Non-locally reacting liner modeling and validation

Sound propagation through propagation through a duct with non-locally reactive multi-cavity resonator lining has been investigated. Two prototype muffler configurations were acoustically tested in the Boeing Interior Noise Test Facility (INTF). The acoustic performance of the two mufflers was predicted using a finite element method (FEM) implemented in Comsol Multiphysics, a commercial general purpose finite element analysis and solver software package. A classic locally reacting impedance boundary condition can not be used since the resonator cavities are large with respect to the acoustic wavelength and acoustic waves can propagate axially inside the cavities. The acoustic fields inside the duct and the cavities are modeled and coupled using the impedance boundary condition of the perforate facesheet. The initial comparisons showed higher acoustic insertion loss predicted by the FEM analysis than the measured test data. These differences occurred for both configurations throughout most of the spectrum and especially at resonance. Subsequent predictions were conducted accounting for gaps in the muffler assembly and the new predictions showed a good agreement with test data. The 2D axisymmetric FEM technique used in the present approach has proved to be successful for the analysis of geometrically complex mufflers. Nomenclature A+ = complex amplitude of input mode A- = complex amplitude of input mode c = speed of sound IL = acoustic insertion loss mJ = first kind Bessel function of order m k = wave number ±xk = longitudinal wave number ±rk = radial wave number L = sound power m = spinning mode number n = radial mode number p = acoustic pressure R = duct radius u = particle velocity in axial direction v = particle velocity normal to the liner Z = specific acoustic impedance ω = angular frequency I