Akademik Veri Yönetim Sistemi
Ege 11th International Conference on Applied Sciences , İzmir, Türkiye, 1 - 03 Haziran 2024, ss.63
In this study, the propagation of higher-order acoustic waves along a duct system, where a semiinfinite circular rigid pipe is placed axially inside an infinite circular rigid pipe, is analyzed rigorously. The cases where the m-th acoustic wave mode is incident from each duct region are studied independently. Hence a complete understanding is developed on the propagation of any given mode in the bifurcated circular duct system. Following a general analysis on modal expressions in each duct region, for each case, first, direct Fourier transform is applied to the Helmholtz equation, boundary conditions and continuity relation, and the problem is reduced into the solution of a Wiener-Hopf equation. Then, considering classical Wiener-Hopf procedure, which involves factorization, decomposition, the principle of analytical continuation and Liouville’s theorem, the solution is obtained in Fourier domain. Finally, applying inverse Fourier transform to the solution, the reflection and transmission coefficients are determined. All the coefficients involve information of the scattered n-th mode due to an incident m-th mode. At the end of the current analysis, graphical results are presented illustrating the effects of the radii of the pipes and frequency. The obtained results can be considered as scattering matrix elements for a future study, and by the use of the Building Block Method, many complicated duct systems can be analyzed. This approach will be useful in some applications of aeroacoustics. Furthermore, the existence of uniform mean flow may also be taken into account in such future studies.