtye et al.15, and Miller andMeecham16
performed cross-correlation studiesbetween unsteady surface
pressures and noise fieldmeasurements for the tip region of an
isolated wing,single slotted flap, and triple slotted flaps,
respectively.The side edges of the multiple flaps were found
tosignificantly exceed other airframe noise sources16.
The 1990's produced an increase in airframe noiseresearch
activity17, particularly due to the NASAAdvanced Subsonic
Technology (AST) program.Several tests are particularly notable. A
4.7% scaleDC-10 aircraft model was tested in the NASA Ames 40by 80
foot wind tunnel, as reported by Bent et al.18,Hayes et al.19 and
Guo et al.20,21. Inflow microphones,a phased-microphone array, and
a parabolic mirrordirectional microphone system were used along
withunsteady surface pressure sensors on inboard andoutboard flaps.
The flap edge noise was found to
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dominate other noise sources. Significant correlationswere found
between edge pressures and the measurednoise21. Noise reduction
concepts were evaluated22. Aseries of tests of a large unswept wing
(2.5 ft. chord)and half-span Fowler flap were conducted in the
NASAAmes 7 x 10 foot wind tunnel, as reported by Storms etal.23,
Horne et al.24, and Storms et al.25. The testsprovided basic
aerodynamic data and, although thetunnel was hard-walled, limited
acoustics were obtainedusing large phased arrays of microphones.
Acomputational study by Khorrami et al.26 providedsubstantial
agreement with the data. This was used toexamine two possible noise
source models, namely, avortex-instability model and a shear layer
vortex-sheetmodel.
The present paper concerns a wing and flap modeltested in the
Quiet Flow Facility (QFF) at NASALangley. The model is a NACA
632-215 wing with a30% chord half-span Fowler flap. This is the
same asthat used in the aforementioned 7 x 10 foot wind tunneltest
at NASA Ames, except here the model is about onehalf the size. As
reported by Macaraeg17, this model inthe QFF has provided the means
to closely examine theaerodynamic and acoustic physics for slats
and flaps.Measurements of the flow field in the QFF, byRadezrsky et
al.27 included hot-wire, hot film, 5-holeprobe surveys, laser light
sheet, and flap surface oilflows. These measurements revealed a
dominant flapvortex structure resulting from the merger of
twoupstream vortices _ one strong vortex, formed from thepressure
side to around the flap edge, and a weakervortex formed at the flap
side edge on the suction side.In the vicinity of the trailing edge,
the vortex is farremoved from the flap surface. Computational
effortsby Khorrami et al.28 and Takallu and Laflin29 usingReynolds
Averaged Navier-Stokes solutions (RANS)duplicated the key mean
features of the edge flow.Streett30 developed a computation
framework for thesimulation of the fluctuating flowfield associated
withthis complex flap-edge vortex system. Streett'scomputations,
utilizing a calculated mean flow field28,further crystallized the
shear layer instability andvortex-instability disturbance models2 6
for noiseproduction. Linear stability analysis determineddominant
frequency ranges of unstable flowdisturbances31. Guo32,33, in a
similar time frame,followed with a semi-analytical and
semi-empiricalprediction model of this shear layer
instabilitymechanism. Predictions from this model comparedwell with
flap edge noise data when certain scaleparameters were used.
The initial aeroacoustic measurements for aninstrumented version
of the above model tested in the
QFF were presented by Meadows et al.3 4.Measurements included
flap-edge noise-source locationmapping by a large directional
(phased) microphonearray system, flap-edge noise spectra and
directivity bya smaller array, and cross-spectra between
unsteadysurface pressure sensors about the flap edge. Details ofthe
microphone array design and methodology used inthe testing was
presented by Humphreys et al.35.Microphone array testing
methodology was refined andquantified using the QFF systems, as
reported byBrooks et al.36. The present study builds upon
thiswork.
In this study, the generation and radiation of flapedge noise
for the flat (or blunt), flanged, and roundflap edge configurations
are examined. The basic flowpattern about the edge is studied using
ComputationalFluid Dynamic (CFD) calculations and measured
staticpressure distributions. Simplified flow calculations arethen
developed to provide key aerodynamic parametersneeded for noise
prediction and scaling. Cross-spectralamplitude and phase between
unsteady surface pressuresensors over the flap edge surface are
analyzed toreveal the character of the hydrodynamic pressure
fielddue to turbulent flow and the near-field flap-edge
noisegeneration. Coherent Output Power (COP) spectradiagnostics
using the measured pressures and the noiseprovide a measure of the
noise source distribution alongthe flap edge. The noise source thus
determined isexamined for consistency with the previouslymentioned
shear layer instability mechanism26,30,33. Forthe flat edge flap,
separate noise prediction methods aredeveloped and validated from
(1) a causality approachthat connects the noise to the
cross-spectra between thesurface pressure and far-field noise
throughfundamental aeroacoustic formulations and (2) an edge-noise
scatter solution. Both methods utilize the surfacepressure
measurements on the suction and pressuresides near the flap edge.
Next the noise spectra anddirectivity are presented for three edge
configurationsfor different surface roughness, flap angles, and
flowspeeds. The spectra are then examined for scalabilityfor each
configuration using flap mean lift andboundary layer thickness
descriptions.
TEST SETUP AND METHOD
The test model apparatus is shown mounted in theQuiet Flow
Facility (QFF) in Fig. 1. The QFF is a quietopen-jet facility
designed for anechoic acoustic testing.For the present airframe
model testing, a 2 by 3 footrectangular open-jet nozzle is
employed. The model isa NACA 632-215 main-element airfoil (16 inch
chordand 36 inch span) with an attached half-span Fowlerflap (4.8
inch chord). The flap is attached by an
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American Institute of Aeronautics and Astronautics
4
adjustable set of "U" brackets to minimize bracketinterference
with the ideal flap flow field. The model isheld in place by
vertical side plates, which arethemselves rigidly mounted to side
plate supports of thenozzle. In the photo, the model is visible
through thePlexiglas windows located on the side plates. The
mainelement airfoil and flap are instrumented with staticpressure
ports and unsteady pressure sensors34.
A view of the main element and flap in the vicinityof the flap
edge is sketched in Fig. 2. The flat edge flapis shown accompanied
by edge modifications. Whenattached, the flange edge produces a
cavity depth of 1/8in. The flange thickness is 0.05 in. The round
edgeattachment is a half-circle cross-section shape thatmatches the
airfoil contour. The effect of surfaceroughness on the flap edge
noise was examined byapplying grit. For the flat edges, #60 grit at
a density ofabout 70 particles per square inch was applied on
theedge and both suction and pressure side surfaces over a2 in.
span. For the round edge, #120 grit at about 800particles per
square inch was applied, but was restrictedto one half of the round
edge surface area - towards theflap's pressure side. The intent of
the grit was toproduce thickened and well-developed
turbulentboundary layers in the vicinity of the side edge. Forthis
paper, the main element angle was set at 16° andtwo flap angles,α
=29° and 39°, were tested. The gapand overlap settings for these
angles are shown in Fig.3. The positions of the flush-mounted
unsteadypressure sensors in the flap edge vicinity are shown inFig.
4. The chordwise distance from the leading edgeis x and the
spanwise distance from the side edge is y .
FIGURE 1. Test apparatus with SADA mounted on pivotalboom in
QFF.
MAINELEMENT
FLAP
Flat Edge
Flange
Flat Edgewith Grit
Round Edge
Round Edgewith Grit
FIGURE 2. Sketch of flap edge treatments.
29°
39°
MAINELEMENT
GAP
OVERLAP
FLAP
normalized to main
29o 39o
GAP:
OVERLAP: 0.0242 0.0132
0.0227 0.0231
element chord length
FIGURE 3. Flap and gap geometry.
As will be discussed, the sensors of present interest arethose
on the pressure and suction surface. Thesesensors are Kulite model
LQ-34-064-5A. They arealigned spanwise at .06, .81, and 1.81 in.
(sections A, B,and C, respectively) from the edge. The
chordwiseposition for each sensor is given in Table 1.
The far-field acoustics of the model are measuredby Small
Aperture Directional Array (SADA), which isseen in Fig. 1 to be
mounted on a pivotal boompositioned by rotational stepping motors.
The SADA isalways 5 ft. from the center of the main element
trailingedge. It consists of 33 B&K 1/8-inch
microphonesprojecting from an acoustically treated metal frame.The
aperture of the array is small, with a maximumdiagonal aperture of
7.76 inches. The small sizereduces bias error by locating all the
microphones in the
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American Institute of Aeronautics and Astronautics
5
array within approximately the same source
directivity,regardless of SADA’s elevation or azimuth positionabout
the model. In Fig. 5, the SADA measurementpositions are drawn in a
side view (opposite side to thatof Fig. 1) of the test setup. The
SADA is shown locatedin a plane perpendicular to and centered on
the span ofthe model, corresponding to zero azimuthal angle (ψ
=0°). The position of SADA in the photo of Fig. 1corresponds to an
elevation angle φ = -124° in thedrawing. In Fig. 5, the SADA is
seen positioned at φ =107°, on the pressure side of the model. The
open jetshear layer boundaries (defined at 10% and 90 % of
thepotential core velocity) are shown as measured alongthe ψ =0°
plane. A mean shear line is shown, which ispart of a curved
three-dimensional mean shear surfacedefined mathematically from the
shear layermeasurements. This is used in SADA processing
todetermine shear layer refraction corrections. Thedrawing
illustrates the refracted noise ray path from theflap edge source
region to the microphone.
x
EDGE PRESSURESIDE
SUCTIONSIDE
13
10
11
12
14
15
16
17
18
20
19
21
22
23
24
25
26
27
30
31
32
333435
36
37
38
39
40
41
42
43
44
45
46
47
29
1
2
3
C B A A B Cy
FIGURE 4. Drawing of unsteady surface pressure
sensordistribution.
10111213141516171819
0.120.540.951.371.782.623.033.363.990.12
202122232425262729-
0.952.623.453.990.121.783.453.990.00
-
303132333435363738-
0.120.951.782.202.623.033.360.000.12
-
394041424344454647-
3.022.181.350.934.804.683.021.350.93
-
x(inch)#
Sensor Coordinatesx(inch)# x(inch)# x(inch)#
yC = 1.81 inchyA = 0.06 inch yB = 0.81 inch
TABLE 1. Pressure sensor coordinates.
NOZZLE
-56o
-73o
= -39o
-90o
-107o
-124o
141o
124o
107o
90o
73o
= 56o
FLOW
SADA
SIDE PLATE
MODEL
φ
φ
MEANREFRACTEDRAY PATH
MEANSHEARLAYER
FIGURE 5. Sketch of test setup. The noise ray path from theflap
edge to the SADA is illustrated.
Data acquisition and post-processing
The array microphones and surface pressuresensors employed
acquisition hardware consisting oftransient data recorders
controlled by a workstation. All35 microphone channels (including 2
referencemicrohones) were recorded with a 14-bit dynamicrange,
simultaneously with 32 pressure sensor channelsusing a 12-bit
range, at a sampling rate of 142.857 kHz.Two million 2-byte samples
were taken for eachacquisition. The microphone signals were high
passfiltered at 300 Hz. All channels had anti-aliasing filtersset
at 50 kHz, which is substantially below the 71.43kHz Nyquist
frequency.
Microphone and pressure sensor calibration datawere accounted
for in the post-processing. For theSADA microphones, regular
pistonphone and injectioncalibrations of amplitude and phase were
made.Amplitude and phase calibrations for the pressuresensors
employed a miniature speaker-driver capable ofhigh frequency
output. The measured outputs werereferenced to the output of a 1/8
in. B&K Model 4133microphone. (The high frequency outputs of
thepresent Kulite sensors are unfortunately limited. In thisreport,
surface pressure spectral data is limitedgenerally to 13.5 kHz,
where flat frequency responseand signal-to-noise are good.) Initial
post processing ofthe test data begins with the computation of the
cross-spectral matrix for each data set. The computation ofthe
individual matrix elements is performed using FastFourier
Transforms (FFT) of the original data
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American Institute of Aeronautics and Astronautics
6
ensemble. All data are segmented into 1000 non-overlapping
blocks each containing 212 samples,yielding a frequency resolution
of 34.88 Hz. AHamming window is used.
A conventional beamforming approach, employingmatrices of
cross-spectra between the arraymicrophones35,36, is used to
electronically “steer” thearray to chosen noise source locations.
The processingaccounts for mean amplitude and phase changes due
torefracted sound transmission through the shear layer tothe
individual microphones of the arrays. A meanrefracted ray path is
illustrated in Fig. 5. The correctionterms are calculated33 using
Snell’s law in Amiet’smethod37, modified to account for a curved
three-dimensional mean shear surface defined in the shearlayer. A
key feature of the array processing is thatspatial resolution (or
sensing area over noise sourceregions) can be controlled
independently of frequencyand steering-direction over broad
frequency ranges.The microphone shading algorithms methodology
usedis adapted from Refs. 38 and 39 and evaluated withrespect to
the present test in Refs. 35 and 36. Note thatfor each test case,
the cross-spectral matrix has acorresponding background matrix
subtracted from it toremove extraneous system noise (measured
microphoneand sensor noise for zero tunnel flow speed). The
arrayprocessing references levels to an equivalent singlemicrophone
measurement. Spectra data are determinedfor each narrowband
frequency (34.88 Hz resolutionbandwidth) of interest. Other
spectral bandwidths thatare presented in this paper are formed from
thenarrowband spectra.
FLAP EDGE FLOW FIELD
In this section, the basic flap edge flow isexamined with
respect to parameters required toevaluate the unsteady surface
pressures and relatednoise field.
Basic aerodynamics
Extensive aerodynamic measurements for thepresent model have
been reported by Radezrsky et al.27.The model was shown to function
as a high-lift device,with the main element and flap properly
interactingaerodynamically. The elements are close enough thatthe
flow acceleration about the leading edge of the flapsignificantly
reduces the required pressure recovery atthe main element trailing
edge, but the elements areseparated sufficiently so that the
viscous boundarylayers do not merge. This increases the overall
lift,especially on the main element, compared to liftsobtainable
separately. The QFF facility produces a
maximum Mach number of 0.17 for this modelconfiguration, which
corresponds to a main elementchord Reynolds number of 1.7 x 106. In
order tomaintain attached flow on the flap, the boundary
layertransition was fixed by serrated tape applied to thelower
surface of the main element at 30% chord and onthe leading edge of
the flap. Pressure coefficient plotsrevealed very similar
performance to the somewhatlarger Reynolds number conditions of the
similarmodel23 tested in the Ames closed wall 7 x 10 foottunnel. In
the QFF, the flap angle with respect to themain element was α = 29°
and 39°, whereas the mainelement was set at 16° and 20° angle of
attack to thetunnel centerline. (Note that 16°, for the main
element,is approximately equivalent to an angle of attack ofabout
5° in the closed wall tunnel.) The flap flow fieldwas found to be
dictated almost entirely by the flapangle, which is measured with
respect to the mainelement, and not the main element angle.
For the present QFF testing, pressure and liftdistributions for
the flap are presented in Fig. 6. Themain element angle was 16°.
The gap and overlapsettings, shown in Fig. 3, differ only slightly
from thoseof Ref. 27. Static pressure coefficient distributions
atthree spanwise locations of the flap are shown in Fig. 6for the
tunnel Mach number M0= 0.17 for the two αvalues. The spanwise cuts
are shown for y c/ = 0.027,0.208, and 1.875. The ratio y c/ is the
distance fromthe flap edge compared to the flap chordlength c . Aty
c/ = 1.875, at the center of the flap section, theexpected
two-dimensional lift distribution behaviorwith high suction peaks
is shown for both angles. Asy c/ decreases (meaning the flap side
is approached),the high suction peak at the forward (leading
edge)stations are reduced and the pressure differentialdiminishes.
Near the side edge, a low-pressure regionexists at a downstream
section of the chord, which isdue to a strong vortex being formed
on the suction side.Also shown in Fig. 6 is the normal force
(normal tochordline) coefficient CN , with respect to c , versusy
c/ . An additional y c/ location of 0.625 isrepresented here. It is
seen that the sectional lift isdiminished as the side edge is
approached except for anincrease very near the edge due to the
presence of thestrong vortex on the suction surface. At the
inboardstation y c/ = 1.875, CN = 1.213 and 1.567 for α =29° and
39°, respectively. The ratios of CN and αvalues show almost a
linear dependence of lift to flapangle.
The vortex found on the suction surface near theflap edge was
shown in Ref. 27 to be a result of thestrong primary vortex and a
weaker vortex merging.
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American Institute of Aeronautics and Astronautics
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0 1-2
0
2
4
x/c
y/c = 0.0271
CP
0 2
1
2
y/c
CN
0 1-2
0
2
4
x/c
y/c = 1.875
CP
0 1-2
0
2
4
x/c
α = 29oα = 39o
y/c = 0.2083
CP
FIGURE 6. Pressure coefficient distributions and normal
forcecoefficient distribution for two flap angles.
The primary vortex is formed along the pressure side(bottom)
edge and grows in size in the streamwisedirection, and a weaker
vortex is formed near thesuction surface edge. Steady RANS
computations ofRef. 28 found agreement with the basic
measuredfeatures of the merger of the dual vortex system and
thegeneral location of the resultant vortex. For both theexperiment
and calculations, the vortex bursts above thesuction side surface
for the 39° flap angle case. Thisbursting occurs when the local
flow angularity is toohigh or the axial velocity component is too
low. Figure7 shows portions of the RANS solutions for the twoflap
angle QFF test cases of the present study. Thecontours show lines
of constant static pressure on thesurface. Intervals between the
lines correspond tointervals in Cp of .346. The two component
vectors
shown are the calculated velocities over a projectedsurface
defined at 0.035 in. (approximately a boundarylayer thickness)
above the suction and pressuresurfaces. Only the edge velocity
vectors from thepressure side are seen because of the oblique view
ofFig. 7. The flow about the side edge surface is omittedfor
clarity. The vector pattern clearly shows thepresence of the
resultant vortex and its strong influenceon the flap edge flow
field. The vortex is traileddownstream of the model, but the
vectors show theformation of the vortex is essentially attached at
the top(suction) edge surface. The attachment is seen to bejust aft
of mid-chord for the 29° flap angle case, butslightly forward of
mid-chord for the 39° flap angle.The vortex strength is mostly
defined by the strong
sheared-flow velocity across the pressure surface edgewhich
wraps around the vortex and "feeds" it.
α = 29°
M =0.170
α = 39°
M =0.170
FIGURE 7. CFD results of flap-edge-flow velocity vectors
inplanes parallel to and .035 inches above the surface.
Of primary interest for this study are flowparameters that
provide guidance in determining noisesources and provide pertinent
input to prediction theory.If the flap edge noise problem is indeed
an edgescattering problem, one would view the boundary
layercharacter and associated velocities as primaryparameters. One
should be able to tie these to surfacepressure data to validate the
noise source _ somewhatsimilar in approach to that done in Ref. 6
for trailingedge noise. We direct our attention to the edge
pressuresensors on the suction and pressure sides. These wouldbe
the only sensors in the strong edge flow field and, atthe same
time, be in the near field of such a scatteringphenomenon. They
should therefore be representativeof the source region. Note that
the flap side-edgesurface, between the suction and pressure sides,
hasgenerally lower velocity and its sensors (#1 through #9)
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American Institute of Aeronautics and Astronautics
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10111213141516171830313233343536
.010
.010
.010
.030
.050
.030
.040
.050
.120
.010
.020
.020
.025
.030
.030
.030
.21 (.222)
.21 (.222)
.23 (.222)
.22 (.222)
.24 (.222)
.35 (.285)
.33 (.285)
.31 (.285)
.25 (.285)
.13 (.215)
.19 (.215)
.21 (.215)
.22 (.215)
.22 (.215)
.22 (.215)
.20 (.215)
77 (90)90 (90)85 (90)73 (90)82 (90)54 (51)48 (51)52 (51)58
(51)28 (34)38 (34)35 (34)33 (34)32 (34)31 (34)32 (34)
.020
.012
.025
.050
.050
.045
.045
.060
.150
.025
.020
.020
.025
.030
.030
.030
.22 (.237)
.27 (.237)
.29 (.237)
.265 (.237)
.33 (.237)
.32 (.331)
.30 (.331)
.28 (.331)
.24 (.331)
.15 (.253)
.205 (.253)
.205 (.253)
.205 (.253)
.22 (.253)
.21 (.253)
.205 (.253)
82 (90)82 (90)68 (90)80 (90)76 (90)43 (46)46 (46)60 (46)65
(46)10 (24)28 (24)26 (24)25 (24)25 (24)25 (24)27 (24)
CFD Values ( Simple Model Values) for MO = 0.17
= 39O= 29O ααSensorNumber inchinch δδ MCMC
( =.0314)( =.0453) δδ
deg.deg. βCβC
TABLE 2. Calculated edge flow boundary-layer thickness
andvelocity values.
SurfaceSensor U(z)
Top View
SensorSurface
Wake Sh
eet
βc
β
Uc
U(z)
UcConvective
Velocity
Shed Wake Sheetx x
x
yy
Sideedge
z
FIGURE 8. Flow above a surface sensor and an idealizedshed
instability wave geometry at edge of flap.
are not considered here as representative of the sourceregion
(although they are in the near-field of suchscatter). In Table 2,
for the sensors indicated, valuesare given for the near boundary
layer thickness δ , thecorresponding Mach number Mc , and flow
angle βc ,determined over planes parallel to the surface and
atheight z = δ above the surface. The choice of δ ispartially
subjective. It corresponds to the outer edge ofthe shear flow
nearest the surface. An illustration of thevelocity field U z( )
above an edge sensor is shown inFig. 8. The top view shown defines
the angle βc fromthe normal to the edge. The subscript designation
c(for convective) is used to indicate the flow above thesensors is
assumed to also represent any movingdisturbance or flow structure
that may cause noise-producing pressure scatter at the edge.
Thehypothesized convecting wake sheet illustrated in Fig. 8will be
subsequently discussed.
For both flap angle cases considered, Table 2indicates that δ ,
Mc , and βc remains generallyinvariant along much of the pressure
side edge. Theflow speed Mc , as well as the cross-flow (or
spanwise)
component of velocity M Cosc cβ , exceed the tunnelvalue of
M0=.17. On the aft (downstream of mid-chord) suction side edge,
where the attached vortexflow comes off the surface past the edge,
the flowvelocities are even higher, reaching up to about twicethe
free-stream value. Forward on the suction sideedge, the velocities
are lower than those aft and thecross-flow diminishes greatly with
flow skew angle βcapproaching 90°. An unexpected result, to the
presentauthors, for the CFD flow field is the lack of
anticipatedchanges in δ and Mc values with changes in flapangle.
Expected increases in Mc did not occur withincreased flap angle,
even in regions further away fromthe surface. It should be
mentioned that Ref. 28 notedthat the solutions, while remarkably
good overall indefining basic flow features, found disagreements
withmeasured velocities on the order of 10 to 15%.Concerns about
the thickness of the shear layer werealso expressed. It was
suggested in Ref. 28 thatimprovements may be needed with regard to
gridresolution and turbulence modeling. Because of theimportance of
these parameters to the present effort,alternate calculations are
made and are presented in thefollowing section. The CFD solution,
however, isutilized in providing a reference for primary
flow-fieldfeatures.
Simplified edge flow calculations
Simple aerodynamic modeling is used here to takeinto account
Reynolds number and flap angle effects inthe definition of boundary
layer thickness and velocityvalues. This complements the
description of thecomplex three-dimensional flow field given by the
CFDsolution.
From thin airfoil theory40, the sectional lift per unitspan ′L
equals
′ = = =∫L ρ ρ γU U dx q cCc
N0 0
0
0Γ (1)
where ρ is the medium density and Γ is the airfoilcirculation
given an incoming stream velocity of U0.The circulation density γ
of the vortex sheet definesthe airfoil in the stream from the
leading edge at x= 0to the trailing edge at c , where c is the
chordlength (ofthe flap in the present case). The dynamic pressure
isq U0 0
2 2= ρ / and CN is the sectional lift coefficientdefined by Eq.
(1). Figure 9(a) shows a sketch of aninboard section of the flap
where the flow is essentiallytwo-dimensional. The velocity jump
across the airfoilsheet is γ ( )x u usu pr= − , where usu is the
velocityalong the suction side and upr is that along the
pressure
side. The mean or average velocity jump over the chord
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American Institute of Aeronautics and Astronautics
9
Uo
Γ
Γ
A'B'us
up
(a) flap inboard section flow (b) bound and trailed flap vortex
circulation
ΓΓroro uν
uνuν(c) model flap vortex circulation model showing forward
section cut A' and aft section cut B'
FIGURE 9. Illustrations for simplified flap edge
velocitycalculations.
is ( ) /u u U Csu pr mean N− = 0 2 . The average values ofusu
and upr are thus
( ) ( / )u U Csu mean N= +0 1 4
and (2)
( ) ( / )u U Cpr mean N= −0 1 4
Along with the streamwise flow component above,the cross-flow
component is required to estimate theedge flow. For this purpose,
Figure 9(b) illustrates asomewhat heuristic flap vortex model,
where the boundcirculation of strength Γ of the flap is
transitioned to atrailed wake vortex of the same strength at the
edge.Figure 9(c) shows a forward section view (cut A' in Fig.9(c))
where the vortex of core radius r0 , is 'drawing'fluid at velocity
uv from the pressure side into itself. It
is assumed that the vortex does not greatly affect theedge flow
on the upper suction side at this section.(Note that any
contributions from "secondary" vorticesare ignored.) For the aft
section (cut B') flow, the samebasic vortex 'draws' fluid at the
same velocity uv from
both the pressure and suction sides. The maximumvelocity of the
vortex is at the core radius and equalsuv . The velocity
description chosen for the vortex isthe Scully model41,42 which
distributes the circulation tosimulate the effects of viscosity.
The velocity due tothe vortex is given in terms of the radius r
from thecenter;u = +( / )[ )]Γ 2πr r /(r r2 2 0
2 . (For an ideal point
vortex, the bracketed term, [ ], would be unity.)Equating u uv =
at r r0= , we obtain
u U C cv N= 0 8/ πr0 (3)
where the strength Γ is obtained from Eq. (1). UsingEqs. (2) and
(3), the velocities on the edge surfaces maybe determined. For the
pressure side,
U u upr pr mean v= +( )2 2
and (4)β = −Tan u upr mean v
1[( ) / ]
For the suction side, on the aft section where the vortexcrosses
to the upper surface, Usu is similarly expressedbut the subscript
su replaces pr . On the forwardsection, Usu , however, is simply
taken as ( )usu mean andβ ≈90°. In Table 2, values of these
velocities (in termsof Mach number) and angles are given in
parenthesis tocompare with corresponding CFD values for
thedifferent sensors. The pr and su subscripts aredropped. The
values were calculated using r0 =0.4 tmax and previously mentioned
value of CN =1.213for α = 29° and CN =1.567 for α = 39°. The
maximumflap thickness is tmax =0.55 inches. The value used forr0
appears to give velocities and angles in nominalagreement with the
CFD values, but unlike the CFDvalues have the physically expected
flap angledependence.
Also listed in Table 2 (in parenthesis) arecalculated
approximate values of shear layer orboundary layer thicknesses δ
that one can compare tovalues that are determined from the CFD flow
fieldpreviously discussed. The calculated values weredetermined by
equations and extrapolated equations ofRef. 10, as defined below.
The boundary layerthickness at the trailing edge for an
untrippedsymmetric NACA 0012 airfoil at zero degrees angle ofattack
is empirically determined to be (Eq. (5) of Ref.10)
δ01 6569 0 9045 0 059610
2
= ⋅ − +c LogR LogRc c[ . . . ( ) ] (5)
where R cUc = 0 / ν is the Reynolds number based onchordlength c
and ν is the medium kinematicviscosity. At an angle of attack of α
(taken as flapangle here) to the flow, the pressure side thickness
δcan be related to δ0 by
δ δ α/ .00 015910= − (6)
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American Institute of Aeronautics and Astronautics
10
where α is angle in units of degrees. Note that Eq. (6)is newly
determined here based on the data in Fig. 7 ofRef. 10. It replaces
Eq. (8) of Ref. 10 in order to bemore valid for large angles. The
values of δ using Eqs.(5) and (6), are 0.0453 in. and 0.0314 in.
for 29° and39° at M0= .17. These are somewhat larger than
thatlisted in Table 2 for the sensors on the pressure andsuction
sides.
In this paper, δ is used as a normalizing parameterfor surface
pressure and overall flap noise spectra. Alsoused in normalizations
are δ values for roughenedsurfaces. This is approximated by the
result of aninterpolation of δ0 between the untripped (Eq. (5))
andheavily tripped boundary layer cases of Ref. 10. Theresult is a
replacement for Eq. (5) for lightly trippedsurfaces,
δ01 787 0 9045 0 059610
2
= ⋅ − +c LogR LogRc c[ . . . ( ) ] (7)
Another normalizing parameter is an average Mcvalue at the edge
defined as
Ma
U uc vAVG = +1
002 2 (8)
UNSTEADY SURFACE PRESSURESAND ANALYSIS
Surface pressure spectra and acoustic sourceidentification
Figure 10 presents the unsteady surface pressure(auto-) spectra
Gs for four suction-side edge sensors
and two pressure-side sensors (#32 and #34) forM0=.17. As
previously stated, the data presented inthis paper are limited to
regions of flat frequencyresponse for the sensors. It is a
one-third-octave-bandpresentation, with the dB levels referenced to
p0
2 ,where p0= 20µPa is the standard acoustic reference.In Fig.
10(a), for α =29°, the levels are shown to bequite variable between
sensors with the highest on thesuction side at sensors #12 and #16.
Referring to Figs.4 and 7, these two sensors are at opposite sides
of theprimary flap edge vortex on the suction surface. Atα =39°,
some relative level changes occur for allsensors. Referring to
Table 2, one does not see anyobvious correspondence between the
velocitydefinitions over the surface at the sensors and thespectral
levels. Figure 11 presents M0=.07, .11, and
.17 data for two sensors normalized by q Uc c2δ / , where
q Uc c= ρ2 2/ . This type of normalization is common
for surface pressure spectra under turbulent boundarylayers, an
example being Ref. 6. The values for Uc aredetermined as Up and Us
from Eq. (4), as was done to
obtain values for Table 2. The values for δ areobtained from
Eqs. (5) and (6). These values depend onvelocity and flap angle,
but not chordwise location. Itis seen (by the degree of data
coalescence) that whiletunnel velocity dependence is partially
captured, it isnot consistent between flap settings. The
spectralshapes for each sensor apparently depend greatly on
theparticular flow phenomena occurring about it _
therefore, the local flow phenomena apparently changewith angle
and velocity variations. The parametergrouping does not capture
this. It is noted that the use ofthe δ and Uc values from Table 2
based on the CFDresults produces no improvement in
normalizationsuccess. It is expected that any such
normalizationsshould be more successful at sensor positions
moreinboard, away from the edge.
(a) α =29°
5 10 15Frequency f1/3 (kHz)
110
115
120
125
130
135
140 M0 = 0.17 αf = 29O
12
Sensor
16
GS,dB1/3
17
15
3432
Suction side: # 12, 15, 16, 17Pressure side: # 32, 34
(b) α =39°
5 10 15Frequency f1/3 (kHz)
110
115
120
125
130
135
140 M0 = 0.17 αf = 39O
16
Sensor12
GS,dB1/3
1532
34
17Suction side: # 12, 15, 16, 17Pressure: # 32, 34
FIGURE 10. Surface pressure spectra for pressure sensors atedge
of flap for M0= .17 for different flap angles.
Figure 12 shows some spectral characteristics thatcan provide a
basis for a noise mechanism hypothesis.The auto-spectra Gs are
given for edge and inboardsensors for both the suction and pressure
sides. Thespectral resolution is ∆f = 244 Hz but the levels
arereferenced to a ∆f = 1 Hz bandwidth. For the suction
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American Institute of Aeronautics and Astronautics
11
1 2 32πf1/3δ/U30
35
40
45
50
55
60 Sensor 16 α = 29O
M0 = 0.17
M0 = 0.11
M0 = 0.07
(GS) 1
/3U
c1
0lo
g
q2 c
δ
(a) sensor #16 for α =29°
1 2 32πf1/3δ/U30
35
40
45
50
55
60 Sensor 34 α = 29O
M0 = 0.17
M0 = 0.11
M0 = 0.07(GS) 1
/3U
c10
log
q2 cδ
(b) sensor #34 for α =29°
1 2 32πf1/3δ/U30
35
40
45
50
55
60 Sensor 16 α = 39O
M0 = 0.17
M0 = 0.11
M0 = 0.07
(GS) 1
/3U
c10
log
q2 cδ
(c) sensor #16 for α =39°
1 2 32πf1/3δ/U30
35
40
45
50
55
60 Sensor 34 α = 39O
M0 = 0.17
M0 = 0.11 M0 = 0.07
(GS) 1
/3U
c10
log
q2 cδ
(d) sensor #34 for α =39°
FIGURE 11. Normalized pressure spectra for different anglesand
flow speeds.
50
60
70
80
90
100
110
dB
34
16
23
21
42
46
40
Sensor
SU
CT
ION
PR
ES
SU
RE
-180
-90
0
90
180
360fd- a0deg 34x42
34x4034x46
34x35
PRESSURE SIDESENSORS
ONLY
ϕ
0 5 10 15Frequency (kHz)
0
90
180
270
360
40x21
34x1642x23INBOARD EDGE
INBOARD
OPPOSITE SIDESENSORS
ONLY
degϕ
FIGURE 12. Pressure spectra and cross-spectral
phaserelationships for edge and inboard sensors on suction
andpressure sides of flap. The spectral resolution is ∆f = 174
Hz,but levels are referenced to ∆f = 1 Hz.
side, the inboard sensors #21 and #23 are comparable inlevel to
one another and are lower than the edge sensor#16 levels by about
15 dB at 5 kHz. For the pressureside, the levels of the inboard
sensors #40 and #42 arecomparable, to one another, and are lower
than edgesensor #34 by over 15 dB at 5 kHz. The levels for
thefarther inboard sensor #46 are even lower. Thischaracteristic of
increased surface pressure spectrallevels, as the edge is
approached from inboard iscounter to that found for the classical
turbulent-boundary-layer (TBL) trailing-edge (TE) noise
scatterproblem6. (There, of course, the radiating edge is
thetrailing edge rather than the present flap side edge. Inthat
case, the hydrodynamic (TBL) pressure field isintense upstream of
the edge. But very near the edge,the levels decrease, because of
pressure scatter (near-field noise) that prevents a pressure
differential at theedge.) Therefore, the noise level behavior of
Fig. 12
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American Institute of Aeronautics and Astronautics
12
suggests a different mechanism than that for the TBL-TE noise
problem. This is correspondingly true for thephase behavior to be
discussed below.
Sensor # 40, 4234 45, 46
16 21, 23
Turbulence
Turbulence
a0
a0
+ Noise
- Noise
Uh
U'h
Uc
Shear layer / wakeinstability dipoles
FIGURE 13. Hypothesized flow and acoustic features
affectingunsteady surface pressures at sensors.
The hypothesized mechanism for the present flapedge problem is
illustrated in Fig. 13, which showsflow-field influences on
unsteady surface pressures.The subject sensors of Fig. 12 are shown
mounted in a"section cut", the edge sensors are located at yA and
theothers are at yB and yc of Fig. 4. The edge #16 and#34 sensors
are not aligned chordwise. Theconceptional illustration is
consistent with the shear-layer instability models26,30,33 for
noise production.Shear layer instabilities are shown being shed
atvelocity Uc at the edges near sensors #16 and #34.
ThevelocitiesUc , Uh, and ′Uh should be of the same orderof
magnitude to that of velocity uν of Fig. 9(c). Theflow is
relatively smooth on the pressure side butbecomes turbulent, and
convects at say velocity Uh, asit moves around the edge towards the
suction side. Thesuction side turbulence is within the fringes of
theprimary vortex and convects at velocity ′Uh above thesurface.
Figure 13 represents the shear layer instabilitynoise source as
dipoles (that are distributed chordwise).A portion of the noise
that is radiated travels along thesurface in the spanwise direction
at the speed of sounda0 . Both dipoles radiate to both sides with
oppositesigns (180° out of phase). Of course Fig. 13 is asectional
presentation. In reality there are a number ofindependent dipoles
radiating at different sections _ theeffective number of which
depend on disturbancecorrelation scales.
The observation that the noise levels of Fig.12 arediminished as
distance from the edge is increased isconsistent with the model of
Fig. 13. The phasebehavior is also consistent as is now shown. The
phaseϕ between sensor #34 and the inboard sensors, on thesame
pressure side, is normalized by subtracting( / )fd a0 ⋅360, where f
is the frequency and d is the
distance from #34 to the other sensors (that onedetermines from
Table 1). A result of zero degreeswould show that the correlated
components of therespective sensors are the same signals that are
simplytime-delayed at the speed of sound. The results shownin Fig.
12 show this to be generally true, except for a30° to 60° offset.
However, note that in Ref. 6, thescatter term for TE noise was
found to have a 45° offsetin scatter-pressure phase (in addition to
that due to timedelay) between the edge near-field and a point
awayfrom the edge. Hence, one would expect a similarfunctional form
for this scatter problem to that of Ref.6. Additional confirmation
of the conceptional modelis provided in Fig. 12 by the phase of
sensors onopposite sides of the flap. The phases are notnormalized.
It is seen that for sensors away from theedge, there is roughly a
180° shift over much offrequency range. At the edge sensors #16 and
#34, anapproximately 180° phase is attained near 4 kHz. Atlower
frequencies, the phase is dominated byhydrodynamic convective
effects, symbolized in Fig. 13by turbulence moving at Uh. The
linear phase slope,starting near zero frequency, suggest that Uh
betweenthe sensors is about .22 times a0 . Similar values werefound
for ′Uh using the sensors on the suction sidesurface. This compares
favorably with computed (CFDand simplified) convective velocities.
It was found thathydrodynamic-convection-effects generally
dominatethe phase relations between most edge sensors, as wellas
those over the suction surface. Most of these effectsare not
directly related to noise production. However,this does not mean
that the individual sensor auto-spectrum is not dominated by noise
related effects _ itjust means that the hydrodynamic effects are
largerscale and thus correlate better over distance. Thepresent
edge sensors are deemed too far apart for cross-spectra to
determine pertinent noise source information,such as scale
lengths.
Figure 14 serves to summarize key features of thesurface
pressures. The figure presents chordwisedistributions of integrated
surface pressure levels forsensors, at sections A, B, and C of Fig.
4, for bothpressure and suction sides of the flat edge flap forα
=29° and 39°. The levels result from integrating thespectra from
4.0 to 13.5 kHz. The low frequency limitof 4.0 kHz was chosen in
order to de-emphasize purelyhydrodynamic effects (see discussion
above). For bothflap angles, the levels at the suction side edge
(A)appear peaked in the general locations of the
chordwiseextremities of the vortex on the suction side. On
thepressure side, one peak is observed near the flap mid-chord. The
inboard sections (B) and (C) have levels
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American Institute of Aeronautics and Astronautics
13
Suction Side 39°
0 0.2 0.4 0.6 0.8 1
Pressure Side 39°
80
90
100
110
120
130
140Suction Side 29°
ABC
0 0.2 0.4 0.6 0.8 1
80
90
100
110
120
130
140Pressure Side 29°
FLAT EDGEO
vera
llS
urfa
ceP
ress
ure
(4
to13
.5kH
z)
x/c x/c
FIGURE 14. Chordwise distribution over FLAT edge flapregion of
band-limited overall surface pressure levels forα =29° and α =39°.
M0= .17.
Suction Side 39°
0 0.2 0.4 0.6 0.8 1
Pressure Side 39°
80
90
100
110
120
130
140Suction Side 29°
ABC
0 0.2 0.4 0.6 0.8 1
80
90
100
110
120
130
140Pressure Side 29°
x/c x/c
ROUND EDGE
Ove
rall
Sur
face
Pre
ssur
e(
4to
13.5
kHz
)
FIGURE 15. Chordwise distribution over ROUND edge flapregion of
band-limited overall surface pressure levels forα =29° and α =39°.
M0= .17.
that are relatively uniform over the chord andsubstantially
lower than the edge levels. Section (C)levels are generally lower
than those of section (B).This is consistent with the noise
mechanism modeling
depicted in Fig. 13. The higher levels on the suctionside for
the inboard sensors, with respect to the edgelevels, are expected
to be due to the presence of strongturbulence on the suction
side.
Figure 15 presents chordwise level distributions forthe round
edge flap sketched in Fig. 2. The character ofthe distributions is
somewhat similar to that of the flatedge, but the section (A)
sensor levels are reduced tonearly that of the inboard sensor
levels. This is becausethey are further inboard of the edge than
was case forthose on the flat edge flap. The noise mechanismdetails
that are depicted in Fig. 13 are not directlyapplicable to this
round edge flap case. However, flowshear / boundary layer
instabilities still should be thebasic mechanism, but with a
different scatteringgeometry and correlated fluctuation length
scales.
Coherent Output Power analysis
The surface pressure levels in Figs. 14 and 15 donot necessarily
indicate the local noise-source strengthdistribution. The inboard
levels contain substantialcontributions from hydrodynamic
convection effectsand noise radiating along the surface _ not
sources ofnoise. (Note that strictly speaking, in terms of
theFfowcs Williams and Hawkings equation43, the inboardpressures
are by definition part of the noise region thatshould be accounted
for. This is discussed in the nextsection.) The edge sensors for
the flat edge flap,however, are in the near-field of the source and
canrepresent the source, except to the extent that it isaffected by
non-radiating fluctuating pressurecomponents. This section is
concerned with providingsome measure of the noise source
distribution along theflap edge.
The Coherent Output Power spectrum44 is definedas
COPG
GGs
a s
aa s s= =
,,
2
2γ (9)
where, for present purposes, this is the spectrum of thesurface
pressure sensor (subscript s) output that iscoherent with the SADA
array (subscript a) outputwhen steered to this surface sensor(s) on
the flap. Theauto-spectra are Ga and Gs . The cross-spectrum
between signals is Ga s, and the coherence is γ a s,2 . The
phase associated with COPs is the cross-spectral phaseϕ a s, .
In the present data processing, a data-block time-shifting
procedure is used to avoid serious bias andstatistical errors, as
well as to put the data in a useful
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American Institute of Aeronautics and Astronautics
14
phase format. The microphone raw time data are timeshifted
(offset) by an amount close to the value of τ a s, ,which is the
time required for noise to be transmittedfrom the sensor to the
array. The array processingshear-layer refraction correction code
determines τ a s, .(The τ a s, values were evaluated to be accurate
withinless than the time it takes to acoustically travel
.25inches.) Final adjustment to obtain the full τ a s, shifteffect,
for each individual microphone and sensor, isdone in the frequency
domain. With regard to the cross-spectrum, this effectively puts
the source region in"retarded" coordinates, where the phase related
to noisetransmission time is removed, that is
( ), ,,,G G ea s a s
j
a s
a sτ
ωτ= −
and (10)( ), , ,,ϕ ϕ ωττa s a s a sa s = −
where the radian frequency ω π= 2 f .
-40
-20
0
10lo
g()
γ2 a,s
Frequency (kHz)0 5 10 15 20 25-180
-90
0
90
180
ϕ -ωτdeg
a,sa,s
20
40
60
80
100
120
dB
COPGG
G
a
s
sas
FIGURE 16. Coherent Output Power spectral processingresults, for
the flat edge flap, relating the sensor #34 pressuremeasurement and
the SADA noise measurement for M0= .17and α =39°. The spectral
resolution is ∆f = 34.88 Hz, butlevels are referenced to ∆f = 1
Hz.
Suction Side 39°
OverallCOPS phase supressedCOPS with phase
0 0.2 0.4 0.6 0.8 1
Pressure Side 39°
80
90
100
110
120
130
140Suction Side 29°
0 0.2 0.4 0.6 0.8 1
80
90
100
110
120
130
140Pressure Side 29°
FLAT EDGE
Ove
rall
Sur
face
Pre
ssur
e(
4to
13.5
kHz
)
x/cx/c
FIGURE 17. Chordwise distribution over FLAT edge flap
ofband-limited overall surface pressure levels and related
COPlevels for α =29° and α =39°. M0= .17.
Suction Side 39°
0 0.2 0.4 0.6 0.8 1
Pressure Side 39°
80
90
100
110
120
130
140Suction Side 29°
0 0.2 0.4 0.6 0.8 1
80
90
100
110
120
130
140Pressure Side 29°
OverallCOPS phase supressedCOPS with phase
ROUND EDGE
Ove
rall
Sur
face
Pre
ssur
e(
4to
13.5
kHz
)
x/c x/c
FIGURE 18. Chordwise distribution over ROUND edge flap of
band-limited overall surface pressure levels and related
COPlevels for α =29° and α =39°. M0= .17.
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American Institute of Aeronautics and Astronautics
15
Figure 16 shows results of COP processing forsensor #34
(pressure side) with respect to the output ofthe SADA when steered
to the sensor for the test caselisted. The SADA is positioned at φ
= 107°. The twoauto-spectra, the cross-spectrum, and the COPs
spectra
are shown. (Note that the differences in surfacepressure
auto-spectrum smoothness are related only toan application of a
calibration transfer-function. Aspreviously mentioned, the surface
pressure data shouldbe accurate below about 13.5 kHz.) The
difference inlevels between Gs and COPs is 10
2Log a s( ),γ , which isshown in the figure. As is shown in the
next section, ifa surface element (represented here by sensor #34)
is adirect radiator to the noise field, one would expect thephase (
), ,ϕ τa s a s to equal a constant -90°. The phase isshown in Fig.
16 to be generally constant, but at a phasevalue on the order of
-40° or -50°. However, this isconsistent with a 45° offset expected
for an edge in ascatter field as mentioned in the last section.
Thisphase behavior will be again discussed.
Figure 17 presents chordwise distributions ofintegrated
surface-pressure COP levels for the edgesensors (along section A).
For comparison, the auto-spectra distribution from Fig. 14, for the
sameintegration frequency range, is shown. No data frominboard
sensors are shown because these are assumednot to be in the noise
source region. The COPdistributions represent more realistic
distributions ofnoise source strength distribution than does the
auto-spectra. The COP results eliminate that portion ofsurface
pressure that is not related to the noise field. Sonon-radiating
hydrodynamic fluctuation contributionsare removed, which lowers the
COP levels with respectto the auto-spectra levels. Also, however,
there is anadditional cause of the lower levels for the COP
results.The correlation area that each sensor represents is
smalland there are a large number of correlation areas overthe flap
edge which contribute to the total noise. Forexample, if there were
uniform noise source strength(say with no non-radiating
hydrodynamic fluctuationspresent) and the COP were uniformly 20 dB
lower thanthe auto-spectra, one could hypothesize that there
are"effectively" 100 independently radiating noise sourceareas
across the flap edge. Figure 17 shows two COPdistributions. One is
where phase is not considered inthe integration (straight
pressure-squared typesumming) of the frequency bands. The
otherdistribution is where the phase is used in the
integration(vectorial type summing). The latter is lower in
leveland is the preferred presentation because those portionsof
hydrodynamic and/or acoustic fluctuations, whichare related to
noise production only in an indirect way,
are substantially eliminated. Consider the COP peaknear 20%
chord for the phase-suppressed distributionon the suction side for
α =39°. Phase data (not shown),indicate that the fluctuations which
cause the high COPlevels were related to turbulence and/or noise,
that arein turn correlated with noise production at anotherportion
of the edge. Since the phase ( ), ,ϕ τa s a s has to beconstant for
that portion of COP related to the directradiation from the sensor
to the microphones, thesumming of COP bands vectorially can
substantiallyremove (bias against) the "indirect" contributions
toCOP. This should make the COP more representativeof the actual
source distribution. The COP distributionsin Fig. 17 show that, for
both of the flap angles, thenoise is most strongly radiated near
65% chord on thesuction side and near 50% on the pressure side of
theflap edge.
Figure 18 shows COP results for the round flapedge, in the
format of Fig. 17. The same commentsapply here, as for the flat
edge flap, except that the edgesensors may be not be fully in the
source region, asmentioned for the auto-spectra integrated level
plots ofFig. 15. Still, one can make the statement that
thechordwise noise source appears clearly and stronglylocated near
60% chord for both pressure and suctionsides for both flap
angles.
NOISE PREDICTIONS BASED ON SURFACEPRESSURE SPECTRA
Causality spectra prediction
A causality spectral approach is developed in thissection that
helps establish the relative and quantitativeimportance of the
noise source regions of the flap.Previous success has been found by
Siddon45, usingcross-correlation methods and the acoustic
relationshipsof Curle46, in determining surface noise
sourcedistributions. This causality approach employed
cross-correlations between surface pressure sensors andmicrophones.
For several simple and small surfaceshape cases under Siddon's
study, the method provideda physical characterization of the noise
source.However, when the sources were non-compact,acoustically or
aerodynamically, the phase variationsgreatly hindered correlation
function interpretation andtheir usefulness. In this paper, we
revisit the causalityidea using spectral methods and for the first
timevalidate a causality prediction with measurement for
adistributed source.
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American Institute of Aeronautics and Astronautics
16
The noise field is given by the Ffowcs Williamsand Hawkings
equation43 (a form similar to Curle'sequation but generalized for
arbitrary fluid and surfacemotion). For low-Mach number flows and
for surfaceswith steady (or no) motion with respect to the
observer,distributed volume quadrupole and surface monopolesource
components in the equation are negligible.Assuming surface shear
stresses are small compared tolocal surface pressures, the
following equation form canbe found, relating the acoustic pressure
p ta ( , )x atlocation x and time t to the surface pressure ps ( ,
)y τ atposition y and retarded time τ
p ta r
r
r
pdSa
s
S
( , )/
( / )
( , )( )
( )
xn rM r
yy
0y
= ⋅− ⋅
∫
1
4 102π
∂ τ∂τ
(10)
Figure 19 shows the geometry of the flap in theopen jet tunnel
flow of Mach number M U0 0= / a0 ,where U0 is the tunnel test
section velocity. Theelemental surface area dS( )y , at y with
normal n, isseen with respect to a ray path of length r = r ,
wherer x y= − . Shear layer corrections performed in the
MeanShearLayer
xx'
SADA(Actual Observer)
r'
r Uoθ
θ’Uoτ
n
n
dS(y)
(EffectiveObserver Position)
FIGURE 19. Flap surface geometry with respect to ray path
tonoise observer.
array processing code corrects the results at the actualSADA
out-of-flow position to an 'effective' observerposition x in an
extended flow field without a shearlayer. The medium speed of sound
is denoted by a0 .The retarded time is defined implicitly by
τ τ= − −t ar U0 / 0 (12)
as pointed out by Guo33. In the far-field limit for x ,
p ta rD
Cosp
dSaS
s( , )( , )
( )( )
xy
yy
=
∫
1
4 02π
θ ∂ τ∂τ
(13)
where D r= − ⋅1 M r0 / ≈ 1 − ⋅M x x0 / andCos rθ = ⋅n r / . The
retarded time becomes
τ ≈ − ′( )t ra0
(14)
where ′ ≈r rD2 , which is shown in Fig. 19. Thedistance ′r ,
which is used in the shear layer processingcode35 of this study, is
that between the effectiveobserver position and source position in
an idealquiescent acoustic field. In this coordinate system,Cosθ is
replaced by Cos r′ = ⋅ ′ ′θ n r / . Upon definingthe Fourier
transform
ℑ = =−
−∞
∞
∫[ ( , )] ( , ) ( , )p p e dt Ps s j t sy y yτ τ ωω (15)
ℑ − ′ = − − ′[ ( , / )] ( , ) /∂∂τ
ω ω ωp t r a j P es sj r ay y0 0 (16)
so the Fourier transform of the acoustic field is
Pj
a rCos P e dSa
S
sjkr( , ) ( , ) ( )
( )
x y yy
ω ωπ
θ ω= −′
′∫ − ′4 0 (17)
where k a= ω / 0 . Multiplying both sides of Eq. (17) bythe
complex conjugate of Pa ( , )x ω and taking theensemble average, we
get the auto-spectrum of thenoise field
G P Pa a a= ∗ ( , ) ( , )x xω ω
= −′
′∫ ∗ − ′ja r Cos P P e dSS
a sjkrω
πθ ω ω
4 0 ( )( , ) ( , ) ( )
y
x y y (18)
Now upon evaluating this with respect to elementarysurface areas
∆S( )y , the following results
G P Pa a a= ∗
= −′
′∑ ∗ − ′ja r Cos P P e SS
a sjkrω
πθ
4 0 ∆∆
( )
( )y
y (19)
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American Institute of Aeronautics and Astronautics
17
The components, making up the sum in the right handside of Eq.
(19), are defined here as the causalityspectra associated with the
surface area elements ∆S( )yand represent their contribution to the
total noise Ga .The auto-spectrum Ga must be a positive real
quantity,while the components are complex quantities. Equation(19)
is valid under the present assumptions, inparticular that only
surface dipole noise sources areimportant, and that the sum is
taken over infinitesimal∆S( )y areas over all of S( )y . Equation
(19) includesall the hydrodynamic pressure fluctuations
(correlatedor not between different ∆S( )y areas), as well as
relatedpressure scatter (near field noise). It is important tonote
that non-radiating turbulence hydrodynamiceffects, with their
various complex phase contributions,may greatly dominate the
individual terms. The fullevaluation of the sums are needed to
completely self-cancel the non-radiating contributions. Such
concernsnot only apply to Eq. (19) but also to the FfowcsWilliams
and Hawkings equation in general.
In those practical application cases where ∆S( )ymust be finite
in size and limited in number, the validityof Eq. (19) requires
that ∆S( )y be chosen andinterpreted carefully. As previously noted
indiscussions pertaining to Fig. 17, many of the pressuresensors of
the present problem were found to be indeeddominated by non-noise
producing hydrodynamic andacoustic effects, for which portions are
correlated withthe noise. The use of the edge sensors only for the
flatedge flap should reduce extraneous 'noise' in anyprediction and
data comparison. The model thenreduces to a line of dipoles along
each side edge, withthe presence of the inboard flap surfaces not
included inthe solution for the acoustic radiation. To account
forthe "half-baffle" acoustic effect of the inboard surfaces,the
solution can be multiplied by a factor of two (2).This should give
an accurate presentation for small ′θ .
For the present study, Eq. (19) is evaluated usingdata from the
flat-edge flap. Our attention is restrictedto the edge sensors
#1-18 and #30-36 as representingthe source region. The following
relation is evaluated
G P Pa a a ii
= ∗∑
= ′′
−′ ∗∑24 0
2
1ω
πθ
π
a
Cos e
rP e P L
j
ajkr
s
i
[ ] ( ) l (20)
where the additional factor of 2 included is discussedabove. The
cross-spectral term containing the retarded
time shift is identified as ( ), ,Ga s a sτ of Eq. (10). The
area ∆S( )y has been replaced by Ll1. We takeL to bethe sum of
correlation length scales that sensor irepresent and, nominally,
the sum of all L equals theedge circumference. The correlation
length scale l1 in
the flap longitudinal direction (spanwise direction inFig. 4) is
taken as Uc / ηω . This relationship for scalelength is often used
in turbulent boundary layer (TBL)pressure scaling. In the present
study, the availabledata provided no satisfactory means to
determine valuesof η . In Ref. 6, η values for a TBL was found to
be.14 and .19 for the cases examined. For the followingpredictions,
we use the value η =.3. This choice isdiscussed in a following
section.
Causality predictions and comparisons withmeasured noise is
presented in Figure 20 for the flat-edge flap at M0 = .07, .11, and
.17 with α = 29°. TheSADA is positioned at 107°. Two causality
predictionresults are shown. The predictions based on Eq. (20)are
the prediction curves showing the lower levels. Theassociated phase
for the M0 =.17 speed case is shownplotted below the spectra.
Ideally, the phase of Gashould be zero. However, the phase is seen
to beapproximately 30° to 50°. This is consistent with
theaforementioned 45° phase shift in the edge sensorpressures
located in the near-field of the edge scatter. IfGa were fully
evaluated over the whole surface (notpossible with limited data)
then the phase would beexpected to be near zero. The other
causality predictionresults shown are where the phases in Eq. (20)
aresuppressed for each individual contribution. Forcingphase to be
zero removes additive random phase errorin the cross-spectra and
errors related to time delayvariability for each sensor. It may,
however, add biaserror of an unknown amount by adding
correlatedcomponents, when they would otherwise properlycancel.
Still the results appear to compare well over thewhole spectra
range. For the α = 39° case, the sameprediction comparisons are
made. This is shown in Fig.21 in the same format as Fig. 20. For
this case, thepredicted levels are lower than measured
levels,particularly for the causality predictions where phase
isincluded. Note correspondingly that substantiallylarger phase
variations are seen compared to those inFig. 20. This indicates
that these predictions based ononly the edge sensors are less
representative of the totalnoise production. The influence of the
burst vortex,associated with this α = 39° flap angle case, may
causethe noise source region to be more distributed over
thesurface.
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American Institute of Aeronautics and Astronautics
18
0 5 10 1510
20
30
40
50
60
70
80
90
10logG
M0=0.17
MeasuredCausality prediction
Causality prediction(phase suppressed)
α = 29°
a
M0=0.11
M0=0.07
0 5 10 15Frequency (kHz)
-180
-90
0
90
180
CausalityPhase(deg)
M0 = 0.17
FIGURE 20 Causality noise prediction comparisons for flatedge at
different tunnel speeds for α =29°.η =.3, ∆f =244 Hz.
0 5 10 1510
20
30
40
50
60
70
80
90
10logGM0=0.17
MeasuredCausality prediction
Causality prediction(phase suppressed)
α = 39°
a
M0=0.11
0 5 10 15Frequency (kHz)
-180
-90
0
90
180
CausalityPhase(deg)
M0 = 0.17
M0=0.07
FIGURE 21. Causality noise prediction comparisons for flatedge
at different tunnel speeds for α =39°. η =.3, ∆f =244 Hz.
Scatter edge noise prediction
Brooks and Hodgson6 used the trailing edge noisetheory of Howe47
and measured surface pressures topredict trailing edge noise due to
the passage at theedge of turbulent boundary layer flow. The
presentedge noise problem is that of shear layer wakeinstability
and resultant shedding of unsteady vorticityfrom the edges. Howe's
theory was developedprimarily with the former case in mind.
However, thesolutions should be generally valid here as long as
onerestricts attention to pressures in the immediate vicinityof the
edge and that certain parameters can be properlydefined. Figure 8
is used to illustrate several parameterchoices in doing this. For
the velocity field U( )zabove an edge sensor, a local maximum of
magnitudeUc is reached at a height δ . These values correspondto
those listed in Table 2, along with correspondingskew angle βc .
One hydrodynamic wavenumbercomponent of the instability wake sheet
is shown inFig. 8 as being shed from the edge region. It isassumed
that this sheet perturbation (shown as acorrugation) convects at
this same speedUc and angleβc after it leaves the surface. It is
also assumed that theedge sensor is in the very near field of the
edgeshedding and that the local edge thickness is muchsmaller than
the related acoustic wavelength.
Equation (72) from Howe47 (Eq. (32) from Ref. 6)gives the noise
spectrum Ga at a location in the farfield due to the trailing edge
(TE) noise from a thinplate of length L , in terms of the TE
pressure field.This is, in the present terminology,
Ga =
2 21 1 12 0
2
2 21
πθ ϑ β
θrU L
a
Cos Sin Cos
M M M Cosc c
or U r Uc
+ − −
( / )
( ) ( ) ( )
⋅−∞
∞
∫ Π te Sin a d( , / , )µ ω θ ω µ1 0 1 (21)
where θ is the observer angle defined in Fig. (19). Theobserver
azimuth angle ϑ is measured from thenegative of the y axis shown in
Fig. 4 (ϑ equals 180°along the spanwise surface and equals 90°
normal toand above the flap surface). The Mach number termsare M U
Sin ar0 0 0= θ / , M U Cos aU r cc = ϑ / 0 , andM U Cos a
U c c1 0= β / . Equation (21) ignores one of the
Mach number terms of Ref. 47, see Ref. 6. The integralis taken
over a pressure wavenumber spectrum functionΠ te with respect to
the wavenumber µ1 for the
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American Institute of Aeronautics and Astronautics
19
direction normal to the edge. In evaluating the integral,we use
the definition of Π te from Ref. 6 (Ref. 47 usesan alternate but
consistent definition), to obtain
Π te s ted Gµ π1 3−∞
∞
∫ = ( ) /l (22)
where ( )Gs te is the surface pressure spectrum at theedge and
l3 is the correlation length scale in the lateral(edgewise along
chord) direction. The assumed form of
l3 is
l3( )ω
βςω
= U Cosc c (23)
The noise is predicted as a sum of contributionsfrom individual
edge lengths each represented by anedge sensor. Similar to Eq. 20
for the causalityprediction, the total noise is
G Ga a ii
= ∑[ ] (24)
where each [ ]Ga i is determined using Eqs. (21), (22),and (23).
As mentioned for the longitudinal scale factor
l1 in the last section, correlation scales for the
presentmechanism were not determinable from the presentdata. In the
following predictions the value of ς = 2.0is chosen compared to a
value of 0.6 (measured for theproblem of a TBL pressure field) used
in Ref. 6. Thischoice and other assumptions are discussed in the
nextsection.
The predictions are compared to measured noisefor the two flap
angles at different tunnel speeds in Fig.22. The measured noise
spectra are the same aspresented in Figs. 20 and 21. The chosen
value of ςresults in good agreement for the 29° flap angle, as
wellas the low speed conditions for the flap angle of 39°.The
higher speeds for 39° show predictions to be lowerthan measured.
This general trend, of course, was alsofound for the causality
prediction comparisons usingthe same sensors. One can then suggest
that for the 39°flap case, where the vortex is known to burst, the
edgesensors may not fully represent the noise productionregion.
Discussion of prediction results
The present predictions strongly support the basicnoise
mechanism model of Fig.13 for the flat-edge flap.
0 5 10 15Frequency (kHz)
10
20
30
40
50
60
70
80
90
10logG
M0=0.17
PredictedMeasured
α = 29°
a
M0=0.11
M0=0.07
(a) α =29°
0 5 10 15Frequency (kHz)
10
20
30
40
50
60
70
80
90
10logGM0=0.17
PredictedMeasured
α = 39°
a
M0=0.11
M0=0.07
(b) α =39°
FIGURE 22. Scatter-theory noise prediction comparisons forflat
edge flap at different tunnel speeds for two flap angles.ς = 2.0.
∆f = 244 Hz.
The good prediction results show that the edge sensorscan
properly represent the noise source region.However, the prediction
and data comparisons suggestthis may not be fully true for the
vortex bursting case,where the noise is under-predicted. It is
likely that thesource is just more distributed over the surface.
(At thelow speeds of the present test, it is unlikely that
anyvolume noise source terms contribute significantly _
even with vortex breakdown.) The two predictions aredifferent in
their input requirements. The causalityprediction and the COP
analysis can be regarded asbeing related, because of their
dependence on cross-spectral processing between the noise and the
surfacepressure sensors. Note that the causality predictionsrequire
little flow information input, with velocityentering only through
the definition of correlationlength. The causality prediction is
primarily one of a
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American Institute of Aeronautics and Astronautics
20
noise-correlated force distribution definition, modeledhere as a
line-dipole taking the surface into accountacoustically only
through the multiplicative factor oftwo. The scatter edge noise
prediction is more of a"full" prediction, which more properly
includes sourcedirectivity in the solution. It requires more
flowinformation than the causality prediction. However, forboth
predictions, the lack of knowledge about pertinentcorrelation scale
lengths required assumptions. Thevalues for decay factors η and ς
were chosen to rendergood overall quantitative comparisons.
Thesecorrespond to scale lengths of l1 ≈ .4 in. and l3 ≈ .06in. at
5kHz. The ratio l l1 3/ ≈7 is compared to a valueof about 4 for the
different scatter noise problem (TBL-TE) of Ref. 6. Still, the
ratio l3 / δ ≈1.5 appears to be"reasonable" for the present
mechanism, although
l1 / δ ≈10 may not be. Subsequent investigationsshould reexamine
the correlation scale issue,particularly key parameters such as the
disturbancevelocity magnitude Uc and skew angle βc .
Still,uncertainty about correlation length presentations doesnot
undermine the basic physical understanding andtheoretical context
gained from the present predictioncomparisons.
NOISE DIRECTIVITY ANDSPECTRA SCALING
Noise source distribution from array scanning
Acoustic results from the array are shown in Fig.23 for the flat
and round flap edges. The results areobtained from the SADA by
electronically scanning aplane projected through the airfoil main
elementchordline. The position of the SADA corresponds tothe model
being in an "over-flight" position. An outlineof the main element
is shown with the leading edge at24 in. and trailing edge at almost
40 in. in tunnelcoordinates. The flap is on the right and the edge
isseen centered in the picture. The dB levels shown arethe outputs
of SADA when it is steered to the scanninglocations. The contour
levels are highest at the flapedge location. These levels at the
flap edge have beenshown36 to be the levels that a single
microphone wouldmeasure from the flap edge. The rapid roll-off in
levelsaway from the flap edge shows the sharpness of thearray in
rejecting unwanted extraneous noise fromregions other than the
edge. The contours shown arefor 12.5 kHz one-third octave levels.
Because of themicrophone shading algorithm methodology35,36,
otherfrequencies from 10 to 40 kHz show similar spatially-invariant
patterns. At lower frequencies, the resolutiondecreases (patterns
widen) and the array rejection ofextraneous noise is reduced. Still
the levels from the
vicinity of the flap edge should have littlecontamination for
frequencies above approximately 3kHz. The spectral output of the
SADA should hencerepresent only that noise which is radiated from
theflap-edge region. Noise directivity (shown in thefollowing
section) is mapped by placing the SADA at aseries of elevation and
azimuthal angles, whilemaintaining a constant distance of 5 ft.
from the flapedge region.
f1/3 = 12.5 kHz
ROUND M0=0.17
FLAT M0=0.17 FLAT M0=0.17
ROUND M0=0.17
Spanwise location (in)
Cho
rdw
ise
loca
tion
(in)
30
40
50
48 46
48
50
4852
56
6058
54
46
50
29o
6866
64 6258
56 54
60
58 5452
5250
52
5248
50
39o
-10 0 10
30
40
50
64 6260
5856 52
50 4848
48
58
54
5048
46
48
29o
-10 0 10
72 706866
64
62
6058 54
525052
54
54
5258
39o
FIGURE 23. Noise source distribution contours over the flap-edge
region using the SADA for flat and round edges at the twoflap
angles. SADA position is θ =107° and φ=0°. One-thirdoctave levels
for f 1/3 = 12.5 kHz.
Directivity
Figure 24 shows the model with the flap-edgedirectivity contour
mapped over a spherical surface,defined by the SADA positions. The
measurements arefor the flat edge flap model for α =39° and
M0=0.17.For the 6.3 kHz one-third octave frequency bandshown, the
directivity on the pressure side of the modelis most intense
“underneath” the model. This is theside that an observer would
"see" when an aircraft fliesoverhead. On the suction side of the
model, the levelsare less but are seen to increase in the
downstreamdirection. Figure 25 are pressure-side directivity
mapsfor α =29° and 39° and selected frequencies rangingfrom 3.2kHz
to 40 kHz. These maps are flattenedversions of the spherical
surfaces shown in Fig. 24.The positive azimuthal angles ψ are on
the flap side ofthe model. The elevation angles φ with the
smaller
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American Institute of Aeronautics and Astronautics
21
values (at the top of the plots) are in thedownstream direction.
For this flat flap-edgeconfiguration, the directivities have a
simple dipole-likeshape at lower frequencies with the dipole axis
orientedinline with angle φ at 90° to 107° and ψ=0°. Forhigher
frequencies (>12.5 kHz), the directivity has amore “baffled”
dipole character with stronger levels onthe flap side (ψ negative).
The directivity for the flangeedge is shown in Fig. 26, where at
lower frequenciesthe levels and patterns are similar to the flat
edgeresults. However, at higher frequencies, the
directivitypatterns are somewhat more complicated and the levelsare
higher. Results for the round edge flap are evenmore complicated
with generally higher levels andmultiple directional peaks;
suggesting a more complexedge noise source (pressure scatter region
of surface)than that found for the flat edge. With the
applicationof grit to the pressure side of the round edge flap,
thelevels decrease to approximately those seen for the flatedge
flap. However as Fig. 28 shows, the directivityremains just as
complex as the round edge without grit.
63
6465
66
67
68
69
70
71
72
72
71
70
Pressure Side
Suction SIde
FLOW
DirectivitySurface
Flap
MainElement
Edge
φ=107°
ψ=15°ψ=0° ψ=-15°
φ=56°
φ=73°
φ=90°
φ=124°
φ=141°
FIGURE 24. Flap edge noise directivity over 3D "surface"
defined by the SADA measurements. One-third octave levels
for f 1/3 = 6.3 kHz.
Spectra and scaling
One-third octave spectra for the three flapconfigurations are
shown in Fig. 29 for the SADAlocated at θ =107° and φ=0°. The round
edge is seento be the loudest configuration at low frequencies but
isthe quieter at higher frequencies than both the flat andflanged
edge flap. For the flanged edge flap, the broadspectral peak at
higher frequencies is particularly strong(and thus troublesome).
Figure 30 shows spectra fordifferent tunnel speeds for all three
configurations, plusthe flat and round edge configurations with
grit applied.The spectral level dependence on tunnel speed is
seento be the most important, followed by flap angle andthen by the
application of grit. The grit serves to trip theboundary layers
causing them (and thus the off-the-edge shear layers) to become
more turbulent andthicker. Noise levels are reduced.
The spectra of Fig. 30 are scaled by normalizingthe levels and
frequencies with McAVG from Eq. (8) and
δ from Eqs. (5) and (6) for the basic configurations,but from
Eqs. (7) and (6) where grit is applied. Figure31 presents this
scaling. The levels are referenced tothe fifth power of the Mach
number term. The levelsare not taken to depend on δ . This
normalization thusignores a slight decrease in low frequency noise
foundfor the flat edge when grit is used, but is consistent
withnegligible change in low frequency noise for the roundedge when
grit is used (see Fig. 30). The primary effectof thickness δ is
(taken as) to simply shift the noiselevels to a lower frequency
based on the Strouhalnumber f UcAVG1 3/ /δ . Note that the
normalizationbrings the spectra for the flat edge, with and
withoutgrit, into good general agreement. However, thereappears to
be some speed or Reynolds numberdependence in spectral shape not
accounted for. Thenormalization for the round edge is quite
successful.The spectra data for the with- and without-grit
casesappear well matched and coalesced. The spectralnormalization
for the flanged edge is also generallygood. A lack of coalescence
is seen over the broadhigh-frequency peak, likely related to the
flange cavity.For all configurations, significant success is found
incapturing the flap angle α dependence through the useof velocity
UcAVG . Because this velocity depends on the
flap CN , it provides the appealing connection between
noise and flap loading.
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American Institute of Aeronautics and Astronautics
22
6.3 kHz
12.5 kHz
20 kHz
40 kHz
3.2 kHz
ψ (deg)ψ (deg)
φ(deg)
φ(deg)
φ(deg)
φ(deg)
φ(deg)
FLAT EDGE29o 39o
FLOW
68
67
70
69
69
68
-30 -15 0 15 30
56
73
90
107
124
141
7374
75
76
77
78
76
-30 -15 0 15 30
56
73
90
107
124
141
65
63
6059
64
-30 -15 0 15 30
56
73
90
107
124
141
71
72
73
72
71 70
-30 -15 0 15 30
56
73
90
107
124
141
60
58
5656
59
59
-30 -15 0 15 30
56
73
90
107
124
141
68 67
68
67
64
66
-30 -15 0 15 30
56
73
90
107
124
141
5555
57
58
57
-30 -15 0 15 30
56
73
90
107
124
141
6465
666767
62
-30 -15 0 15 30
56
73
90
107
124
141
59
60
5556
60