NUMERICAL INVESTIGATION OF BVI MODELING EFFECTS ON HELICOPTER ROTOR FREE WAKE SIMULATIONS

Transcription

1 4 TH INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES NUMERICAL INVESTIGATION OF BVI MODELING EFFECTS ON HELICOPTER ROTOR FREE WAKE SIMULATIONS X. K. Zioutis, A. I. Spyopoulos, D. P. Magais, D. G. Papanikas Fluid Mechanics Lab., Mechanical Engineeing. and Aeonautics Depatment, Univesity of Patas, Geece Keywods: helicopte aeodynamics, BVI, oto wake Abstact This pape pesents the influences of numeical Blade Votex Inteactions (BVI) simulation on the computational esults of oto blade downwash distibution and ailoading. This investigation is pefomed on the basis of a developed computational pocedue utilizing Votex Element Method fo oto fee wake computations. By these means wake votices ae modeled by a seies of discete votex elements and induced velocity on oto disk is calculated fo the distoted wake geomety, integating Biot-Savat law in closed fom ove each one of them. Bound ciculation vaiations and unsteady blade ailoading as a esult of the nonunifom induced downwash ae computed utilizing a blade element like method. Wake oll up pocess, votex coe modeling, voticity dissipation and elastic blade motion ae some of the aeodynamic topics modeled with special cae in the developed pocedue. Using the computational flexibility of Votex Element Method, BVI locations ae captued and the phenomena ae categoized as paallel, pependicula and oblique egading thei oientation elative to oto blade. The coesponding intensity and locus fo each categoy ae calculated via a lifting suface methodology taking into account compessible blade flowfield. In addition, with the developed pocedue the influence of each BVI phenomenon is isolated and its influence on blade downwash and ailoads distibution is demonstated. The computational esults of BVIs location and stength distibution on oto disk, ae compaed with expeimental data of blade ailoading fo a numbe of decent and level flight conditions. These data ae deived fom model-oto wind tunnel tests, pefomed in the duation of joined Euopean eseach pogams. 1 Intoduction Among the most impotant phenomena chaacteizing helicopte oto wake ae the close encountes of oto blades with tip votices, which ae known as blade-votex inteactions o BVIs. Duing these inteactions a oto blade passes close to, o even hits, a concentated votex and both the local blade suface pessue and the distibution of voticity in votex coe egion ae alteed. The esulting suface pessue fluctuations poduce highly unsteady ailoads and intense noise adiation. Thus BVI phenomena have a majo impact on blade vibation and ae esponsible fo the chaacteistic sound of the otocaft in flight egimes whee blade and wake ae in poximity. Because of thei significant impotance on oto aeodynamics and acoustics, investigation of BVIs was the subject of seveal expeimental eseach effots [1,,3], aiming to povide bette physical undestanding of the phenomena. In addition seveal effots have been made fo the development of computational models to adequately incopoate BVIs in numeical oto flowfield simulations [4,5,6]. The wok epoted hee aims to pesent the influence of BVI numeical modeling on pedicted oto ailoads, non-unifom downwash and on computed oto wake geomety. Roto 1

2 X.K. ZIOUTIS, A.I. SPYROPOULOS, D.P. MARGARIS blade and wake computations ae based on a developed pocedue [7] utilizing the fee wake concept, with the adoption of Votex Element Method (VEM) fo wake simulation. The oveall oto wake voticity is assumed to consist of thee inteacting pats, the concentated tip votex and the spead tailing and shed voticity at the inboad egion of the blade. Each of these pats is epesented by a multitude of finite votex elements eithe of line o suface type. Votex elements mutual influences and oto downwash distibution ae calculated by integating individual element contibutions on total induced velocity at the coesponding points. Blade dynamics have been adequately incopoated taking into account fist mode of flapwise blade bending. Roto ailoads ae calculated with the application of a blade element type methodology, which combines lifting line and lifting suface concepts. In geneal fee wake methods coupled with non-cfd codes fo blade calculations is a computationally efficient and elatively accuate pocedue compaed to consuming 3-D Eule/ Navie Stokes solves, but special phenomena such as BVI must be modeled with cae to impove the effectiveness of the method. Taking advantage of the computational flexibility of the developed pocedue, extensive modifications have been made to include detailed BVI simulation. A distinction is made egading the elative position of blade and inteacting votex, and each BVI event is designated as oblique, paallel o pependicula [8]. Paallel BVI is usually obseved on the advancing side while pependicula BVI is common ove the font and ea of the disk [9]. Appopiate modeling is applied based on theoetical [10] appoaches and the esults ae compaed with expeimental measuements. The exta shedding of nea wake due to local changes in bound ciculation is simulated and fomulas ae developed to calculate the influences on oto blade. Special attention has been given on modeling BVI effects on votex coe stuctue and decay, which ae impotant fo subsequent inteactions of the same votex and detemine the final computed wake geomety. Possible votex coe busting is examined fo evey BVI event unde specified citeia and its popagation on votex filament is computationally simulated. The esults of BVI modeling and computational teatment ae compaed with expeimental data fo seveal flight conditions. These data ae deived fom model-oto wind tunnel tests pefomed in the duation of joined Euopean eseach pogams [11]. Roto Aeodynamic Flowfield Analysis.1 Fee Wake Concept One of the most impotant chaacteistics of helicopte oto blades is that they tend to stay in close poximity to thei wake, long enough to expeience significant influences on thei aeodynamic pefomance. This is mainly due to the non-unifom downwash induced on the oto disk and to the close encountes between the blades and concentated votices of oto wake. These impacts on blade aeodynamics have thei coesponding effects on oto aeoacoustics and as a conclusion any methodology tageting to calculate oto aeodynamics o acoustics must be based on a eliable simulation of the complicated wake flowfield. Fo this pupose, seveal appoaches have been intoduced, some of them using CFD methods [1] and othes adopting Lagangiantype techniques such as votex methods due to Choin [13] o the "fee" wake concept. The late is a continuous impoving methodology, which due to ecent yeas eseach has became a poweful aeodynamic tool fo the pediction of oto induced flowfield [14,15]. The wok pesented hee is based on the fee wake concept with the application of Votex Element Method. Wake voticity can fom eithe concentated filaments o distibuted sufaces, which ae moving andomly in 3D space. The objective of VEM is to simulate these fomations of voticity with simple computational elements, in ode to pedict the velocity field induced on the oto disk and in the wake itself. Fo this pupose discete staight o cuved votex line segments and votex sheet

3 NUMERICAL INVESTIGATION OF BVI MODELING EFFECTS ON HELICOPTER ROTOR FREE WAKE SIMULATIONS elements ae used. Though the movement and decay of these elements, as they inteact with each othe, the distoted oto wake geomety is obtained. Consevation of ciculation dictates that the voticity stength shed at specific spanwise locations behind each oto blade is detemined by ciculation gadients on the blade. Spanwise ciculation vaiations on oto blade geneate tailing voticity, g n, whose diection is paallel to the local flow velocity (figue 1). On the othe hand, azimuthal vaiations poduce shed voticity adically oiented, g s, due to the tansient peiodical natue of the oto blade flowfield. Depending on its stength and its spanwise oigin, the wake voticity can fom eithe concentated votex filaments o spead votex layes. g bv(, ψ) Modeling of bound ciculation distibution Ψ g n g s Inboad voticity distibution g bvm ( ψ) Tip votex Fig. 1. Modeling of oto blade bound ciculation distibution and wake voticity fomations. The stength of evey votex element used is deived fom bound ciculation distibution (figue 1). In geneal, the bound ciculation cuve can be assumed with a peak, g bvm, nea the blade tip while being zeo at the tip itself. This steep gadient ceates a high stength tailing votex sheet, which apidly olls up and foms the concentated tip votex. Due to its stength, tip votex dominates oto wake flowfield and the accuate calculation of its geomety is the fundamental concen of any oto wake flow simulation. Inboad voticity shed at blade's wake foms thin layes spead as long as the blade span. This pat of oto wake is ceated due to g v adial and azimuthal bound ciculation vaiations fo the tailing and shed wake voticity espectively. With VEM implementation these pats of oto wake ae epesented with votex sheet elements [7]. The influence of wake votices to oto downwash can be computed utilizing potential theoy elations, such as the Biot-Savat low. With known oto downwash distibution, blade section aeodynamics can be calculated via a lifting line-blade element method, which is valid fo the high aspect atio helicopte oto blades. The pesent analysis assumes that the helicopte oto pefoms a steady state equilibium flight, implying that fowad flight speed, oto otational speed, tip path plane oientation and wake geomety emain constant with time.. Roto Aeodynamic Calculations Distoted wake complexity makes the calculation of oto downwash almost impossible with a diect numeical integation of the Biot-Savat law ove the actual wake, and this pocedue is used only fo simplified appoaches such as the igid o semi-igid wake assumptions. The utilization of discete computational elements (votex lines and sheets) by VEM fo oto wake simulation, convets diect integation in a closed fom integation of the Biot-Savat law ove the known spatial locations of these elements. The contibution of a votex line segment i to the induced velocity w ij at an abitay point in space j, is given by the elation 1 gi ( ijm k ek ) dk wij = 3 4 (1) π k e ijm whee ijm is the minimum distance fom votex line i to the point j, e the unit vecto in k the diection of the votex segment, g i the ciculation stength of the votex segment and k the coodinate measued along the votex segment. With a easonable step of discetisation, the simplification made to the k 3

4 X.K. ZIOUTIS, A.I. SPYROPOULOS, D.P. MARGARIS actual wake geomety can be ovecome. Fee wake computation is an iteative pocedue, which initiates fom igid wake geomety. Each iteation defines a new position of each votex element, taking in account the contibutions of all the wake elements to local flow velocity. At the end of each iteation a new distoted wake geomety is calculated which is the stating point fo the next cicle. This scheme continues until distotion convegence is achieved. A pictue of the final distoted wake geomety fo a specific expeimental test case is given in figue. Vetical distance, m ROTOR DISK (TPP) ψ=180 o c T /σ = ψ=0 o µ = M t = 0.64 R = m c = 0.11m Downsteam distance, m Fig.. Distoted fee wake geomety calculation fo an expeimental test case of climb conditions. Two tip-votices ae shown fo claity stating fom blade tips located at 0 o and 180 o of azimuth angle Roto blade dynamics influence the angle of attack distibution seen by the blade, and theefoe alte the bound ciculation distibution. Due to out-of-plane motion, oto blade balances the asymmety of oto disk loading. Fo studying oto aeodynamics and acoustics at low advance atios, blade flapwise bending can be epesented with a simple mode shape, without significant loss of accuacy. In geneal the out of plane deflection z(,t) can be witten as a seies of nomal modes descibing the spanwise defomation z(,t ) = k=1 nκ ( )qκ ( t ) () whee n κ is the mode shape and q κ (t) is the coesponding degee of feedom. Fo the developed pocedue only the fist flapwise bending mode shape is used, n=4-3, which is appopiate fo blade's basic bending defomation [16]. By these means a detailed oto induced downwash distibution is obtained by fee wake calculations. Sequentially, blade section angle of attack distibution is computed by α 1 (, ψ ) = θ ( ) tan ( u u ) P T (3) whee u P is the ai velocity pependicula to No Featheing Plane (NFP) which includes nonunifom oto downwash, u T is the tangential velocity to blade aifoil, both nomalized by tip speed ΩR, and θ() is the collective pitch angle (since NFP is taken as efeence). With known angle of attack and local velocity, a bladeelement type methodology is applied fo blade section lift calculations. The above computational pocedue is extensively documented in efeence [7]..3 Votex coe modeling Any computational pocedue fo oto wake analysis includes a numeical epesentation of tip votex stuctue and evolvement in the wake envionment. A geat deal of the cuent knowledge about these impotant aeodynamic issues has been deived mainly fom expeimental measuements. As a esult empiical elations ae commonly used fo the detemination of citical paametes fo tip votex physical modeling such as the votex coe adius, the velocity distibution at the coe egion and the viscous coe gowth. Since VEM is based on a potential field solution such as Biot-Savat law fo the calculation of the velocity induced by votex elements to abitay points in space, singulaities ae expected to occu close to these elements. Due to the absence of viscosity effects, the velocity calculated in close poximity to these elements tends to be infinite. In ode to emove these singulaities and model the effects of viscosity in a convenient way the votex coe concept is intoduced. The coe adius is defined as the distance fom the coe cente whee the maximum tangential velocity is obseved. A coesponding expession fo the adial ciculation distibution 4

5 NUMERICAL INVESTIGATION OF BVI MODELING EFFECTS ON HELICOPTER ROTOR FREE WAKE SIMULATIONS inside the coe egion is intoduced in the computations, which altes the velocity induced fom a votex element. Outside the coe egion the induced velocity has an appoximately potential distibution which tends to coincide with the Biot-Savat distibution faily away fom the votex line. Seveal expeimental and theoetical woks have been pesented [17,18,19] whee velocity measuements have been taken in the coe egion and coesponding adial ciculation distibutions have been extacted. Accoding to Vatistas [19] a seies of tangential velocity pofiles in the votex coe is given by the elation g Vθ ( ) = (4) π n n ( ) 1 / n c + whee g is the ciculation of the votex line, n is an intege vaiable, is the adial distance fom the votex cente and c is the coe adius. Using this elation fo diffeent values of n, the velocity pofiles of some well-known coe models can be deived using the nondimensional adius = /. Fo n=1 the coe c model of efeence [0] is deived g θ ( ) = (5) π ( 1 ) V c + Fo n= the model poposed in efeence [1] by Bagai-Leishman is deived g Vθ ( ) = 4 (6) π c 1+ while votex coe adius was expeimentally found to be between 5-7% of blade chod. A compaison of the above two votex coe models as well as Rankine and Lamp-Oseen [] models, which wee fitted in a least-squae sense with expeimental data, is given in [1]. The Kaufmann-Scully coe model [0], is slightly undeestimating the peak tangential velocity at ealy wake ages and impoving late while the Bagai-Leishman votex was in best ageement with expeiments between the fou models. With the application of votex coe ciculation distibution, the velocity induced by the votex elements is alteed. Using the Kaufmann-Scully model the velocity induced to a point j fom a finite staight votex line segment i, of constant ciculation g i, with abitay oientation consideing the elative geometical distances,, is given as whee N = w i j i1, j i, j g i N = i1, j i, j (7) 4 π D ( + )[ 1 ( ) ( )] i1, j i,j i1,j i, j i1,j i, j D = + c ( ) i1,j i,j i1,j i,j ( i1,j + i,j i1,j i,j ) Fo the pesent computational pocedue both of the above coe models Kaufmann-Scully and Bagai-Leishman wee included as compaable options to descibe the coe of line and sheet votex elements. 3 Numeical Blade Votex Inteaction Simulation Blade Votex Inteactions ae known cucial phenomena fo helicopte oto flowfield pedictions. This is because they affect both the votex filaments of oto wake and the aeodynamics of otating blades. When a concentated votex comes vey close to a otating blade, expeiences a shap incease of its diamete so damatic that is often mentioned as votex coe "busting". The voticity stuctue in the coe egion is influenced and the esult is the enlagement of the coe adius while the ciculation of the votex line is conseved. Seveal models have been developed to simulate this phenomenon and explain the associated effects on blade suface pessue distibution [1,4]. Fo the developed pocedue the coe "busting" model is applied which imposes a steep incease of the votex coe adius. Afte numeical investigation and compaisons with expeimental data, a bust coe adius about 10 times the value of c was found to be adequate. The bound ciculation distibution is also + 5

6 X.K. ZIOUTIS, A.I. SPYROPOULOS, D.P. MARGARIS alteed when a concentated votex passes in close poximity to a oto blade due to shap induced downwash fluctuations. The change of ciculation poduces an additional shedding of voticity in the nea wake behind this blade, which in tems affects the induced velocity distibution on the blade in an opposite manne than this of the concentated votex. Thee ae two main difficulties on applying a numeical model to pedict the effects of this phenomenon on the computed blade downwash and ciculation. Fist a minimum distance has to be defined so that evey votex filament close method poposed by Johnson [15], has been adopted. The votex-induced-ailoads ae calculated fo an infinite aspect-atio wing in a subsonic, compessible, feesteam. A staight, infinite votex inteacts with the wing at an abitay angle Λ fom the wing cente line as shown in figue 3. The ciculation at any spanwise station P n along the blade as a function of Mach numbe Μ, angle Λ, vetical distance h and spanwise distance b between BVI location P c and station P n is given by the elation Γ ( ) b sin Λ Γ d ( b sin Λ + cos Λ) = an π πvb d sin Λ ( sin Λ + cos Λ) + ( h + c ) α Vb 1 n= 0 an d b n= 0 d sin Λ n b [ + b ] ( b ) ( sin Λ + cos Λ) + ( h + c ) o n b b + [ ( b sin Λ + cos Λ) + ( h + cn ) + bo ] + 4( b sin Λ + cos Λ) ( h + cn ) n n o (8) than it to a oto blade must be consideed involved in a BVI event. This distance is denoted by h in figue 3 and its magnitude has to be extenally imposed to the computations as a esult of expeimental obsevations and paametic numeical investigations. Fo the pesent wok a value of 0 votex coe adii was found to give ealistic pedictions fo blade aeodynamic magnitudes. Fig. 3. Blade and votex line elative positions fo lifting suface theoy solution. The second difficulty comes fom the fact that lifting line method cannot adequate descibe the shedding of exta nea wake due to local bound ciculation changes. To account fo these effects a fomula, based on a lifting suface The expessions fo detemining the constants in equation (8) depend on the values of Mach numbe and angle Λ [3]. As aleady mentioned in pevious paagaphs, VEM povides a tanspaent insight of oto wake and blade flowfield. Taking advantage of this featue, the oientation of evey votex element elative to the inteacting blade is computed and the BVI event can be designated as paallel, oblique o pependicula. These designated numeical esults of BVI type and location ae compaed to theoetical conclusions fo diffeent numbe of oto blades and advance atios. A eliable pediction of the stength of each BVI event is anothe issue of numeical simulation. If a ealistic pictue of the location and stength of BVI events on oto disk is numeically ceated, the factos that geneate these phenomena can be taced and thooughly examined. Well known factos that affect the multitude and intensity of BVIs ae design paametes such as blade shape and oto contol inputs such as commanded pitch imposed to oto blades. The fome affects the ciculation of the 6

7 NUMERICAL INVESTIGATION OF BVI MODELING EFFECTS ON HELICOPTER ROTOR FREE WAKE SIMULATIONS tailing tip votex and the late detemines the oientation of oto disk elative to the flight path. Especially fo descending flight conditions whee the numbe of BVIs inceases, poducing extensive noise emission and stuctual vibations, numeical simulations can help to detemine the optimum oientation of oto disk fo a given flight path. 4 Results and Discussion One of the fist simplified assumptions fo oto tip votices geomety is the undistoted o igid wake geomety. This geomety is close to eality fo the aea just below oto disk whee each tip votex is not seiously distoted by the velocity induced fom its neighboing votices. Fo this geomety the locations on oto disk whee BVI is possible to occu can be calculated by the elations ( i - 1) π cos ψ - = cos + Nb π sin ψ - N ( i - 1) b = sin ( ψ δ ) µδ ( ψ δ ) (9) (10) whee is oto adius, δ is the age of a point on tip votex, ψ is the azimuth angle of the blade which ceated the votex, N b is the numbe of blades, µ is the advance atio and i= 0,..,N b. The values of (, ψ) fo which equations (9), (10) ae simultaneously satisfied give the locus of all potential BVIs on oto disk. Fo a two bladed oto these locations ae shown in figue 4. These locations ae calculated by the developed computational pocedue fo igid wake geomety and ae pesented in figue 5 demonstating the efficiency of the computations. Fig. 5. Calculated locus of all possible BVIs on oto disk assuming igid wake geomety in fowad flight conditions. The actual geomety of a helicopte oto wake is distoted compaed to its initial helical fom, because of flight velocity and the mutual inteactions between tip votices. The steady state distoted wake geomety is computed by an iteative pocedue in which the stating scheme is igid wake geomety. Fig. 4. Theoetical locus of all possible BVIs on oto disk assuming igid wake geomety in fowad flight conditions (fom efeence [9]). Fig. 6. Calculated locus of all possible BVIs on oto disk based on distoted wake geomety in fowad flight conditions. 7

8 X.K. ZIOUTIS, A.I. SPYROPOULOS, D.P. MARGARIS The distotion of wake votices changes the locus of the possible points whee they intesect with oto blades. To compae with the igid wake case, figue 6 pesents the computed possible BVI locations fo the distoted geomety of the two-bladed oto. As can be seen in figue 6 the diffeences compaed with the igid wake case occu at the lateal sides of oto disk, which is expected because the lateal distotion of tip votices is geate as they pass close to each othe at these potions of oto disk. Helicopte flight conditions have a majo effect on the numbe, location and intensity of BVI phenomena. In geneal tip votices tend to evolve below oto disk at the moment they emanate fom blade tips. When the helicopte pefoms a descent flight, oto is oiented noseup while moving fowad and tip votices ae foced to pass though the oto disk. As a esult the numbe of BVIs is substantially inceased and descent flights ae known to poduce intense noise and vibations. In an opposite manne, expeimental obsevations show that climb flight conditions poduce low noise levels and educed blade vibations. Flow visualization esults fo such cases [11] lead to the conclusion that due to flight conditions, tip votices depat fom the aea below the oto just afte thei fomation and they don t inteact as much with the otating blades. Simulated flight conditions fo seveal expeimental test cases show that computational esults obtained by the developed pocedue, ae in accodance with the above obsevations fo BVIs numbe and locations. The following figues pesent computed BVI locus fo one level case and two descent cases with vaying descending angle (positive tip path plane angles coespond to nose up oientation of oto disk). Fig. 8. Locus of calculated BVI events fo a distoted wake geomety and descent flight conditions with c T /σ =0.0571, µ=0.14, α TPP =6.8 o and M t =0.64. Fig. 9. Locus of calculated BVI events fo a distoted wake geomety and level flight conditions with c T /σ =0.0571, µ=0.7, α TPP =-1.0 o and M t =0.64. Fig. 7. Locus of calculated BVI events fo a distoted wake geomety and descent flight conditions with c T /σ =0.0571, µ=0.11, α TPP =11.87 o and M t =0.64. As shown in the above figues, computations veify what is aleady discussed. Level flight has the smallest numbe of BVIs and they ae mostly gatheed at the advancing 8

9 NUMERICAL INVESTIGATION OF BVI MODELING EFFECTS ON HELICOPTER ROTOR FREE WAKE SIMULATIONS side of oto disk. This means that at small ages afte thei shedding, tip votices inteact with the following blades mostly in pependicula oientation. Figues 7 and 8 demonstate the influence of inceasing descent angle on BVI numbe and locations. A notice can be made about the pediction of BVIs in paallel oientation elative to oto blade fo the highly descending conditions with o descent angle [11]. shown in the contou plot of figue 10. The downwash distibutions at the aea of the calculated BVI location fo the cases of including and excluding this paticula BVI event ae computed and thei diffeences ae contoued in figue 10. Fo the BVI event shown in pevious figue, the coesponding changes in blade section lift coefficient ae shown in figue 11. Load fluctuations because of blade suface pessue changes ae calculated when the BVI event is taken into account as expected and in this case the ageement with the expeimental data fo blade section lift is faily impoved. By these means, numeical BVI simulation can help to locate aeas on oto disk which geneate intense BVI noise and blade fatigue fo pedetemined flight conditions. Fig. 10. Contous of downwash velocity changes when including and excluding an isolated BVI event. The intensity of the specific event and its influence on downwash distibution is demonstated. C L With BVI Without BVI Expeimental c T /σ = α TPP =-6.8 o µ = Μ t =0.64 R = m c = 0.11m Azimuth Angle [deg] Fig. 11. Compaison of azimuthal blade section lift distibution fo including and excluding an isolated BVI event fo an expeimental test case of climb flight conditions. These specific inteactions ae pedicted mostly at the advancing side which is consistent with obsevations mentioned in efeence [9]. The influence of an isolated BVI event is Refeences [1] Hone M B, Galbaith R A, Coton F N, Stewat J N, and Gant I. Examination of votex defomation duing blade-votex inteaction. AIAA Jounal, Vol. 34, No. 6, pp , [] Wittme K S, and Devenpot W J. Effects of pependicula blade-votex inteaction pat1: tubulence stuctue and development. AIAA Jounal, Vol. 37, No. 7, pp , [3] Kitaplioglu C, and Caadonna F. Aeodynamics and acoustics of blade-votex inteaction using an independently geneated votex. Ameican Helicopte Society Aeomechanics Specialists Confeence, San Fancisco CA, [4] Rahie G, and Delieux Y. Influence of votex models on blade-votex inteaction load and noise pedictions. Jounal of Ameican Helicopte Society, Vol. 44, No. 1, pp 6-33, [5] Rule J A, Epstein R J, and Bliss D B. Unsteady compessible bounday element calculations of paallel blade-votex inteaction. Jounal of Ameican Helicopte Society, Vol. 44, No. 4, pp , [6] Caadonna F, Kitaplioglou C, McClue M, Baede J, Leishman G J, Beezin C, Visintaine J, Bidgeman J, Buley C, Epstein R, Lyintzis A, Koutsavdis E, Rahie G, Delieux Y, Rule J, and Bliss D. Methods fo the pediction of blade-votex inteaction noise. Jounal of Ameican Helicopte Society, Vol. 45, No. 4, pp , 000. [7] Spyopoulos A I, Fagias A P, Papanikas D G, and Magais D P. Influence of abitay votical wake evolution on flowfield and noise geneation of helicopte otos. nd Congess of Intenational 9

10 X.K. ZIOUTIS, A.I. SPYROPOULOS, D.P. MARGARIS Council of the Aeonautical Sciences, Haogate U K, Pape ICAS 0394, pp , 000. [8] Kishnamoothy S, and Mashall J S. Theedimensional blade-votex inteaction in the stong votex egime. Physics of Fluids, Vol. 10, No. 11, pp , [9] Leishman G. Pinciples of Helicopte Aeodynamics, 1st edition, Cambidge Univesity Pess, 001. [10] Johnson W. Calculation of blade-votex inteaction ailoads on helicopte otos. Jounal of Aicaft, Vol. 6, No. 5, pp , [11] Splettstoesse W R, Niesl G, Cenedese F, Nitti F, and Papanikas D G. Expeimental esults of the euopean HELINOISE aeoacoustic oto test. Jounal of Ameican Helicopte Society, Vol. 40, No., [1] Ahmad J, and Duque E. Helicopte oto blade computation in unsteady flows using moving oveset gids. Jounal of Aicaft, Vol. 33, No. 1, pp 54-60, [13] Choin A J. Computational Fluid Mechanics, 1st edition, Academic Pess, [14] Bliss D B, Teske M E, Quackenbush T R. A New Methodology fo Fee Wake Analysis Using Cuved Votex Elements, NASA CR-3958, [15] Johnson W. A Compehensive Analytical Model of Rotocaft Aeodynamics and Dynamics, NASA TM- 8118, [16] Johnson W. Helicopte theoy, 1st edition, Pinceton Univesity Pess, 1980, nd edition, Dove, [17] Bhagwat J M, and Leishman G J. Coelation of helicopte oto tip votex measuements. AIAA Jounal, Vol. 38, No., pp , 000. [18] Windnall S E, and Wolf T L. Effect of tip votex stuctue on helicopte noise due to blade votex inteactions. AIAA Jounal of Aicaft, Vol. 17, No. 10, pp , [19] Vatistas G H, Kozel V, and Mih W C. A simple model fo concentated votices. Expeiments in Fluids, Vol. 11, pp.73-76, [0] Scully M P. Computation of helicopte oto wake geomety and its influence on oto hamonic ailoads, ASRL TR 178-1, [1] Leishman G J, Bake A, and Coyne A. Measuements of oto tip votices using thee-component lase dopple velocimety. Jounal of Ameican Helicopte Society, Vol. 41, No. 4, pp , [] Lamb H. Hydodynamics. 6th Edition, Cambidge Univesity Pess, 193. [3] Johnson W. A lifting suface solution fo votex induced ailoads. Jounal of Aicaft, Vol. 9, No. 4, pp ,