Stability of Symmetric Vortices over Slender Conical Bodies at High Angles of Attack," AIAA Paper 2001-2845

Analyses are presented for the stability of a symmetric vortex pair over slender conical bodies in inviscid incompressible ow under small perturbations at high angles of attack. The bodies considered include circular cones and highly swept at-plate wings with and without vertical ns, and elliptic cones of various eccentricities. The three-dimensional problem is reduced to a vortex stability problem for a pair of vortices in two-dimensions by using the conical ow assumption, classical slender-body theory, and postulated separation positions. The stability of vortices is then analyzed by a new method presented in a companion paper by the same authors. It is shown that the vortex asymmetry over a circular cone at high angles of attack is a result of the vortex instability under small anti-symmetric perturbations. There exists an intermediate cone with a nite thickness between the thick circular cone and the thin at-plate delta wing, for which the symmetric vortices change from being unstable to being stable at a given angle of attack. The eects of the n height and the separation position on the stability of the vortices are studied. Results agree well with known experimental observations. I