FLOW-FIELD SADDLES AND THEIR RELATION TO VORTEX ASYMMETRY

The relationship of flow field saddles to the formation of asymmetric vortices is studied by employing a conical Navier-Stokes equation solv er. Local grid resolution studies were used to demonstrate the importa nce 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 Bow illustrate a saddle poi nt shift mechanism providing an explanation for the necessity of adequ ate grid resolution in this region. Also studied were the paths and fi nal solutions obtained with perturbed and unperturbed local time-stepp ing procedures, and a perturbed time accurate method. The results indi cate that the final solutions are virtually identical and that the sam e general transient paths are followed. However, these paths are not i dentical to those obtained with a quasi-steady pitch up of the cone in which an abrupt shift from symmetric to asymmetric results occurs. Fi nally, 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 inciden ce ratios at which symmetric vortices are formed, a saddle point appea rs and when vortex asymmetry occurs, although the solver does not comp ute accurately the higher incidence hows which were reported to be non -conical in the experiments. The quasi-steady pitch up cases also show ed remarkable qualitative similarity to the experimental data. (C) 199 7 Elsevier Science Ltd.