Tuned optimization of extended reacting acoustic liners

Abstract

A finite element Galerkin formulation was employed to study the optimum attenuation and reflection characteristics of acoustic waves propagating in tw0 dimensional straight ducts with extended reacting absorbing walls without a mean flow. The reflection and transmission of acoustic energy at the entrance and the exit of the duct were determined by coupling the finite element solutions in the absorbing portion of the duct to the eigenfunctions of an infinite, uniform, hard wall duct. In the frequency range where the duct height and acoustic wave length are nearly equal, power attenuation contours were examined to determine conditions for minimizing acoustic transmission through the duct. The extended reacting liners were found to significantly minimize the reflective characteristics of the duct rather than to increase absorption in the liner. Thus, extended reacting wall liner properties can be theoretically chosen to yield large impedance mismatches in an open straight duct