Acoustic Resonance in a Cavity with a Shear Layer Passing Above the Downstream Edge

Abstract

Cavity flow-acoustic resonance may occur in flow past shallow cavities and lead to very high unsteady sound pressure levels. It involves a coupling between the shear-layer instability wave and acoustic disturbances through the scattering processes at both ends of the cavity.Following Kerschen and Tumin (2003) we developed a theoretical model for flow-acoustic resonances in a two-dimensional, rectangular cavity under a subsonic flow with the shear layer passing above the cavity trailing edge. The theoretical model combines propagation of the flow and acoustic disturbances in the cavity with local analyses and a fully theoretical treatment of the scattering processes at the cavity ends. Our analysis extends the work of Alvarez, Kerschen, and Tumin (2004a,b) by introducing a parameter for the wall-normal distance between the mean shear layer and downstream cavity edge into the analysis of the scattering problem at the downstream end of the cavity. The influence of the finite shear-layer thickness on the evolution of the instability wave across the opening of the cavity is included following the analysis of Fang (2017). In addition to the primary loop consisting of the shear-layer instability wave and lowest-order upstream-propagating acoustic mode in the cavity, our model includes a secondary feedback mechanism involving the downstream-propagating acoustic mode. It predicts the resonant frequencies and growth or decay rates of the global modes, accounting for cavity length-to-depth ratio. The distance between the mean shear-layer and downstream cavity edge was found to have no significant influence on the predicted frequencies of the resonant modes. Our results also indicate that the secondary feedback loop is unimportant for the cavity resonance under the conditions investigated. Varying the mean shear-layer height above the downstream cavity edge, however, can affect the global mode stability by shifting the growth rates from positive to negative (or vice versa). In general a greater shear-layer height lowers the growth rates of the global modes, eventually leading to them being damped.