A numerical model for thin airfoils in unsteady compressible arbitrary motion

Abstract

A numerical method based on the vortex methodology is presented in order to obtain unsteady solution of the aerodynamic coefficients of a thin airfoil in either compressible subsonic or supersonic flows. The numerical model is created through the profile discretization in uniform segments and the compressible flow vortex singularity is used. The results of the proposed model are presented as the lift and the pressure coefficient along the profile chord as a function of time. The indicial response for the unit step change of angle of attack and unit sharp-edged gust response of the profile are also obtained numerically. The results yielded by the present methodology are also compared with solutions available in the literature

Numerical investigation of the effects of compressibility on the flutter of a cantilevered plate in an inviscid, subsonic, open flow

“…In order to validate the aerodynamic model, we have considered both the damped and undamped oscillatory motions of a rigid plate -characterized by two shape functions: ψ 1 (x) = 1 and ψ 2 (x) = −x-and computed the evolution of the lift and the leading edge pitching moment (positive nose-up) coefficients along the time given some arbitrary initial conditions. The results obtained with the present method -valid for the permanent regime-have been compared to those obtained with (i) the modified Hariharan-Ping-Scott (HPS) time-domain, finite-differences method [35,36,50] and (ii) the Hernandes-Soviero (HS) time-domain, vortex-lattice method [37,46,47].…”

“…By contrast, the curves corresponding to Mach numbers from 0.01 to 0.2 seem to be almost identical -something expectable since, in that, range, the fluid can be considered incompressible-, and the same happens to those corresponding to Mach numbers from 0.8 to 0.99. In order to check the obtained results, the dimensionless flutter speed is plotted in figure 9 as a function of the upstream Mach number for ρ * = 0.6 and compared to that obtained by Colera and Pérez-Saborid [35][36][37] by two different time-domain methods: the modified HPS [35,36] and the HS [46,47] methods. As can be seen, the agreement between the results of these methods is very good, except for the HS method, which does not provide the incompressible solution at M ∞ → 0.…”

“…Compressibility effects on the flutter of a cantilevered, two-dimensional plate in a compressible, subsonic flow have been previously studied by Tanida [45] -who developed a compressible doublet-lattice method in the frequency domain for a plate in channel flow, but used only one Galerkin mode to describe its motionand by Colera and Pérez-Saborid -who used first a compressible vortex-lattice method [37,46,47] and later a finite differences method [35,36] to study a single case of a plate of given mass and stiffness-. The aim of this work is to generalize these investigations by performing a parametric study of the flutter speed and the flutter frequency of a two-dimensional, cantilevered plate in a compressible, subsonic flow as a function of its mechanical properties and the upstream Mach number.…”

Review of vortex lattice method for supersonic aircraft design

“…Another numerical method by Hernandes [32] is proposed for the unsteady solution of the aerodynamic coefficients of thin profiles in subsonic but also supersonic compressible flow. This model is made through the aerofoil discretisation in uniform segments and the singularity used is a vortex incompressible flow.…”

Unsteady Aerodynamics of Deformable Thin Airfoils

“…Jones' work comprised of correcting the angle of attack for the downwash velocity generated by three dimensional effects. Other work has been done investigating the problem of unsteady compressible flows, including work by Hernandes and Soviero [22].…”