The acoustic generation mechanism in an open cavity is numerically investigated in this thesis. The flow and acoustic field of a rectangular open cavity are simulated to investigate the feedback loop of cavity resonance, and it is found that there are large differences of flow pattern and resonance frequency in different resonance modes. The characteristics of wave propagation and phase variation are analyzed by using cross-correlation analysis in both space and time. Although sudden phase shifting by 90 degrees in pressure appears near the downstream edge outside of cavity, no phase shifting appears on the surface inside the cavity. This phenomenon is directly related to phase lag.
Newly developed concepts of the acoustic generation mechanism in an open cavity are suggested. They are about effective length and phase lag. The effective length is defined as the distance between the vortex generation point and the vortex collapse point, which is shorter than the geometrical cavity length used in the original Rossiter’s equation. When a vortex is collapsed, the acoustic wave is generated at the surface of the cavity. The generated acoustic wave propagates forward and excites the shear layer, which induces a vortex, directly before the acoustic wave excites the flow on the surface of the leading edge. Therefore, the length from the vortex generation point to the vortex collapse point is suitable for the effective length. The phase lag is defined as the phase difference between the vortex collapse point and the acoustic source point on the surface. 0 is adequate for phase lag when acoustic source point exists inside the cavity, 1/4 is adequate when acoustic source point exists outside of the cavity. This is the same phenomenon as the results of cross-correlation. The phase lag corresponding to 1/4 of a period occurs near the downstream edge outside of cavity, but this location is not the point of major acoustic source. The integral form of Rossiter’s equation is derived by using developed concepts and compared with exact frequency obtained directly from the far-field acoustic signal of numerical simulation to validate the accuracy of these concepts. The predicted Strouhal numbers of this equation show good agreements with the exact ones in various conditions, which demonstrates the developed concepts are correctly expressing the mechanism of cavity resonance.
The physical phenomena of rectangular open cavities with lids are additionally investigated in this paper. The characteristics of cavity resonance and acoustic propagation are analyzed according to the geometric variation of lids located on the edges of the cavity. The existence of lids changes the resonance frequency, sound pressure level, and directivity of acoustic propagation. The lid induces an additional up and down oscillation at the opening and this becomes an acoustic source propagating to the upper direction. As the lid length becomes longer, Strouhal number becomes smaller. Steady mode occurs when the ratio of the opening length to the momentum thickness is smaller than a certain value. As lid thickness becomes thicker, the transition of Rossiter’s mode occurs from the second mode to the first mode. The major noise source of the first mode is located on the surface outside of the cavity, whereas that of the second mode is located on the surface inside of the cavity. The effects of different location of the opening are investigated. The central open cavity shows larger fluctuations than the others. Because for the other cases the viscous effect on the wall suppresses the rotating flow inside the cavity and induces the vortex convection speed in shear layer to become slow. Cross-correlation analysis and the integral form of Rossiter’s equation are used to analyze the transition of Rossiter’s mode and explain the sudden change of resonance frequency.
The phase variation of pressure is analyzed around cavity to explain the reason why sudden phase shifting by 90 degrees appears near the downstream edge outside of cavity, and no phase shifting appears inside of cavity. When pressure wave approaches the downstream edge, it is shown that pressure contours attached to the forward facing wall inside of cavity. Because of this phenomenon, the pressure below the downstream edge keeps the same phase as that in front of the downstream edge, and there is no phase shifting inside of cavity. When the flow passes the downstream edge, compression effect in pressure field occurs in front of the cavity and secondary vortex is generated behind of cavity. These induce time delay corresponding to 1/4 times of a period. Therefore there is sudden phase shifting by 90 degrees in pressure near the downstream edge outside of cavity. These results support that 0 is adequate for the phase lag when the acoustic source point exists inside the cavity for the second mode, 1/4 is adequate when the acoustic source point exists outside of the cavity such as the first mode.
