RECENT RESULTS ABOUT FAN NOISE - ITS GENERATION,RADIATION AND SUPPRESSION

Charles E. FellerNatinnal Aeronautics and Space Administration

Lewis Research CenterCleveland, Ohio 44135

ABSTRACT

A review of recent developments at NASA Lewis about fan noise including

• _ its generation, radiation characteristics, and suppression by acoustic treat-: _ ment is presented.

I

_ In fan noise generation, results from engine and fan experiments, usinginflow control measures to suppress noise sources related to inflow distortionand turbulence, will be described. The suppression of sources related to in-flow allows the experiments to focus on the fan or engine internal sources.Some of the experiments incorporatedpressure sensors on the fan blades tosample the flow disturbances encountered by the blades. From these data someinferencescan be drawn about the origins of the disturbances. Also, hot wiremeasurements of a fan retor wake field will be presented and related to thefan's noise signature.

The radiation and the suppression of fan noise are dependent on the a-coustic modes generated by the fan. It is unfortunate that these are usuallynet known in any detail, nor is there a really simple way to measure them.Some progress has been made in describing fan noise suppression and radiationby relating these phenomena to the mode cutoff ratio parameter. In addition

, to its utility in acoustic treatment design and performance prediction, cutoffi ratio has been useful in developing a simple descrip: on of the radiation pat-

tern for broadband fan noise. Some of the newer fir_dilgsusing the cutoff, _ ratio parameter will be presented. Numerical methods have also been under_ i study for sound radiation and suppression. Some comparisons of mlmerical the-! ory with experimental data are presented to illustrate the potential of these

methods.

INTRODUCTION

This paper reviews some of the research at the NASA Lewis Research Centeron fan noise. From a theoretical viewpoint, the fan remains one of the least

'i quantified of the noise sources in a turbofan engine. Even from this. viewpoint, the physics of fan noise generation mechanisms seem to be well

understood so that it is not the problem. Rather the problem seems to be that' fan noise, even if consideration is restricted to tone noise at subsonic tip

speed, is a consequence of several separate, simultaneous sources that dependon unsteady flows and other iactors present which are all poorly quantified.

f Coupled with this are questions of whether the sound field will propagate(i.e., whether it is cutoff), how much sound is transmitted through eitherupstream or downstream blade rows, and how the sound radiates through theinlet and exhaust flow fields. All of these questions affect the far fielddirectivity of fan noise, which is the end objective. Then, in addition tothe tones, one must also consider broadband noise and, for supersonic tipspeed fan operation, multiple pure tone or buzz saw noise.

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Perhaps it was realization of the complexity of fan noise, as the fore-going discussion suggests, that caused Cumpsty in his 1977 review of turbo-machinery noise to lament the "sharp division between theory and experiment"(ref. 1). In his view, theoretical models were simplified to the point thatthey had no relevance to experimental configurations, while experiments weredevoted to the acquisition of overall noise with little finesse in the acqui-sition or the evaluation of the data. While experiment and theory are notcompletely reconciled today, it is the author's opinion that considerable pro-

gress has been made over the last few years since Cumpsty's review and that itis continuing.

In the present paper, all aspects of the fan noise problem will beconsidered - generation, duct propagation and radiation; however, the majoremphasis will be on fan noise generation. The various topics will be present-ed in the following order: ]/

1. Simulation of flight fan noise in static tests.

2. Rod wake-rotor interaction theory for single mode propagation.

3. Rotor wake-stator noise experiments in simulated flight.

4. Duct acoustics

In recent years a significant fraction of fan noise research has beendirected toward the _o-called forward velocity effects problem. Flight fan inoise is less than static test fan noise. The reason is that the inflow in

static tests is turbulent and contains flow distortions, perhaps from rig sup- iport wakes or other sources, that are either not present or are greatly dimin-ished in flight. Research has focussed on the development of suitable flow-straighteningdevices to condition the inlet flow. References 2 to 14 containa large fraction of this work.

Within NASA, the forward velocity effects program utilized a Pratt andWhitney of Canada JT15D turbofan engine and fan stage that were staticallytested at NASA Lewis and flight tested at NASA Langley. The reconciliation ofstatic and flight fan noise requires not only obtaining static data that du-plicates flight data, but also the correct application of other factors asso-ciated with flight such as convective amplification. The NASA program willprovide information about these related flight effects on fan noise when it iscompleted. Preliminary results from this program based on a workshop held atNASA Langley in January, 1982 will be published as a NASA Conference Publica-tion (ref. 15). In this paper results from the static test research will pri-

marily be discussed.

In an effort to relate experiment and theory more closely, a unique andreasonably controlled experiment was performed with the JT15D engine utilizingrods just upstream from the fan to create the noise. An inflow control devicewas used in this experiment to suppress the noise sources related to inflowdisturbances, thus emphasizing the rod wake source. The results from thisexperiment and their comparison with generation theory reported in reference16 will be described. The theory develol_nentcan be found in reference 17.This significant experiment has also found important use in suppressor andradiation theory validation, as will be seen.

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In a similar vein, the rotor wakes and noise from a fan stage have beenmeasured as a function of axial spacing. This experiment is unique because ofthe clean flow forward velocity environment (g by 15 Foot Anechoic WindTunnel) in which it was performed. The rotor wakes were measured at severalradial positions. This data will be available for use in noise generation 'theory. Similarly, two stator sets were tested to evaluate the effects ofstator number and chord. At present the comparison of these data with thetheoretical model has not been completed but a san_oleof the results from ref-erences 18 and Ig will be presented.

Other fan noise research is concerned with duct acoustics the propagationand attenuation of sound in acoustically treated ducts, and its radiation tothe far field. An understanding of duct acoustics and radiation are essentialin the fan noise problem. The usual in-duct description of fan noise is interms of duct modes. The number of modes that can propag_,tein a duct isapproximately proportional to the square of the product of sound frequency andduct diameter (ref. 20). At the frequency of fan tones the number of modesthat can propagate is quite large. In static fan-testing without flow condi-tioning, it appears that all of the possible modes are present (ref. 21).This may also be the case for broadband noise; however, in flight or statical-ly with a flow straightener, the number of modes at the fan tones may be verylimited. In this case the sound is due to interaction between blade rows such

as rotor wake-stator interaction, and the modes generated are determined bythe numbers of blades and vanes in the blade rows, as described by the Tyler-Sofrin cutoff theory (ref. 22).

A considerable simplification in handling the mode_, especially when alarge number is present, has resulted from the recognition that the pertinentphenomena concerning mode behavior (i.e., propagation, attenuation, optimumimpedance, and radiation) are all correlated by the single mode-related para-meter, cutoff ratio (refs. 21 to 27). All modes having similar values of cut-off ratio behave alike. Some of these important duct acoustics results willbe included in this review.

As in other fields, there has been a significant effort to treat ductacoustics and sound radiation problems using numerical techniques. This workhas been reviewed recently by Baumeister who has pioneered this field (refs.28 and 29). Several results using this approach will be presented to illus-trate the power of the technique.

SIMULATION OF FLIGHT FAN NOISE IN STATIC TESTS

As outlined in the Introduction,this research is concerned with the de-velopment of a flow straightener to be installed on an engine or fan inlet tominimize turbulence and distortions present in the inlet flow, which interactwith the rotor blades to generate noise, mostly at the fan fundamental tone.Inflow control devices have all been constructed from honeycomb, often in con-Junction with screens or perforated plates. In addition to smoothing the in-flow, the stucture is required to allow the sound field to propagate unalteredin level and directivity. _

• Inflow Control Design

There was not very much concrete information to guide a design of thesedevices. The problem was thought to be due mostly to the ingestion of atmos-

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pheric turbulence and based on the results of Loehrke and Nagib (ref. 30),screen_ were introduced downstream of the honeycomb. Most of the designchoices seem to have been based on general knowledge and intuitive reasoning.Thus the honeycomb cells were a igned with potential flow streamlines and openarea ratios of screens and perforated plates were chosen to keep pressuredrops small. Honeycomb cell length/diameterratios ranged from about two toeight. Structure size ranged frem equal the fan diameter (in-duct placement)to about four times the fan diameter.

The construction method and features also had to be established. Con-

cerns included the thickness of support ribs, the presence of corners formedby the junction of flat panels, and the achieving of a disturbance-free at-tachment of the structure to the nacelle. The sketches of figure I illustrateP

the three sizes of inflow control structure experimentally studied at theLewis Research Center, along with some pertinent construction details and di-

, me:'sions. The photographs in figure 2 show the devices installed on the JTISDengine at the Lewis outdoor test stand and on the JT15D fan in the Lewis an-echoic chamber.

Experimental Evaluation Criteria

The effectiveness of the_e inflow control structures has been experimen-tally determined with a JTI5D engine and fan stage using far-field directivityas the primary indicator. To help in the diagnosis, pressure transducers wereflush mounted on the fan blades at several spanwise and chordwise locations,as shown in figure 3. The unsteady pressures sensed b) these transducers werein response to velocity perturbations encountered by the blades. The velocityperturbations could arise from inlet turbulence and flow distortions, from thepotential field of downstream stators or struts, and also from sound waves.These all appear as unsteady disturbances to the rotating fan.

Finally, an experiment was performed with each inflow control device todetermine whether it introduced a sound transmission loss. The experimentinvolved the introductionof an array of 41 equally spaced rods just upstreamof the fan face, as shown in figure 4. The wakes from these rods constitute asound source that dominates all other sources and is unaffected by the pres-ence of the inflow control structure. Thus, if the inflow control structurecaused a transmission loss, it could be detected by comparing far field direc-tivity patterns with and without the structure in place.

Experimental Observations and Interpretations

Data from the JT15D engine with and without inflow control device i willbe compared in terms of each of these indicators: (a) far-fleld sound; (b)blad_ pressures; and (c) rod generated sound (ref. 12). The data are all at afan speed of 10,500 rpm corresponding to a tip relative Mach number of 0.917.

Far-field sound. - Figure 5 compares narrowband spectra measured in thefar field at 40" from the inlet. By comparing figures 5(a) and (b), it can beseen that the broadband noise was not affected by the inflow control devicebut the tones were generally reduced, the fundamental by about 10 dB and thesecond harmonic by about 5 dB. Interestingly, the third harmonic showed anincrease of about 2 dB. The reduction of 10 dB is evidence that inflow tur-bulence and distortions clearly dominate the sources of the fan fundamental

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tone. On the other hand, the lackof changein broadbandlevel indicatesthatthis noise is not relatedto inflowturbulenceor distortions.

Figure6 comparesthe directlvitiesof the narrowbandfan fundamentaltone and the broadbandlevelat the fundamentaltonefrequencywith and with-out the inflowcontroldevice. Again it can be seen that the inflowcontroldevicehad no effecton the broadbandnoise at any angle,while the tonewasreducedby a largeramountforwardof 40" than aft. The tone directivltywiththe inflowcontroldeviceinstalledhad a more lobularshapethan withoutit.As will be shownlater,this shape is largelydue to a singlesoundmode, as-sociatedwith an interactionbetweenthe fan rotor,and the six engine inter-nal supportstrutsdownstreamof the fan stators. This internalsourcelimitsthe amountthat the fan fundamentaltone can be reducedin the JTI5Dengine.

Bladepressures.- Figure7 comparesspectrafrom a blade-mountedpres-sure trak,sducerwith and withoutthe inflowcontroldevice. The tones inthese spectraoccur at multiplesof the shaftrotationalfrequencyand,as themiddle abscissascalesuggests,these are interpretedas the circumferentialmode orders q of the inflowdistortion. The lowerscalegives the circum-ferentialacousticmode number m correspondingto the interactionbetweenany harmonicdistortion q and the 28 blades B of the JTI5 fan. In gener-al, m - B - q. In order to propagatein the duct,an acousticmodemust spinat a ratedescribedby the Tyler-Sofrincut-offtheory(ref.22). For the fanspeedof figure7, cut-offoccursfor mode numbersover 23 or lessthan 23correspondingto distortionharmonicslessthan five and over 51.

Withoutinflowcontrol(fig.7(a)),the spectrumconsistsof peaksatevery shaftharmonicin the frequencyrangeof the spectrum. Basedon theprecedinginterpretation,thismeans that all the modes that can propagateshouldbe presentin the sound field. Unfortunatelythe blade pressuredatado not suggestwhat the mode amplitudesare.

In contrast,the spectrumwith the inflowcontroldevice(fig.7(b)) isreducedto peaksat distortionharmonics q of i, 2, 5, 6, and 12. The con-clusionis thatmost of the peaks in the baselinespectrumwere the resultofturbulenceor otherdistortionsenteringthe inletthatthe inflowcontroldeviceeliminated. The five or so peaks remainingwith inflowcontrolarepresumablydue to spatiallyfixed disturbancessuch as the six structuralstrutsjust downstreamof the fan stators.

That theseare spatiallyfixeddisturbancescan be reasonablydemonstrat-ed by examiningthe signal-enhancedwave form and i_s spectrum. This waveform averagedover 200 rotor revolutions(fig.8(a)) and shows the presenceoffixedpatternsof I, 6, and 66 peaks per revolution. The spectrumof thiswave form (fig.8(b)) confirmsthe presenceof peaks phase-lockedwith therotorat q . 1, 2, 5, 6, and 12. The peak at q. 66 appearsin spectracar-riedout to its frequency. It is due to the 66 statorsin the JT15b fan. Ofthe peaks present,those at q - 6 and 12 yield progagatingacousticmodes thatare presumablythe primarycauseof the residualfan fundamentaltone,ob-

: servedwith the inflowcontroldevice. The peak at q . 6 is probablyrelatedto the six enginesupportstrutsmentionedearlier. Accordingto the previousdiscussion,these shouldgeneratean acousticmode,m. 22, with 22circumferentiallobes. To evaluatethisconclusion,two pressuresensorswereflush-mountedwithinthe JTID inletat the sameaxial planebut 1/44of thecircumferenceapart. If therewere a 22 lobepattern,these sensorsshould

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sense the same signal with a 180" phase difference. The measured traces,shown in figure 9, show this result precisely which seemsto confirm the pres-ence of the 22 lobe acoustic mode. These distortions are also the source of afundamental tone in flight, if they are indeed the consequenceof someengine-related internal flow disturbance. The data, however, do not revealwhether the sources are within or external to the engine. That has to comefrom other evidence or reasoning. For example, the once per revolution source(q. 1) may be due to the presence of a ground plane, whereas q . 6 appears tocome from the enginestruts. ,

Rod-generatedsound.- The 41 rodsconstitutea distortionhavingaharmonicnumberof 41 and, fromthe precedingdiscussion,shouldgeneratea13-Iobeacousticmode whose strengthis independentof inflowturbulenceordistortions.It is this sound fieldthatwas used to determinewhethertheinflowcontroldevicealtersthe sound transmission.Figure10 comparesthefar-fielddirectivitiesof the rod-generatedtonewith and withoutthe inflowcontroldevice. It also shows the tonedirectivitywithoutrodsor inflowcontrolfromfigure6. The strongcontribqtionof the rod sourcecan be seenin the rangefrom 30 to 60°. It can also be seen that the directivitywashardlyalteredby installationof the _nflowcoD1troldevice,hence,theconclusionthat it does not affectsoundtransmission.The sameconclusioncan be drawnfrom comparingthe broadbandlevelsat the tone frequency,asalso shown in figure10.

Summaryand LimitedComparisonswith FlightData

It has been demonstratedthat an inflowcontroldevicedoes not alter thesound transmissionand can reduceor eliminatethe noisecausedby inflowtur-bulenceor distortionsby smoothingthe inletflow. The use of inflowcontrolhas a11owedstaticexperimentsto focuson the internalengineand fandesign-relatedfan noise sources. Already,theseexperiments,even those in-tendedonly to validateand demonstrateinflowcontroldevices,haveprovided

• improvedunderstandingof fan noise. For example,it appearsthat inflowtur-bulenceis not the dominantcauseof fan broadbandnoise,a new conclusion.As anotherexample,with inflowcontrol,the rod data haveservedas a reason-ablydefinedcontrollednoise sourcethat has been usefulin validatingsourcenoisemodels,radiationor directivitymodels,and acoustictreatmentdesignprocedure(aswill be seen in subsequentsectionsof thispaper). The experi-ments havealso revealedthat enginedesignfeatures(e.g.,supports)can be asourceof fan noise thatcould have been overlookedin the past since theycould not havebeen identifiedin statictests. Clearly,the inflowcontroldevice is an importantsuccessin fan and engineacousticexperimentation.Althoughthe evaluationis not yet completeand is complicatedby some sig-nificantflighteffects,the preliminarycomparisons,made at LangleyResearchCenterbetweentheir JTISDflightdata and Lewis staticdata, showthat manyfeaturesof the flightdata are reproducedby staticdata obtainedwith inflowcontrol(ref.15).

Figure11 comparesflightand staticspectrawith ICD No. 12 from theJTI5D. Exceptfor a reductionof about6 dB in the broadbandlevelin flight,the spectra,includingthe absenceof a fan fundamentaltone,are quitesimllar. The shift in broadbandlevel is largelydue to a shift to a lowerengineoperatingline in the flightdata. Figure12 comparesthe flightandstatictonedirectivities.Again the.agreementis good at anglesfrom about50- and aft. At anglesforwardof 50 , the flightdata roll off fasterthan

to the staticdata, possiblydue to a real flighteffectsuch as convective6

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T

Lamplification. In any case, we conclude that the inflow control device ap-pears to do a reasonable job in solving the fan static testing problem.

COMPARISON OF THEORY WITH SINGLE MODE EXPERIMENT

The experiment with the 41 rods as a noise source was described earlier.The rod wakes generated a fan tone that dominated or controlled the measureJnoise and since the wakes from the rods are known, the experiment offered a , .,unique opportunity for comparison with theory. The theory, developed in ref-erence 17, is three-dimensionaland treats the source as noncompact. Detailsof the results presented here are given in reference 16. Figure 13 compares :the measured and calculated fundamental fan tone power due to the 41 rod wakesinteractingwith the JTI5D fan. The comparison is shown as a function of fanspeed and displays the individualmode powers as they begin to propagate. The !agreement is excellent over the entire speed range. It is interestingthatthe increase in tone power is not monotonic with speed, either experimentallyor theoretically. Also the modal power mix varies with speed.

These two results, if general, illustrate the difficulty of developing auniversal fan noise correlation. The next elements needed in the theoretical

development are to incorporate a far field directivity model and to accountfor the modal-scattering that may occur as the inlet duct changes geometryfrom annular to circular. The agreement between theory and experiment interms of sound power provides some confidence that the aeroacoustic modelingis valid and can give useful results if the input disturbance is adequately ,known. A more important practical case than inflow distortion-rotor interac-tion is rotor wake-stator interaction, which is considered in the next section.

ROTOR WAKES AND NOISE

The experimental results were obtained in the Lewis 9 by 15 Foot AnechoicWind Tunnel using a fan simulator (refs. 18 and Ig). The installation in thetunnel is shown in figure 14. With a low tunnel velocity, the inflow into thefan is smooth enough that the noise due to this source is not a problem andthe experiment can focus on rotor-stator interaction noise. In the experi-ments the wakes and resulting noise of a 15-bladed rotor, rotor 55, were meas-ured as a function of ,-otor-statoraxial spacing for two stators as shown infigure 15. The stators had vane numbers of 25 and 11 that resulted in cutoffand cuton, respectively, of the fundamental tone due to rotor-stator interac-tion. There were also more propagating modes at each of the higher harmonicswith the 11-vane stator than with the 25-vane stator. The 11-vane stator has

a larger chord than the 25-vane stator since solidity was maintained constantand, thus, the dynamic response of the 11-vane stator shoud be different fromthat of the other because of its lower reduced frequency (ratio of gust wave-length to stator chord).

Rotor Wakes

The wakes were measured with stationary cross film anemometers located inthe stator, leading edge-plane midway between adjacent vanes as shown infigure 16. The films were alined, as shown in figure 17, to measure thestreamwise and upwash velocity co_onents at the stato, leading edge. Wakemeasuren_nts were obtained at four radial immersions from near the rotor tipto vicinity of the hub. The fixed reference frame data were digitally proc-

(

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essed and combined with the fan rotational velocity to obtain the wake profilein the rotating reference plane.

Figure 18 shows the rotor relative and upwa_h velocities as a function ofradial position. The profiles, showing seven consecutive blades of the 15rotor blades, represent averages from 500 rotor revolutions. These data areat a fan tip speed of 560 ft/sec, corresponding to 80 percent of design speed,and a downstream distance of 1.23 aerodynamic rotor chords. It can be seenthat the wake profiles are nearly identical from blade to blade. Away fromthe tip the profiles are about as expected; however, near the Lip a doubledefect appeared, probably due to the presence of a tip vortex that lies aboutmidway between adjacent wakes. The wake defect amplitude decreased inwardfrom the tip but then showed an increase at the location nearest the hub.

The upwash velocity component is more important to noise generation.There is a one-to-one frequency correspondence between the wake and sound har-monics. Thus, the spectral content of the wakes is of direct interest.Figure 19 shows the spectrum of the up.'ashwave form, shown in figure 18(b) at30 percent of the span from the tip. At this intermediate position the spec-trum levels show a regular falloff with increasing harmonic number. Figure 20shows the levels of the first four harmonics as a function of distance down-stream from the rotor. Data are shown at the 30 and 9 percent spanwise posi-tions. At 30 percent span, the harmonic order remained constant with in-creasing distance and the higher harmonics appeared to decay faster than thefundamental, an expected result. On the other hand, near the tip, the secondharmonic was largest and decayed slower with increasing downstream distance.Initially the third harmonic was also greater than the fundamental which, how-ever, became larger at the farthest position. This unusual behavior at thetip must be related to the tip vortex. It is complicated not only by the wakedecay that occurs, but also by the ability of the vortex to migrate radiallyas it moves downstream.

These wake velocity harmonic amplitudes are the necessary input para-meters to a rotor-stator interaction noise theory. As these data show, thewake from a rotor can be rather complex. Their representation by a simpleGaussian profile may not be adequate in many cases and this could lead to thepoor agreement between theory and experiment, discussed in the Introduction.This may also be _n example of the concerns that Cumpsty alluded to.

Rotor Wake-Far Field Noise Experiment

Narrowband spectra of the inlet quadrant sound power measured for the twostator sets are shown in figure 21 at 80 percent of fan speed. With the25-vane stator the fundamental tone amplitude was quite low because the modesdue to rotor-stator interactionwere cutoff; hence, the tone, not being de-pendent on the interaction, was weak. In contrast, the fundamental tone domi-nated the spectrum for the 11-vane stator. Here there was a propagating modefrom interation.

The variation of inlet sound power for the first three harmonics is shownas a function of rotor-stator spacing for both stators in figure 22. In gen-eral, the levels decreaseo with increased spacing. The exception was the fun-damental tone. For the 25-vane stator, as described, there were no propagtingmc_es and this tone decreased only slightly with increased spacing. For thell-vane stator, the tone decreased at first and then leveled off or increased

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slightly as spacing was increased. This behavior is likely a consequence ofthe behavior observed for the fundamental harmonic of the tip upwash velocity,which followed the same trend.

Because tip velocities are highest, it might have been expected theywould control the sound generation; however, as was discussed earlier, thebehavior of the wake velocity harmonic content with downstream distance couldnot have been anticipated from existing wake models. These data strongly re-inforce the conclusion that knowledge of the wake structure is essential forpredicting the rotor-stator interaction noise from fans. At present there isan effort underway at Lewis using these data to evaluate a theoretical model;the preliminary results are encouraging. This effort will include the diffi-cult but necessary next step of going to the far field which requires the ad-dition of a sound radiation model.

DUCT ACOUSTICS

Duct acoustics research can be conveniently s_parated into analytical andnumerical methods. In the following discussion, analytical results based onthe cutoff ratio approach will be presented, followed by a summary of a recentnumerical study. Finally several other interesting results from analyticalstudies will be presented.

Analytical - Cutoff Ratio Approach

The in-duct sound field generated by a fan stage is ordinarily defined interms of spinning modes, as was discussed in the Introduction. For a circularor annular duct, two indices representing the circumferential and radial modeorders are required. Fan broadband noise and fan tones, when generated stat-ically without inflow control, appear to consist of all the propagating modesthat the duct can sustain (ref. 21). At fan tone frequencies they may numberin the hundreds. In view of the large number of modes possible and in recog-nition of the extreme difficulty in measuring the mode content or calculatingit, the theoretical behavior of modes was examined to find some simplificationthat would make the handling of duct-related problems more tractable. In de-termining the optimum impedance (resistance and reactance) for various soundmodes propagating in a circular duct with sheared flow, Rice (refs. 23 and 31)observed that modes with widely differing mode indices required, for a givenfrequency, duct velocity and boundary layer thickness, the same optimum imped-ance (resistance and reactance), and had the same theoretical attenuation.The correlation parameter was mode cutoff ratio and was immediately used asthe basis of a suppressor design method (ref. 32). In subsequent papers, in-let and aft sound radiation and duct termination loss were also correlatedwith cutoff ratio (refs. 21 and 26). These phenomena were then incorporatcdinto the suppressor methodology to yield a prediction of far field attenuationdirectivity, the ultimate goal (refs. 27, 33, and 34). As a part of the meth-od, a modal density function based on cutoff ratio was derived which allowedthe mode distribution to be easily biased toward or away from cutoff (ref.20). In addition to describing attenuation directivity, the method alsodescribes the attenuation of the suppressor at off-design cutoff ratios andoff-design sound frequencies. Finally, to understand the physics of ductacoustics better, it was shown that cutoff ratio is related to modepropagation angle, a somewhat more basic parameter that also could have beenused as the basis of the method (refs. 24 and 25).

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Suppressor properties and cutoff ratio. - A sawling of these results' follows, starting with the correlation Of optimum resistance with cutoff ra-. tio, _howing boundary layer thickness as a parameter (t . boundary layer

thickness/duct radius) (fig. 23). The correlation equation (curves) agrees" with the exact calculatlon (data points) very we11, and ali the modes lle on a

single line for a given boundary layer thickness. The effect of bo-'|

layer thickness is small for modes near cutoff but is large for _"have high cutoff ratio. In the latter case, the mode propagation , , Csmostly axial and the wave is refracted by the boundary layer. At , ,mode propagation direction is transverse and no refractlon _ccurs.

Exact calculations of the optimum reactance arc _w) in figure 24 ks afunction of mode-cutoff ratio. Again, cutoff ratio c',I_,.es the data onto a

! single line for each value of boundary layer thickness, ,nich is very well1 described by the correlating equation. The dependence of optimum reactance on

boundary layer thickness shows trends similar to those of resistance for thek same reason.

i

Finally, figure 25 shows the maximum sound power attenuation (that at theoptimum inpedance) as a function of cutoff ratio. The calculations are for amatrix of modes with lobes I, 7, and 10, each with radial orders of I, 2, 5,and 10. With the exception of radial orders t and 2 at a lobe of I, the dataare moderately well collapsed by cutoff ratio. For moderote to high values ofcutoff ratio, the attenuation varies inversely with cutoff ratio. The highattenuations at low value of cutoff ratio occur because these modes propagatetransversely and are easier to absorb than those at high cutoff ratio, whosepropagation is more axial.

These correlations with cutoff ratio clearly reveal the utility of cutoffratio in suppressor design. In the next section, its utility in sound ratia-tion will be discussed.

Radiation and cutoff ratio. - Rice has also derived very useful approximationsbased on cutoff ratio for the directivity of single modes and multimodal dis-tributions with equal power per mode. Both inlet and exhaust duct radiationhave been treated, including the effect of the shear layer for exhaust radia-tion. Since most of the energy ,n a single mode is carried by the principallobe, it becomes important to predict the directivity angle where it peaks.

Figure 26 shows the angle of p(-incipallobe peak as a function of cutoffratio for the case of no external flow (static testing). The effect of ductMach number is also shown. Increasing the duct Mach number causes both theInlet-and exhaust-radiated sound to radiate to more forward angles. In fact,aft sound modes approaching cutoff are radiated well into the i;_letquadrant.At go', the overhead position during flyover, the aft radiated sound occurs inmodes well above cutoff. Based on the earlier discussion of maximum attenua-tion this noise would be difficult to suppress. In contrast, the inlet noiseat gO" is due to modes very near or at cutoff, these being very easy to sup-press.

The approximate exhaust radiation model based on cutoff ratio can be

checked by co_)arison with exact solutions obtained by the Wiener-Hopf meth-od. Figure 27 compares the approximate and exact methods for a single mode.The agreement between t);_two methods is very good. Mode-lobe patterns arereproduced as is the angle marking the zone of silence. In the exact solu-

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tion, some sound reaches angles within this zor_ebut the approximate methoddoes not permit sound to enter the region because of its geometric acousticcharacteristics. The approximate method thus appears to contain all the es-sential features of aft duct sound radiation, including the effects of ductMach number and the external jet shear layer.

In the inlet there is no shear layer to contend with but the effect ofduct Mach number predicted by the approximate method is of some concern. Thereis no exact solution for inlet-radiatedsound for the static test case, withno external flow but a duct Mach number. The Wiener-Hopf method only givesresults f_r two cases: uniform flow everywhere and no flow. An attempt wasmade to validate the inlet radiation, using data for the rod-generated tonefrom Lhe JT15D engine that was described earlier (ref. 35). This comparisonis shown in figure 28. In this figure, the lobe due to the rod wake-fan inter-action is compared with the approximate method result and the Wiener-Hopf solu-tion for flow everywhere. The data show the expected forward translation ofthe mode as engine speed was increased. This is due to the increase in modecutoff ratio and is shown by both models. At the two lower speeds, the approx-imate model, duct flow alone, appears to match the data better; however, atthe two higher speeds, the exact solution based on uniform flow everywhereseems to provide the better match. The results, therefore, are not whollyconclusive and additional ,:orkwill be needed to resolve this issue. The numer-ical method of the following section while it cannot handle these nigher auctMach numbers at present, will ultimately be capable of solving this problem

Directivity models for broadband sound and for other multimodal casessuch as for tones, due to inflow distortion or turbulence, are of some impor-tance. A case that has received some attention, because it appears to fitthese two situation, is a multimodal model with 'allthe possible propagatir_gmodes present with equal sound powers. The model, described in reference 21

for inl_ts, is based on cutoff ratio. The model yields a very simple expres-sion, pc = 2 cos T, where pc is the mean square sound pressure and vis the far-field directivity angle. This equation is compared in figure 29with the exact result obtained by summing the levels of all the propagatingmodes. In this case there were over 1000 modes. The agregment is excellent.

A similar comparison is made ic_figure 30 for exhaust radiated noise, asdeveloped in reference 26. The model yields the expression

P2 - 2(i- MD2) [MD + (I- MD2)COS, ]

where MD is the duct Mach nun_)erand the other synW)olsare as previous1)defined. Th_s equation is compared, in figure 30, with the exact result ob-tained by sunning over all the propagating modes calculated by the Wiener-Hopfmethod. For the condltions shown, there were 101 propagating modes. Theagreement between the approximate and exact multtmodal models is very good,except at the forward-or inlet-quadrantangles where the directivity by theapproximate method falls off more rapidly than it does by the exact method.The approximate method describes the angle for the zone of silence correctlybut, again, does not permit any sound within this zone.

Once again these results illustrate the utility of Cutoff ratio as a toolfor describing sound propagation and radiation, and for understanding thephenomena that occur.

11

1983005668-011

Numerical Methods

The potential for handling variable area inlet or exhaust ducts withtheir complex flow gradients provides motivation for solving duct acousticspropagation problems numerically. Soft-walls as well as radiation to thefar-field can be handled. As a special case, the sonic or aear-sonic inletwas of interest. Numerical analysts have explored finite difference and fi-nite element methods and steady Jtate and transient formulations of the prob-lem. Most of the phenomena of interest are described by linear theory. Theimportant exception is the near-sonic or sonic inlet where nonlinear theory ;sapparently required.

The experimental data from the JT15D engine with rods (already mentionedseveral times) have been compared with results of nunw.ricalcalculations inreference 36. In the experiment, the far-fie!d directivities of the rod-generated fan tone were measured with a hard-walled inlet and an acousticall)treated inlet. The acoustic liner was designed for the particular mode(13,0), using the cutoff ratio procedure mentioned earlier. The numericalmethod coupled a finite element solution in the duct, capable of handlingacoustically treated walls as well as hard walls, with an integral solution Inthe far field.

: Figure 31 shows the inlet with the acoustic treatment and the tone-

generating rods. Of interest is the very large radius of the inlet lip em-ployed in these static tests. Figure 32 con_oaresthe experimental and theo-retical results. The numerical method agrees with the data very well. Thefigure also shows a calculated directivity curve according to the Wiener-Hop_method discussed earlier. The agreement between this calculation and the datais very good from the peak angle forward. Aft of the peak the Wiener-Hopfmethod greatly overpredicts t_e data. This result is probably due to the in-ability of the Wiener-Hopf method to account for the very thick-lipped inlet,since this method can only handle a very thin-inlet lip. The results point toa considerable acoustic shielding of the aft angles by the inlet lip. Theinlet Mach nunW)erin the experiment was too low to have had a significanteffect.

Figure 33 shows the measured a,ldpredicted attenuations as a function ofliner resistance. It can be seen that the numerical method agrees very wellwith the data. At this engine speed, the rod wakes generate a single propa-gating mode that was input into the calculations. Since the sound field doesconsi_ of a single mode, the attenution di-ectivity should not be a functionof ahgle. The data, shown for four angles, confirm this conclusion within ascatter of about +I dB.

The potential and versatility of the numerical methods are clearly demon-strated by these comparisons. The chief limitationof the method, at present,is the lack of storage capacity in the conq)uterto handle propagating modes(well above cutoff) with short axial wavelengths. The convective effect ofincreasing inlet Mach nunW_erserves to shorten _avelength further andaccentuate the limitation. These facts limit the method to lower sound fre-quencies and duct Mach nuni)ers.

1983005668-012

I

l

Other Analytical Development

There _re other re_ults that will only be briefly discussed, In the areaof duct propagation, Cho (refs. 37 and 38) showed that there Is no mode-scattering in traveling through a variable area duct, if the flow gradients

: are not too large (as is probably true for most practical cases), Cho (ref.)g) also developed a th-ory describing the refraction of a sound ray by the

. flow near the inlet lip, which llemodeled _s a vortex,

In suppressors,a theory for extendeu reaction {bulk absorber) liners i$ "being developed that will permit the propor design ot extended reaction liners(ref, 40), Already the theory explains the increased bandwidth absorption by

, these liners, The grazing flow impedance of Helmboltz resonators (perforatedplate over honeycomb) has also been successfullym_ _led (ref. 41),

CONCLUDIN& REMARKS

The results presented in this paper, largely from activities at the LewisResearch Center, have been selected to illustratethe _ignlficantprogress inall aspects of fan noise. Whereas earlier work without inflow control did notdisplay much sensitivity to fan design for the large rotor-stator spacingsemployed in high bypass engine fan sta_es, later research with inflow control,by flow straightenersor actual forward velocity, has revealed a great deal otsensitivity to design. Many of the theoretical results predicted such as mode

• cutoff radiation patterns, and suppressor performance are observed both qual-itativelyand quantitativelywith inflow control.

Fan noise generation ,_dels, now predicting ,_de amplitudes and phases,are currently being moditled to include duct propagation and radiation so thatfar-fleld dlrectivity patterns can be predicted. Suppressor performance is

: also being predicted in term_ ot far-field dlrectivity patterns. The numerl-cal approach to propagation and radiation, if it can be extended to higherfrequency and duct M_ch nu,_er, will contribute notably to these capabilities.

It Is the author°s opinio, that, although the problems are not fullysolved, there has been considerable _dvancement in all aspects of fan noise.

REFERENCES

, I. Cumpsty, N. A.: A Critical Review of [urb_nachineryNoise. J. FluidsEng., Vol. g_, no. 2, June Igll, pp. _1B-293.

2. Feller, C. E.; and Groeneweg, J. F.: _u_nary ot Forward Velocity Effectson Fan Noise. AIAA paper I/-1319, l_t. Igll. (NASA TM-1312_.)

: 3. Lowrie, B. W.; and Newby, D. R.: TileDesign and Calibration of a• Distortlon-Reducln9_creen for Fan Noise Testing. AIAA paper ll-I)Z3,

Oct. 191l.

4. Cocking, B. L.; and Ginder. R. B.: lhe Effect of an Inlet FlowCo,ditloner on Fan Distortion Iones. AIAA paper II-t3_4, Uct. tglI.

5. Blankenshlp, G. t.: Effect ot Forward Motio, on lurbomachlnery Noise.AIAA paper 11-1346. lkt. Igll.

lJ

1983005668-013

6_ JonesW. L.; McArdle,J. G•; and Homyak,L.: Evaluationof Two InflowControlDevicesfor FlightSimulationof Fan Noise Using a JTISD Engine.AIM paper79-0654,Mar. Iglg. (NASATt6-79072.)

7. Ho, P. Y.; and Smith,E. B.: An InflowTurbulenceReductionStructurefor ScaleModel Fan Testing. AIM paper79-0655,Mar. 1979.

8. Kantola,R. A.; and Warren,R. E.: Reductionof Rotor-TurbulenceInteractionNoise in StaticFan Noise Testing. AIM paper 79-0656,Mar 1979.

g. Ginder,R. B.; Kenison,R• C.; and Smith,A. D.: Considerationsfor theDesignof InletFlowConditionersfor StaticFan Noise Testing. AIMpaper 79-0657,Mar. 1979.

10. Rogers,D• F•; and Ganz,U.W.: AerodynamicAssessmentof Methodsto +:SimulateFlightInflowCharacteristicsduringStaticEngineTesting.AIAA paper 80-I023,Mar. 1980.

II• Atvars,Y•; and Rogers,D. F.: The Develol_nentof InflowControlDevices "for ImprovedSimulationof FlightNoiseLevelsduringStaticTestingof aHBPRTurbofanEngine. AIAA paper 80-1024,June1980.

12. McArdle,j. G.; etal.: Comparisonof SeveralInflowControlDevicesforFlightSimulationof Fan Tone Noise usinga JTISD-IEngine• AIAA paper80-1025,june,1980. (NASATM-81505.)

13. Perracchio,A. A.: Assessn_ntof In-FlowControlStructureEffectivenessand DesignSystemDevelopment.AIAA paper81-2048,Oct. 1981.

14. McArdle,J. G.; Homyak,L.; and Chrulski,D. D.: TurbomachineryNoiseStudiesof the AIResearchQCGAT Enginewith InflowControl. AIM paper81-2049,Oct. 1981.

15. Chestnutt,D., ed•: Simulationof Fan Noise in Flightand FlightEffects. NASA CP 2242, Sept.,1982.

16. Kobayashi,H.; and Groeneweg,J. F.: Effectsof InflowDistortionProfileson Fan ToneNoise AIAA J , Vol. 18, no. 8, Aug., 1980,p. 899-906.

17. Kobayahsi,H.: Three-DimensionalEffectson Pure ToneFan Noise Due toInflowDistortion•AIAA paper 78-1120,July 1978. (NASATM-78885.)

" 18. Shaw,L. M.; and Balr_nbin,J. R.: RotorWake CharacteristicsRelevanttoRotor-StatorInteractionNoise Generation.AIAA paper81-2031,Oct. 1981. (NASATM-82703.)

19. Woodward,R. P.; and Glaser,F. W.: Effectsof Blade-VaneRatioandRotor-StatorSpacingon Fan Noise with ForwardVelocity. AIAA paper81-2032,Oct. 1981. (NASATM-82690.)

14

i

1983005668-014

20. Rice, E. J.: Modal Density Function and Number of Propagating Modes inDucts. Presented at the 92nd Accoustical Society of A_rica Meeting,(San Diego, CA), Nov. 16-19, 1976. (NASA TM-73539.)

21. Rice, E. J.: Multimodal Far-Field Acoustic Radiation Pattern Using ModeCutoff Ratio. AIAA J., Vol. 16, no. 9, Sept. 1978, pp. 906-911. (NASATM-73721.)

22. Tyler, J. M.; and Sofrin, T. G.: Axial Flow Compressor Noise Studies.SAE Trans., Vol. 70, 1962, pp. 309-332.

23. Rice, E. J.: Optimum Wall Impedance for Spinning Modes-A CorrelationWith Cutoff Ratio. AIAA paper 78-193, Jan. 1978. (NASA TM-73862).

24. Rice, E. J.; Heidmann, M. F.; and Sofrin, T. G.: Modal PropagationAngles in a Cylindrical Duct with Flow and their Relation to SoundRadiation. AIAA paper 79-0183, Jan. 1979. (NASA TM-79030.)

25. Rice, E. J.: Modal Propagation Angles in Ducts with Soft Walls and theirConnection with Suppressor Performance. AIAA paper 79-0624, Mar. 1979.(NASA TM-79081.)

26. Rice, E. J.; and Saule, A. V.: Farfie|d Radiation of Aft Turbofan

Noise. Presented at the 99th Meeting of the Acoustical Society ofAmerica, (Atlanta, GA.), Apr. 21-25, 1980. (NASA TM-81506.)

27. Rice, E. J.; and Sawdy, D. J.: A Theoretical Approach to SoundPropagation and Radiation for Ducts with Suppressors. Presented at the101st Meeting of the American Acoustical Society, (Ottawa, Ontario), May18-22, 1981. (NASA TM-82612.)

28. Baumeister, K. J.: Numerical Techniques in Linear Duct Acoustics - A

Status Report. J. Eng. Ind., Vol. 103, Aug. 1981, pp. 271-281.

29. Baumeister, K. J.: Numerical Techniques in Linear Duct Acoustics -1980-81 Update. Presented at the ASME 102nd Winter Annual Meeting,(Washington, D.C.). Nov. 15-20, 1981. (NASA TM 82730.)

30. Loehrke, R. I.; and Nagib, H. M.: Control of Free Stream Turbulence byMeans of Honeycombs: A Balance Between Suppression and Generation.Fluids Eng., Vol. 98, no. 3, Sept., 1976, pp. 34_-353.

31. Rice, E. J.: Acoustic Liner Optimum Impedance for Spinning Modes withMode Cutoff Ratio as the Design Criterion. AIAA paper 76-516, July 1976,(NASA TM X-73411.)

32. Rice, E. J.: Inlet Noise Suppressor Design BW_thodBased Upon theDistribution of Acoustic Power with Mode Cutoff Ratio. Advances inEngineering Science. NASA CP-2001, Nov. 1976, pp. 883-894.

33. Rice: E. J.; and Heidelberg, L. J.; Comparison of Inlet Suppressor Datawith Approximate Theory Based on Cutoff Ratio. J. Aircraft, vol. 18, no.10, Oct. 1981, pp. 810-817.

15

1983005668-015

34. Heidelberg, L. J.; Rice, E. J.; and Homyak, L.: Experimental Evaluationof a Spinning-Mode Acoustic-Treatment Design Concept for AircraftInlets. NASA TP-1613, 1980.

35. Heidmann, M. F.; Saule, A. V.; and McArdle, J. G.: Analysis of RadiationPatterns of Interaction Tones Generated by Inlet Rods in the JT15DEngine. AIAA Paper 79-0581, Mar. 1979, (NASA TM-79074.)

36. Baumeister, K. J.; and Horowitz, S. J.: Finite Element-lntegralSimulation of Static and Flight Fan Noise Radiation from the JT15DTurbofan Engine. NASA TM-82936, Aug. 1982.

37. Cho, Y. C.; and Ingard, K. U.: Closed Form Solution of Mode Propagationin a Nonuniform Circular Duct. AIM J., Vo1. 20, No. 1, Jan. 1982,pp. 39-44.

38. Cho, Y. C.; end Ingard, K. U.: Mode Propagation in Nonuniform CircularDucts with Potential Flow. AIAA Paper 82-0122, Jan. 1982. (NASATM-82776.)

39. Cho, Y. C.; and Rice, E. J.: High-Frequency Sound Propagtion in a

Spatially Varying Mean Flow. Paper presented at the lOOth Meetin9 of theAcoustical Society of American, (Los Angeles, CA.), Nov., 1980. (NASATM 81751).

40. Hersh, A. S.; Walker, B.; and Dong, S. B.: Analytical and ExperimentalInvestigation of the Propagation and Attenuation of Sound in ExtendedReaction Liners. AIAA Paper 81-2014, Oct. 1981.

41. Hersh, A. S.; and Walker, B.: Fluid Mechanics Model of the HelmholtzResonator. NASA CR-2904, Sept. 1977.

16

1983005668-016

ORIGINALPAGE iSOF POOR QUALITY

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1983005668-017

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1983005668-018

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1983005668-019

ORIGINALPAGE 13OF POOR QUALITY

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1983005668-020

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1983005668-022

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1983005668-023

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1983005668-024

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1983005668-025

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1983005668-026

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1983005668-028

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1983005668-029

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1983005668-030

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1983005668-032

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1983005668-033

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