Unsteady Aerodynamic Coefficients Obtained by a Compressible Vortex Lattice Method

Unsteady solutions for the aerodynamic coefficients of a thin airfoil in compressible sub- or supersonic flows were studied. The lift, the pitch moment, and the pressure coefficients were obtained numerically for the following motions: the indicial response (unit step function) of the profile, that is, a sudden change in the angle of attack; a thin profile penetrating into a sharp edge gust (for several gust velocity ratios); a thin profile penetrating into a one-minus-cosine gust, that is, atypical gust used in commercial aircraft design; the oscillating airfoil; and the interaction of the profile with a convected (from convection phenomenon) vortex passing under the profile, a phenomenon known in the literature as blade vortex interaction or, for a profile case, airfoil-vortex interaction. The present work uses a numerical approach based on vortex singularity. The numerical model was created through the profile discretization in uniform segments, and the compressible flow vortex singularity was used. The results available in the literature are based on approximated exponential equations or computed via computational fluid dynamics. Thus, the purpose of this method is to obtain results as accurate as those from approximated equations and significantly faster than those done via computational fluid dynamics.