4 l r d AlAA Acrospacc S c il?ccr Mec mg and E r h h i t

J a n u a r y 10-13, 2005, Reno. Neifada

Control of Cavity Tones i11 Supersonic Flow

High levels of acoustic noise can be p r o d ~ ~ c e d when a cavity, such as an open aircraft bay, is exposed t.o a supersonic cross-How. The noise is d ~ t e to ;I fttedtnck loop between shear layer distutbanccs a t cavity lip and acoustic wavcs insidc cavity. Rcccrttly it has bccn sllowrl in modcl-scalc wind tunncl tcsts that microjcts can bc uscd vcry cflcctivcly for supprcssing cavity toncs by placing t h m i along the lcading cclgc and thercby disrupting ttlc loop. To achieve the goal of deriving an opt.inial control strategy for cavity noise reduction based on microjets, an inoovative cavity acoustics model is devc!loporl in this paper that rigorously explains the role of microjets in cavity noise suppression and predicts the magnitude of noise reduction for a givcn control input ( tha t is the stcady pressure at which the rnicrojcts are fired). Thc model is developed using a physics-based systcrnatic frarncwork govcrncd by thc sta~lclard acroacoustic equation to cxplairl the cavity tones. Thc introduction of microjcts is treated as a momentum addition t,erm that acts as an active damper and suppresses the tones. The model is validated through comparison of its noise recluction predictions with cxpctin~cnts done using thc Florida Statc CJr~ivcrsity cavity and wind tunnel for different nlicrojct prcssurcs.

I. Introduction

H I G F I nvisc Icvcls can b: producctl when a cavity. mcll as tllc (JPCII iritcrn;.~l 1 x 1 ~ of an aircraft. is esposcil 10 a11 t:xt t,rxa.l cross-fIc IW. Soise Ievt:ls of' ; ~ ~ . i ) l i r l ( l 170 (It3 ~loist: I I ; I V ( > 1)t!e11 ol).st!r\;e(i i l l R (:;wil.y ~~rlder . \;I;1(.11

2.0 f low. ' iL.i illt~st,ri~ted ill Figure I . Such lluisr Irvels c m potenti;~lly Iw l ~ i ~ r i l ~ h ~ l to the strucr.~iral life of wilpon systclns insidc a 1,-eapon hay and to landing gcnr cl(:plo~mcnt.

Figiwc 1. High acoustic I oise inside a cavity c x - Figure 2. Illr~stratinn of optimal closed-loop con-

1)oscd to cxtcrual cross-flow with A1 = 2.0, R c = :3 trol strategy to bo 1-?lnployed in this paper for cav-

111illion (based on cavity Icngth) and L,Q = 5.1. ity noise rcduction.

A. Prot)lr:m Statement

c . x l ) t~~ . i t~ le~~t i~ l il~\;t,siigt~i,io~~s! ze ro fd ~ I I 011 I ~ I P ~ ; I ( I ~ I I ~ ~!(I:I) ~ l ~ i ( . ~ o j t ~ l > ,IS t111, 1110st t4i't,(:tive ; L ( : I I I ~ I O ~ for ril\,ity 1:uise ~.ccluc.iion. that nsc,\ thc S I I I ~ I I I P S ~ florv ratc. l'l~is pnpi'l. I l ( , ~ ~ , l t q~s il ~ ~ l o d t + l ) i ~ c d optinla1 clmcd-loop .

C ' . ~ ~ w i ~ l ~ t 'c; '200-5 hy t l v , a ~ t t l m * . I ' I I ! ~ I ~ s I I I , < ~ I > \ , 111 , \ I B ! ~ , ~ W ~ ) I I I I I \ ~ I ~ I ~ I , , , I \< I , ~ I I ~ ~ ~ I I ~ < - , I I I ( I . \ d r o f ~ a t i t i ~ . I n ? t\:itlt

1 , 1 l l ~ l ~ ~ l l ~ l 1 .

43rd AIAA Aerospace Sciences Meeting and Exhibit10 - 13 January 2005, Reno, Nevada

AIAA 2005-793

Copyright © 2005 by . Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

c:on~~.ol st~.alt,gy tiv t.his l ~ ~ u l ~ l t ~ n l . ' I his s t~x tcgy i.\ cl~,pic.rc:d i l l Fig111.c: 2. ' 1 ' 1 1 ~ ~)~.c!ss~ir,c~ sc.i~s~.)rs 011 t 11c c:;rvity \%~11k I ! w w r e 11oise l )as t~ l or] hid^ I I I ~ ( . O I I I rol i r l ~ ~ u t , whilh in t hi5 ( ;t>t\ i > 1.11e .sleii(l,~ I ) I Y Y S I I I . ~ ;it, t v l l i ( ~ l ~ 1,11(,

~nir.ru,ier.s can l~c. f i r d ;it thc 1c;lcling rtlgcs. i:: givc.ii. 'l'h? I I I I . ~ ( ! ~ to h.? t ~ l l ~ p l u y d f1.r L Y ) I I T . ~ O ~ ~ ~ I o I I ~ ( ~ r1wcssiKi1y I N ? I ~ ~ ~ ( ~ I I ~ ( ~ I ~ - I . ) I ~ ~ ~ ! I ~ ; I I I ( ~ par;~~ll(~Lrir (,say: 111

t1111s ;tIlowing for (,lose(l-loo11 opt,i~uimtion. Tile I I I C J ~ ~ I S I I O I I I I I iilsu 1v1i;d)I~~ ( X ~ I , I I I , ~ t , h ~ ( v r ~ w t trt~11(1 i l l 1 1 1 ~

c.l~;tr~gtfi ill OASPL (Overall So~rntl P r e s s ~ ~ r e Le\.el) ol' prrss~lrt. sensors wit 11 \,itriation in control i ~ i p l ~ t . From whilt k~llows, it is cxpccttil t ha t for a11 urlcor~t.rollccl ca\-it\; and for a cavity \ritll ~ i~ l i fo rm spilnivisc

~r~icro,jet firing. the flow (Iyr~arrrics illsitlc is t , n ~ ~ ~ t l i ~ r ~ e ~ ~ s i u n n l , n;hilr t i ~ c flow tly~ian~ics clt~c to ~ l o n - ~ ~ r ~ i f ~ r r r t 1iri11~ is ~.l~r(~e-cli~~ie~~sio~~;~l. H P I I C ~ . t,hr pal)el, firhi ( l isc~~ssc~s ii t \ ~ : o - ( l i r ~ ~ ( ~ ~ ~ s i o ~ ~ > t l ~r~o(lel \.;~li(l for 1 1 1 ~ ~ IIO-(Y)III 1-01 and unifc)r~ii firing cases, i~iltl thcii a three-dii~icnsio~i:~l ~norlol valid fcx noli-uniform firing. 'l'llc t t ~ r c c ca.scs a.1.t. clt$c~tcd in I?igllrc :;. I'hc: thrcc!-tfirl~crlsi(.~~~iil r11otic:I i!: s u l ~ s o q n t ~ ~ t l y i~scd f o ~ tlc:vc!lopi~~g tlit. apprc)pri;~.tc:

unifi~rni firing

Figure 3. Classification of models used for various t,ypes of cavity-unrler-extmal-woss-flow prohlems in this paper.

B. Background

- - - - - - .- - - - - Fluid-Resonant (transverse, acoustic)

subsonic supersonic

Fig111 r, -I Diili~rrr~t flow regimcs zeen by a cav- ~ l y ur~rlrr cxtwnal rros5-strcarrt.

wht:rc f.\, is t he freql~ency JTIz) c)f t11c .\:ti1 ~llotle. .\- =-

1.2: . . ., p is a phase constant l x t w w n the clc.)um.itrc:au~ p1~)l)- agatiug \:ortical d is turhanct .~ and the 11pst ream pr ( - ) l ) i~z i~ t i~~g acoustic waves, I l k is i l vort icity parameter.

is tht: spccific 111:;1t ratio. p iuld A. i11.v typicdly ot)tairlcd (wlpiri(:idly. TIIC Rossitcr's r i ~ o d i h ~ ( l f(~m11111;i is oi)titiil(d hy i r i i ~ t d ~ i ~ ~ g of t.i~ric: s (~ id (~s of t 1 1 ~ s h ? ~ r IiiJT'r Os(~i~~i~t , iO~ls : ~ ~ l d a(:c)llstic W;ivCS, \i:h(~l'o 'ti111(! sGII('s' rcfws t o thc fi.c~l~c'r~c*y illltl [)llasc of osdl i~t io l l .

Thcrc arc currently two iutcrprcd ;rtioils for t h : rlrivil~g rr~oc~~larlisrrl for (:;wit!; t,ollc? 1111(101. 1<ossit('r 1110(1(: i l l l(I ill'(>

l i - (i, -1

__.--*-- l e l i i e t l i F i r . T i 1 : 1 1 i s 1 I y i e ,

~,,,,,,daly C O G ~ I: , ) .~~ n i m n e ~ i ~ a r y t l o ~ ~ L ~ l , l l p l , ~ , c ~ , f , , , , l

is the ~ ~ ~ o n ~ e u t a r y tlow separatioll a t tllc Ir i i t l i~g that , s c l m n ~ i o n I ~ I I I I ! : I U U I ~ I ~ I L I I ~ I ~ I I C C , L ~ ~ ~ ) t ~ ~

wner slicdd~ng s e.:r layel result,s in periodic sheddin: of locializt-:d vo~.tic.is. A lit- erature sl.lrvey. Ilowever, i~ dicat,c:s t hat ~ u r t ical shctldin:: Figure 6. Two interpretations of the dl-iv- has not heen o h s e r ~ ~ d at a'l 1\Tad1 n~unbers (only h n - e e u irlR mec.l;ll,isln for cavity toiles rll,del. exter.Ila~

C. Contributions of Pa ow

This p p e r uses the f r a ~ n e w ) .1i of T;rm i a ~ l t l I Jlock' i111 , l Ilil;iirin a r ~ d C'o\wt!' t o tlrvelop ;I lo\\, orc1c.r p;~ran~c:t I-if: model for the Rossit t r totIri. An ol.clc>~.-of-~n;~gi~i t I I ~ I I . a~lal>.sis performed on the Navier-Stolwb eq11i1 t ic1115

( k t c : r ~ ~ ~ i w s t,llc s i ~ ~ ~ p l i f i ( ~ t i p,( ww1i11~ ( q ~ i i ~ t i o i ~ f b ~ , t h , , ;ii.it~- w o ~ ~ s t i c s , which is t11c Wit\:(' u111:1tion. si~uiliw to r{ds. '~. ') T h so111tio11 of' t l ~ i s ( , ( l~~ i i t io i~ k ( I o ~ I ~ ~ I I I I I ~ ~ ~ I t11c t(:cli~iq~i(:s of Grc~w ' s f1111ct.ioi1. M T I I O ( I of i~uiigc!:: i u ~ d 1)r1.)1xsr orthogou il ( l( ,(x)~~~l)osit iou. Y' I I I I i i~st, t . \ ~ o s0111tion t ( d ~ ~ ~ i i l ~ w s im2 s i~ id i l r to Iicf..', ' i111t1

t11v List I I I ( S ~ I I O ( I is ;L co11ti.i )11tio11 of t11is l)i11)(\1 1 I : ~ t c ~ ii11~)ortimtly; this (IOCIIIII(:II~ l)ropost,. i111 ori,qii~i~l I ( X . ~ I I I ~ ~ I I ( \ of i ~ ~ ( ~ ~ r p o ~ ; t t i ~ ~ g I I ( , (,Ll.w,t I,[ I I I ~ I ~o,j(,t - , t ~ < I C . I I I ~ L ~ O U in s ~ ~ p p n : s s i ~ ~ g t l ~ ( > (,i~vity { O I I ~ ~ ~ . '1.111' I I I O Y I

releva~lt ~ i ~ i c r v j t ~ t , - c ~ e ~ ~ t ~ ~ ~ ~ l t ~ ~ ~ ~ ( . O I I I 1.01 1 K I I X I I lvt tSr 1, r 1 I I , , \ , i t y uoiw r d w t i u n prob11~11. ~ ( I I ~ I I ~ ifi(~(1 ll~i,s \vork. is t h : ~ ~ i i c r o ~ j v t . - ( ~ x t o ! ~ ~ ~ I!-11o\v I I I O I I I I ~ I I ~ 11111 I ! I I \ ; I , I I 1 0 . . ~ ( l ( l i t i ~ ~ ~ i l l l y , this pi.\l>t'r i(lerlt ific!h t l i + , ~~~~( l t~ r l ! . i l y ,

11. Scope of Paper

111. Cavity Tones in the Absence of Microjets

A. Cavity Acollstics M d e l

Thc riiotivatiori ht.11iritl t,hc )roposc:tl rc>cl~~c:c:tl-ord(>r rriotlcl (to 1)o 11sct1 for cwity torios c:oi~trol) lies iu two indcpontltrut pior~ccring \\:or ;s 114. Till11 i111cl illld Biliirlill ill~d COW'T~.!) During t , h ~ t l ( ~ i l t l ( > of 1970; t.hCsc i1llt~lOI3 dcvt!lOp(Y\ Kllc (]('Is pl.('(\i('tillg th(: fl'C(~1.1~11Ci~~ Of t h ~ tOll(Y ill il ~wO-dilll(!ll~~Ollill ~.('('tilll~lllill. cavity ~ i r~dor c:xt(:si~al flow. 1'11(: i\(t)~thtie. J)I.CS(:IIC(~ of th : trailing cdgc arid (:ii~ity walls wits r~~otlvllc~tl t)y ;I

periodic line source i ~ t the t rililillg c'cl,qt: t111t1 s~~ i t ab ly placed images of tlie line sources rr:~sl)c~c.ti\.c~l\.. ?‘lit‘ model agreed well with expc.ri~ncnt;~l rc.sdts for speeds ranging from low subsonic to 1c)w sr~pcwo~lic Iiows ( d l = 0.1 - 1.2). Thesc studics arc 1 1 ~ 1 ~ 1 as i i starting point fbr constructing tlie desired r t~d~~rc~c l -o~~c l~~r 1111)cle1.

Since t,lw cavity tones are cJsse~~t i ; t i l ~ . ; I iwo-cli~nensiond pl~enomenon, we consitlcr n tno-d i~~~tb~~s ic i~~al reducecl-orclrr rnotlel for tho siurlcl. Thc: 1i1( t l v l ( fo~~ii t i i~ is rcstrict~td to t l i ~ irit,(md (:il\:it,~ V O ~ I I ~ I I V k)o1111(l('(~ 1)y t [I( ' (m.it,v a d l s illid th(!

r - I

I Bascd OII s l~ado~vgr t~pl~ ; > ~ l t l 1'I\' vis~~i~liztitioii studies,' L ---. - - .

the following ass~uiipt io~~s a1 : I I I ~ ~ I , \\.it11 wgarcls to the ill- 1. t,erilal cmity flow field:

Figlire 9. I l l~lstrat io~t of t tte assrunptioris behind the reduccd-order cavity acoustics model.

where 11' is the prrAss~u-t. pert~irlmtion tieltl, and '7" is the speed of se.)untl itwitlt! tl~t.: cavity.

Li! e..................... ..............................

1. C. 0 Ylacc~ncnt nfsourcc and its Imityzb to take care ot'r~grl

: c.wity walls i 1 ) I bounda~y contlttions) 0

Figure 10. Illustr;~tior~ of tltr rrtrthotf of images for solv- ing the pressure perturbation field inside the cavity under external cross-flow.

Figure 1 1 . Matc.hirtg of tixperimental and rt~odcl-preriic:tt!d S l'i,s at the cavit.y leading edge. The experintent was conducted with external flow l ~ a v i ~ ~ g 21 - 2.0, Re - :{ mil- liot~ (tmsed ort c:avit,v 1t:rtgtlt) itl~d cavity t l a v i ~ ~ g 1 - . 1. ~~rrccrl ; i ir~ty in txperitncrltal SPL WAS i.0 5df: at~cl unc.crt.aintv i t r frequency -4UfIz wl~irli is 0.8',; of t Irt. clontinant tone.

IV. Effect of Microjets 011 Cavity Tones

A. Noise Suppression Setup Using Nlicrojets

TI;n-i~lg tlerivrtl the uncontrolled cavity noise field: me now rxpl~.)rt~ ways o f suppressing the ravity tones. One \\-;I!- is to disrupt the feedback loop t.liat causes the tones, tliert:l~y rtdri t . i~~g the acol.~stic noise level. This c;ln

r ( ~ i ~ / i z ( d 1))' piwsiw illi(1 i l ( ; t i ~ ~ (hi ( ; i ; s I0~iitfXI tit tIl0 l('ildi11~ 0 1 ' t r i l i h g (YIgC. 11 dCtid(!d I'(!Vk!Wr Of ~iWi ty ~~c)isc: s~~l) l ) rcss io~i tccl~niquc~s is given ill Chtt;~f(:stir, ot. i11.I" 111 ;~ciclitiori: r(!(~wt ~~lodf:l-s(:al~ wi11(1 t ~ ~ n r i o l

a , ,, tc.st,s ~,clrfor~rlotl 1111tlor tllv HIFEX P r o ~ r i u ~ l ~ . " hit\;(> s l ~ o w r ~ t l ~ i ~ t ~~~ic.ro.j(:ts i:iln h 11sc:d v c ~ y c!fkc.t,ivr:ly for s~~lq)r(:ssiiig c:;n:ity t,oric:s by pl;~c:il~g t l ~ c w :iloug tllc: I c d i u g i ~ l g v i ~ ~ i t l tllc:rol)y t l i s r ~ ~ p t i i ~ g tllc loop. Whilr tlw c~~~r ro r~ t l ? ; a~v;tilnl)lc air i~i,jcctior~ actuators ncvd a s ig~~if i ( : i~ l~t , lllilss flow (1-10% or higlwr) t o bc cffwti\:o~ 111i(.ro,it%ts require less t11an I%.. ' T h e rcfereuce mass flow I~c re is t IIC. ~ I I I ~ L I I I ~ of free flow t,l~rouph a n area equal r o tlw citvity side wall. Microjets lirtw the acldit iu~id adva~~ta ,qv of' l~igli l~lorr~ei~tt lrn flux wlien con~pared to c ) l I l t ~ ttir i~ijectioi-I systems.

Figure 12. Experimental arrangement for realizing control in t l ~ e FSIJ cavity. T h e control input is given in t t . 1 r r l 5 o f the three rilicrojet pressure h a ~ ~ k s , from hottorn t o top.

f3. Observations After l Jsirig Microjets

Table 1. Dotrl ina~~t cavity fi erluer~cy preciic.tt:tl by 1110(lel and obtained fro111 experirrrerlt,~ cio~le or1 F S U cavity (under A / - 2.0 and Re = :j nlillion fiow). R e is based on cavity length.

V. Cavity Acorlstic.5 hlodel in the Presence of R'Iicrojets

A. Uniform Control Cz sr! ~ --

T l t e st~tis(~ri~)t /I I . ~ I ' I T S t o t l t t , I t i , ; ! ~ ~ t l i i( .rr>i~ 1 I,!., ,it, I.+ IW ,I! 1 lte tr~it.rojet I I ( - I Z Z I ~ exit: sul)scri~)t w, r(,fiw to t i ~ ( , I I M V ~ I I 11111li,\t I I I . I > I ( I <,ul( .! i1,11 Ilow lm)[~~,t.ti(~s. { I i ~ i l ( l 1 ,,I,, I / I ( 1 1 . , ! I , , i . I , - I ( I ~ I ; I ~ < I I . I I , S ~ I ~ > I I I ( I flow sl)t!t~I. -4 is ! I t < , ~tli(.rojl,t c~~~,. .->t~~Iio~! : I I I , ; ~ '\

i h I 111, I I I I I I I I N , ~ oC ilii(.to,jc~!~. I ),, I: i I I I ( . , I \ I . \ .:I( I : i , 1 1 i o i l ( ih 1 1 ~ t ~ i l l l ( ' l l h i 0 l l i l l Iwiitt(litl,y I ; I ~ ( , I - 1 l~i(.lw(.,h ' 1 1 I l i t . ( i l l t i \ I t . i t t / L

how t l ~ c f o r ( ~ i n ~ tor111 011 t : ~ right 11:111(l si&\ of this (yuatiou (m tw ot)tair~ln(i fro111 t11c iwntro1)ic flow l t i o ~ s l ~ i p i 1 i t 1 ~~i(:~.o,jct 11ozz1(~ (vxit: wit11 tlw 111Cilll I IOZZ~C flow ~ \ ~ S I I I I I ( Y ~ to I:)(: iwllt,r~pi(: i 1 1 d

soiric.. '1'110 rr~icro,j(t flow striictitro at t11c rlozzlo cxit is il111str;ttcd in Figuro I I i311(1 tlw d~::ti~ilf'(l (I(:rix'i~tioii of the forcing term is given . r ~ Sahoo."

After deriving the forcing funcl ivn, Green's functiori and method of images can be ~ ~ s c d to get. the pressure field inside the cuntrc~llecl cay-ity: a s before. Using the separatio~i of variables p' h. F ( x , y ) P ( f ), the governing equation for Green's f'l~nrtio 1 is g i ~ w by (details given in Sahoo"):

1 -) RT,) pl 1 [)pi, \ - 1 u p\</ p,, a!, ( 9)

Figure 15. Flow vis~lilliziltio~t z e r ~ l l t ~ for t h e FSlJ cavity. Shown hcrc .ire the 111car1 tinrrsverse ve- locity gradient t at the microjet ~~cizzlc exit for different microjet pressures. Extw n,11 How condi- tior~s: \ I = 2 O a d Hc. ( r ~ ~ i l l ~ c t r ~ ( I J , I v ~ on ravitj length). Cavity dirr~~.rrsio~r: I 1 ) - ; .

Forc.ir~g Terul _+ ,),, ( i . ~ . . lwcomcs negligible) d t c r some time t - t,. This is ill~lstrnt.c(l in Figl~res Ili ancl lie tia ' eyn, , h. So t& O,,II,;: t - t ~ 1 1 1 is st;itrlied oft' aher time t = t , alrd tire dn~npin: bctor ~ I I P to ~~~ ic ro j e t . ilitrodl~ction

\mplltud~ of I)%~ Figure 17. Response of measured a t t he lead- ing edge (LE) for 30 psig rriicrojet pressure. The

Figure 16. 7- irrrlls d sieasurcd a t initial coilditiorls (at 1 - 0) cor rosporid to uncon-

the leading edge for 90 p i g I ~icrojet pressure. Ex- trolled cavity coridition a n d wcrc: + - 0 (0 and

terrlal How conditions. 11 2 0 and Re - 3 mil- - ';, - - O (arbitrary). Also. 1 refers to the time pe- lion (based oil cavitb Irr~gtt ). Cavity tlirnerision: riod corresponding to the dorn~nant cavity tone. L I D = 5 1. External How co~iditioris: ,I/ = 2 1, al~t l He = 3 mil-

lion (based on cavity length). Cavity dimcrrsion: L ' D = 3 1.

is then:

Figure 18. hlodel prediction ver5us experimentally observed OASPL reductiot~ corre~:)orrding to the pressure transducer locatiurl a t the rrliddle o f the leading edge. External flow conditions: 1 2 0 and Re 4 4 million (based un cavitj length). Cavity dimension: LIL) = 5 1. Uncertainty in experimental OASPI,: I1 UdB.

Figure 19. Iblodel predictio 1 versus experitnen- tally observed SPI, spc:ctruni corresponding to the pl-esst~t.tt t ,ransd~~ct?r Ior:;~t.iorl at the middle of the Ieadir~g edge and 30 psig nli.:ro.jct pressure. Ex- ternal How conditions: I I = 2.0 and Re = :< mil- lion (twred on cavit.y length). Cavity dimension: L L - I . . C'rlcct.tairlt,y in experirnental SPL: 1 0 . 5 r l l : . Uncertainty in frequ~:ncy: 140Hz .

160-

Figure 20. Expr.rit~~eritally observed SPL spec-

60

150- 40

h

t r a corresponcling t o t he pressure transducer lo- cation at the middle of the lrading edge. The two spectra are for the ~ l~ ic~o j ( . tw>f f r l ~ ~ d 30 psig mi- crojet prcssurc rcspi.clivclv Exttv rtal flow condi- tions: 51 = 2 U and Re - : nlilliun (based on cavity length). Cavity dirnen\lor~ I 1 I ) - i 1. Uncer- tainty in cxperinlet~tal SI'I 0 ,111f. Uncertainty in frequency: 1 1 0 1 f .

No control

20

00 #\, '\ .' 'y' '4' ', ,

120- 80

I-,? ' r , ., /b" * .,'. -',,.a

110 , ..-L

60 2 4 6 8 10 2 4 6 8 10 Frequency (kHz)

Frequency (kHz)

of the r i ~ t d ; u ~ t~.ulls\:c~se 111ic-cr.jt7r \.elocit!. grirc1it:ut. Tlicc ~uic.roje:t velocity graclient varies wit11 i~icrcasir~g microjet pressure a s shown ti Figi~rc. ! . -I . Clearly thr silt ~1rw.t ion i l l the microjet velocity gradie11L resdts in sfituration i r ~ ~ ~ o i s e recluctior~ insidc the, c;r~.it,y. Tlie reason 1 ; ~ t he satl~rotion in microjel velocity gnc.liwt is not cleirr at this stage b ~ ~ t thc following c:tll~i~t,i~li that rrI;~tc~s the microjet mean velocitj- graditwt to t lw barrel shocl.; shape ; ~ t t,he cxit of tlw microjet uomlr provic.lts sollie insight,. The tlerivation cletails of this equation are g i \ w ~ in SRIIOO '"

B. Non-Uniform Control Case

Table 2. All possible acousti.: tones in the 3-D FSU cavity 1111(lt?r A1 = 2.0 a d H.e = 3 rr~illiorl flow. Re is tmsed on cavity ler@h.

of their self-sustainirg n : t t ~ ~ ~ e and this p h e ~ i o ~ i ~ e ~ ~ o n is t~vo-e l i~ i~ t~ t~s io~~al (i.e.: is restricted t o the strca~nwiw a d t ra l~s~wx: plane). So t lie guvenl i~~g eqrlatio~~s fur the, ~~~rc~o~~trol lccl and co~~trollecl tl~ree-cli~~~e~~sio~li~l caxs are Erps. (2) and (7) :.espectiwly, i.e. same as i l l the. t\\.o-rlin~ensional model. except that separation of varial~les for the pressure perturlmtion field ill I-he tli~~~t~-tIilli~~~~siol~a.l case is given by:

Hrre the i~~cliviclr~al terms artt d e h ~ r c l iu Secticm I\. I t hllo\z.s t l ~ a t 1 1 ( t ) cwsis ts of' two c.olill)onruts: ( i j ( w11ich is the mean t r a n s w l x ulicn),ic:t velocily g r ; d i c ~ ~ t a t the cavity ltv(1i11g edge ant1 is i r ~ d r p e u t l ( > ~ ~ t of'

time, a i d [ i i ) t h e rest of' tlic c-sprc>sic)n which arc tlt:pendcl~t ou the ~rlnhicut noise c~nd t l ~ u s 011 tilr~td. It idso t'i~llo\vs that a n incrtwt: ill E resr~lts in a larger value of' .f'l ( t ) and t h ~ s causes a gre i~ter rcd,lc.t,iolr iu

the cavity mise level. We now wek t o find thc rc~latio~isliip 1)etwcrn thc con t ld input, p,, nnil the tI;~~npirr=; factor. f'l ( t ) . From t h e resldts of' t i o ~ v v i sua l i za t i~~ i~ o x p ~ r i ~ n c ~ n t s s110wn ill Figure 13: it follows thnt < ;In(-]

I),, i r i c w i ~ s i ~ ~ g f l m c t i o ~ ~ s o f (::i(:Ii ot1it.r. I ~ l o r c ~ ~ c ~ ~ ~ , if \V(: rc~)lii(:(\ < by p,, ill E ( p . ( Ix) i ~ r ~ t l r (mov(s tl1(1 tirtlc?-tl(~l)(~i1c1c:nt tcxrrl idtogc~t h(!r, Wc! gvt tht. f o l h ~ i r l g ~)iLril~~lt'tU':

VI. Optimization of Control Input for Microjet-Based Cavity Noise Suppression

A. P r o b l e m Forrnula t ior i

B. Standard Optilrlal Control Soliitioll Methods

C . New Approach for Optimixirlg Coiltrol Input

I . Measure pressurt: d a t . ~ ~ t'ron~ ~ V I I W I . ~ distributed at a particular :r:. (1 with vnryi~rg 7. R I I ( / t. tor t l ~ t ~ castt

of flow without ~nicroj its.

Figure 21. Rlo<lel 1 , r c dict l o r velsus cxperi~nental l~ observed SPL speclrunl (a) a11<1 OIZSI'L redt~clion (b) correspondi~~g to t t ~ e prr\,ur.c trartsdiicer location at the middle of the leading edge. Exttyr real tlow cotlclitiotls: A / - 2 0 and tic, - , n ~ ~ l l i o c ~ (I,.t\ed on cavity length). Cavity dimension: L I D - i I . Unrertairlty i l l experimental SPL: -dil. Urlcer.t,~~t~ty i t ] rrecluciicy: & 1011~. The 111ictoJet pressure nari~ing concc.~ilio~r I - t~.tsed on Figure I,.

Figitre 22. Model prediction versus experimen- tally ohrerved OASPL reduction corresponding to the pressllrc trausducer location at the rnid- dle of the trailing edge. Ext( rnal flow concli- tions: i l l - 2 0 and He - .3 million (based on cavity length). Cavity dirrwnsior~: / . / I 3 = 5 1. The uncertnir~ty in the pressure sensor rcading was il ;dB a n d in frequency was IICIH:. Also the initial conditior~s for determining (I,, were:

$ = 1 98 and - O (arbitrary).

E. R e s u l t s of Opt i r l~ iza t io r i of C o i l t r o l I n p u t

VII. Summary

Tllis p t l l t ~ is ( . o ~ ~ ( v r i ~ e d with high noise in ct cavity c:tevelopccl n.hcn r~x l jos~d t o an external supersonic flow. The li:x11 ~~oisc , I t w l can potentidly 1)e hi11.111f1ll to t h ( ' s t r u ~ t ~ i r ; t l l i f t * of' \ \ . t 5 ; t l ) ~ ) n systt~111s inside a weapon bay ;t~i(l t,o li111(1i11g g('i\r ( l q ~ l o y ~ ~ ~ ~ r i t , . T11c ~ioisv is ( f ~ l t ' t , ~ i t f(:c:tll);~d< 1001) I ) c , t \ \ - t ~ ~ l ~ s l ~ ( - i ~ Iilyc~ distllrl)a~~c*cs iit t h ~ ci~\-i[\, l i l ) ; I I I ( I i ~ c o ~ ~ ~ t i ( * \V;IW,S i ~ ~ s i d ( > t , h ~ ( , i ~ \ ~ i t ~ - . A gr0111) of ~ ( W : ; I ~ ( * ~ I , ~ Y Y I I U ( I V Y t 1 1 ~ HIFEX F ' r0~ra111~~". ' h i s S~IOIVII I l ~ i t t ; i l l (,ff'(>(.tiw 111(:th1 of s ~ ~ l ) p r c s s i i ~ g lioisv is 1)y intro(l11(411g t~~ ic~ ,o , j ( , t s i11011g tlw ( , i l~it)- l w d i ~ ~ g edge i111(i t l~cwd)!- tlicrrlptiug tl~c, locq). I;) ;tc.l~ivvc~ t h goal o f tlt,rivil~$ ; I I I I ) l ) t i~ i~; t l (.ol~trol st,r;it(>gy for cavity 1lOiW 1.(~(~11c.l ;oil I)its('tI 011 Illi(:I'O,jct~. this papol. fOc.ll~(:s 011 t11(' (~c ' \ ' (xlol) l l lc ' l l f t b t ' i l ~ . ~ ~ / l l ( ~ ( . ' d 01.(1(:1. ('iwity ilCOll~ti(:~ rr~od(,l thitt ri:;or1,11-,1\- ( ~ ~ l ) l i \ i ~ ~ s t11v rolv o f thty 1r1ic:rojc.t~ ill ~ ~ ~ p l ) r c ~ > s i r ~ g 1lo;sc' i~tsitlt- t h , c.;wity itritl protlicts the ~ I I I I O ~ I I I ! of tloiw 1~~111(. tvl for :I g i ~ w ~ st(b:t(l>. I ) I . I ~ S ~ I I ! . I ~ 1 ~ 1 . o I i l t ~ I I I I ( I ( > I , \Y!I!! 1 1 I I I ~ ( ~ ! ~ ~ ~ o [ s : I I , ~ ~ l i~wl . I I I O ( I I , I is d t ~ v ( ~ 1 0 ~ ~ ~ ~ i I I,< ; ) ] I ~ I I I I O I : , ~ ~ i \Y l,igoro~is I'ri11111w)rl< l > i t ~ ( , ( l 1 ) I I t 11t) -1 it 1 1 ( 1 , t ! I I il<!l ();I(.( PI IS^ ic. w111atio11 wit 11 t l i c ~

~iiicro,jt>th I,$.~II;. i ~ ~ f ~ o c i ~ ~ r r c - l ,hl.ul~gll ia iirolnt.lltlilti ;~d(litiolr tt,rui t11;it ;tc.t.. ~r i l l 1 , r i . t i \ ; c : cln~npw.

hc:l~i~vic)r of tl1(.9 rliic.ro,jcts. Fiuiilly. a co1r11);wisc)u study was d m ~ e l ) t ~ t , w f ~ ~ ~ i t i i h w ~ ~ t acl ~ 1 ~ 1 1 o r s ~ ( v l lor uoise s ~ ~ l ) p r e s s i o ~ i in ~i cavity.

Tht. actuators con~parecl irert, t.he syi~tlletic jet. t110 dead\. I w l i ~ t : ! ~ ~ ( l g e I h v e r , speakers. powered resorlallw t~.rl.)c+ 1)111stvl Iluitlic: a.ctuators; tile vortex rod t o ~ c ~ t l ~ c ~ ~ . \&-it11 lli~t top spoiler ulid ~ ~ ~ i c r o j e t . ~ . It wa.s fot~lltl t h t rnicrojrts pc+rli)r~n as good as other actl~atorh i l l t t w ~ of' SI'T. ~ d u ~ t i o ~ ~ n ~ ~ d pt!rf(-)rm Ijrt,trr than ot,ht?rs in t w m s of OASPT, rt.:duction but 11sing :-\..rry lo~v nix . . ; H I I Y . III l ) ; ~ r t i r ~ ~ l a r . tlie FSI:' cavity exhibited 9 d n O:\SPI, ;111tl il r11itsim11111 of :!O tlB SPI, r c d ~ ~ c t i o i ~ i t r tl~c' ( I o l ~ ~ i ~ ~ ; i ~ l t ~ O I I P . illso. t t l ~ 111i~r~)jt:t.-l)i1~(~(1 il(:t~~;itOr W ; I ~ tc.stc~l 0 1 1 i l 4 ti111cs s r i d ( ~ j - ~ ~ p ( m ~ i t y ( i ~ ) ~ ~ ~ l ) i ~ r c , c l t o the' I;SI; i.;~\.ity) ilt t l ~ . 130vi11(: Polyso~~i( . W i i ~ d ? ~ I I I I I ( ~ ~

at I~ighor 51ii1.h ~ ~ I I I I I ~ K T S ;LIN ])~rfi)rr l~(vl siitisfitctoi.ii?. (witit 10 (11: Oi\SPL. m t l a I I I ~ I S ~ I I ~ I I I ~ ~ of 20 (In SPL ~ x d ~ ~ c t i o ~ ~ : i t t IIC ( I o ~ i l i r ~ i ~ ~ ~ t t( 11f.1). 111 (.o11('111sioi1. I I I ~ ( . ~ O J ( T S l~ro~.ir lc~ i\ r01111st ~ O T V - I I I ~ L S S - ~ I ~ ~ ~ I - I I I O I I I ( ~ I I ~ 11111-flow- I ) ~ I \ ( Y [ ; \vt I L I ~ cv S ~ ~ S ~ ( , I I I t l ~ t 11 rs ~ K V I I ( h ~ ~ ~ o ~ ~ q t r i ~ t v ( i t I I I J I , , \ ~ ~ t ~ ~ w t t t ! ; \ . I I S I Y I t ( I S I L ~ ) I ) ~ . ( ~ ~ S 11oise\ 111 i r c i~vit j? I I I I ( ~ ~ , I ,

(:XI I : ~ I I ~ s111)(,1,so11ic fion-.

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