The effects of flow on Helmholtz resonators

A theoretical investigation into the effects of flow on Helmholtz resonators has been carried out in order to improve the predicted performance of resonators. The presence of a mean flow in the duct to which the neck of the Helmholtz resonator is attached has a great influence on the acoustic performance of the resonator, resulting in a discrepancy between the predicted and the measured results. Some conventional methods to predict the acoustic performance of resonators in the presence of the mean flow have been found to be incorrect in some aspects. Thus, with correct mathematical understanding, a revised transfer matrix showing improved prediction of acoustic performance in terms of the insertion loss for a side-branch resonator is presented. As an extension of this study, a semi-empirical approach has resulted in revised transfer matrices for extended inlet and sudden expansIon silencer elements. The revised transfer matrix for a sudden expansIOn resonator gives quite good correlation between predicted results of reflection coefficient and experimental results obtained by Ronneberger [1]. An approach to calculate the change in the acoustic impedance of a side-branch resonator caused by mean flow effects has also been presented, using the profile of the motion of the shear layer over the orifice of the Helmholtz resonator neck. Both laminar and turbulent profiles of the grazing flow have been considered. In this approach, a good qualitative agreement with Ronneberger's [2] theoretical and ill experimental result was seen in the case of laminar grazing flow. The same approach as that used for laminar grazing flow was made for turbulent grazing flow. However, in the case of turbulent grazing flow, this approach was found to be of dubious value. An attempt was made to calculate the change in acoustic impedance due to mean flow by making use of a feedback relationship between a resonator volume flow and an orifice volume flow in a coupled resonator-flow system. In this attempt, the coupled system was studied using observed values for the vortex convection speed over the orifice and the phase relationship between the two volume flows. This approach has been used successfully to predict the resonant characteristics of self-excited osci lIations, but did not prove sufficiently accurate or robust to determine the flow-induced change of impedance for forced oscillation.