Extension to Nonlinearities and Unsteady Flow Regimes
As mentioned in Chapter 5, Sec. 24, analytical redundancy for fly-by-wire control system safety will become feasible only when vehicle system identification operates well under all flight conditions, and not just where linearized, small perturbation equations of motion apply. For this reason, and to generate practical design information, there has been an effort to extend identification to nonlinear and unsteady aerodynamic regimes. The extended Kalman filter mentioned in the previous section can generate full nonlinear aerodynamic models, such as Cm (a,8,q,…), and not just aerodynamic stability derivatives at various operating points.
The transfer function model for unsteady flow (Chapter 10, Sec. 6.1) has been used successfully at the DLR to model lift hysteresis at the stall for the Fairchild/Dornier Do 328 transport. The procedure (Fischenberg, 1999) is in several parts, starting with a steady-state approximation for the point of trailing-edge flow separation at high angles of attack, using static wind-tunnel data. Time dependency is introduced by the assumption that the separation point can be modeled as the solution of a first-order differential equation, equivalent to a single-pole transfer function. A final assumption is that the lift coefficient in trailing-edge separated flow is a function of the separation point, using a model proposed by Kirchoff. Four parameters of the model remain to be identified in flight testing, but when these are found, good comparison of flight measurements of lift coefficent with the modeled values is obtained (Figure 14.18).
The significance of this work is that once the unsteady lift parameters of representative lifting surfaces can be predicted, the basis is in hand for predicting unsteady values of complete airplane stability derivatives. Those derivatives are computed from the forces and moments of the lifting surfaces and the fuselage-type shapes that make up a complete configuration. Future work in this area will presumably deal with leading – edge flow separation models, which are characteristic of thin wings with sharp leading edges, and with predictive models for the unsteady vortex flows that can affect stability derivatives. Stall hysteresis for airfoils with sharp leading edges is discussed by Covert (1993).