kim, hyo wan and duraisamy, karthikeyan and brown, richard ... · eﬀect of rotor stiﬀness and...

Kim, H.W. and Duraisamy, K. and Brown, R.E. (2009) Effect of rotor stiffness and lift offset on the aeroacoustics of a coaxial rotor in level flight. In: 65th American Helicopter Society Annual Forum, 27-29 May 2009, Texas, USA.

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Effect of Rotor Stiffness and Lift Offset on the

Aeroacoustics of a Coaxial Rotor in Level Flight

Hyo Won Kim∗ Karthikeyan Duraisamy Richard E. BrownPostdoctoral Research Assistant Lecturer in CFD Mechan Chair of Engineering

Rotorcraft Aeromechanics Laboratory

Department of Aerospace Engineering

University of Glasgow

Glasgow G12 8QQ

United Kingdom

Abstract

The acoustic characteristics of a twin contra-rotating coaxial rotor configuration with significant flapwisestiffness are investigated in steady forward flight. The Vorticity Transport Model is used to simulate theaerodynamics of the rotor system and the acoustic field is determined using the Ffowcs Williams-Hawkingsequation implemented using the Farassat-1A formulation. Increasing the hub stiffness alters the strengthsof the blade vortex interactions, particularly those between the upper and lower rotors, and affects theintensity and directivity of the blade vortex interaction noise produced by the system. The inter-rotor bladevortex interaction on the advancing side of the lower rotor is the principal source of the most intensivelyfocused noise that is generated by a conventionally articulated coaxial rotor system. For stiffened coaxialrotors, this particular inter-rotor blade vortex interaction is weakened as a result of a broad redistributionin lateral loading, yielding a reduction in the intensity of the noise that is produced by this interaction.The spanwise distribution of loading on the rotors of a stiffened coaxial system can be modified furtherby altering the lateral partition of lift (or lift offset). It is shown that decreasing the lift offset has theeffect of counteracting the redistribution of loading due to flapwise stiffness and hence increases the bladevortex interaction noise as well as the power consumed by the rotor. Conversely, a reduction in both thepower consumption and the blade vortex interaction noise is observed if the lift offset is increased, withthe maximum benefit of lift offset being achieved at high speed. The computational results suggest thatthe noise from the dominant inter-rotor blade vortex interaction can be ameliorated through the use of liftoffset control on stiffened coaxial systems, to the extent that the noise produced by this interaction canbe made to be comparable to that produced by the other, weaker interactions between the two rotors ofthe system.

Nomenclature

Symbols:

CMx rotor rolling moment coefficientCP rotor power coefficientCT rotor thrust coefficientMtip tip Mach numberNbt total number of bladesR rotor radiust observer timeyLOS lateral lift offsetΓ circulationµ advance ratio

∗Corresponding author; e-mail: [email protected]

Presented at the American Helicopter Society 65th AnnualForum, Grapevine, TX, 27–29 May 2009. Copyright c© 2009by the American Helicopter Society International, Inc. Allrights reserved.

ν non-dimensionalfirst harmonic flapping frequency

Ω rotor rotational frequencyψ blade azimuth

Abbreviations:

BVI blade vortex interactionLOS lift offsetVTM Vorticity Transport ModelSPL sound pressure level (dB)OASPL overall SPL (dB)BVISPL blade vortex interaction SPL

(mid frequency 5–40/rev) (dB)

Note: throughout this paper, the lower rotor of the coax-ial system should be taken to rotate anticlockwise, and theupper rotor to rotate clockwise, when viewed from above.

1

Introduction

Modern requirements for helicopters with increasedspeed and load-carrying capabilities have promptedseveral novel configurations to be explored. Onesuch approach, put forward by Sikorsky AircraftCorporation and called the ‘X2’ concept, is athrust-compounded, rigid coaxial helicopter. Themain rotor system of the X2 technology demon-strator consists of a twin contra-rotating coaxialrotor that is very stiff in both flap and lag [1]. Asimilar technology, though different in its detaileddesign, was employed in the Advancing Blade Con-cept (ABC) rotor of the Sikorsky XH-59A [2]. Theadvantage of a stiff coaxial system over a conven-tionally articulated system is that, at high forwardspeeds, most of the lift can be carried on the ad-vancing sides of the rotors where the dynamic pres-sure is high. Consequently, the high lift coefficientsassociated with the retreating side of convention-ally articulated rotors can be alleviated within thestiffened rotor system, with consequent benefits forthe power consumption of the rotor. Since the twinrotors counter-rotate, the aerodynamic rolling mo-ment that results from any lateral imbalance in thedistribution of lift on one of the rotors can be coun-teracted by the production of an equal and oppo-site rolling moment by the other rotor of the sys-tem [3–5].

In a previous study [6], the conventionally ar-ticulated coaxial rotor was shown to consume lesspower than the equivalent conventional single ro-tor. This reduction was shown to be mainly dueto a reduction in the induced component of powerthat is consumed by the coaxial rotor compared tothe equivalent single rotor. Furthermore, increas-ing the flapwise stiffness of a coaxial system hasbeen shown to reduce its induced power consump-tion further [7]. There is an added advantage for acoaxial configuration over a conventional main ro-tor – tail rotor configuration in that the need forthe tail rotor is eliminated. This is because the re-quired torque balance is achieved inherently withinthe contra-rotating main rotor system. It should beborne in mind, however, that the additional powerconsumed by the tail rotor in a single rotor plat-form decreases notably as the forward speed is in-creased [8], and also that the drag penalty associ-ated with the enlarged rotor mast of the coaxial ro-tor, particularly for the conventionally articulatedsystem, increases with speed [9].

In terms of acoustic performance, previous stud-ies have suggested that a coaxial rotor generateshigher sound pressure levels than an equivalent sin-gle rotor in level flight [10–12]. This is perhaps un-surprising since coaxial rotors have an additionalsource of noise, compared to single rotor systems,that results from the interaction between the wake

of the upper rotor and blades of the lower rotor ofthe system. Indeed, for the articulated coaxial ro-tor, the most intense impulsive noise is generatedby inter-rotor blade vortex interactions (BVIs) onthe advancing side of the lower rotor [12]. Thenoise associated with these BVIs has been shownto intensify with increasing flight speed due to theincreasing strength of the interaction between thewake of the upper rotor and the blades of the lowerrotor.

Many of the aerodynamic and aeroacoustic at-tributes that are unique to a stiff coaxial systemarise from the manner in which the load is dis-tributed over the rotor discs. The load distributionon a stiff coaxial system is fundamentally differ-ent to that on a conventionally articulated systemin that the loading on the stiff coaxial system isheavily biased towards the advancing sides of itsrotors. As a result, the effective lift vector neednot act through the centre of each rotor of the stiffcoaxial system. The lift offset1 (LOS), can be con-trolled by applying differential cyclic pitch betweenthe upper and the lower rotors [1,2], and the asso-ciated redistribution in loading can be exploited toimprove the performance of the rotor [1]. While itwas initially believed that the power consumptionand stability characteristics of the XH-59A werelargely insensitive to any variation in the lift off-set [2], it was later shown that the efficiency of theX2 rotor could indeed be optimised using lift off-set control [1]. Improvements in the performanceof the X2 rotor at high forward speed, as predictedusing Sikorsky’s design software and reported byBagai [1], should result from increasing the lift off-set and redistributing the loading towards the re-gion of higher incident velocity on the advancingsides of its rotors.

The ability to modify the loading distributionon the rotor by controlling the lift offset offers thepossibility of altering the character of the inter-rotor interaction which is known to be the princi-pal source of noise within the coaxial rotor config-uration. Despite increasing interest in the perfor-mance of coaxial rotor systems, detailed aeroacous-tic analyses, particularly for stiff coaxial systems,are rarely found in the open literature. The aim ofthis paper is to lend insight into the acoustic char-acteristics of a stiff coaxial rotor in forward flight,with specific focus on the effect of flapwise stiffnesson the contribution that is made by the blade vor-tex interactions within the system to the acousticsignature of the rotor. In addition, the sensitiv-ity of the acoustic signature of the coaxial rotor tochanges in its lift offset is investigated.

1Lift offset is defined as the lateral distance between thecentre of rotation of the rotor and the point through whichintegrated effective lift of the rotor acts.

2

(a) Teetering rotor (a) Teetering rotor

(b) Rigid rotor (b) Rigid rotor

Circulation, Γ Blade loading

Figure 1: Distributions of circulation and blade loading on upper and lower rotors of the coaxial system at advanceratio µ = 0.12 and thrust coefficient CT = 0.0048. Teetering and rigid rotors compared.

Computational Model

The Vorticity Transport Model (VTM) developedby Brown [13, 14] has been used to simulate theaerodynamics of the coaxial rotor. In the VTM,the aerodynamics of the rotor blades are modelledusing an extension of the Weissinger-L formulationof lifting-line theory in conjunction with look-uptables for the sectional aerodynamic characteristicsof the blade sections. The equations of motion ofthe blades, as forced by the aerodynamic loadingalong their span, are derived by numerical differen-tiation of a pre-specified non-linear Lagrangian forthe modelled system. The VTM uses an Eulerianrepresentation of the vorticity in the rotor wake,which is advanced through time by solving the in-compressible Navier Stokes equations in vorticity-velocity form on a structured grid surrounding therotor. The problem of numerical diffusion of vor-ticity that is endemic to more conventional CFDtechniques is avoided by explicitly conserving thevorticity within the flow by using this approach.The vorticity transport equation is solved using afinite volume TVD-type scheme which allows theintegrity of the vortical structures in the wake tobe preserved for long times. The VTM is thus ide-ally suited to resolving the detailed features of theinteractions between the upper and lower rotors ofthe coaxial system that are known to be significantsources of noise [7, 12].

The acoustic field generated by the rotor systemis determined using the Farassat-1A formulation

of the Ffowcs Williams-Hawkings equations [15].Since the blade surface is represented by a series ofpanels along the length of the blade, the force con-tributed by each panel is treated as a point acous-tic source at the panel collocation point. The in-stantaneous acoustic pressure at any given observerlocation is then given by the sum of the contribu-tions from all the point sources that are presentin the computational domain. Since the lifting-line model assumes an infinitesimally thin blade,the thickness noise is modelled independently us-ing a source-sink pair attached to each collocationpoint [16]. Noise due to quadrupole sources is ne-glected in the present work. The coupled VTM-acoustics methodology has been used previously topredict the acoustics of the HART II rotor [17],where good agreement between the computed pres-sure time histories and sound pressure levels wasdemonstrated against measured data for three rep-resentative flight conditions involving strong BVIs[18].

Rotor Configuration

The rotor configuration used in this study mimicsthat used by Harrington (referred to as ‘rotor 1’in Ref. 19), which consisted of identical, twin, two-bladed contra-rotating rotors with a teetering hub.Flapwise stiffness in the system is modelled by ap-plying a spring across each of the flapping hingesof the rotor independently. The stiffness of the

3

Table 1: Summary of rotor dimensions

Rotor radius 3.81mRotor speed 37.52 rad/sTip Mach number 0.42

springs is chosen to give the desired natural flap-ping frequency of the rotor blades. To match theflight conditions of the original experiments con-ducted by Dingeldein [20], where the power con-sumption of Harrington’s rotor was measured insteady forward flight, the tip Mach number, Mtip,was set to 0.42. As in the experiment, the ro-tor was simulated at a constant thrust coefficientCT = 0.0048, and, in all cases, the system wastrimmed to zero overall yawing moment using dif-ferential collective pitch input. In all simulatedcases, coupled longitudinal cyclic control inputs tothe individual rotors of the coaxial system wereused to tilt the thrust vector forward in order torepresent the propulsive force required to overcomethe drag of a fuselage with a flat-plate area of 0.02times the rotor area (as was done in Dingeldein’sexperiment).

Two different methods of applying the lateralcyclic pitch input required to trim the coaxial ro-tors were implemented. In the first method, thecyclic pitch inputs to the upper and lower rotor arecoupled such that both rotors receive the same con-trol inputs. The coupled cyclic input is then usedto achieve overall zero lateral force and moment onthe system. The second method uses independent(differential) cyclic pitch inputs to the individualrotors of the coaxial system and is applied exclu-sively to the coaxial rotors with non-zero flapwisestiffness. This method allows the lateral lift offseton the rotors to be controlled whilst still maintain-ing zero overall rolling moment on the system.

In all the analyses presented in this paper, theacoustic sources are scaled to represent the noisethat was generated by the specific rotor that wasused by Harrington and Dingeldein in their experi-ments. The dimensions and relevant operating con-ditions of this rotor are summarised in Table 1.

Effect of Rotor Stiffness onAcoustic Characteristics

The effect of hub stiffness on the acoustic char-acteristics of the coaxial rotor is investigated bycomparing the behaviour of the teetering configu-ration to that of two other rotor systems that aregeometrically identical but have different flapwisestiffnesses. The first case to be considered is that ofthe stiffened system with a flap spring selected togive a natural frequency of the first flapping mode

of 1.5Ω. The second case to be considered is thatof the completely rigid system with infinite flapwisestiffness. The rotor blades themselves are assumedto be rigid in order to simplify the comparison be-tween the various cases that are presented. By thisartifice, any obscuration of the fundamental aero-dynamics that underpin the acoustic behaviour ofthe system that might arise, for instance, from thedetails of mode shapes, is avoided. Furthermore,the chosen values of stiffness have been shown pre-viously to yield reasonable approximations [7] tothe dynamic behaviour of representative full-scalesystems such as the XH-59A [4, 5]. In order to ex-pose the effects of hub stiffness, the acoustic char-acteristics of these stiffened systems are comparedto those of the original teetering configuration asused in Dingeldein’s experiments. Detailed analy-sis of the acoustic properties of the stiffened coaxialrotors in forward flight is limited however to tworepresentative flight speeds (at advance ratios ofµ = 0.12 and 0.24) in order simply to contrast thedifferences in the behaviour of the systems at lowand at high advance ratio.

Consequences for BVI Noise

It was shown in Ref. 7 that stiffening the hub of acoaxial system results in a broad redistribution oflift over the rotor discs (see Figure 1). The load onthe stiffened system is redistributed laterally suchthat the advancing blades carry higher lift (and viceversa for the retreating blades) than when the hubsof the rotors are articulated. As a consequence, thestrengths of the trailed tip vortices of the stiffenedsystem are modified and this results in a subtlydifferent wake structure to that of a conventionallyarticulated system. The change in the strength ofthe vortices is not severe enough to distort the waketo the extent that the positions of the BVIs on therotor discs are affected significantly, however. Thisnotion is supported by the comparison of the BVIpatterns shown in Figure 2 for the rotors with dif-ferent stiffnesses. In this figure, the positions ofthe BVI events in both low and high speed flightare seen to be largely independent of the flapwisestiffness of the hubs of the rotors. More impor-tantly, though, the strengths of these BVIs, par-ticularly of the inter-rotor BVIs on the advancingside of the lower rotor, can be seen to be modified(as indicated by the density of the contour lines)by changing the stiffness of the rotor. The changein strength of the BVIs is a direct consequence ofthe lateral redistribution of loading across the ro-tor disc that arises due to the introduction of hubstiffness.

The relative strength and intensity of these inter-actions has a profound effect on the acoustic signa-ture of the rotor system. The strength of the acous-

4

µ = 0.12 µ = 0.24Upper rotor Lower rotor Upper rotor Lower rotor

(a) Teetering rotor

(b) Rotor stiffened to give first flapping frequency ν = 1.5

(c) Rigid rotor

Figure 2: BVI patterns on the upper and lower rotors of the coaxial system, visualised using contours of inflow.Advance ratio µ = 0.12 (left) and µ = 0.24 (right).

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6

Figure 4: Geometry of the principal inter-rotor BVI onthe advancing side of the lower rotor. Teetering andstiffened rotors compared at advance ratio µ = 0.12.

tic radiation from the rotor is directly related to thetime rate of change in blade loading, and hence therapid changes in loading on the blades due to theblade vortex interactions shown in Figure 2 play animportant role in determining the overall acousticcharacter of the coaxial rotor system.

Figure 3 compares the BVI sound pressure levelthat is observed on a horizontal plane, located 1Rbelow the hub of the lower rotor, for the coaxialsystems of various stiffnesses when operating at ad-vance ratio µ = 0.12. Also shown in Figure 3 is thetime history of the acoustic pressure at the localisedpeaks (acoustic hot spots) on the observer plane asindicated in the diagrams to the left of the figure.It should be noted that, for both the stiffened andthe rigid coaxial rotors, the distribution of acous-tic sound pressure on the plane below the rotorcontains two localised peaks in the observer plane.One peak is directly below the advancing side ofthe lower rotor and the other is below the rear ofthe disc. Interestingly, the hot spots below the ad-vancing side of the lower rotor of the stiffened andthe rigid rotors coincide with the only distinct peakin the acoustic signature of the articulated coaxialrotor, suggesting a common aerodynamic origin forthis feature.

Close examination of the time histories of acous-tic pressure at the hot spot below the advancingside of the lower rotor, as shown in Figure 3, revealsthat the acoustic signal from both the stiffened andthe rigid rotors have a peak that occurs at an ob-server time t = 0.036 s, albeit with much reducedamplitude and impulsiveness compared to a simi-lar peak in the acoustic pressure that is generatedby the teetering configuration at the same observer

time. The highly impulsive peak in the acousticsignal generated by the teetering configuration wasshown in Ref. 12 to be due to a parallel BVI onthe advancing side of the lower rotor. It is clearlyevident in Figure 4, which compares the geometryof this particular inter-rotor BVI for the teeteringand stiffened configurations, that, at the time ofits impingement, the interacting vortex is alignedwith the blade along a large proportion of its span.The change in the strength of this BVI that resultsfrom a change in the stiffness of the rotor can be in-ferred from the density of the contour lines at an az-imuthal location of approximately 45 in Figure 2.The effect on the acoustic signature of the rotorof the weakening of this BVI can be inferred fromthe distribution of acoustic sources on the lowerrotors of both the stiffened and the rigid systems,as shown in Figure 5. This figure shows the sourcedensity of the noise due to blade loading (evaluatedfrom the loading noise term in the Ffowcs Williams-Hawkings equation and scaled by the local panelarea) in ‘source time’ i.e. at the time correspond-ing to the location of the blade when the sound wasgenerated. The distribution of the source densitydefined in this way will of course differ for each ob-server location. The plot is thus generated fromthe perspective of an observer located at the BVIhot spot below the advancing side of the lower ro-tor. The region of concentrated source density atapproximately 45 azimuth that is present for theteetering rotor is not visible in the distributions forthe stiffened rotor and the rigid rotor. Instead, theregion of high acoustic source density is shifted out-board towards the tip region of the advancing side.This is a result of the increased loading gradient inthis region of the rotor disc compared to that of theteetering rotor (see Figure 1). These observationsreveal that the focusing of the distributed acousticpressure to form the sharp peaks in acoustic pres-sure at the hot spot below the advancing side of thelower rotor is a direct consequence of the impulsivenature of the parallel blade vortex interaction onthe advancing side of the lower rotor.

The secondary hot spot that is located below therear of the disc, again for both the stiffened andthe rigid rotors (see Figure 3), originates from theBVI on the retreating side of the lower rotor. Incontrast to the weakening of the vortex that is in-volved in the inter-rotor BVI on the advancing sideof the lower rotor as the stiffness of the system is in-creased, the vortex that interacts with the retreat-ing blade of the lower rotor is strengthened. Thisis because this vortex originates from the advanc-ing blade of the upper rotor where the loading isconcentrated as the rotor is stiffened. As this vor-tex passes the retreating blade of the lower rotor,it yields an intensified inter-rotor BVI compared tothat generated within the teetering rotor system.

7

Lower rotor

(a) Teetering rotor (b) Rotor stiffened to ν = 1.5 (c) Rigid rotor

Figure 5: Acoustic source density (loading noise, Pa/m2) on the lower rotor of the coaxial system as evaluatedat the BVI hot spot directly below the advancing side of lower rotor found at advance ratio µ = 0.12. Also shownas a white line is the locus of sources corresponding to observer time t = 0.037 s, in other words to the time whenthe acoustic peak is observed in Figure 3.

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Figure 6: BVI sound pressure levels (5–40Nbt/rev) in decibels on a plane 1R below the hub of the lower rotor(left) and time history of acoustic pressure over one rotor revolution (right) at the BVI hot spot below the rear ofthe rotor disc. Advance ratio µ = 0.12.

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Figure 7: BVI sound pressure levels (5–40Nbt/rev) in decibels on a plane 1R below the hub of the lower rotor (left)and time history of acoustic pressure over one rotor revolution (right) at the BVI hot spot marked ‘B’. Advanceratio µ = 0.24.

9

Lower rotor

(a) Teetering rotor (b) Rotor stiffened to give ν = 1.5 (c) Rigid rotor

Figure 8: Acoustic source density (loading noise, Pa/m2) on the lower rotor of the coaxial system as evaluated atthe BVI hot spot found at advance ratio µ = 0.24. Also shown as a white line is the locus of sources correspondingto observer time t = 0.05 s (and 0.134 s), in other words to the time when the acoustic peak is observed in Figure 7.

The time histories of the acoustic pressure shownin Figure 6 reveals the peaks that are associatedwith this interaction to occur at an observer timeof t = 0.070 s (and 0.154 s) and to culminate inthe hot spot below the rear of the disc for boththe stiffened rotor and the rigid rotor. It is alsoclear from this figure that the pressure pulse dueto the inter-rotor BVI on the retreating side of thelower rotor is more impulsive in character for thestiffened rotor than it is for the rigid rotor.

It is interesting to note that the relative impul-siveness of the acoustic signature that is predictedfor the stiffened and the rigid rotors is quite differ-ent, as is the maximum sound pressure level at thetwo hot spots below the rotor. Since an increasein the flapwise stiffness in the rotor system acts tobias the loading on the rotors towards the tips oftheir advancing sides, one might expect that thestrengths of the inter-rotor BVIs would be mostextreme in the limiting case of infinite stiffness.The rigid rotor should thus have the weakest acous-tic radiation from the advancing side of the lowerrotor and, similarly, the greatest amplification ofnoise below the retreating side of the lower rotorof the three systems that were examined. In thatrespect, the trends observed above may seem some-what counter-intuitive. It should be borne in mindthough that the strength of a BVI event, and thusthe amplitude of the associated acoustic radiation,is not dependent solely on the strength of the vor-tex that interacts with the blade, but is also sen-sitive to subtle variations in the miss-distance andrelative orientation of the interacting vortex withrespect to the blade. Whilst the assumption of in-finite stiffness yields a reasonable representation ofthe level of stiffness that is achievable in practicalrotor systems, the results presented here indicatestrongly that incorporation of the blade dynamics,

including the structural deformation of the blades,is adviseable in any detailed study of a real heli-copter system in order to capture accurately thesesecondary effects before any concrete conclusionsregarding its acoustic performance are drawn.

It is evident from Figure 7 that, at high advanceratio (µ = 0.24), the direction of propagation ofthe BVI noise is focused along the fore and aft axisof the coaxial system, particularly for the stiffenedrotor and the rigid rotor. The source of this ra-diation is the parallel BVI that takes place whenthe blade is close to the point of maximum inci-dent velocity (at ψ = 90) on the advancing sideof the lower rotor, and its longitudinal directivityis because, during a parallel vortex interaction, theradiation of sound is highly focused in the directionperpendicular to the blade [21,22]. This particularinteraction is responsible for the peaks in the acous-tic pressure that occur at observer time t = 0.05 s,as shown in Figures 7 and 8. For the teetering con-figuration, this peak in acoustic pressure is highlyimpulsive in character. In the case of both the stiff-ened and the rigid systems, as shown in Figure 7,the impulsiveness of this particular inter-rotor BVIis ameliorated through the weakening of the inter-action that results from the offloading of the re-treating sides of the rotors. The reduction in BVInoise that is associated with an increase in hub stiff-ness, of about 2–3 dB as observed on the horizontalobserver plane below the rotor, appears to be rel-atively limited compared to the reduction of 8 dBthat is observed at low advance ratio (µ = 0.12). Itshould be borne in mind though that the effect ofthickness noise becomes significant at high speedsand hence may obscure the interpretation of theoverall acoustic pattern of the system. The signif-icance of the thickness component of the noise isdiscussed in more detail in the following section.

10

(a) Teetering and stiffened rotors compared (b) Stiffened and rigid rotors compared

Figure 9: Geometry of the principal inter-rotor BVI on the advancing side of the lower rotor. Advance ratioµ = 0.24.

The subtle differences in the exact location of thehot spots and in the direction of propagation of theBVI noise that is observed at high advance ratio forthe various rotor systems can be attributed to dif-ferences in the relative orientation of the blades andthe interacting vortices. These differences originatefrom the effect of flapwise stiffness in modifying thedynamic behaviour of the blades, notwithstandingthe fact that the imposed trim conditions on therotor system are identical in all cases. As a result,small differences in the orientation of the blade dur-ing this interaction yield subtle differences in thedirection of noise propagation for the three differ-ent rotor systems. These smll geometric differencesare revealed in Figure 9 which shows the influenceof hub stiffness on the geometry of this particularinter-rotor BVI.

Consequences for Far-Field Noise

The characteristics of the far-field noise radiatedby the rotor can be understood by considering thedistribution of sound pressure on a hemisphericalsurface of radius 2R, centred at the hub of the lowerrotor of the coaxial system. To an observer in thefar-field, this surface can be considered as a hemi-spherical source of sound with the same acousticproperties as the rotor system. Figures 10 and 11show maps of the sound pressure level on this hemi-spherical surface that are generated by the rotorswith the various hub stiffnesses at advance ratiosof µ = 0.12 and 0.24 respectively. At low forwardspeed (µ = 0.12), the distribution of BVI noiseon the hemispherical surface for the range of stiff-nesses shown in Figure 10 is entirely consistent withthe distribution of sound pressure on the horizon-

tal observer plane shown in Figure 3. The signifi-cant reduction in the maximum far-field BVI noiseof approximately 7 dB for the stiffened rotor and8 dB for the rigid rotor compared to that of theteetering configuration is also consistent with thedistribution of sound pressure on the horizontal ob-server plane described earlier.

Interpretation of the far-field noise for the highspeed case requires more care since Doppler am-plification causes the contribution from thicknessnoise to become more significant as flight speedis increased. This is shown clearly in Figure 12where, at high speed (µ = 0.24), a significant dif-ference between the total BVI noise and the com-ponent due to loading is apparent. At low speed(µ = 0.12), however, there is no notable differencebetween the total BVI noise and the loading noise.Indeed, when the thickness component of noise isincluded in the analysis at high speed, the point ofmaximum BVI sound pressure level lies within theplane of the rotor. Figure 11 hence shows only theloading component of the BVI sound pressure levelon the hemispherical surface in order to allow anunbiased representation of the BVI noise character-istics in the far-field. The change in the directivityof the BVI noise towards the front left of the rotoris consistent with the change in the directivity ob-served on the horizontal observer plane as shownin Figure 3.

The maximum overall sound pressure level onthe hemispherical surface, at both µ = 0.12 andµ = 0.24, does not appear to be affected signifi-cantly by the introduction of stiffness into the rotorsystem (see Figure 12). This suggests that, despitethe significant reduction in the BVI noise that isachieved by increasing the hub stiffness, the sig-

11




Figure 10: BVISPL in decibels on a hemispherical surface of radius 2R centred on the hub of the lower rotor.Advance ratio µ = 0.12. (Left: isometric view. Right: top view.)

12




Figure 11: Loading noise BVISPL in decibels on a hemispherical surface of radius 2R centred on the hub of thelower rotor. Advance ratio µ = 0.24. (Left: isometric view. Right: top view.)

13

60

65

70

75

80

85

90

95

100

105

Teetering Stiff 1.5Ù Rigid

Ma

xim

um

SP

L(d

B)

OASPL (Total noise)

OASPL (Loading noise)

BVISPL (Total noise)

BVISPL (Loading noise)

(a) µ = 0.12 (Note that in Ref. 12, the loading OASPLand BVISPL noise for an equivalent single rotor werefound to be 92.9 dB and 72.7 dB respectively.)

60

65

70

75

80

85

90

95

100

105

Teetering Stiff 1.5Ù Rigid

Ma

xim

um

SP

L(d

B)

OASPL (Total noise)

OASPL (Loading noise)

BVISPL (Total noise)

BVISPL (Loading noise)

(b) µ = 0.24 (Note that in Ref. 12, the loading OASPLand BVISPL noise for an equivalent single rotor werefound to be 94.3 dB and 64.4 dB respectively.)

Figure 12: Comparison of maximum OASPL and BVISPL (of total noise and loading noise only) in decibels ona hemispherical surface of radius 2R centred on the hub of the lower rotor.

nificance of the low harmonic noise increases also,thus offsetting to a certain extent the benefits ofstiffening in terms of overall sound pressure level.The results presented above suggest, however, thatthe intensity and directivity of the noise that is pro-duced by the inter-rotor BVIs could quite feasiblybe altered by careful partition of the loads betweenthe upper and lower rotors of the stiffened coax-ial system. Furthermore, individual rotor controlin the context of stiffened coaxial systems, for ex-ample by using differential cyclic pitch inputs asdescribed in the following section of the paper, isknown to offer significant flexibility in controllingthe load distribution on the rotors and may poten-tially also be exploited to alter the low harmonicacoustic characteristics of the coaxial system.

Effect of Lateral Lift Offset

The results of the computational results presentedabove suggest that a marked reduction in the BVInoise that is produced by the coaxial rotor mightresult from the introduction of significant flapwisestiffness into the system. This reduction appearsto be a direct result of the weakening of the in-teraction between the lower rotor and the wake ofthe upper rotor wherein the principal inter-rotorBVI that is responsible for a significant propor-tion of the acoustic radiation from the system isreduced in its severity. This weakening occurs prin-cipally because the tip vortex that is trailed fromthe retreating blade of the upper rotor is reducedin strength due to the offloading of this part of therotor that results from the introduction of flapwisestiffness into the system. The marked reductionof the intensity of the BVI noise that results fromthis change in the loading distribution on the ro-

tor leads to the speculation that it might be possi-ble to modify further the acoustic characteristics ofthe stiffened coaxial rotor by exacerbating the lat-eral asymmetry of the loading distribution on theupper rotor. In a stiffened coaxial rotor system,the lateral distribution of loading on the rotors canbe modified readily, while still maintining overalllateral trim, by applying a differential cyclic pitchinput to the upper and lower rotors of the system.

The lift offset is defined as the lateral distancebetween the centre of the rotor and the point ofapplication of the lift vector of the rotor. Hence,for a rotor producing a rolling moment, CMx, andoverall thrust, CT , the lift offset, yLOS , measuredas a fraction of the rotor radius, R, is simply

yLOS = CMx/CT . (1)

The effect on the acoustic properties of the stiff-ened coaxial rotor of changing the lateral distribu-tion of loading on the rotors has been investigated.The effective lateral lift offset of the stiffened coax-ial system has been controlled by applying indepen-dent lateral cyclic control inputs to the upper andlower rotors of the system in order to modify therolling moment generated by each rotor whilst stillmaintaining an overall trim condition of zero netrolling moment. The results presented henceforthare obtained by altering the lift offset by approxi-mately 20% to either side of the baseline value thatwas obtained when using coupled cyclic control toboth the upper and the lower rotors. The baselinevalues of the lift offset, as measured from the simu-lations presented in the previous section, are foundto be dependent on the flight speed. For both thestiffened rotor and the rigid rotor, the baseline liftoffsets are measured as yLOS = 0.14R and 0.29Rat advance ratios of µ = 0.12 and 0.24 respectively.

14

0

0.0001

0.0002

0.0003

0.0004

Stiff 1.5Ù Rigid Stiff 1.5Ù Rigid

Co

effic

ien

to

fP

ow

er,

CP

LOS -20%

Baseline

LOS +20%

ì =0.12 ì =0.24

0

0.0001

0.0002

0.0003

0.0004

Stiff 1.5Ù Rigid Stiff 1.5Ù Rigid

Po

we

rC

oe

ffic

ien

t,C

P

?

? Profile components

?

Figure 13: The effect of lift offset on the power con-sumption of the stiffened coaxial rotor and the rigidcoaxial rotor in forward flight.

All other aspects of flight condition and trim aremaintained exactly as those of the simulations pre-sented in the previous section.

Figure 13 shows the influence of lift offset on thepower consumed by the stiffened and the rigid coax-ial systems. At both high and low forward speed,the power consumed by the rotors is seen to re-duce as the imposed lift offset is increased. Theresults presented in this figure are consistent withpreviously published work [1] that has suggestedthat increasing the lift offset might improve the effi-ciency of the stiffened coaxial rotor. The reductionin power is found to be greater at the higher ad-vance ratio where a reduction of approximately 8%is predicted if the lift offset is increased by 20%.It is interesting to note, though, that the reduc-tion in the overall power consumption observed inthis figure originates almost exclusively from a re-duction in the induced power consumption of therotor. In fact, the VTM suggests that the profilecomponent of power should increase somewhat asthe lift offset is increased, particularly at higherforward flight speeds.

Beyond illustrating the favourable effects on ro-tor performance of increasing the lift offset, furtheranalysis of cause and effect will be avoided heresince such a discussion would digress too far fromthe acoustic focus of this paper. The results pre-sented in this section do raise the question, how-ever, as to whether the imposition of significant liftoffset might have the same positive effect on theacoustic characteristics of the stiffened coaxial sys-tem as it appears to have on its performance. Thisaspect is discussed in detail in the next section ofthis paper.

Acoustic Characteristics

Figure 14 summarises the influence of lift offset onthe maximum sound pressure level that is observedon the horizontal plane located 1R below the hubof the lower rotor. At low advance ratio (µ = 0.12),the maximum sound pressure level that occurs onthe observer plane appears to be relatively insensi-tive to changes in the lift offset. At high advance ra-tio (µ = 0.24), however, a notable sensitivity of themaximum sound pressure levels to the imposed liftoffset is observed. It is interesting to note thoughthe opposing trends in the overall sound pressurelevel (OASPL), which increases with increased liftoffset, and the BVI sound pressure level (BVISPL),which decreases with increased lift offset. This ap-pears to be due to a secondary effect which is dis-cussed later.

The major source of noise in the mid-frequencyrange, as identified in the previous section of thepaper, is the inter-rotor BVI that occurs on the ad-vancing side of the lower rotor. Figure 15 shows thechanges in the lateral distribution of blade loadingon the upper and lower rotors of the coaxial sys-tem that result from altering the lift offset. It isapparent from the figure that, as the effective liftis offset further outboard towards the tip of theadvancing side of the disc, the lateral distributionof loading on the rotor is modified such that theloading peak on the advancing side is increased inamplitude. The tip loading on the retreating side,on the other hand, is shown to be reduced as aresult of this change in the lift offset. The tip vor-tex trailed from the retreating blade of the upperrotor is thus reduced in strength (as is the equiva-lent vortex trailed from the retreating blade on thelower rotor). Bearing in mind that the vortex thatis associated with the principal sound-generatinginteraction is trailed from the tip of the retreatingblade on the upper rotor of the system, this chainof cause and effect conspires to ameliorate the load-ing component of the BVI noise by weakening theprincipal inter-rotor BVI when the lift offset is in-creased.

Figure 16 shows the effect of lift offset on theacoustic source density on the lower rotor and re-veals that the acoustic source at the location ofmaximum sound pressure level is concentrated atthe location of the principal BVI. It is also evidentin this figure that the region of high acoustic sourcedensity on the lower rotor is increasingly confinedto the BVI location as the lift offset is reduced.

Figure 14 shows that the overall sound pressurelevel (OASPL) also increases as the imposed lift off-set on the system is increased. Figure 17 shows theeffect of lift offset on the time history of the acousticpressure observed at the point of maximum soundpressure on the observer plane 1R below the rigidcoaxial rotor at advance ratio µ = 0.24. The signal

15

100

102

104

106

108

110

112

LOS -20% Baseline LOS +20%

OA

So

un

dP

ressu

reL

eve

l(d

B)

ì =0.24

ì =0.12

Stiff (1.5Ù) - Total Noise

Stiff (1.5Ù) - Loading Noise

Rigid - Total Noise

Rigid - Loading Noise

(a) OASPL

78

82

86

90

94

98


BV

IS

ou

nd

Pre

ssu

reL

eve

l(d

B)

ì =0.24

ì =0.12



Rigid - Total Noise


(b) BVISPL

Figure 14: Effect of lift offset on maximum SPL as observed on a horizontal plane 1R below the hub of the lowerrotor.

(a) LOS -20% (b) Baseline (c) LOS +20%

Figure 15: Effect of controlling the lift offset on the azimuthal variation of blade loading for the rigid coaxial rotorat advance ratio µ = 0.24. The distribution is sectioned to expose more clearly the effect of lift offset on the lateraldistribution of loading on the upper and lower rotors.

plotted in this figure has been filtered to containonly the first ten harmonics of the rotor rotationalfrequency. It is clear from this figure that the peakto peak variation in the low harmonic component ofthe acoustic pressure signal is increased by increas-ing the lift offset and vice versa. This observationcould perhaps have been inferred from Figure 15where the maximum blade loading was shown toincrease as a larger lateral lift offset is imposed onthe rotors.

As was done in slightly different context earlierin this paper, the effect of lift offset on the radi-

ation of noise to the far-field can be estimated bycalculating the acoustic pressure on a hemisphereof radius 2R centred at the hub of the lower rotor.The effect of lift offset on the maximum sound pres-sure levels observed on this hemispherical surfaceis summarised in Figure 18. A striking similarity inthe trend shown in this figure to that observed onthe horizontal plane 1R below the rotor (as shownin Figure 14) is clearly apparent. This is a strongindication that the influence of lift offset on thenoise produced by the rotor has the same physicalorigins as the effect of stiffness as described earlier

16

Lower rotor

(a) LOS -20% (b) Baseline (c) LOS +20%

Figure 16: Acoustic source density (loading noise, Pa/m2) on the lower rotor of the rigid coaxial system asevaluated at the BVI hot spot at advance ratio µ = 0.24.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16−10

−5

0

5

10

15

Observer Time, (s)

Aco

ustic

Pre

ssur

e (P

a)

LOS −20%BaselineLOS +20%

t

Figure 17: Time history of acoustic pressure over onerevolution of the rigid coaxial rotor, as observed at theBVI hot spot at advance ratio µ = 0.24. Acoustic signalfiltered to include only the first 10 harmonics of therotor rotational frequency.

in the paper.The greatest sensitivity to the imposed lift off-

set, as shown in Figure 18, is seen in the loadingcomponent of the BVI noise at high advance ratio.Furthermore, it is only at this advance ratio thata significant disparity between the total noise andloading noise is observed. This is because the effectof the thickness component of noise becomes signif-icant at high speeds. The thickness noise, however,is propagated primarily within the plane of the ro-tor. The loading noise is directed primarily out ofthe plane of the rotor, and hence has greater signif-icance for the overall acoustic signature of the rotorsystem. Figure 18 thus suggests that an effectivereduction in BVI noise of about 2 dB is achievable,at least for the present rotor configuration, by in-creasing the lift offset by 20%.

On the other hand, the maximum BVI noise levelfor the stiffened coaxial rotor increases, though onlyby about 0.5 dB, when the lift offset is increased by20% at advance ratio µ = 0.24. This rise in theBVI noise level is somewhat unexpected consider-ing that an increase in lift offset acts to weaken theinter-rotor BVI that is primarily responsible for theacoustic radiation of the system, as described ear-lier. Figure 19, which shows the effect of lift offseton the distribution of loading noise within the BVIfrequency range, reveals the hemispherical observersurface to contain two acoustic hot spots (marked‘B’ and ‘B2’), however. Figure 20, showing thetime history of acoustic pressure at the hot spotsmarked ‘B’ together with the density of acousticsources on the lower rotor for the two cases pre-sented in Figure 19, reveals that the acoustic sig-natures that are associated with the two differenthot spots are significantly different in character andthus most likely are caused by distinctly differentmechanisms. The highly impulsive nature of thepressure peaks shown in Figure 20(a) is indicativeof their origin in an intense BVI within the rotorsystem whereas the much less impulsive nature ofthe peaks shown in Figure 20(b), although similarin amplitude to those of Figure 20(a), suggests thattheir origin is to be found in a BVI of lesser inten-sity. Indeed, the former, more intense interaction iscaused by the direct, parallel impact of tip vortexon blade that is associated with the primary BVIon the advancing side of the lower rotor. Closerinvestigation reveals the latter, less intense interac-tion to be induced by a slightly earlier interactionbetween the same blade and the vortex sheet thatis generated inboard of the tip vortex that is asso-ciated with the primary BVI. These observationscan be confirmed as follows.

In Figure 20(a), the locus of sources, correspond-ing to the observer time at which the largest peak in

17

96

99

102

105

108


OA

So

un

dP

ressu

reL

eve

l(d

B)

ì =0.24

ì =0.12



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(a) OASPL

78

82

86

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94

98


BV

IS

ou

nd

Pre

ssu

reL

eve

l(d

B)

ì =0.24

ì =0.12



Rigid - Total Noise


(b) BVISPL

Figure 18: Effect of lift offset on maximum SPL as observed on a hemispherical observer surface of radius 2Rcentred on the hub of the lower rotor.

(a) Baseline (sound pressure at ‘B’ is 80.2 dB and at ‘B2’ is 78.9 dB)

(b) LOS +20% (sound pressure at ‘B2’ is 78.7 dB and at ‘B’ is 80.7 dB)

Figure 19: Loading noise BVISPL (in decibels) on a hemispherical surface of radius 2R centred on the hub ofthe lower rotor. Coaxial system stiffened to ν = 1.5 with different lift offsets at advance ratio µ = 0.24. (Left:isometric view. Right: top view.)

18

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16−4

−2

0

2

4

6

8

Observer Time, (s)

Aco

ustic

Pre

ssur

e (P

a)


t

(a) Baseline (locus of sources on right corresponds to observer time t = 0.063 s)

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16−4

−2

0

2

4

6

8

Observer Time, (s)

Aco

ustic

Pre

ssur

e (P

a)


t

(b) LOS +20% (locus of sources on right corresponds to observer time t = 0.034 s)

Figure 20: Time history of acoustic pressure over one rotor revolution (left) and the acoustic source density(loading noise, Pa/m2) on the lower rotor of the coaxial system stiffened to ν = 1.5 (right) for different lift offsetsat advance ratio µ = 0.24. Both plots as evaluated at the BVI hot spot marked ‘B’ in Figure 19.

the acoustic pressure occurs, is indicated as a whiteline on the plot of the acoustic source density. Theresulting locus for the baseline rotor is very similarto that shown in Figure 8 and confirms that theparallel inter-rotor BVI shown in Figure 9 is theprincipal source of noise at the hot spot marked‘B’ in Figure 19(a).

In contrast, the broad range of azimuth that isoccupied by the region of high source density shownin Figure 20(b), for the case of increased lift off-set, is consistent with the non-impulsive charac-ter of the peak observed in the time history con-tained in the same figure. The locus of sources,corresponding to the observer time at which thispeak occurs, is positioned at an azimuth of approx-imately ψ = 40 on the lower rotor of the coaxialsystem. Figure 21 shows the rotor and its wake atthe corresponding instant and reveals the blade ofthe lower rotor to be interacting closely with the in-board vortex sheet that is generated behind one ofthe blades of the upper rotor. The weakness of this

vortex sheet compared to its associated tip vortexand the almost tangential orientation of the sheetto the trajectory of the blade results in a weaker,more prolonged interaction that is consistent withthe acoustic source distribution that is shown inFigure 20(b).

As the lift offset is increased, the strength of theprimary inter-rotor BVI is reduced to such an ex-tent that this particular interaction is no longer themost significant contributor to the maximum BVIsound pressure level that is observed on the hemi-spherical observer surface. Indeed, Figure 20 showsthat although the two hot spots (marked ‘B’ and‘B2’) are located at approximately the same posi-tion regardless of lift offset, the hot spot associatedwith the parallel interaction (‘B’ in Figure 19(a))is the more intense in the baseline case whereas thehot spot associated with the sheet interaction (‘B’in Figure 19(b)) is the more intense when the liftoffset is increased.

These observations show that it might indeed be

19

Figure 21: Close passage interaction between a bladeof the lower rotor and the vortex sheet shed by a bladeof the upper rotor. Stiffened system at advance ratioµ = 0.12.

possible to exploit lift offset to reduce the acousticsignature of the stiffened coaxial rotor system, butalso caution that the benefits of such a strategymay be limited by the emergence of other, per-haps unforseen but nonetheless inherent interac-tions within the system as the dominant contrib-utor to the acoustic characteristics of the system.

Conclusions

The aeroacoustic characteristics of a coaxial ro-tor with significant flapwise stiffness are computedusing the Farassat-1A formulation of the FfowcsWilliams-Hawkings equation coupled to the Vor-ticity Transport Model and compared to those ofa conventionally articulated coaxial rotor both inlow speed and in high speed forward flight.

The most prominent source of impulsive noise ina conventionally articulated coaxial rotor system isa strong, parallel interaction which occurs betweenthe blades on the advancing side of the lower ro-tor and the tip vortices that are generated by theblades on the retreating side of the upper rotor.

Introduction of significant flapwise stiffnessyields a marked reduction in the BVI noise thatis produced by the coaxial system. This is a directconsequence of the weakening of the principal inter-rotor BVI as a result of the broad redistribution inlateral loading on the upper rotor that accompa-nies the introduction of flapwise stiffness into thesystem. This weakening occurs simply because thetip vortex that is associated with the primary inter-action is reduced in strength as the blades on the

retreating side of the upper rotor are offloaded. Theintroduction of significant flapwise stiffness into therotor system that was studied yields a reduction inmaximum BVI sound pressure level, as measuredon a hemispherical surface located two rotor radiifrom the rotor hub, of approximately 7–8 dB at ad-vance ratio µ = 0.12, and 6–11 dB at advance ratioµ = 0.24.

The spanwise distribution of loading (i.e. the liftoffset) on the rotors of a stiffened coaxial systemcan be modified by differential cyclic pitch input.It is shown that increasing the lift offset producesa notable reduction in both the power consumedby the rotor and also the BVI noise, particularly athigher advance ratio. Simulations of a rigid coax-ial system suggest that a reduction of about 2.1 dBin the BVI noise and 6.8% in power consumptionmight result from increasing the lift offset by 20%from the nominal baseline value at advance ratioµ = 0.24. The effectiveness of lift offset in reducingthe acoustic signature of the rotor at high forwardspeed is constrained, however, because an interac-tion between the blades of the lower rotor and thesheets of vorticity that are trailed from the inboardparts of the blade of the upper rotor replaces theparallel BVI on the advancing side of the lower ro-tor as the dominant source of noise within the sys-tem.

The results presented in this paper thus showthat it might indeed be possible to exploit lift off-set to reduce the acoustic signature of the stiffenedcoaxial rotor system, but also caution that the ben-efits of such a strategy may be limited by the emer-gence of other, perhaps unforeseen but nonethelessinherent interactions within the system as the dom-inant contributor to the acoustic characteristics ofthe system.

It should also be borne in mind that, while theassumption that the dynamics of the stiffened coax-ial system can be characterised using a flap springin conjunction with otherwise rigid rotor bladesmight yield a reasonable global representation ofthe overall aeroacoustic characteristics of the rela-tively generic coaxial rotor modelled in this study,direct application of the results presented here toreal helicopter configurations may have to await theincorporation of a structural dynamic model to ac-count more fully and accurately for the flexure ofthe blades.

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18Kelly, M.E., Duraisamy, K., Brown, R.E.,“Blade Vortex Interaction and Airload Predic-tion using the Vorticity Transport Model,” Amer-ican Helicopter Society Specialists’ Conference onAeromechanics, San Francisco, CA, 23–25 January2008.

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kim, hyo wan and duraisamy, karthikeyan and brown, richard ... · eﬀect of rotor stiﬀness and...

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