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NASA Technical Memorandum 106364AIAA-93--4322 i .PMixing Noise Reduction for RectangularSupersonic Jets by Nozzle Shapingand Induced Screech Mixing

Edward J. RiceNational Aeronautics and Space AdministrationLewis Research CenterCleveland, OhioandGanesh RamanSverdrup Technology, Inc.Lewis Research Center GroupBrook Park, Ohio

Prepared for the15th AIAAAeroacoustics Conferencesponsored by the American Institute of Aeronautics and AstronauticsLong Beach, California, October 25-27, 1993

I IASA(NASA-TM-106364) MIXING NOISEREDUCTION FOR RECTANGULARSUPERSONIC JETS BY NOZZLE SHAPINGAND INOUCEO SCREECH MIXING (NASA)12 D

N94-14208

Unclas

G3/02 0189380

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MIXINGNOISEREDUCTIONOR RECTANGULAR SUPERSONIC JETSBY NOZZLE SHAPING AND INDUCED SCREECH MIXING

byEdward J. Rice*

National Aeronautics and Space AdministrationLewis Research CenterCleveland, Ohio 44135

and

Ganesh Raman**Sverdrup Technology Inc.

NASA Lewis Research Center GroupCleveland, Ohio 44135

Abstract

Two methods of mixing noise modification werestudied for supersonic jets flowing from rectangularnozzles with an aspect ratio of about five and a smalldimension of about 1.4 cm. The fn'st involves nozzlegeometry variation using either single (unsymmetrical) ordouble bevelled (symmetrical) thirty degree cutbacks ofthe nozzle exit. Both converging (C) and converging-diverging (C-D) versions were tested. The doublebevelled C-D nozzle produced a jet mixing noisereduction of about 4 dB compared to a standardrectangular C-D nozzle. In addition all bevelled nozzlesproduced an upstream shift in peak mixing noise which isconducive to improved attenuation when the nozzle isused in an acoustically treated duct. A large increase inhigh frequency noise also occurred near the plane of thenozzle exit. Because of near normal incidence, this noisecan be easily attenuated with wall treatment. The secondapproach uses paddles inserted on the edge of the twosides of the jet to induce screech and greatly enhance the

jet mixing. Although screech and mixing noise levels areincreased, the enhanced mixing moves the sourcelocations upstream and may make an enclosed systemmore amenable to noise reduction using wall acoustictreatment.

Introduction

The objective of this research is to study ways inwhich the noise of a supersonic rectangular jet can besignificantly reduced using excitation or other shear flowcontrol means which could find practical application in a*Lewis Distinguished Research Associate, retired,Member AIAA**Research Engineer

Copyright 1993 by the American Institute of Aeronauticsand Astronautics, Inc. No copyright is asserted in theUnited States under Title 17, U.S. Code. The U.S. Govern-ment has a royalty-free license to exercise all rights underthe copyright claimed herein for Governmental purposes.All other rights are reserved by the copyright owner.

single or multiple jet mixer or ejector device. It isintended that this excitation device be a natural sourcewhich feeds upon the steady flow for its energy ratherthan requiring an external power source of any kind. Theemphasis of this work was to investigate geometries whichwould be used internal to a shroud and this has led to theconcentration on near-field hydrodynamic and acousticfields. Two approaches to improving the performance ofsuch devices seem obvious. The first is to cause thedireetivity of the internally generated mixing noise to bemore normal to the acoustic treatment surface whichwould make the suppressor much more effective. Anattempt to accomplish this first objective led to thedouble-beveled nozzle tests which are reported here. Insome, but not all cases, the directivity was significantlychanged for the mixing noise frequencies of interest, andthe jet noise was reduced significantly. Thus the bevellednozzle may be a candidate for the internal mixer-ejectorswhere properly designed acoustic treatment might be usedto further exploit the directivity changes. The secondapproach is to increase the mixing rate of the jets to movethe jet noise source back toward the nozzle lip and thusprovide a longer propagation length for an acoustic liningto reduce the internal mixing noise. Mixing enhancementof the supersonic jet flow from a converging-divergingrectangular nozzle operated at design pressure wasobtained using paddles to induce screech and cause jetflapping.

Seiner and Krejsa I have discussed the status ofsupersonic jet noise reduction relative to the supersonictransport. A large reduction in jet noise will be necessaryfor such an aircraft to meet anticipated noise goals. Thework reported in this paper is intended to explore the twoapproaches mentioned above to help provide an efficientmethod to achieve some of this required noise reduction.

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A . . Flow quality control--., _.....I--, ,.nnular nngs _ _ _

r Air supply ', ,__ (_1"kf-_ _ I..-_

i n,eX_.lnflow conditioningFigure 1. Schematic of supersonic jet flow rig

Tam 2 and Lilley 3 have provided excellent recent reviewsof the fundamentals of jet noise production. The idea thatthe jet noise is intimately involved with the large coherentstructures produced in the jet mixing process isparticularly relevant here. This paper reports researchbased upon the manipulation of these structures to try toeffect a jet noise reduction.

Seiner _ et al. and Ponton 5 et al. have extensivelymeasured the noise produced by supersonic rectangularjets. Wlezien and Kibens 6 have conducted experiments onthe noise generated by supersonic jets formed by roundnozzles with unsymmetrical exits. One additional elementfound in the research reported here is that some of thenozzles are converging-diverging nozzles running nearlyshock free at the design pressure differing from thepreviously reported converging nozzles with the resultingstrong shock structures. A second additional element isthat the jet instability and thus the large coherentstructures are manipulated to alter the jet noise. Also thedouble bevelled converging-diverging nozzle discussedhere has the flow emerging almost axially rather thanbeing diverted to the side as in the converging nozzles ofreference 6.

This paper represents an extension of the workreported by Rice and Raman 7,s. In reference 7 the use ofpaddles was first introduced to induce a resonant screechtone to provide greatly increased jet mixing. In reference8 the supersonic flow fields for the bevelled rectangularnozzles were presented. In both references 7 and 8 theconcentration was on the aerodynamics of the processwhile in this paper the acoustic effects are emphasized.

Air Flow FacilityExperiment

A schematic drawing of the flow facility used in thisexperiment is shown in Fig. 1. The high pressure airenters at the left into the 76 cm diameter plenum where itis laterally distributed by a perforated plate and a screen.Two circumferential acoustically treated splitter rings

Figure 2. Rectangular nozzle and paddles

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remove the upstream valve and entrance noise. The flowis further conditioned by two screens before undergoingtwo area contractions of 3.5 and 135 for the rectangularnozzles used in this experiment. The nozzle shown inFig. 1 is not drawn to scale but is greatly enlarged.Nozzles and Paddies

A close-up view of the nozzle is shown in Fig. 2. A6.4 nun microphone is seen taped to the nozzle justbehind the nozzle lip. A set of full length paddles (76mm) are mounted in their support structure. Thisstructure has three-dimensional movement and paddlespacing adjustment which are remotely controlled fromthe control room. On the paddle support shafts the tubingfor the total pressure taps can be seen. These pressuretaps face toward the nozzle and are flush with the flowside of the paddle. There are also strain gages mountedon the paddle support posts. These measure the axialforce on the paddles.

The five nozzle geometries tested in this program areshown in Table 1. The dimensions shown are the nozzleexit long dimension (L), exit small dimension (_x_, andthe throat dimension (H_. Note there are three mainnozzle types: single-bevelled (3C), straight (4C, 6CD),and double-bevelled (9C, 9CD). All bevel cuts weremade at thirty (30) degrees from the exit lip. The straightand the double-bevelled types have both a convergingversion which was operated under-expanded and aconverging-diverging version which was run at designpressure ratio. All of the nozzles were made from fl0 mmcopper pipe. Internal forms were forced into the pipe asthe exterior was hammered until the form proceeded tothe proper axial location. A separate internal form witha 2.5 degree half angle was used to shape the divergingportion of the C-D nozzles. Nozzles 4C and 6CD hadfinal mill cuts applied to the internal surface at the exit toprovide more accurate dimensions. The throat and exit

TABLE 1. NOZZLE

dimensions were accurate and uniform to about 0.1 ram.It should be noticed from the above description of thenozzles that these are not precision polished specimens.It was felt that this level of sophistication was sufficientfor the first cut screening reported here and that anyphenomenon requiting extreme accuracy and polishedsurfaces could not be maintained in practice in an actualengine.Acoustic Instrumentation and Procedure

During acoustic data acquisition the nozzle wasmounted as shown in Fig. 2 in the vertical position (alongwith the paddles if they were used). The microphoneshown strapped to the nozzle was removed. A 6.4 mmmicrophone with windscreen was mounted facingupstream in a three dimensional traversing mechanism.The microphone traverse was computer controlledproviding 7.62 cm increments during an axial traverse.The microphone was manually moved in the transversedirection to start a new axial traverse. In the verticalplane (Z-X plane through the large dimension of thenozzle) axial traverses from X = -22.9 cm to +1.22 mwere performed at Z = 7.62, 10.2, 12.7, 15.2, 22.9,30.5, 38.1, 45.7, and 53.3 cm. The vertical planetraverses were conducted above the nozzle away from thefloor. In the horizontal plane (Y-X plane through thesmall dimension of the nozzle) axial traverses from X = -7.62 cm to + 1.22 m were performed at -Y = 7.62, 10.2,12.7, 15.2, 17.8, 20.3, 25.4, and 30.5 cm. The axialreference was the nozzle exit. A single microphone wasused thus eliminating the problem of differences in multi-channel systems. The microphone was calibrated using astandard piston-phone. The aerodynamic instrumentationused in these experiments has been thoroughly discussedin reference 7.

The acoustic signal was analyzed using a digital twochannel instrument. The narrow band spectrum was

CONFIGURATIONS TESTEDNOZZLE CONFIGURATION L, nun I-Iexit, n'lnl

3C Single-Bevel, Converg. 66.0 13.54C Straight Exit, Converg. 65.8 13.26CD Straight Exit, C-D 68.1 14.1

Htlna,lnnl ASPECTRATIO13.5 4.89313.2 4.96912.5 4.817

9C Double-Bevel, Converg. 64.8 13.7 13.7 4.7289CD Double-Bevel, C-D 69.3 13.3 11.7 5.200

3

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convened to 1/3 octave data using a computer. All noisedata reported here are thus 1/3 octave data except whentones may be discussed.

Acoustic Results

The results of the two experiments will now bepresented. The first set of results show the noise of thebevelled rectangular nozzles compared to the conventionalrectangular nozzles. Each comparison will be made forthe same types of nozzles (either converging orconverging-diverging). The comparisons are madebetween nozzles 9CD and 6CD, 9C and 4C, and 3C and4C (see Table 1). The acoustic data at the extreme limitsof our traversing mechanism might be considered to stillbe near-field (25 to 100 times the nozzle smalldimension), but it should be sufficiently close to far-fieldto be used at least for comparative purposes.The second phenomenon of induced screech using theconventional converging-diverging rectangular nozzle(6CD) will then be presented. The results will show theeffect on the jet mixing and the jet mixing noise sourcelocation. The acoustic data will be very near-field sincethis induced screech mixing method would most likely beused within the shroud of a mixer-ejector system and onlyin such a system would there be an acoustic advantageusing this mixing enhancement method.Acoustic Benefit of Bevelled Nozzles

The evaluation of the acoustic benefit of bevellednozzles is quite a complex process since the benefit issituation or hardware dependent. For example, it will beshown below that a bevelled rectangular nozzle withsupersonic flow operated out in the open is noisier than itsbaseline counterpart because it produces about anadditional ten decibels of very high frequency broadband

Y-O. Z-45.7 cm, ZIHna=34.5

> 110 "

= :_.z a _ ---e- -2zs -182w ir._r..m ._..ra..Q "_"" "'{D'" 0 0G: . uJ .-._-.- 22.9 16,2

_ --e- ..8 _.s--_ 90 _/ ---0 .... S4.4 64.8O --B-- 114.3 80.8(/)

1/3 ocTAVE FREQUENCY, KHZFigure 3. Noise spectra for nozzle 6CD, Mexp = 1.395, s idel ine

plane of large nozzle dimension, 45.7 cm from axis

noise near the plane of the nozzle exit. However if thisnozzle is enclosed in a properly designed acousticallytreated shroud as in a mixer ejector, this excess noisedoes not present a problem. We will attempt to showhere that the bevelled nozzle provides a noise directivityand spectrum shift that can be beneficial if the system isproperly designed. The noise directivity shift is preciselythe property mentioned in the Introduction section whichhas been sought to render the mixing noise moreamenable to attenuation by acoustic liners. A completeanalysis of the acoustic benefits of the bevelled nozzle isbeyond the scope of this paper, but some of the acousticelements which must be considered in such an analysiswill be discussed.

The measured noise spectra for the baseline C-Dnozzle 6CD are shown in Fig. 3. All of the data are fora constant distance sideline of 45.7 cm from the nozzleaxis in the plane of the large nozzle dimension. Sevenequally spaced axial positions are shown from behind thenozzle plane (-22.9 era) to quite far downstream from thenozzle (114.3 era). For later more detailed analysis,twenty positions spaced at 7.6 cm are available but theywould unnecessarily clutter the graph. As would beexpected, near the nozzle exit plane the noise spectra isdominated by very high frequency noise. As themicrophone is moved downstream, the mixing noisecentered at 2.5 kHz becomes dominant and is seen topeak somewhere between 68 and 94 cm (actually 84 cm)at a level of 121.1 dB.

The noise spectra for the double bevelled C-D nozzle9CD measured at the same sideline positions are shown inFig. 4. The very noticeable difference in these spectrafrom those of Fig. 3 is the nearly ten decibel increase inthe very high frequency noise mainly near the plane of thenozzle. It is tempting to attribute this high frequencynoise increase to shock associated broadband noise aspresented by Tam and Tanna 9 and Tam 1et al. since the

: 120 Y =0. Z -45 .7 cm , Z /H o_a r_ 4. 3 n..r:l.-o. _.:t,-::_,S_2_-?> 110 ..._Z._. __._.__.._'. "_0,,, ..._._:._e," ...a.-. o o-" l-.,,,w.._...__,.:,_p_ .-__-.-22.9 17.IO.o -___.o"'_ "_ ---_-. 4s.:Z _ --_-- 68.6 51.4"_ 90 _ .-.e .... 94.4 s&eO ---I-- _ _ 4._ 8s.7O

1/3 ocTAV| =FREQUENCY, KHZFigure 4. Noise spectra for nozzle 9CD, Mexp = 1.425, sideline

plane of large nozzle dimension, 45.7 cm from axis

4

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125.Jtllm .3..o..E_.E].._

120 _zr.__._. _. c_.E]"

,,, _,z_..-"_ ._' _ --I" ?_ -"1..._m 110tu _'E] ''D.E3]' f F, HZ --'l'l,-in" I2" H _ 16oo,', 105 .J_ ,-.G.-.- 250Oz o_ -0,- 4000

' Y-0, ZI45.7 CM, _32.3 --I-- 12500100 ..... ' ' ' '3_0 ' _ ...... ' ' ' ' ' '-20 -10 0 10 20 40 50 60 70 80 90

AXIAL DISTANCE FROM NOZZLE EXIT, X/I-bxltFigure 5.Axial distr ibut ion of sound pressure level , s idel ine Z=45.7 cm

Nozzle 6CD, Idexp=1.395frequency relationship to mixing noise is about correct .However, this jet is properly expanded and does not havesufficiently strong shocks to sustain a significant screechtone even near the nozzle lip (about 138 dB). It ispossible that the oblique bevel of this nozzle exit haspromoted the dominance of oblique instability modeswhich was the reasoning behind trying such a nozzle.The source of this high frequency noise is unknown atpresent. As mentioned earlier, this high level noisedominates the spectrum only near the plane of the nozzlewhere it would experience nearly normal incidence ontoan acoustic liner in a properly designed shrouded mixer-ejector. It is thus of no consequence for the purposes ofthis study but could pose a problem for otherconfigurations.

Other characteristics of the nozzle 9CD noise spectracan be seen in Fig. 4. The mixing noise peak has shiftedto a higher frequency of 4 kHz. The peak occurs at X =68.6 cm at a level of 116.9 dB. The reduction in thepeak mixing noise level from 121.1 to 116.9 dBrepresents an obvious advantage for the bevelled nozzle.However, the shift in the location of this peak from 84 cm

> 115WI'-'1

or"0."1Z

mm_ 125 I'i'I'I"'I120 _e;

._ .__.._.-._ EI.P--_ ,a_-_'2_N'_._110 __.t_--_" O.._3._3-_ f F. HZ --i-_r._.D.._z.r ,600105 '2' _- .-.E}-- 2500

_ _ --_'-- 4000__r_-o,z-45.7,Z/I-k_34.2 --B-- 12500

100 ",r_ . , . , , _ , , , _ _ . , . , , , , , ,-20 -10 0 10 20 30 40 50 60 70 80 90AXIAL DISTANCE FROM NOZZLE EXIT, Xll-le_

Figure 6.Axia l distribution of sound pressure level, sideline Z=45.7 cmNozzle 9CD, _1.425

to 69 cm represents another advantage for the bevellednozzle which is not quite so obvious. The upstreamlocation of the peak means that the noise must propagatea longer distance to reach the end of a given mixer-ejectorsystem and in addition could be propagating at a largerangle to the jet axis. If used in conjunction with aproperly designed and located acoustic liner in a shroudedconfiguration, the more normal angle of incidence of thenoise on an acoustic liner will provide improved acousticsuppression for a given liner length.

Cross plots of the data in Figs. 3 and 4 are shown inFigs. 5 and 6. The latter plots show the direetivityinformation more clearly and are simplified by using onlyrepresentative frequencies. The peak frequencies of themixing noise, 2500 Hz and 4000 Hz, for the two nozzlesare retained. The one-third octave band at 12,500 Hz isused as representative of the high frequencies withoutcontamination from screech tones or harmonics wherethey occur. The 1600 Hz band represents broadbandnoise below the mixing noise peaks for any of the nozzlesstudied here. The bands at 5,000 Hz and 10,000 Hz wereavoided to eliminate the screech tone and harmonic whenthey occurred (underexpanded converging nozzles).Bevelling the nozzles when screech occurs produces verylarge screech level reductions but this was not theemphasis of this study.

The same noise characteristics discussed relative toFigs. 3 and 4 can be seen more clearly in Figs. 5 and 6.In addition the difference between the noise level curvesin Figs. 5 and 6 are plotted in Fig. 7 which provides agood condensation of the acoustic differences betweennozzles 9CD and 6CD. The large increase in highfrequency noise is evident near the plane of the nozzleand the jet mixing noise reduction is evident in the downstream direction. This sound pressure level differenceformat will be used to present the results for theremainder of the nozzle configurations. The frequencies

10 F,HZ-..o.--- 1600I'I'I .-.E}-,- 2500

i /,,'d, , -,,,,- 40o0 --I-- 12500

0.i _ i.i_i I"I i _ m.I "D

Z 0 _I--l-I--I I --i- --

o -5 _V_L _C-,ING-OIVERGING _._._._ GY-O; Z-45.7 CIM

"10.20 '.1' 0 ' _ '110 ' _lg ' 310 ' 40 ' frO " 60 " ;0 ` _tO ' _0 'AXIAL DISTANCE FROM NOZZLE EXIT, X/l'knm

Figure 7. Sound pressure level difference, sideline Z-45.7 cmSPLNOTamo- SPI._oz.SCD,design pressures

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at the peaks of the mixing noise remained at 2500 Hz and4000 Hz for the straight and bevelled nozzles for all ofthe configurations.The acoustic influence of using a double bevelled exitwith a converging rectangular nozzle operatingunderexpanded is summarized in Figure 8. The largeincrease in the sound pressure level ,SPL, at highfrequencies near and ahead of the plane of the nozzle exitis again evident. The very large reduction, nearly 12dB,in mixing noise at 2500 Hz in the far downstreamdirection is evident. However, now a 5 dB increase inmixing noise at 4000 Hz is seen. This is mainly due toa large upstream directivity shift and high frequency shiftof the mixing noise for the double bevelled nozzle. Anacoustic liner would have to absorb this 5 dB hump tomake this geometry effective. This may be quite possibledue to the upstream directivity shift of the noise.The final bevelled nozzle geometry is the singlebevelled converging nozzle, 3C. The acoustic data forthis nozzle are compared to the standard straight exitconverging nozzle, 4C, in Fig. 9. The data were takenon the bevelled side (higher SPL side) of thisunsymmetrical nozzle. Again the high frequency SPLincrease is evident near the plane of the nozzle andsubstantial mixing noise reductions are evident in thedownstream direction.

It is evident from the acoustic data presented abovethat all jets from the bevelled rectangular nozzles havesome common properties. All had large increases in highfrequency noise near the plane of the nozzle. This shouldnot be a big problem when an acoustically lined duct canbe used around the jets because of the upstream positionand normal to the wall directivity of the source. Allgeometries had reductions in the level of the mixing noiseat far downstream positions and a shift to higherfrequency at the peak. A more detailed study must bemade to determine how to best take advantage of these

10 - F, HZ:ii. 1 --e-- 16oom ,-.El-.- 2500

"l- I _ --/_-- 4000

i 5 ", ,z.:_..T_, --=-- 12500o - _=-'_-.!._ JL_ _ _Z _ -- U _J_IP"_ "_ I-U-I=: ,E)...Ey"ET -

#- DOUB.E _ CONV_eNG _'__Z.m -1 0 Y-0, Z-4S.70g ,E]...E)..E],.i3

, i , f i I , i , _ , i , i , i ' 710 " i , i ,-20 -10 0 10 20 30 40 50 60 80 90AXIAL DISTANCE FROM NOZZLE EXIT, X/H_

Figure 8. Sound pressure level dif ference, sidel ine Z=45.7 cmSPLNOZ.gC- SPI.Noz.4c, design pressures

properties when a bevelled nozzle might be used withacoustic treatment on the walls of a mixer-ejector system.Aerodynamic Properties of Bevelled Nozzles

The supersonic jet flow field from bevelled rectangularnozzles was the subject of the study reported in reference8. All of this information is not repeated here, but someflow properties can be summarized which are useful in thecurrent discussion. Jets from bevelled convergingrectangular nozzles are deflected from the axial directiondue to the transverse pressure gradient present at thebevelled exit. This property was also evident in the roundjets reported by Wlezien and Kibens6. The singlebevelled nozzle flow diverts unsymmetrically from theaxis. The double bevelled nozzle flow spreadssymmetrically about the jet axis and was observed toproduce increased mixing over the other geometries asmeasured by mass entrainment. This nozzle might be anexcellent choice for some applications which areconsistent with these flow properties. The doublebevelled converging-diverging rectangular nozzle producesa-jet with very little divergence over that of the straightexit CD nozzle. This is probably due to the inability ofthe transverse pressure gradient to exert an influenceacross the supersonic flow in the diverging nozzle exit.Acoustic Propagation Angle

The upstream shift in the axial position of the peak inthe mixing noise of the jets from the bevelled nozzles isbeneficial if acoustic linings are to be used in the duct ofa mixer-ejector system. It is of interest to determine ifthe upstream shift was caused by an upstream shift in thesource location or by an increase in the radiation angletoward the sideline. To study this effect in anapproximate manner the acoustic data was analyzed in the

10[i F. I-[Z"I'I'I _ 1600

m 5 --_-- 4000-- --I-- 12500OI,LI

-=#- s_.E BEVELCONVERCa_G _-0_'"E}..G 1_,_10 y-o, Z-45.7 CId-2o'-;oo;o 3'o40so;o ;o io,o

AXIAL DISTANCE FROM NOZZLE EXIT, X/Hex=tFigure 9. Sound pressure level difference, sideline Z=45.7 cm

SPI.Noz.ac - SPLNoz.4c, l_xp=1.40

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=2N

X

NNOZitt5iiiOZI-

3O

2O

10

40 CONV_GING-IZVERGING NOZZLES ."_11D ES IG N PR ES SUR E . ." , ,- -/L IN ES ARE RE GRE SSI ON UNES . .r 'l , ,_//.J

NOZ."" --0"- 0C0 2500-..o.. god 4000n" o'7-

If:;:"" .-.e-.- 6130 2500--IB-- 6C0 4000

o ;o '2'0 3'0','o' s'o'io '7'0DISTANCE FROM NOZZLE EXIT, X/Hex_

Figure 10. Loci of maximum radiat ion, nozzles 9CD and 6CD

following way. In the plane of the large nozzlecoordinate, at each constant sideline distance (Z) the axiallocation (X) of the maximum sound pressure level waslocated for each frequency. These coordinates are relatedto but not equal to the peak contours in the acousticradiation pattern. Since the radiation of interest here,mixing noise, propagates at an angle to the downstreamaxis, the maximum coordinates derived above would beslightly upstream and outboard from the actual peak.However, the maximum radiation coordinates aresufficient for comparative purposes and are plotted in Fig.I0 for the two converging-diverging nozzles 6CD(straight) and 9CD (double-bevelled). The loci for twofrequencies, 2500 and 4000 Hz, are shown which are thepeaks in the mixing noise spectra at the Z=45.7 cmsideline for the two nozzles. The lines through the dataare the linear regression curve-fits. Note that theregression lines for a given frequency are parallel to eachother for both frequency cases. The curves for nozzle9CD are just shifted upstream from those of nozzle 6CDwhich indicates a source position shift with no radiationangle shift. The lines for 4000 Hz are at a greater angle

40 _C._N@ NOZZLESLINES ARE REGRESSION LINES

-r )"l /, ,P'

X

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=K

NX