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.