Unsteady Aerodynamic Coefficients Obtained by a Compressible Vortex Lattice Method

Abstract

Unsteady solutions for the aerodynamic coefficients of a thin airfoil in compressible subsonic or supersonic flows were studied. The lift, the pitch moment, and pressure coefficients were obtained numerically for the following motions: the indicial response (unit step function) of the profile, i.e., 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 and sinusoidal gust, i.e., a typical gust used in commercial aircraft design; oscillating airfoil; and also the interaction of the profile with a convected (from convection phenomenon) vortex passing under the profile, a phenomenon known in literature as BVI (Blade Vortex Interaction) or for a profile case AVI (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 (CFD). Thus, the purpose of this method is to obtain a more accurate computation compared to those of approximated equations, and quite faster than those done via CFD. The results yielded by the present methodology were also compared with solutions available in the literature. The results were obtained for subsonic and supersonic flow in compressible environment.