[American Institute of Aeronautics and Astronautics 38th Aerospace Sciences Meeting and Exhibit -...

(c)2000 American Institute of Aeronautics & Astronautics or published with permission of author(s) and/or author(s)’ sponsoring organization.

AIAA 2000-0607 FREE-WAKE ANALYSIS FOR CALCULATING THE AEROACOUSTICS OF A WING-FLAP CONFIGURATION Trevor H. Wood Sheryl M. Grace Aerospace and Mechanical Engineering Department Boston University, 1 IO Cummington St., Boston, MA 02215

38th AIAA Aerospace Sciences Meeting and Exhibit

January lO-13,2000/Rena, NV

1

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FREE-WAKE ANALYSIS FOR CALCULATING THE AEROACOUSTICS

OF A WING-FLAP CONFIGURATION Trevor H. Wood*

Sheryl M. Grace+ Aerospace nnd ~echanicnl Engineering Depnrtment

Boston University, 110 Cummington St., Boston, MA 02215

An efficient me%hod for predicting the aeroacoustic performance of high-lift wing configurations is applied to a rectangular wing-flap system in impulsively started flow. The flow is assumed attached, inviscid, subsonic, isentropic, and irrotational outside the surfaces of the wing and wakes. An unsteady panel code is used to solve for the perturbation velocity potential on the wing surfaces. The wakes are modelled as thin vortex sheets whose strengths are determined by the unsteady Kutta condition at the sharp trailing edges. A free-wake analysis is used for the wake evolution, and results are compared to a simple flat-wake model commonly used for fixed-wing solutions using panel methods. The surface potential solution on the wing and flap and the potential jump across the wakes are then used to evaluate the acoustic signal in the far field. Results show that the simple flat-wake model overpredicts the radiated sound energy level.

Nomenclature 4 = * - U,z, perturbation velocity pot,ential UCC freestream velocity L Length scale (appr. 777 chord) 2 = 6 + lJm& linearized material derivative

L = urn/c, speed of sound Mach number

;=&TF ,non-linear source terms Prandtl-Glauert parameter

CP coefficient of pressure I,P acoustic intensity, power P power level T* retardation time n out,ward unit, normal vector (“, t), (Y, T) position, time of solrce & observer s wing and wake bounding surface

Subqcripts: cc freestream value i ith spatial coordinate (TE) panel adjacent to trailing edge

Overscripts: Prandtl-Glauert space t,ime derivative unit, vcctol

I

Introduction

A IR.FR.AI\IIE noise is 110w ii dominant, source of noise for approaching/landing aircraft,. Source

localization measurements show that in some cases, the noise radiated from the high-lift systems domi- nates over engine noise as an aircraft passes directly overhead.’ A fundamental understanding of the generation of airframe noise and the development of efficient, prediction methods for airframe noise are, thus, highly important if future progress in aircraft noise reduct,ion is to be made.

I\/lany empirical and computational investigations of high-lift systems and their associated noise have led to important observations and insight, regarding the dominant sources of the radiated soured.“-* In particular, the influence of wakes and shear layers emanating from sharp trailing edges and sides edges of slats and flaps arc thought, to be responsible for the tonal, or narrow-band, acoustic responses observed. The interaction of these shear layers with the solid surfaces can lead to feedback and enhance acoustic radiation.

n4ost of the computational techniques Currently used to investigate high-lift noise involve finite diff’cr- ence solutions to the RANS equations using various turbulence moclels. Due to the existing limitations on computational power, those methods often focus primarily on two-rlimcnsional geometries. Thcre- fore, the exclusive use of these methods limit,s the impact of quantit,ative noise cstimatcs 011 high-lift,


systems design. It is the objective of this project to develop an efficient rnodel of the wakes a.nd shear layer generation to allow for first order noise esti- mates to be obtained with much less computat,ional expense. To be an effective design tool, the method must be able to model three-dimensional complex geometrical configurations and include the interaction of all noise sources simultaneously. To a.chieve both the generality and computational efficiency re- quired, a boundary element or panel method is em- ployed to describe the fluid flow around a lifting wing.

The development of the method used here was initially described in [Ref.91 and was applied to t,he rectangular wing-flap configuration similar to that shown in Figure 1. Those preliminary results as-

a) 3-D view

’ ij U-

w -N

f 0.05

b) 2-D view

Fig. 1 View of wing-flap geometry

sumed a flat-w~~ke geometry which is unphysical. III reality, the evolution of the wakes are affected by t,he unst,cxdiness in the surrounding fluid, the proximity of the wakes to the flap, and the intrinsic instabili- ties. Thus, the flat-wake assumption suppresses any spectral structure associated with a wake-body feedback mechanism. The present investigation extends t,he results of [R.ef.S] by allowing the wakes from the main clement and flap to evolve freely with the local fluid velocity. It, is shown that the free-wake t,rajec- tory affects the coherence of the sound it radiates; t,hus, the noise predictions from t,hc free-wake analysis are less than those predicted using the flat-wake model. The inherent wake instabilit,ics and can be captured with a free-wake analysis do not appear in this simulation beca.use of insufficient, flow pf2tur- bations. With the inclusion of unsteady boundary layer or turbulence 11lode1s to excite the wake insta- bilities, the acoustic output may be cnhancetl. This will be a focus of future research.

Method An approximation to the Navier-Stokes equations

for an isentropic flow past solid object,s at, high Reynolds numbers is given by the inviscid Euler equations with additional models accounting for vis- cous effects. When the flow remains attached over the solid surfaces, the predominant effect of viscos- ity is the generation of wakes at the trailing edges of each wing element,. At high Reynolds numbers, these wakes may be modelled as thin vortex sheets. The flow field outside the solid surfaces and wakes is potential which can be decomposed into a uniform freestream and a perturbation due to the presence of the solid bodies and wakes. Further, it, may he shown that the perturbation velocity potential, 4, satisfies the convective wave equation”

M2 024 - - O”@ = 0, Dt’

where the freestream is assumed, (without loss of generality) to flow parallel to a, and (T accounts for the nonlinear terms which include refraction and steepening effects. For subsonic flows (M < 0.3), o may be neglected. lo, l1 In Prandtl-Glauert space, defined as

(g-j = Fr22,Z3,t- !!$), ( the convective wave equation takes the form of a standard wave equation. The solution can be writ- t,cn, using the classical Kirchhoff integral equation, as

c&x, t) , for x in field I= ;J(x,t) ) for x on wing (3)

0 1 for x inside wing

where r* = t - 7:/C, S: = /3/M, and 7’ = 1% - ?I. The terms in the integrand represent monopole and dipole sources, respectively.

Equation (3) may be solved numerically for 4 on the surfaces by discretizing the surfaces, assuming C#I is approximately constant on each surface clement (i.e., panel), and associating X with collocation points located at the centers of each panel. This results in a matrix equation of the form (dropping t,ildes for clarity)

AMERICAN INSTITUTE OF AElIoNAUTlCS AND .kSTKONAUTIC:S


where the indices i, j, and n correspond to the collocation point, panel, and time iteration, respectively, yc, locates the center of the jth panel, and (B) and (W) refer to the wing and wake surfaces, respectively. The normal perturbation velocity, 21, = &$/&, is determined by the impermeability boundary condition,

U,- n+v,=O, (6)

for a steady wing, and the potential jump on the wake, A$, is determined by the unsteady Kutta condition

(7)

Across infinitely thin shear layers, &$/an is contin- uous and thus the monopole source strength is zero

main element with a .NACA 6412 flap was chosen

on the wakes. At each time step, the corners of for the section profile of the rectangular wing, which

each wake panel are moved a distance U,At, where had an aspect ratio of 6. The leading edge of the

U, is the convective velocity. The preliminary re- flap was placed 0.03 (in units of main chord length)

sults of [Ref.91 use a simple flat-wake model which upstream of and 0.05 below the trailing edge of the

fixes U, to be identically Uoo~; a free-wake analysis main element. Flap deflections between 5 and 30 de-

is obtained by using the local fluid velocity for U,, grees were considered. The entire wing was inclined

obtained by taking the gradient in ji of Equation (3). at 5 degrees angle of attack to the flow. See Figure 1

The velocity influence of a constant strength doublet for a view of the geometry.’ The transient problem

panel is equivalent to that of a vortex ring; the ve- of impulsively started flow was chosen as a canoni-

locity influence of a straight-line segment of a vortex cal problem which can be related to real situations

ring is given by the Biot-Savart Law, of unsteady motion (e.g., flap deployment, sudden gusts, etc.)

A4 r1 XC2 r1 C2 1 1 --- "12 = 4x lrl X r212 + d2 r0 ' Tl (8)

T2

where rr and r-2 are the end positions of the vortex segment relative, to the observer point as shown in Figure 2, r, = rl - rz, and 6 is a regularization parameter. Because of the singular influence of a line vortex, regularization methods are necessary to sta- bilize the numerical integration of the wake evolution as random numerical error will otherwise result in unphysical wake shapes. l2 For the results presented in this paper, 6 = 0.1 was chosen in accordance with typical values used in [Ref..lZ].

Once the near-field surface potential is determined, it can be substituted into Equation (3) to calculate the far-field potential. The pressure in the field is then obtained using Bernoulli’s Equation.

Results The transient response to a suddenly accelerated

wing was calculated assuming homogeneous initial conditions at t = 0. Compressibility effects were ignored (M = 0) for this preliminary investigation; thus, GT,, in Eq. (5) vanishes and the retarded time, r*, reduces to the observer time. Velocities are nondimensionalized by the freestream velocity which is chosen to flow in the x1 direction. A NACA 23012

P(x)

Fig. 2 Schematic for Biot-Savart influence of a straight-line segment.

The evolution of the total lift on the main element and the flap are shown in Figure 3. A monotonic increase to the steady-state lift is observed for the main element, whereas the lift on the flap is seen to initially overshoot its steady-state value. This overshoot is due to the proximity of the flap to the main element and its wake. The mean difference between the flat-wake and free-wake results for all flap deflections is approximately 4% and 6% for the main element and the flap, respectively. The surface distributions of the perturbation velocity potential and the pressure coefficient are shown in Figure 4 (on p.4) for a 20 degree flap deflection at time t = 2. The.free-wake and flat-wake results are shown with solid and dashed lines, respectively. The potential jump across the wakes is shown downstream of the surface potential distributions; the large deviation at the end of the wakes are primarily. due to the large geometrical differences between the wake shapes as the flat-wake model neglects the wake rollup around the starting vorticity. The wake shape from the free- wake calculation is shown in Figure 5. In Figure 4, the flat-wake results are seen to exhibit a greater lift than that calculated using the free-wake analysis.

The far-field pressure was evaluated at 40 points along a circle that has a 500 chord radius and was centered at the centerspan section’s leading edge.

3 AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS


“0 0 5 7.i:nc

I.5 2

i( 1 Gz .- -1 -2 2? c-” cl.1 *

” LL

“0 0,s rilne

I.5 2

a) Fht Wake

“0 03 TiLc

I.5 2

31 1

“0 0,s Tike

1,s 2

b) Frer Wake

Fig. 3 Evolution of total lift per wing element. Flap deflections increase from 5 to 30 in steps of 5. The lift increases monotonically with S.

The fly-over signals are shown in Figures G and 7 for t,llc vclocitJy pot~enthl, coefficient, of prcss~m, a~1 ilV(!1;Lge radial acoustic int~crlsit~y, wlicre the fiy-ovcq, tlircc:tion is clefiiied li0l~lii;il Lo t,lie fl.O(!St~l.~~illll ;lntl (li- m:t.ly l~chv (on the pressllrcb sitlr of) tlicl wiilg, a11t1 t,llcl ilV(‘r:lKt! radi;il ac~oiistic~ iiit,c~iisit,y is tlcfiilc~l l)y”’

<I,. >= $[(c,,+z$) Ed,. (‘3)

Tile sign& ge~~(!ritt,(~d Ilsing the free-wake ;maly- sis arc vcq similar t,o t,llosc: using t,lie flat-wdul motlrl. Tlic iiiiport,mt, tlist,irlc:tiun wc~irs at, earl) t,iiim whtr tl(lviihOlls ill t,llc! posit,ioli of 1.11e st,;irt,- iilg \mt,os of t,licl imin (~l(flllmt~ II;I\Y: ;L sigilific,;ult. (sf1;:cI. (luch t,o t,lic: itit,(br;i(.t ioil wit.ll t,lio 11;111. B(Y;IIISC: t.ll(! flXT \Vill<C‘ Of t,ll(! lnihk ~~l(L1llO1ll. I);lSSC!S 11111(~11 C:lOSC~l

- - II 6 . Flat-Wake - Flee-Wake

0 ? .

01 .

Sfreamwise

a) Potclltisl

Fig. 4 Surface potential and pressure distributions along the centerspan for 20 degree flap deflection at time t = 2.

to the flap t,han the flat w;th, the early t,iinc~ varia- t,ioils in the far-ficltl pressure aid ;tcmist,ic iriteiisity arc! cs],fx:t*cxl.

T11tb clirc~c%vit,ics of thcb t,<)t,id ruliill acmlst,ic. in- t,c!llsit,y arc s11ow1l in Figure 8. BW;IUW of dl(l ill- c,oiill)~(!ssil)ility assuiilpt,ioii risctl in ol)t,;hiilg t.hesc l)r(~liitiiiiary rcsult,s, iLIly fiow tlist,rirhnc:c itiflriciic:cs id1 poiiit,s in ~)llil,SC!; tllus, t,hct thchvity is pI‘~~lOlll- iiimt,ly tlipolar wit,11 the peak radi;~t~ioii dose! Lo the lift axis. A slight t,ilt.irlg of t,lltr tlipolo from t,llc: vtrrti- C;LI axis arises IVX;LIISC~ of tile wake gc~omctry ilIlt t,llr: st,rcamwisc! gra(1ient.s of th surfau> source strc~iigths. Th leak ratliation fum tllc fht-v&c! rcsu1t.s is sw11 t.0 I,(, sliglit,ly overl)l’c~tlic:t,c1(1 and t.ilt,d ;dt. 011 t,lic> lm5slirc~ sitle.

II!, iilt,cgriiLiiig t,lic! ;Ivc~r;igo ratli;il ;ic:ousl.ic: iiikii- sit,v i11.01111~1 t.llcs t’;lr-lidtl 111~‘;15111~~‘11i~:lII. c:irc:l(~. ;L 1110;1- Slll~(’ Of’ t,ll(: iIVC!r;lgC’ ;lc,orisl,ic: ])OhY!l’ l’il(li;Lt.(:(l ;l.lOllg


t,lIc! t,wo-tliIIIeIIsioni~l c:cillt,c:rsp;lIl I)liulC dliring t,llo so- IIItion t,inIo int,erv;Il T is oht,;liIIc!d; i.e..

The dimensional scalings L E 10 III; pu 2 1 kgjm”~ anti u, N 35 m/s wcrc used as Lypical values for low-SpCCtl, lOW-iLlt,it,Utle flight,. A s0uIltl power l(~\%l ‘P may now be defined 1)~

<r> ‘P = lOlog,,, -

( > pTY!f ’ (

where q.,>f = 1 x IO-“IV. Figure 9 sl10\\3 tlict variation bf P with flap deflection iIIlgl(! for ht,li

free- and flat-wake mod&. Here, it is SwII thilt th

flat-wake model overpredicts the r;4iation by about, 0.02316 - 0.0879 dB when compared to the fr(~+\vi~ke results.

The Fourier transforrns of the fly-over acoust,ic: in- t,eIIsit,y signals are given in Figure 10. No appreciable tlifference in the SpCCtriL is ol)served from the simple flat-wake Inodel. In these conil,IIt,;It,ioiis, t,lic nat,u- ral SllC!iX layer inst,abilit,ic!s which can l>c c:apt,urc!d l)y the free-wake analysis itre not. prc:sc!nt, tlue t,o il lack of sufficient flow p(-~I.t,Iirl);It,ioIis. If il model for l~oundary layer or inflow turbulence were iIic:lutletl, ii

tlifierent SpCCtritl character would IX expected. Per- hiips with the inclusion of the resident vorticity in the slat cove for high-lift systems with leading-edge sla.ts, sufficient lift, fluctuat,ions will be observed itIld

the shear layers will respond more actively. These conjectures, however, arc topics of future rese;i.rc:h for this project,.

Conclusions A11 efficient. method for c:;ilculat,ing the Iioisc r;i-

cli;I.ted froIn high-lift, syst,cms is applied to a rectangular wing-flnp configuration. .411 unst,oatly pilIld

Incthod is chosen t,o solve the flow field. The flow is assumed attached, inviscid, subsonic, isentropic:, and irrotational everywhere but on t,lie solid surfaces of t,lIe wing and in the wakes. The first order pcrtur- bation t,o the freestream vclocit,y potential may bc described in tcrIns of monol~o1e and tlipolc soiirces tlistributcd along the wing and IviIlte sIIrf;tc:c:s, whew tht: source strengths arc tl~~terruined t,lIrouglI t.lIe l.)o~mtlary contlitions. The acoustic: field is t,lIcu tl(:- t~~~rIIiiric~1 from ;I direct KirclilIr)ff int,egrat.ioII of I,licsc surface sources. The wakes slietlding froiII t,licl slI;irp trililillg edges of the wing arc nIodo11ctl iisiIIg the unsteady Kutta c~ontlit,ioIi to ensure fiiiit,c trailing c!tlge velocities. The wakes evolve freely under the influences of all the solid surfaces and walccs aid die frcest,rc!;mI.

This IIIet,lIo(l 1~s IWW ~Isc:tl to rnotlcl t,hc iIIIpul- Si W’ly Still-t.Cll IlO\\: ;IrOulltl ;I 1.CCt,illlg.lll;ll. n-Q ilIl<l

fl;ll) to iII\:est,ig;tt,t! t,lIe eff’ec:t, of fl>Il) tleflect,ion. TlI~sc~ rcsult,s show that. a fiat-wake Inoclel (oftcii 1Iselt1 foi fisetl-wing i~erOtl):Il&I~li(: ~:~ll~~ll1i~t,iOIlS) overpredicts t,lic sound radiated l~c:ause the wake roll-up tends t,o retl~~cc the coherence of the wake sources. T11c results also show that the spectral response of the system is relatively unchanged when the free-wake evolution is cniployt~l. The passage of the w;~ke from t,lIo Inain element over t,hc flap >3,l>p(!ill'S nut, Lo I)rovitlc ii sufficiently strong interactiori to promot,c: HlIc:t,uatioIIs in t.lIe vortex sheet,. The starting vort,cs serves Lo gcncratc ;I iiot;il~l~i iIiter;~cl,ioIi only in t,lic c;ii~ly time of the solIIt,ion. Bcc;uisc! of t,lIe co~ivcx-

lion of this tlist~Iirl~;mc:e, the perturbation is swift,ly tliminis1iet1.

The preliminary investigation of using pant-:l m0tli& to efhciently coniput,e the aeracoustics of high-lift, systems is il1IIlOSt complctc. Next,, the aero- dynamics and aeroacoustics of a full span wing-slat, configuration will 1~ calculated and the rcslilts will 1~: cumpared to the two dimensional results of Guo’” ant1 esperiment~al clata. Second, an invcst,igation of side-edge flap noise will follow where t,lIe slIr!iIr lap instability will bc iIiodf~1lf~d by allowing for nwlw gen- Cl’iLtiOIl at, all Slliirp bends in the wing geoInet,ry in :IcltlitioII to the trailing edge. Again, expcriIncnt;tl and computat,ioIIal data will help fully valitlate the method at this point.

Acknowledgments The authors would like to thank Kadin Tscng: md

Luigi Merino for the enlightening discussions. THW w\;ould like to thank the National Sciences and I+- gincering Research CouiIcil of CiuIada arId Boston 1JIIiversity for tin;I.ncially supporting the rcsoarch.

References


-0.2 - x”

-0.4 -

-0.6 -

0 0.5 1 2.5 3

b) 2-D view

Fig. 5 Free-wake geometry for 20 degree flap deflection at time t = 2.


x ld aJ

-0.5 -1

j-I: -2.5

0.5 1 1.5 2 x 1o-7

-5 2 g -1c

-15

0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2 Time Time Time

x 1o-6 5J

2.5

I x 1o-1s r

15

Fig. 6 Signals observed at the ‘flyover’ location (500 chords below t,he wing) using the flat-wake model. Flap deflections increase from 5 to 30 in steps of 5. The amplitudes increase monotonically with 6.


0.5 1 1.5 2 x 1o-7

2.5

2

1.5 0.5 1 1.5 2

x 1o-7 -2 -4

3 -6 z -8

-10 -12 -14 * .

(I.5 -1 1.5 2 x 1o-6 .

0.5, 1 1.5 2 x 1o-6

-1

73 d-J-- g

2

-3

-4 0.5 1 1.5 2 0.5 1 1.5 2

Time 0.5 1 1.5 2

Time Time

I 15

x lo-l5 r

10

5

Fig. 7 Signals observed at the ‘flyover’ location (500 chords below the wing) using the free-wake calculation. Flap deflections increase from 5 to 30 in steps of 5. The amplitudes increase monotonically with 6.

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(c)20%0 American Institute of Aeronautics & Astronautics or published with permission of author(s) and/or author(s)’ sponsoring organization.

Main

Main

Flap a) Flat Wake

Flap b) Free Wake

Total

Total

Fig. 8 Centerspan directivity plots of < I,. > r4. Flap deflections increase from 5 to 30 in steps of 5. The intensity increases monotonically with S.


10 15 20 Flap Deflection, 6

25

Fig. 9 Total planar acoustic power level radiated in centerspan plane.


.

\

---_ ------

” e ‘I I II,,,,,,, I I1 I I I I I I

‘-,-1-s-,1,-1-1-1

---9----- ---

10-17- 0

2 Frequency

a) Flat Wake

- OS r-l -- IO 1-1. 15 ,<,,I 20

- 25 -- 30

2 Frequency

Fig. 10 Acoustic spectra of Hyover int.ellsity signals. Flap deflections increase from 5 to 30 in steps of 5.

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