aircraft noise reduction technologies a bibliographic review

Aerospace Science and Technology 12 (2008) 1–17

www.elsevier.com/locate/aescte

Aircraft noise reduction technologies: A bibliographic review

D. Casalino a,∗,1, F. Diozzi b,2, R. Sannino b,3, A. Paonessa c

a Rotorcraft Aerodynamics and Aeroacoustic Department, Italian Aerospace Research Center, via Maiorise, Capua, I-81043, Italyb Documentation Center, Italian Aerospace Research Center, via Maiorise, Capua, I-81043, Italy

c Acoustics Department, Alenia Aeronautica, viale dell’Aeronautica, Pomigliano d’Arco, I-80038, Italy

Available online 22 October 2007

Abstract

A bibliographical review of the main technologies employed for the mitigation of aircraft noise is presented. According to a component-based approach, analytical and semi-empirical models of the aeroacoustic mechanisms involved in the noise generation from airframe and enginecomponents are presented as a key element of the noise reduction technology. These models, developed in the past to investigate the influence ofsome design parameters on the overall acoustic levels, are nowadays powerful design tools when employed in a multi-disciplinary optimizationframework. In this spirit, the recent achievements in the numerical prediction of complex aeroacoustic phenomena through CFD/CAA techniques,not addressed in this work, provide a complementary approach to experiments to improve the accuracy of the available analytical and semi-empirical models. The bibliographical style of the paper is guaranteed by a qualitative description of the underlying physical mechanisms andtheir mathematical idealization. The reader is therefore remanded to the cited works for a deeper analysis.© 2007 Elsevier Masson SAS. All rights reserved.

Keywords: Aircraft noise; Airframe noise; Fan noise; Jet noise

1. Motivations

Aircraft and aero-engine manufacturers are exposed to acontinuously growing demand for quieter aircraft. This is dueon one hand to the increased community expectation for qual-ity of life, and on the other hand to the necessity to compensateboth the growth in air traffic and the encroachment of airport-neighboring communities.

Since the theoretical work by Sir James Lighthill in 1952[99] on sound generated aerodynamically that led to the firstpredictive model of jet noise, many progresses have been madein the physical understanding of several aeroacoustic mecha-nisms and their mathematical representation. Recent achieve-ments in the numerical modeling of complex phenomena, like

* Corresponding author.E-mail addresses: [email protected] (D. Casalino), [email protected]

(F. Diozzi), [email protected] (R. Sannino), [email protected](A. Paonessa).

1 Senior research engineer.2 Head.3 Information specialist.4 Head.

1270-9638/$ – see front matter © 2007 Elsevier Masson SAS. All rights reserved.doi:10.1016/j.ast.2007.10.004

the screech tone generation in supersonic jets [13,156], con-tribute to extend the knowledge domain beyond the empiricalevidence of these phenomena.

The growth in the theoretical description of many aeroa-coustic mechanisms in the past fifty years has been accom-panied by a progressive reduction of aircraft noise. Since theSixties the historical aircraft noise trend shows a reduction ofabout 20 EPNdB, mostly due to the progressive introductioninto service of high-bypass turbofans and more effective nacelleacoustic treatments. Since the Eighties, however, the noise re-duction trend has not been so significant. Therefore, any furthernoise reduction is very difficult to be achieved without affectingthe aircraft operating cost.

Due to the progresses achieved in reducing the propulsivenoise and due to the expected reduction with the entry into ser-vice of ultra high-bypass ratio turbofans and novel noise controldevices, on modern civil aircraft the engine noise is expected tobe comparable and even lower than the airframe noise gener-ated by the high-lift devices and by the undercarriage.

From these considerations it is clear that aircraft man-ufacturers have to comply with a new emerging necessity:the environmental concern, in terms of acoustic and chemicalpollution, must be considered as a driving factor in the de-

2 D. Casalino et al. / Aerospace Science and Technology 12 (2008) 1–17

sign and operation of any new commercial aircraft. In otherwords, the preliminary design of an aircraft is the result ofre-defined tradeoffs between operating costs and environmen-tal performances, in a multi-disciplinary framework involvingaircraft operational factors, aircraft/engine performances, air-frame/powerplant noise modeling, powerplant emission model-ing, and operational costs.

Since multi-disciplinary/multi-objective optimization pro-cesses relies on fast numerical methods, a great deal of interesthave been devoted during the last years to the re-discovery andimprovement of analytical models for both airframe and pow-erplant noise prediction. The works recently published by An-toine and Kroo [8,9] and by Lilley [100,104] provide elegantexamples of how the noise requirement can drive the aircraftdesign and its operation.

The main goal of the present paper is to provide a literaryreview on the subject of airframe, fan and jet noise theory. Em-phasis is placed on fully analytical or semi-empirical modelsthat are commonly used by the major aerospace research estab-lishments. For each noise generation mechanism, an overviewof the main noise mitigation techniques is also provided. Thisreview constitutes a knowledge basis for the development of alibrary of methods for aircraft noise prediction to be exploitedin the joined AleniaAeronautica/CIRA research programmes.

2. Airframe noise

The aerodynamic noise generated by all the non-propulsivecomponents of an aircraft is classified as airframe noise. Formodern high-bypass engine powered commercial aircraft, theairframe noise represents the main contribution to the over-all flyover noise levels during landing approach phases, whenthe high-lift devices and the landing-gear are deployed. Fivemain mechanisms are recognized to contribute significantlyto the airframe noise: (i) the wing trailing-edge scattering ofboundary-layer turbulent kinetic energy into acoustic energy,(ii) the vortex shedding from slat/main-body trailing-edges andthe possible gap tone excitation through nonlinear coupling inthe slat/flap coves, (iii) the flow unsteadiness in the recircula-tion bubble behind the slat leading-edge, (iv) the roll-up vortexat the flap side edge, (v) the landing-gear multi-scale vortexdynamics and the consequent multi-frequency unsteady forceapplied to the gear components. All these mechanisms havebeen addressed both experimentally and theoretically since theSeventies. The most complete review on the topic is due toCrighton [31], who contributed considerably to the mathemat-ical modeling of several aeroacoustic mechanisms. Nowadaystheoretical knowledge of the flow phenomena involved in theairframe noise generation, together with the achieved readinesslevel of several numerical methods in the CFD/CAA domain(not addressed in this paper), are favorable conditions for asignificant technological advancement in the field of airframenoise control and reduction. As a consequence, a great effortis currently undertaken by the main aircraft manufacturers fordeveloping novel high-lift devices and optimized landing-gearassemblies.

2.1. Analytical models

2.1.1. Trailing-edge noiseIn clean configuration, the main source of airframe noise is

represented by the wing trailing-edge noise. A solid surfaceimmersed in a turbulent flow has a dual influence on the ra-diated acoustic field. On one hand, it affects the structure of theflow field and, consequently, of the aeroacoustic sources. Onthe other hand, it constitutes an acoustic impedance discontinu-ity which affects the scattering of the acoustic waves. The noisefrom a trailing-edge is a singular problem for which a wrongseparation of these two effects can lead to wrong theoretical re-sults.

A trailing-edge in a fluctuating flow field generates an un-steady vortical wake. This phenomenon can be regarded asan unsteady boundary-layer separation due to the fluid viscos-ity. An inviscid model of the vortex shedding process consistsin prescribing an edge condition. Since the vortex sheddingsmears the singular behavior of the flow at the trailing-edge,a Kutta condition is commonly imposed at the trailing-edge,which requires that the flow velocity is finite at the edge. Thephysical relation between the smoothing effect due to the vor-tical wake and the Kutta condition is not completely clear.The experimental works of Archibald [10] and Satyanarayanaand Davis [152], for example, show that the Kutta conditionis only partially fulfilled at the trailing-edge of an airfoil in ahigh-frequency perturbed field. A viscous flow, in fact, has acharacteristic relaxation time over which the flow reacts to animposed disturbance. If this relaxation time is greater than thecharacteristic period of the perturbation field, the flow wouldnot have enough time to fully satisfy the Kutta condition. Fromthese preliminary considerations it follows that the aeroacousticsources are significantly affected by the hypothesis made on thebehavior of the flow at a trailing-edge. This is a first difficulty inmodeling the trailing-edge noise. Another difficulty lies on thefact that an edge does not distinguish between an acoustic anda vortical disturbance. As a result, the unsteady pressure fieldinduced by the wake itself can couple with the vortex sheddingprocess causing an increase of the noise levels. A further dif-ficulty is related to the refraction effect of a boundary shearflow. This imposes some restrictions on the applicability of anacoustic analogy model that requires a clear separation betweenthe vortical aeroacoustic sources and the diffracting effects dueto the edge. Depending on the strategy used to face these dif-ficulties, different theoretical results have been obtained in thepast.

Crighton [28], following the work of Orszag and Crow [128],investigated the interaction between an acoustic incident field,an unstable shear layer and a flat-plate trailing-edge. He showedthat, at low Mach numbers, a Kutta condition induces a changein the flow velocity dependence of the acoustic intensityfrom U4∞ to U2∞, provided that the vortex-sheet is unstable.Jones [89] investigated the diffraction of the acoustic field gen-erated by a source near the edge of a semi-infinite flat-plate.He concluded that the Kutta condition generates an intensebeaming effect along the plane of the plate. Crighton and Lep-pington [34] did not obtained significant effects on the acoustic

D. Casalino et al. / Aerospace Science and Technology 12 (2008) 1–17 3

radiation due to the Kutta condition. Davis [35] investigatedthe effect of the Kutta condition on the flat-plate problem andconcluded that, without a Kutta condition, the far-field noise ex-hibits a sin2(θ/2) directivity pattern and a U3∞ acoustic powerlaw. Conversely, with a Kutta condition, a beaming effect alongthe wake takes place and the noise intensity level increases asU∞. Howe [83], in his comprehensive review work, pointedout that both Crighton’s [28] and Davis’ [35] analysis were er-roneous since not compatible with a far-field wave radiationcondition. Howe [82] demonstrated that the imposition of theKutta condition removes the flow singularity at a sharp edge.As a consequence, it always leads to a reduction of the noiselevels. The wake intensity, in fact, is related, both in amplitudeand phase, to the incident vortical disturbances and generatesa sound field which cancels the one generated by the incidentturbulent field.

A different view of the trailing-edge problem consists infocusing separately on the acoustic scattering properties ofthe edge, and the fluctuating pressure field close to the edge.Ffowcs Williams and Hall [48] and Crighton and Lepping-ton [32,33] examined the scattering problem in the context ofLighthill’s acoustic analogy theory. They related the acousticfar field to the turbulent quadrupole sources. Chase [21,22] andChandiramani [20] proposed a procedure to relate the far-fieldacoustic spectrum to measurable statistical properties of the hy-drodynamic pressure field in proximity of the edge. These prop-erties are formally synthesized by the wavenumber/frequencyspectrum of the driving pressure field. Rienstra [142] examinedthe half-plane scattering problem of an acoustic incident field inthe presence of a vortex-sheet shed from the trailing-edge. Heshowed that the vortex shedding process extracts energy fromboth the incident acoustic field and the mean flow, thus reducingthe far-field noise intensity. However, the interaction betweenthe trailing-edge and the unsteady pressure field induced by thewake generates a noise radiation whose energy may exceed thatabsorbed by the wake.

Crighton [29], using the method of matched asymptotic ex-pansions, determined the noise radiated by a line-vortex con-vected past the edge of a semi-infinite flat-plate under the in-fluence of its image vortex. The intensity of the acoustic fielddriven by the vortex-induced hydrodynamic field was demon-strated to have a sin2(θ/2) directivity pattern and a third powerdependence on the flow velocity. The latter result was in agree-ment with the general result obtained by Ffowcs Williams andHall [48] and Crighton and Leppington [32] according to whichthe effect of the interaction between a fluctuating turbulent flowand the edge of a semi-infinite plate is to increase the far-fieldacoustic intensity by a factor M−3∞ . In fact, as demonstrated byObermeier [127], the acoustic energy radiated by a vortex fila-ment in free space or in the presence of an infinite rigid platefollows a sixth power law.

Amiet [3,6] related the acoustic spectrum to the wall pres-sure spectrum through an airfoil response function. In order touse a wall pressure distribution with the same characteristicsit would have in the absence of the trailing-edge, he assumedthat the turbulence was statistically stationary when convectedpast the trailing-edge. A concentrated dipole sources induced

by the turbulent flow near the trailing-edge was used to modelthe noise radiation. The airfoil response function used by Amietwas obtained under the assumption that, at high frequency, asrelevant for a trailing-edge noise problem, the leading- andtrailing-edge noise scattering can be taken into account sepa-rately in an iterative converging procedure [5]. This approachhad been already applied by Landahl [97] to an infinite-spanairfoil embedded in a parallel gust of arbitrary wavelength,and later on by Adamczyk [1] to an infinite-span swept winginteracting with an oblique gust. Amiet [5] extended Adam-czyk’s analysis in order to account for a difference betweenthe free-stream velocity and the convection velocity of the gust.In recent years trailing-edge broadband noise models of Amiettype, involving iterative leading- trailing-edge corrections, havebeen developed and validated against experimental data in prac-tical cases representative of airframes, wing turbines, helicopterblades and fan cooling systems by Roger and Moreau [117,118,147,148].

Howe [82] investigated the general problem of the noisefrom an airfoil interacting with a frozenly convected turbulenteddy. By supposing a small flow Mach number (M2∞ � 1), heassumed an incompressible potential flow. The acoustic prob-lem was then formulated in terms of Howe’s [81] acousticanalogy theory describing the noise generated by vorticity andentropy gradients. In the limit of a frozen convection hypoth-esis Howe showed that, when a line-vortex is convected pastthe edge of a half-plane, a Kutta condition results in a vor-tex shedding that exactly cancels the sound generated by thevortex-edge interaction. Furthermore, in the case of an acousti-cally compact airfoil, the effect of the vortex shedding is tocancel the field diffracted by the trailing-edge. Since the ful-fillment level of the Kutta condition decreases as the frequencyof the perturbation flow increases, the effectiveness of the vor-tical wake in reducing the radiated noise decreases at higherfrequency. As a consequence, a trailing-edge in a turbulent flowacts as a source of high-frequency noise.

Howe [83] revisited the problem of the trailing-edge noiseand formulated a generalized theory. This includes, as spe-cial cases, the models developed by Ffowcs Williams andHall [48], Crighton [29], Chase [21,22] and Chandiramani [20].All these models were shown to give essentially the same re-sults when properly interpreted. In particular, the so-called car-dioid sin2(θ/2) directivity law and the fifth power scaling lawof the acoustic intensity on the free-stream velocity were recov-ered. Moreover, Howe investigated the influence of the Kuttacondition on the noise levels by assuming a wake convectionvelocity w which differs from the convection velocity v of thevortical disturbances within the boundary-layer. He found thatthe effect of the Kutta condition is to reduce the sound pressurelevel by a factor (1 − w/v)−2, which diverges when the Kuttacondition is fully satisfied (w = v).

A first experimental validation of the trailing-edge noise the-ory by Howe was carried-out by Brooks and Hodgson [16] whomeasured the noise generated by a NACA-0012 airfoil in a lowMach number flow at several angles of attack and with dif-ferent degrees of edge bluntness. The airfoil was provided ofroughness trips on both its sides in order to ensure a well de-


veloped turbulent boundary-layer. In order to investigate thevortex shedding process in terms of wake convection velocityw, as proposed by Howe [83], Brooks and Hodgson carried-outcoherence measurements between a cross hot wire just down-stream of the edge and a wall pressure transducer close to theedge. No vortex shedding was detected. From this result and theverified consistency of the evanescent wave model proposed byChase [22] in the edge region, they concluded that a vanish-ing wake velocity can be used in the trailing-edge noise model.In addition a good agreement with the theoretical U5∞ acousticpower law and the sin2(θ/2) directivity pattern was found.

2.1.2. Flap side-edge noiseOne of the most effective sources of airframe noise at take-

off and landing conditions is due to the vortical flow aroundthe side edge of a deployed flap. The physical mechanism offlap side-edge noise generation can be described as follows.The pressure jump across the upper and lower surfaces of theflap creates a recirculating flow around the side edge. The shearlayer detaches at the side edge of the flap and rolls up to a singlevortical structure. This is responsible for two noise generationmechanisms: the first is due to a direct interaction between theshear layer fluctuations and the sharp edge, the second is due tothe induction of unstable oscillation modes in the vortical struc-ture. In addition, vortex breakdown has been observed at highflap angles as an additional noise source mechanism.

The problem of sound generation by the vortex roll-upabout a deflected side-edge has been investigated analyticallyby Hardin [73] and by Howe [84]. The model put forward byHardin is based on the analogy according to which, the tran-sient streamwise vortex roll-up can be seen, in a plane normalto the edge and the flow direction, as a two-dimensional vor-tex that is swept around the edge of half-plane under the effectof self induction. The model presents strong analogies withthe trailing-edge noise model proposed by Crighton [29] andtherefore suggested the same U5∞ acoustic power law and thesame sin2(θ/2) directivity pattern. A drawback of this analyti-cal model is that, not only the hydrodynamic field, but also thedriven acoustic field is assumed to be two-dimensional.

A different model was proposed by Howe [84]. By usingan acoustic analogy approach, he separated the sound gener-ation mechanisms from the acoustic edge scattering problem.Thus he represented all the involved vortex dynamic processesin terms of a prescribed statistical surface pressure distribution,and focused on the Green’s function of a simplified geometricalconfiguration. In particular, he obtained analytical expressionfor a finite chordwise slot in a wing with an otherwise straighttrailing-edge, both in the low- and high-frequency limit. Themost important result obtained by Howe is that the radiation ef-ficiency of the side-edge sources is greater for low values of thedimensionless frequency referred to the slot clearance and thespanwise flow velocity. This is because, at low frequency thesound generation mechanism is well represented by a dipole-type source, whereas at high frequency the sound generationmechanism is dominated by a monopole-type source that re-produces the mass flux through the slot.

A flap side-edge noise model derived on the basis of theaforementioned analyses have been recently validated againstexperimental data by Molin et al. [115].

2.1.3. Slat/flap cove and trailing-edge noiseWhile the dominant sound generated by a slat wing compo-

nent is of broadband nature and due to the flow recirculatingbubble behind the leading-edge and to turbulence convectedpast the trailing-edge through the gap, there exists a certain ex-perimental evidence of tonal noise radiation. This is commonlyattributed to the vortex shedding from the blunt trailing-edge. Incertain cases, however, a surprisingly high tone have been ob-served, that disappears when the slat deflection angle is slightlymodified. This behavior was attributed by Khorramiet al. [92]to a feedback loop between the slat trailing-edge and the mainwing surface which drives the vortex shedding frequency. A nu-merical demonstration of the gap whistle generation has beenpursued by Tam and Pastouchenko [167]. The predicted tonefrequencies was shown to agree fairly well with a simple alge-braic model of feed-back loop based on the principle of cause-effect phase compatibility.

2.1.4. Landing-gear noiseThe sound generation mechanism from a landing-gear is due

to the vortex-force generated by the quasi-periodic unsteadyflow separation behind the different structural components. Themechanism is similar to the so-called Aeolian tones genera-tion from circular cylinders [18,133], but complicated by thesimultaneous shedding from bodies of different size and shape,and by the mutual vortex interactions. The resulting noise is ofbroadband nature, spanning over a wide interval in the audibil-ity range. The dipolar character of the source mechanism resultsin U6∞ acoustic power scaling law. However, due to acoustic in-stallation effects, a destructive interference of sound generatedby dipoles in the vertical plane, i.e. generated by vorticity vec-tor components parallel to the reflecting airframe panels, mayoccur, thus resulting in a quadrupole source degeneration anda corresponding U8∞ acoustic power scaling law. Several semi-empirical models have been developed by aircraft manufacturesboth in the US and Europe. The Airbus model, for instance, hasbeen recently applied to evaluate the impact of a low noise gearon the overall airframe noise [114].

A further installation aspect that should be addressed inlanding-gear noise modeling is the excitation of some cavitymode in the wheel wells. Three different mechanisms of tonalnoise response of a cavity flow exist. The first one is due to afeedback cycle generated by the coupling between the wavesgenerated when the shear layer vortical fluctuations impingeon the downstream edge, and the vortex shedding from theupstream edge [23,75,76,85,86,149,165]. The second mecha-nism involves a volume mode fluctuation of the recirculatingbubble induced by a coupling with a standing wave across thewidth or along the length of the cavity. The third mechanism isa Helmholtz resonation occurring when the flux mass acrossthe cavity neck balance the fluid volume stiffness. A com-plete review of self-sustaining mechanisms in cavity flows isdue to Rockwell and Naudascher [146]. Fortunately, realistic


cavities, in the presence of uncontrolled grazing flow regimes,seem to respond only in their depth mode [14,40]. The resultingacoustic field can be easily modeled by extrapolating the inter-nal cavity pressure levels at the depth mode frequency to the farfield with a monopole directivity pattern.

2.1.5. Component-based empirical and semi-empirical modelsThe airframe noise source breakdown presented in this sec-

tion constitutes the basis for a component-based comprehensiveaircraft noise modeling. The typical approach consists in de-scribing the acoustic far-field spectrum as resulting from theuncorrelated superposition of different effects, each related tomacroscopic flow quantities via ad-hoc scaling laws. Severalparameters appear in this kind of comprehensive representationthat must be determined through dedicated experimental cam-paigns or numerical simulations.

The comprehensive aircraft noise model which is universallyaccepted, because of its wide experimental validation under-taken in the US, is that one developed by Fink [51,52]. A sim-ilar approach, but involving different component noise models,have been recently proposed and validated experimentally byLilley [104]. Both the Fink’s and Lilley’s model are based ontuning coefficients that must be evaluated experimentally.

A drawback of Fink’s model is that the high-lift device noisedoes not account for the flap side-edge noise, which is demon-strated to predominate on the trailing-edge noise. Taking advan-tage of this newly accepted source component breakdown andof the recent achievements in phased microphone array mea-surement techniques, Guo et al. [68] developed a fully empiricalairframe noise model.

A different approach has been recently developed by themain aircraft manufacturers, although few papers have beenpublished on the subject. It consists in performing Reynolds-averaged Navier–Stokes simulations to obtain the characteristicvelocity and length scales to be used in analytical models. Anapplication to trailing-edge noise predictions in the context ofmultidisciplinary design and optimization has been publishedby Hosder et al. [80].

2.2. Technologies for control and reduction

2.2.1. Trailing-edge noiseThe fundamental concept behind a trailing-edge noise mit-

igation is that of modifying the surface impedance close tothe edge in order to reduce the impedance jump felt by ed-dies convected past the edge. This can be realized by usingporous edges, by applying compliant brushes or by using saw-tooth edges. The latter technique also reproduces the effect ofa swept angle between the edge and the spanwise vortex com-ponents, resulting in a trailing-edge noise reduction accordingto theory [83]. Although the simultaneous use of sawtooth andporous edges may result in a more significant noise mitigation,full scale experimental campaigns carried out in the US [15]showed that only the sawtooth trailing-edge reduces the EPNLby 2 dB. The sawtooth edge has been also used to reduce thetone noise generation from a slat trailing-edge.

2.2.2. Flap side-edge noiseIn order to reduce the flap side-edge noise, different flow

control strategies have been proposed in the recent years. Pas-sive control devices include flap-tip fences [159,176], poroustreatment of the flap-tip region [7,137], serrated trailing-edgecorners, the so-called “noise weeder” [122], and small vor-tex generators referred to as microtabs [122]. Active controltechniques consist in blowing continuously air into the vorticalstructure in order to counteract the vortex roll-up, and to dis-place the vortical structure away from the solid surface [93,94].Both passive and active devices have been shown to mitigatethe flap side-edge noise. However, performing a comprehen-sive technological evaluation of the different devices is a quitehard task.

2.2.3. Slat noiseThe development and test of noise reduction devices for the

high-lift devices, the slat in particular, are constrained by thefact that these devices must not reduce the lift coefficient of thewing. Three technologies for slat noise reduction have been pro-posed and tested, both in the US and Europe. The first consistsin applying brushes [24] or serrated tabs on the slat suction sidenear the trailing-edge [122]. This allows to mitigate the vor-tex shedding, resulting in a quite significant reduction of thecorresponding tonal noise peak. The second slat noise reduc-tion technique consists in filling the volume of the recirculatingbubble behind the leading edge, resulting in a quite significantreduction of the broadband noise levels [39,122]. Finally, thethird technology consists in using slat gap acoustic liners. Thisdevice has the advantage of not affecting the aerodynamic prop-erties of the wing. The use of liners is legitimated by the factthat the high-frequency wave emitted from the trailing-edge canbe attenuated via multiple reflections on the two sides of thegap, during the wave travel from the trailing-edge to the lowergap opening. The slat gap liner noise mitigation properties havebeen recently demonstrated by Smith et al. [158].

2.2.4. Landing-gear noiseThe reduction of bluff gear components and the passive con-

trol of vortex shedding via splitter plates behind the cylindri-cal struts are the solutions commonly adopted to reduce thelanding-gear noise. In addition, a practical alternative to a struc-tural re-design of the gear consists in using add-on fairingsand covers. The noise reduction potentialities of several add-on devices applied to a full-scale A340 landing gear have beendemonstrated by Dobrzynski et al. [38].

2.3. Research trends

Three main trends in the airframe noise research can beobserved. The first consists in combining all the available sin-gle source models into comprehensive tools where the severaltuning parameters are obtained either through dedicated exper-iments or advanced CFD simulations. These tools can be usedto perform tradeoff studies during preliminary design stages,when the focus is on multidisciplinary design and optimiza-tion. The second research trend is the increasing use of CFD


simulations to design and optimize noise reduction devices. Inaddition, the numerical simulation contributes to increase thephysical knowledge of the sound generation mechanisms and tothe improvement of the source models. Finally, the third trendin the field of airframe noise consists in developing advancedmeasurement techniques that permit to discriminate betweenconcurring noise generation mechanisms, and to generate data-bases for the validation of predictive numerical tools.

3. Fan noise

In turbofan aero-engines, noise is generated by the inter-action between flow non-uniformities and rotating bladed andstator vanes. In modern high-bypass-ratio turbofans, the noisegenerated by the fan system exceeds the one generated by thecompressor and by the turbine stages.

Due to a coupling between the aeroacoustic excitation mech-anisms and the duct acoustic modes, in subsonic blade tipconditions the “rotor-locked” constant dipole source drives anevanescent duct mode that is attenuated during the sound trans-mission through the duct. Only higher order blade-passage-frequency harmonics generated by the flow unsteadiness dueto the rotor–stator interaction mechanisms can be transmittedthrough the duct. Conversely, at supersonic blade tip conditions,the rotor-locked shock wave system generates propagative mul-tiple pure tones at harmonics of the rotational shaft frequency,the so called “buzz-saw” noise.

The fan-noise interactional sources are concentrated near theblade leading- and trailing-edges. Leading-edge sources on therotor blades are generated by inflow disturbances such as in-gested atmospheric turbulence, duct boundary layer turbulenceand interaction with flow distortion. Leading-edge sources onthe stator vanes are generated by the quasi-periodic impinge-ment of the rotor viscous wake. Trailing-edge sources on boththe rotor blades and the stator vanes are generated by smallscale vortical disturbances convected past the trailing-edge. Therotor–stator interaction noise has both a tonal and a broad-band spectral content. The tonal spectral components are dueto the “deterministic” interaction between the coherent part ofthe rotor wakes and the stator vanes, whereas the broadbandspectral components are generated by the turbulent vortical dis-turbances. A spectral broadening around the blade passage fre-quency harmonics is also observed, which is due to a randommodulation of the wake/stator interaction process.

The reduction of fan noise radiation to the far field can bepursued by five generical concepts: (i) mitigation of the in-teraction mechanisms through an optimal design of the rotorblades and the stator vanes, or via flow control techniques thatreduces the velocity deficit in the rotor wakes, (ii) tuning ofthe stator cascade parameters in order to reduce the aerody-namic response to an impinging gust, (iii) tuning of the rotorblades and stator vanes numbers in order to drive only fewpropagating (cut-on) duct modes, (iv) use of passive/active ductwall treatments in order to attenuate the sound during trans-mission through the duct, (v) manipulation of sound diffractionmechanisms at the inlet lip and exhaust nozzle via advanced na-celle devices, such as the negatively scarfed inlet or the serrated

by-pass nozzle. Since the first two noise mitigation concepts re-quires analytical models that highlight the mutual influence ofall the design parameters, a brief overview of the some avail-able analytical models is presented hereafter. In addition, sincethe optimization of both passive and active control devices re-lies on duct noise transmission models and far-field radiationmodels, a short review of the available transmission/radiationanalytical models is presented. Finally, an overview of the maintechnologies for fan noise reduction and control is drawn.


3.1.1. Gust–airfoil interaction modelsThe unsteady pressure field induced by a vortical flow con-

vected past a blade generates an unsteady force on the bladeand interaction noise in the far field. Convected vortical dis-turbances that have a regular space-time structure are modeledas velocity gusts. For examples, the tip-vortices shed from he-licopter blades that impinge with regularity on the followingblades can be described as an oblique harmonic gust. The sameapproach is used to model the interaction between the rotorwake and the stator vanes in a fan system. Theories of blade–gust interaction are also used to model the blade aerodynamicresponse to a turbulent stream. In this case a Fourier decompo-sition of the impinging vorticity field is used to determine theblade response to the superposed Fourier gust components.

A gust–airfoil interaction is predominantly affected by thegust orientation with respect to the airfoil leading edge, and bythe characteristic wavelength of the gust. The gust orientationdepends on the value of two angles. The first one is that formedby the vorticity vector and its projection onto the airfoil plane.The second angle is that formed by the projection of the vortic-ity vector onto the airfoil plane and the airfoil leading edge. Thelatter angle is usually referred to as skew angle. The effects ofthe gust skew angle and wavelength on the unsteady pressurefield are described by the model developed by Graham [63],according to which the space of solutions of a gust–airfoil inter-action problem can be divided into two sub-spaces, dependingon the value of a gust parameter. This parameter is related to thefree-stream Mach number, the gust wavelength and the skewangle. Each solution subspace can be represented by a modelproblem whose solution is known. Any solution of a blade-vortex interaction problem can be related to the model solutionof the corresponding subspace through appropriate similarityrules. The two model solutions are that of an incompressibleoblique blade–vortex interaction, and that of a two-dimensionalcompressible problem.

The earliest incompressible gust–airfoil interaction modelswhere developed in the Twenties, when the aeroelastic phe-nomena associated with the increased flight speeds became acritical element of aircraft design. The first gust–airfoil inter-action theory for incompressible flows was put forward by vonKármán and Sears [181]. This theory, based on the conceptsof circulation theory [180], recovers the results predicted byTheodorsen [173] for a flat-plate in a small amplitude sinu-soidally oscillatory motion, and some results obtained by Küss-ner [96]. On the basis of von Kármán & Sears’ [181] unsteady


airfoil theory, Sears [154] derived an analytical expression forthe unsteady lift induced by a vortical sinusoidal gust convectedpast a thin airfoil. Later on, Filotas [50] extended Sears’ analy-sis to an oblique sinusoidal gust.

The mathematical treatment of a linearized gust–airfoil in-teraction problem consists in splitting the velocity field intothe sum of a solenoidal (rotational) part and a potential (irro-tational) part. The solenoidal part is a known function of theimposed upstream disturbances and represents a vortical wavedecoupled by the steady-state aerodynamic field. The potentialpart is an unknown function of both the mean flow and the vor-tical disturbances. The solenoidal and the potential parts arecoupled by the boundary conditions on the airfoil surface. Fora compressible flow the potential part of the unsteady velocityfield is governed by a constant coefficient, homogeneous, con-vective wave equation that reduces to a Laplace equation if theflow is supposed to be incompressible.

Theoretical studies of the unsteady aerodynamic field past anairfoil in a compressible flow were carried out by Possio [136]and by Amiet [4,5]. The first one obtained an integral equa-tion relating the pressure field on the surface of a thin airfoil toa sinusoidally fluctuating velocity field around the airfoil. Thesecond one proposed analytical procedures for the gust–airfoilinteraction problem in the high- and low-frequency limit.

The time-average flow about a real airfoil with finite thick-ness, camber and angle of attack is no longer a parallel uniformflow. Goldstein and Atassi [62] developed a second order the-ory for the gust–airfoil interaction problem that accounts for thedependence of the unsteady velocity field on the mean potentialflow around the airfoil. They showed that the vortical waves aredistorted by the mean flow around the airfoil and that the dis-tortion affects significantly both the amplitude and the phaseof the unsteady velocity field. In the case of a thin airfoil withsmall angle of attack and camber, Goldstein and Atassi’s sec-ond order theory provides explicit analytical formulas for theunsteady lift induced by longitudinal and transverse gusts.

A typical aeroacoustic approach takes advantage of theacoustic analogy theory in order to relate the acoustic far fieldto the pressure distribution on the airfoil surface. Widnall [184]investigated the sound generated by the interaction between atwo-dimensional airfoil and an obliquely incident vortex. Theairfoil was assumed to be chordwise compact, but not neces-sarily spanwise compact. The vortex was supposed to remainstationary as it was convected past the airfoil. The velocityfield induced by the vortex was decomposed into Fourier com-ponents. These components were introduced into Filotas’ [50]airfoil response function in order to determine the fluctuatingpressure field on the airfoil surface. Finally, the sound gener-ated by the blade–vortex interaction was determined by usingthe pressure field induced on the airfoil surface. Amiet [2] de-scribed the acoustic field generated by an airfoil immersed in aturbulent flow. He related the spectral behavior of the far pres-sure field to the spectral properties of the incident turbulentflow. In the case of an airfoil in a low Mach number stream, theSears’ function was used as airfoil response function. Amiet [4]demonstrated that a generalized Prandtl–Glauert transformationcan be used to reduce a small perturbation problem in a com-

pressible stream into a standard wave equation in a mediumat rest. Furthermore, in the low-frequency limit, the second-order time derivative in the transformed wave equation can beneglected leading to a Laplace equation. The solution of thisLaplace equation can be matched to an outer compressible so-lution that provides the acoustic far field.

Amiet [5] proposed an analytical procedure to calculate theunsteady lift induced by a compressible high-frequency gust ona thin airfoil. The method was based on the assumption that, asshown by Landahl [97], the leading edge and the trailing-edgeaerodynamic problems, at high frequencies, can be separatelysolved and matched in a converging iterative scheme. Amietsolved the leading edge and the trailing-edge problem in termsof Schwartzchild solution up to a second-order matched solu-tion. Martinez and Widnall [108] used the first two terms in theseries of Adamczyk’s [1] iteration scheme in order to predictthe pressure field induced by an oblique high-frequency com-pressible gust on a rectangular thin blade. A three-dimensionalsurface pressure distribution was recovered by means of a span-wise Fourier superposition of two-dimensional solutions. Mar-tinez and Widnall [109] extended their previous formulationto the case of a rotating blade encountering an oblique high-frequency gust. The pressure field on the blade surface wasbuild via a spanwise Fourier superposition of two-dimensionalsolutions, but having linearly increasing magnitudes along theblade span.

A different aeroacoustic approach consists in solving thelinearized Euler equations by means of singular perturbationmethods that provide matched near- and far-field solutions. My-ers and Kerschen [123,124] developed analytical models forthe compressible, high-frequency interaction between a gustconvected by a subsonic mean flow, and a cambered airfoil atnon-zero incidence. The mean flow distortion effects due to theairfoil angle of attack and camber where highlighted. Later onEvers and Peake [42] extended the formulation to a transonicmean flow.

3.1.2. Gust–cascade interaction modelsThe singular perturbation solutions of high-frequency gust–

airfoil interaction problems have been also applied to gust–cascade interaction problems by Peake and co-workers. Peakeand Kerschen [132] and Evers and Peake [43] investigated thesound generated by the interaction between convected vorticaland entropic disturbances and a row of blade with small butnon-zero camber and thickness, at a non-zero incidence angle.The multiple interactions between the sound and the cascadewere included in the model, providing analytical expressionsfor the forward noise radiation. Analogously to the gust–airfoilinteraction problem, a significant sensitivity of the far-fieldnoise to the flow distortion around each leading edge and tothe blade geometry was predicted. However, by integrating theeffects of a full incident turbulence spectrum, a quite less sen-sitive noise level was predicted. Therefore the authors arguedthat the tonal noise components generated by rotor/stator singleharmonic gust interaction is significantly affected by the bladegeometry. Conversely, the broadband part of the noise spectrumis less significantly affected by the blade geometry.


Other gust–cascade interaction analyses were carried out byHanson and Horan [72] and by Hanson [69]. Later on, moreexhaustive models were developed by Hanson for a tandemblade row configuration, with the aim of describing the reflec-tion/transmission effects and other unsteady coupling mecha-nisms.

3.1.3. Rotor–stator reflection/transmission modelsThe rotor viscous wakes and the blade tip vortices that inter-

act with the downstream stator vanes generate acoustic wavesthat should be transmitted through the rotor blade row beforereaching the nacelle inlet. In addition, a portion of the acousticenergy is back reflected by the rotor and should be transmittedthrough the stator vanes before reaching the nacelle exhaust.

The occurrence of resonance phenomena due to the mutualacoustic scattering of a cascade tandem system has been in-vestigated analytically by Woodley and Peake [186,187]. Theyshowed that the a tandem cascade system can exhibit two typesof resonance: (i) a cut-on/cut-off resonance associated withthe gap between the rows, (ii) a resonance of the downstreamrow driven at low frequencies by a vorticity wave produced bytrapped duct modes in the upstream row, and at higher frequen-cies by radiation modes between the blade rows.

The mode trapping and rotor/stator unsteady coupling of thepressure and vortical waves have been also addressed by Han-son in two works. Firstly, the author investigated the tonal ro-tor/stator interaction in two-dimensional coupled cascades [71].Later on, the author addressed the problem of broadband noisegeneration in a coupled rotor/stator system [70], by making useof the harmonic cascade theory put forward by Glegg [58]. Themain conclusion of this latter analysis was that the unsteadycoupling between the rotor and the stator blades enforces thebroadband noise levels.

3.1.4. Nacelle noise transmission modelsThe sound generated by rotor/stator interaction in subsonic

rotor tip conditions, as well as by the rotor alone in supersonicrotor tip conditions, propagates through the nacelle duct in thepresence of a non-uniform mean flow and acoustic treatment onthe duct walls.

In the case of infinite constant area duct with constant im-pedance type boundary conditions and a uniform axial flow, thepropagation of harmonic acoustic disturbances is governed bythe convected Helmholtz equation whose solution, due to thegeometry simplicity allowing separation of variables, can beexpressed as a superposition of eigensolutions or modes [44,135].

In the case of a slowly varying circular annular duct withflow and impedance walls, Rienstra [143] extended the modalsolution through an elegant application of a perturbative analy-sis based on the multiple-scales approach. The key points ofRienstra’s analysis where: the use of an approximate axial meanflow solution, the use of the impedance wall condition obtainedby Myers [125] for a non-uniform mean flow grazing a curvedsurface, and the generalization of the analytical solution to thetransition from annular to hollow duct.

Although the multiples-scales approach applied to ductpropagation models was already known before, Rienstra’sanalysis represented a real breakthrough in the theory of ductacoustic. Starting from Rienstra’s work, in fact, several levelsof sophistication have been reached in recent years, leading toa predictive analysis approach that in many practical situationis more robust and reliable than a numerical approach. An ex-tension of the multiple-scales modal solution to a generic ductcross section has been presented by Rienstra [144]. This analy-sis includes the treatment of the cut-on/cut-off transition in avarying area duct. Extensions to sheared and swirling meanflow have been proposed by Cooper and Peake [26,27] and byVilenski and Rienstra [64].

An additional research trend in the field of duct acousticsis represented by the analytical modeling of the sound trans-mission in the presence of a spliced acoustic treatment. Testeret al. [171] have recently developed and verified numericallya model for the sound scattering by liner splices. They havequantified the influence of the splice number and thickness onthe re-distribution of the incident mode energy among scatteredduct modes.

The technological impact of the models developed by theaforementioned authors is not only due to their high sophisti-cation level. An additional value is represented by the fact thatmost of these models have been verified through fully numeri-cal solutions, and are presented in a easily reproducible way, asalso relevant for the verification of numerical approaches [19,145,161].

3.1.5. Nacelle inlet/exhaust noise radiation modelsInlet/exhaust nacelle radiation models have been developed

in the past for the idealized configuration of a semi-infiniteunflanged circular or annular duct of negligible lip thickness.These models are based on the Wiener–Hopf technique appliedat different levels of geometry/flow complexity. Two flows con-figurations are commonly addressed: the first is the case of aconstant internal/external flow, which is representative of aninlet flow in cruise conditions, the second is the case of twoco-axial internal/external flows with discontinuous conditions,which is representative of an exhaust flow in generic flightconditions. However, the latter flow configuration is to be com-pleted with a cylindrical vortex sheet shed from the exhaust lipand convected downstream. This results from the satisfactionof a Kutta condition that permits to remove the singularity ofpressure at the lip due to the absence of viscosity in the fluidmodel.

For inlet noise radiations, several models have been pro-posed in the past [79,140,153], starting from the analyticaltreatment of an unflanged duct in the absence of flow put for-ward by Levine and Schwinger [98]. The main interest of thesemodels lies in the simple relationship between the angular loca-tion of the main lobe radiation peak and the cutoff ratio of theradiated duct mode.

For exhaust noise radiations, two major contributions aredue to Munt [121] and Rienstra [141]. Munt obtained an an-alytical solution for a discontinuous jet pipe flow supportinga shear layer developing from the pipe lip, whereas Rienstra


obtained an analytical solution for an annular exhaust with aninfinite centerbody and in the presence of a constant flow. Thesetwo geometry/flow configurations have been recently mergedby Gabard and Astley [53] who obtained solutions for the ideal-ized aero-engine bypass duct radiation problem. More recently,Demir and Rienstra [36] extended the formulation to accountfor a lined center body and a co-axial flow with discontinuousthermodynamic properties.

3.1.6. Liner impedance modelsIn order to attenuate the fan noise transmitted along the na-

celle ducts, the inner walls of aircraft engines are lined withpanels of acoustic treatment. The acoustic liner may cover mostof the available surface, both in the inlet and exhaust ducts, asresulting from an optimization procedure involving antagonistfactors like the installation of anti-icing systems.

The key parameter in the liner optimization process is theacoustic impedance. This is comprised of a real part, the resis-tance, and an imaginary part, the reactance. The first step in theliner design consists in estimating the values of the liner resis-tance and reactance that ensure the maximum sound attenuationfor a prescribed duct modal content, over the frequency rangeof interest. The second step consists in selecting a liner classthat matches as close as possible the optimal resistance and re-actance values for each frequency band of interest.

The acoustic treatment used to line an aero-engine wallsare of resonator type, consisting in one or two sandwich lay-ers. A single degree of freedom (SDOF) panel is constitutedof a porous sheet, a cellular separator such as honeycomb, anda solid backplate. A two degree of freedom (2DOF) panel isconstituted of a porous sheet, two layers of honeycomb sep-arated by a porous septum, and a solid backplate. Both SDOFand 2DOF liners are effective over narrow frequency ranges andmust be tuned on one or two fan tones, respectively. Typically,the acoustic properties of this class of treatment do not dependon the amplitude of the incident acoustic wave (linear behav-ior) up to a high value of the incident sound pressure level atwhich the liner resistance starts exhibiting a dependence on theincident wave amplitude (nonlinear behavior). The first recog-nition of this dual behavior is due to Melling [110] who arguedthat, in the linear regime, the micro flow in the orifice is laminarand the dissipative (resistive) losses may be of Poiseuille typeor Helmholtz type. In both cases the losses are due to viscousdissipation in the shear layer. This hypothesis have been par-tially confirmed through recent direct numerical simulations byTam and Kurbatskii [166] who observed, in the linear regime,a jetlike flow close to the orifice openings and a strongly oscil-latory boundary layer. In the nonlinear regime, Melling arguedthat a turbulent jet takes place at the mouth of the resonator andthe primary dissipation mechanism is turbulence. This mecha-nism was not confirmed by the numerical analysis by Tam andKurbatskii who observed a vortex-shedding mechanism takingplace at certain acoustic frequency bands, which is responsiblefor the conversion of acoustic energy into kinetic energy andfurther viscous dissipation into heat.

Several analytical models describing the behavior of a linerhave been developed in the past. A good review on the topic

is due to Zorumski and Tester [189] and, more recently, toMotsinger and Kraft [120]. At the present time, however,the bast practice in vogue is to predict the liner impedanceby means of semi-empirical methods obtained by regressionof experimental data. The recent works by Kraft et al. [95],Jones [88] and Hersh and Walker [78] provide examples of thesemi-empirical approach.


3.2.1. Fan assembly designThe best practice in reducing the fan rotor/stator interaction

noise consists in using the so-called “Tyler and Sofrin selec-tion rule” [175]. This is based on the identification of suitablerotor blades and stator vane numbers, such that the resulting in-teraction tones are cut-off and therefore do not propagate. Themodel is based on an elegant manipulation of Fourier series forthe prediction of the rotor/stator interaction tones, and simpleproperties of the duct eigenvalues.

A second strategy to reduce the fan interaction noise con-sists in using the theoretical arguments arising from the gust–cascade interaction models in order to reduce the unsteadyforce induced by the rotor wake on the stator vanes. A sim-ple rule consists in exploiting the property according to whichthe unsteady lift on the blade decreases as the reduced fre-quency of the impinging gust increases. A simple way to reducethe reduced frequency is to increase the chord of the statorvanes [37]. Another method used to mitigate the unsteady forceon the stator vanes consists in increasing the rotor/stator dis-tance, but this causes performance degradations and weight in-crease. A quite best practice consists in designing swept andleaned stator vanes [41,188] so that the interaction between therotor wake and the stator leading edge does not occur simulta-neously along the whole span. In addition, the swept stator tipresults in an increased rotor/stator distance, without any weightincrease.

A third strategy, which is indeed an extension of the pre-vious one, consists in using the theoretical arguments arisingfrom the rotor–stator reflection/transmission models in order todesign a fan assembly in which acoustic coupling phenomenacan be exploited in order to generate intrinsic antagonist wavephenomena. To the authors knowledge, no applicative work hasbeen published on this topic.

3.2.2. Fan trailing-edge blowingThe interaction between the viscous wakes of the rotor

blades and the stator vanes is a primary source of rotor–statorinteraction noise. This can be reduced by filling the wake byblowing air into the wake from a slot in the rotor blade trailing-edge. A proof of this concept has been put forward by Sutliffet al. [160] who observed that, by using a blowing rate of 1.8%of the fan mass flow rate, a significant reduction (from 8 to20 dB) of the tonal peaks at the first three harmonics of theblade passage frequency can be attained both in the inlet andexhaust ducts.


3.2.3. Acoustic treatmentAs previously stated, a good review on the subject is that

by Motsinger and Kraft [120]. Recent researches are mostlyconcerned with: (i) the use of zero-splice liners that enable fullattenuation thanks to absence of acoustic mode scattering [56];(ii) hybrid passive/active acoustic treatments [55]; (iii) the useof integrated anti-icing/liner systems at the nacelle lip [131].

3.2.4. Active controlBecause of fuel efficiency factors, the bypass ratio of civil

aircraft engines is expected to be increased from less than 10to about 15 in a near future. A drawback of ultra high by-pass ratio aero-engines is the reduced efficiency of the passiveacoustic treatment. On one side, the increased rotor diameterresults in lower blade passage tones, which are more diffi-cult to be absorbed by means of a passive liner. On the otherside, the reduced nacelle diameter-to-length ratio results in rel-atively shorter liners, with a consequent reduced absorbing ef-ficiency. These considerations have motivated the developmentand experimental proof of active control devices for fan tonalnoise [107,174,185]. A technological assessment of differentactive noise control strategies is currently undertaken by theaero-engine manufacturers.

3.2.5. Negatively scarfed intakeThe negatively scarfed intake has the potential to reduce in-

let radiated fan noise. On one side, the extended bottom line lipredirects a part of the acoustic energy upwards and away fromthe ground, as resulting from a combined effect of lip diffrac-tion and mean flow refraction. On the other side, the longer lipallows the inclusion of additional acoustic liner. Experimentalproofs of concepts have been carried out in recent years [11,25,116], showing the acoustic benefits of this novel technology.A broadened technological evaluation involving several aspectsis currently undertaken by the major aircraft and aero-enginemanufacturers. The asymmetric shape of a scarf inlet, in fact, isresponsible for an azimuthal flow distortion along the duct [57]that may result in additional fan interaction noise, thus over-whelming the acoustic benefits of the scarfed inlet. In addition,there are general factors as weight and other aerodynamic as-pects that must be assessed in a multi-disciplinary evaluationprocess [157,182].

3.2.6. Bypass exhaust lip serrationExperimental campaigns [129] have demonstrated that the

presence of serrations (or ‘chevrons’) on the nozzles of highbypass ratio turbofan engines yields a reduction in peak turbu-lence intensity in the bypass/freestream shear layer. This mayresult in a reduction of the secondary jet noise. Since, serrationsare present on both primary (core) and secondary (bypass) noz-zles, the effects of the serration on the bypass modal diffractionat the secondary nozzle are not completely clear.


Two major research trends in the field of fan noise reductionand control can be observed. The first consists in developing

analytical models of growing sophistication level, both for thenoise generation, and for the nacelle transmission and externalradiation. The verification of these models is supported by thenumerical solution of the flow governing equations. The secondresearch trend consists in developing advanced passive/activecontrol techniques through combined experimental and numer-ical investigations. The estimation of the cost/benefit balancefor each noise reduction device is the key point of a difficulttechnological assessment.

4. Jet noise

The progressive introduction into service of first generationturbofan engines during the Fifties and the Sixties contributedto a 20 EPNdB reduction of aircraft noise certification lev-els. Successive noise improvements due to second generationturbofans were achieved through a progressive increase of thebypass ratio, balanced by a mitigation of the increased fan noisethrough improved acoustic treatments.

In modern high-bypass-ratio turbofan engines, the jet stillcontributed to about a half of the overall acoustic energy duringtake-off. For this reason, the jet noise remains the most ferventaeroacoustic research area, since the establishment of this topicin the Fifties.

The main difficulty in the prediction of jet noise is due to thelack of a general theory describing the turbulent fluctuations ina jet flow. For this reason, a first principle jet noise theory is notyet available. However, the basic mechanisms involved in thesound generation were established from the beginning, thanksto the several implications of Lighthill’s acoustic analogy [99].

In subsonic jets, the small-scale turbulence is believed to bethe dominant source of noise. Even though large-scale coherentturbulent structures and instability waves have been observedin a wide range of Reynolds numbers, these structures are noteffective aeroacoustic sources. However, they play a crucialindirect role on the jet noise generation, by enhancing the tur-bulent mixing and the consequent jet spreading.

In supersonic jets, even though a direct empirical evidence isdifficult to be achieved, large-scale coherent turbulent structuresand instability waves are believed to be very effective aeroa-coustic sources [163].

The universal character of the small-scale turbulent fluctua-tions contributes to the success of predictive models based onthe acoustic analogy theory. This models describe the mecha-nisms of “mixing noise” generation in subsonic jets. The samemechanisms are present in supersonic jets, but in this case otherphenomena predominate. The convection of instability waves orcoherent turbulent structures at supersonic speed is responsiblefor the generation of “Mach waves”. In addition, when shockcells are present in the jet plume, the interaction between shearlayer vortical disturbances and the shocks generate a broadband“shock associated noise”. Finally, upstream propagating shockassociated pressure disturbances can excite instability waves inthe shear layer through receptivity mechanisms at the nozzlelip. As a consequence, a feedback coupling can occur with tonalnoise selection and generation of the so-called “screech noise”.Analytical models and semi-empirical predictive methods are


available for each of these jet noise generation mechanisms.These models are briefly reviewed in the following subsections.


4.1.1. Mixing noiseFrom the publication of the first aeroacoustic theory by

Lighthill in 1952 [99] until the earlier Seventies, most of theanalytical work on jet noise was focused on Lighthill’s acousticanalogy. The main result of Lighthill’s theory was the so-called“eighth power law” of the jet noise intensity versus the jetvelocity. This law was confirmed through extensive experi-mental campaigns [183]. Further analytical improvements ofLighthill’s theory were mainly concerned with the extensionto moving jets [46], the modeling of the turbulence correlationtensors [47,138] and consequent removal of the Doppler singu-larity, the analysis of the mean flow convective effects [60,139],and the description of the so-called Mach wave radiation oc-curring when vortical disturbances are convected at supersonicphase speed [49]. Several reviews on this subject can be foundin the literature [30,103].

In the earlier Seventies, Lush [106] observed that the pre-dictions of Lighthill were not uniformly valid. This indicatedthe necessity of alternative models for sound generation andpropagation within the jet plume. Phillips [134] argued that thediscrepancies between Lighthill’s model and the measurementsat low observation angles away from the jet axis was due tomean flow refraction effects. Hence he re-arranged the govern-ing mass and momentum equations in the form of a convectedwave equation with a specified source term. Although exact inthe sense that no assumptions were made in his derivation, theapplication of Phillip’s theory led to the undesirable propertythat some sound propagation terms were included in the sourceterm. Lilley [101] remedied to this by deriving a third orderconvective wave equation for transversely sheared mean flowsin which all the linear propagation terms are removed from thesource term. Several reviews on this subject can be found in theliterature [61,102].

Tester and Morfey [172] obtained high-frequency solutionsof the Lilley’s wave equation for a sheared jet and determinedsemi-empirical solutions of the radiated acoustic field. This ap-proach is the basis for modern semi-empirical jet noise mod-els described hereafter, which are based on Reynolds-averagedNavier–Stokes mean flow solutions.

A commonly accepted feature of the mixing noise fromhigh-speed jet is that it consists of two components. The firstone is associated with large-scale vortical fluctuations in thejet plume and is predominant in the aft quadrant close to thejet axis. The second component is associated with fine-scaleturbulence and is predominant in the forward quadrant and atnear-normal angles to the jet-axis. Due to the more universalcharacter of small-scale turbulent fluctuations, this second mix-ing noise component can be predicted on the base of statisticalturbulence models and acoustic analogy formulations, as dis-cussed in Section 4.1.5.

Recently, Tam and Auriault [164], Tam et al. [168,169] andFedorchenko [45] have formulated alternative theories of mix-

ing noise generation in jet sheared flows, by evoking somepredictive discrepancies of Lighthill’s theory. Their conjecturesabout the acoustic analogy have stimulated an animate debateamong several researchers [119].

4.1.2. Mach wave radiationVortical disturbances frozenly convected through a sheared

jet flow do not radiate sound until their phase velocity is su-personic. The phase velocity of a compact turbulent eddy iswell represented by the eddy convection velocity. The pressurefluctuations driven by turbulent structures convected at super-sonic phase speed interfere constructively in the direction ofthe angle between the normal to the Mach cone attached to theeddies and the direction of the convective motion, usually de-noted as “sonic angle”. As described by Ffowcs Williams andMaidanik [49], the acoustic power associated with the Machwave radiation scales as the cube of the jet velocity. As a con-sequence, a saturation process occurs when the jet velocity isincreased from low subsonic values, at which the acoustic in-tensity scales as the eight power of the jet velocity, to highsupersonic values, at which the acoustic intensity scales as thecube of the jet velocity.

4.1.3. Shock associated noiseWhen a supersonic jet nozzle operates at adapted ambient

conditions, no shock cells are generated in the plume. In thiscase, the only noise generation mechanisms is associated withthe small-scale turbulence mixing noise and Mach wave radi-ation. The mixture of these two mechanisms is commonly re-ferred to as supersonic turbulent mixing noise [162]. Two com-monly observed features of this noise generation mechanismare: (i) the high directionality, with downstream predominantradiation between 25◦ and 45◦ from the jet flow direction, (ii) abroadband power spectral density spanning over about two fre-quency orders, with a very smooth peak separating a variationlaw as the square of the frequency on the left, from a variationlaw as the inverse of the frequency on the right.

When a supersonic jet is not operated at perfectly expandedconditions, a quasi-periodic shock cell pattern appears in the jetplume. The interaction between the vortical disturbances in thejet stream and the shock fronts generates additional noise, re-ferred to as shock associated noise. The main property of thisnoise component is that its spectral peak frequency decreasesaway from the downstream flow direction. In addition, the as-sociated acoustic power level exhibits an opposite directivitybehavior with respect to the mixing noise. As a consequence,the acoustic radiation in the jet rear arc, at observation anglesgreatest than 90◦, is commonly dominated by the shock asso-ciated noise. This behavior has been described by a simple andelegant phased point-source array model by Harper-Bourne andFisher [74]. They assumed that the source of shock associatednoise is a synchronized array of periodic point monopoles lo-cated at a distance equal to the length of the shock cells. Thephases of adjacent monopoles are assumed to be correlated bythe time taken for turbulent eddies to be convected from onepoint source to the next. The resulting acoustic waves inter-fere constructively along observation angles which depend on


the acoustic frequency, according to a behavior analogous tothat of a directional antenna. Starting from the basic conceptof a phased array of sources, Tam and Tanna [170] developeda predictive analytical model of the broadband shock asso-ciated noise. By employing sophisticated mathematical tech-niques and elegant use of statistical models of vortical insta-bility waves, they obtained a compact semi-empirical formulafor the acoustic power spectral density that provides favorablecomparisons with experimental data.

4.1.4. Screech tonesThe noise spectrum of chocked jets is characterized by the

presence of discrete harmonics referred to as screech tones. Thefundamental tone arises at the same frequency all along the ob-servation arc. This frequency appears to be a lower bound forthe central frequency peak of the shock associated noise. Thissuggested a relationship between screech tones and shock as-sociated noise. In fact, as illustrated by Tam [162], the screechtone frequency corresponds to the phased array frequency at anobservation angle of 180◦. The shock associated waves propa-gating in the upstream direction are those enforced by a feed-back loop involving instability waves generated in the shearlayer close to the nozzle. The occurrence of harmonics of thefundamental screech tone is attributed to nonlinear propagationeffects in the jet plume.

4.1.5. RANS-bases semi-empirical modelsThe idea of extracting from a RANS aerodynamic solution

the statistical turbulent quantities required by an acoustic anal-ogy model to predict the far-field noise radiated by a jet is veryold. One of the earliest RANS-based mixing-noise model is im-plemented in the NASA code MGB, from the initials of itsinventors Mani, Gliebe and Balsa [12]. The MGB code usesa RANS mean flow solution to define local length scale, timescale, and source strength parameters for a source model. Thisis based on a simplified Lighthill quadrupole source term withan approximate high-frequency solution of Lilley’s equation forpropagation to the far field. MBG predictions have been heavilyused by industry and NASA for the last twenty years and, overtime, its accuracy has been increased. More recently, Khavaranand co-workers [90,91] have removed many of the limitationsof the method by reformulating both the propagation and noisesource models into the jet-noise code MGBK. Methods of thiskind are usually referred to as semi-empirical, since the RANSturbulence model itself is semi-empirical.

Tam and Auriault [164] have proposed a RANS-based pre-diction scheme for the fine-scale turbulence mixing noise com-ponent of jet noise. In their formulation a modified k–ε turbu-lence model provides parameters for a semi-empirical space-time correlation function of turbulent fluctuations. The aeroa-coustic source term, however, is not based on Lighthill’s anal-ogy. By analogy with the gas kinetic theory, they postulated arelationship between the turbulence kinetic energy and the fluc-tuating pressure. An adjoint field was then used to project thenear-field source onto the far field. Morris and Farassat [119] ar-gued that the Tam and Auriault’s model provides better resultsthan previous Lighthill’s type models, not because of some flaw

in the acoustic analogy approach, but thanks to a better model-ing of the turbulence statistics.

RANS-based methods provide good predictions for genericaxi-symmetric or rectangular nozzles, but they are often unableto account for nozzle design changes, such as the addition ofchevrons [105]. In addition, they do not perform well at thelow- and high-frequency ends of the acoustic spectrum. Thefundamental limitation of the RANS-based approaches is in thenon-universal character of the turbulent fluctuations and to thedifficulty in computing the space-time velocity correlations bymeans of RANS approaches.


In order to mitigate the noise generation from high-speedjets, several passive and active flow control techniques havebeen developed and tested in the years. Passive control is ac-complished by modifications of the nozzle shape (e.g. serration,beveling, tabs, etc.). Active control is accomplished by addingmass or energy to the flow in order to excite flow instabilitiesor affect the flow through the generation of new flow structures(e.g. streamwise vortices). Active control is further divided intotwo categories: open-loop and closed-loop. In the open-loopcontrol, actuation take place based on a predetermined law. Inthe closed-loop control, real-time information from sensors inthe flow are used to drive the actuation process. Only open-looptechniques have been successfully applied to jet noise mitiga-tion.

The basic concept behind passive control techniques is theenhancement of jet mixing through the generation of stream-wise vorticity. The same concept is applied in open-loop controloperated with steady mass or energy injections into the flow, orwith pulsating injections at frequencies which are much lowerthan any instability frequency of the flow. Conversely, whenactive control is operated at frequencies in the range of flowinstability frequencies, the noise mitigation mechanism is in-timately related to the aeroacoustic efficiency of the excitedvortical jet mode, which ultimately acts as an attractor of tur-bulent kinetic energy.

The most popular passive and open-loop active flow controltechniques for jet noise mitigation are overlooked in the follow-ing sections.

4.2.1. Nozzle tabs and chevronsThe rate of mixing of the jet and the surrounding fluid can

be increased by the presence of small tabs on the nozzle [67,151]. Unfortunately, the increased mixing, while reducing low-frequency noise, generates excessive high-frequency noise thatmay overwhelm any acoustic benefit. In addition, tabbed noz-zles always result in thrust loss.

As an alternative to tabbed nozzles, serrated nozzles edge,or chevrons, have been recently proposed. These devices arethe current state of the art in jet-noise mitigation technology formedium- and high-bypass turbofan engines [17,77,129,155].Analogously to tabs, the triangular serrations in the nozzletrailing-edge induce streamwise vorticity into the shear layerthat leads to increased mixing and reduced length of the jet


plume. However, since the penetration into the flow is lowerthan that occurring with tabs, the mixing enhancement occurswith a minimal engine performance penalty. Experimental testsshow a complex dependence of the noise benefits from a seriesof geometrical parameters, such as the number of chevrons andthe level of penetration of the chevrons into the flow. The sin-gle and mutual influence of these parameters on the jet noisegeneration mechanisms is still unclear.

Recently, non-uniform circumferential chevron distributionsand shapes have been successfully used in order to exploit thecircumferential non-uniformity of the flow in realistic installedengine configurations [111–113].

4.2.2. Nozzle beveling and axial misalignmentBeveled primary nozzles have been proposed by Viswanathan

[177–179] for both single and dual-stream jets, as a way toreduce the jet noise at both subsonic and supersonic operat-ing conditions. Although the mechanisms according which thenoise reduction occurs, the beveled noise exhibits strong az-imuthal variations of the far-field noise levels with respect tothe axi-symmetric nozzle. Significant reductions of the noiselevels below the longer nozzle lip have been observed. In addi-tion, the acoustic power spectral density is significantly affectedall along the observation arc, revealing an energy re-distributionamong the involved noise generation mechanisms.

An analogous concept based on the forcing of non-axi-symmetric flows has been proposed by Papamoschou [130].This concept consists in tilting downward, by a few degrees,the secondary flow with respect to the primary flow. The dual-stream axial misalignment results in a lower convective Machnumber of the turbulent structures in the shear layer. Noise re-duction at all frequencies have been documented, manly in theaft radiation arc.

4.2.3. Distributed nozzleThe distributed exhaust nozzle concept is based on the

idea that the spectral content of jet noise can be dramaticallychanged by splitting the exhaust plume through an array ofsmaller jet plumes. Each plume generates a higher frequencynoise, resulting in a global noise benefit, due to the more effec-tive atmospheric absorption at higher frequencies. In addition, ifthe distributed nozzle assembly is properly designed, the plumecoalescence occurs at lower velocity with respect to the sin-gle plume exhaust, thus resulting in lower low-frequency noise.An example of distributed exhaust nozzle is reported by Gaetaet al. [54]. Other configurations are described in the review byGliebe et al. [59].

4.2.4. Microjet injectionThe air, water and aqueous microjet injection is extensively

used in the jet noise research area. Water, in particular, is widelyused to reduce large pressure fluctuations occurring in super-sonic jets, as well as the blast wave generated at the ignitionof the solid propellant in the rocket motor of a space launcher.Experimental studies clearly show that the water injection sig-nificantly affects the shock cell structures, with consequent ben-efits on the shock associated noise. Several examples of water

microjet injection to supersonic aero-engines jet plumes havebeen published recently [65,126], showing reductions in bothshock associated noise and Mach wave radiation. The use ofpassive air microjet injection or synthetic jet actuation showless significant noise benefits [66]. Moreover, open-loop controlthrough unsteady rotating microjet injections may even result inincreased noise levels [87].


The recent achievements in the numerical simulation of real-istic high-speed jets and the associated noise is bringing a newvigor in the investigation of the physical mechanisms involvedin the jet noise generation [13]. These simulations, based on thedirect solution of flow governing equations filtered at the sizeof the computational mesh, generate huge data bases enablingstatistical analyses and different kinds of noise-flow cross cor-relations.

The research in the jet noise mitigation is mainly focusingon the experimental investigation of the influence of parametersinvolved in passive/active flow control devices. In addition newpassive/active control devices have been recently introduced.The use of plasma actuators distributed inside the nozzle to ex-cite azimuthal instability modes in the jet is one of the activecontrol technique recently proposed [150].

5. Summary

In this paper we have used a bibliographical approach to de-scribe qualitatively the underlying mechanisms involved in thegeneration of aerodynamic noise in modern aircraft for civiltransportation. Analytical or semi-empirical models of thesemechanisms are presented as a key element for the assessmentof noise mitigation technologies. After a great deal of theoreti-cal work during the Sixties and the Seventies, and the develop-ment of advanced numerical techniques in the last twenty years,the recent trend is to use the numerical solution of the governingequations in order to develop and improve fast predictive tools.Due to the growing diffusion of industrial software that allowto easily integrate different numerical analyses, tradeoff studiesand multi-objective/multi-disciplinary optimizations are a com-mon practice during the preliminary design of novel aircraft.This is particularly useful, for instance, to assess the influenceof a noise mitigation device on the aircraft operating cost. A re-view of the main established technologies for airframe-, fan-and jet-noise reduction and those currently under evaluation isalso presented. Although many scientific and technological el-ements have not been addressed, we believe that this work maybe useful for a rapid access to bibliographic information in thefield of aircraft noise reduction.

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