On the Nonlinear Lift Characteristics of Slender Bodies at Incidence

Abstract

Nonlinearity in normal force for a slender body with small incidence to flow is discussed by the asymptotic expansion method under the usual assumptions, 1>>e>>1/√Rn and k=β/e=O (1), where e is a slenderness parameter, β an angle of attack, k relative angle of attack, and Rn Reynolds number. The main purpose of the present paper is to develop the method to determine the separation line and the strength of the vortex sheet separating from there. The near field is composed of continuous vortex sheet whose complex potential is expressed with the circulation as a parameter, which is measured from the end point of vortex sheet to the point considered. Kutta's condition to be used to determine the strength density of the vortex sheet near the separation line is proposed by investigating the characteristics of the governing equation of vortex sheet shape. It is shown that this condition is consistent with the vortex conservation law. A method is proposed to solve simultaneously potential stream-lines and boundry layer parameters including the effects of the vortex sheet by only one marching downstream. The shape of the vortex sheet and the separation line are calculated and the normal force coefficient is compared with experimental results.