Two-dimensional, incompressible unsteady airfoil theory is based on a set of fairly compact equations for conservation of mass and momentum (i.e., the potential flow equations) that can be transformed into vorticity equations. Glauert expansions of the terms in these equations are very useful in both the solution and the interpretation of thin airfoil theory. With these expansions in hand, a simple step response for the velocity field due to a single, trailed vortex leads immediately to the Laplace-form and frequency-form of the lift deficiency function (i.e., the Theodorsen function) and to the step response of an airfoil, the Wagner function. These forms are related to each other through their Fourier transforms. The same Glauert expansions can also yield finite-state inflow models, in which the induced flow is represented in terms of a finite number of states that measure the strength of closed-form potential functions. Models can be developed either from the vorticity equations or from the potential flow equations. Because of the singular nature of the twodimensional problem, there are singularities that arise in both derivations; but these can be treated by noting that the wake does not trail to infinity. As a result, the infinity can be approximated yielding convergent inflow models by either approach. Numerical results have shown that the finite-state results give good correlation with the more conventional, frequency-domain versions. The advantages of the finite-state methodology, however, are clear: (i) the inflow theory can be coupled with lift models other than the simple non-penetration boundary condition of classical theories; (ii) finite-state models are in a matrix form that allows them to be easily assembled together with structural models for aeroelastic computations; (iii) the finite-state models permit solutions in either the time domain, the frequency domain, or the Laplace domain for arbitrary forcing functions and even for unsteady free-stream. Thus, they can be applied to a much wider variety of problems than can classical approaches.
Two-dimensional incompressible unsteady airfoil theory. An overview
Zweidimensionale Theorie der inkompressiblen instationären Profilumströmung. Ein Überblick
Journal of Fluids and Structures ; 24 , 3 ; 295-312
2008
18 Seiten, 9 Bilder, 1 Tabelle, 27 Quellen
Article (Journal)
English
Unsteady oscillation of a deformable airfoil section in incompressible flow
Online Contents | 2009
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