Aggregated Lifting-line Vortex Modeling for Unsteady Aerodynamics*

Lightweight aircraft are vulnerable to flow separation induced by gusts. For purposes of regulating flight in the presence of such gusts, it is important to estimate the flow behavior and the instantaneous aerodynamic forces. Our objective is to predict the aerodynamic response of a finite wing in a free stream to a gust in a robust, but computationally cheap way. For this purpose, we propose an aggregated lifting-line vortex model and explore its validity. The model consists of three parts: a steady lifting line model, a collection of unsteady vortex filament loops, denoted as the outer model, and a series of two-dimensional unsteady potential flow models, distributed over the span of the wing and denoted as the inner models. The gust response of the wake behind a finite wing in a free stream is then modeled as a perturbation to the steady wake, where the steady wake is represented by the lifting line model vortex filaments and the perturbation is represented by the inner model point vortices and the outer model vortex filaments.