Acoustic scattering matrices for higher-order modes for simple orifice configurations with flow

Frequency domain simulations are conducted to compute the acoustic scattering matrices of higher-order modes for an in-duct orifice configuration with a flow of air at a Mach number of 0.2 in the orifice at ambient conditions. The scattering matrices are of crucial importance for low-order modelling in acoustic network models or even in field methods, where two domains are acoustically coupled through a scattering matrix. The numerical simulation is based on a high fidelity hybrid CFD/CAA approach, in which the CAA discretization is performed in a stabilized Finite Element method solving the linearized Navier-Stokes equations. The comparison of the numerical results to experimental data is in good agreement. It is shown that on basis of a circumferentially standing mode assumption theoretically a 4 by 4 matrix is necessary to fully capture the interaction between the propagating modes in case of frequencies above the cut-on frequency of the first transverse mode. To provide a sufficient data base to solve for the entire scattering matrix, 4 independent states of the system have to be provided, which are realized by a variation of the two source-location and two-load approach together with the Multi Microphone Method (MMM). It is further shown that the scattering, i.e. the reflection, transmission and also absorption, between longitudinal modes and the first transverasal mode is very weak and can, in this particular case, be neglected. It is therefore possible to determine the scattering matrices those mode forms separately leading to two independent matrices, each of which is only of the dimension 2 by 2.