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. The study is based on a fixed aspect ratio of D/L = 2.632, subjected to two Mach numbers of 0.2 and 0.3 (with the focus on the latter) at three different angles of inclination (α = 30◦, 60◦, and 90◦). Fully turbulent boundary layers generated from independent precursor simulations are employed upstream of the cavities. The simulation results show significant differences in aeroacoustic response between inclined and orthogonal cavities, particularly at M∞ = 0.3, where the inclined cavities exhibit stronger resonances (by more than a 20 dB) at a lower peak frequency (St = 0.276) compared to that of the orthogonal cavity, which occurred at St = 0.849. Acoustic modal analysis identifies these frequencies as the 1st and 2nd eigenmodes, respectively. Further analysis shows that the disparity in mode selection between the orthogonal and inclined cavities is linked with the hydrodynamic modes (vortex dynamics) that pair with the acoustic modes. In the orthogonal cavity, a 2nd hydrodynamic mode prevailed where two relatively small vortices were travelling across the cavity opening simultaneously. In the inclined cavities, however, a single large-scale roll-up vortex, a 1st hydrodynamics mode, is generated in relation with strong Kelvin-Helmholtz instability in the shear layer. More importantly, the vortex spends a substantial amount of its lifetime growing in size without travelling downstream rapidly. This results in a longer crossing time per cycle which correlates with the 1st acoustic eigenmode frequency (St = 0.276). In addition, an aeroacoustic resolvent analysis indicates that inclined cavities amplify acoustic responses more effectively and exhibit weaker source-sink cancellations than the orthogonal cavity. These mechanisms are identified as the primary contributors to the enhanced aeroacoustic responses in the inclined cavities. Finally, it is proposed that the ratio between acoustic particle displacement and momentum thicknesses may be used as a criterion to predict the onset of deep cavity resonance with the distinctive vortex dynamics identified in this paper.