Subsonic Flow over a Thin Airfoil in Ground Effect: a Functional Analytic Approach

Abstract

In this work, the problem of subsonic compressible flow over a thin airfoil located near the ground is studied. A singular integral equation, also known as the Possio integral equation [29], that relates the pressure jump along the airfoil to its downwash is derived. The derivation of the equation utilizes the Laplace transform, the Fourier transforms, the method of images, and the theory of Mikhlin multipliers. The existence and uniqueness of solutions to the Possio equation is verified for the steady state case through the concepts of the finite Hilbert operator, the Tricomi operator, and contraction mappings. Moreover, an approximate solution to the Possio equation, based on a linear approximation, is obtained. The aerodynamic loads are then calculated based on the approximate solution. Finally, the divergence speed of a continuum wing structure located near the ground is obtained based on the derived expressions of the aerodynamic loads.