Estimation of Possible Excitation Frequencies for Shallow Rectangular Cavities

The physical processes that sustain discrete-frequency oscillations of cavities adjacent to compressible flow are modeled analytically, yielding a formula which predicts excitation frequencies as a function of Mach number and cavity geometry. These physical processes are similar to those used by Powell in describing the mechanism underlying the production of edge tones. The empirically determined constants appearing in Rossiter's formula for excitation frequencies are computed from the model. It appears that instability of the shear layer as well as interaction between the shear layer and the cavities' trailing edge is required to sustain discrete-frequency oscillation. It is suggested that the simultaneous excitation of two or more discrete frequencies (which are not harmonic), as have been observed in practice, correspond to the simultaneous participation of two or more vortex sheet displacement modes. The model analyzed yields qualitatively correct acoustic mode shapes in the cavity. Theoretical results include the calculation of possible excitation frequencies over the range 0.8 ^ M ^ 3 for rectangular cavities and show their dependence on cavity depth. Analytic results are in general agreement with experimental data.