Controlled Transition Simulations on an Axisymmetric 8-Degree Compression Ramp at Mach 5

Numerical investigations are conducted to investigate the transitional shock-boundary-layer interaction (SBLI) on a hollow cylinder flare geometry at Mach 5. The flow conditions are matched as closely as possible to those used in experiments at the Mach 5 Ludwieg Tube (LT5) at the University of Arizona (UA). A variation of the geometry used in the experiments was used for the numerical simulations with a flare angle of 8◦. This case was previously identified as only convectively unstable, with no signs of an absolute/global instability. The linear regime is investigated using local linear stability theory (LST) and low amplitude controlled forcing simulations. An oblique 1st mode/shear-layer mode is found to be amplified for a range of azimuthal wavenumbers. Subsequently, highly resolved direct numerical simulations (DNS) are performed in order to investigate the possibility of an oblique breakdown scenario, dominated by the 1st mode/shear-layer mode. Contours of the azimuthal averaged skin friction over time, show that the separation region for the transitional flow contracts compared to the laminar base flow. Pressure amplitude spectra show the amplification of the nonlinearly generated signature modes, consistent with an oblique breakdown scenario. Time averaged skin-friction coefficient and Stanton number, and their Fourier transformed amplitudes, indicate the formation of streaks that appear already inside the separation bubble. Towards the end of the computational domain, smaller structures can be observed in the instantaneous pseudo-Schlieren contours visualizations indicating that the late nonlinear stages of the transition process have been reached.