Subsonic Indicial Aerodynamics for Aerofoil's Unsteady Loads via   Numerical and Analytical Methods
  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. 
Marco Berci and Marcello Righi
physics.flu-dyn math.OC