Investigation of analytical unsteady and quasi-steady methods accuracy at different reduced frequencies and effect of compressibility and its correction on these methods

Responses of airfoils unsteady aerodynamics have important role in rotary-wing and aeroelasticity problems. Numerical analysis of unsteady flows usually needs more time. Therefore, engineering use quasi-steady and analytical methods for solving oscillatory airfoils. In the present research, the responses of the analytical unsteady and quasi-steady methods are calculated for plunge and pitch motions at different reduced frequencies and Mach numbers. One of Mach numbers is incompressible and the other is compressible. Compressibility correction is also applied for compressible Mach number. A numerical inviscid code is developed based on central finite volume method to solve unsteady flow equations in the arbitrary Lagrangian-Eulerian formulation for moving boundary problems. The results of the quasi-steady and analytical unsteady methods are compared with numerical code results. An implicit dual time scheme is applied for time discretization in CFD code. The analytical unsteady method is chosen Theodorsen method. Results show the finite volume method is an accurate method and the analytical method is in good agreement with numerical code in incompressible flows. The compressibility correction improve the results in compressible flows.