  This study deals with generating aerodynamic indicial-admittance functions
for predicting the unsteady lift of two-dimensional aerofoils in subsonic flow,
using approximate numerical and analytical formulations. Both a step-change in
the angle of attack and a sharp-edge gust are suitably considered as small
perturbations. Novel contributions concern both a systematic analysis of the
computational simulations process and an effective theoretical synthesis of its
outcome, providing with sound cross-validation. Good practice for generating
the indicial-admittance functions via computational fluid dynamics is first
investigated for several Mach numbers, angles of attack and aerofoil profiles.
Convenient analytical approximations of such indicial functions are then
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
parametric formula is newly proposed for modelling the latter as function of
the Mach number in the absence of shock waves, while damped harmonic terms are
effectively introduced for better approximating the former. Appropriate tuning
of the analytical expressions is also derived in order to mimic the numerical
solutions and successfully verify the rigor of superposing circulatory and
non-circulatory theoretical contributions in the light of computational fluid
dynamics. Results are finally shown and critically addressed with respect to
the physical and mathematical assumptions employed, within a consistent
framework.
