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1 28 THT INTERNATIONAL CONGRESS OF O THE AERONAUTICAL SCIENCES AERODYNAMICS ANALYSIS OF CYCLOIDAL ROTOR Hu Yu, Tang Jiwei, Song Bifeng School of Aeronautics, Northwestern Polytechnical Univeristy Julius_hu@hotmail.com Keywords: Cycloidal propeller, L-B Dynamics stall model, Cyclogyro Abstract An improved aerodynamics model for cycloidal propellers based on Leishman-Beddoes( (LB) dynamical stall model is presented in this paper. validations are made between experimental data results from presented model. validations proved that presented model is applicable for cycloidal propeller performance evaluation under hovering status. Based on analysis with calculation results, some of mechanisms about how efficiency of cycloidal propeller could be improved are revealed. 1 Introduction Cylcoidal rotor is a rotor system that blades rotate around an axis parallel to its span wise direction [1-3], usually used by cyclogyros, LTAs boats. pitch angle of each blade varies cyclically by an eccentricc such that blades experiences positive angles of attackk at both top bottom positions of azimuth cycle. resulting time-varying lift drag forces produced by each blade cann be resolved into vertical horizontal direction. Varying amplitude phasee of cyclic blade pitch can change magnitude direction of net thrust vector produced by cyloidal rotor. flow on blades is strongly unsteady when cycloidal propeller rotates, thus it is very difficultt to predict aerodynamics performance. re aree two categories of aerodynamics computation model for cycloidal propeller, CFD oretical- experimental method. m With a CFD tool, we can make a goodd understing of flow field around cycloidal rotor, it is helpful for more efficient design. However, a problem caused by using CFD iss its long computation time, thus is not very suitable for preliminary design d optimization. This is why oretical-experimental method is needed. Mcnabb model [4] is one of most famous oretical-experimental aerodynamics force model for cycloidal propeller. lift computation is based on ordorson oscillating airfoil ory blade element ory. zero-lifting drag in steady s flow is used as value in unsteady flow. And induced drag of blade is calculated with a formula, which includes a modified Oswald Efficiency factor derived from experimental data. n t thrust power can be calculated. However, e Mcnabb model does not consider t effects of fluid viscosity, flow separation e shed vortex on leading edge of blade, thus it is only suitable for cycloidal propellerr in whichh blades experience low reduced frequency small angle of attack. In this study, a new aerodynamics force computation model m for cycloidal propeller is

2 Hu Yu, Tang Jiwei,, Song Bifeng 2 aerodynamics model based on LB dynamic stall model primary parameters of cycloidal rotor include airfoil, disc diameter,, blade span, number of blades, chord, offset distance offset azimuth angle. Fig.1. is a sketch mapp of cyclocopter with four cycloidal rotors[5]. Figure 1. cyclocopter with four cycloidal rotors 2.1. LB dynamic stall model underlying mechanism of LB model is indicial aerodynamic responses - changes in aerodynamic forces with respect to a step change in aerofoil pitch angle or pitch rate. For an arbitrary continuous motion, corresponding total aerodynamic responsee is found by using this approach in conjunction with superposition principle [9].[ details of LB dynamic stall model are introducedd in reference [6-9]. 2.2 Methodology presented. model is based on state- space based Leishman-Beddoes model[6-9], which can consider effects off airfoil flow separation, thus precision of zero-lifting drag is improved. Based on analysis, some mechanisms about aerodynamics of cyclorotor are revealed.. presentedd aerodynamics modell is derivedd from Mcnabb model[4]. Leishman- Beddoes dynamic stall model [5-8] is introduced, soo that blade element lift drag can be evaluated with high accuracy onset of flow separation also can be predicted. A local coordinate system is attached to each blade, LB dynamic stall model blade element ory are used to calculate blade force at each time t step within each cycle, n se force components are transformed into global coordinate systemm addedd up to get instantaneous thrust of cycloidal rotor, 2 2 A ( A Z ) ( A X ) (1) power, P 360 o o 0 N Where A Z, AX is verticall horizontal thrustt respectively, D is blade drag, V t iss blade tangential speed, N is blade number, is azimuth angle. Compare induced velocity with given initial value when a periodic calculation is finished, if e difference between two values is lesss than predefined error, stop iteration; elsee use dichotomy d method to get a new induced velocity until it converged. proposed model needs two constants thatt appear in equations about induced velocity induced drag coefficient [4].[ Using helicopter momentum ory, inducedd velocity of e air throughh cycloidal rotor is given by following equation, Thrust V induced 2* * Constt * A (3)) induced drag coefficient is: C D C Where D0 ( D* V ) t 2 C L * AR* Eff (4) is air density, C D0 (2) is projected area, is zero-lift drag, AR is aspect ratio, Eff is Oswald efficiency. A 2

3 AERODYNAMICS ANALYSIS A OF CYCLOIDAL ROTORR constants Const Oswald factor Eff are set to be 0.26~0.55, 0.6~1.5 respectively according to statisticss data from experimental results. experimental data results from proposed model match well, thus high accuracy of proposed model can be proved Validation comparison between analysis experiment [1,2] is shown in Fig2. It can be seen that computation results of thrustt power coincide with experimental dataa well. refore proposed model constants presented above are applicable for cycloidal propeller performance prediction under hoveringg status. (a) thrust vs. RPM (b) power vs. RPM Fig.2 comparison between analysis experiment 3. Computations Analysis All computations are based on 4-bladed cyclorotor. According to computation results, effects of several parameters, such as shape of rotor disc, blade pitching amplitude blade chord, on hovering performance are investigated. Fig.2. shows performance of cyclorotor with blade chord length of 0.015m 0.02m 0.025m. Computation results indicate that larger chord, higher lift. However, power loading decreases a little bit as chord length increases. But for same s thrust, rotation speed s of cyclorotor with shorterr chord will be significantlys y higher than that with longer chord.. This results in much higher centrifugal force acting on blade whichh causes higherr bending moments also results in much higher forces imposed on control mechanism which will reduce r mechanical efficiency. (a) thrust vs. RPM (b) powerr loading vs. disc-loading Fig 2 performance of cyclorotor with different blade chord length 3

4 Hu Yu, Tang Jiwei,, Song Bifeng effects of variations in blade pitching amplitude are shown in Fig.3. Comparisons are made for blade pitch amplitude of 25,30, From results, it can be seen that best efficiency was achieved for 25 pitching amplitude, followed by 30,35 40 respectiv vely. It also can be seen that at same RPM, cyclorotor produces larger force as pitching amplitude increases. Since higher pitch angle causes higher AOA hence higher blade lift forces. For a single pitching blade with high aspect ratio travels forward, it will stall before pitching amplitude reaches 20. But blades remain un-stalled on cyclorotor at such a large pitch angle as 40. From computation it is found that induced downwash velocity experienced by blade is comparable to tangential velocity. refore, even thoughh pitch angle is very high, large induced downwash decreased effective blade angles of attack. This prevents blade from stall. However, for a given thrust, smaller blade pitching amplitude needs much higher rotating speed. This causes higher mechanical loss which may lead to a lower total efficiency. Higher rotation speed also introduces higher blade bending moment. (a) thrust vs. RPM (b) power Loadingg vs. disc-loading Fig 3 performance of cyclorotor with different blade pitching amplitude 4 Conclusions An aerodynamics analysis model based on LB dynamic model is presented. high accuracy proves that this model is applicable for cycorotor performance prediction under hovering status. computation results show that: a). larger blade chord, t higher thrust. But efficiency varies a little l bit as chord increases. For a given thrust, larger blade chord is preferred. b). induced downwash in cycloidal rotor cage is comparable too blade tangential velocity, thuss bladess remained un-stalled at such a large pitch p angle as 40. And results indicate that larger pitching amplitude, larger thrust, but small pitching angle has better efficiency. Since for same thrust, smaller bladee pitching amplitude needs higher rotating speed thus resultss in higher mechanical loss, optimization that t involves aerodynamics, structure mechanical analysis shalll be made to find best pitching angle. Acknowledgment This project is surported by Program for New Century Excellent Talents in University, from MOE, P.R.China P References [1] Hu Yu, Lim L Kah Bin, Hu Wenrong. Research on Performance off Cyclogyro. AIAA , 2006 [2] Seong Hwang, Seung Yong Min, Min Ki Kim, et al. Multidis-ciplinary Optimal Design of Cyclocopter Blade System. 46th AIAA/ ASME/ASCE/ /AHS/ASC Structures, Structural Dynami-cs & Materials Conference,18-21 April 2005, Austin, Texas. [3] Gil Iosilevski, Yuval Levy. Aerodynamics of Cyclogiro. 3rd AIAA Fluid Dynamics Conference Exhibit,23-26 June 2003, Orlo, Florida. [4] Michael Lynn L Mcnabb. Development of A Cycloidal Propul-sion Computer Model Comparison with Experiment. sis for Master s Degree, Mississippi State University, 2001 [5] Seong Hwang, H Seung Yong Min, Choong Hee Lee et al. Experimental Investigation of VTOL UAV CyclocopterC r with Fourr Rotors. 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, Materials Conferenc, April 2007, Honolulu, Hawaii [6] Leishman,J.G.,Beddoes,T.S, A Generali- 4

5 AERODYNAMICS ANALYSIS OF CYCLOIDAL ROTOR zed Model For Airfoil Unsteady Aerodynamic Behavior And Dynamic Stall Using Indicial Method. Proceedings of 42nd Annual Forum of American Helicopter Society, Washington DC, June [7] Leishman JG,Beddoes T S, A Semi Empirical Model For Dynamic Stall. Journal of American Helicopter Society, (3), [8] Leishman,J.G., Nguyen, State-Space Model For Unste-ady Airfoil Behavior. AIAA Journal, Vol. 28, No.5, 1999 [9] Leishman, J.G., Nguyen K.Q, State- Space Model For Unsteady Airfoil Behavior. AIAA Journal, Vol. 28, No.5, 1990 Copyright Statement authors confirm that y, /or ir company or organization, hold copyright on all of original material included in this paper. authors also confirm that y have obtained permission, from copyright holder of any third party material included in this paper, to publish it as part of ir paper. authors confirm that y give permission, or have obtained permission from copyright holder of this paper, for publication distribution of this paper as part of ICAS2012 proceedings or as individual off-prints from proceedings. 5