Continuous-Time State-Space Unsteady Aerodynamic Modeling for Efficient Loads Analysis

The present paper proposes a continuous-time state-space formulation of the unsteady vortex lattice method, which is derived through a discretization of the governing advection equation for transport of vorticity in the wake. A continuous-time system is obtained by only discretizing the advection equation in space, while retaining the derivative with respect to time. The discretization in space is based on the discontinuous Galerkin method. The present method can be applied to any arbitrary nonuniform wake discretization and can be extended to higher-order panel methods or a nonflat wake shape. The method is extended to compressible flows by applying the Prandtl-Glauert transformation. The time-dependent terms in the small disturbance potential equation are neglected. Thus, incompressible flow solution procedures are applied with minimum modifications to unsteady compressible problems. The benefits are demonstrated by applying the model to the gust analysis of a general aircraft wing, varying the time step, and introducing a nonuniform wake discretization, resulting in a reduced model size for a given accuracy. The resulting continuous-time state-space model can be used for efficient loads analysis of general aircraft wings including the effects of compressibility and allows for easy integration with structural or flight dynamic models for efficient aero(servo)elastic analyses.