Numerical investigations of the linear and nonlinear transition stages for a hollow cylinder ŕare at Mach 5

Direct numerical simulations (DNS) were carried out in order to investigate the linear and nonlinear transition stages for a shock boundary layer interaction (SBLI) on a hollow cylinder ŕare geometry at Mach 5. The geometry and ŕow conditions are matched, as closely as possible, to those used in the experiments at the Mach 5 Ludwieg Tube (LT5) at the University of Arizona (UA). While for the experiments a 15^◦ ŕare angle was used, for the numerical investigations several additional ŕare angles were considered. For the investigations presented in this paper łforced" and łunforced" simulations were carried out. For the łforced" simulations three-dimensional wave packets were introduced, that were generated by a short-duration pulse disturbance. The initial forcing amplitudes of the pulse disturbances were chosen to be small in order to assess the linear stability behavior. In addition to the łforced" simulations, łunforced" simulations were also carried out for all the ŕare angles considered, in order to explore if absolute/global instabilities are developing from the discretization and round off errors. The low amplitude wave packet simulations for different ŕare angles showed that the shear layer of the separation bubble is unstable with respect to axisymmetric and oblique traveling waves. For ŕare angles greater than 8^◦ streamwise streaks developed near the reattachment location for both the forced and unforced simulations. A comparison between the forced and unforced simulations indicates that for the larger ŕare angles an absolute instability mechanism may be responsible for the streak development.