Introduction to Unsteady Aerodynamics
So far, when considering static aeroelastic effects in Chapters 8 and 9, the aerodynamic surfaces (such as wings) have been in a steady condition and so the resulting forces and moments have been steady (i.e. constant with time). However, for flutter, manoeuvre and gust response analyses the behaviour of aerodynamic surfaces under dynamic motion is required and it is necessary to include the effect of the aerodynamic surface motion upon the resulting forces and moments. These so-called unsteady effects are an outcome of the changing circulation and wake acting upon a moving aerofoil, and can have a considerable influence upon the resulting aerodynamic forces and moments. Consequently, a more sophisticated analysis is required than simply considering the angle of incidence. Most aeroelasticity textbooks cover unsteady aerodynamic effects (Scanlan and Rosenbaum, 1960; Fung, 1969; Bisplinghoff et al., 1996; Hodges and Pierce, 2002; Dowell et al., 2004).
In this chapter, the two-dimensional inviscid, incompressible flow over a thin, rigid section aerofoil undergoing small amplitude heave and pitch motions will be considered. Starting with the effect of a sudden step change in incidence on the lift acting on an aerofoil, the lift and moment resulting from a harmonically oscillating aerofoil in a steady flow will be investigated, followed by consideration of how a general motion would be dealt with. Analytical models, using the so-called oscillatory ...