Numerical Investigation of the Trapped Modes in the Presence of Non-Potential Flow

A calculation method is proposed to investigate trapped modes in a rigid waveguide with rigid obstacles in the presence of non-potential steady mean flow in a two-dimensional coordinate system. This method facilitates the investigation of trapped modes in the presence of non-potential flow. A coupled calculation method that combines computational fluid dynamics and computational aeroacoustics is used. Galbrun's equation of aeroacoustics is used and discretized by the finite element method. The boundary condition corresponding to the unbounded domain is modeled by the perfectly matched layer technique. The proposed approach facilitates the investigation of the trapped modes generated by obstacles with different geometrical shapes. The effects of both the dimensions of different geometrical shapes (e.g., thin plate, rectangular, and elliptical) and the presence of the non-potential flow on the trapped modes are studied. It is observed that the non-potential flow alters the pressure distribution around the obstacle and the frequencies of the trapped modes. The results show good agreement with the literature. Also, experimental investigations are performed to validate the model.