Prediction of loaded airfoil unsteady aerodynamic gust response by a locally analytical method

Abstract

A complete first-order model is formulated to analyze the effects of steady loading on the incompressible unsteady aerodynamics generated by a two-dimensional gust convected with the steady mean flow past an arbitrary airfoil at finite nonzero angle of attack. A locally analytical solution is then developed in which the discrete algebraic equations which represent the flow field equations are obtained from analytical solutions in individual grid elements. The unsteady flow field is rotational and is linearized about the full potential steady flow past the airfoil. Thus, the effects of airfoil geometry and angle of attack are completely accounted for through the mean potential flow field. The steady flow is independent of the unsteady flow. However, the strong dependence of the unsteady flow on the steady effects of airfoil geometry and finite angle of attack are manifested in the unsteady boundary conditions which are coupled to the steady flow. A body-fitted computational grid is utilized. Analytical solutions to the transformed flow equations in individual grid elements are then developed, with the complete solution obtained by assembling these locally analytical solutions. This model and locally analytical solution are then applied to a series of airfoil and flow configurations. The results demonstrate that accurate predictions for the unsteady aerodynamic gust response are obtained only by including the coupled steady flow effects on the unsteady aerodynamics. Thus for cambered, or cambered and thick airfoils at zero or finite angle of attack, or a thin flat plate airfoil at a nonzero angle of attack, the model and solution developed herein accurately predict the gust response. It was also demonstrated that the classical small perturbation combined transverse and chordwise gust models yield accurate predictions only for the special case of a thin flat plate airfoil at zero angle of attack, i.e. only when the chordwise gust is zero.