| The quarter wave resonator, which produces a narrow band of high acoustic attenuation at regularly spaced frequency intervals, is a common type of silencer used in ducting systems. The presence of mean flow, however, is likely to promote an interaction between these acoustic resonances and the flow. The coupling for some discrete flow conditions leads to the production of both large wave amplitudes in the side branch and high noise levels in the main duct. Thus, the quarter wave resonator may become a noise source rather than a silencer. The present approach uses computational fluid dynamics to determine both the mean flow and acoustic fields simultaneously by solving the unsteady, turbulent, and compressible Navier-Stokes equations. By coupling the interaction between the mean flow fluctuations and vortices with the acoustic field, this method is capable of determining when flow-acoustic coupling occurs and how variations in the geometry and flow conditions influence the acoustic pressure amplitudes. Direct comparisons with experiments are made, providing a much needed validation for this approach. Computer-generated smoke visualization of the unsteady shear layer between the main duct and the side branch matches experimental smoke plots available in the literature, indicating that the physics behind the flow-generated noise is properly reproduced. The modeling of an experimental side branch flow facility confirms that the present method is capable of predicting the flow-velocities at which the coupling occurs. Computations performed by varying the dimensions of the side branch and main duct for a fixed set of boundary conditions reveal that shortening the length of the side branch tends to increase the noise generated by the coupling, while decreasing the side branch depth in the flow direction tends to narrow the velocity range over which the coupling occurs. The detailed computations are also used to study how the vortex formation changes as the pressure amplitudes and flow conditions in the system are varied. Finally, the examination of the energy transfer between the flow and acoustic fields reveals that when the flow-acoustic coupling is present a net acoustic source is generated near the open end of the side branch. |
