Acoustics of 90 degree sharp bends. Part I: Low-frequency acoustical response

The acoustical response of 90 degree sharp bends to acoustical perturbations in the absence of a main flow is considered. The aeroacoustical response of these bends is presented in part II [1]. The bends considered have a sharp 90 degree inner edge and have either a sharp or a rounded outer corner. They are placed in pipes with either a square cross-section (2D-bends) or a circular cross-section (3D-bends). The acoustical performance of a numerical method based on the non-linear Euler equations for two-dimensional inviscid and compressible flows is checked and its ability to predict the response of 3D-bends is investigated. The comparison between 2-D and 3-D data is made for equal dimensionless frequencies f/f_c where f is the frequency of the acoustical perturbations and f_c is the cut-off frequency of the bends. In the case of a bend with a sharp inner edge and a sharp outer corner, the 2-D numerical predictions agree with 2-D analytical data obtained from a mode expansion technique and with 2-D experimental data from literature and our own 3-D experimental results. In the case of a bend with a sharp inner edge and a rounded outer corner, the 2-D numerical simulations predict accurately the 2-D experimental data from literature. However, the 2-D numerical predictions do not agree with our 3-D experimental data. The acoustical response of 3D-bends appears to be independent of the shape of the outer corner. This behavior is quite unexpected.