Hysteresis and Bifurcation Analysis of A Fighter and A Delta Wing at High Incidence

Hysteresis and bifurcation analysis has been performed on experimental results of a fighter in steady coning motion and a delta wing in free-to-roll motion. There are bi-stable asymmetric solutions for the fighter at high incidence. Applying certain perturbations or changes in coning rate can switch over the forebody vortices from one stable solution to another and result in corresponding lateral-directional aerodynamic loads. The basins of those two solutions are not equal. Both the angle of attack and coning rate are found to be control variables in the bifurcation behavior of the forebody vortices. When the coning rate is higher than a threshold value, definitive hysteresis characteristics can be observed. The threshold rate increases as the angle of attack increases. In the case of a delta wing model, the solution of the system exhibits different bifurcation structures over the investigated range of angles of attack and release roll angles, reflecting the experimentally obtained multiplicity of roll attractors. These bifurcation and hyteresis characteristics have been physically explained in the domain of asymmetric cross-flow separation and the vortex breakdown movement respectively.