Scattering Matrix Evaluation with CFD in Low Mach Number Flow Ducts

We present an efficient methodology to perform calculations of acoustic propagation and scattering by components in ducts with flows. In this paper a methodology with a linearized Navier-Stokes equations solver in frequency domain is evaluated on a two-dimensional geometry of an in-duct area expansion. The Navier-Stokes equations are linearized around a time-independent mean flow that is obtained from an incompressible Reynolds Averaged Navier-Stokes solver which uses a k-ε turbulence model and adaptive mesh refinement. A plane wave decomposition method based on acoustic pressure and velocity is used to extract the up and downstream propagating waves. The reflection of the acoustic waves by the induct area expansion is calculated and compared to both measurements and analytical models. Frequencies in the plane wave range up to the cut-on frequency of the first higher order propagating acoustical mode are considered. The reflection is presented in a scattering matrix form that can be used in acoustical two-port calculations on complex duct systems such as exhaust system mufflers and ventilation systems.