Instability and Transition on the ROTEX-T Cone-Flare in Supersonic Quiet Flow

Measurements of the mean flow and associated instabilities of a transitional separation bubble induced by a shock-wave/boundary-layer interaction (SWBLI) were obtained using high-speed schlieren imaging on a 19.2% scaled ROcket Technology EXperiment–Transition (ROTEX-T) cone-flare-cylinder model in the NASA Langley Supersonic Low Disturbance Tunnel under quiet flow conditions, with freestream unit Reynolds numbers ranging from 4.7 M/m to 23.7 M/m and at nominally zero angle of attack. Laminar base flows were computed, and the convective evolution of modal boundary-layer instabilities was simulated using a hybrid framework that combines the linear parabolized stability equations with the harmonic linearized Navier–Stokes equations. At lower freestream unit Reynolds numbers, an axisymmetric laminar separation bubble formed in close agreement with the baseflows, whereas at higher, the separation bubble became transitional. Spectral methods were used on the schlieren measurements to identify the dominant instability mode frequencies and their spatial characteristics. Modal stability analysis captured both the frequencies and structures of the dominant convective instabilities, demonstrating excellent agreement with experimental results. The multi-scale unsteady dynamics of the SWBLI comprised both relatively low-frequency breathing modes, on the order of 1 kHz, and significantly higher-frequency instability waves in the 30–50 kHz range near reattachment, associated with Mack’s first-mode instability. To examine the role of nonlinear interactions in the transition process of the SWBLI, higher-order spectral methods were employed on the experimental measurements, revealing that the process is strongly driven by cascades of energy transfer through both sum- and difference-frequency interactions localized at reattachment.