Effect of mean flow on the trapped modes of internal cavities

Flow‐excited acoustic resonance of trapped modes in ducts has been reported in different engineering applications. The excitation mechanism of these modes results from the interaction between the hydrodynamic flow field and the acoustic particle velocity, and is therefore dependent on the mode shape of the resonant acoustic field, including the amplitude and phase distributions of the acoustic particle velocity. This paper investigates numerically the effect of mean flow on the characteristics of the resonant trapped modes for a cavity–duct system, which is known to generate strong resonances at moderate Mach numbers. The numerical simulations are performed for two dimensional planar and three dimensional axisymmetric geometries at different flow Mach numbers up to 0.3. A two‐step numerical scheme is adopted in which the mean flow is solved in the first step, and in the second step a system of linearized acoustic perturbation equations is used to predict the acoustic field. Comparison of the results with the available experimental data illustrates that the current approach can predict accurately the dependence of the trapped mode frequency on the mean flow Mach number. More importantly, as the Mach number is increased, the acoustic pressure is observed to develop an axial phase gradient and the amplitude and phase distributions of the acoustic particle velocity are found to change significantly near the cavity shear layer. These results demonstrate the importance of considering the effects of the mean flow on the flow‐sound interaction mechanism.