Copyright ©1996, American Institute of Aeronautics and Astronautics, Inc.

AIAA Meeting Papers on Disc, May 1996A9630813, AIAA Paper 96-1698

Prediction of blade vortex interaction aerodynamics for a higher harmoniccontrolled rotor

Syed R. AhmedDLR, Inst. fuer Entwurfsaerodynamik, Braunschweig, Germany

AIAA and CEAS, Aeroacoustics Conference, 2nd, State College, PA, May 6-8, 1996

An unsteady 3D panel method is applied to compute the subsonic aerodynamics of a four blade rotor operating underHigher Harmonic Controlled (HHC) pitch input. The blades are of finite thickness and the full span free wake issimulated by a vortex lattice which evolves as the computation proceeds. Three flight conditions: baseline, withoutHHC input, minimum noise, and minimum vibration with 3 per/rev. HHC inputs are the subject of study. Predictedpressure distribution, chordwise and spanwise for all three cases, is in fair agreement with wind tunnel results. Timehistory of pressure at selected chordwise and spanwise stations captures the basic trends of the experimental results.Blade-vortex interaction loci in rotor disk and tip vortex trajectories predicted are in good agreement with resultsobtained at ONERA and experiment. The shift of tip vortex trajectory with HHC input is correctly simulated by thecode results. (Author)

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Prediction of Blade Vortex Interaction Aerodynamicsfor a Higher Harmonic Controlled Rotor

AIAA-96-169896-1698

A96-30813

S. R. AhmedDLR, Institute of Design Aerodynamics

38108 Braunschweig, Germany

Abstract

An unsteady 3-D Panel Method is applied to compute thesubsonic aerodynamics of a four blade rotor operating un-der Higher Harmonic Controlled (HHC) pitch input Theblades are of finite thickness and the full span free woke issimulated by a vortex lattice which evolves as the computa-tion proceeds.

Three flight conditions: Baseline, without HHC input, Min-imum Noise and Minimum Vibration with 3-per-rev. HHCinputs are the subject of study. Predicted pressure distribu-tion, chordwise and spanwise for all three cases is in fairagreement with wind tunnel results. Time history of pres-sure at selected chordwise and spanwise stations capturesthe basic trends of the experimental results.

Blade Vortex Interaction Loci in rotor disc and tip vortextrajectories predicted are in good agreement with resultsobtained at ONERA and experiment The shift of tip vortextrajectory with HHC input is correctly simulated by thecode results.

Nomenclature

cCPCTMa, MaHov

r,Rt,AtV..X,Y,Z

"tPP

= blade chord= static pressure coefficient= rotor thrust coefficient= Mach number, Mach number of blade tip

during hover= radius, rotor radius= time, time interval= translation speed of rotor= Cartesian coordinates

= shaft tilt angle= angle, of rotor tip path plane

(referenced to horizontal plane)= azimuth angle, azimuthal step

of computations= rotor advance ratio

1. Introduction

The noise radiation from civil and military helicopters is aproblem of major concern. The characteristic impulsivenoise of a helicopter with a dominant mid-frequency con-tent is most annoying for the human ear. For military heli-copters, propagation of the low frequency impulsive noiseover large distances ahead of the aircraft increases the riskof its early detection.

The primary source of noise generation on the helicopter isthe main rotor. Two distinct aerodynamic phenomena inthe rotor flow field are responsible for the impulsive noiseradiation. On the advancing side, the addition of translatoryand rotational motion can lead to creation of pockets ofsonic flow near the blade tips which appear and collapse asthe blade rotates from the advancing to the retreating side.An intense High Speed Impulsive (HSI) noise is generatedwhich propagates mainly in the plane of the rotor anddirectly ahead of the aircraft. HSI noise is of concern formilitary detection.

The second source of impulsive noise - specially at loweroperational speeds - is the Blade Vortex Interaction (BVI)noise caused by the abrupt and unsteady pressure fluctua-tions on the rotor blades due to interactions with tip vorti-ces of the preceding blades. Such interactions are mostsevere during descent or manoeuvring flight when the rotorwake is raised towards the rotor plane and the tip vorticescome very close to or collide with the blades. BVI noisepropagates forward along a plane slanted downwards to therotor plane. This feature of the BVI noise makes it a majorsource of community annoyance during helicopter landingsin densely populated urban areas since the frequency con-tent of this noise is in the range to which human beings areextremely sensitive.

The physics of BVI is extremely complex and is not fullyunderstood. In spite of the impressive investigations per-formed to date, only limited progress has been made toinhibit the BVI noise. Past research - both theoretical andexperimental - has shown the key role rotor wake geometry

Copyright © 1996 by Dr. S. R. Ahmed. Published by theAmerican Institute of Aeronautics and Astronautics, Inc.wife permission.

plays during B VI. The roll-up of the wake shed from bladetrailing edge into discrete tip vortices, their spatial trajec-tory, strength and unsteady deformation under mutualinteraction due to rotor downwash, blade translation androtation, etc. are all processes whose correct simulation in atheoretical approach is a prerequisite for the accurate pre-diction of the unsteady pressure distribution on rotor bladesduring BVI. As mis data serves as input to the noise radia-tion calculations, also the accuracy of the noise predictiondepends on the quality of the aerodynamic input

Representative examples of work in the United States tosimulate rotor wakes with vortex lattice and constant vor-ticity contour methods are to be found in [1], [2] and [3].An evaluation of these techniques by Torok et al. [4]showed a qualitative similarity between the predictions andan acceptable accuracy for the computed blade lift InEurope, a number of vortex lattice free wake codes havebeen developed over the last years (see [5] to [10]) whichtreat the inviscid incompressible flow around rotors assum-ing zero thickness blades or subsequently correct theresults for the finite blade thickness. Of special interest inthe context of this paper is the work done at ONERA inFrance reported by P. Beaumier and P. Spiegel [11]. Theaerodynamic part of this multi-component code consists offollowing modules: MESIR, which represents the bladewith a lifting line and the full span wake with a vortex lat-tice. The geometry of the full span wake is prescribed tostart with and relaxed step by step till convergence isobtained for the circulation, in the rotor disc. This full span"free wake" is rolled into discrete vortices in the moduleMENTHE. Unsteady pressure (difference) distribution onthe zero thickness blade is computed with a third moduleARHIS. This involves 2-D strip type of calculations withcorrections for finite blade span and subsonic compressibi-lity corrections with Prandtl-Glauert rule.

Besides the aforementioned potential theory approaches,more rigorous methods which solve the Euler orNavier-Stokes equations (see for example [12] to [16]) arealso frequently applied to describe the rotor flow. Theinherent dissipation of such numerical schemes needs cor-rective measures which add to the computational expense.Currently such methods are not suitable for large scale cal-culations needed in the early design phase of rotors.

The contents of this paper represent an attempt to simulatethe aerodynamics of a multiblade rotor operating underHigher Harmonic Pitch Control (HHC). The HHC tech-nique is considered to have a substantial potential to reducethe intensity of BVI phenomena and thus reduce the BVInoise (see for example [17], [18] and [19]). The code usedis the Unsteady Panel Method Code (UPMC) applied ear-lier to the computation of pressure distribution on multib-

lade rotors in hover and forward flight and wings inoscillatory motion [20], [21]. The aerodynamics calculatedby this code were used in [22] to predict the acoustics ofmultiblade rotors in forward flight

2. Description of the Method

Panel methods are numerical schemes for the solution ofpotential flow problems and are capable of treating flowsabout complex three-dimensional configurations. In thespecific case of unsteady rotor flows the boundary condi-tion of flow tangency on the blade surface at every instantin time need to be imposed on the solution. A detaileddescription of the 3-D unsteady panel method used for theresults of this paper is given in [20,21 and 22].

The model of the lifting rotor blade used here (at any timeinstant) consists of (Fig. 1):

• a source/sink distribution of unknown strength over theblade surface

• a doublet distribution of unknown strength (but of pre-scribed chordwise variation) over the mean surfaceinside the blade

• a zero-thickness elongation (2% of local blade chord)of the blade trailing edge (Kutta panel) carrying a dou-blet distribution of unknown strength.

The numerical procedure consists of dividing the blade,the internal and the wake surfaces into finite surface ele-ments (see Fig. 1). The unknown source/sink or doubletstrength on each surface element is assumed to be con-stant. Additionally, the equivalence of constant strengthdoublet panels and vortex rings ([23]) is used to replacethe doublet panels by vortex rings of same strength placedon the perimeter of the doublet panels. Induced velocitiesfor a quadrilateral doublet panel are then, for example, cal-culated from the four vortex line filaments at the paneledge using Biot-Savart law.

Imposing the flow tangency condition at a number of dis-crete points P on the blade and Kutta panel surface leads toa system of linear algebraic equations whose iterativesolution gives the strength of the singularities for each ofthe generic points P at a time instant t As mentioned ear-lier, the variation of circulation strength on the profilemean line is prescribed. The circulation strength of theKutta panel is set equal to mat at the trailing edge. Oncethe Kutta panel strength is known the relative strengths ofall vortex panels on the mean surface are known.

The calculation proceeds hi the following manner:

At time t = 0, the rotor is impulsively started from rest

from a given azimuthal position. At this instant, there is nowake. With the solution of the system of equations, thestrength of the singularities on the blade surface and circu-lation strength of vortex rings on Kutta panels is known.Using these singularities, the induced velocities at thedownstream corner points (e.g. A and B in Fig. 1) of Kuttapanels are evaluated. A straight vortex element is releasednow from the trailing edge of each Kutta panel. The endsof this vortex element are moved with the calculated in-duced velocities plus the velocity components due to trans-lation, rotation and other motions of the blade over a timeinterval At. This vortex filament, together with the so cre-ated downstream segments and the Kutta panel trailingedge, comprises a quadrilateral ring vortex (A, B, C, D inFig. 1). Its strength is equal to that of the Kutta panel fromwhich it was released. This row of vortex panels releasedfrom the Kutta panels is the increment of the blade wakeafter At. The distortion of the "wake" is effected by thediffering velocities with which the end points of the re-leased vortex filaments move. Once a row of vortex panelshas been assigned a certain spanwise variation of circula-tion, the circulation distribution for this particular row ofpanels remains constant as the wake panels move and dis-tort in space. This fulfills the dynamical boundary condi-tion of zero pressure difference across the wake [24]. Forthe next time step, the system of equations is solved anew,taking into consideration now the induction of the first rowof vortex panels at all collocation points. This process is re-peated until the blade aerodynamics converge to a desiredbehaviour.

The term "free wake" is used in the literature to denote var-ious methods - not necessarily identical - employed tocompute the rotor wake geometry. For example, "wake"can mean only the tip vortex trajectory. Its geometry maybe prescribed initially and relaxed iteratively, as the com-putation proceeds to obtain a "free wake" which is tangen-tial to the velocity vector in the flow field. The same proce-dure can be applied to a full span wake (simulated with avortex-lattice) whose spatial geometry is, to start with, pre-scribed. Also this wake, relaxed iteratively, leads to a "freewake".

In the present code the full span vortex-lattice wakeevolves as the computation proceeds and is at every timeinstant tangential to the flow field velocity vector and thus"free". All inductive interactions - between wake vor-tex-lattice elements as well as between the blades and theirwakes - are considered at every time step. It is contendedthat this is a more correct physical description of the wake.

3. Experimental Data

The test data used in this paper is part of a comprehensivedatabase obtained in the framework of Higher HarmonicControl Aeroacoustic Rotor Test (HART) in the Ger-man-Dutch Wind Tunnel (DNW) in The Netherlands inJune 1994. This major co-operative research effort wasjointly conducted by the US Army, DLR, DNW, ONERAand NASA. Some important results of the experiments,test set-up and operation are reported in depth in [25].Among the data measured, of interest in the context of thispaper are: (1) unsteady blade surface pressure (over theprofile) at three radial sections, and (2) geometry of a seg-ment of two consecutive tip vortices at blade azimuth ofV = 35°.

The test object was a 40% dynamically and Mach-scaledmodel of the 4 blade hingeless BO- 105 main rotor oper-ated in the 8 m x 6 m open jet test section of DNW. The 4m diameter rotor had blades of 121 mm chord, NACA23012 profile, standard rectangular planform and a linear-8° twist At three radial stations (r/R = 0.75, 0.87 and0.97) subminiature pressure sensors were installed flushwith blade surface to acquire the pressure data. In all 112sensors were arranged over the blade section at these radialstations as shown in Fig. 2. The signal of each pressuresensor was digitized at a rate of 2048 per revolution whichcorresponds to a resolution of about 0.18 degree in azi-muth.

The higher harmonic pitch was obtained by superimposinga nP (n-per-revolution) swashplate motion upon the basiccollective and 1-per-revolution cyclic control inputs. Datafrom the following three cases is used in this paper forcomparison with the predictions. They all simulate a 6° de-scent flight for an advance ratio \l = 0.15, thrust coeffi-cient Cj. = 0.0044, shaft tilt as = 5.3°, and tip path planeangle a.tpp = 3.8° and hover Mach No. at blade tip

Case 1: Baseline without HHC input

Case 2: Minimum Noise with 3-per-rev. HHC input of0.8 degree amplitude

Case 3: Minimum Vibration with 3-per-rev. HHC inputof 0.8 degree amplitude imparted at a phase an-gle different from Case 2.

A novel Laser Light Sheet (LLS) method, described in de-tail in [25] and [19] was employed to determine the geom-etry of tip vortex segment at an azimuth angle y = 35°,considered to be in the vicinity of angle where most severeBVI is expected. This data is used here to compare withthe predicted rotor wake geometry.

4. Results

The main emphasis of the present computations lies on theevaluation of the unsteady pressure distribution on the ro-tor blades and the wake geometry for the baseline casewithout HHC input and the two other cases (MinimumNoise, Minimum Vibration) with HHC inputs.

In the panel method simulation of the blade surface, thiswas represented by 34 panels along the profile and 11 pan-els along the blade span which gives a total of 374 panelsper blade for the 4 blade rotor (see [20]). The wake of ablade thus consists of. 12 trailing and 11 shed vortex fila-ments per time step. The calculation was performed over3.25 rotor revolutions for the selected three cases. Startingwith a coarse time step of 22.5 degrees azimuth anglemaintained over one revolution, this was reduced monoto-nously at the start of the 2nd revolution in steps of 2.5° toreach a step size of 2.5° which was then maintained con-stant for the rest of the calculations. The purpose of startingthe calculations with a coarse time step is to save computa-tion time. The transition from coarse to fine step size intro-duces some instability in the numerical scheme which de-cays subsequently as the compulation proceeds. However,this means that the computation has to be continued over alarger number of steps which partly offsets the gain ef-fected by the choice of coarse step size at the beginning.This aspect is not addressed further in this paper as it needsfurther study.

4.1 Pressure Distribution over Blade Surface

A comparison of the computed pressure distribution overthe blade chord at the radial station r/R = 0.75 and a rangeof azimuth angles y for the baseline case without HHC in-put is shown in Fig. 3-. The full line is the predicted pres-sure and the open symbols data from DNW tests during theHART campaign.

In general the agreement of prediction and experiment isfair. Discrepancies are apparent in the rear half on the bladeupper side and forward half of blade lower side. Also theequality of pressure at the trailing edge appears in the pre-dictions to follow a different trend compared to the experi-mental behaviour. Among the possible reasons, two seemto be significant The code does not simulate the elastic de-formation of the blade which may account for the discrep-ancy on the rear half of the upper surface and forward halfof the lower surface. Poor agreement in the trailing edgevicinity is probably caused by a "too early" discontinuationof the calculations indicating that the blade wake has notyet attained its "final" form.

To check on the spanwise agreement of the predicted pres-sure distribution with experiment, this is plotted in Fig. 4

for three radial stations r/R = 0.75,0.87 and 0.97. Consid-ered is again the baseline case without HHC input and anazimuth angle y = 45°, which is considered as a locationwhere noise significant blade vortex interactions takeplace. Also here the quality of agreement between predic-tion and experiment at the further outwards lying stations(r/R = 0.87 and 0.97) is fair and the deviations exhibit thesame trend as seen in Fig. 3. It is interesting to note thenegative pressure predicted on the lower side of the bladeat the outermost radial station, a consequence of the nega-tive blade twist at this station.

The effect of HHC input on the pressure distribution isseen in the comparison presented in Fig. 5. Shown is thepressure distribution over chord at three radial stations forthe Minimum Noise case with HHC input, again at theB VI critical azimuth angle \|f = 45°. A significant decreaseof lift at all radial stations (as compared to the baselinecase) and the negative peak pressure on blade lower side isobserved. This is a direct result of the 3-per-revolutionHHC input superimposed on the basic collective and1-per-revolution cyclic inputs to the blade pitch. Also herethe quality of agreement between theory and experiment issimilar to that in Figs. 3 and 4 indicating bat HHC inputs,as expected, modulate the blade Lift mainly hi the azi-muthal direction.

42 Pressure Time History

A critical test for the pressure results is the prediction of itstime history. As "the BVI phenomena are most severe nearthe blade leading edge, the variation of pressure on bladeupper surface over azimuth at a selected chord station andthree radial stations for the baseline case are comparedwith experimental results of DNW in Fig. 6. There is aslight difference between the cbordwise location of theprediction and experiment viz. 3.9% for theory versus 3%for the DNW experiment. Since this is the closest colloca-tion point of chosen blade surface discretisation which cor-responds to the sensor location at 3% chord, the predictedpressure time history at this location has been selected forthe comparison.

As evident from Fig. 6, the basic trends of the pressuretime history with BVI induced pressure fluctuations in thefirst and fourth quadrant and a relative smooth variation hithe second and mud quadrant are captured by the theory atall three radial stations. However, quantitative differenceswith respect to magnitude, phase and number of pressurefluctuations are also to be seen. Obviously these differ-ences are primarily caused by differences in the predictedwake geometry and the experimental results. In reality, ini-tial full span wake rolls up into discrete tip vortices whosetrajectories may be causing a different spatial and temporal

blade vortex interaction process as the theory which as yetdoes not incorporate a wake sheet roll up model. Anotherreason may probably be that the chosen azimuthal step ofthe computations, vis. A\|r = 2.5°, needs to be decreasedfurther to capture more correctly the number of B VI occur-rences as well as the amplitude of the pressure pulses.

Fig. 7 demonstrates the type of agreement obtained be-tween the predicted and experimental time histories for theMinimum Noise case where again the same chordwise andspanwise location results have plotted as in Fig. 6. Alsohere the nature of discrepancies between theory and exper-iment is similar to the Baseline case. An additional sourcehere could be the elastic torsional deformation of the blade- not considered in this analysis - which can significantlychange the blade twist distribution especially withmulti-per-revolution HHC control inputs on the blades.

Some more information about the pressure time history atvarious downstream chord locations x/c on the blade uppersurface is presented in Fig. 8 for the outermost radial sta-tion r/R = 0.97 of the Minimum Noise case. Also this com-parison shows that the analysis captures the basic trends ofthe pressure variation reasonably well in spite of the short-comings noted above. For the location x/c = 0.21, the ex-perimental curve shows near azimuth angle of 90° a dip inthe pressure variation which is apparently an experimentalerror. The pressure peaks, especially in the third quadrantdecrease in intensity with progressively increasing value ofx/c. The experimental curves do not indicate a shift ofphase hi the peaks at different chordwise locations whichindicates that the interacting vortex has its axis about paral-lel to the blade axis.

4.3 Blade Wake and BVI Locations in Rotor Disc

As mentioned earlier, the wake of the rotor blades is simu-lated over the whole blade span with a vortex-lattice whichevolves (and increases in length) as the computation pro-ceeds. A top view of the wake is shown in F'g- 9 a forblade no. 1 of the Baseline and Minimum Noise case. Forclarity the wake for only about 1 1/2 last rotor revolutionsand with a 5 degree azimuthal resolution is depicted. Simi-lar wakes are emitted from the trailing edge of the otherthree blades and are simulated concurrently in the analysis.The outer edge of the wakes from blade nos. 1,2,3 and 4 isdepicted in the Figs. 9 b. c. d and e. The downstream partof the wake edge exhibits a peaky trajectory. The reason ispartly the initially coarse azimuthal computation step ofA\j/ = 22.5° and also the ensuing mutual induction be-tween the vortex-lattice elements as the wake evolves.Since the analysis lacks currently a model to simulate theroll-up process of the full span wake sheet into "tip vorti-ces", the trajectory of "the wake edge is assumed to be the

trace of the "tip vortex". For the purpose of finding thepossible blade vortex interaction locations in the rotor disc,the downstream peaky part of the wake edge trace issmoothed with a spline fit. The so obtained "tip vortex"trace for the individual blades is used then to mark the pos-sible blade vortex interaction locations in the rotor disc.The vertical (Z-) coordinate of the tip vortex trace is ig-nored for this representation.

Fig. 9 depicts a snapshot of the wake for a particular azi-muth angle. For example, when the blade no. 1 advances90° (anti-clockwise) in azimuth, its tip vortex tracechanges in shape from that shown in Fig. 9 b to that shownin Fig. 9 e. At each intermediate computation step, the tipvortex trace progressively departs from that of Fig. 9 b andmoves towards the shape of Fig. 9 e. If all locations ofblade leading edge/vortex intersection (for all blades andtheir tip vortices) are plotted for the last rotor revolution,one obtains the loci of the possible BVI in the rotor disc.

Fig. 10 shows the BVI loci, obtained as explained abovefor the three cases Baseline, Minimum Noise and Mini-mum Vibration compared with similar results obtained atONERA, left column (see [11]), and experimental data ofDNW, right column, [19]. Bold lines are the result ofpresent code, and the lines connecting the symbols in theleft column of Fig. 10 the theoretical results of ONERA.The procedure for obtaining BVI loci from measured pres-sure data is explained in [19]. The basic idea is to identifythe occurrence of a BVI on the basis of peaks and valleysin the measured pressure time history at x/c = 3%. Exceptin the earlier part of the 1st quadrant and the later part of4th quadrant, the BVI loci of the present code agree quiteclosely with the ONERA predictions. Deviations are moremanifest in the inner part of the rotor disc. Also reasonableagreement of present results with the experimental data ofDNW (right column in Fig. 10), especially on the retreat-ing blade in the 4th quadrant, is obtained.

These results justify the assumption made in the currentstage of the present code to equate the wake edge geome-try with the tip vortex trace.

4.4 Tip Vortex Location

A prediction of the tip vortex trace in a top view for bladenos. 2 and 3 is compared with DNW test data in Fig. 11 forthe three different cases: Baseline, Minimum Noise andMinimum Vibration. The azimuth angle chosen is \y = 35°for which LLS measurements were performed in the windtunnel. The X- and Y-axis in the schematic sketch (top leftof Fig. 11) describe a horizontal plane passing through therotor center. The computed vortex traces for the three casesshown are projected hi this plane.

Even though the LLS results are to be considered as quali-tative, the agreement of the predicted vortex traces with themeasurements is encouraging. Of interest is the compari-son for the Minimum Vibration case where the experimentsindicate the emission of two counter-rotating vortices fromthe blade tip region as shown by the double row of symbolshi the bottom right of Fig. 11. This phenomena is a conse-quence of the negative lift at the blade tip. The theoreticalmodel of wake employed in the present code does not havethe wake sheet roll-up capability and thus this phenomenais not captured.

Fig. 12 shows the vortex trace for the three cases studied inthe vertical Z'X* -plane where Z' is the rotor shaft axis, asindicated in the schematic sketch at the top left. Z' corre-sponds, but for the shaft tilt angle ocs, to the vertical direc-tion Z of the XYZ coordinate system. The measured coor-dinates of the tip vortex segments have been projected inthis plane and the head on angle of view is as indicated bythe arrow in the sketch at the top right The blade positionindicates the nominal rotor plane perpendicular to the shaftaxis.

Except for the Minimum Vibration case, also here a rea-sonably good correlation between prediction and experi-mental data for the vertical position of the tip vortices isobtained. A comparison of the vortex traces for the Base-line and Minimum Noise case shows that with the HHC in-puts in the latter case, the vortices move from their almostinplane position to that below the rotor plane. This appearsto be one of the significant reasons for the noise reductionobtained since with the larger separation distance betweenthe blades and the vortices, the intensity of blade vortex in-teractions is drastically reduced. However, the vertical dis-tance between the blade and the vortices of Fig. 12 is notactually the "miss-distance" since the BVI critical parallelinteractions between blade no. 1 (see Fig. 11) and the vorti-ces happen at an azimuth of roughly \p = 50° whereas theresults shown in Fig. 12 are for y = 35°.

The theoretical results for the Minimum Vibration case arein poor agreement with experiment and do not, for reasonsexplained earlier, show the existence to two tip vortices perblade. Qualitatively, the movement of the tip vortices to aposition above the rotor plane is correctly predicted.

It follows from the results of Figs. 11 and 12 that the effectof HHC inputs on the .vortex trace is more effective in thevertical rattier than in the horizontal plane. This appearsplausible since the translational and rotational velocity ofthe rotor blades essentially governs the in plane and down-stream convection of the tip vortices which are not affectedby the HHC inputs. On the other hand, the vertical move-ment of the tip vortices due to mutual inductions does de-

pend on the strength of the vortices, which varies accord-ing to the HHC schedule employed.

Similar results have been obtained at ONERA and dis-cussed in depth in [11].

5. Conclusions

The results shown in this paper demonstrate the ability ofthe developed code to compute the subsonic aerodynamicsof multiblade rotors with profiled blades of finite thick-ness. Since arbitrary motion of the blades is allowed, thisapproach permits, as a single code, the unified treatment ofvarious flight conditions and rotor operational inputs, in-cluding HHC.

Blade surface pressure distributions, chordwise and span-wise are hi fair agreement with the experimental data ob-tained in the DNW for die three cases studied. Discrepan-cies are observed on the upper rear half and lower forwardhalf of the blade' surface. The reasons for this are believedto be the torsional elasticity of the blade (not considered inthe analysis), probably also the necessity to continue thecomputation over a larger number of steps and the use ofcoarse azimuthal steps in the beginning of the computa-tion.

The comparison of pressure time history at selected chordstations of blade profile with corresponding experimentaldata reveals discrepancies in the number of BVI peaks andtheir magnitude as well as phase differences. No singlereason can be advanced as explanation for this and theseresults need more detailed investigations. Time historycomparisons are very important in view of the use of suchresults for noise prediction analysis and represent a severetest of the code prediction capability.

In spite of the simple approach used to equate the tip vor-tex trace with the edge of the full span wake, the loci of theBVI hi the rotor plane exhibit strong similarity to the re-sults obtained at ONERA and are in fair agreement withDNW results indicating the physical realism of the freewake concept of.the present code.

The comparison of tip vortex trace of individual rotorblades in a horizontal and vertical plane with correspond-ing experimental data are in qualitative agreement (exceptfor the Minimum Vibration case) with the experimentaldata.

The occurrence of two tip vortices per blade in the Mini-mum Vibration case, as evidenced by the DNW experi-ments, is not reproduced by the present results since awake sheet roll-up model is not incorporated in the currentstage of the code development. However, the trendwise

shift of the tip vortex trace below the rotor plane for theMinimum Noise and up above the rotor plane for the Mini-mum Vibration case are correctly predicted. This meansthat the HHC inputs are translated by the code into corre-sponding physically realistic shifts in the wake geometry.

6. Acknowledgment

The test data used in this paper was obtained during a mul-tinational HART test campaign under the auspices of USArmy, DLR, ONERA, NASA and DNW. The author grate-fully acknowledges the permission to use the data by thesponsoring authorities.

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[12] Kroll, N.: Computation of the Flow Fields of Propel-lers and Hovering Rotors Using Euler Equations.12th European Rotorcraft Forum, Gannisch-Parten-kirchen, Germany, Paper No. 28, Sept. 1986

[13] Strawn, R.C. and Earth, TJ.: A Finite-Volume EulerSolver for Computing Rotary-Wing Aerodynamics onUnstructured Meshes. 48th AHS Forum of theAmerican Helicopter Society, Washington, DC, June1992

[14] Strawn, R.C. and Barth, TJ.: A Finite-Volume EulerSolver for Computing Rotary-Wing Aerodynamics onUnstructured Meshes. J. American Helicopter Soc.,Vol. 38, No. 2, pp. 3-13, Apr. 1993

[15] Rai, MM.: Navier-Stokes Simulations of Blade-Vor-tex Interaction Using Higher-Order AccurateUpwind Schemes. 25th AIAA Aerospace SciencesMeeting, Reno, NV, Paper No. 87-0543, Jan. 1987

[16] Srinivasan, G.R.; Raghavan, V.; Duque, E.P.N. andMcCroskey, WJ.: Flowfield Analysis of ModernHelicopter Rotors in Hover by Navier-StokesMethod. J. American Helicopter Soc., Vol. 38, No. 3,pp. 3-13, July 1993

[17] Hardin, J.C.: Concepts for Reduction of Blade/VortexInteraction Noise. J. of Aircraft, Vol. 24, No. 2, pp.120-125, Feb. 1987

[18] Yu, Y.H.: Rotor Blade-Vortex Interaction Noise:Generating Mechanisms and its Control Concepts.American Helicopter Society Specialists Meeting onAeromechanics Technology and Product Design for21st Century, Bridgeport, CT, October 11-13,1995

[19] Splettstoesser, W.R.; Kube, R.; Seelhorst, U.;Wagner, W.; Boutier, A.; Micheli, F.; Mercker, E.and Pengel, K.: Key Results from a Higher HarmonicControl Aeroacoustic Rotor Test (HART) in theGerman-Dutch Wind Tunnel. 21st EuropeanRotorcraft Forum, St. Petersburg, Russia, Paper No.I-7, Aug. 30-SepLl, 1995

[20] Ahmed, S.R. and Vidjaja, V.T.: Unsteady PanelMethod Calculation of Pressure Distribution on BO105 Model Rotor Blades and Validation withDNW-Test Data. 50th Annual Forum of theAmerican Helicopter Society, Washington, DC, MayII-13,1994

[21] Ahmed, S.R. and Vidjaja, V.T.: NumericalSimulation of Subsonic Unsteady Flow around Wingsand Rotors. AIAA Applied AerodynamicsConference, Colorado Springs, CO, 1994

[22] Yin, J.P. and Ahmed, S.R.: Prediction - and itsValidation - of the Acoustics ofMultiblade Rotors inForward Flight Utilising Pressure Data from a 3-DFree Wake Unsteady Panel Method. 20th EuropeanRotorcraft Forum, Amsterdam, The Netherlands,Oct. 4-7,1994

[23] Lamb, H.: Hydrodynamics. Dover Publications, NewYork, USA, 1932

[24] Summa, J.M.: Potential Flow about Three-Dimen-sional Streamlined Lifting configurations with Appli-cation to Wings and Rotors. SUDAAR Rep. No. 485,Stanford University, USA, 1974

[25] Mercker, E. and Pengel, K.: Flow Visualisation ofHelicopter Blade Tip Vortices - A Qualitative Tech-nique to Determine the Trajectory and the Position ofthe Tip Vortex Pattern of a Model Rotor. Proceedingsof 18th European Rotorcraft Forum, Avignon,France, 1992

'CO

Body Surface Panel(Source/Sink Distribution)

Kutta - Panel

Trailing Vortex

X Shed Vortex

Mean Surface Panel(Vortex Lattice)

Fig. 1 Numerical Model of Rotor Blade and Wake

r/R= 0.75 0.87 0.97! ! Ii i i

AIRFOIL : NACA 23012 mod

Fig. 2 BO-105 Blade Planform and Location of Pressure Sensors

r/R = 0.75 Base line without HHC

Present codeAO Experiment DNW

.1 .6 .1 I.ICHORD X/C

-c,

= 135"

.1 .6CMOKO X/C

-c,

Fig. 3 Pressure Distribution over Blade Chord at r/R = 0.75 for various Azimuth Angles \j/. Base line case withoutHHC. Comparison Theory and Experiment.

Base line without HHC

.— Present code

AO Experiment DNW

-c p

r/R= 0.97

.1 .6CHORD X'C

Rg. 4 Pressure Distribution over Blade Chord at \y = 45° and various Radial Stations r/R. Baseline case without HHC.Comparison Theory and Experiment.

Min. Noise

.—. Present code

AO Experiment DNW

Fig. 5 Pressure Distribution over Blade Chord at y = 45° and various Radial Stations r/R, Minimum Noise Case withHHC. Comparison Theory and Experiment

11

r/R= 0.75 - - - - Present code: x/e = 0.39———— Experiment ONW: x/c a 0.30

Bose line without HHC

90 180 270AZIMUTH ANGLE C06GR.3

360

Fig. 6 Pressure Time History at x/c = 0.39 and various Radial Stations r/R. Baseline case without HHC. ComparisonTheory and Experiment

---- Present code: x/c = 0.39——— Experiment ONW: x/c a 0.30

90 180 270AZIrXJTH ANGLE CDEGR.3

360

Fig. 7 Pressure Time History at x/c = 0.39 and various Radial Stations r/R. Minimum Noise Case with HHC.Comparison Theory and Experiment.

x/c = 0.90 . x/c = 0.96\^—— ,-•—

90 180 270AZinUTH ANGLE CDEGR.3

360

Fig. 8 Pressure Time History for various Chord Stations x/c. Minimum Noise case with HHC. Comparison Theory andExperiment

12

Base line Min. Noise

Fig. 9 a) Full Span Wake of Blade No. 1 for tne Baseline and Minimum Noise case and b), c), d) and e) Wake edgetrace of Blade Nos. I,2,3and4

13

Blade 18!ad82BladesBlade 4Event A2JEvent A3 \OACICEvent fit r**"5

Event R2J

= 0 *

Base line

DNW

Experiment DNW

Present code

Min. Noise

-1.0 -0.5 0.0 O.S 1.0 tap.

MESIR

Min. Vibration

-1.0 -0^ 0.0 O.S

Fig. 10 B VI Loci in Rotor Disc for the Baseline, Minimum Noise and Minimum Vibration cases. Left columncomparison of prediction with ONERA results [II], right column comparison with DNW results [19].

14

Wind Base line

Blade No.3

Blade No.2V = 305°

Vortex No.Blade No.4

= 125°

= 35°Blade No.1

....--"'"^jpt. !\ Vortex No.5\

_••' Vortex No.6

OA Experiment DNW _/

Min. Noise Min. Vibration

Fig. 11 Comparisoti of Tip Vortex Trace of Blade Nos. 2 and 3 withDNW experiments [19]. Top view for the Baseline,Minimum Noise and Minimum Vibration case.

15

Blade No.4

// Vortex No. No.1

Z (mm)

400-.

200-

-200-

Blade

Vortex No. 5 Vortex No. 6

= 305°

Angle of viewfor Z-R-plot

Base line-400 J

Z'(mm)

400 T

200-

0.0 -0.25 0.50

0 -

-200-

-400-

Min. Noise

0.0 0.25 0.50

Z" (mm)

400T

200-

o -

-200-

-400-

Min. Vibration

0.0 0.25 0.50

Experiment DNW• Vortex No. 5A Vortex No. 6

0.75 1-0

Vortex No. 5V\ .^' -•-... ..-••'"" •

--" -AVortex No.6

0.75 X,/R' 1.0

Vortex No. 5

_.\.

. .̂......-̂ - -....Vortex No.6

0.75 v-'/n' 1.0:/R'

Fig. 12 Comparison of Tip Vortex Trace of Blade Nos. 2 and 3 with DNW experiments [19]. Side view for the Baseline,Minimum Noise and Minimum Vibration case.

16