Acoustic scattering and mode interaction in bifurcated circular waveguide structures with reacting liners and discontinuities

Acoustic scattering and nonlinear dispersion phenomena play a crucial role in the design and optimization of waveguide systems for noise control in engineering applications such as HVAC systems, aircraft engines, and industrial gas turbines. In this study, we investigate the scattering characteristics of a bifurcated circular cylindrical waveguide with a particular focus on the effects of reactive acoustic liners and step-discontinuities. Unlike prior studies that typically analyze either acoustic liners or step discontinuities in isolation, this work integrates both mechanisms within a unified framework, providing new insights into their combined influence on wave propagation. The impedance conditions at the fluid-liner interface are formulated to evaluate scattering under different configurations, while the mode-matching (MM) technique is employed to determine eigenfunction expansions and solve the governing equations. The accuracy of the solution is validated through power conservation and matching condition reconstruction, ensuring the robustness of the methodology. The findings reveal that reacting liners effectively attenuate fluid-borne modes by preventing transmission up to a critical frequency where secondary modes become dominant, whereas step-discontinuities exhibit the opposite trend. The study further demonstrates that scattering behavior can be optimized by adjusting the radii of circular waveguide regions, leading to enhanced performance under liner conditions compared to step-discontinuities. Additionally, varying liner sizes or discontinuity heights significantly affects energy flux reflection and transmission, with higher frequencies amplifying scattering effects. These results provide a comprehensive framework for designing advanced noise control solutions in waveguide systems and offer valuable guidelines for practical engineering applications.