AlAA 90-0183 Application of the Computational Aeroacoustics Method to an Advanced Counterrotating Propfan Configuration J. Kim Texas A&M Univ. College Station, TX

28th Aerospace Sciences Meeting January 8-1 1, 1990/Reno, Nevada

For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics 370 L’Enfant Promenade, S.W., Washington, D.C. 20024

AIAA.90.0183 APPLICATION OF THE COMPUTATIONAL AEROACOUSTICS METHOD TO A N ADVANCED COUNTERROTATING

PROPFAN CONFIGURATION t .Jinhnn Kim

Tex;,s ,\&?I I 'nivrrsity Cdl rgr S ta t ion , Teras

U

Y

P r r d i c t i o r L d ' h m e n i r El_o_w_ E i 4 d

' l he propellrr gcomctry used for this scgmrnt of the study is tha t of an eight hladc propfan with two roivs counirrrotating as shown in Figure 1. T h r nacelk is axisymmetric a n d t h r f low is assnmrd periodic Ix twern any 1x0 hladcs. Thcrrforc, t he dOmRin o f interest can he lirnitcci t o thc spacr hetiwen thc siiction and compres~ sion surfaces of two adjacent hlades on the propell?r. Thc Eiilcr cquations ncci i rately model the inviscid n o n ~ linear behavior including shock marts and tip vortices.

.A numerical flow field solvw called "SSTACE" has h e m dociimented by Celrstina, k,liilac, and Adamczyk". .As pointed ou t by Celestina, et.al, this numerical ap- proach u t i l i z e a simulation of the time areragcd t h r r r dimensionat inviscid Row field of a countPrrotating pro- pcl ler configuration as well a5 a s i n g l ~ disk propeller. This niimcrical analysis employs a four~stage Rungr- Ku t t a i n t e g d i o n scheme to march the equations for- ward i n timc toward an asymptotic limit. Numerical damping i s iequircd by the differencing methorl for sta- bility in threc dimensions. Since i t is time averaged, n o unsteady compcrnrnt is predictrd.

Figiirc 3 iIioii.5 t hc coordinatk system of computa~ tional d o m a i n T l i i s so lver typically u s e s a n enhanced grid consisting ,,f W axial points, 36 radial points, and 16 nzimrithal p i n t s a s shnwn Figorc 4. 'Thus, a realistic rlcmstic s>/uti<m l i i ls heen ohtirined from the SSTAGE: c o d r by virtiic 01 th r increased grid resolution. To solve thr ~ v c ~ a g c - p t m a g e q u a t i o n system through a nmlti- b la i l r row machinr, a mesh i s ncedcd for each hlarlr rrm which contains t h r a r i d and radial coordinates (of all hla& rows. 'Tliiis for a single-stage machine, two grids wmld h~ gmcratrd anrl each assigncd the thickness and pwinri of one of the two hladc rows. I I o w r v ~ r , ra rh mesh

:I ., ,x,:>f<,rm asisyrnnictrically t o i l l e c n o r d i t ~ a t ~ ~ a ,,f : I I t / ~ c ~ blade r,nvs. Thus . t h r amm~rtry ic s q i - a r a t ~ . I into hladc and nonhlade sections from inlet to cxit. An axisymmetric algcbraic mesh is generated us^

ing unr-dimensional splinr fits and the axial and radial coordinates are common to all t h e grids in t h r me rid^ ional plane. To c.oroplete the grids, t h r tangential mesh lines are gmerirted rising spline fits taking into account lilade thickncss and blade count. For t h r c u r r m t s tudy , the grid contains 11.1 axial, 36 radial, and 15 azimuthal points with 26 points lying forward of th r front hladr, 20 points axially both hladrs, 23 points 1xtivt-m bladrs. and 23 points aftrr the rear bladp. Both blades contain 22 equally spacrd points in the radial dirrction with th r remaining 13 points spacpd from thc hladr t ip to thc free strram. No mrsh clustzring was used in the azimuthal direction, however 20 rqiially spaced points axially o n Imth hladrs, 24 pointk between blatles, anrl 23 points iiftcr the war blade are used. Both bladcs contain 22 rqnally spaced points in the radial direction with th r remaining 14 paints spaccd from the hlade tip to t l r r free st.ream. ?io mesh clustering \vas used in the az: iinollial dircction. The major intmest in this numerical approach is I,,) obtain acoustic so l~ i t ions for a n adanncci i :--~

proprller configllration. These thcorrtical pwdictions will thcn be compared wi th cspcrime-ntnl results with rrgards to 0.ASPL for t h c ncor is t ic near field at fixrd observer locations.

It is assumed that the ahsolutc flow f ir lr l xppronch- ing a n d leaving the prnpdler is subsonic. This implies that, four conditions must he specificd at thc upstream boundary and crnly one at the downstrram boundary.

the upstream tmondary arc updated based on a local nn- st,eady onr-dimensional flow model in which the cntropy is ilssiimcd constant with time and uniform in space. r h l n d a r y conditions at thc farfield houndary arc em- ployed hasrd on a onc-dimensional unsteady flow rnodcl identical to the on? employed a t th? upstrrani hoond- ary. At periodic Row boundaries, t h r flow is required to exhihit a spatial periodicity equal t o the pitch of t he blade mw. Thus, any infwmation rrqiiired from a cell which 'ies adjacent to a pcriodic houndary hiit outside inc m m p *ntional domain is ohtainrrl from ir w l I x.:ltich a l s o l i < v i i i jarpnt t o a priiodir hni lndary hiit i s iiisidc I h r computational domain. Since the flux is zero on solid surfaces, only the pressure need he known. This ran he extrapolated from the interior or determined from a n adaptation to the present system of equations of a nor- mal pressure gradient condition. T h r present ntimcrical s d w r ut i l i zes the second on the huh and extrapolation for t h r hlade sorfacc.

. > I he axial velocity component and the flow properties at

.As m r n t i o n d earlier, this numrrirnl solver necds artificial viscosities for convergence. To suppress odd- c w n point deconpling in the solutinn, dissipative aloes are usrd in each direction. T h e maximum permissihle time strp for this schrme is restricted hy t h r Courant numtxr(CF1,) s ta ld i ty limit. There are a numher of nays to drtrrminc convcrgrncc of the utliacd simnla- lion. n y computing the time drrivativr ,If density, and th? numher of supersonic points according to the num- h ~ r of cyrlcs, the convergencc of the Row fidd solution may hP fonnd. T h e author chccked t h r convergrncc of thc solution by measuring the L , nnrm o f thc difference c o f t h e axisymmctrically averaged solutions. When the I ? nnrm shows a drop of turn orders of magnitude, the rrdnction was judgcd suffirient to consider thc nhtained solutions convcrgrd and was arrircd at after approx- imately ,Lo00 c.ycle itcrations. At the spinner-nacrlle srgmrnt of t h r model, the discrrpancies of th r flow field indicates that the physical domain did not conform to R

sting having the same diametcr as the sting attachment at I L P end of the rnodcl ns shown Fignre 4-(a) . Tlius at thc spinnwnacrl le nose scction, the flow ficld solut ion

docs not match w I I with enprrirnrntal ilatai7. Thp lincar a m u s t i c prulirt ion methodology has

h r n suffiricntly accurate t n traw th r noisc lcvel i n a rotating system for low I l a r h numbers. IIowrver, the transonic propfan with highly sivppt and highly loaded lhladcs produc.c high tip Mach nomhers and thus the compI<,tr fcirm of non-linrar Ffowrs-\\'iIliams Ilnmking~ rrjiiati,>n is requirrd to prrdicl acoustic solui . ,ns RCCI I -

where, P,,, is a rrfrrence pressure taken as 20 , ,Po

rach harmonic cimtrilnition. Finally, O:\SPL can he obtained by logarithmic stin, of U

Sincr the flow field incliidcs the shock ivavs spstrrn, t h r quadrap& nnn-linear e f k t s are accounted for i l l t IIC acoustic solution.

Ef fec ts t o t h e C o i n p u t n t i o i d Acous t ic S o l u t i o n s

. .

In utilizing the nu rn~r i ca l analysis rncthodol~~gy. it is important to invcstigate the optimum grid si??, c s ~ pccially the azimuthal grid for acoustic solutions. Th i s w d d result in fauorublr acoustic results with less niriri~ tiry size and obttlin solutions with l&wr id i i c s of c i n n ~ p u t r r tinic. Another subject of importance is tlic cficits <>i artificial viscosity on the theorctical acoiistic snIuti<iii t o determine reasonable damping values. 1. Effects of t l ie naiiirritlial gr id p o i n t s

.is discnssed in the previous section, tlir c ~ ~ m - i i t rnrthodology provides acoustic solntiuns by transforril- irig the nzirnothal coordinate in thc rotating coord inat r s y s t r m the flow firld solv'cr i n to the 011sc~vcr tinw i n stationary coordinates. Thus , it is ,obvious t h a t a& ditional information hetivren blades s i - i l l prodiicr m i r ~

time history. 'Therrforc, the invrstigntion of thc nurw l x r of stalions corrrsponding tc, the aximuthnl grid i i i

t h r rompntationnl domnin that m>iild provide q1t:dificd amustic results is necessarily requircd. P,>r this s tudv . t h r number of azimuthnl grid points was increased fri,in 9 to 1.5 to 21 points without clustering. 21 points r d i ~ ally IYCTP used equally spaced from th r nacelle/spiiiner t o the bladc t ip , a n d 15 grid points from the hlarle tip t o the outer boundary. .Axially, the lrading rdge of thr front row of t h r blades is located at tlie 27th grid p i n t folloivcd hg th r trailing edge at the 17th grid point arid air q u a l l y s p a c ~ d . Similiary, the Icrrding edge < o f thr front bladc is nt t he 7151 grid point and the trailing cdgr is locatrrl at ttw Blst grid point using no clustering. l:,,r Ihc investigation of t h r naimothnt grid points affecting t h r acoustic solution, thc flow field solver emplovcrl a Coltrant number 01 5 with second and fourth smoc>tli~ ing valiics ( d 2 and 1.32. Thc s t u d y of the refincrrwnt of thc mrsh >rill addressed the effcct of thc numbcr of

b l a t l r ~ t ~ ~ - l ~ l a d r dirrctionnl grid points o n t h r compniitii- lional acoustic solntions. .\s esprctctl, an azimnthaily rnhanc rd grid mil l provide b r t t e r shock wave st rur t i : i r a s wrll as produce a mtiw realistic f requrncy sp rc t r a l i y vi r tu? of t h r rnnrr dctiiiled acoustic t imr histor?.

;\s indicated in Figures 5 and 6. t h e w s u l t s o b t a in rd t i - i t h 9 u imuth i i l gr id points I p r d i c t a s m a l l p r c s ~

S \ ~ W chiingrs RS ii ftini.tir,n < > f t i in?. The comprcssiori

rralistic acoiistic solutions with regards t o thc prcssiirc ./

L d

I , 1. A s shown in Figimps 8 arid 9. as highrr damping vaiites am arloptrd, cxccssiw smoothing of thr pressure timr history i s n h t n i n d and rrlatinrly small armistic ~ T C F S I I T ~ = changes is prrdictrd. . \ s shoxn in thesr Fig- ures, morr than 1 kPa of thr acoustic prrssrtre d i f f c r~ m r r is ohscned . A l s o as shown in Figurc 9, the maxi- mum of compression and the minimum of suc t ion time i s slightly changing as the artificial visrosity is increased. A s shown in Figure 10, the OASPI. valrirs indicated that rxcessivc damping v i r l d d excessivrlp loner noise values. This rrsolt is significant when rxamining thr highrr harmonic numhers where the- sound prrssurc I p w l decrrasr i s ~ign i f i can t '~ . Thr srrond and fourth damp- ing vf 8 and 118 prrdicted an awragc of :3 d n lowrr, and the second and fourth damping of 16 and 1;4 pre- dictrd awrage of 8 dB loirw t h a n the wcond a n d follrth damping of 2 and 1, '32. Hoivrver, t h r highrr clamping v a h ~ s did provide. fastrr c o n ~ r r g ~ n r r id i h r i h ~ field solution. The usual convrigcncr was a f t r r 1000 itera- tions, h u t in the second and foiirth darnping of 16 and 1/4 case, the Row field solution convrrgrd af tcr irppmx- irnatcly 1500 itrration. Thus as predictrd earlier, RSCCS- sivr artificial viscosity provides incorrrct s o l u t i o n s due to cxccssive smoothing, and for thc currcnt theordicnl approach, the second and fourth damping values of 2 a n d 1/32 i s suggested. This approach ~ronld then yield a r r rp tah l r pcrformmre and acoustic solutions.

' l h r advanced propfller t~scd for the currrnt study i s rde r r rd to a s thc F7iA7 configuration, atid thc cvrrc- sponrling aconstic erprriment utiliacd a scaled version of thr LDF. As shown in Figure 2. the forimril pmpeller is nominally 'X.5 inchrs in diamctrc ivitb t h r aft pro- peller having a dinnrrtrr of 23.9 i n c h r s and a nominal blade spacing oi L.16 inches. Thr design chnrartcr ist ics

of t he 8 hp 8 propcllcr has a cruis? XIach nirmhrr of 0.72, a nominal cruise t i p speed o f 780 i t , ' s c c , corr*sponding tc, a n advanrr ratio , I f 2.82. Thr huh to tip ratic, is 0.42 a n d t h r grrmetric t i p sweep angle i s 34" fir front and 31" for the rear hlarle. Thr drsign I m w r coeffirirnt hased on a n n o l u 5 ~ T P B i s 1.16.

The acoustic characteristics of tlir P7,'\7 propcllcr n ~ ~ e mrnsiirrd i n 1he S:\S.l LrRC 8 by A It w i n d t u n n f l using p r r s s ~ ~ r c transdoccrs rm!~rddrd i n a plate sus- pendcrl from t h e wiling as shown i n Fixurr I I . TI,? plat? translatcs f w w d and act along f r o m th r t!ir.nel wiling a n d was positioned 7.35 inchrs (0.3 dinmetrr) from the front propdler tip. As shown in Figure 12: s r i ~ tmtcen t ransduwrs w r c rmhedded along the renterline o f t h plate. At thr platr location testcd: I I t r a n s d w ?rs w r w act ive consisting of 1 , 2: .1, 6 , 8, 9, 10, 12, 1.4, 16 and 17. .As mcntioncd carlim, t h e plate was drsignecl t o 1)r movahlr forward and aft in t h r w i n d t u n n d to p o ~ bitit,n ninP traiisrlrirrrs directly a h m r a point halfway l w t w m thc pitch changr axis ,,f t h r f ront i i n d rear prc p d k v . Thr t r m s d u w r nnglcs. ~ P : I S I I T C ~ ~.IC>III thr k,,,

I

m r d pmpc l l c r axis ranged f n m -17O for t ransducrr 1 to 133" for tmnsduccr 17. Trsts v e r r cmductr.cl at \lad, n u m l w s of 0.72, 0.76 and 0.80 at Z P ~ O drgrre angle of attack. 'The forward propeller rotates a t appmxirnately th r drsign rotational s p e d , and the aft prq>c l lw 50 r p m faster i n the attempt to obtain the seprrate tones ,of the fowartl and aft prupellers. The theorrtical results a re obtained for all rrperimrntal micr<lphonc locations". For the cnrrrnt s tudy however. the microphone Ic,cati,m nornher 6, 8, 9, 10, 12 and I t hare h c m ch,,sen. 1. -11, = 0.72 C o m p a r i s o n

Frc~m the Figure 7, v rp&rr i cn ta l da ta for O.\SPI. are c<,mpar~d t o tlic aconst ic thcorct ical prcdirt ions. .As shown i n Figure 7 : tlir O:\SPL has v a l i i ~ s u p to a p p i o r ~ irnatrly i6OdR with th r highrst OASPI. located slightly forward of hoth blades. 'The input rotational speed as

n o t 4 rarlicr o f t h r front l i larie is 8258 rpm a n d the aft i b 8306. 'Therrfore thr slightly highrr rpm of war hlat les rornparcd t o t h c f ront rcsdts in a slightly higher OASPI.. :\s mmtionrd , d t w t o t h r diffcrencr txtwerw thc computational grids and physical fclrms Crf the I.'L>F at t h r cnos~ part. thc Iprrtliction a t thc front part ,of th? nacrllr does not match iid with esp?rimrntttl data. I n t l i ~ rrgion l x t w w n Ihladr rows; t h r va l l ry ,>f the sound pr 'ssurc lcvcl band i s ~ , i ~ s r r v c d ' ~ . S,>tc that the loca- t ion of thr trailing rdgr (of th? f ront I~lades wrrrsponds

10 I - l i and the location of the leading edge of the rear l~ladr is a t 71, thrrefcre it is crbsrrrcd that t he rallcy is nrarrr t o the f ront 1,lade row, i .c.. the noise- band ,of ! l ip rrar Iilarlcs i s significantly grrater than thc f r m t tiiadrs. l i c ~ w v ~ r : th r cuppositc trrnd is o h s r r v ~ d and

2. .lfx = 0.76 C o m p a r i s o n For means of comparison to the rxperimcntal

aroiistic resiilts, the theoretical pressure time history and O.ASPI, have heen ,obtained as shown in Figures 13 and 1.1. .At t h r microphcrnr location 6, where th r up- stream region o f the f r w t blade, as shown in Figure 13, the acoustic pressure variation is not so significant. But . a t microphone location 9, xhcrr t h r f r m t blade Ioca td , the compression peak is dominant sirnilar to that of th r JI, = 0.72 cas?. . i t right aftrr the war hlad? h a t i o n , mherr the mirrophonr nurnhrr I2 l o c a t d , !hr t r m d of the acoustic prrssmr is oppipsite to that of frurlt blade location due to the countrrrotation of th r two h lade rows. Finally, the OASPI. pwdictions rnatchrs ivcll with the rxperirnmtal data as shown in Figure 1.4. 3. .\I, = 0.80 Coinparison

Shown in FigurPs 15 and 16. the thwwt ica l a c o u 5 ~ tic solution is ohtained for comparisons t u th? r x p r r ~ imrntal acoustic rrsults. In Figure l5> the throrr t i ia l acoustic presstire t ime history is predicted, and shows as t h r ohsrrver location approaches the front hlatlr row the armistic pr'ssure c h a n g ~ is significant. I n Figiirr 15, at microphone location 9 where the front hlade row i j

(1. thr iliffwrncr of thc a r m s t i c ~ , T C S F U T C indica! 1s

appmxiniately 1.2 kPa. ;\Is", the counterrc,tati,,n ,)f t l i c

hlarlrs caused the opposite trend of the acoristic p ~ s -

sure between the front blade location and the r ~ a r hIa& location. For the prediction of the Ot\SPL, as showrr in Figure 16, the prediction does match to an acr:q~tal,le level with esperimcntal data.

4

Stinitnary and Conc lus ions

.I numerical prediction of the acoustic near field ill- cluding non-linear effects using thrce dimcnsional flow f i ~ l d simulation has been demonstrated. Srrcral corn-

putatii,nal parameters which effect the acoustic r c s d t s have h w n inrrst igated under various numerical rondi. lions. It has shown that the effects of the mesh spacing and the artificial viscosity arr significant 11, thc amcrstic

results a n d should be chosen prnprrly. .The l i rni tat i<in of cnniixitrr t ime a n d mmiorv sizc restrict t h e rtcsi i l i i t ior i

of the grid sizp. Too coarse azimuthal mcsh spacing in- dicated l u x OASPL because of the lack of information between the blades which produced unrealistic pressure time histories of the rotating system. Sumerical dissi- pation also indicated a significant effect t o the acoustic rrsults. Too high a numerical dissipation did yield Ion

O.\SPI. vlaim due to the excessive smoothing to thr flow firld solution, and could b e obsrrved in the acons~ t ic p r ~ s s u r e time history.

T h r thcoretical acoustic results were compared with s e i ~ r a l crperirnental results obtained a t .M% = 0 . i 2 , 0.76 and 0.80 by 3AS.A LPRC. Generally, those results matched well for O.ASPL and the first through

resolution of t h r grids in the azimuthal plane mould pro- vide a hetter prediction for the higher harmonic nitm- lhers due tu the additional information provided to t h r Fourier series presentation.

I n conclusion, the numerical acoustic methodology i n v r d g a t r d for the LDF advanced propeller configil- ration encourages the uti l izat ion of this methodology to any rotating system and is considcred more cfficimt than thc Ffoivcs- Williams Hairkings equation. This con- clusion is emphasized i{ the acoustic solution a t a large mimhpr of ohservor locations arotind a rotating syst rm i s required.

A c k n o w l e d g e m e n t

fourth harmonic number tg . It is evident t ha t the higher W

__ 'Shis rcsrarch was supported by a N.\S;\ Lewis I<c~

brnri-h C r n t r r YAG 3-35L. ~ R.efereiires

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.'1. Fiirassat. I?., " ' lhcory < , f SCisc Gcnrra t ion f r i ~ r n

nncl .\222 (1954).

U'

\loring l?,)dics v i t h a n .\ppIicati<m tn Hrlict,ptcr Rocrs , " N.4S.i I I f - k i ! (~!~'ii).

I. Farassat. 12. a n d nroivn, l' . I . , ":\ N w Cnpability for I'rwlicling Ht,iicoptt,r Rutor a n d Propcller Yi ise

Including thc Effect of Forward !dotion," XASA 'T!J X ~ 7 4 0 3 i ( 1 9 i 7 ) .

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6 , Woan, C. J . and Gregorek, G. \I., ''The Exact XVII- rnrrical Calculation of Propcller Noisc," .AI.A.-\ Pa- per 30, 78-1122 (1978).

7. Martin, R. h1, and Farassat, F., "User's Slanoal for Cornpoter Program to Calculatc Discrete Fre- qurncy Yoise of Conventional and .\dvanced Pro-

8. Farussat, F. and Succi, C. P., " A R e v i w o f pro^

pcllrr Discrctr Frrquency Yoise Predicton Tcchnol- cagy with Emphasis on Two Current Methods for 'Tim? Domain Calculations," J . Sound and Vibra- tion, 7 1 , Xo. 3; pp. 399-119 (1980).

9. Succi, G . P,., "Design ,of Quiet Efficient Pro-

IO. Ilanson, D. B. and Fink, 11. R., "The Importance of Quadriipole Sources in Prediction of High Speed Propeller Noise," .J. Sound and Vibration, 62, Un. l (1979) .

i I . Kurkan, K. D., vvn Lavantr, E. and Bobcr, I,. J . , "Xumcrical Evaluation of Propeller Noise I n c l i d ing Yon-Linear Effccts," A J . A A Paper So. $4-2301

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13. Kmkmi, K.D., and von Lavante, E. and Roller. I>. J.,"Xurnrrical Evalution of Propeller Noise Includ- ing Xonlinrar Effccts," .\I.AA J . , \:ol. 21, No. 6,

14. LVhitr, 'l'..A., "Yrirnericai Evaluation of Propeller Xoisr Including Yon~linear Effects," .\laster of Sci- r n c ~ Thcsis, Texas .\&\.I I'niversitx (198.1).

I.?. I:orsyth, f ) . l V . : a n d Korkan, K.D., "C'ornp\itational .\eri~acoustics of Proprllrr Y n i v i n t h r \ car and h r Field," .AI:\:\ Paper No. 87-025.1 (1987).

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19. Kim, J inhan , ".\ : . .st ion of thc Cornputati,,nal Aeroacoiistics J f ~ t h m l IO an .\drxnccd comPuta. tional Propfan Configiirati<,n," JIaster of Scirnce Thrsis, Teext,s . \ & A I I.nivcrsity (1989).

v

l ~ e i ~ c r s , ~ : NASA n1 83135 (1981).

peiiers,:' S A E P ~ ~ , ~ ~ N~). 7 9 0 ~ (1979).

- (198.1).

pl, 1 n i n - i o . i j (1986).

,.

Firwe 1. The UDF Propeller Configuration.

30.35 cn (11.95 I N . )

31.1 cn (12.25 I N . )

C O m R L l N E

PITCH CWVIC? U E S

UXT i o u Lwin6 EM

J ( R a d i a l )

K ( A z i m u t h a l ) - -

I ( A x i a l )

L e a d i n g Edge T r a i l i n g Edge T i p Nunlber of B l a d e 1=27 1=47 5=21 8

8 F r o n t Blade After 111, de 1-71 1-91 5 - 2 1

Figiirc 3. Coordinate Systein of UDF Counter- rotii':,,g Prc,prller Contlgurittion for Nunierical Solvrr.

Fignrc +(a). Constant < Cut for Forward and Aft P r n p ~ I I ~ r s .

8

Figure 4-(r) . Constant Cut for Rear Propeller.

h 2.00 d GRID COMPARISON Oeeeo 11 4 x 3 6 ~ 9 IL MACH NUMBER = .72 114x36~15 3 1.50 r/U = 1.6 & m 114x36~21 v

3 1.00

D $ 0.50 l=l !% 0.00 IL

2 -0.50 E; 5 -1.00 0 2-1 .50

2 12 22 32 42 52 62 ?2 82 92 102 112 AXIhl. 1,OCATION

6 0 L u

Figure 7. Overall Soriiid Pressure Level as a Function of Axial Locat,ion for Tlrrer DiffPwiit. Aaiiiiutlial Grid-.

h 2.00 I

d DAMPING COMPARISON MIC NUMBER = 9

3 1.00 1

-2.00

Figure 5 . Pressure Time History at Axial Loca- tion I=37 for Three Diffrrciit Aaiinuth;d Grids.

Figure 8 . Pressure Tiinc History at Axial Lor;i- ti011 T-37 for Tliree Different Damping V:drir.s.

d GRID COMPARISON OBea 11 4 x 3 6 ~ 9 08880 114x36~15 B 114x36~21

1.00 1 E I-, VI 0.50 VI w K 0.00 P. 2 - 0.50 b

0 2 - 1 . 5 0 MIC NUMBER = 12

9 -1 .00

Figure G . Prrssorr Tiinr History at Axial Lorn. tion L O G for Three Different Aai~nuthal Grids,

DAMPING COMPARISON MIC NUMBER = 12

G€€€O 2 SECOND 1/32 FOURTH OeSLa 8 SECOND 1/8 FOURTH - & ! a 1 6 SECOND 1/4 FOURTH

2 -1.50

IO -2.00 0-

TIME (mSEC) Figure 0. Pressure Tim? History at Axial Lor;,. \ ,

W tiori I=9B for T h r e ~ Different Damping V:rlnrs.

9

2 SECOND 1/32 FOURTH 8 SECOND I/8 F O U R M

16 SECOND 1/4 FOURTH Cozm EXPERIMEM

AXIAL LOCATION Figlire 10. Overall Sound Pressure Level as a Fuiictioii of Axial Location for Thrce Differelit Damping Values.

1.53 n ( 5 FT)

(Z+.FT)

10

19

16 17

AFT

3 4 5

I

8 9

10

11 12 13 14 15 16 I-j f 17

Figure 12. Transducer Positions on Traiislatiiig Aroustir Plate.

MACH NUMBER ~ .76 OBBBSMIC NO. = 6 OBeBOMIC NO. = 9 m M I C NO. = 12

m

v

2 1.00

2 0.50 VI w p: 0.00 a

-0.50 c g-1.00 0 2 -1.50

-2.00 -4 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

TIME ( m S E C ) Figure 13. Pressur? Tiiiir History at 4xial I.oratioii I=lG. 37 i t u d 06 for = 0.7G.

Figure 14 . Fiiirction of Axial Locatio11 for .If, = 0.7G.

Overall Sound Prcssure Lcvt-l its a

MACH NUMBER = .80 OBBBSMIC NO. = 6 [%830 MIC NO. = 9 1.6 Rti

v GDbE = /l4x36x15 m M I C NO. = 12

-2.00 0.0 L i 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

TIME ( m S E C ) Figiirr 1 5 . Pressiirr Tilire History at Axial Location I=lG: 37 and OG for 21, = 0.80.

wcn NUMBER = .so 1 1 ~ x 3 6 ~ 1 5 r/R - 1.6 R q O G EXPERIMENT I

60 2 12 22 32 42 52 62 72 62 92 102

AXIAL LOCATION Figiirp 1G. Ovrrilll Soiiiid Pressurc Lcvt.1 i t s n " Firiirtion of Axial Location for .\I, = 0.80.