In this study, a mathematial formulation for evaluating performance of the duct system including curved bends was derived by using the method of separation of variables and the numerical transfer matrix. The higher order acoustic modes of curved duct bends were considered in analyzing the three-dimensional behavior by using the eigenfunction expansion technique. This analysis method has the benefits of fast calculation time, small computing memory, and ease in use. The derived theory was applied to the simple curved expansion chamber, the Herschel-Quincke tube, the curved chamber, and the curved duct with a splitter for analyzing the acoustical characteristics. Predicted results were compared with experimental ones and they showed good agreements.
Based on the acoustical characteristics of the curved duct bends, it is found that the classical plane wave theory adopting the straight duct with an equipvalent length to the curved duct bend can lead to erroneous results when the normalized maximum pressure of the fundamental mode in the curved duct bend is greater than 1.3.
Parametric studies were performed for the sound attenuation in the curved chamber and the curved bend with a splitter by investigating the effects of geometrical parameters:the position of the splitter, the overall angle, the installed position and the material properties of porous material for right and the acoustical admittance boundary conditions. Based on the information from these parametric studies, an experimental design method was suggested for finding the optimal acoustical design parameters, and the example simulations for fulfilling the various object functions were shown in order to verify the applicability of the method. It is thought that the proposed design methodology can be useful in setting the design guideline of the passive silencing systems.
