Modeling Unsteady Aircraft Aerodynamics Using Lorenz Attractor: A Reduced-Order Approach for Wing Rock

Abstract

This paper presents a novel modeling approach for unsteady aircraft airflow, leveraging the Lorenz attractor framework. The proposed model is based on the force distribution exerted by a lift-generating wing on the surrounding fluid. It distinguishes between turbulent and nominal components of the force distribution, with the nominal force distribution modeled to peak at the wing and decay linearly into the free stream. This separation allows the turbulent component to be represented by a transport equation that is influenced by flight conditions, specifically dynamic pressure and angle of attack. Consequently, the Navier-Stokes equations, along with the turbulence transport equation, can be transformed into a reduced-order model characterized by three scalar ordinary differential equations - similar to the Lorenz attractor. This resulting system effectively captures chaotic behavior, facilitating the exploration of complex dynamics without the computational demands of solving the full Navier-Stokes equations. A simulation trade study is conducted that models wing rock phenomena at high angles of attack, demonstrating the effectiveness of the proposed approach in capturing the intricate dynamics of unsteady aircraft aerodynamics.