An enhanced analytical method for the subsonic indicial lift of two-dimensional aerofoils - with numerical cross-validation

Aerodynamic indicial-admittance functions are generated for the unsteady lift of two-dimensional aerofoils in subsonic flow, using an enhanced theoretical formulation which grants effective synthesis. Both a step-change in the angle of attack and a sharp-edge gust are considered as the flow perturbation. Convenient analytical approximations of the indicial functions are obtained by generalising those available for incompressible flow, taking advantage of acoustic wave theory for the non-circulatory airload and Prandtl-Glauert's scalability rule for the circulatory airload. An explicit formula is proposed for modelling the latter as function of the Mach number in the absence of shock waves, while damped oscillatory terms are introduced for better approximating the former. Indicial-admittance functions are then obtained for the lift development of a wing aerofoil using Euler-based simulations at several Mach numbers, thus providing with sound cross-validation. Appropriate tuning of the analytical expressions is also derived in order to mimic the numerical solutions. The rigor of superposing circulatory and non-circulatory theoretical contributions is thus verified in the light of computational fluid dynamics and all results are addressed with respect to the physical and mathematical assumptions employed, within a consistent framework.