Unsteady aerodynamic uncertainty estimation and robust flutter analysis

Unsteady aerodynamic uncertainty affects the critical worst-case flutter boundary directly. The modeling and bound estimation of aerodynamic parameter's uncertainty are presented in this work. The nominal unsteady aerodynamics due to modal motion is calculated by the routine doublet lattice method (DLM). Then three different aerodynamic uncertainty hierarchies under the structured singular value (μ) framework are constructed by using the linear fractional transformation technique. These aerodynamic uncertainty hierarchies are aerodynamic influence coefficients, modal pressure coefficients and general aerodynamic influence coefficients, respectively. The ANSYS/CFX commercial software is applied to compute the accurate unsteady pressure coefficients for each mode. The uncertainty bounds for pressure coefficients at different reduced frequencies are estimated by interpolating method. Consequently, the deterministic robust flutter velocity is analyzed in the frequency domain with μ method. Two numerical cases are applied to validate the above framework. One is a NACA0012 wing section. The other application is a three dimensional AGARD445.6 aeroelastic wing. Results indicate that when aerodynamic pressure uncertainty is considered, the worst-case flutter velocity decreases about 13.3% than the nominal flutter velocity in NACA0012's application. This uncertainty bound estimation method can get an actual aerodynamic bound in aeroelastic applications.