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A physical model to study the acoustic resonance induced by the wake flow of a cylinder in a flow duct is established. This model consists of three meshless submodels operated in the time domain, including the discrete vortex method (DVM) for vortex shedding, the vortex sound theory for sound radiation and the time-domain boundary element method (TDBEM) for sound propagation within the duct. In addition, the acoustic particle velocity is calculated to take the sound feedback effect into consideration, which makes the coupling process between flow and sound field to be bi-directional. The distribution patterns of vortex street behind the cylinder and the acoustic β-mode within the duct are reasonably depicted. And both the qualitative and quantitative results of resonant frequency and amplitude can be fully compared with the previous experiment data, especially, the lock-in phenomenon is well captured. The lock-in regime depicts as a competition between the vortex shedding frequency (fs) and the inherent frequency of β-mode (fa). And two lock-in patterns, the synchronous regime and βmode dominant regime, are identified according to the mismatch between fs and fa. This physical model provides the proper characteristics of acoustic resonance as observed in experiment, and helps to get a more detailed understanding of the lock-in mechanism. INTRODUCTION Aeolian tone, caused by vortex behind bluff bodies in flow, has received continuous attention since 1870s. And it is well known that the frequency of aeolian tone is always identical with the vortex shedding frequency, which varies linearly with the flow speed in the free space. However, if a bluff body is placed in a confined space, such as a flow duct, the sound generation process becomes much more complicated, because of the fierce vortex sound interaction under proper conditions. This phenomenon is recognized as acoustic resonance, which is usually accompanied with unique high sound pressure level (SPL, even over 170dB). It cannot only cause severe noise pollution issues but also lead to performance deterioration or even catastrophic damage to the facility. These dangers, undoubtedly, should be avoided in various military and civilian engineering applications, such as combustion chambers of rocket (Karthik et al., 2008), compressors of aeroengine (Parker, 1968; Liu et al., 2018), front grills of automobile (Yokoyama, 2013), tube banks of heat exchanger (Shaaban and Mohany, 2018) and so forth. Consequently, the relevant researches are greatly motivated. Although the general process of acoustic resonance has been proposed, the underlying mechanism of vortex sound interaction is still an open issue. To explore the underlying mechanism, a simplified system like a single cylinder in a flow duct is preferred instead of the complicated situations occurring in the above-mentioned engineering applications. Acoustic resonance in a duct induced by wake flow from an inner circular cylinder has been widely studied since the 1950s, and the research progresses are summarized in some review papers (Blevins, 1984; Mohany, 2012, etc.). Through detailed flow visualization measurement, the high correlation between resonant sound and wake vortex shedding process has been substantiated. On one hand, when an intense tone noise is excited, the vortex shedding becomes highly coherent in the streamwise direction and forms a succession of vortex clouds. On the other hand, if the wake flow is disturbed by turbulent devices, such as small rods, the resonance could be fully eliminated (Katasonov et al., 2015). A thorough investigation on the vortex sound interaction would do benefit to the basic understanding of the acoustic resonance mechanism. Certain progress has been made in this issue with the help of numerical methods, however, it is far from satisfactory, as how to simulate the coupling between vortex and sound is still a difficult task even in nowadays with the highly developed computer science, due to the large difference in spatial scale of the unsteady flow and sound variations. Most of the previous researches are based on the decoupling method, and the effect of feedback

A Physical Model of Flow-Induced Acoustic Resonance in a Duct Containing a Circular Cylinder