null
(Ed.)
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)
as well 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.
more »
« less