Sound propagation in rigid bends: a multimodal approach.

The sound propagation in a waveguide with bend of finite constant curvature is analyzed using multimodal decomposition. Two infinite first-order differential equations are constructed for the pressure and velocity in the bend, projected on the local transverse modes. A Riccati equation for the impedance matrix is then derived, which can be numerically integrated after truncation at a sufficient number of modes. An example of validation is considered and results show the accuracy of the method and its suitability for the formulation of radiation conditions. Reflection and transmission coefficients are also computed, showing the importance of higher order mode generation at the junction between the bend and the straight ducts. The case of varying cross-section curved ducts is also considered using multimodal decomposition.