Acoustic Transfer Matrix Reconstruction and Analysis for Ducts with Sudden Change of Area

Abstract

In many fields of application, the acoustic properties of fluid machinery are of growing importance. To determine these properties, it is often a reasonable approximation to model a complex geometry as a network of acoustic elements. Acoustic elements can be characterized by their transfer matrices. An acoustic transfer matrix describes the transformation of the acoustic field variables by an acoustic element as a function of frequency. It is a quantitative assessment for the modification of the acoustic wave characteristics. This paper describes a procedure for the estimation of acoustic transfer matrices by means of computational fluid dynamics (CFD). A transient solution of the Navier-Stokes equations is performed, using a compressible, low Mach-number RANS scheme with broad band excitation of the flow variables at the boundaries. On the basis of the resulting time series for pressure and velocity, the transfer matrix for an acoustic element is estimated by application of a system identification procedure based on the Wiener-Hopf equation. Sudden changes in cross section of ducts are very common in acoustic designs, e.g. in mufflers or combustion chambers. Therefore, the transfer matrix of this element is important for the design of flow systems involving acoustics. The sudden change in cross sectional area between two pipes is used as a test case for the CFD-based estimation method for acoustic transfer matrices. The method is validated against experimental data, finite element calculations, as well as an analytical description.