Modeling wave scattering in impedance-lined duct networks with expansion chambers

This article presents a general framework for predicting acoustic wave scattering in ducted systems with expansion chambers and dissipative linings, as commonly encountered in engineering noise-control devices. The method represents the acoustic field in each duct segment through orthogonal modal expansions consistent with the local boundary conditions and enforces continuity conditions at the interfaces to determine the reflected and transmitted wave content. Model verification is carried out using representative benchmark configurations excited by a piston-type source. The results show that acoustic linings substantially impact propagation and resonance behavior through changes in modal wavenumbers and coupling between modes. Parametric comparisons between single- and double-lined expansion chamber designs demonstrate that introducing an additional lined cavity strengthens modal interactions, shifts resonance features, and improves attenuation over a broader frequency range. The proposed formulation is computationally efficient, physically interpretable, and readily adaptable to practical duct geometries and lining specifications, making it suitable for the design and optimization of waveguide-based noise mitigation components in applications such as HVAC networks, exhaust systems, and aero-engine ducting.