State-Space Modeling of Viscous Unsteady Aerodynamic Loads

Abstract

In this paper, we summarize our recently developed viscous unsteady theory, which couples potential flow with the triple-deck boundary-layer theory. This approach provides a viscous extension of potential-flow unsteady aerodynamics. As such, a Reynolds-number-dependent transfer function is determined for unsteady lift. We then use the Wiener–Hammerstein structure to develop a finite-dimensional approximation of such an infinite-dimensional theory, presenting it in a state-space model. This novel nonlinear state-space model of viscous unsteady aerodynamic loads is expected to serve aerodynamicists better than the classical Theodorsen’s model because it captures viscous effects (that is, Reynolds number dependence) as well as nonlinearity and additional lag in the lift dynamics; it also allows simulation of arbitrary time-varying airfoil motions (not necessarily harmonic). Moreover, being in a state-space form makes it quite convenient for simulation and coupling with structural dynamics to perform aeroelasticity, flight dynamics analysis, and control design. We then develop a linearization of such a model, which enables analytical results. Subsequently, we derive an analytical representation of the viscous lift frequency response function: an explicit function of both the frequency and Reynolds number. We also develop a state-space model of the linearized response. We finally simulate the nonlinear and linear models to a nonharmonic small-amplitude pitching maneuver at a Reynolds number of 100,000 and compare the resulting lift and pitching moment with those obtained from potential flow; this is in reference to relatively higher-fidelity computations of the unsteady Reynolds-averaged Navier–Stokes equations.