Chapter 8 dealt with low speed aerodynamic nonlinearities but the flow was allowed to be compressible; the semi‐empirical aerodynamic methods presented can in principle be used up to transonic Mach numbers. The major aerodynamic nonlinearities in this flight regime are shock movement and shock‐boundary layer interaction, which can cause flow separation. More detailed modelling of these nonlinearities can only be carried out by means of high fidelity Computational Fluid Dynamic simulations, which are beyond the scope of the present book. As a consequence, there will be no further discussion of transonic aerodynamic nonlinearities.
In the present chapter, we will present aeroelastic phenomena that occur at supersonic and hypersonic Mach numbers. Supersonic flight conditions are defined by while hypersonic flow usually involves . There is a simple 2D quasi‐steady aerodynamic model that is valid throughout these two flow regimes, referred to as piston theory. The resulting aerodynamic models are nonlinear but the nonlinearity is weak so they are most often linearised. We will apply piston theory to two problems: a 2D airfoil oscillating in a supersonic/hypersonic flow and panel flutter.
9.2 Piston Theory
Piston theory (Lighthill ...