Spinning dynamics of self-excited azimuthal acoustic modes in cavities

Abstract

The coupling between the shear layer separating between axisymmetric leading and trailing edges and the azimuthal modes of a cavity may result in self-excited spinning acoustic resonance. Notably, the spinning direction remains one of the less understood features of the coupled mode dynamics. In this work, compressible large eddy simulation is used to model the excitation of azimuthal acoustic modes in rectangular cavities. To verify the effect of aspect ratio on the resonant acoustic mode excitation, three cavities with aspect ratios W/H = 1.0, 0.95, and 0.90 are considered, all with the same shear layer length. While the square cross section cavity excited a pure spinning mode similar to that for a circular cavity, a small deviation from the square geometry in the coupled acoustic-flow fields leads to an attenuation of the acoustic mode amplitude. This attenuation results from a change in the phase characteristics, which impacts the spinning mode behavior. A slight side length mismatch drives a frequency difference between the two superimposed degenerate modes, resulting in a periodic reversal of the spinning direction. As the mismatch increases, the shear layer fails to excite one of the two modes, leading to the dominance of the other, and the aeroacoustic mode becomes fully stationary. More importantly, the shear layer follows the acoustic mode behavior such that the separation point changes its spinning direction accordingly. Consequently, the shape of the shear layer changes over time, resembling a clockwise helix, a counterclockwise helix, or crescent pairs closely following the acoustic mode.