A 3D axisymmetric CFD/CAA approach is proposed to simulate sound wave propagation in axisymmetric duct flows. The main idea is to calculate each azimuthal mode using a Fourier transform and decomposition for the azimuthal coordinate φ. Optimized high-order schemes are employed for both the space discretization and time stepping. A buffer zone type boundary condition has been found to be very reliable and stable, while offering the possibility to formulate an accurate non-reflective sound source boundary condition. The proposed procedure has been validated successfully using a number of different examples.
Furthermore, the acoustic mode cuton/cutoff transition phenomenon in a hard-walled duct is studied for no-flow as well as with flow cases. Two different mean flow assumptions have been compared with special attention to the turning plane. The turning plane predicted with an artificial quasi-1D potential flow agree well with the theoretically predicted location. However, the numerical results based on the real 2D Euler flow deviate from the analytical results. This indicates that the mean flow plays a very important role in the determination of the turning plane in addition to the known duct geometry effect.
The main advantages of the proposed 3D axisymmetric CFD/CAA approach are twofold. First, it is very efficient compared with full 3D computations for axisymmetric duct flows. Secondly, this approach is rather straightforward and its suitability can be extended to more complex mean flow cases, such as non-homentropic mean flows (through the introduction of the energy equation) or flows with swirl, which forms the focus of current work. The soft wall boundary condition has not been implemented in the present procedure, but its development and validation is planned in the near future. One drawback of the 3D axisymmetric approach is that it cannot be applied to a fully 3D flow and geometry, such as a scarfed inlet. Therefore, fully 3D numerical methods are still necessary in certain cases.