Aeroelastic Analysis of a Hingeless Rotor Using a Dynamic Wake Model

H ELICOPTERS operate various excitations, such as aerodynamic loads impinging upon the rotating rotor and mechanical loads due to engine reactions. Hence, they sometimes experience severe vibrations. These vibrations may restrain the helicopter from performing its full capability andmay reduce the life of thevehicle. In particular, extreme vibrations due to aeroelastic instability, which is induced between the unsteady aerodynamic forces and the flexible rotor blades, may degrade safety of the whole aircraft. Therefore, an accurate estimation of the aeroelastic characteristics is essential to successful design and development of a helicopter. Aeroelastic analysis of a rotor system generally requires application of both structural dynamics analysis, which determines accurate motion of the blade, and aerodynamics analysis that accounts for the effects of the rotor wake. Analysis approaches range from simple one-dimensional beam model and blade element momentum theory to the most complicated ones, such as computational structural dynamics (CSD) and computational fluid dynamics (CFD). However, because of the computational resource and time requirement, fluid–structure coupled analysis using simple models is more preferable, especially in the stage of preliminary design, than CSD and CFD model is. In the structural analysis, one of the most preferred approaches is to use a one-dimensional beam model with cross-sectional analysis. In the previous work by Hodges [1] and Bauchau and Hong [2], the large-deflection beam theory was used for aeroelastic analysis in order to account for the geometrical nonlinearity. This theory can handle high-order nonlinear models easily. However, it also has limitation in estimating lateral shear deformation and warping of the cross section due to torsion. Therefore, in order to compensate such limitation, it requires accurate cross-sectional coefficients to be estimated separately. The structural analysis of a composite blade is completed with the use of anisotropic beam cross-sectional analysis based on Atilgan and Hodges [3] and Jeon et al. [4]. In those works, Atilgan and Hodges [3] and Jeon et al. [4] investigated influence of the structural parameters, such as flexibility and shape, upon aeroelastic stability. Both of the researches adopted a simple two-dimensional quasisteady aerodynamics with a linear inflow [4]. Regarding the aerodynamics, the key challenge lies in an accurate estimation on the rotor wake and its impact on the aerodynamic forces. Estimation of the wake can be conducted using various methods ranging from a simple linear inflow model to CFD. Most linear inflow models used by the previous researcherswere not capable of capturing unsteady or three-dimensional aerodynamic effects such as tip relief, which has a critical impact on aerodynamic damping. To estimate the wake more accurately, Yoo et al. [5] used a free-wake analysis for an aeroelastic analysis of a hovering rotor. Smith [6] applied CFD to the static aeroelastic analysis of a hovering rotor. The free-wake analysis and CFD are highly sophisticated aerodynamic analyses. However, because those generally require significant computational resources and time, it may not be appropriate for fluid–structure coupled analysis in the preliminary design stage. One of the alternative ways that use a feasible amount of computational resource and account for the effects of a finite number of rotor blades, which is a crucial factor of an aeroelastic analysis, is the dynamic wake model proposed by He [7]. It is capable of capturing the effects of tip relief and unsteady aerodynamics appropriately, at a low advance ratio (0:0 0:15). Andrade and Peters [8] examined the impact of the collective pitch-angle variation upon a hovering helicopter, in which the dynamic wake model was used with a corrected Reynolds number. Their analysis was more time-efficient than 3-D aerodynamics modeling and more accurate than 2-D modeling. Nagabhushanam and Gaonkar [9] applied the same dynamic wake model to an aeroelastic analysis of a rigidbladed rotor in forward flight. This Technical Note presents an aeroelastic analysis using the large-deflection beam theory, which includes high-order nonlinearity, and reinforced by the composite blade section coefficients. The linear inflow and the dynamic wake models are employed. The linear inflow model will be appropriate for use with the structural analysis, especially at every time step, because its inflow distribution is determined by the overall thrust. However, inflow will be determined by the lift distribution over the rotor disk in the dynamic wake model, and thus its aerodynamic information cannot be transferred to the structural analysis at every time step. Thus, in the present Note, the dynamic wake model and the structural model will be combined with each other in such a way that the inflow can be updated and information can be exchanged at each revolution. In addition, the mechanism of aeroelastic instability will be investigated by evaluating the aeroelastic stability using different linear inflow and dynamic wake models at a low advance ratio. Received 17 February 2011; revision received 3 June 2011; accepted for publication 6 June 2011. Copyright © 2011 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 0021-8669/11 and $10.00 in correspondence with the CCC. ∗Ph.D. Candidate, Department of Aerospace Engineering, San30 Jangjeon-dong Geumjeong-gu; junbbai@pusan.ac.kr. Student Member AIAA. Associate Professor, Department of Aerospace Engineering, San30 Jangjeon-dong Geumjeong-gu; daedalus@pusan.ac.kr. Member AIAA (Corresponding Author). Ph.D. Candidate, School of Mechanical Aerospace and System Engineering, 335 Gwahangno Yuseong-gu; sjryu1004@kaist.ac.kr. Professor, School ofMechanical Aerospace and SystemEngineering, 335 Gwahangno Yuseong-gu; inlee@kaist.ac.kr. Senior Member AIAA. Associate Professor, School of Mechanical and Aerospace Engineering, 599 Gwanangno Gwanak-gu; ssjoon@snu.ac.kr. Senior Member AIAA. ∗∗Research Engineer, Department of Rotor System, 115 Gwahangno Yuseong-gu; shine@kari.re.kr. JOURNAL OF AIRCRAFT Vol. 48, No. 5, September–October 2011