Mode interactions of a high-subsonic deep cavity

To understand the interactions of the acoustic modes associated with the tunnel walls and the cavity oscillations in the experiment, flows over a deep cavity having a length-to-depth ratio L/D = 0.42 at high subsonic speeds with and without an upper tunnel wall were investigated by using an implicit large-eddy simulation with an adaptive local deconvolution method. The results of the simulations with the upper tunnel wall converge well to the experimental results as the resolution increases. However, in the simulations without the upper tunnel wall the flow converges to a different mean state. The mode interactions were analyzed by using a Dynamic Mode Decomposition (DMD) method based on a memory-efficient snapshot algorithm. It was found that nearly trapped global modes, which have almost zero upstream and downstream radiation, can occur. The interactions of the trapped modes, the acoustic resonant modes in the cavity, and the shear-layer modes can be observed in the DMD modes of the flow with the upper tunnel wall, which results in the enhancement of harmonic modes and the existence of higher-order modes. In the flow without the upper tunnel wall, the pressure waves can transmit freely away from the cavity, but the interactions of the acoustic resonant modes and the shear-layer modes can also be observed when the frequencies of both kinds of modes coincide. The effects of the ratio of the cavity depth to the tunnel height (D/H) on the formation of trapped modes were also investigated. As the ratio D/H decreases, the frequency window of the trapped modes shrinks and finally closes, which is consistent with a theoretical model. It can be concluded that the effects of the upper tunnel wall on the dynamics of the cavity flow are strong and are promoted by the interactions of different kinds of modes. The appearance and enhancement of high order harmonic modes in the high-subsonic deep cavity are due to the effects of the trapped modes, but are not due to the directly reflected pressure waves from the upper wall.