Aerospace Science and Technology 29 (2013) 175–184 Contents lists available at SciVerse ScienceDirect Aerospace Science and Technology www.elsevier.com/locate/aescte Analysis of a structural-aerodynamic fully-coupled formulation for aeroelastic response of rotorcraft G. Bernardini, J. Serafini, M. Molica Colella, M. Gennaretti ∗ Mechanical & Industrial Engineering Department, University Roma Tre, Via della Vasca Navale 79, 00146 Rome, Italy article info abstract Article history: Received 23 May 2012 Received in revised form 20 February 2013 Accepted 8 March 2013 Available online 21 March 2013 Keywords: Computational aeroelasticity Rotary wing aeroelastic response Boundary-element-method aerodynamics This paper deals with a computational aeroelastic tool aimed at the analysis of the response of rotary wings in arbitrary steady motion. It has been developed by coupling a nonlinear beam model for blades structural dynamics with a potential-flow boundary integral equation solver for the prediction of unsteady aerodynamic loads around three-dimensional, lifting bodies. The Galerkin method is used for the spatial integration of the resulting differential aeroelastic system, whereas the periodic blade response is determined by a harmonic balance approach. This aeroelastic model yields a unified approach for aeroelastic response and blade pressure prediction, that may conveniently be used for aeroacoustic purposes. It is able to examine configurations where blade–vortex interactions occur. Numerical results show the capability of the aeroelastic tool to evaluate blade response and vibratory hub loads for a helicopter main rotor in level and descent flight conditions, and examine the efficiency and robustness of the different numerical solution algorithms that may be applied in the developed aeroelastic solver. Comparisons among aeroelastic predictions based on different aerodynamic models are also presented.  2013 Elsevier Masson SAS. All rights reserved. 1. Introduction The aim of this work is to present some features and recent advances of a computational tool for the analysis of the aeroelastic response of rotary wings. Rotorcrafts are affected by strong cou- plings between elastic deformations and aerodynamic loads, which significantly contribute to the vibrations transmitted to the fuse- lage, as well as, to the emitted noise. A great variety of flight conditions may be experienced by rotary-wing aircraft, each yield- ing specific aerodynamic environment and corresponding elastic response. For instance, during descent flights of helicopters, strong BVI (Blade–Vortex Interaction) characterizes both vibrations and noise levels and accurate simulation tools are required for reliable predictions of the corresponding aeroelastic responses. Commonly, in computational tools aimed at the aeroelastic analysis of rotors the aerodynamic loads are determined through sectional theories that take into account the effects of the in- flow induced by the wake [13]. Wake inflow may be evaluated in several ways, ranging from the application of semi-empirical static- inflow analytical models [5], up to free-wake computational solu- tions [14], including the use of dynamic inflow models [20]. At the same time, the sectional load models may take into consideration the complex dynamic stall effects through semi-empirical models [16,15]. In the last decade, the inclusion of free-wake inflow within * Corresponding author. Tel.: +39 (06) 57333260; fax: +39 (06) 5593732. E-mail address: m.gennaretti@uniroma3.it (M. Gennaretti). tools for the analysis of rotor aeroelastic response has become a largely applied solution procedure (see, for instance, Refs. [17,4], and Ref. [19] where a dual vortex free-wake code is applied for rotor aeroelastic and aeroacoustics purposes). The computational aeroelastic tool for rotary wings analyzed here is the result of the research work presented and validated by the authors during the last years [6,7,2]. It uses a three- dimensional, unsteady, Boundary Element Method (BEM) aerody- namic solver based on an integral formulation for potential flows suited for the prediction of strong BVI effects [7]. This solver can be applied both for direct evaluation of the aerodynamic loads and for calculation of the wake inflow to be used within a sectional aerodynamic load model. For this work, the blade structural model is based on a nonlinear, bending-torsional, theory for nonuniform, homogeneous, isotropic, rotating, straight beams undergoing mod- erate deflections [10]. In the past decades, several authors have faced the problem of developing more advanced structural dynam- ics models, that are valid for applications concerning composite- material blades, curved-axis blades and blades undergoing large deflections (see, for instance, Refs. [1,3,25,12,22,21]). However, here the emphasis is on the structure/aerodynamics coupling and nu- merical strategies to solve the resulting differential formulation, and hence the introduction of a more complex blade structural model is beyond the scope of the paper and would appear as an unnecessary complication of the problem. The Galerkin ap- proach is applied for the space integration of the resulting set of integro-differential equations, with the natural modes of vibration of a cantilever, nonrotating beam used as test and trial functions 1270-9638/$ – see front matter  2013 Elsevier Masson SAS. All rights reserved. http://dx.doi.org/10.1016/j.ast.2013.03.002