Kim, H.W. and Duraisamy, K. and Brown, R.E. (2008) Aeroacoustics of a coaxial rotor in level flight. In: 64th American Helicopter Society Annual Forum, Montreal, Canada. http://eprints.gla.ac.uk/5004/ Deposited on: 11 March 2009

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Aeroacoustics of a Coaxial Rotor

in Level Flight

Hyo Won Kim∗ Karthikeyan Duraisamy Richard BrownVisiting Researcher Lecturer Mechan Chair of Engineering

Rotorcraft Aeromechanics Laboratory

Department of Aerospace Engineering

University of Glasgow

Glasgow G12 8QQ

United Kingdom

Abstract

The aeroacoustic characteristics of a coaxial system with teetering rotors in level forward flight are com-pared to those of an equivalent articulated single rotor with the same solidity. A lifting line representationof the blade aerodynamics is coupled to Brown’s Vorticity Transport Model to simulate the aerodynam-ics of the rotor systems. The acoustic field is determined using the Ffowcs Williams-Hawkings equation.Acoustic analysis shows that the principal contribution to noise radiated by both the coaxial and equivalentsingle rotor systems is at the fundamental blade passage frequency, but that the coaxial rotor generateshigher sound pressure levels (by 10 dB for the evaluated configurations) than the equivalent single rotorat all flight speeds. The sources of blade vortex interaction (BVI) noise are investigated and the principalBVI events are identified. For the coaxial rotor, the most intense impulsive noise is seen to be generatedby the inter-rotor BVI on the advancing side of the lower rotor. The impulsive noise that is generated byblade vortex interactions for the equivalent single rotor reduces in amplitude as the strength of BVI eventson the rotor decreases with forward speed. Conversely, the BVI noise of the coaxial rotor intensifies withincreasing flight speed due to the increasing strength of the interaction between the wake of the upper rotorand the blades of the lower rotor. The impulsive noise due to BVI for the coaxial rotor is found to be higherby 20–35 dB compared to the equivalent single rotor. The overall and impulsive noise characteristics ofthe coaxial system are found to be weakly sensitive to changes in rotor separation and the relative phasingof the rotors.

Nomenclature

Symbols:

CP rotor power coefficientCT rotor thrust coefficientF force vectorM Mach numberR rotor radiusa0 speed of soundpL acoustic pressurer observer distance from sourcet timeµ advance ratioτ acoustic source timeψ blade azimuth

∗ Postgraduate Research Student, Imperial College Lon-don, United Kingdom

Presented at the American Helicopter Society 64th AnnualForum, Montreal, April 29 – May 1, 2008. Copyright c© 2008by the American Helicopter Society International, Inc. Allrights reserved.

Abbreviations:

BVI blade vortex interactionSPL sound pressure level (dB)OASPL overall SPL (dB)BVISPL blade vortex interaction SPL

(mid frequency 5–40/rev) (dB)

Important note: throughout this paper, the lower rotor ofthe coaxial system should be taken to rotate anticlockwise,and the upper rotor to rotate clockwise, when viewed fromabove. In single rotor simulations, the rotor should be takento rotate anticlockwise when viewed from above.

Introduction

A recent resurgence of interest in the coaxial rotorconfiguration has been prompted by its potential tomeet modern requirements for helicopters with in-creased speed and load carrying capabilities. Theobvious advantage of a coaxial rotor over a con-ventional main rotor-tail rotor configuration is the

elimination of the need for a tail rotor as the re-quired torque balance is achieved inherently withinthe contra-rotating main rotor system. This ap-pealing advantage of contra-rotating twin coaxialrotors prompted some of the early rotorcraft pi-oneers to exploit the configuration, yet, the sin-gle main rotor-tail rotor configuration remains theprevailing platform for most military and civil he-licopters.

There has been a significant research interest inthe characteristics of coaxial rotor aerodynamics inseveral countries including Russia, the US, the UKand Japan (see Ref. 1). Unfortunately, most of theexisting literature has failed to provide a truly faircomparison of the relative performance of conven-tional and coaxial rotors. A recent study has ar-gued that the fairest comparison between conven-tional and coaxial rotors is on the basis of equal so-lidity, and identical overall blade number and aero-dynamic properties. On this basis the coaxial rotoris shown to consume less power, mainly due to itsslightly lower consumption of induced power com-pared to the equivalent single rotor (Ref. 2). Theadvantage of the coaxial rotor system in terms ofreduced power requirement was shown to be en-hanced by the introduction of significant flapwisestiffness (Ref. 3). Additionally, compared to sin-gle rotor systems, coaxial rotors with significantflapwise stiffness can operate at lower tip speedsthan the equivalent articulated system, thus offer-ing the potential to postpone the detrimental ef-fects of compressibility on aerodynamic and acous-tic performance to higher forward speeds (Ref. 4).

While the aerodynamic characteristics of coaxialrotors are not as well studied as those of conven-tional rotors, detailed investigations of the acousticperformance of coaxial rotors are even more rare inthe open literature. In the early 1980s Peterson andMosher (Ref. 4) conducted a full scale wind tunnelexperiment on Sikorsky’s XH-59A rotor. In thistest, acoustic measurements were obtained over arange of rotor lift coefficients, advance ratios andshaft angles. The conclusions from this study werethat the noise level of the coaxial system increaseswith loading on the rotor and as the shaft angleapproaches zero just as observed in the case of atypical single rotor. The microphone array usedin the experiment was too sparse to reveal anydetail of the acoustics radiation pattern that wasgenerated by the rotor but some anomalies in themeasured data were attributed to impulsive effects.Blade vortex interaction (BVI) noise was specu-lated to be influenced by the distribution of liftbetween the upper and lower rotors but unfortu-nately, within the scope of the experiment, no firmconclusions could be drawn on the effect of inter-actions between the upper and lower rotors andtheir consequences for the resulting acoustic char-

acteristics of the coaxial system. More recently,Boyd et al. (Ref. 5) provided a numerical com-parison between the acoustic signature of a Bo105model rotor that was similar to the rotor used inthe HART II experiments described in Ref. 6, anda fictitious coaxial system, consisting of two Bo105rotors contra-rotating about the same axis. Thewakes of the rotors were approximated by a systemof single tip vortices. In this comparison, it wasfound that the coaxial system generated higher BVInoise compared to the single rotor system. It wasalso observed that the interference effects betweenthe upper and lower rotors of a coaxial system hada significant effect on its resulting acoustic char-acter. Based on comparisons against experimentalresults from the HART II rotor test (Ref. 6), it wasconcluded, however, that a vortex filament modelmay not have been accurate enough to representthe wake to the detail required for accurate acous-tic predictions.

Aeroacoustics is a rapidly maturing disciplineand its application to helicopter rotors is a veryactive field of research (refer to Ref. 7 for a reviewof recent accomplishments). Coaxial rotor systemsgenerally do not seem to have been subject to de-tailed aeroacoustic study, however. The aim of thispaper is to compare the aeroacoustic characteris-tics of a coaxial rotor system with those of an aero-dynamically equivalent, conventional single rotor.Since a significant part of the lower rotor of thecoaxial system operates in the wake of the upper ro-tor, additional noise associated with the inter-rotorBVIs (which do not occur on a single rotor) can beexpected, and a detailed study of these interactionsand the associated noise produced by a coaxial ro-tor operating in forward flight is presented.

Computational Model

Aerodynamics

The Vorticity Transport Model (VTM) developedby Brown (Ref. 8) and extended by Brown andLine (Ref. 9) is used for the aerodynamic compu-tations presented in this paper. In the VTM, aWeissinger-L version of lifting line theory is used(along with a look-up table for the two-dimensionalaerodynamic characteristics of the rotor blade sec-tions) to represent the blade aerodynamics in con-junction with an Eulerian representation of the dy-namics of the vorticity in the rotor wake. The con-vection algorithm implemented in the VTM is par-ticularly effective in controlling the local rate ofnumerical dissipation of vorticity, allowing the in-tegrity of vortical structures in the rotor wake to bepreserved for many rotor revolutions. The use ofan adaptive grid system in a semi-Lagrangian man-ner to track the evolving vorticity field enhances

the computational efficiency of the method. Theoverall cell count is reduced by using a sequence ofnested grids in which increasingly coarser cells arearranged with increasing distance from the rotor.In this respect, the VTM is thus particularly wellsuited to resolving the wake-induced interactionsbetween the twin main rotors in the coaxial config-uration, and hence the sources of acoustic radiationwithin the system.

Acoustics

The acoustic field of the rotor system is deter-mined using the Ffowcs Williams-Hawkings equa-tion (Ref. 10). The instantaneous acoustic pres-sure, pL(t), at a given observer location due to adiscrete point force F moving at Mach number M ,is given by

pL(t) =1

4πa0

[∂

∂t

(Fr

r(1−Mr)

)+

a0Fr

r2(1−Mr)

]

τ(1)

where a0 is the speed of sound, r is the distancebetween the observer and the source, Fr = F · r,and Mr = M · r. The term in the square bracket isevaluated at the source time τ at which the soundwas emitted. The integral in Eq. 1 is implementednumerically using the Farassat-1A formulation inwhich the source time derivatives are transformedto observer time derivatives (Refs. 7, 11). Sincethe blade surface in the aerodynamic model is rep-resented by a series of panels, the force contributedby each panel is treated as a point source locatedat the collocation point of the panel. The noiseproduced by these sources is then propagated ac-cording to Eq. 1. The aerodynamic effects of thethickness of the blade are introduced through alook-up table of airfoil characteristics, but the lift-ing line model within the VTM otherwise assumesan infinitesimally thin blade. The thickness noiseis thus modelled independently using a source-sinkpair attached to each panel along the length ofthe blades (Ref. 12). Noise due to quadrupoleterms is neglected in the present work. The cou-pled VTM-acoustics methodology has been usedpreviously to predict the acoustics of the HARTII rotor (Ref. 13), where good agreement betweenthe computed pressure time histories and soundpressure levels was demonstrated against measureddata for three representative flight conditions in-volving strong BVIs.

Rotor Configuration

Model Geometry

The rotor configuration used in this study mim-ics that used by Harrington (referred to as ‘rotor

1’ in Ref. 14), consisting of two identical articu-lated two-bladed rotors that contra-rotate aboutthe same axis. The rotor blades are untwisted andhave symmetrical NACA four-digit airfoil sections.While the blade planform has a linear taper, thethickness along the span of the blade changes ina non-linear fashion. The span of the rotor bladefrom the centre of rotation to the tip is 3.81m andthe overall solidity of the coaxial rotor is σ = 0.054.The upper and lower rotors are separated verticallyby 19% of the rotor radius.

Unlike in the original experiments described inRefs. 14 and 15 (and also in Ref. 5), where com-parisons of the performance of the coaxial rotorwere made against one of its own constituting ro-tors, in this work, aerodynamic and acoustic com-parisons are made against a suitably defined singlerotor with equal solidity and the same blade ge-ometry as the coaxial rotor. This allows for anacoustic comparison between two systems in whichthe rotor blades operate within a comparable aero-dynamic environment. Thus, bearing in mind thatthe coaxial rotor consists of two two-bladed rotors,the equivalent single rotor consists of four co-planarblades. To match the original experimental setup,the hubs of the coaxial rotor are modelled to have ateetering configuration while the equivalent singlerotor is given a fully articulated hub. It should benoted that the loading distribution on coaxial ro-tors with articulated hubs, and hence their acous-tic behaviour, can be significantly different to thatwhen rotor has some degree of hub stiffness. Theeffects of hub stiffness on the acoustic properties ofthe coaxial system are not considered in this paper,however.

Trim Method

The trim algorithm implemented in the VTM isa first-order dynamical system where the rate ofchange of the control inputs are driven by the differ-ence between prescribed target values of the rotorforces and moments and their instantaneous val-ues. A more detailed account of the trim model canbe found in Ref. 3. In all cases considered in thepresent study, the coaxial rotor system is trimmedto zero net moment in yaw using differential collec-tive pitch input to the upper and lower rotors whilstsatisfying a pre-specified thrust requirement. Thecyclic pitch inputs to the upper and lower rotorare coupled so that both rotors receive the samecontrol inputs. The coupled cyclic input is usedto tilt the thrust vector forward in order to gener-ate a propulsive force while maintaining zero lat-eral force on the system. Although the fuselage isnot explicitly modelled, the effect of the fuselageon the propulsive force required from the rotor isrepresented by the drag of a flat plate with an area

0

0.001

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0.007

0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006

Power Coefficient, C p

Th

rustC

oe

ffic

ien

t,C

T

Coaxial Rotor (Experiment)

Coaxial Rotor (VTM)

Equivalent Rotor (VTM)

(a) Hover, Mtip = 0.45

0

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Advance Ratio, ì

Po

we

rC

oe

ffic

ien

t,C

P

Coaxial Rotor (Experiment)

Coaxial Rotor (VTM)

Equivalent Rotor (VTM)

(b) Steady forward Flight, CT = 0.0048, Mtip = 0.42

Figure 1: Comparison of predicted power consumption of coaxial rotor against experimental measurements inhover and forward flight.

of 2% of the rotor disc area to follow the approachthat was adopted in Dingeldein’s experiment.

The equivalent single rotor is trimmed to thesame overall forces and moments as the coaxial ro-tor system at the same forward speed thus yieldinga fair comparison between the performance of thetwo systems.

Aerodynamic Verification

The experimental measurements of the powerconsumption of Harrington’s ‘rotor 1’ inhover (Ref. 14) and in forward flight (Ref. 15)provide a valuable set of data against which toassess the ability of the VTM to predict theaerodynamic performance of coaxial rotors.

Figure 1 shows a comparison between this dataand the power consumption of the coaxial rotor aspredicted by the VTM. The predictions of the VTMcorrelate well with the experimental results in bothhover and forward flight. While the trend withinthe experimental data is well captured, the powerrequirement of the coaxial rotor in forward flight isslightly under-predicted by the VTM.

Figure 1 also compares the power consumptionof the coaxial and equivalent single rotor systemsand shows that the coaxial rotor consumes slightlyless power than the equivalent single rotor in al-most all flight conditions. The reduction in power ismost pronounced at high thrust in hover and at lowforward flight speeds. The majority of the powersaving on the coaxial rotor originates from a reduc-tion in the induced component of power that comesabout through the subtle redistribution of loadingon the rotor disc that results from localised interac-tions between the upper and lower rotors (Ref. 2).

The observed agreement between the predictedperformance of the coaxial rotor system againstthis well-regarded set of experimental data lends

confidence in the ability of the VTM to providethe acoustic model with a reliable loading patternon the rotors from which the sound radiation fromthe system can be computed with some confidence.

Acoustic Analysis

Detailed analysis of the acoustic characteristics ofthe coaxial rotor and the equivalent single rotorin forward flight is limited to two representativeflight speeds (advance ratios of µ = 0.12 and 0.24)in order simply to contrast the differences in thebehaviour of the system at low and high advanceratios. Figure 2 shows the structure of the respec-tive wakes in forward flight at these advance ratios.The gross features of the far wakes of both configu-rations are superficially very similar at the low ad-vance ratio: both wakes clearly show the helicoidalindividual blade vortices to roll up to form a pairof large ‘super-vortices’ some distance downstreamof the rotor disc. There are, however, interactionalaerodynamic features in the coaxial system that arenot found on the conventional rotor. In particu-lar, the complex manner in which the tip vorticesfrom the upper and lower rotors interweave in thegap between the two rotors leads to a complicatedpattern of inter-rotor BVIs that are obviously notencountered with the conventional system. The tipvortex dynamics during the formation of the super-vortices of the coaxial system is also considerablymore complicated than for the conventional rotor— as can be seen, the individual tip vortices fromthe upper and lower rotors wind around each other,at least at this advance ratio, to form a single pairof super-vortices rather than, as might be imagined,forming two distinct structures, one for each rotor.As shown in Fig. 2(b), this interaction is counter-acted to a certain extent at the higher advance ratioby the forward tilt of the rotor. This tilt, together

(a) Advance ratio µ = 0.12

(b) Advance ratio µ = 0.24

Figure 2: Overall wake structure in forward flight visualised by a surface of constant vorticity. (Left: equivalentsingle rotor. Right: coaxial rotor. Coaxial rotor: Wake from upper rotor shaded darker than that from the lowerrotor.)

with the increased convection rate of the vorticityin the wake, acts to maintain the separation be-tween the wakes that are produced individually bythe upper and lower rotors until significantly fur-ther downstream.

Overall Noise Characteristics

Figure 3 shows a contour plot of the overall soundpressure level (OASPL) that is produced on a hor-izontal observer plane located at a distance of onerotor radius below the hub1 by the coaxial rotorand its equivalent single rotor at an advance ratioof µ = 0.12. The noise levels are seen to peak ata sequence of ‘hot spots’ that are located directlyunderneath the tips of the rotor discs. Figures 4and 5 show the time history and frequency spec-trum, respectively, of the acoustic pressure at thehot spot at the rear edge (at ψ = 0◦) of each of therotor systems. As is typical of measured acousticdata from conventional helicopters in both modeland flight tests (e.g. Refs. 6 and 16), the majorcontribution to the noise produced by the equiv-alent single rotor is at very low frequencies (lessthan five times the blade passage frequency). Atthe corresponding locations of maximum noise on

1For the coaxial system, the observer plane is located onerotor radius below the hub of the lower rotor.

the observer plane, the SPL of the coaxial rotor isfound to be around 10 dB higher than that of theequivalent single rotor. This trend appears to per-sist for all advance ratios between µ = 0.12 andµ = 0.24.

Figure 4 shows that the noise due to the lowerrotor of the coaxial system is highly impulsive evenat the location of maximum overall noise. Cor-respondingly, it is evident from Figure 5 that thenoise of the coaxial rotor is distributed over a muchwider range of frequencies than that produced bythe equivalent single rotor. Similarly though to thesingle rotor, the main contribution to the noise pro-duced by the coaxial rotor is at low frequency. It isworth noting that the low frequency noise is relatedto the low harmonic airloads on the rotor blades.Impulsive noise that is radiated to the ground, onthe other hand, is primarily caused by wake in-teractions. In a coaxial rotor system, interactionsbetween the wake produced by the upper rotor andthe blades of the lower rotor act as an additionalsource of noise that is not present in a single ro-tor system. Given the focus of this paper on theacoustics of coaxial rotor systems, further discus-sion will concentrate on the high frequency noisethat is associated with these BVIs.

x/R

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Figure 3: Overall SPL in decibels in forward flight at µ = 0.12. (Direction of flight along positive y-axis.)

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ustic

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ssur

e (P

a)

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(b) Coaxial rotor

Figure 4: A time history of acoustic pressure over one rotor revolution one rotor radius below the tip of the rotordisc at ψ = 0◦ for µ = 0.12.

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102

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ure

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l (dB

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(b) Coaxial rotor

Figure 5: Frequency spectrum of the sound pressure level one rotor radius below the tip of the rotor disc at ψ = 0◦

for µ = 0.12. The vertical dotted line represents the fundamental blade passage frequency.

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Figure 6: BVI sound pressure levels (5–40/rev) (in dB) at µ = 0.12.

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Figure 7: BVI sound pressure levels (5–40/rev) in decibels for individual rotors in coaxial configuration at µ = 0.12.

BVI Noise Characteristics

The contour plots presented in Fig. 6 (and also inFig. 11) contrast the distribution of SPL on the ob-server plane in the BVI frequency range (computedby aggregating the acoustic energy in the Fouriermodes ranging from 5/rev to 40/rev) for the equiv-alent single rotor and coaxial rotor.

For the equivalent single rotor at an advance ra-tio µ = 0.12 (Figure 6(a)), two BVI hot spots areevident on the observer plane. One of these is sit-uated directly below the advancing side of the ro-tor and the other below the retreating side. Sucha radiation pattern is typical of a single rotor inforward flight (Refs. 6, 13). It is well recognisedthat the dipole nature of the loading noise resultsin a propagation of sound that is directed primar-ily downwards (Ref. 16). The hot spots are thuspositioned roughly beneath the corresponding po-sitions on the rotor where the BVI sources are mostintense, that is, where the combination of miss-distance and alignment of the passing vortices re-sults in the strongest impulsive loads on the rotorblades.

For the coaxial rotor (Figure 6(b)), the highestsound pressure is concentrated under the advancingside of the lower rotor. The sound pressure levelat the hot spot (marked by a circle in the Figure)is appreciably higher (by 16 dB) than the highestsound pressure level generated by the equivalentsingle rotor (Figure 6(a)) at this flight condition.

Figure 7 shows the separate contributions fromthe upper and lower rotors to the noise generatedby the coaxial rotor. The figure shows the lowerrotor to be the dominant source of noise on the ob-server plane below the rotor, as might be expectedfrom the additional wake interactions to which thelower rotor is subjected. This inference is sup-ported by Figure 8 in which the time history ofthe acoustic pressure at the hot spot on the ad-vancing side of the lower rotor is shown over onerotor revolution. The two highly impulsive peaks inthe acoustic pressure correspond to identical eventson each of the two blades of the lower rotor of thecoaxial system. The origin of these impulses canbe understood by considering the distribution ofthe acoustic sources on the blade over a single rev-

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ssur

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Figure 8: Time history of acoustic pressure at the BVI hot spot (see Figure 6) for coaxial rotor.

524028164

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(a) µ = 0.12

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Figure 9: Acoustic source density (loading noise, Pa/m2) on lower rotor of coaxial system as evaluated at theBVI hot spot. Also shown (as a white line) is the locus of sources corresponding to time t = 0.036s in (a) andt = 0.049s in (b)

(a) Overall structure (b) Tip vortex from one blade of upper rotor

Figure 10: Tip vortex structure of coaxial rotor at µ = 0.12 showing inter-rotor BVI via parallel impingement.

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Figure 11: BVI sound pressure levels (5–40/rev) in decibels at µ = 0.24.

olution of the lower rotor. Figure 9(a) shows thedensity of the noise sources due to loading (eval-uated from the loading noise term in Eq. 1 andscaled by the local panel area) in ‘source time’ i.e.corresponding to the location of the blade when thesound was generated. It should be noted that thedistribution of source density will of course differfor each observer location. The plot is thus gener-ated from the perspective of an observer located atthe BVI hot spot below the advancing side of thelower rotor. Furthermore, the plot is constructedfrom the sources located on only one of the blades.Also indicated in Figure 9(a) (as a thick white line)is the locus of all the sources that contribute to thenoise at the specific observer time (at t = 0.036sin Figure 8(a)) corresponding to the peak in im-pulsive noise. It is evident that the intense inter-action at the azimuthal location of ψ ≈ 45◦ (corre-sponding to the locus of sources contributing to thenoise at t = 0.036s) is responsible for the impulsivenoise. Figure 10(a) shows the overall structure ofthe wake at the instant at which one of the bladesof the lower rotor is at an azimuth of ψ = 45◦. InFig. 10(b) some of the detail of this plot is sup-pressed to show the specific inter-rotor BVI thatis responsible for the impulsive noise. It is evidentthat during this BVI, the blade on the lower rotorpasses directly through the axis of a trailing vortexfrom the upper rotor. Furthermore, the trailingvortex is essentially parallel to the blade span atthe time of impingement, thus generating a highlyimpulsive incident velocity field over a significantportion of the blade span.

At higher advance ratio (µ = 0.24), the char-acter of the BVI acoustic pattern generated by theequivalent single rotor is somewhat different to thatobserved at lower advance ratio. The hot spot un-der the advancing side shifts towards the front ofthe rotor disc (to approximately ψ = 170◦ as shown

Figure 12: A rotor blade of the equivalent single rotorat µ = 0.24 interacting with tip vortex from precedingblade at ψ ≈ 170◦. Trailed vorticity generated by thisblade is shaded dark to highlight secondary trailing vor-ticity generated by this interaction.

in Figure 11). The primary origin of the noise atthis hot spot is an oblique blade vortex interactionas shown in Figure 12. Even though the BVI is notparallel, the prolonged interaction (from ψ ≈ 90◦

to 270◦) generates high intensity noise. Interest-ingly, the figure also shows secondary trailing vor-tices that are generated as a result of the abruptchanges in loading along the span of the blade thatare induced by the BVIs. The pattern of BVIs onthe rotor disc at this advance ratio is somewhatsparser than at lower advance ratio. Indeed, theincreasing forward tilt of the rotor disc with for-ward speed that is required to provide the propul-sive component of force on the system increasesthe miss-distance between the wake vortices and

Figure 13: Tip vortex structure from the upper rotor ofthe coaxial system impinging on an advancing lower ro-tor blade showing parallel inter-rotor BVI at µ = 0.24.

the blades and thus acts to weaken the strength ofindividual BVI events.

On the other hand, the BVI induced sound pres-sure level on the observer plane for the coaxial rotorhas the same qualitative pattern at high advanceratio as observed at lower forward flight speed. Thelocation of the hot spot moves further inboard asshown in Figure 11(b), but the highly impulsivepeaks in the time history of the acoustic pressureseen for µ = 0.12 persist at µ = 0.24 (see Fig. 8).The amplitude of the peaks in the acoustic pres-sure at high forward speed are significantly largerand occur slightly later than at low forward speed,however. The high intensity BVI that is evident atan observer time of t = 0.049s corresponds to thesource time indicated by the white line (at roughlyψ = 80◦) on the plot of decomposed noise sourcesdue to loading shown in Figure 9(b). The impulsivenoise field appears to be dominated by a BVI eventthat occurs as one of the rotor blades approachesthe azimuth at which it experiences maximum in-cident velocity. Figure 13 captures the wake struc-ture at instant at which one of the blades of thelower rotor is at an azimuth of ψ = 80◦. The fig-ure shows the blade to be interacting strongly witha tip vortex that is generated from the upper ro-tor. As at lower forward speed, the axis of theinteracting vortex lies almost parallel to the blade,resulting in a highly impulsive change in loadingalong its span and significant acoustic radiation.

Even though the intensity of the BVIs on theequivalent single rotor reduces with forward speed,the BVI sound pressure level on the observer planeone radius below the rotor is significantly higherfor both rotors at µ = 0.24 than at µ = 0.12. Thisseeming anomaly in the case of the equivalent rotor

is a result of the dominance of the near field con-tribution to the loading noise (the second term inEq. 1). Furthermore, the noise from the equivalentsingle rotor is less impulsive when compared to thecoaxial rotor.

Far-Field Noise

In the following discussion, sound pressure levelson a hemispherical observer surface of radius 2R,centered at the rotor hub (in the case of the coaxialrotor, at the hub of the lower rotor) are considered.This representation of the acoustic field generatedby the rotor is useful for purposes of interpretingfar-field acoustics as the surface can roughly be con-sidered as a hemispherical source of sound with thesame acoustic properties as the rotor at its centre.Figure 14(a) shows the maximum SPL (OASPL)on the hemisphere at three forward flight speeds.For both the coaxial system and the equivalent sin-gle rotor, the rate of increase of the OASPL withflight speed is roughly similar although the coaxialrotor is consistently noisier by approximately 8 dB.

For the equivalent single rotor, the contributionof the BVISPL to the overall SPL increases sig-nificantly as the advance ratio is increased fromµ = 0.12 to 0.16 as shown in Figure 14(a). Onthe other hand, Figure 14(b) shows the loading-induced component of noise in the BVI range to re-duce with increasing flight speed. This trend arisesfrom the increased disc tilt that is required to gen-erate the propulsive force at higher speeds as de-scribed earlier. The increase in the impulsive noisein the BVI range of frequencies in Figure 14(a) forthe equivalent single rotor is thus due to intensifi-cation of thickness noise at higher flight speeds.

As explained in the previous section, for thecoaxial system, the inter-rotor BVIs are intensi-fied as the forward speed is increased. Indeed,Figure 14(b) shows a rapid increase in the load-ing noise within the BVI frequency range as flightspeed is increased. Figure 15 shows the associatedcontours of SPL mapped on to the hemisphericalobserver surface at various forward speeds for thecoaxial rotor. Note that in this case, the hemi-spherical surface extends above the level of thelower rotor hub by 0.2R to capture the in-planepropagation of noise from this rotor as the forwardspeed is increased. The directivity of the far-fieldnoise, as observed in this figure, shifts towards thefront of the rotor. This is because of the primaryBVI occurring at a later azimuth as the speed offlight is increased. A similar trend in directivity ofimpulsive far-field noise, though at a reduced SPL,was observed for the equivalent single rotor.

0.12 0.14 0.16 0.18 0.2 0.22 0.2460

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Figure 14: Maximum OASPL and BVISPL in decibels at Mtip = 0.42 on a hemispherical observer surface ofradius 2R, centered on the rotor hub.

Implications ofMinor Design Changes

Since BVI noise propagates in the direction of theground, the high BVI noise levels generated by thecoaxial system in comparison to the equivalent sin-gle rotor may work against the certification androutine use of coaxial rotor helicopters. For theconfiguration evaluated in this work, the intenseimpulsive noise that is generated by the coaxialrotor has been shown to be primarily due to theinter-rotor blade vortex interaction on the advanc-ing side of the lower rotor. There is, however, acertain amount of design flexibility inherent in thecoaxial system for instance, rotor separation andblade phasing, that may be optimised to alter thisinteraction, with the aim of alleviating impulsivenoise. In order to gain a nominal assessment ofthe sensitivity of the noise radiated by the coaxialsystem to such design changes, two representativeconfigurational modifications to the original coax-ial system were performed:

First, a change of blade phasing was considered.The original configuration was such that the bladesof the top and bottom rotors were aligned with eachother at azimuthal angles of 0◦, 90◦, 180◦ and 270◦.This phasing was altered, such that blade over-passage was shifted to 45◦, 135◦, 225◦ and 315◦.

Second, an increase in rotor separation was con-sidered. The vertical separation between the topand bottom rotors was set to 0.247R, amountingto an increase of 30% compared to that of the orig-inal configuration.

Figure 16 shows the effect of these design changeson the BVI sound pressure levels (at µ = 0.12) ona horizontal plane one rotor radius below the hubof the lower rotor. This figure should be comparedto Fig. 6(b). The change in rotor phasing does notaffect the maximum sound pressure levels and ap-

pears simply to shift the location of the BVI hotspot. This is an important result since it suggeststhat the intensity of BVI noise produced by thecoaxial system may not be sensitive to rotor phas-ing. Although the results are not shown here, theoverall noise levels were also found to be unaffectedby rotor phasing. The four OASPL hot spots, how-ever, were found to be 45◦ out of phase with thoseshown in Figure 3(b). The increased rotor sepa-ration causes a decrease of 2 dB in the maximumBVI sound pressure level. The weight, drag andstructural dynamic penalties of the elongated mastmay not be justified for such a marginal reductionin noise levels.

Conclusions

In this study, the aeroacoustic characteristics of acoaxial rotor in forward flight is compared to thoseof a suitably defined aerodynamically equivalentsingle rotor.

In the intermediate far-field (less than two rotorradii from the rotor disc), the main contributionto the noise generated by both the coaxial and theequivalent single rotor systems is at the fundamen-tal blade passage frequency. The coaxial rotor ex-amined is this study is consistently noisier than theequivalent single rotor by approximately 10 dB. Asexpected, the noise generated by the coaxial rotorexamined in this study is highly impulsive, princi-pally as a result of blade-wake interactions on thelower rotor.

The BVI loading noise for the equivalent singlerotor reduces with increasing forward speed as thedisc tilt required to provide the propulsive forcecomponent to the system increases the miss dis-tance between blades and vortices and reduces thestrength of individual BVI events. The BVI noiseof the coaxial rotor is intensified due to the increas-

(a) µ = 0.12

(b) µ = 0.16

(c) µ = 0.24

Figure 15: BVISPL in decibels for coaxial rotor on a hemispherical surface of radius 2R centered on the hub ofthe lower rotor. (Left: isometric view. Right: top view.)

x/R

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Figure 16: BVI sound pressure levels (5–40/rev) (in dB) for coaxial rotor with design changes at µ = 0.12.

ing strength of the interaction between a tip vortexfrom the upper rotor and the advancing blade ofthe lower rotor with increasing forward speed. Theimpulsive noise due to BVI on a hemispherical sur-face that is located two rotor radii from the rotorhub is about 20–35 dB higher for the coaxial rotorthan for the equivalent single rotor, depending onthe forward speed of the rotor.

The higher BVI noise of coaxial rotor helicopters,may ultimately hinder routine use in civilian andmilitary applications, but it may be possible to op-timise the design of the rotor to mitigate the noiselevels.

A change of blade phasing between the upperand lower rotors had a marginal effect on the noisecharacteristics of the coaxial system. An increase of30% in the separation distance between the upperand lower rotors similarly resulted in a marginaldecrease in overall and BVI noise, suggesting therelative insensitivity of the configuration to suchstrategies.

References

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4Peterson, R.L., Mosher, M., “Acoustic Measure-

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13Kelly, 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.

14Harrington, R.D., “Full-Scale-Tunnel Investiga-tion of the Static-Thrust Performance of a CoaxialHelicopter Rotor,” NACA TN-2318, March 1951.

15Dingeldein, R.C., “Wind-Tunnel Studies of thePerformance of Multirotor Configurations,” NACATN-3236, August 1954.

16Schmitz, F.H., “Aeroacoustics of Flight Vehi-cles: Theory and Practice,” NASA Reference Pub-lication 1258, Vol. 1, Chapter 2, August 1991,pp. 65–149.