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LIST OF FIGURES . . . . iv ...... Just as in the previous case, the half width zx/2in the x, z plane grows lineartywith x .... the frequency spectrum of e for various positions along the centerline of the jet for 15 < x/D < 140 ..... Aerosonic games with the.
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.LANGLE'," _¢caE_\R_lCENTER LIBRARY,NASA HA,_5_PTON; VlRG_N_4

FFNo672 Aug 65

NationalAeronautics and SpaceAdministration

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Ame=ResearchCenter

StanfordUnlvarslty

JIAA TR - 47

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ON THE STRUCTURE OF AN UNDEREXPANDED RECTANGULAR JET (NAS&-CR-16973q)

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S_HUCTUEE

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N83-15591

U_DEREZP&NDED EECTANGULA_ dET {Stanford

Univ.) 53 p gC A0q/MI"AOI

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CSCL 20D

Unclas G3/34

080q2

A. Krothapalli, Y. Hsia, D, Baganoff, and . K, Karamcheti

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STANFORD UNIVERSITY



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_epanment of Aeronautics and Astronautics Stanford,California 94305

JULY 1982

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JIAA TR-47

ON TIIESTRUCTURE OF AN UNDERE.\TANDED RECTANGULAR JET

A. KrothapalliD Y. Hsia,D. Baganoff, and '

K. Karamchcti

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The work preserted here has beensupported by the Air Force Office of Scientific Research under contract F49620-79-0189. /

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ABSTRACT



An experimental investigation has been carried out on an underex.pandedjet of air issuing from a converging rectangularnozzle of moderate aspect ratio. Schlieren pictures

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of the flow field along with hot-wire measurementsI in the jet were obtained at different pressure ratios. At the pressure ratio corresponding to the maximum screeching sound,

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. Schlierenphotographs show a very strong organized cylindricalwave pattern on either side of the jet, with their respective sources being located at the end of the third shock cell. Associated with this wave pattern is a large increase in the angle of spread of the jet. It is shown that the self excitation helps to induce large-scah vortical motions in the jet both in thc plane containing the small dimension of the nozzle and in the plane containing the long dimension of the nozzle. However, the locations of these structures are different in the two planes. Nevertheless, the characteristic Strouhal number eo,.responding to these large-scale structures in both planes is the same and equal to 0.12. The influence of.the self excitation on the mean velocities and rms intensities has also been investigated. For the full range of pressure ratios st.udied, similarity was found both in the mean velocity and rms intensity profilesin the two central planes beyond 80 widths downstream of the nozzle exit. However, the shapes of the similarity profiles are differentin the two planes. For the downstream distances studied, complete axisymmetry (identical mean velocity profiles in both planes) was not found, which suggests it may persist for a.large distance downstream of the nozzle exit.

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AGKNOWLEGMENTS

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We are indebted to many colleagues, visitors, and students of the Joint Institute ror Aero_lautics and Acoustics for helpful discussions and suggestions. \Ve are also grateful to

Professor D.G.Cright0n andProfessor C.K.Tam for their encouragement andsuggestions during {hecourseof this wol'k.

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TABLE OF CONTENTS

ABSTRACT. . . ...................................... •

ACKNOWLEDGMENTS LIST OF FIGURES

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ii iv

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INTRODUCTION

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4 7

a. FlowVisualizationStudy .......................... b. Total PressureMeasurements..............

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d. RMS Intensities ...................................

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CONCLUSIONS .......................

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REFERENCES

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APPARATUS, INSTRUMENTATION AND PROCEDURES RESULTS AND DISCUSSION ..............................

e. MeanVelocityField ...................

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LIST OF FIGURES

Figure 1.

Sehemaiic diagram of rectangularnozzle and entry region.

Figure 2.

Schlieren pictures of the jet in the z, y plane. AR _ 16.7,D ._ 3ram.

Figure 3.

Schlieren pictures of the jet in the x, z plane. AR -- 16.7,D -- 3ram.

Figure 4.

Schlieren pictures of the jet in both x, y and _, z planes. AR _ 10, D --"5mm.

Figure 5.

Schlieren pictures of the jet in the x, y plane, witha reflecting surface placed parallel to the jet axis. AR -- 10,D -- 5mm.

Figure 6.

Schlieren picture of the jet in the x, y plane with a reflecting Surfaceplaced at 135 to the jet axis. AR _ 10,D -- 5ram.

Figure 7.

Variation of the pitot pressurealong the center line of the jet.iR -- 3.8.

Fi_lre 8.

Pitot pressure profiles in the x,y plane near the nozzle exit, g -- 0.

Fi_lre 9.

The decay of the mean velocity along the centerline of the jet.

Fi_lre 10.

Mean velocity profiles in the x, y plane,_z-- O. R -- 2.7,

Figure 11.

Mean velocity profiles in the x, y plane, z--0.

Figure 12.

Mean velocity profiles in tile x, z plane, y --"O. R -- 2.7.

Fi_lre 13.

Mean velocity profiles in the x, z plane,_y -- 0. R -- 3.8.

Figure l.I.

Growth of a rectangularjet with down stream distance.

Figure 15.

Growthof a rectangular jet with down stream distance. R

Figure 16.

Variation of rms intensities along the centerline of the jet.

Figure 17.

Schlieren pictures of the jet in both x, y and x, z planes, R -- 3.8.

Fi_|re 18.

Osciilograms of hot wire signal along the centerline-of the jet, R -- 3.8.

Fi_lre 19.

Specturm of hot wire orhot film voltage fluctuations along the centerline of the jet., R -- 3.8.

Figure 20.

Distribution of rms intensities in the x, y plane, z -- 0. R -" 3.8.

Figure 21.

Distribution of rms intensities in the x, z plane, y -- 0. R "--3.8. iv

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R =-3.8.

3.8.

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INTRODUCTION

The increased interest in V/STOL aircraft has caused a great deal of attention to be_:fOcussedon jet flows exiting from rectangular nozzles. In particular, the mixing characteristics of an underexpanded jet exiting from a €°nver_ng rectangular nozzle of -

moderate aspect ratio is of great interest. As part of an ongoing program at Stanford.to study" the mixing characteristics of single and multiple rectangularjets both in free and

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confined configurations, a systematic investigation has been carriedout on the structure of

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a jet issuing from a moderate aspect ratio rectangularnozzle at flow speeds ranging from low subsonic to supersonic. The detailed measurementsof the mean and turbulent velocity

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components of an incompressible jet was reportedby Krothapalli, et ai., 1981. The effect of the exit Math number on the overall flowfield of a subsonic compressiblejet was studied by IIsia et.al., 1982a. This paper reports the results of a study of a supersonic rectangular jet (choked at the nozzle exit). In all these investigations the nozzle used was the same, thus providing an opportunity to assess systematically the various changes brought about ................

by.thexarying flow conditions.

._ _...............................

It is wellknownthat the structureof a chokedunderexpanded jet displaysdifferent features to those ot_subsonic and ideally expanded or shock free supersonic jets. These features include discrete tones in the sound spectrum, known as screech tones, under certain conditions and an accelerated spreading of the jet withenhancedmixing.Thejet =screech"

phenomenon;an oscillatoryconditioncommon to underexpanded jet flows,is describedby Powell 1053, as arising through a feed-back mechanism. A disturbance in the jet shear layer is convected downstream (assumed amplified in passing downstream) and strikes a cell boundary, scatteringintensesound at that point. This sound propagates through"the ambient medium in the upstreamdirection,',.ndinteracts with the jet shearlayerclose ,

to the jet exit, giving rise to a new downstream travelling disturbance that continues

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the cycle. The essential element of the eyeh is the amplification of the downstream

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travelling disturbance. This process maintains itself mainly because the enerb-D" lost through scattered radiation and viscous effects is resupplied to the propagating disturbance by an

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instability of the flow. The detailed mechanism of screech tone generation is yet to be understood, although the general nature of the feedback loop, was treated by Powell who 1

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1 developed a simple relation between tone frequency, cell size, and operating conditions. Under certain conditions, the concomitant sound production accelerates the spreading of

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the jet and enhances mixing, ltowever, the conditions for tile existence or absence of such a phenomenon cannot yet be predicted. A considerable amount of experimental data is available in the literature to charac/

terize tile near sound field of a choked underexpandedjet (Powell 1053a, 1053b; Lassiter and ]lubbard 1956; Davies and Oldfield 1062; Hammitt 1061; llarper-Bourne and Fisher 1073; \Vestley and \Voolley 1073; Sherman, Glass and Dullep 1976; Krothapalli, Baganoff, llsia and Karamcheti 1081, 1082). Most of the work reportedin the literature has been ,associatcd with the flow field"ofan axisymmetricjet. Although the structure of a rectangular jet exhibits some features similar to that of an axisymmetric jet, there exists•some important differencesbetween the two flows. Some of these differenceseven make experimental !

stud.v easier. For example, the nearly two-dimensional structure of the disturbances and their associated sound fields near the nozzle exit are easily identified in flow visualization pictures because of the long optical path length present• It is thus experimentally attractive to study the interaction between the sound field and the mean and turbulent components of the flow for the flow exiting from a rectangular nozzle. The effect of acoustic feed back on the spreading and deca_ of an ax.isymmetric underexpandcd jet was first studied by Glass 1008. However, his experimental study was limited to the measurement of gross properties of the flow because of his use of a pitot tube in the experiments. None of the works that followed presented information regarding the effects of screech tones or organized sound waveson the turbulent structure of the flow; in particular, none on the rectangularjet, the objective of the present paper. The detailed structure of the near sound field and its source for an underexpanded jet operating at maximum screech condition is to be given in a separate paper by Krothapalli et al., 1982. The principal parameters or variables governing the flow of a free rectangular jetare the pressure ratio/_ (stagnation pressure/ambient pressure}, Maeh number At, and, Reynolds number Re, the turbulence level of the flow at the exit of the nozzle, the conditions of the medium into which the jet is issuing, and the aspect ratio of the nozzle. In the present investigation the pressure ratio, R, was varied from 2 to 5.8. Thisinterval corresponds to a Mach number range, based on fully expanded iscntropic flow, of 1.05 to 2

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1.8. Tile Reynolds number employed here is based on the width D of tile nozzle (small dimension) and _iven by Re -- Me.D/v, where a and v are the speed of sound and kinematic viscosity of the ambient medium respectively. This Reynolds numberwas varied from 7.2 × 104 to 1.0 × 105 in the experiment. A rectangular nozzle of aspect ratio 16.7 was studied. The inlet geometD' of the nozzle was designed specifically to obtain a low turbulence level at the exit plane of the nozzlei The total-pressure profileat the exit plane of the nozzle was found to be quite fiat.



APPARATUS, INSTRUMENTATION

AND PROCEDURES

A high-pre_ureblow-downtype airsupplysystemwas used to provide the airflowto .

a c_,_lindrical settling chamberhavingdimensionsof i.75mlong and 0.6m in diameter. Tile

temperature inthesettlingel,amberwasmaintained at a constanttemperature, usual;yat room temperature,to an accuracyof about 0.SQCoverthe duration of each test. Bef0re reaching the nozzle, the air was passed through an adapter, containing six screens set 5era apart, to minimizedisturbancesat the nozzle inlet. The ratio " teas between the adapter and the nozzleexit was about 40. Two nozzlesizes wereusq...,a the study. The dimensionsof the rectangularexit of the small nozzleusedwas 50ram long (L} by &r ,n wide (D). Tile exit dimensionsof the large nozzlewere50ram long and 5ram wide. The nozzleexit in eachcase was precededby a 40ram longsmooth rectangularChannel(50ram × 3mm and 50ram )4 5ramrespectively).The 3ram nozzleusedin the investigation,shown schematicallyin Figure 1, was a singlecentral lobe of a multi-lobednozzle employedin a relatedinvestigation. Mostofthe detailedmeasurementsweremadeusingthe 3ram nozzle. The experiment made use of tile same modeland .-.!rsupply system as that describedby Krothapalliet al., 1081. A 7ram thick acoustic insulationwas used to coverall exposed surfaceson tile nozzleto minimizeacousticreflectionsfrom these surfaces. A conventionalSchlierensystemwas usedforflow-,.sualizationpurposes.Tileconfiguration employedwas a single pass design, with the optical axis folded twice using two 25cm diameter,3.05m focal length Sphericalmirrors.Tile light sourceemployedwas a stroboscopic flash unit having a 1.511see flash duration. The stroboscopicfeaturewas used for visual observationswhile singlepulses wereused for photographicrecords.

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For downstreamdistances X/D less than 15, wherethe velocitiesare high and the flowcontainsshock waves,measurementswereconfinedto the use of a pitot tube having an external diameterof about 0.46 mm and a diameterof the sensing tube of about 0.25 ram. Further downstream,in regionswhere the flowis known to be subsonic, hot-wire and/or hot-film_,anemometrywas used. All velocity measurementswere made with a DISA55 MI0 constant- temperature anemometer in conjunction with a DISA 55 M°5 linearizer. The hot wire used was a 4 i ]

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DISA 55 PII single normalplatinum-coatedtungstenwire with a ,"lqm diameter and l'nm length. The hot film used was a DISA 55 R31, a wedgesha_ed 0.51_m quartz



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coated nickel sensor with a 0.2mm width and lmm length. The frequencyr_poase of

the hot-wireelectronics, in responseto a squarewavetestwiththeprobeplacedin a -

high speed (M = 0.8) low turbulencejet, was approximately40 Kllz. The hot-wireand

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hot-film probeswere calibratedusing a low turbulence air jet regulatedby a DISA 55 D00 calibrationunit. The flowvelocity, with correctionfor compressibility,is obtained as an analog Voltage. The hot-wireoutput voltagewas lineariTedfor tile velocityrange 20m/see-to 280m/see, with the output voltage E directly proportionalto tile velocity U(E = KU, whereK is aconstantselectedinconjunctionwiththe linearizergaincontrol). Similarl.v,the hot film output voltage was linearizedfor tile velocity range 20x,_/sectG 300m/see. Despite tile directproportionalitybetweenthe fluidvelocityand the hot-wire voltageduringcalibration,the hot-wirefluctuation voltagee, in a turbulentcompressible flow,will depend additionallyupon fluctuationsin the densityand the total temperature (llorstmann and Rose,1977).Lackingpropermeans to accuratelycorrectvelocitydata for tht.'sefluctuations, rms values will be expressedin termsof _ --< e >/E (where < e > denotesrms),whicl| becomesequalto the turbuh.nceintensity < tt > /U h_rlowMath numhers.The detailedcalibrationprocedureusedis given by llsia et al., 19.q2b.

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The signal fromthe linearizerwasp_qsedthrougha DISAtype55D31digitalvoltmeter, a DISAtype 55D35rms unit, and a TSI model 1076voltmeterto get the mean and rms values. Integration times with these instrumentscan be selected in discretesteps from 0.1 to 100see, and I0 see ;v_qtypicallyused. Spectral me.'Lqurements weremade using a Nicolettype 660Bspectrum analyzer. A cartesiancoordinatesystem (X,]', Z), definedin Figure1, was employedwith its originlocated on the centerlineof the jet. Hot-wireor hot-filmtraverseswere made in the two central .\°,Y and X, Z planes at streamwiselocations(X) from 40D to 160D. In all the measurements,the sensorwire w_s orientedparallel to the Z axis. Mean velocity measurementsweremade acrossthe entirejet in order to establish the symmetry" of the flowabout the centralplanes, however,only the data foreach half plane willbe presented. The controllingparameterin tiffsinvestigationwas the stagnationpressure,po,which variedfrom80p_iato 85psia, and was maintainedwithin an accuracyof _ 0.02psia. This 5 N

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rangecorrespondsto nozzlepressurerativs(stagnationpressure/ambientpressure}varying from 2 to 5.8. The temperature in the settling ehambe_was maintained to within 4-0.5°C of the ambient te.'nperature. Experiments were.conducted for a number of pressure ratios

using both nozzles, however, only a limited selection is presented here• The detailed hot"

wire measuremenls were made using the 3ram nozzleand were limited to the three pressure ratios R _ 2.7, R _ 3.8, and R _ 5.4.

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RESULTS AND DISCUSSION

(a) FlowVisua;izationStied) /

TypicalSchlierenpicturesof tile flowissuingfrom the 3ram nozzlefor three different pre._sureratios are shown in Figure2. The knife edge was orientedparallelto :.hejet axis in these photographs.The Schlierensystem was purposelyadjustedto enhancethe view of the wavestructt:rein the outer region,rather_hanto showthe details of the jet flow. Consequently,features such as shock cell structureare not seen clearly iu these photographs. Tile long optizal path assoc!atedwith the rectangu!argeometry mak.=_ pos_ihlet" _ viewingof wavesystems that otherw;.sewouldnot easily be seen These

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picturesdisplaythe flowfield fromthe ,Iozzleexit to a down-streamlocation of about

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30D.

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For pressureratiosR > 1.9,theflowbeyondthenozzleexit issupersonicandresult_in the formationof a seriesof shockcells,az showninFigure2. The most strikingobservation for tile three easesshown ih tile figure arethelarge cl',angesin tile angle of spreadof '

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the jet, the appearanceof .a very strong organizedwavepattern, and tlie developmenl of a M ,.'h wave radiation pattern atthe highest pressureratio. ,:or example,the total anglo of spread of the jet is about 20° for both the lowest(R -- 2.7) and thehighest (R "-"5.4) pressureratios,while the total angleof spreadis abou! 3_° at the pressureratio for maximumscreech sound r_diati0n(R "- 3.8). Associatedwith the large spreadi,g rale is an organizedcylindricaldoublewave pattern which origin,_tesalterLativclyfrom the two sidesof the jet. The center of the arcs formedby the sound wavo.son each side can be locatedand iden_.ified as the source for each wavesystem. This source is loca:ed approximatelyat the end of the third shock cell (x/D -- 7). Thepicture seems to suggest that a principalwavelength exists and that this wavelength "s the Samefor all directions of propagationof the wave. The secondwavefront seen inthe figureintroddcesa second and much shoriercharacteristiclength, which correspondsto a frequent) much too high to recordwith:brdinarydetectors. A similar doublewavepattern was observedby Powell 1053c. in his edge tone excitation of rectangularjets. For the pressureratio R _ 5.4, high frequencysound waves,emanatingat an angle of about 45° t'_,tie directionof the stream, can be seen radiatingfroma regioncloseto the jet exit. This apparentradiation 7

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. F._._._._,,_v.N-_w--_:._.z-,._,,-.:--_--,-/.,._-o_-

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_.,s,_o,..-_._,,z_.,..,._..-,.t_..._.,,_[.-_.-.,_.._._.--..-F_7_

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/E, which allows direct comparison with other work. In

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incompressible flow this is equal to the ratio < u >/U.

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Figure 16 shows the downstream variation of the centerline fluctuation intensity --< e >/E0 for three differentpressure ratios. The mean voltage E0 is obtained from the relation Eo --" KUo, where U0 is the calculated mean velocity at the center of the nozzle exit plane, assuming ideally expanded isentropic flow, and K is a constant obtained

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from tile calibration plot of the ]inearizedmean hot-wire voltage versus tile mean velocity, The value of K is the same for all the data plotted here. Although this approach may not correctly represent the precise downstreamvariation of < u >/U, ....

the relative trends

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between the various sets of data are expected to be valid[ For the underexpanded jet, a hot-film probe was used to make measurements for locations of x.less than 40D, while a hot-wire probe was used for x greater than 40D. For clarity, a line is drawn through the dat.l points for the case of//_ 3.8. Also included in the figure are the •resultsfor a high speed subsonic (M _ 0.8)jet, depicted by tile solid linewhich is an average of tile data points not. shown here. For this case, there is no known acoustic excitation present

•...

in the flow, thus giving a basis for comparisonwith the undcrexpandedjet data. As seen the magnitude of _ increases sharply close to the jet exit, reaches a maximum value at x/D _

10, and then decreases monotonically. Such a behavior is common to most of

tile naturally occurring (non excited) axial turbulence intensity profiles in subsonic jets. Generally, a peak in turbulence intensity occurs near the end of the potential core, which is a result of fluctuations induced by the interaction of the shear layers. The amplitude and position of the peak can be varied significantly by a controlled acoustic excitation of the jet near the nozzle exit plane; see for example Zaman and Hussain i981. In the self ..

similar region of.the underexpandcdjet, i.e. for x/D > 80, except in the case of/_ -- 3.8, the variation of _ with x has a behavior similar to that of the subsonic jet. l|owcver, the magnitude of _ at a given location increases with increasing pressure ratio. For the case

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of maximum screech sound radiation, i.e. for/? = 3.8, the profile shows a distinct peak at x/D = 80, followed by a faster decay in comparison with the two other cases.-It was found that for 15 < x/D < 50, the magnitude of _ decreases like X-ff 2. As discussed 15



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below, this type of profile seems to be a result of acoustic excitation in the jet. A weak acoustic excitation is also present for the other two pressure ratios (see Figures 2a and 2c), and is exhibited here by a small increase in turbulence intensity at z/D

90, for R -- 2.7.

For an excited plane jet, it has been shown by Hussain and Thomson 1980, that the excitation appears to directly affectthe fluctuation intensity and is more pronouncedon the centerline than in the shear layers. From results for acoustically excited axisymmetric and planarjets, it is found that a peak in centerline turbulenceintensity occurs in the regionof interactionof large scale vortical structures, usually appearing near the end of the potential '"

core (ltussain and Thomson 1980, Zaman and ltussain 1980). As has already been seen in Figure 2b, such structures are present in the regionjust d6_¢nstreamof the acoustic source.

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Since a peak is observed in the distribution of _ at X/D -- 80 and in view of the above discussion, one would expect to see large-scalevorticalstructures in a Schlierenphotograph

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of the flow field at this location. To explore such a possibility, Schlieren photographs for both the z, y and x, z planes, covering the region from the nozzle exit to a downstream ..........

location of about 110D, were taken as shown in Fi__ure17..Because. the available optical ....... _ ._ setup could not view the entire flow field simultaneously, two photographs in each plane _ ...... ]='=*_" were taken at separate times using a common referencelocation and assembled as shown. in the figure. Together with the cylindrical wave patteren found in the near sound field of the _, y plane (Figure 17a), large scale coherent structures are observed developing along

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the jet boundary in the regionof the acoustic source ( also see Figm'e 2b and 4). Further ._. away from the source no such distinct structures are visible, however, there are large

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random eddies present on the edges of the jet. Figure 17b shows the flow field of tile jet in the x,z plane, and for x/D greater than 50 a distinguishable large scale structure is strongly suggested by lhe picture. A dotted line presumably representing such a feature is superimposed on the picture. A typical wave length •deduced from the picture is found to be equal to about 8cm. On comparing a series of randomly selected pictures of this plane, there does not appear to be a repeatable pattern in their arrangement. However, the "wave length" and overall size of these structures match rather well. A more definitive argument °: concerning the existence of these structures must include quantitative data. With this .

objective in mind, oscillograph records of hot-wire outputs and their respective frequency spectra were studied. \

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Oscillograph records of e fluctdations along the centerline of the jet, for 40 < x/D < 140, are shown in Figure 18 for R -- 3.8. All the traces have identical Vertical and horizontal scales. As the probe is traversed downstream, low-frequency oscillations dominate the signal, with a recognizableperiodicity appearing in the trace at x/D --- 80.

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The period can be estimated and is found to be equal to about Ims (the corresponding" frequency is 10001tz), while the signal at x/D -- 40, i.e. trace (a), is dominated by

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more random high frequency fluctuations. Following the argumentsof Brown and Roshko .i076, the mean scale of the flow in the x, z plane must increase linearly with (x - x0). Consequently, it follows that the mean spacing and the mean size of the eddies or large scale structures also increase linearlywith (x- x0). The consequenceof increasing spacing

o,

leads to a decreasing frequency, which is consistent with the observations made from the oscillograms.

--.

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TIie passage frequencyof the large scale structures at a given location can be obtained o .

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by studying the frequency spectra of the hot wire signal at that location. Figure 19 shows the frequency spectrum of e for various positions along the centerline of the jet for 15 < x/D < 140. The horizontal scale is in kilohertz, the range of.which varies for some of th_ plots. Forx/D < 40 a strong peak around 17.Skllz isobserved and found to be equal to the fundamental frequencyof the near acoustic field. From a phased locked Schlicrcn movie of the flow field for a 5ram nozzle (Krothapalli et ai. 1082), it was found that the frequency witli which the large scale structures pass any station in the x, y plane was identical to the fundamental frequency of the near sound field. Several additionaldiscrete frequencies in the range O-20kllz are also observed in these plots. With increasing distance downstream, the spectral energTshifts toward the low frequencies. At x/D := 80, in addition to other low frequencypeaks, a distinct peak at 104811zis observed, which is close to the frequency obtained from trace (c) of Figure 18. This frequency then corresponds to the passage frequency Ofthe large scale motions observed in Figure 17b. To further verify this, one can calculate the frequency based on the spacing of two adjacent structures in Figure 17b and the mean convection velocity. The convection velocity of these structures varies from

"

0.5U€ to 0.7Uc. For x]D=

80; we have for the ccnterline velocity Uc --15Ira/see;

and

assuming an averageconvectionvelocity of 0.6Uc, one obtains a frequencyof about 111811z, :

which is quite close to the measured frequency. It is also interesting to note that the ratio of frequenciesfor the dominant components in the two planes is equal to about 10.7, which 17

+

happens to be the aspect ratio of the nozzle. From the above it may be suggested that acoustic excitation with sources Joeated at x/D'
80 suggest that the flow in the z, z plane reaches a self similar state. In light of these measurements (both mean and rms profiles) it may be suggested that the flowfield of a rectangular jet reaches self similar states in both planes at locations 19

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dc.wnstream of the crossover point. However, the shapes of the self similar profiles are "

_ifferent in the t_o planes. Furthermore, it appears that complete axisymmetry of the jet may not be reached wRhin a reasonable(of engineeringinterost}distance downstream.

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The profiles of _ at diffcreat downstream locations for R --- 2.7 and 5.4 in both the x, y and x, z planes (not shown here), show a similar behavior as discussed above, except for the enhanced effects of acot:stic excitation, i

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CONCLUSIONS



/An objective of this work was to study the mean and turbulev.tvelocity fields of an underexpanded rectangularjet of moderate aspect latio.. While investigating this problem., we encountered two major factors influencing the overall flow field of the jet. One is to be expected and is the effc_t of the density ratio between thejet and tl,e ambient air. The second factor, typical of und.hrexpandedjets, is the generationof "screech" tones and their influence on the structure of the jet. Although discrete tones or "screech" tones are found in the near soundfield of the jet for all pressure ratios above tile criticat pressure ratio (i.e. R -- 1.9-),they are most intense and have greatest effect onthe ¢.verallflvw field

........

only in the range of pressure ratios from 3 to 4. The maximum screech _ound radialion

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occurs in this cxperiment at a pressure ratio of 3.8. When the jet is operating,outside this range of pressure ratios, the influence of screech tones:is less important, as compared to

i

the effectsof varyingdensity,on the meanand turbulencevelocitylleldsof the jet. From the Schlieren photographs st udied, the following observations are made. For the condition of maximum screech sound radiation, a very strong organized cylindrical wave

patternis observed,whichoriginatesalternatelyf:ome.,och sideof thejet. The sourcefor this wace system is located approximately at the end of the third shock cell and serves a.s an acoustic e._itation for the entire jet flowfield. Associated with tile presence of the wave s.v_temis an incre_qedspreading rate of the jet in the plane containingthe small dimension

ofthenozzle..Whenthefrequency ofthe acousticexeitation!ieswithinthe instabilityband for a plane incomprt_sible jet, it serves to introduce large scale coherent structures in the turbulent flow. Such structures are observed h_re in hoth planes of the jet. llowe_"er, in the x,y plane they appear just downstream of the ._coustic source, i.e. at z/D = 10, while in the x,.." plaI:e they are observed at downstream locations of x/D greater d|an ' "

:about 60. The existence of these large scale ._tructures at differentdownstream locations in the two planes was also confirmed by oscillograph records of hot-wire signal_ and their respective frequency spectra. The Stroahal number for these organized motions was found



-:.....

i 4i....

to be equal to 0.12, which is clerse_o the most unstable frequency"for the antisymmetric modes of the planar incompressible jet. The frequenck.'sin the two plant,s thus scale with the aspect ratio of the nozzle. These observations are supported by the theoretical work 21

y " '

o.

l"

I"

- .....

.

.

of erighhm lOT3, who studied till, stability of a jet wilh an l,llil|tie cr_s-seeliuu, lie retold

.

that ill the ease of,spatialb' gruwitlgdisturbane(.,s,modes representing sidi,waysoseili:llto. paralh,I to the major axis, or lungdimensi,mof the ,ozzh,, have a small growth rate, while those reprt.,seutiuga flapl)i||g motioapai'allelto the minoraxis, orsmall di||te||sio,t of the nozzle, have a large growth rate.....

!

j I t ]

The mean nmi rms inle||sil.v iirolih,s-. for .rid gr_'aterthan 80, ilth_th the relltral -x,.v nltd.1",.."plaues,exhil|it separate geometricalst|hilarityia their respectiveplanes,II|t|s st|ggesti||g that eoml|lete axisymmetrv(i.e. i,lel:tiealprolih.sia b_:thpit:re,s)of the jet may :mr be achieved withia a |easouable distance downstream.This is iu eolltrasl to om.,s i|ltt|itive mdiou Ihat a reeta||gular jet sh_ald reachea ¢0mpleleaxis.vmnletrieslate iu a rdativel.vshort distaltee dowu,_lre:m| of the nozzh,exit. ...

'

". ...........

lu the abqelleeor aeot|stie exeitati,_nvL'ilhincreasingpresstlreratio (iuereaseiu rest,r'.'_firpresst,re), a drerra.seiu the spreadingaugle of the jet was observt.d.Similarobserva-

i i

tiolls l,aveals,|l,eeu||tad|.iu studi|.'sofothersupersolfie ..,hear layersa||dis assoeiah, d with

i

the illereasinK density of lhe jel.

!

" ..........

°.

.

REFERENCES

Abramovich, G.N. 1983. The theory of turbulent jets. M.I.T. Press, Cambridge, Mass. I •

J

Brown, G.L., and Roshko, A. 1974. On density effects and large structure in turbulent mixing layers. 64, 745-816. Crighton, D.G. 1073. Instability of an elliptic jet. J. Fluid Mechanics. 89, 655-672. Crow, S.C., and Champagne, F.It. 1971. Orderly structure in jet turbulence. J. Fluid Mechanics..18, 567Davies, M.G., and Oldfield,D.E.S. 1062. Tones from a chocked axisymmetric jet. ACOUSTICA. 12, 257°277. '....... Gla_¢,ILD. 1068: of acoustic feedback on the spread AL.L.k Journal. 6, Effects 1800-1897. --- and decay of supersonicjets. Gutmark, 465-.195. E., and Wygnanski, I. 1976. The planar turbulent jet. J. Fluid Mechanics. 73, ilammitt, G.II. 10{31.Tile oscillation and noise of aiz overpressure sonic jetl J. Aerospace Sciences. Vol. 28, No. O,673-680. ]larDcr-l_)urne, :\(b\IH) CP-131.M., and Fisher, J.M. 1973. The noise from shock waves izisupersonicjets. llsia, Y., I¢.rotl!apalli,A., Baganoff,D., and Karamcheti, K. 1982a. Efft,cts of Much number on the development of a subsonic rectangularjet. ,_U\ Paper No. 82-0219. llsia, 'Y., I¢.rothapalli,A., Baganoff, D., and Karamcheli, K. 1982b. The structure of a subsonic compressible rectangular jet. Joint Institute for Aeronautics and Acoustics Iteport TR-.I3, Staffford University. |htg_ain, F.M.K.A, and Thompson, A.C. 1980. Controlled symmetric perturbation of the plane jet: An experimental stud), in the initial region. J. Fluid Mechanics, I00,397-431. lqrothapalli, A., Baganoff, D., and Karamcheti, K. 1081. On the mixing of a rectangular jet, J. Fluid Mechanics., 107, 201-220. Krothapalli, A, Baganoff, D., Hsia, Y., and Karamcheti, K. 1981. Some features of tones gt,net:at.edl_yan underexpandcd rectangular jet. ALU\ Paper No. 81-0060. iqrothapalli, A,, Baganoff, D., Hsia, Y., and Karamcheti. 1082. On the mechanisms of tone generation in an underexpanded rectangular jet. In preparation.

•.

23

)

.

"4. ..........

"

"

La.qsiter,W.L., and Hubbard,tt.1!. 1056. The near noise field of static jets and some model studies of devices for noise reduction. NACA Report 1261. Lowson, V.M., and Ollerhead, B.J. 1068. Visualization of noise from cold supersonicjets. The J. of the Acoustical Society of America, 44, 624-630. Maydew, C.R., and Reed, F.J. 1003. Turbulent mixing of conlpressible free jets. AIAA Journal, 1, 1643-16.14 ..... Poldervaart, J.L.,Wijnands, J.P.A., and Bronkhurst, L., 1073. Aerosonic games with the aid of control elements and externally generated pulses. AGARD CP-131. :'

_

Powell, A,, 1053a. On the noise emanating from a two dimensional jet above critical pressure. The Aeronauticas._uarterly, IV, 103-122. Powell, A., 1053b. On the mechanism of chocked jet noise. Prec. Phy. Series B, 66, 1039-1056.

Soc. London,

Powell, A., 1053c. The noise of chocked jets. J. of Acoustical Society of America, 25, 385-389. Morkovin, M.V., 1081. Private C_,,nmunication. Sate, II., 1060. The stability and transition of a two dimensional jet. J. of Fluid Mechanics, 7, 53-80. !

Schlichtin_, H. 1980. Boundarylayer theory. McGraw llill. Sherman, M.P., Gl_s, R.D., and Dulleep, G.K. 1976. Jet flowfi_ldduring screech. Applied Scientific Research, 32, 283-303. -

Thomson, A.P. 1974. Compressib!- fluid dynamics. McGrawllill, Chapter 4, pp 2'2'2. \Vcstley, R., al_d\Voolley, II.J. 1073. The near field sound pressureof a chocked jet during screech cycle. AGARD CP-131. Zaman, Q.M.B.K., and tlussain, F.M.K.A. 1980. Vortex pairing in a circular jet undt,r controlled excitation. Part 1. General jet. response. J. Fluid Mechanics, 101, 449-.191.

.

Zaman, Q.M.B.K., and tlussain, F.M.K.A. i981. Turbulence suppression in free sh,,ar flows by contr011cdexcitation. J. Fluid Mechanics, 103. 133-159.

\

24

"

° "

...

!

:

• :

. ,

OR;G!T_,_L ?.4_LZV3 OF POORQUAL|I_/

Table 1

-

"

Geometry or

Characteristic

the nozzle

.:dimension D

velootty

0.3cm

3.8

Seotangular AR:16.7

.'"

• -.

Pressure ratio

Frequenoy St=

U

Hz 17,500

eonTnents

rd/U 0.12

Present results

q3Om/s

Reotangular _R=lO

0.5em

3.5 q18m/s

10,000

0.12

Present results

l! ]I

Reotangular AR=12.75

0.635cm

3.67 _23m/s

7,375

0.11

Hammitt

!

Reotangular

0.305c_

3.67

0.135

Powell

AR=5_83 Rectangular

q23m/s 0.18_n

AR=I.7 Axlsymmetrlo

Axtsymmetrie

18,750

--

3.17

31,6q0

0,1q

Powell

qO3m/s 2.5qem

1.27cm

3.67 q23m/s q.O

tl

i ",000

0.2"

9,428

0.275

"-'N_e'l'_ ''_'"

_" Sherman et al.

q35ml-

-i

i i

...... : '_

9

I

_'

llOmm

xx

oo

'2"

;

0_

To settling ____

45°

.

.

_ ,.



chamber

,.

..

_

_"

l3, |

mm_

.. .

=_g "_" .





;. '_

z_w [

x, _T

Figure 1." Schematic diagram of rectangular nozzle and entry region. .......

.............

1

-

-.

"

.:_,

R=2.7

R=3.8

R=5.4 OO O_

Figtsre 2.

Schlieren

pictures of the jet in the 1, y plane...|it

=

16.7,1) = 3ram. .

r-m

R=2.7

Figure 3.

R=3.B

R=5./.,

Schlieren pictures of tile jet in the z, z plane. AI? -- 16.7, D -_ 3ram.

88

_ i

\

R=3.7 Figure

4.

Schlieren pictures or the jet in both x, y and _, z planes. .tl_ _ IO,1_----5ram.

\

\

R=3.7

--

Figure 5.

Schlieren pictures or the jet in the x,y plane, wltb a reflecting surface placed parallel to tile jet axis. All -- 10, D -- 5ram.

ORIGINALPACt _S OF POORQUALITY I

Pi!

R=3.7

Figure 6.

Schlieren picture of the jet in the _, y plane with a reflecting surface placed at 135 to the jet axis..IR -- 10,/) -- 5ram.

_-

4.0

.......

(

3.2

oo

2.4

_"

•.

-

•.

_

P02

'

"_a 1.6

1").8 -

0

'

0

!

Figure 7.

I

8

I



!

16 '

%

I

:

24

Variation of the pitot pressure along the center line of the jet. I1 ----3.8.

,I

i i i

_"

",

.:'

-_ ."

-:

-

'"

"_°

_- _'.

" :

. ",.

", "

.

" • .-

._

-

"._"



",.,.



.'-

"-',

"

;

_

. ....



_

_o'_:_".'-" .

....

..

ORIGII'|ALp._,GE1$ OFpOOR QUALIFY

.,

-

-"

_

:._''i:_,". :-.-,_:_

._ ...

7";



_.:

-.

.

........

42

. ,,

"

!:

• L .L

6 0

0

1

2 Ylmm)

i

;

J° p

.

•Figure 8.

i

-,.

i . _.

Pitot pressure profiles in the x,y plane near the nozzle exit, Z -- O.

I

Q, x/D = O.1;0, x/D -- i.0.

it !

t

! i

i d' _

,. I

\



I

..,,

--=_s_"", '

_

'

" "

/

./ .. -

ORIGINAL PAGe. I_

OF POOR QUALITY

,6r_

.

•5

El •



[]

.

"'¢ Uc

0 R=2.7, Ue=3g3m,,_ A 3.8 433

"'i

.2

[]

5.4

',1

I

I

Z.0

50

/:,,(D [] A O (i)

4 76

I

,_

I,

I

I.

100

I

150

.

Figure 9.

The decay of the mean velocity along the centerline of the jet. " It = '.'.7: _ It = 3._: [] It = r,.I.

\

.8 __) 1.0

im 6

u

_.....

m

U

41 ,t

O0 •

0 ,-"_'+

o_

.2 -

0

0

#g

I

.1

j

_o

.2

.3

Y/'X-Xo Figure lO. Mean velocity profilesin

the x,y planet z=0.

.r/l) = 1.10: (1!1711).

,.'|it

!?

2.7;0 ,

•/!: = Io; A ,,/!)= _o;[] .,/i)=_o; G}.x/l)= Ioo:_ . .It = ._.'1;.....

= :|,% (';lillnark

nnd

%%')'_lh'll|ski

-:

:i! i i

,',

|

-

°

°°;

1 •O__"_,

"

, "_"

_

@

........ . i_ A

-Q

U Uc

E_

.,._ .2

Mean

Velocity

.|

m

% oA_

.2 Y_X

11.

'"

,::

.i

,