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.
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机译：四分之一波谐振器是在管道中使用的一种常见类型的消音器，它以规则的频率间隔产生窄带的高声衰减。但是，主管道中平均流量的存在可能会促进这些声波共振与流量之间的相互作用。在某些离散流动条件下的耦合会导致在侧支中产生较大的波幅并在主导管中产生高噪声，从而将四分之一波消音器转变为噪声发生器。本方法采用计算流体动力学（CFD），通过求解不稳定，湍流和可压缩的Navier-Stokes方程，对低马赫数下的流与声共振之间的这种复杂相互作用进行建模。 Ziada目前的计算与实验之间的比较[PVP-Vol。 258，ASME，35-59（1993）]具有两个同轴侧分支的系统表明，该方法能够再现流-声耦合的物理性质并预测当耦合发生时的流动条件。 Howe的理论[IMA J. Appl。数学。 [32，187-209（1984）]然后确定一个周期内声功率产生的位置和时间。
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