Characteristics of shoulder separation bubble and internal hydrodynamic-acoustic modes in a supersonic inlet

This study investigates the unsteady characteristics of the shoulder separation bubble induced by shock wave-boundary layer interaction (SWBLI) in a supersonic inlet by conducting wind tunnel tests and three‑dimensional (3D) flow simulations. Results show that the separation bubble induces 3D vortex structures subject to sidewall interferences, and the reattachment point exhibits large‑amplitude streamwise oscillations ranging from x/H = 11.3 to 12.6 at Mach number Ma = 4.0 ( x and H are the streamwise position and the isolator height, respectively), thus being identified as the primary source of fluctuating energy in the flow field. Spectral proper orthogonal decomposition (SPOD) is applied to the time‑resolved shadowgraph images to extract the energetically and dynamically important features at different frequencies of the unsteady flow. The first order mode is the most dominant mode, of which the low‑frequency components are associated with upstream shock oscillations, while the high‑frequency components are mainly concentrated in the region of the reattached shock (RAS). This indicates that the dynamic behavior of the inlet flow is governed by a series of spatial structures at multiple frequencies. Furthermore, an acoustic measurement technique is devised to separate the acoustic component from the mixed fluctuating pressure signals. It is found that the acoustic component dominates the signal in the low‑frequency range (below 500 Hz), whereas the hydrodynamic component prevails in the frequency range above 500 Hz. The frequency-wavenumber results reveal both the downstream‑convecting coherent structures and upstream‑propagating acoustic disturbances, and the analysis of spatio‑temporal correlation further confirms the bidirectional propagation of disturbances, which provides strong evidence for the existence of a self‑sustaining feedback loop. Consequently, the separation bubble behaves as a multi‑frequency dynamic system, sustained by a self‑sustaining feedback loop that links downstream pressure disturbances to the upstream separation. The findings laid a solid foundation for subsequent research on the flow instability and pressure load control of supersonic inlets.