Influence of Propagation Equations on the Scatter Matrix for Ducts Carrying Non-Uniform Mean Flow

Abstract

One dimensional linear acoustic network models are commonly used for the acoustic design of duct systems. These models are advantageous since they allow the characterization of the scattering matrices for individual elements, independent of the upstream or downstream components. For an intake or exhaust assembly, the individual elements can be combined by a simple multiplication of the individual matrices to assess the propagation characteristics of the whole system under consideration. The determination of the scattering matrix coecients can be carried out in an analytical, numerical or experimental way. Since analytical methodologies are limited to uniform or simplied mean ow assumption and an experimental determination is expensive and time-consuming, a numerical method using the time-domain Linearized Euler Equations (LEE) is discussed in this paper. These equations allow to study the aeroacoustic transmission characteristics in a non-uniform mean ow, determined by Reynolds averaged Navier{Stokes (RANS) calculations. An inherent problem of the use of the LEE for acoustic propagation, is the fact that they do not only model propagation of acoustic waves, but also support the propagation of entropy and vorticity waves. An excitation of the vorticity- and entropy modes can lead to \unphysical and even \unstable results. Using an irrotational formulation of the LEE, or suppressing the mean ow gradient terms from the LEE, resolves the problem of instability. In this paper, the eects of these dierent types of equations are evaluated for a simple three-dimensional rectangular expansion chamber.