Non-linear theory of steady forces on wings with leading-edge flow separation

Abstract

Leading-edge separation from fairly thin wings of moderate or low aspect ratio gives rise to aerodynamic loading and forces that are non-linear with incidence. It is important to be able to estimate these effects theoretically for wings of arbitrary planform. A simplified mathematical vortex model has been devised by Gersten for wings in steady incompressible flow. This model in conjunction with Multhopp's linear lifting-surface theory provides the basis of the present method. The investigation covers a variety of planforms, and each type serves to illustrate different facets of non-linear theory and its numerical application. Many comparisons between the calculated results and wind-tunnel measurements are used in a critical appraisal of the method. When there are leading-edge vortices or extensive regions of separated flow, the calculated total lift and pitching moment give a decisive improvement on linear theory. Analysis shows a simple correlation between the centre of non-linear lift and the linear aerodynamic centre. The spanwise distributions of lift and local centre of pressure on rectangular wings are well predicted, but the calculated loading on swept wings appears to be unrealistic. An alternative treatment of the mathematical model on the basis of slender-wing theory illustrates some defects of the method in its present form. It might be developed to simulate the rolling-up of vortex sheets into concentrated vortices. However, the reliability of the present method for steady aerodynamic forces appears to justify its immediate extension to the oscillatory problem of slowly pitching wings of arbitrary planform at high mean incidence.