Asymptotic theory of flow separation from wings of low aspect ratio

Abstract

Numerous methods have been developed to calculate the aerodynamic characteristics of wings of low aspect ratio in the case when there is flow separation from the wing edges. Among the methods based on direct solution of the three-dimensional Euler equations there are the method of discrete vortices [1, 2] and the panel method [3]. In addition, numerical and asymptotic methods [4, 5] based on the theory of slender bodies [6] are used. One of the most important shortcomings of this theory is the dependence of the flow pattern at a given section of the wing on only the upstream flow. The obtained solutions therefore contain no information about the influence of the trailing edge of the wing, on which, as is well known, the Chaplygin-Zhukovskii condition is satisfied. The aim of the present paper is to construct an asymptotic theory of higher approximation and a corresponding numerical method for calculating flow separation from wings of low aspect ratio in which this shortcoming is absent.