Flow field saddles and their relation to vortex asymmetry

Abstract The relationship of flow field saddles to the formation of asymmetric vortices is studied by employing a conical Navier-Stokes equation solver. Local grid resolution studies were used to demonstrate the importance of capturing the leeside saddle point and the secondary separation and reattachment points. The transient solutions from the unconverged symmetric flow to the converged symmetric flow illustrate a saddle point shift mechanism providing an explanation for the necessity of adequate grid resolution in this region. Also studied were the paths and final solutions obtained with perturbed and unperturbed local time-stepping procedures, and a perturbed time accurate method. The results indicate that the final solutions are virtually identical and that the same general transient paths are followed. However, these paths are not identical to those obtained with a quasi-steady pitch up of the cone in which an abrupt shift from symmetric to asymmetric results occurs. Finally, the qualitative accuracy of the conical results is assessed by comparisons of the spherical cap streamlines with experimental results of Lowson and Ponton. Excellent agreement is obtained for the incidence ratios at which symmetric vortices are formed, a saddle point appears and when vortex asymmetry occurs, although the solver does not compute accurately the higher incidence flows which were reported to be non-conical in the experiments. The quasi-steady pitch up cases also showed remarkable qualitative similarity to the experimental data.