State Space Modeling of Viscous Unsteady Aerodynamic Loads

In this paper, we started by summarizing our recently developed viscous unsteady theory based on coupling 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-dependence could be determined. We then developed a finite-state approximation of such a theory, presenting it in a state space model. This novel nonlinear state space model of the viscous unsteady aerodynamic loads is expected to serve aerodynamicists better than the classical Theodorsen's model, as it captures viscous effects (i.e., Reynolds number dependence) aswell as nonlinearity and additional lag in the lift dynamics; and 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 proceeded to develop a linearization of such a model, which enables analytical results. So, we derived an analytical representation of the viscous lift frequency response function, which is an explicit function of, not only frequency, but also Reynolds number. We also developed a state space model of the linearized response. We finally simulated the nonlinear and linear models to a non-harmonic, small-amplitude pitching maneuver at 100 - 000 Reynolds number and compared the resulting lift and pitching moment with potential flow, in reference to relatively higher fidelity computations of the Unsteady Reynolds-Averaged Navier-Stokes equations.