|M.Sc Thesis||Department of Aerospace Engineering|
|Supervisors:||Assoc. Prof. Iosilevskii Gil|
|Dr. Eran Arad|
|Full Thesis text|
Out of plane forces caused by asymmetrical vortices on slender bodies at high angles-of-attack has been extensively investigated for over four decades, mostly experimentally and numerically. Based on these studies, it is commonly accepted today that the source of asymmetry is associated with small asymmetric disturbances on the nose apex, which are amplified by flow instability. Yet no rigorous theoretical analysis has been offered to support this assumption. The current combined analytical and numerical study is a step in this direction.
The current study addresses equilibrium positions and stability of a pair of vortices behind a slender body at angle of attack. Two approaches were adopted - an analytical, based on a series of simplifying assumptions which are specified below, and numerical, based on CFD simulations. At each step, analytical results were validated against simulations, with generally good agreement between the two.
To simplify the analytical approach, the flow was assumed incompressible and inviscid. Vorticity was assumed to be concentrated mainly in a thin region close to the body surface and in a pair of thin vortex sheets starting at the body surface and rolling up to form a pair of (not necessarily symmetric) vortices in the wake of the body. Outside these limited regions the flow was assumed entirely irrotational. The creation of vorticity on the surface of the body was modeled using Kutta hypothesis.
Under these assumptions, stationary locations of the pair of vortices in the wake of a conical slender body have been found. These are the extensions of the well-known Föppl solution for the stationary locations behind an infinite cylinder. The vortices were found to be unstable to anti-symmetric disturbances at high angles-of-attack and stable to both symmetric and anti-symmetric disturbances at low angles-of-attack. The ratio K of tangents of the semi-apex angle and the angle-of-attack was identified as the parameter that determines the stability of the vortices.