Numerical investigations of an airfoil in a nonuniform stream

Abstract

The nonlinear differential equation for the flowfield around an airfoil in a two-dimensional nonuniform parallel stream is solved by the finite difference method. The numerical results show that even for a thin airfoil at small angle of attack, the stagnation pressure and the vorticity carried by the streamline passing around the airfoil are significantly different from the corresponding values carried by the undisturbed streamline through the body under the linearized approximation. When the deviation upstream from the uniform flow is represented by a Gaussian profile to simulate the velocity increment behind a propeller, the numerical results show that there is an optimum vertical location of the airfoil relative to the upstream profile for maximum lift. A correlation between the maximum lift and a nonuniformity parameter of the upstream profile is obtained. This parameter is a combination of two parameters, the maximum velocity deviation and the spread of the nonuniformity. When the upstream velocity profile changes from one uniform stream to another through a layer with a steep velocity gradient, there is a significant gain (loss) in lift, if the vorticity is in the same (opposite) sense as the circulation around the wing. A more drastic change in lift occurs, however, when the circulation is in the opposite sense as the vorticity. This occurs when the layer with a steep velocity gradient passes over the upper surface of the airfoil. This phenomenon of a sudden change in lift is of importance when an airplane encounters an atmospheric disturbance.