Nonlinearity in Lift of Slender Bodies at Incidenc

Abstract

Nonlinearity in normal (lateral) force for a slender body with small incidence to flow is discussed by the asymptotic expansion method under the assumptions, 1>>β>>ε>>1/√Rn and (ε/β) 1/2>>β, where β is an angle of attack, ε a slenderness parameter, and Rn the Reynolds number. The theory is developed utilizing a slender body theory technique. The near field is composed of two vortex layers extending downstream infinitely in cross flow direction. Kirchhoff's dead water theory is applied to the cross flow with the inclusion of three-dimensional effect which increases the velocity between the vortex layers in a lateral section. The first term of the normal force coefficient is derived only from the near field consideration and expressed by lateral drag coefficient of the Kirchhoff's theory. The second term is derived by considering the increase of lateral flow velocity by the effect of vortex layers in the vortex field, which is a flow field existing between the near and far fields and consists of vortex layers of finite extension. The second term of the coefficient is obtained analytically by assuming the form of vortex layers and the strength of vorticity. The obtained results are compared with experimental results.