Subsonic Flow over a Thin Airfoil in Ground Effect

TL;DR

This paper analyzes compressible subsonic flow over a thin airfoil near the ground, deriving a singular integral equation to determine pressure and aerodynamic loads, and assessing the divergence speed of the wing structure.

Contribution

It introduces a derivation of the Possio equation for ground effect in compressible flow and verifies solution existence, providing a basis for aerodynamic load calculations.

Findings

Derived the Possio equation using advanced transforms and methods.

Verified existence and uniqueness of the solution.

Calculated aerodynamic loads and divergence speed for ground-effect wings.

Abstract

In this paper, the problem of compressible flow over a thin airfoil located near the ground is studied. A singular integral equation, also known as Possio equation, that relates the pressure jump along the airfoil to its downwash is derived. The derivation of the equation utilizes Laplace transform, Fourier transform, method of images, and theory of Mikhlin multipliers. The existence and uniqueness of solution to the Possio equation is verified for the steady state case and an approximate solution is obtained. The aerodynamic loads are then calculated based on the approximate solution. Moreover, the divergence speed of a continuum wing structure located near the ground is obtained based on the derived expressions for the aerodynamic loads.