Mode-Merging Design Method for Nonlocally Reacting Liners with Porous Materials

Abstract

A mode-merging design method (MMDM) for bulk liners with porous materials is proposed to maximize transmission losses in flow ducts. The eigenequation and its partial derivative equation governing the coupled acoustic fields in the duct and backchamber are derived, from which the merging double eigenvalue is obtained at a target frequency for a single incident circumferential mode. The crucial liner parameters (namely. the chamber depth and the flow resistivity of the porous material) can be optimized simultaneously. A finite element propagation model is employed to evaluate the MMDM-based design for a finite-length liner, demonstrating the effectiveness of the method for selected typical design cases. It is found that mode merging can be realized for a nonlocally reacting liner, with or without a perforated plate, mainly for protecting the porous material inside its chamber. The MMDM, under the assumption of an infinite-length liner, can give an almost globally optimal design for a finite-length liner when the length exceeds five times the duct diameter. It is expected that the proposed MMDM can be useful in the preliminary designs for actual bulk liners due to its rapidness and accuracy.