Acoustic resonance may occur in heat exchangers such as gas heaters or boilers which contain tube bundles. This resonance is classified in self-excited oscillation, and feedback effect between vortex shedding and sound field plays important role. The final goal of our study is to develop a method by which to predict the resonance attack critical gas flow velocity and maximum resonance amplitude at the design stage. In order to reach this goal, it is essential to formulate the feedback effect between vortex shedding and a resonance mode concerned, and to execute a stability analysis of the resonance mode. There are two mechanisms in the feedback process: as the acoustic resonance grows, vortex strength is increased and vortex shedding synchronization grows.
This paper is concerned with the proposal of phenomenological model suitable to explain this mechanism and the formulation of these kinds of feedback mechanism with the use of this model. The model adopts vortex shedding wake oscillator model which is effective for tube vibration problems. Tube vibration movement is replaced by acoustic particle movement. Another improvement of our study is the introduction of statistical modeling of the wake oscillator to express vortex shedding synchronization effect. Here, the randomness of vortex shedding is explicitly modeled by a probability density function of the phase of the oscillator, and this function depends on the level of acoustic resonance. Based on these ideas to express the vortex/acoustics interaction, the formulas of stability analysis were derived.