Modelling of Aerodynamic Interactionsin

Compound Helicopters

Carlos Santos SousaUndergraduate Student of Aerospace Engineering

Instituto Superior TécnicoTechnical University of Lisbon

November 2010

Abstract

The prediction of aerodynamic interactions has been shown to earn careful consideration in helicopterdesign because of their consequences to the handling qualities, dynamics and performance. Underforward flight condition at moderate advance ratio, aerodynamic interactions may manifest as highlevels of vibration and noise or as large nose-up pitching moments acting on the helicopter. To examinethese effects, a generic coaxial helicopter with a hingeless hub and rigid blades is investigated in forwardflight. This helicopter model is compounded in propulsive thrust by a tail-mounted propulsor and isrepresentative of modern helicopters. The correct prediction of the detailed evolution of the vortexstructures within the helicopter rotor wake is essential for the analysis of aerodynamic interactions. Thisis properly addressed by using lifting-line theory coupled to an Eulerian Vorticity Transport Model tocompute the vorticity generation at the rotor blades and its subsequent evolution. It consists in a finitevolume boundary-free model that solves the vorticity equation and circumvents the problem of excessivenumerical diffusion of vorticity that limits standard CFD-based techniques. Numerical simulations onseveral combinations of the components that constitute the helicopter model were carried out andtheir aerodynamic behaviour was compared against the results for the full helicopter in order to betterunderstand the origins and effects of the interactional phenomena. It is shown that the effects of someaerodynamic interactions present can be directly ascribed to a particular event like the impingement ofthe main rotor wake into another component while others may manifest in a more subtle way, like themutual interaction between the wakes generated by different rotors or the displacement of the mainrotor wake caused by an airframe component.

Notation

R rotor radiusΩ rotor rotational speedµ advance ratio~V∞ freestream velocity vectorvi inflow velocity~w wake-induced velocity vectorΓ matrix of vortex loop strengthsK trim coupling matrix~ζ vorticity vector~S vorticity source vector~CF vector of force and moment coefficientsCF rotor force coefficientsCM rotor moment coefficientsCW helicopter weight coefficientCD helicopter drag coefficient

CT rotor thrust coefficientCP rotor power coefficient~θ vector of control inputsθ0 collective pitch angleθ1s sine cyclic pitch angleθ1c cosine cyclic pitch angle

subscripts/superscripts

u upper rotor` lower rotorp propulsorx, y, z components of the orthonormal

Cartesian spaceb bladeav long term average∗ trim target

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Introduction

Conventional single rotor helicopters are often lim-ited in forward flight as a result of asymmetric flowconditions encountered by the rotor. On the ad-vancing side of the rotor, the blades rotate forwardand so the air speed experienced by a blade is aresult of its rotational speed together with the for-ward flight speed of the aircraft. In the retreatingside the rotational speed and forward speed sub-tract. Therefore a blade travelling in the advancingside will generate higher lift than in the retreatingside, giving rise to a rolling moment. The solutionadopted by the conventional helicopter is to imple-ment flap hinges, allowing the blades to move outof the plane of rotation and preventing the rollingmoment to transmit to the hub and fuselage. How-ever this causes the rotor disk (tip path plane) totilt rearwards. The typical solution is to feed theblades with cyclic pitch such that the lift is reducedin the advancing side and increased in the retreat-ing side. The amount of cyclic pitch must increasewith forward speed in order to counteract the re-ward tilt of the rotor disk. However, it is limitedby the stall of the root sections of the retreatingblades. Hence, conventional helicopters could nottake the full advantage of the lift potential of theadvancing side and, at the same time, they requirelift from the retreating side which is less capableof supplying it. Another limitation on the perfor-mance of the conventional helicopter at high for-ward speed arises from the compressibility effectsat the tip of the advancing blades.

Significant increase in the forward flight speedand improvements in the performance were suc-cessfully achieved by the compound helicopter. Itdeparts from the conventional helicopter in that itrelies in extra surfaces for the generation of lift, likewings and rotors, and extra devices for the genera-tion of propulsion, like propellers or turbojets. Thelift provided by the extra surfaces allows the mainrotor to be unloaded, thus alleviating the retreat-ing blade limitation. The propulsion generated bythe auxiliary devices is also beneficial since it maycontribute for a reduction of the required disk andfuselage tilt for a given forward speed and as a re-sult a reduction of the required cyclic pitch.

One way to eliminate the problem of blade stallthat limits the forward speed of a helicopter is touse two counterrotating rotors in a coaxial arrange-ment. A survey on the coaxial rotor research inseveral countries from the early 50’s up to the 90’sis given in Ref. [1]. From all the coaxial rotor sys-tems that have been investigated, the AdvancingBlade Concept (ABC) rotor is given special em-phasis in this paper, and is described in detail in

Ref. [2]. The ABC development started in 1964and was tested on the XH-59A research helicopterbuilt by Sykorsky Aircraft Corporation, with thefirst prototype flying in 1973. It consists in a twincounterrotating coaxial main rotor system. The ro-tor blades are very stiff and are rigidly attachedto the rotor hub, using only pitch bearings, whicheliminates the natural tendency of the rotor disksto tilt rearwards. Instead, the rotors will gener-ate large rolling moments about the hub. Sincethe coaxial rotors rotate in opposite directions, itis possible for each rotor to generate rolling mo-ments that are equal and opposite, thus not affect-ing roll trim. The ABC rotor is designed to carrylarge rolling moments and so the retreating bladescan be unloaded, thus alleviating the problem ofblade stall, while the lift generated by the advanc-ing blades can be increased, taking advantage ofthe lifting capability of the advancing blades. TheABC rotor also provides substantially higher con-trol power than conventional single rotors, whichleads to higher manoeuvrability.

Since the two counterrotating rotors alone canprovide means for yaw control of the aircraft, thetail rotor no longer is required to provide torquereaction. Thus, the helicopter can be further com-pounded in propulsive thrust by replacing the con-ventional tail rotor with an auxiliary propulsion de-vice. This device further contributes to unload themain rotor system allowing for a reduction in therotational speed of the main rotor and thus delayingthe compressibility effects on the advancing bladesto higher forward speeds. The Sykorsky’s X2 re-search helicopter implements such concepts. It uti-lizes a pusher propeller at the tail to augment thepropulsion provided by its ABC rotor.

Although the compound helicopter has remark-able performance capabilities, the development ofprototype helicopters have been hampered by un-predictable aerodynamic interactions between theirvarious components, leading to continued designchanges. For instance, at a particular forward flightspeed range the main rotor wake my interact withthe horizontal tailplane causing a sudden and highnose-up pitching moment to act on the aircraft,which may have a large effect in the trim of theaircraft. Aerodynamic interactions may thus havea negative impact on the performance of the heli-copter, and are responsible for unsatisfactory flightdynamics and handling qualities, high vibrationand noise.

The ability to accurately and reliably predict theaerodynamic interactions between the several com-ponents of the helicopter remains to be achievedand is a topic of current research. However, com-putational programs for helicopter rotor wake mod-elling have progressed to a stage where some as-

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pects of these interactions can be modelled to anappreciable degree of realism, Ref. [3]. In par-ticular, the Vortex Transport Model (VTM) is aCFD technique that simulates the vorticity domi-nated aerodynamic environment of the rotor wakedirectly as a time-dependent vorticity distributionsurrounding the helicopter. It utilizes the vorticity-velocity formulation of the Navier-Stokes equa-tions, hence allowing more control of the effects ofnumerical diffusion of vorticity. The VTM tech-nique is described in some detail in Ref. [4].

This paper aims to investigate the aerodynamicenvironment of a compound coaxial helicopter im-plementing an ABC-type main rotor system and anauxiliary tail mounted propeller in forward flightwith advance ratio of 0.15. This investigation com-prises a quantification and characterization of themost significant aerodynamic interactions betweenthe various components of the helicopter and itsconsequences to their loading distribution and per-formance. In order to identify the processes in-volved in the aerodynamic interactions betweenthe main rotor, fuselage and propulsor, the aero-dynamic characteristics of several combinations ofthese components are compared.

Description of the SimulationModel

Helicopter Geometry

The geometry of the helicopter is presented in fig-ure 1. It was designed to be representative of mod-ern compound coaxial helicopters like the X2 re-search helicopter.

Figure 1: Geometry of the simulation model in-cluding a generic ABC-type coaxial rotor and a tailpropulsor.

Although the main rotor and propulsor hubswere not modelled computationally, they are rep-resented in the drawing of figure 1 for geometrical

clarity. The helicopter is comprised of a stream-lined fuselage and horizontal tailplane, a twin coax-ial main rotor and an auxiliary propeller mountedat the tail of the helicopter.

Main Rotor System

The main rotor consists of two rotors of equal char-acteristics placed in a coaxial configuration. Thelower rotor rotates clockwise and the upper rotorrotates anti-clockwise, when viewed from above.The main rotor has a solidity of 0.127, equivalentto the solidity of the XH-59A helicopter. The up-per and lower rotors are separated from each otherby 0.139R, where R denotes the main rotor radius.Each rotor is composed of three blades. Each bladeis designed with linear taper and -10° of non-lineartwist and its airfoil section is a NACA 23012. Theblades are modelled as rigid and are rigidly at-tached to the hub, except for feathering motion.The geometric properties of the main rotor are sum-marized in table 1.

Table 1: Main rotor and propulsor characteristics

Main rotor PropulsorRadius 5.5 m 0.28R

Nr. of rotors 2 1

Nr. of blades 3 per rotor 5

Root cut-out 0.12R 0.20Rp

Twist −10° −30°

Chord Tapered (2 : 1) 0.18Rp

Airfoil NACA 23012 NACA 0012

The main rotor blades are modelled computa-tionally according to the Weissinger L-method, tobe described in section .

Auxiliary Propulsor

The auxiliary propulsor consists of a five-bladedpusher propeller and is mounted at the tail of thehelicopter such that its axis is aligned with the lon-gitudinal axis of the fuselage. Each blade has -30°of linear twist and no taper. The airfoil section usedfor each blade was a NACA 0012. The rotationalspeed of the propulsor is 4.25 times that of eachrotor of the coaxial system. Like with the mainrotor, the blades of the propulsor are modelled asrigid, with only feathering motion. The geometricproperties of the propulsor are summarised in table1.

The modelling of the propulsor blades in thecomputer follows the same method used for the

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main rotor blades, and is described in section .

Fuselage and TailplaneThe shape of the fuselage was designed to be simi-lar to that of modern compound coaxial helicopterslike the XH-59A or the X2 research helicopters.The fuselage is rigid and includes two side pods anda horizontal tailplane, which was rigidly attachedto its tail. A summary of the geometric propertiesof the fuselage is given in table 2. The horizontaltailplane features a NACA 0012 airfoil along its en-tire span and has no twist or taper. The tailplanewas placed such that its chord is parallel to thehorizontal plane, x− y.

Table 2: Fuselage geometric properties

Fuselage length 2.04R

Fuselage maximum width1 0.1891`

Tailplane span 0.3201`

Tailplane chord 0.0835`

Shaft inclination angle 4° (forward)

Coordinates2 of:

Lower rotor hub x 0.3825`

Lower rotor hub z 0.1930`

Upper rotor hub z 0.2610`

Propulsor hub x 1.0395`

Propulsor hub z 0.0555`

1Excluding tailplane.2Relative to fuselage nose.

Both fuselage and tailplane are modelled as a setof discrete triangular or quadrilateral panels. Eachpanel represents a closed loop of vorticity and eachsegment of a panel forms a vortex filament of con-stant strength. Then the velocity at the centroidof each panel may be decomposed into two contri-butions: the velocity induced by any vortex fila-ments and the velocity induced by any other vor-ticity within the flow, ~w. The vorticity strength ofeach vortex loop is set to satisfy the boundary con-dition of zero normal flow across the solid surfaceand at the centroids of the respective panel. Thiscondition yields the following system of equations,(

~V∞ + ~w)i· ~ni +

N∑j=1

aijΓj = 0, (1)

for i = 1, . . . , N , and where the aij are knowninfluence coefficients and Γj are the vortex loopstrengths that are to be computed at each com-putational time step.

For a lifting body, in addition to the N equationsgiven by (1) applied to all the panels, another con-dition must also be satisfied in order to fix the pre-cise value of the circulation around the body. Thisis the Kutta condition, which is satisfied along theentire trailing edge of the tailplane. Note, however,that the viscous wake of the non-lifting componentsof the configuration is not modelled at present.

Computational ModelThe evolution of the flow past the helicopter andits aerodynamic response has been simulated usinga coupled lifting-line – Vorticity Transport Model(VTM). This model is comprehensively explainedin Ref’s. [5, 4]. The VTM solves a form of themomentum equation alone, known as the vorticityequation, on a Cartesian grid surrounding the heli-copter. This model assumes the flow to be inviscid,and the vorticity, ~ζ, generated by the rotor bladesis modelled as a local source of vorticity, ~S. Then,the equation of vorticity may be expressed as

∂~ζ

∂t+(~V · ∇

)~ζ =

(~ζ · ∇

)~V + ~S. (2)

According to this equation, vorticity is first gen-erated locally by numerically defined surfaces im-mersed within the fluid and is evolved through athree-dimensional computational domain under theaction of the local velocity field. Hence, the prob-lem can be conceptually divided in two parts. Thefirst part is the model of the evolution of the ro-tor wake in a computational grid as described byequation (2) and the second part is the model ofthe blade aerodynamics that provides the vorticitysource to be interpolated into the aforementionedcomputational grid.

The blade aerodynamics are modelled with amodified version of the Prandtl lifting-line theory,known as the Weissinger L-method, Ref. [6]. Themethod consists in dividing each blade into a fi-nite number of discrete panels along its span. Eachpanel represents a horseshoe vortex with the boundvortex positioned at the 1/4-chord. For each timestep the blade rotates within the flow and a new rowof spanwise panels consisting of trailed and shedvorticity is created in a fixed position relative tothe trailing edge of the blade. This process is re-peated at each time step, thus generating a vortexlattice that is allowed to convect by the local flowvelocity.

At each time step the local flow velocity, ~Vb,is calculated for each blade panel at a collocationpoint positioned at the 3/4-chord. Then the no-flow penetration condition is imposed at each col-location point, which forces the velocity componentnormal to the blade at those points to be zero. This

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results in a set of simultaneous equations that canbe solved for the bound vorticity over the blade, ~ζb,and the strength of the trailed and shed vorticityproduced over that time step. This, in turn, can beexpressed as the source term of equation (2),

~S = −d~ζbdt

+ ~Vb∇ · ~ζb (3)

where the first term on the left hand side representsthe shed vorticity and the second term the trailedvorticity.

Trim ModelThe trim algorithm implemented in the VTM is re-sponsible for the equilibrium of forces and momentswithin the system, such that the helicopter is capa-ble of maintaining its steady level flight condition.Thus, it consists in the process of continuously ad-justing the control inputs during the numeric sim-ulation and so it can be summoned in the form ofa first order dynamic system,

d~θ

dt= ~f

(~θ)

(4)

where ~θ is the vector of pitch inputs given by

~θ =[θu0 , θ

u1s, θ

u1c, θ

`0, θ

`1s, θ

`1c, θ

p0

]T(5)

and ~f is a vector valued function that gives a linearrelationship between the rate of change of the con-trol inputs and the instantaneous resultant forcesand moments acting on the system,

~f = K(~C∗F − ~CF

). (6)

The matrix K is a 7 × 6 coupling matrix and isintroduced in [7] (although not taking into accountthe propulsor control input). The vector ~C∗F con-tains the prescribed target load coefficients on thevehicle, given by

~C∗F = [−CD, 0, CW , 0, 0, 0]T (7)

where ~CF represents the vector of overall aerody-namic force and moment coefficients that are pro-duced by the rotors and other lifting components,and may be written as

~CF = [CFx , CFy , CFz , CMx , CMy , CMz ]T . (8)

and the weight coefficient CW is fixed at 0.012 andCD = 0.00072 based on an equivalent flat-plateparasite-drag area of 1/25th of the main rotor discarea at µ = 0.15.

After the initial conditions have been set, the sys-tem would evolve through a transient phase until

the aerodynamic environment and loads eventuallyreach a steady state. Static equilibrium may thenbe pursued if the equilibrium equations are formu-lated in terms of the long-term average of forcesand moments. Hence, the system is considered tobe trimmed when

~C∗F − ~CavF = 0 (9)

where ~CavF designates the long-term average of ~CF .

VTM Validation

A validation of the VTM in hover and forward flightis reported in Ref. [7], where the VTM predictionswere compared to the experimental data set ob-tained from the work of Dingeldein, Ref. [8]. Thisdata was collected from wind-tunnel tests of a coax-ial rotor system under static-thrust conditions forhover and forward flight at several advance ratios.The coaxial rotor system was part of an actual he-licopter and had a diameter of 25 feet and a rotorspacing equal to 19 percent of its radius. Each ro-tor featured two blades attached to a simple huballowing for feathering motion and the total solid-ity of the coaxial configuration, based on the pro-jected area, was 0.054. The hubs were assembledinto their respective drive shafts through a singlehorizontal pin, thus forming a teetering design. Acomplete description of this rotor system is givenin Ref. [9]. The coaxial rotor was trimmed in yawand its thrust coefficient and tip speed were heldconstant throughout the experiment.

Figure 2 compares the VTM predictions of thevariation of total power with advance ratio againstthe experimental data of Dingeldein.

Figure 2: Comparison of the overall power con-sumption with advance ratio in forward flight be-tween the VTM simulations and Dingeldein’s ex-perimental data. (Adapted from Ref. [7].)

Two different cases were considered for the VTMsimulation. The first case consists in a single simu-

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lation where the coaxial rotor was accelerated fromhover to µ = 0.35 and yielded a data set calledVTM-dynamic. The second case consists in a sim-ulation where the advance ratio was held fixed foreach of the advance ratios of interest and the dataset obtained was called VTM-static. Also plottedin this figure is the curve labelled ‘VTM-dynamic(filtered)’ that was obtained from the dynamic databy removing all fluctuations at greater that blade-passing frequency.

The VTM predictions for the total power con-sumption revealed a good agreement with Din-geldein’s experimental data, with the static caseyielding a slighter underprediction of power con-sumption in hover and in forward flight for therange of advance ratios between about 0.14 and0.20, and a small overprediction beyond. The fil-tered dynamic case also revealed a slight underpre-diction for all the advance ratios of the experimen-tal data.

Results

A summary of the results obtained for the heli-copter model flying forward at advance ratio 0.15is given here. In order to better understand theaerodynamic processes in which the several com-ponents of the helicopter interact with each other,three different configurations were simulated withthe VTM program. The first configuration consid-ers the main coaxial rotor only and models the flowthrough the rotor as if it was operating in isolation.The system is allowed to grow in complexity by theinclusion of the tailplane, thus forming the secondconfiguration simulated. Then the full configura-tion is considered were the fuselage and tailplaneare assembled into the second configuration.

Isolated Coaxial Rotor

Figure 3 shows a perspective view of the main rotorand the set of tip vortex structures produced byits blades. The surface that bounds these vortexstructures was obtained directly from the vorticityfield around the rotor and consists in the set ofall points were the magnitude of the vorticity isconstant. Distinct colours are associated with theiso-surfaces of vorticity generated by each of themain rotors.

As the blades rotate they generate tip and rootvortices that are convected downstream. The tipvortices interact with each other in such a way asto destroy the idealized helicoidal structure (typi-cal at lower advance ratios) to form a pair of con-centrated, counterrotating “super-vortices” at thelateral edges of the wake. Since the main rotor is

trimmed to achieve force and moment equilibrium,the relative strengths of these super-vortices is notnecessarily equal. This can be seen from the skewof the root vortex structures towards the port sideof the configuration.

Figure 3: Iso-surfaces of vorticity magnitude gen-erated by the main rotor operating in isolation atadvance ratio µ = 0.15. (Iso-surfaces from differentrotors rendered separately in distinct colours.)

Figure 4 shows the distribution of nondimen-sional inflow velocity, −viR−1Ω−1, along two rep-resentative blades, one on the upper and the otheron the lower rotor, as a function of their azimuth.

Figure 4: Distribution of inflow over the blades ofthe upper and lower rotors during a complete rotorrevolution. Left: upper rotor. Right: lower rotor.

This figure provides the temporal evolution ofthe inflow at the blades of the main rotor. Thereare three important features that characterise theaerodynamic interactions at the upper and lowerrotors:

• The localized curved ridges represent a veryhigh inflow gradient experienced at discrete lo-cations of the blade. These severe gradientsarise due to the passage of tip vortices pro-duced by previous blades close to the repre-sentative blade. The tip-vortices may be gen-erated by blades from a different rotor thanthe representative blade. As a result, the lower

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rotor presents additional ridges that are pro-duced by the close-passage of the tip-vorticesfrom the upper rotor. This interference effectbetween the tip-vortices and the rotor bladesmay cause strong Low Speed Interactions.

• The straight ridges in a radial direction rep-resent high gradients of inflow over the entirespan of the blade and are experienced over ashort period of time and at a frequency of 6rev−1. They are only clearly visible on thelower rotor of figure 4. This type of interfer-ence is responsible for High Speed Interactionsthat may constitute a source of high vibrationand noise.

• A complex pattern of curved ridges at the rearpart of the rotors also represent very high gra-dients of inflow and are an effect of the interac-tion between the root vortices the rotor blades.

Figure 5 shows a contour plot of the blade loadingdistribution experienced by a representative bladeof both rotor disks and during one rotor revolu-tion. The loading on the blade is higher in theregion close to the tip and in the advancing sideof both rotors, which is a consequence of the rigidrotor system that was employed in the simulations.Thus the advancing blades are allowed to operateat higher lift coefficients even if that implies no sig-nificant contribution to the overall lift by the re-treating blades. This is one of the salient aspectsof the ABC rotor.

Figure 5: Distribution of loading over the blades ofthe upper and lower rotors during a complete rotorrevolution. Left: upper rotor. Right: lower rotor.

Coaxial Rotor and Auxiliary Propul-sor

Figure 6 shows a contour plot of the y-component ofnon-dimensional vorticity (normalized by its max-imum value ζmax) in a x − y section plane. Thisfigure depicts the process in which the main rotorwake impinges on the propulsor, affecting all its

rotor disk area. The wake produced by the propul-sor is distorted by the influence of the main rotorwake. When acting alone, the propulsor generatesa steady cylindrical wake with an horizontal axis.However, when operating together with the mainrotor, its wake is quickly skewed downwards and isdeformed under the action of the main rotor vor-ticity.

Figure 6: Contour plot of the y-component of vor-ticity in the x− z plane for the configuration com-posed of the main rotor and auxiliary propulsor.Region of |ζy/ζmax| < 0.06 not plotted for clarity.

The aerodynamic interaction between the mainrotor and propulsor also manifests directly onthe propulsor loading. Figure 7 shows the meanand root-mean-square (RMS) components of theblade loading distribution over a representativeblade. The main rotor wake effectively distort thefreestream velocity at the vicinity of the propulsordisk. Thus, the loading distribution over the bladesof the propulsor is similar to that of a rigid rotorin forward flight, instead of the expected hover likepattern.

Figure 7: Distribution of blade loading over a rep-resentative blade of the auxiliary propulsor as seenfrom behind the helicopter when operating togetherwith the main rotor. Left: mean loading. Right:RMS fluctuation in loading.

The propulsor will thus generate not only a nose-up pitching moment but also a yawing moment(taking the hub of the lower rotor as the referencepoint). The localized patches of high RMS fluctu-ation in the loading distribution correspond to re-gions of high unsteadiness of the velocity field at the

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propulsor disk and is a direct effect of the passageof the tip and root vortices from the main rotoracross these regions. The fluctuations in loadingover the blades of the propulsor translate into highlevels of vibration that, if not properly addressed,may be transmitted to the fuselage and to the mainrotor mast.

Complete Configuration

Figure 8 was obtained from the difference betweenthe contour plot of figure 4 and an equivalent plotwith respect to the complete configuration.

Figure 8: Distribution of the difference in inflowbetween the complete configuration and that com-prised of the main rotor and auxiliary propulsor.Left: upper rotor. Right: lower rotor.

Figure 9: Distribution of the difference in bladeloading between the complete configuration andthat comprised of the main rotor and auxiliarypropulsor. Left: upper rotor. Right: lower rotor.

It is apparent that the difference in inflow overthe forward half of both disks is generally positiveand becomes predominantly negative over the rearhalf. This reflects the adjustment of the blade pitchangles that was required to trim the complete he-licopter. Two different features are known to con-tribute to the modification in the longitudinal gra-dient of inflow. Firstly, the inclusion of the fuselageleads to an upflow over the forward part of both ro-tors and a downflow at the rear part. Secondly, the

longitudinal cyclic pitch had to be adjusted such asto balance the strong nose-up pitching moment pro-duced by the tailplane. This moment is a direct ef-fect of the impingement of the main rotor wake intothe tailplane and forms an important aerodynamicinteraction, known as ’pitch-up’, that has causedsignificant problems in flight dynamics and controlin helicopters in the past decades, [10]. Figure 9shows the difference in blade loading distributionover a representative blade of the upper and lowerrotors of the full configuration. The modificationin the loading distribution is compatible with themodification of overall pitching moment introducedby the tailplane.

Figure 10 shows the thrust coefficient producedby all the blades of the upper and lower rotors as afunction of main rotor azimuth. It also shows therespective frequency spectrum that was obtainedthrough a Discrete Fourier Transform of the signal.There is a significant unsteadiness for both the up-per and lower rotors that is a consequence of theseveral aerodynamic interactions that involve themain rotor blades. The higher amplitude of thesignal occurs at 3 rev−1 and can be attributableto the aerodynamic properties of the rigid bladesthat constitute each rotor of the coaxial system andalso to the blade-vortex interaction between the tipvortices and the rotor blades. The second higheramplitude occurs at 6 rev−1 and is mainly due tothe blade over-passage type of interaction. Sincethe lower rotor is more influenced by the upper ro-tor than the converse, the amplitudes of the thrustvariation tend to be higher for the lower rotor.

Figure 10: Thrust coefficient generated by the up-per and lower rotors of the coaxial system as a func-tion of azimuth and respective frequency spectrumfor the complete configuration.

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Figure 10 reveals that the thrust coefficient pro-duced by the upper rotor is higher, in the mean,than the lower rotor. This is a requirement im-posed by the trim routine, in order to achieve over-all yawing moment balance of the system.

Figure 11 shows the thrust coefficient of thepropulsor when operating as part of the full con-figuration. The thrust variation is highly unsteadyin nature but, as opposed to the main rotor thrust,the higher amplitude component of the signal is nota multiple of the number of blades of the propul-sor. This is the signature of the strong aerodynamicinteraction between the main rotor wake and thepropulsor that consists in the impingement of tipvortices from the main rotor into the propulsor diskat a 3 rev−1 frequency.

Figure 11: Thrust coefficient generated by the aux-iliary propulsor over a complete main rotor revolu-tion as a function of main rotor azimuth and re-spective frequency spectrum for the complete con-figuration. (Thrust coefficient defined on the basisof the rotational speed, Ωp, and radius, Rp, of theauxiliary propulsor.

The second higher component of the thrust sig-nal of the propulsor disk occurs at a frequency of21.25 rev−1 and is due to the interference effect be-tween the propulsor wake and the propulsor blades.Since the propulsor is relatively far downstream ofthe main rotor, the 21.25 rev−1 frequency modula-tion of the main rotor thrust signal is insignificant.

Conclusion

The aerodynamic interactions between several com-ponents of a compound coaxial helicopter modelhave been investigated computationally through a

coupled lifting-line – VTM program. The heli-copter model employed in this study is representa-tive of a generic modern helicopter that exploit theAdvancing Blade Concept. This concept featurestwo rotors arranged in a coaxial configuration androtating in opposite directions. The blades of eachrotor are very stiff and are rigidly attached to thehub except for feathering motion. The helicoptermodel is also compounded in propulsive thrust withthe addition of a pusher propeller mounted at therear of the fuselage.

A range of aerodynamic interactional phenomenawas identified and characterised for this generic he-licopter model, at the advance ratio of µ = 0.15.The following main conclusions can be drawn fromthe results of the present work:

• The main rotor is responsible for the genera-tion of strong tip and root vortices that areconvected downstream. The tip vortices fromthe upper and lower rotors interact with eachother and tend to roll-up and merge into apair of concentrated vortex structure or “super-vortex”.

• The inflow velocity field over the upper andlower rotors is characterised by a longitudinalgradient over the whole rotor disks and severalhigh localised gradients that are identified bycurved ridges in the contour plot of the inflowdistribution over the rotor disks. The longitu-dinal gradient describes the variation of inflowthat is required in order to achieve momentequilibrium of the system and is influenced bythe fuselage. The strong curved ridges repre-sent localised gradients of inflow induced bythe trailed tip vortices produced by the rotat-ing blades as they pass close to the rotor plane.The radial ridges represent the interference be-tween the vorticity bound to a blade from onerotor as it passes directly over (or underneath)a blade of the other rotor.

• The fuselage induces a displacement of the ve-locity field in the vicinity of the main rotorthat is characterized by an upflow in the for-ward half of the main rotor and a downflowover the rear half.

• The inclusion of the fuselage and tailplane inthe model resulted in a high nose-up pitchingmoment leading to an increase in the longitu-dinal gradient of inflow, and a redistribution ofblade loading over the upper and lower rotorssuch as to balance the overall pitching momentof the helicopter.

• The variation of thrust produced by the mainrotor with azimuth revealed high unsteadiness.

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The dominant frequency of the thrust signalwas 3 rev−1 that is not only a direct effect ofthe blade-vortex interaction but is also a con-sequence of the aerodynamic properties of theblades. The amplitude of the 6 rev−1 com-ponent also contributed significantly for theunsteadiness of the thrust variation and is at-tributable to the blade over-passage type of in-teraction.

• The high amplitude of the 3 rev−1 componentof the propulsor thrust variation indicates apowerful interaction between the main rotorwake and propulsor that consists of the inges-tion of main rotor tip vortices by the propulsor.This causes the propulsor to act as a strongsource of dynamic excitation of the fuselage.Although this excitation might be amelioratedif the phasing of the upper and lower rotorsis changed. The propulsor wake interacts withthe propulsor blades at a higher frequency of21.25 rev−1, although at lower amplitude thanthe 3 rev−1 component.

Acknowledgements

The author would like to thank Dr. R. E. Brown(Mechan. Chair of Engineering, University of Glas-gow) for the opportunity to develop this work inthe former Rotorcraft LABoratory (RLAB) – De-partment of Aerospace Engineering, University ofGlasgow; to Dr. H. W. Kim for his support andassistance with the data obtained with the VTMcomputer program and to all the members of theformer RLAB.

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