Classical, unsteady, thin-airfoil theory has been an integral part of performance and aeroelasticity calculations for the past 70 years. The theory is based on potential flow with a non-penetration boundary condition on a thin surface in two dimensions. Extensions have made the theory applicable to lift, moment, and drag in the presence of time-varying free-stream, with subsonic compressibility effects, and including trailing-edge flap deflections. When combined with simple empirical corrections to account for blade thickness, this theory has become the core of blade airloads calculations for rotorcraft; and it provides the baseline around which dynamic stall and other corrections are made. In this paper, the classical theory is extended in four ways. First, the theory is reformulated to apply to an airfoil that is performing large frame motions with respect to the air mass. This extension is important in applications to rotorcraft for which the blade can experience large, rigid-body translations and rotations. Second, airfoil motions within the frame are allowed to include completely general dynamic deformations of the cross-section. These could include dynamic trailing-edge flap motions, dynamic droop motions, or dynamic changes in camber (to name a few). Third, the theory is formulated in terms of generalized deflections and generalized forces within that frame, which leads to mass, damping, and stiffness matrices for the generalized airfoil motion. This makes it convenient to assemble this theory with finite-element codes or modal analyses. Fourth, although most of the applications herein are in the context of a two-dimensional flat wake in the frequency domain (as in Theodorsen theory), the theory is cast such that it can be coupled with any unsteady wake model desired, including three-dimensional wake models such as vortex-lattice. Comparisons with other theories will show that this new theory includes (and agrees exactly with) the classical theories of Wagner, Theodorsen, Garrick, Loewy, Greenberg, and Isaacs when applied to those special cases. Applications to large-motion dynamics reveal that the present model preserves conservation of energy whereas some airloads theories do not. Finally, comparisons with experimental data show that the new model gives good agreement with static or dynamic lift and pitching moments (and with the moment about the flap hinge) for airfoils with camber and trailing-edge flaps.
展开▼
