Novel Discrete-Vortex Method for Unsteady Thin Airfoils

Modeling unsteady flow wakes in reduced-order methods often involves vortex distributions. Specifically, discrete-vortex formulations for shed trailing-edge vortices produce complex wake patterns and structures. Undoubtedly, the Kutta condition plays an essential role in modeling two-dimensional inviscid aerodynamics. In this context, a uniformly convergent series expansion for the bound vorticity has shown robustness in correctly satisfying the unsteady Kutta condition in the thin-airfoil theory framework. Although the proposed methodology has been developed and validated for classical small-disturbance aerodynamic problems, improvements must be made when replacing a continuous vortex sheet with discrete vortices. In this way, a physically-based discrete-vortex model based on unsteady thin-airfoil theory is presented. The novel formulation fully satisfies the unsteady Kutta condition and stands as the basis for further improvements.