Flow-acoustic resonance in deep and inclined cavities

This paper presents numerical investigations of flow-acoustic resonances in deep and inclined cavities using wall-resolved large-eddy simulations. A cavity with $D/L = 2.632$ is subjected to ($M_\infty=0.2$ and $0.3$) at three inclination angles ($α=30^{\circ}$, $60^{\circ}$, and $90^{\circ}$). Fully turbulent boundary layers from precursor simulations are employed upstream of the cavities. The simulation results show significant differences between inclined and orthogonal cavity flows, particularly at $M_{\infty} = 0.3$, where the inclined cavities exhibit stronger resonances (by more than 20 dB) at a lower peak frequency ($St=0.276$) than the orthogonal cavity, whose peak occurs at $St=0.849$. Acoustic modal analysis identifies these frequencies as the 1st and 2nd eigenmodes. Further analysis shows that the mode selection is linked to the hydrodynamic modes that pair with the acoustic modes. In the orthogonal cavity, the 2nd hydrodynamic mode prevails, in which two small vortices travel across the cavity opening. In the inclined cavities, however, a single large-scale roll-up vortex is generated owing to the strong Kelvin-Helmholtz instability in the shear layer. Importantly, this vortex spends much of its lifetime growing in size rather than traveling rapidly downstream, resulting in a longer crossing time per cycle that correlates with the 1st acoustic eigenmode frequency. Furthermore, aeroacoustic resolvent analysis indicates that inclined cavities amplify acoustic responses effectively and exhibit weaker source-sink cancellation than the orthogonal cavity. These mechanisms are the primary contributors to the enhanced aeroacoustic response of the inclined cavities. Finally, it is proposed that the ratio of acoustic particle displacement to momentum thickness can be used for predicting the onset of deep cavity resonance associated with the identified distinctive vortex dynamics.