AIAA 2000-1975 Flap Edge Aeroacoustic …mln/ltrs-pdfs/NASA-aiaa-2000-1975.pdf · δ0 boundary...

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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

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 edgedirection

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 / 0

McAVGaverage Mc , see Eq. (8).

M0 tunnel Mach number, U a0 0/n normal vector to surface at y


2

Rc Reynolds number based on c and U0

pa acoustic pressure time historyps surface pressure time historyPa Fourier transform of pa

Ps Fourier transform of ps

qc dynamic pressure based on convective speedUc

q0 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 density

γ 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 l3

η coherence decay factor for l1

θ angle between n and x , see Fig. 19′θ angle between n and ′x , see Fig. 19

ϑ 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


3

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


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


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


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.


7

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 = 29o

α = 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)


8

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 MC

MC

( =.0314)( =.0453) δδ

deg.deg. βCβC

TABLE 2. Calculated edge flow boundary-layer thickness andvelocity values.

SurfaceSensor U(z)

Top View

SensorSurface

Wake Sheet

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 velocity

along the suction side and upr is that along the pressure

side. The mean or average velocity jump over the chord


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 of

usu 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

02 . (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/ .0

0 015910= − (6)


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= ρ 2 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


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 cδ

(a) sensor #16 for α =29°

1 2 32πf1/3δ/U30

35

40

45

50

55


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


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


M0 = 0.17

M0 = 0.11M0 = 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- a0

deg 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


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


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


ABC

0 0.2 0.4 0.6 0.8 1

80

90

100

110

120

130


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


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 within

less than the time it takes to acoustically travel .25inches.) Final adjustment to obtain the full τ a s, shift

effect, 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 sj

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= .17

and α =39°. The spectral resolution is ∆f = 34.88 Hz, but

levels 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


0 0.2 0.4 0.6 0.8 1

80

90

100

110

120

130


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


0 0.2 0.4 0.6 0.8 1

80

90

100

110

120

130


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.


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 is

shown 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 is

shown 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 be

constant 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.


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

dSa

S

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

r

a0

(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 sj 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

= −′

′∫ ∗ − ′j

a rCos P P e dS

S

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= ∗

= −′

′∑ ∗ − ′j

a rCos P P e S

S

a sjkrω

πθ

4 0 ∆

∆( )

( )y

y (19)


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

= ∗∑

= ′′

−′ ∗∑2

4 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 be

the 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 scale

length 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.


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


-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


-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 2

1 1 120

2

2 21

πθ ϑ β

θr

U 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 , and

M U Cos aU c c

10= 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


19

direction normal to the edge. In evaluating the integral,we use the definition of Π te from Ref. 6 (Ref. 47 uses

an 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 β

ςω= 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 i

i

= ∑[ ] (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.


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°


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


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-third

octave 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


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 normalization

brings 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.


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

64

62

61

57

-30 -15 0 15 30

56

73

90

107

124

141

63

64

66

69

73

70

6863

59

-30 -15 0 15 30

56

73

90

107

124

141

FIGURE 25. Flap edge noise directivity over projected surfacefor FLAT edge flap. M0= .17 and two flap angles (α =29° and39°) for different one-third octave frequencies.

6.3 kHz

12.5 kHz

20 kHz

40 kHz

FLOW

3.2 kHz

ψ (deg)ψ (deg)

φ(deg)

φ(deg)

φ(deg)

φ(deg)

φ(deg)

FLANGE29o 39o

6664

69

69

68

68 67

-30 -15 0 15 30

56

73

90

107

124

141

72

72

73 72

73

73-30 -15 0 15 30

56

73

90

107

124

141

64

62

5857

61

63

60

-30 -15 0 15 30

56

73

90

107

124

141

72

6768

6970

71

71

-30 -15 0 15 30

56

73

90

107

124

141

66

5957

65

6463

62

-30 -15 0 15 30

56

73

90

107

124

141

6869

70

71

7269

67

6664

63

-30 -15 0 15 30

56

73

90

107

124

141

6159

64

65

67

66

66

67

63

65

-30 -15 0 15 30

56

73

90

107

124

141

74

73

74

72

71

70

69

6763

70

73

-30 -15 0 15 30

56

73

90

107

124

141

53

57

60

59

62

56

58

55

-30 -15 0 15 30

56

73

90

107

124

141

69

69

68

67

66

65

64

6562

59

-30 -15 0 15 30

56

73

90

107

124

141

FIGURE 26. Flap edge noise directivity for FLANGE edge flapfor conditions of Fig. 25.


23

6.3 kHz

12.5 kHz

20 kHz

40 kHz

FLOW

ψ (deg)ψ (deg)

ROUND EDGE29o 39o

φ(deg)

φ(deg)

φ(deg)

φ(deg)

φ(deg)

3.2 kHz

7473

72

71 70

69 6766

-30 -15 0 15 30

56

73

90

107

124

141

75

76

75

74

73

72 71

70 6968

68 69

-30 -15 0 15 30

56

73

90

107

124

141

69

68

69

70 70

7171

7267

6663

-30 -15 0 15 30

56

73

90

107

124

141

71

7273

74

75 76

72

-30 -15 0 15 30

56

73

90

107

124

141

70

7172

7374

73 74

71

72

-30 -15 0 15 30

56

73

90

107

124

141

6666

67

68

69

70

70

7371

-30 -15 0 15 30

56

73

90

107

124

141

55

56

5657

56

55

54

57

59

-30 -15 0 15 30

56

73

90

107

124

14166

65

64

63

62

63

67

68

65

66

68

69

-30 -15 0 15 30

56

73

90

107

124

141

5857

58

59

6061

59

62

-30 -15 0 15 30

56

73

90

107

124

141

6262

63

64

6566

67

67 6361

-30 -15 0 15 30

56

73

90

107

124

141

FIGURE 27. Flap edge noise directivity for ROUND edge flapfor conditions of Fig. 25.

6.3 kHz

12.5 kHz

20 kHz

40 kHz

ψ (deg)ψ (deg)

φ(deg)

φ(deg)

φ(deg)

φ(deg)

φ(deg)

3.2 kHz

FLOW

ROUND EDGE W/ GRIT29o 39o

70

70 71

69

68

67

-30 -15 0 15 30

56

73

90

107

124

14174

75

76

74

73

74

73

72

-30 -15 0 15 30

56

73

90

107

124

141

65

66 67

68

66

6563

-30 -15 0 15 30

56

73

90

107

124

14172 73

74 75

76

77 77 77

7675

-30 -15 0 15 30

56

73

90

107

124

141

57

58

59

58

60 60

59

-30 -15 0 15 30

56

73

90

107

124

14167

6869 70

71

72

7375

73

75

70

-30 -15 0 15 30

56

73

90

107

124

141

55

54

56

57

57

55

-30 -15 0 15 30

56

73

90

107

124

14162

63

64

65

67

69

7070

68

66

64

-30 -15 0 15 30

56

73

90

107

124

141

60 59

58 56

5553

52

53

-30 -15 0 15 30

56

73

90

107

124

141

63

61

68

65

6363

64

65

59

62

-30 -15 0 15 30

56

73

90

107

124

141

FIGURE 28. Flap edge noise directivity for ROUND edge flapwith GRIT on surface for conditions of Fig. 25.


24

55

60

65

70

75

80Mo=0.17

39o

29o

FLATROUND

FLANGE

100 101 10250

55

60

65

70

75

SPL1/3

Frequency f1/3 (kHz)

FIGURE 29. Noise spectra for the FLAT, FLANGE, andROUND edges for two flap angles at M0= .17.

CONCLUSIONS

The flat (or blunt), flanged, and round geometriesare flap edge configurations in actual use on aircrafttoday. Spectra and directivity are presented for each toform the basis for semi-empirical predictions. Newscaling methods are given. Significantly, with someexceptions noted, the noise spectra for each edgeconfiguration are very successfully scaled for flowspeed, flap angles, and surface roughness, using thesimplified flow and boundary layer calculation methodsdeveloped herein.

This study also provides an experimental andtheoretical validation that, for the flat flap edge, shearlayer instability and related pressure scatter is thedominant noise mechanism. For a higher flap angle,measured noise levels exceed predictions, whichsuggest additional contributions from surface sourcesthat are not localized to just the immediate edge region.Such a source is likely related to the vortex burstingthat occurs at the higher angle. As with the flat edge,shear-layer instability effects should be responsible fornoise for the rounded flap edge, but the geometricfeatures for the mechanism are different, producingdifferent pressure scatter patterns and noise directivity.The flanged edge flap has an additional (andtroublesome) high frequency noise contribution, likelydue to cavity-type effects.

Several newly applied diagnostic tools based oncross-spectra are used to determine the character of the

29o

39o

29o39o

SPL1/3

Mo=0.17

Mo=0.11

Mo=0.07

100 101 10230

35

40

45

50

55

60

65

70

75

80(b) FLANGE

Mo=0.07

39o


100 101 10230

35

40

45

50

55

60

65

70

75

80

SPL1/3


Mo=0.17

Mo=0.11

Mo=0.07

29o

39o

39o W/ GRIT

(a) FLAT

100 101 10230

35

40

45

50

55

60

65

70

75

80

SPL1/3

29o

39o

39o W/ GRIT

29o W/ GRIT

(c) ROUND

Mo=0.07

Mo=0.11

Mo=0.17


FIGURE 30. Flap edge noise spectra for (a) FLAT edgewith/without GRIT, (b) FLANGE edge, and (c) ROUND edgewith/without GRIT.


25

10-2 10-1 10080

85

90

95

100

105

++ + +

++ + + +

++

++

+ + +

+

Mo=0.17 29o

Mo=0.11 29o

Mo=0.07 29o

Mo=0.17 39o

Mo=0.11 39o

Mo=0.07 39o+

(d) ROUND

SPL1/3-10log M5

cav

f1/3δ/UcAVG

10-2 10-1 10080

85

90

95

100

105

++ + + +

++

++

++

++ +

++ + + + +

+

Mo=0.17 39o

Mo=0.17 39o

Mo=0.11 29o+

(b) FLAT W/ GRIT

SPL1/3-10log M5

cav

f1/3δ/UcAVG

10-2 10-1 10080

85

90

95

100

105

++

++ + + + +

++

++

+ ++

++

+

Mo=0.17 29o

Mo=0.11 29o

Mo=0.07 29o

Mo=0.17 39o

Mo=0.11 39o

Mo=0.07 39o+

SPL1/3

f1/3δ/U

-10log M5

(a) FLAT

c AVG

cav

10-2 10-1 10080

85

90

95

100

105

++ +

+ ++

+ ++ + + + +

++

+

++

++

Mo=0.17 29o

Mo=0.11 29o

Mo=0.07 29o

Mo=0.17 39o

Mo=0.11 39o

Mo=0.07 39o+

(c) FLANGED

SPL1/3-10log M5

cav

f1/3δ/UcAVG

10-2 10-1 10080

85

90

95

100

105

++ + + +

+ ++

++

+

++

++

+

Mo=0.17 29o

Mo=0.11 29o

Mo=0.07 29o

Mo=0.17 39o

Mo=0.11 39o

Mo=0.07 39o+

(e) ROUND W/ GRIT

SPL1/3-10log M5

cav

f1/3δ/UcAVG

FIGURE 31. Scaled flap edge noise spectra for (a) FLAT edge,(b) FLAT edge with GRIT, (c) FLANGE edge, (d) ROUNDedge, and (e) ROUND edge with GRIT.

hydrodynamic flow pressure field and the near-fieldnoise. The noise generation distribution along the flapedge is determined. Two different noise predictionmethods are developed and successfully validated from(1) a causality approach, utilizing cross-spectra betweennoise and surface pressures, and (2) an edge-noisescatter solution. Both methods use unsteady pressuredata taken by sensors at the flat flap edge. A CFD flowsolution is used as a guide for the basic flow patterndescription, but simplified flow calculations provide thenecessary boundary layer flow parameter inputs for thenoise predictions and scaling. The predictions providedifferent but consistent theoretical bases forunderstanding the noise production at the edge.

ACKNOWLEDGMENTS

The authors wish to gratefully acknowledge DanielJ. Stead of Lockheed-Martin for data processing,software development, and analysis. The authors alsogratefully acknowledge Ron C. Verhapen of WyleLaboratories for data acquisition system managementand support.

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