A computational approach for flow-acoustic coupling in closed side branches

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 ducts. The presence of mean flow in the main duct, 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, thereby transforming the quarter-wave silencer into a noise generator. The present approach employs computational fluid dynamics (CFD) to model this complex interaction between the flow and acoustic resonances at low Mach number by solving the unsteady, turbulent, and compressible Navier-Stokes equations. Comparisons between the present computations and the experiments of Ziada [PVP-Vol. 258, ASME, 35-59 (1993)] for a system with two coaxial side branches show that the method is capable of reproducing the physics of the flow-acoustic coupling and predicting the flow conditions when the coupling occurs. The theory of Howe [IMA J. Appl. Math. 32, 187-209 (1984)] is then employed to determine the location and timing of the acoustic power production during a cycle.