Nonlinear Modeling and Identification of Unsteady Aerodynamics at Stall

For an aircraft with delta wing shape, aerodynamics in stall angles-of-attack at both low and high-subsonic Mach conditions is known to be unsteady and nonlinear in nature. In these conditions, the longitudinal aerodynamic loads depend on the history of angle-ofattack and side-slip. The classical method of using damping or acceleration aerodynamic derivatives for modeling the unsteady variation of coefficients is unsuitable. Hence, two novel approaches for modeling aerodynamic loads in these conditions are proposed in this thesis. The unsteady effect in stall conditions at low Mach number is reflected in forced oscillation wind tunnel tests as dependence of longitudinal loads on amplitude and frequency of sinusoidal angle-of-attack input. The variations in longitudinal loads are nonlinear as their power spectrum contains super-harmonics of input frequency. The approaches presented in literature are equivalent when these are reduced to equivalent linear transfer function formulation, while their nonlinear adaptations are semi-empirical or adhoc. Hence, Volterra Variational Modeling (VVM) is proposed as a systematic approach to capture the nonlinear nature of unsteady variations. The VVM is derived from Volterra series as a set of parametric differential equations of the so-called kernel states. The kernel-states have special harmonic input response properties which are leveraged to develop a systematic methodology to capture the nonlinear unsteady variations in pitching moment coefficient. VVM is shown to inherently reproduce the nonlinear features of unsteady aerodynamic loads like amplitude dependence of nonlinear variations, different effective time-scale for pitch-up and pitchdown motions and same number of super-harmonics as seen in the experimental data. Hence, it offers several advantages compared to all the modeling approaches in literature. The VVM is a powerful approach due to following features: (i) Mathematically rigorous structure, (ii) Physical interpretations of parameters, (iii) it facilitates linear analysis of the flight modes (iv) simple identification methodology using forced oscillation wind tunnel test data (v) open to innovations in model structure and estimation technique. These concepts are demonstrated for the Generic Tailless Aircraft and F16XL aircraft using comprehensive sets of wind tunnel test data . The unsteady phenomena at high sub-sonic Mach number is called AbruptWing Stall, and novel model called ”Bifurcational Model of Aerodynamic Asymmetry” is proposed for modeling it. It shown to be a topologically rich structure which can model the static hysteresis and unsteady variations in rolling moment coefficient versus the side-slip angle, in order to reproduce the effects of Abrupt Wing Stall on flight dynamics.