Abstract
A method is presented to model the incompressible, attached, unsteady lift and pitching moment acting on a thin three-dimensional wing in the time domain. The model is based on the combination of Wagner theory and lifting line theory through the unsteady Kutta–Joukowski theorem. The results are a set of closed-form linear ordinary differential equations that can be solved analytically or using a Runge–Kutta–Fehlberg algorithm. The method is validated against numerical predictions from an unsteady vortex lattice method for rectangular and tapered wings undergoing step or oscillatory changes in plunge or pitch. Further validation is demonstrated on an aeroelastic test case of a rigid rectangular finite wing with pitch and plunge degrees of freedom.
Highlights
Closed-form solutions for the attached incompressible unsteady flow problem around a two-Dimensional (2D) airfoil exist in both the frequency domain [1] and in the time domain: Wagner theory [2,3]Finite state flow model [4]Leishman unsteady state space representation [5]For three-Dimensional (3D) wings, there exists one closed-form solution for the unsteady aerodynamics of elliptical wings [2]
In Wagner’s and Theodorsen’s 2D unsteady aerodynamic theories, the wake is still straight and semi-infinite, but its strength varies in the chordwise direction since it is calculated from the unsteady
It can be concluded that the Wagner lifting line method can predict accurately the flutter of a wing with a finite span
Summary
Closed-form solutions for the attached incompressible unsteady flow problem around a two-Dimensional (2D) airfoil exist in both the frequency domain [1] and in the time domain: Wagner theory [2,3]Finite state flow model [4]Leishman unsteady state space representation [5]For three-Dimensional (3D) wings, there exists one closed-form solution for the unsteady aerodynamics of elliptical wings [2]. Closed-form solutions for the attached incompressible unsteady flow problem around a two-Dimensional (2D) airfoil exist in both the frequency domain [1] and in the time domain: . Wagner theory [2,3]. Finite state flow model [4]. Leishman unsteady state space representation [5]. For three-Dimensional (3D) wings, there exists one closed-form solution for the unsteady aerodynamics of elliptical wings [2]. For general geometries, closed-form solutions are usually obtained either from strip theory (see for example Dowell [6]) or from panel methods, such as the Doublet Lattice
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